UNSATURATED SOILS: ADVANCES IN GEO-ENGINEERING
PROCEEDINGS OF THE FIRST EUROPEAN CONFERENCE ON UNSATURATED SOILS, E-UNSAT 2008, DURHAM, UNITED KINGDOM, JULY 2–4 2008
Unsaturated Soils: Advances in Geo-Engineering
Editors
D.G. Toll & C.E. Augarde School of Engineering, Durham University, Durham, UK
D. Gallipoli & S.J. Wheeler Department of Civil Engineering, University of Glasgow, Glasgow, UK
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Table of Contents
Preface
XIII
Organisation
XV
Keynotes Unsaturated soil mechanics in earth and rockfill dam engineering E.E. Alonso & N.M. Pinyol
3
Recent developments in the techniques of controlling and measuring suction in unsaturated soils P. Delage, E. Romero & A. Tarantino
33
Developments in modelling the generalised behaviour of unsaturated soils A. Gens, L. do N. Guimarães, M. Sánchez & D. Sheng
53
A thermo-hydro-mechanical stress-strain framework for modelling the performance of clay barriers in deep geological repositories for radioactive waste L. Laloui, B. François, M. Nuth, H. Peron & A. Koliji
63
Advances in testing techniques A novel suction-controlled true triaxial apparatus for unsaturated soils L.R. Hoyos, A. Laikram & A.J. Puppala
83
A simple shear apparatus for testing unsaturated soils S. Tombolato, A. Tarantino & L. Mongiovì
89
A device for simultaneous measurement of acoustic and hydraulic properties in unsaturated soils L.A. George, M.M. Dewoolkar & C. Wei
97
A modified triaxial apparatus to reduce testing time: Equipment and preliminary results J.C. Rojas, C. Mancuso & F. Vinale
103
A large physical model to simulate flowslides in pyroclastic soils L. Pagano, M.C. Zingariello & F. Vinale
111
Climatic chamber to model soil-atmosphere interaction in the centrifuge J. Tristancho & B. Caicedo
117
Experimental determination of unsaturated hydraulic conductivity in compacted silt J.J. Mu˜noz, V. De Gennaro & E. Delaure
123
Testing for coefficient of permeability of a sandy soil in the residual state zone N. Ebrahimi-Birang, D.G. Fredlund & L. Samarasekera
129
Preparation of unsaturated soils by oedometric compression B. Caicedo, J.C. Ulloa & C. Murillo
135
V
Influence of sample height on the soil water characteristic curve C.N. Khoury & G.A. Miller Observations of unsaturated soils by Environmental Scanning Electron Microscopy in dynamic mode S.D.N. Lourenço, D.G. Toll, C.E. Augarde, D. Gallipoli, A. Congreve, T. Smart & F.D. Evans
141
145
Recent advances in ESEM analysis of partially saturated geomaterials C. Sorgi, V. De Gennaro, H.D. Nguyen & P. Delalain
151
Study of desiccation crack evolution using image analysis S. Costa, J. Kodikara & N.I. Thusyanthan
159
Theoretical analysis of the effect of temperature, cable length and double-impedance probe head on TDR water content measurement A. Tarantino & A. Pozzato
165
Effect of dry density on the relationship between water content and TDR-measured apparent dielectric permittivity in compacted clay A. Pozzato, A. Tarantino, J. McCartney & J. Zornberg
173
Spatial Time Domain Reflectometry (Spatial TDR) – Principles, limitations and accuracy R. Becker, A. Scheuermann, S. Schlaeger, C. Huebner & N. Wagner
181
Spatial Time Domain Reflectometry (Spatial TDR) – On the use in geohydraulics and geotechnics A. Scheuermann, A. Bieberstein, Th. Triantafyllidis, C. Huebner, R. Becker, S. Schlaeger & N. Wagner
189
Water content dynamics in unsaturated soils – Results of experimental investigations in laboratory and in situ A. Scheuermann
197
A new high capacity tensiometer: First results J.C. Rojas, L. Pagano, M.C. Zingariello, C. Mancuso, G. Giordano & G. Passeggio
205
Evaluation of suction measurement by the tensiometer and the axis translation technique S.D.N. Lourenço, D.G. Toll, C.E. Augarde, D. Gallipoli, F.D. Evans & G.M. Medero
213
A system for field measurement of suction using high capacity tensiometers J. Mendes, D.G. Toll, C.E. Augarde & D. Gallipoli
219
Engineering behaviour Water retention behaviour and hydraulic properties Water retention properties of Boom clay: A comparison between different experimental techniques T.T. Le, P. Delage, Y.J. Cui, A.M. Tang, A. Lima, E. Romero, A. Gens & X.L. Li
229
Determination of soil suction state surface in pure and composite clays by filter paper method M. Biglari, A. Shafiee & I. Ashayeri
235
Soil water retention curves for remolded expansive soils K.C. Chao, J.D. Nelson, D.D. Overton & J.M. Cumbers
243
Hydromechanical couplings in confined MX80 bentonite during hydration D. Marcial, P. Delage & Y.J. Cui
249
VI
Effect of temperature on the water retention capacity of FEBEX and MX-80 bentonites M.V. Villar & R. Gómez-Espina Soil-water characteristic curves and void ratio changes relative to suction for soils from Greece M.E. Bardanis & M.J. Kavvadas
257
263
Prediction of soil-water retention properties of a lime stabilised compacted silt M. Cecconi & G. Russo
271
Time dependency of the water retention properties of a lime stabilised compacted soil D.V. Tedesco & G. Russo
277
Retention and compressibility properties of a partially saturated mine chalk H.D. Nguyen, V. De Gennaro, P. Delage & C. Sorgi
283
Effect of grain size distribution on water retention behaviour of well graded coarse material C. Hoffmann & A. Tarantino
291
Water retention functions of sand mixtures E. Imre, I. Laufer, K. Rajkai, A. Scheuermann, T. Firgi & G. Telekes
299
Permeability of a heavily compacted bentonite-sand mixture as sealing and buffer element for nuclear waste repository S.S. Agus & T. Schanz
305
Volumetric behaviour Volumetric behaviour of compacted London Clay during wetting and loading R. Monroy, L. Zdravkovic & A. Ridley Stress path dependence of hydromechanical behaviour of compacted scaly clay in wetting and drying suction controlled oedometer tests at constant vertical net stress C. Air`o Farulla
315
321
Long-term behaviour of lime-treated expansive soil submitted to cyclic wetting and drying O. Cuisinier & D. Deneele
327
Hydro-mechanical properties of compacted sand-bentonite in a semi-arid climate H. Bilsel & A. Iravanian
335
Grain size effects on rockfill constitutive behaviour A. Ramon, E.E. Alonso & E.E. Romero
341
The influence of suction on stiffness, viscosity and collapse of some volcanic ashy soils E. Bilotta, V. Foresta & G. Migliaro
349
Role of critical volumetric water content and net overburden pressure on swelling or collapse behavior of compacted soils I. Ashayeri, A. Shafiee & M. Biglari
355
The changes in stress regime during wetting of unsaturated compacted clays when laterally confined J.L. Brown & V. Sivakumar
361
Compression-induced suction change in a compacted expansive clay A.M. Tang, Y.J. Cui & N. Barnel
369
Theoretical modelling of the compaction curve N. Kurucuk, J. Kodikara & D.G. Fredlund
375
VII
Prediction of the residual void ratio of clayey soils after drying based on their initial state, physical properties and structure M.E. Bardanis & M.J. Kavvadas
381
An evaluation of soil suction measurements using the filter paper method and their use in volume change prediction J.M. Cumbers, J.D. Nelson, K.C. Chao & D.D. Overton
389
Validation of a swelling potential index for expansive soils J.L. Zheng, R. Zhang & H.P. Yang
397
Shear behaviour Effect of moisture content on tensile strength and fracture toughness of a silty soil M.R. Lakshmikantha, P.C. Prat, J. Tapia & A. Ledesma
405
Tensile strength of some compacted fine-grained soils A.J. Lutenegger & A. Rubin
411
Unsaturated characteristics of rammed earth P.A. Jaquin, C.E. Augarde & L. Legrand
417
Experimental study of the influence of suction on the residual friction angle of clays V. Merchán, J. Vaunat, E. Romero & T. Meca
423
Ultimate shear strength of unsaturated soils T.B. Hamid
429
Critical State conditions for an unsaturated artificially bonded soil D.G. Toll, Z. Ali Rahman & D. Gallipoli
435
Determination of the shear strength behavior of an unsaturated soil in the high suction range using the vapor pressure technique T. Nishimura, H. Toyota, S.K. Vanapalli & W.T. Oh
441
Effect of suction on compressibility and shear behaviour of unsaturated silty soil A.R. Estabragh & A.A. Javadi
449
Mechanical behaviour of an unsaturated clayey sand A. Mirzaii, S.S. Yasrebi & B. Gatmiri
453
Shear strength of unsaturated soil and its influence on slope stability O. Tomboy, V. Whenham, M. De Vos, R. Charlier, J. Maertens & J.-C. Verbrugge
459
Behaviour of a silt used in flood embankment construction in Indonesia G. McCloskey, M. Sanchez, M. Dyer & M. Kenny
465
Strength and yielding of unsaturated compacted silt from Beijing – Kowloon railway embankment J.K. Liu & L.Y. Peng
471
Estimation of the shear strength of lean clay based on empirical equations and a laboratory experiment on slope failure J.V. Vasquez & L.M. Salinas
475
Effects of drying and wetting cycles on unsaturated shear strength E.Y.M. Tse & C.W.W. Ng
481
Degradation of compacted marls due to suction changes R. Cardoso & E.E. Alonso
487
VIII
Multiaxial behavior of partially saturated sand at high stresses N. Massoudi, H.-Y. Ko & S. Sture
495
A simple method for the prediction of modulus of elasticity for unsaturated sandy soils S.K. Vanapalli, W.T. Oh & A.J. Puppala
503
Suction effects on the pre-failure behaviour of a compacted clayey soil J.A. Pineda, E.E. Romero & J.E. Colmenares
511
Influence of hydraulic paths on the low-strain shear modulus of a stiff clay J.A. Pineda, A. Lima & E. Romero
519
Drying and wetting effects on shear wave velocity of an unsaturated soil J. Xu, C.W.W. Ng & S.Y. Yung
525
Effects of unsaturated soil state on the local seismic response of soil deposits F. D’Onza, A. d’Onofrio & C. Mancuso
531
Constitutive modelling Thermo-plasticity in unsaturated soils, a constitutive approach B. François & L. Laloui
539
A thermomechanical framework for modeling the response of unsaturated soils S. Samat, J. Vaunat & A. Gens
547
Discussion on meta-stable equilibrium in unsaturated soils E.J. Murray, B.J. Murray & V. Sivakumar
553
Advanced hydro-mechanical coupling for unified constitutive modelling of unsaturated soils M. Nuth & L. Laloui
559
Generalised elasto-plastic stress-strain relations of a fully coupled hydro-mechanical model M. Lloret, M. Sanchez, M. Karstunen & S. Wheeler
567
Effect of degree of saturation on mechanical behaviour of unsaturated soils A.R. Estabragh & A.A. Javadi
575
An improved constitutive model for unsaturated and saturated soils K. Georgiadis, D.M. Potts & L. Zdravkovic
581
Modifying the Barcelona Basic Model to account for residual void ratio and subsequent decrease of shear strength relative to suction M.E. Bardanis & M.J. Kavvadas
589
A cap model for partially saturated soils R. Kohler, M. Hofmann & G. Hofstetter
597
Boundary surfaces and yield loci in unsaturated compacted clay A. Tarantino & S. Tombolato
603
Application to a compacted soil of a Cam Clay model extended to unsaturated conditions F. Casini, R. Vassallo, C. Mancuso & A. Desideri
609
Mixed isotropic-rotational hardening to model the deformational response of unsaturated compacted soils C. Jommi & E. Romero An anisotropic elasto-plastic model for unsaturated soils K. Stropeit, S.J. Wheeler & Y.J. Cui
IX
617 625
An elasto-viscoplastic model for chalk including suction effects F. Collin, V. De Gennaro, P. Delage & G. Priol
633
New basis for constitutive modelling of unsaturated aggregated soil with structure degradation A. Koliji, L. Vulliet & L. Laloui
641
A damage model for unsaturated natural loess submitted to cyclic loading J.M. Pereira, A.N. Ta, Y.J. Cui, J.P. Karam & H.Y. Chai
647
Desiccation shrinkage of unconstrained soil in the saturated phase L.B. Hu, T. Hueckel, H. Peron & L. Laloui
653
Modelling of the collapsible behaviour of unsaturated soils in hypoplasticity D. Mašín & N. Khalili
659
Swelling pressure in compacted bentonite: Laboratory tests and modelling M. Sanchez, M.V. Villar, R. Gómez-Espina, A. Lloret & A. Gens
667
Modelling water retention characteristic of unsaturated soils Y. Wang, G. Wu, S.M. Grove & M.G. Anderson
675
Temperature effect on hydric behaviour for unsaturated deformable soils S. Salager, M.S. El Youssoufi & C. Saix
683
A study of applied pressure on the Soil Water Characteristic Curve J. Zhou
689
Outline of the modelling of the excavated damaged zone in geological barriers C. Arson & B. Gatmiri
695
Numerical modelling Stress path dependency and non-convexity of unsaturated soil models D.C. Sheng, D. Pedroso & A.J. Abbo
705
Implicit integration of an extended Cam-clay model for unsaturated soils R. Tamagnini & V. De Gennaro
713
Parametric investigations on a three-invariant implicit integration algorithm for unsaturated soils L.R. Hoyos & P. Arduino A multi-cell extension to the Barcelona Basic Model W.T. Solowski, R.S. Crouch & D. Gallipoli
721 727
A numerical simulation of triaxial tests of unsaturated soil at constant water and air content by using an elasto-viscoplastic model F. Oka, H. Feng, S. Kimoto, T. Kodaka & H. Suzuki
735
Stress condition of an unsaturated pendular state granular soil C. Medina & M. Zeghal
743
A numerical investigation of steady-state unsaturated conductivity tests G. Steger, S. Semprich, M.P.H. Moncada, T.M.P. de Campos & E. Vargas Jr.
747
Numerical modelling of hydraulic hysteresis in unsaturated soils A.A. Javadi & A.S.I. Elkassas
755
The drift shadow phenomenon in an unsaturated fractured environment Claudia Cherubini, T.A. Ghezzehei & G.W. Su
761
X
Identification of hydraulic parameters for unsaturated soils using particle swarm optimization Y. Zhang, C.E. Augarde & D. Gallipoli
765
A precipitation boundary condition for finite element analysis P.G. Smith, D.M. Potts & T.I. Addenbrooke
773
On boundary condition in tunnels under partial saturation P. Gerard, R. Charlier & F. Collin
779
Numerical modelling of tree root-water-uptake in a multiphase medium S. Hemmati & B. Gatmiri
785
Numerical modelling of the soil surface moisture changes due to soil-atmosphere interaction S. Hemmati, B. Azari & B. Gatmiri
791
Identification of coupled hydro-mechanical model parameters with application to engineering barrier systems T. Schanz, M. Datcheva & M. Zimmerer
797
Surface flux boundary simplifications for flow through clay under landscaped conditions H.B. Dye, S.L. Houston & W.N. Houston
805
Preliminary analysis of tree-induced suctions on slope stability N. Ali & S.W. Rees
811
Numerical predictions of seasonal pore water pressure fluctuations using FLAC tp flow O.C. Davies, M. Rouainia & S. Glendinning
817
Infiltration analysis in unsaturated soil slopes J.F. Xue & K. Gavin
823
Prediction of changes in pore-water pressure response due to rainfall events M. Karthikeyan, D.G. Toll & K.K. Phoon
829
Modelling unsaturated soil slopes subjected to wetting and drying cycles Y.D. Zhou, C.Y. Cheuk, L.G. Tham & E.C.Y. To
835
Numerical analysis of piezocone penetrometer testing in partially saturated marine sediments A. Haghighi, B. Gatmiri, V. De Gennaro & N. Sultan
841
Experimental and numerical studies of the hydromechanical behaviour of a natural unsaturated swelling soil H. Nowamooz, M. Mrad, A. Abdallah & F. Masrouri
847
Numerical modelling of shallow foundations on swelling clay soil using the swelling equilibrium limit G.A. Siemens & J.A. Blatz
855
Meshfree modelling of two-dimensional contaminant transport through unsaturated porous media R. Praveen Kumar, G.R. Dodagoudar & B.N. Rao
861
Numerical modeling of hydraulic behavior of bioreactor landfills M.V. Khire & M. Mukherjee
867
Finite element modelling of contaminant transport in unsaturated soil A.A. Javadi & M.M. Al-Najjar
873
XI
Case studies Gulfs between theory and practice in unsaturated soil mechanics G.E. Blight
883
The repeatability of soil water balances at the same site from year to year G.E. Blight
889
Near-surface movement of water in unsaturated soil during evapotranspiration G.E. Blight
895
Studies of rainfall-induced landslides in Thailand and Singapore A. Jotisankasa, B. Kulsawan, D.G. Toll & H. Rahardjo
901
Field investigation on triggering mechanisms of fast landslides in unsaturated pyroclastic soils A. Evangelista, M.V. Nicotera, R. Papa & G. Urciuoli
909
Mechanical properties of unsaturated pyroclastic soils affected by fast landslide phenomena R. Papa, A. Evangelista, M.V. Nicotera & G. Urciuoli
917
Stability of a tailings dam considering the hydro-mechanical behaviour of tailings and climate factors M.T. Zandarín, L. Oldecop & R.R. Pacheco
925
A simplified model for the evaluation of the degree of saturation in slope stability analysis of shallow soils L. Montrasio & R. Valentino
933
Predicting the variation of stability with time for a slope in Switzerland A. Thielen & S.M. Springman
941
In situ field experiment to apply variable high water levels to a river levee P.A. Mayor, S.M. Springman & P. Teysseire
947
A new treatment for preventing landslides in expansive soil slopes H.P. Yang, Y.X. He & J.L. Zheng
953
Flow processes in the unsaturated Chalk of the Hallue Basin (France) N. Amraoui, H. Machard de Gramont, C. Robelin, A. Wuilleumier, M.L. Noyer & M.J. Feret
959
Loading-collapse tests for investigating compressibility and potential collapsibility of embankment coarse well graded material C. Hoffmann & A. Tarantino
967
An example of the impact of loess soils on foundations and earthworks in Kazakhstan S. Walthall & W.P. Duffy
973
Negative skin friction for cast-in-place piles in thick collapsible loess Z.H. Chen, X.F. Huang, B. Qin, X.W. Fang & J.F. Guo
979
Author index
987
XII
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Preface
This volume of proceedings of the First European Conference on Unsaturated Soils is the first publication to focus on European research developments in geo-engineering applications of unsaturated soils. The resurgence of interest in unsaturated soil research within Europe in recent years has lead to major advances. We are fortunate to have the latest developments reported here, in the 136 papers from leading international researchers and practitioners. The volume contains 90 papers from 15 countries within Europe with a further 46 contributions from 15 other countries. It hence represents European advances in geo-engineering together with an international state-of-the-art perspective on unsaturated soils in 2008. The volume addresses five areas: Advances in testing techniques, Engineering behaviour, Constitutive modelling, Numerical modelling and Case histories. The areas of application include slope stability, foundations, dams, contaminated land, landfill and nuclear waste repositories. It therefore provides a comprehensive collection that we believe geo-engineers will come to treat as essential reference material. Keynote papers from four international leading researchers are contained in the volume. We are grateful for the participation of Professors Eduardo Alonso, Pierre Delage, Antonio Gens and Lyesse Laloui. There is no doubt that these keynote papers will be seen as landmark contributions in unsaturated soil research. The motivation for organising this First European Conference on Unsaturated Soils grew from the MUSE project (Mechanics of Unsaturated Soils for Engineering: http://muse.dur.ac.uk) funded by the European Community. The editors (from Durham and Glasgow Universities) would like to thank our MUSE colleagues from Ecole Nationale des Ponts et Chaussées in France; Universitat Politécnica de Catalunya in Spain; Università degli Studi di Trento and Università degli Studi di Napoli Federico II in Italy for their support, both for this conference and our joint research activities. We would also like to acknowledge the vital role played by the Technical Advisory Committee members who have contributed to the very thorough reviews that have ensured the high technical quality of the papers accepted for inclusion in these Proceedings. We also thank the International Society of Soil Mechanics and Geotechnical Engineering, and in particular Technical Committee 6 on Unsaturated Soils, for their support of the conference. Particular thanks are due to Professor Pedro Seco e Pinto (President of ISSMGE), Professor Neil Taylor (General Secretary ISSMGE), Professor Eduardo Alonso (Chair of TC6) and Professor Gerald Miller (Secretary TC6). We hope that this first conference, and this volume of proceedings, will form the foundation and the impetus for a future series of European Conferences on Unsaturated Soils. We look forward to many such successful conferences and research collaborations in the future. David Toll & Charles Augarde (Durham University) Domenico Gallipoli & Simon Wheeler (University of Glasgow)
XIII
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Organisation
Organizing Committee C.E. Augarde (Durham University) R.S. Crouch (Durham University) D. Gallipoli (University of Glasgow) D.G. Toll (Durham University) S.J. Wheeler (University of Glasgow) Technical Advisory Committee E.E. Alonso (Spain) G.E. Blight (South Africa) J.B. Burland (United Kingdom) Y.J. Cui (France) T.M.P. de Campos (Brazil) R. Charlier (Belgium) P. Delage (France) D.G. Fredlund (Canada) A. Gens (Spain) S.L. Houston (United States of America) D. Karube (Japan) N. Khalili (Australia) L. Laloui (Switzerland) C. Mancuso (Italy) J. McDougall (United Kingdom) G.M. Medero (United Kingdom) C.W.W. Ng (Hong Kong) H. Rahardjo (Singapore) A. Ridley (United Kingdom) M. Sanchez (United Kingdom) T. Schanz (Germany) V. Sivakumar (United Kingdom) A. Tarantino (Italy) H. Thomas (United Kingdom)
XV
Keynotes
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Unsaturated soil mechanics in earth and rockfill dam engineering E.E. Alonso & N.M. Pinyol Universitat Politècnica de Catalunya, Barcelona, Spain
ABSTRACT: The paper examines a few relevant aspects of the design and performance of earth and rockfill dams. It covers the behaviour of compacted soil and rockfill, the generation of pore pressures and deformations during construction, the seepage phenomena during the operation of the dam, the important case of drawdown and a case history of a dam failure at the end of impoundment. It is argued that unsaturated soil mechanics offers today theories, experimental procedures and computational tools which provide a definite advantage over classical design methods. It offers also a new insight into field observations.
1
of the project. Typically, the upstream and downstream slopes should exhibit adequate safety factors at the end of construction, during reservoir impoundment and during the operational phase, including drawdown and long-term steady state conditions as a limiting case. In addition, other failure possibilities should be examined. They include the phenomena of hydraulic fracture and internal erosion. Other aspects are also of concern, such as the deformation of the structure during the construction and operational stages. In virtually all the mentioned topics, concepts developed in unsaturated soil mechanics in the last few decades may be used to gain an improved understanding of relevant phenomena. The paper starts with a review of some key ideas of compaction. The purpose is to add a different fundamental perspective to the powerful and well established concepts of soil compaction. Compacted soils and rockfill are often combined in earth dam design. They exhibit qualitatively similar behaviour against water action. However, basic principles of deformation are substantially different. Both types of materials will be dealt with in this paper. The issue of pore pressure generation during construction, which requires the solution of undrained and consolidation phenomena in unsaturated soils will be developed through some examples. Impoundment introduces two topics: the expected deformation of the dam in the course of partial or total wetting and the stability conditions of upstream and downstream slopes. Consistent answers for both problems require the solution of coupled flow-deformation phenomena under unsaturated (or saturated) conditions. Drawdown conditions will then be described. Some simplified recommendations for design will be reviewed and discussed. A case history of a dam failure during first impoundment will be finally discussed.
INTRODUCTION
Earth and rockfill dams are made of compacted soil and rockfill and, therefore, it is natural to consider their design, construction and performance from the perspective of unsaturated soil mechanics. However, earth and rockfill dams have been designed and built successfully all over the world, centuries before soil mechanics and unsaturated soil mechanics were developed. Accumulated experience and traditional design rules are certainly sufficient to achieve safe designs in practice. Dams are not currently being built in significant numbers in well-developed countries, but new projects are being commissioned in areas of Africa, South America and Asia. Therefore, the interest in these structures should be maintained. There are two additional aspects, which make the subject extremely interesting for a soils engineer, in general, and for specialists in unsaturated soils, in particular. The first aspect is the current trend to use any kind of soil or rock in the design of dams because of sustainability constraints. It is no longer feasible to select ‘‘the best’’ emplacement or to import ‘‘good’’ materials. The second point is that the behaviour of soils and rocks outcropping in tropical areas are not understood as well as more ‘‘regular’’ sedimentary and alluvial formations, often found in temperate climates of the northern hemisphere. Facing these challenges, unsaturated soil mechanics offers today a sufficient degree of development to provide theories and models of compacted soil behaviour, specialised testing and computational tools, which could improve today’s state of the art on earth dam and rockfill engineering. This paper is a contribution in this direction. Earth and rockfill dam design is, first of all, an exercise in ensuring the stability of the structure under a set of conditions expected to occur during the life
3
process. However, it is not easy to distinguish between the effect of the structure and the effect of initial conditions established during compaction. This section initially focuses in some aspects of soil compaction and in the interpretation of soil behaviour within a context of an elasto-plastic framework for unsaturated soils. The BBM model (Alonso et al, 1990) has been chosen as a reference model. Emphasis is placed in the dependence of initial conditions and constitutive parameters with the compaction procedure. The effect of the initial condition induced by compaction on the subsequent mechanical behaviour of a core dam is presented. The construction of San Salvador Dam, an earth and rockfill dam designed to be built in Huesca (Spain), has been modelled under different assumptions of compaction conditions in terms of density and water content. The mechanical response and pore pressure generation during construction will be discussed.
The examples and cases presented are taken from the recent involvement of the authors in a number of dam projects. Material parameters are real in the sense that they have been approximated from actual published on unpublished laboratory tests and field instrumentation results. Extensive use has been made of the coupled flow-deformation computer program CODE_BRIGHT described in Olivella et al. (1996) and DIT-UPC (2002). 2
COMPACTED SOILS
The design of earth dams and the analysis of their behaviour require knowing the response of the compacted fill materials under stress and humidity changes. The behaviour of fill materials depends on the compaction procedure. During compaction, permanent strains are induced which modify the original properties of the soil and its microstructure. The conceptual bases of compaction of fine-grained materials were established in 1933 by Proctor who defined the compaction state by two variables: dry density (γd ) and water content (w). For a given compaction procedure and compaction energy, the soil density reached at the end of compaction depends on the water content of the soil. An optimum or maximum dry density can exist at certain water content, lower than the water content at saturation. In practice, the compacted soil behaviour is characterized by the pair of variables (γd , w) and their significant influence on the subsequent mechanical behaviour of the soil is widely accepted. For instance, it is known that core dams compacted on the wet side of optimum are more deformable and more impervious. Therefore, the risk of cracking and hydraulic fracture is reduced. However, high initial water content may induce the development of high pore water pressures during construction, which increases the risk of instability. Dry of optimum compaction leads to more rigid cores which are prone to collapse upon saturation if the density achieved in not high enough. Deformation may crack these rigid cores and make them more susceptible to hydraulic fracture. Microscopic observations and porosimetry show that the compaction procedure also induces substantial differences in the soil fabric. In particular, several authors have reported the relevant effect of the compaction water content on the microstructure of fine-grained soils (Lambe, 1958; Seed & Chan, 1959; Barden & Sides, 1970; Delage et al, 1996; Simms & Yanful, 2001). Compacted samples on the dry side exhibit a double-structure fabric due to the aggregation of clay particles whereas dispersed fabrics are observed in samples compacted wet of optimum. Differences in the mechanical behaviour of a soil due to compaction conditions are often attributed to these microstructural differences acquired during the
2.1
Basic properties of compacted materials
The dry density (γd ) of a soil induced by compaction depends on the water content (w), the compaction procedure (dynamic and static) and the compaction energy. Figures 1 and 2 show the static compaction curves for different compaction stresses of a low plasticity silty clay from Barcelona (wL = 30.5%, PI = 11.8%, % < 2 μm = 16.1%) and a high plasticity soil—Boom clay—(wL = 56%, PI = 27%, % HR0
1
HR1
HReq SMI
HRSOIL HR1> HRSOIL HR1> HR0
HR1> HRSeq SMI > HRSOIL
WP4 HR0=40%
HReq WP4
0.1 HRSOIL HRSOIL> HR0
0.01 0.00
0.05
0.10 0.15 Water content
0.20
HRSOIL > HRSeq WP4 > HR0
0.25
Figure 20. Equalisation process in the measurement chamber of SMI and WP4 psychrometers. HRb : relative humidity near the wet bulb; HRSOIL : relative humidity of the soil pores; HR0 : initial relative humidity of the soil chamber; HR1 : intermediate relative humidity; HReq : final equilibrated relative humidity. The scheme is for HRSOIL > HR0 (Cardoso et al. 2007).
Figure 18. Comparison between SMI psychrometer data (total suction minus osmotic component) and high-range tensiometer readings. Drying paths on a clayey silt (Boso et al. 2003).
100
Total suction (MPa)
SMI -Drying WP4-Drying Curve SMI (drying) Curve WP4 (drying)
readings of both psychrometers were observed—systematically larger values were detected with WP4 psychrometer—, which increased with total suction of the soil. Cardoso et al. (2007) put forward a possible explanation to account for these discrepancies between SMI and WP4 readings. These authors suggested that the hydraulic paths undergone by the soil during the measurement period inside each equipment chamber were quite different. As observed in Figure 20, the sample in the SMI chamber experiences some wetting due to the relatively fast evaporation of the drop of the wet thermometer, which increases the relative humidity of the chamber to HR1 > HR0 as shown schematically in the figure. The sample at a lower relative humidity HRsoil undergoes some wetting before reaching the equalisation state at HReq SMI , which is the state finally measured by the SMI psychrometer. During the determination of a main drying curve, SMI readings will follow a scanning wetting path, which will end below the main drying curve. On the contrary, the soil inside the WP4 chamber will undergo some drying before reaching HReq WP4 , and it will follow the same intended main drying path during the measuring period. As a consequence, the total suctions measured and the final water contents are slightly different.
10
1
0 0
5
10
15
20
25
water content (%)
Figure 19. Comparison between SMI and WP4 psychrometer data. Drying paths on a compacted destructured argillite (Cardoso et al. 2007).
determination was achieved by constant water content measurements. To compare matrix suction results, a constant osmotic suction of 0.3 MPa was subtracted from total suctions measured by the psychrometer. A relatively good overlapping in the range from 1 MPa to nearly 3 MPa and between the different techniques is observed in the figure. Cardoso et al. (2007) studied the performance of SMI and WP4 psychrometers by evaluating the drying branch of the retention curve of a compacted destructured argillite. As observed in Figure 19, the retention curves display a quite good agreement in the low total suction range from 1 to 7 MPa. However, in the highsuction range (7 to 70 MPa) differences between the
4
CONCLUSION
Some recent developments concerning the three techniques used for controlling suction in unsaturated soils
48
(axis-translation, osmotic and vapour control techniques) and concerning two techniques of measuring suction (high capacity tensiometers and high range psychrometers) have been commented and discussed. The advantages, drawbacks and complementarities of these techniques have been discussed and some recommendations aimed at facilitating their use have been given, based on the experience gained by the authors, their co-workers and data available in the literature. As a general conclusion, it can be stated that the recent significant progresses made in the field of controlling and measuring suction provided further insight into the behaviour of unsaturated soils. The potentialities of these techniques are high and they should keep helping the experimental investigations necessary to better understand the hidden remaining aspects of the hydromechanical behaviour of unsaturated soils.
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ACKNOWLEDGEMENTS The authors acknowledge the fruitful collaboration and discussions with the many colleagues involved in the works conducted: C. Airò Farulla, M. Boso, R. Cardoso, A. Caruso, Y.J. Cui, E. De Col, V. De Gennaro, E. De Laure, A. Di Mariano, A. Dueck, A. Ferrari, Ch. Hoffmann, M. Howat, T.T. Le, A. Lima, A. Lloret, C. Loiseau, A.T. Mantho, D. Marcial, F. Marinho, L. Mongiovi, L. Oldecop, X. Pintado, G. Priol, G.P.R. Suraj de Silva, A. Take, A.M. Tang, A. Thielen, S. Tombolato, T. Vicol, M. Yahia-Aissa. The authors also wish to acknowledge the support of the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTNCT-2004–506861.
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Romero, E. 1999. Characterisation and thermo-hydromechanical behaviour of unsaturated boom clay: an experimental study. Ph.D. Thesis, Universitat Politècnica de Catalunya, Barcelona, Spain. Romero, E. 2001a. Controlled-suction techniques. Proc. 4◦ Simpósio Brasileiro de Solos Nâo Saturados Ñ SAT’2001. W.Y.Y. Gehling and F. Schnaid (eds). Porto Alegre, Brasil: 535–542. Romero, E., Gens, A. and Lloret, A. 1999. Water permeability, water retention and microstructure of unsaturated compacted Boom clay. Engineering Geology. 54, 117–127. Romero, E., Gens, A. and Lloret, A. 2001b. Laboratory testing of unsaturated soils under simultaneous suction and temperature control. Proc. 15th Int. Conf. on Soil Mechanics and Geotechnical Engineering, Istanbul, August 27–31, 2001. A.A. Balkema, Rotterdam, 1: 619–622. Slatter, E.E., Allman, A.A. and Smith, D.W. 2000. Suction controlled testing of unsaturated soils with an osmotic oedometer. Proc. Int. Conf. Geo-Eng 2000, Melbourne, Australia. Spanner, D.C. 1951. The Peltier effect and its use in the measurement of suction pressure. J. Exp. Botany, 11: 145–168. Suraj De Silva, G.P.R. 1987. Etude expérimentale du comportement d’un limon non saturé sous succion contrôlée. Ph.D. thesis, Ecole Nationale des Ponts et Chaussées, Paris. Tang, A.M. and Cui, Y.J. 2005. Controlling suction by the vapour equilibrium technique at different temperatures and its application in determining the water retention properties of MX80 clay. Can. Geot. J., 42: 287–296. Take, W.A. 2003. The influence of seasonal moisture cycles on clay slopes. Ph.D. dissertation, University of Cambridge, UK. Take, W.A. and Bolton, M.D. 2002. A new device for the measurement of negative pore water pressures in centrifuge models. Proc. Int. Conf. Physical Modelling in Geotechnics, 89–94. Take, W.A. and Bolton, M.D. 2003. Tensiometer saturation and the reliable measurement of matrix suction. Geotechnique 53 (2): 159–172. Tarantino, A. 2004. Panel Lecture: Direct measurement of soil water tension. Proc. 3rd Int. Conf. on Unsaturated Soils, Recife, Brasil, 3: 1005–1017. Tarantino, A. and Mongiovi, L. 2000. A study of the efficiency of semi-permeable membranes in controlling soil matrix suction using the osmotic technique. Unsaturated Soils for Asia, 303–308, Toll and Leong eds, Balkema. Tarantino, A., Mongiovì, L. and Bosco, G. 2000. An experimental investigation on the independent isotropic stress variables for unsaturated soils. Géotechnique 50 (3): 275–282. Tarantino, A. and Mongiovì, L. 2000. Experimental investigations of the stress variables governing the unsaturated soil behaviour at medium to high degree of saturation. In Experimental Evidence and Theoretical Approaches in Unsaturated Soils, A. Tarantino & C. Mancuso (eds): 3–19. Rotterdam: A.A. Balkema. Tarantino, A. and Mongiovì, L. 2001. Experimental procedures and cavitation mechanisms in tensiometer measurements. In D. Toll (ed.), Unsaturated Soils Concepts and Their Application in Geotechnical Practice,
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Developments in modelling the generalised behaviour of unsaturated soils A. Gens Universitat Politècnica de Catalunya, Barcelona, Spain
L. do N. Guimarães Universidade Federal de Pernambuco, Recife, Brazil
M. Sánchez University of Strathclyde, Glasgow, UK
D. Sheng The University of Newcastle, NSW, Australia
ABSTRACT: A number of developments for the description of the generalised behaviour of unsaturated soils are presented. They can be considered as extensions of the conventional elastoplastic models developed in recent years to simulate the stress-strain behaviour of this type of soils. The following topics are addressed: the consideration of coupled hydraulic models in a thermodynamical framework, the introduction of structural components in the modelling of expansive soil behaviour and the incorporation of temperature and chemical effects.
1
and, very recently, in Nuth & Laloui (2008) in a rather comprehensive manner. A welcome clarification of this perennial unsaturated soil discussion was provided in Houlsby (1997) by means of the extension, under reasonably general conditions, of the work input for saturated soils to the case of unsaturated soils. This topic is however outside the scope of this paper. The present contribution will introduce, albeit briefly, a number of developments that attempt to extend the modelling of unsaturated soils to deal with more generalised behaviour. The following themes will be considered: i) the modelling of hydraulic behaviour and its thermodynamic consistency, ii) the incorporation of structural considerations in model formulation, and iii) the consideration of thermal and chemical effects. Inevitably, special attention will be given to developments associated with the work of the authors. The implementation of the constitutive models into numerical tools for analysis require also especial attention but this issue is not addressed herein and has been treated elsewhere (e.g. Sheng et al. 2003a, b, Borja 2004, Sanchez et al. 2008, Sheng et al. 2008).
INTRODUCTION
Constitutive modelling of unsaturated soils has progressively incorporated a number of features that are deemed to be necessary to achieve a satisfactory reproduction of their mechanical behaviour. Among them, the following can be mentioned: a central role of matric suction in the description of behaviour, the use of more then one stress variable in the formulation, the recognition that collapse behaviour (i.e. the compression of the soil upon wetting) is irreversible and the increase of shear strength with suction. Another important characteristic is the requirement that a model for unsaturated soils should be compatible with existing models for saturated materials. Based on those considerations, a number of elastoplastic models have been developed in the last few decades to describe, using a variety of approaches, the mechanical behaviour of unsaturated soils (e.g. Alonso et al. 1990, Josa et al. 1992, Kohgo et al. 1993, Modaressi & Abou-Bekr 1994, Wheeler & Sivakumar 1995, Cui et al. 1996, Bolzon et al. 1996, Alonso et al. 1999, Khalili & Loret 2001, Loret & Khalili 2002, Gallipoli et al. 2003a, Russell & Khalili 2006). All those models deal with stress-strain relations. A variety of stress variables have been adopted in the formulation of those models; this issue has been summarized and discussed in a number of publications (e.g. Gens 1995, Jardine et al. 2004, Gens et al. 2006)
2
HYDROMECHANICAL MODELS FOR UNSATURATED SOILS
One crucial shortcoming of many constitutive models for unsaturated soils (especially the early
53
formulations) is that they either do not take into account the hydraulic behaviour of unsaturated soils or they consider it in a manner that is uncoupled from the mechanical stress-strain law. Thus, in the BBM model (Alonso et al. 1990), hydraulic behaviour was simply defined in terms of a state surface. Probably, this issue of the hydraulic component of the constitutive model was first properly addressed by Wheeler (1996) and Dangla et al. (1997) and the first full attempt to couple hydraulic behaviour with a mechanical model for unsaturated soil was presented in Vaunat et al. (2000). In recent years quite a number of constitutive developments have addressed explicitly this question (e.g. Wheeler et al. 2003, Gallipoli et al. 2003b, Sun et al. 2007). As strongly suggested by Houlsby’s (1997) work input equation (neglecting the work dissipated by the flow of fluids), ˙ ≡ ua n(1 − Sr )ρ˙a /ρa − (ua − uw ) n S˙ r W
+ σij − (Sr uw + (1 − Sr )ua ) δij ε˙ ij
a)
b)
Figure 1. a) Hysteretic hydraulic behaviour under constant void ratio. b) SI, SD and LC yield surfaces in three-dimensional space (Sheng et al., 2004).
(1)
the incorporation of an hydraulic component of the model in a coupled manner provides the opportunity of casting the resulting constitutive law in the thermodynamic framework proposed by Collins & Houlsby (1997). In the above expression, σij is the total stress, Sr is degree of saturation, ua the air pressure, uw the water pressure. ρa is the air density, n the porosity and εij the strains. The model proposed in Sheng et al. (2004) has provided an excellent opportunity for such an exercise. The model is defined in terms of Bishop’s stress: (σij )c = σij −ua δij +Sr (ua −uw )δij and matric suction, s(=ua − uw ). The subscript c implies that Bishop’s stress is the constitutive stress. Please note, that in Bishop’s expression the original variable χ (Sr ) has been replaced by Sr . The hysteretic water retention model is presented in Figure 1a; it is composed of a wetting and a drying curve with scanning curves spanning the two. No dependency on void ratio is introduced. The two main water retention curves correspond to the SI and SD yield surfaces that together with the LC yield curve constitute the mechanical part of the model (Figure 1b). In this particular model, the yield surfaces are not coupled but move independently of each other. Accepting the hypotheses that led to Houlsby’s expression for the rate of work input (1) and neglecting the air compressibility term, the plastic component of the work input rate is dW p = (σc )T dεp + nsdSrp
For uncoupled materials, where the elastic modulus is independent of the plastic strains, the plastic work increment can be decomposed into two components (Collins & Hilder, 2002): dW p = dψ2 + dφ
(3)
where ψ2 is the part of the Helmholtz free energy that depends on plastic strains only and dφ is the dissipation increment. The basic thermodynamical requirements on any constitutive model are that i) the dissipation dφ is strictly positive for any non-zero plastic strain, and ii) that the free energy dψ2 yields zero when integrated over a closed loop of plastic strain. In terms of triaxial stress states, the plastic work increment can be expressed as dW p = pc dεvp + qdεγp + nsdSrp
(4)
where pc is the mean constitutive stress, i.e. the mean Bishop’s stress in this case. The last term of the equation is only relevant to yielding in the SI or SD yield surfaces, as the movep ment of the LC yield surface does not contribute to Sr . Therefore, dW p = pc dεvp + qdεγp + (nsI dSrp or nsD dSrp )
(2)
where σc is the constitutive (Bishop) stress and the superscript p denotes plastic.
(5)
In (5), the third term will appear when either the SI or the SD yield curves are engaged. Since both sI
54
3
and sD are known function of the plastic increment of p the degree of saturation and n is independent of dSr , the last two terms of the equation above are integrable and give zero when integrated around a closed loop p of Sr . Therefore, these two terms belong to the free energy dψ2 . To find the first two terms in (4), it is assumed that plastic volumetric and plastic deviator strains are caused only by yielding at the LC yield surface. This is a strong restriction on the role of the SI and SD surfaces. Then: 1 pc dεvp + (nsI dSrp or nsD dSrp ) 2 ⎞ ⎛ p 2 p 2 M2 ) + (dε ) (dε γ v 1 ⎟ ⎜ ζ + ⎝ pc ⎠ p 2 p 2 2 M2 (dεv ) + ζ (dεγ )
The behaviour of expansive clays has always presented challenging aspects concerning their constitutive modelling. Although expansive clays have always been one of the main areas of interest in unsaturated soil mechanics, in recent years this interest has been enhanced because they are widely used as one of the main components of waste-isolation barriers. One of the characteristic features of the behaviour of expansive clays is the irreversible and stress path-dependent behaviour exhibited during wetting. An example is offered in Figure 2 where it can be seen that the volume change of an expansive clay varies strongly depending on the stress path followed. Irreversibility and strain accumulation is also a feature of expansive clay behaviour when drying/wetting cycles are applied (Figure 3). This type of behaviour is difficult to model with conventional elastoplastic models where predicted behaviour inside the yield locus is elastic and, therefore, computed strains will be small and, often, largely reversible. Because the source of expansive clay behaviour lies in the physicochemical phenomena occurring in the vicinity of the clay particle, there is some merit in trying to incorporate explicitly this microstructural level in the model (Gens & Alonso, 1992). The formulation developed contains now two structural levels: a microstructure where the interactions at particle level occur and a macrostructure that accounts for the overall fabric arrangement of the material comprising aggregates and the larger pores. In some cases, for instance in compacted swelling clays, the two structural levels are readily distinguished. See for example Figure 4 where the pore volume distributions for a compacted bentonite at two
dW p =
(6)
where M and ζ are model parameters. The terms of the first brackets are all integrable and give zero in a closed loop. Therefore they are the contribution of the plastic strain work from the free energy and hence correspond to dψ2 . The term in the second set of brackets is not integrable because it involves the plastic shear strain. This term thus corresponds to the dissipation function dφ. dψ2 =
1 pc dεvp + (nsI dSrp or nsD dSrp ) 2 2
p
v
ζ
(7)
p
(dεv )2 + Mζ (dεγ )2 1 ≥0 dφ = pc 2 p p 2 (dε )2 + M (dε )2
INCORPORATION OF STRUCTURAL EFFECTS
(8)
γ
The dissipation function (8) is obviously strictly positive whenever the plastic strains are non zero, as required. It can also be shown that the dissipation function above is a homogeneous function of degree 1 in the plastic strain increments. Equations (7) and (8) indicate that the plastic yielding at the suction-increase and suction-decrease yield surfaces does not contribute to the plastic dissipation, but only to the plastic work. This means that all plastic work associated with a plastic increment of degree of saturation is stored and can be recovered during a reversed plastic increment of saturation. This plastic work is very much the same as the ‘locked-in elastic energy’ due to the shift or back stress (Collins & Hilder, 2002). Ideally, analogous analyses should be attempted concerning other constitutive models. Tellingly, Tamagnini & Pastor (2005) and Santagiuliana & Schrefler (2006) have also examined their particular models in terms of a similar thermodynamic framework.
Figure 2. Volume increase of an expansive clay under different generalised stress paths (Brackley, 1975). NMC denotes Natural Moisture Content.
55
to define carefully the type of suction to be used. Whereas in the macrostructure the matric suction (s) is the relevant one, total suction (i.e. matric plus osmotic suction) has to be used when dealing with the microstructure. The inclusion of the macrostructural level in the analysis allows the consideration of phenomena that affect the skeleton of the material, for instance deformations due to loading and collapse. Figure 5a shows the BBM yield surface (Alonso et al., 1990), defined as:
8 Swelling (%)
3
Dry Density:1.65 Mg/m Vertical Stress: 0.0007 MPa 6
4
2
Shrinkage (%)
0
FLC = 3J 2 −
g(θ) g(−30◦ )
2 M 2 ( p + Ps )( p0 − p) = 0 (9)
-2
where M is the slope of the critical state, po is the apparent unsaturated isotropic pre-consolidation pressure, g(θ) is a function of Lode’s angle and ps considers the dependence of shear strength on suction. The trace of the yield function on the isotropic p-s plane is called LC (Loading-Collapse) yield curve, because it represents the locus of activation of irreversible deformations due to loading increments or collapse.
-4 0
5
10 15 20 Time (days)
25
30
Figure 3. Evolution of shrinkage and swelling in a cyclic suction test (Day, 1994).
Incremental Pore Volume (ml/g)
0.2 Dry density 1.8 Mg/m3
0.16
Intra-aggregate
1.5 Mg/m 3
Inter-aggregate
0.12
0.08
0.04
0 1
10
100
1000
10000
100000
Pore diameter (nm)
Figure 4. Distributions of incremental pore volume for two statically compacted specimens of FEBEX bentonite (modified from Lloret et al., 2003).
different dry densities are plotted. The two structural levels can be easily observed. However, even in more matrix-dominated fabrics, it is still possible to distinguish the behaviour related to the hydration processes close to the particle from the behaviour associated with the overall structural rearrangements of mechanical origin. The model has been developed in terms of net stresses (i.e. the excess of total stress over air pressure) and suction. In this case, however, it is necessary
Figure 5. a) BBM yield surface. b) Microstructural load directions on the p-s plane
56
has a number of advantages (Gens et al., 2006) both for the formulation of the model and for its implementation in numerical codes (Sanchez et al., 2008). An additional advantage of keeping track of two structural levels and, hence, two pore structures, is that important parameters such as permeability can be related to the macrostructural pore sizes since the contribution of the microstructural pores to overall water flow is negligible. This possibility has proved very valuable in the analysis of hydration of engineered barriers for radioactive waste disposal (Sanchez & Gens, 2005). Also, time dependent behaviour arises in a natural way if transient hydraulic non-equilibrium between macrostructure and microstructure is considered, a very plausible scenario. Finally, the incorporation of a microstructural level provides a suitable platform to introduce the effects of new variables as described in the following section.
The position of the LC curve is given by the preconsolidation yield stress of the saturated state, p∗o (hardening variable), according to: p˙ ∗0 = p∗0
(1 + e) p ε˙ (λ(0) − κ) v
(10) p
where e is the void index, ε˙ v is the volumetric plastic strain, κ is the elastic compression index for changes in p and λ(0) is the stiffness parameter for changes in p for virgin states of the soil in saturated conditions. For the microstructural level, it is assumed that the strains arising from basic physicochemical phenomena may be considered elastic and volumetric (Gens & Alonso, 1992). The increment of microstructural strains is then expressed as: ε˙ v1 =
pˆ˙ p˙ s˙ = +χ K1 K1 K1
(11) 4
where pˆ (= p + χ s) is the microstructural effective stress, the subscript 1 refers to the microstructural level, the subscript v refers to the volumetric component of the strains and K1 is the microstructural bulk modulus. The Neutral Line (NL) (Figure 5b) corresponds to a constant pˆ locus and no microstructural deformation occurs when the stress path moves on the NL. The NL divides the p-s plane into two parts, defining two main generalized stress paths, which are identified as: MC (microstructural contraction) and MS (microstructural swelling). In spite that reversible behaviour is assumed for microstructural strains, irreversible behaviour may arise form the effects of those strains on the macrostructure (Gens & Alonso 1992). An assumption of model is that the irreversible deformations of the macrostructure are proportional to the microstructural strains according to interaction functions f . The plastic macrostructural strains are evaluated by the following expression: p
p
ε˙ v2 = ε˙ vLC + f ε˙ v1
TEMPERATURE AND CHEMICAL EFFECTS
4.1 Temperature effects One of the potentially important roles of compacted swelling clays lies in providing the basic material for engineered barriers in high level radioactive waste storage schemes. High level radioactive waste is strongly heat emitting. In this context, thermal effects on behaviour and, more specifically, the variation of swelling capacity with temperature is a significant issue. Figure 6 shows the observed variation of swelling pressure with temperature for a bentonite compacted at dry densities of 1.6 and 1.5 Mg/m3 (Sánchez et al., 2007). It can be noted that swelling pressure decreases with temperature although, even at temperatures as high as 80◦ C, the pressure values are still large. In the model outlined in the previous section, the expansion of the microstructure depends on the microstructural effective stress through a microstructural bulk modulus, K1 (eq. 11). A straightforward extension to the model is to include a dependence of K1 on temperature. The expression used is follows:
(12)
p
where εvLC is the plastic strains induced by the yielding of the macrostructure (BBM ). A first mathematical expression of this conceptual model was presented in Alonso et al. (1999) but, recently, a more convenient formulation based on generalised plasticity concepts has been developed (Sanchez et al., 2005) while keeping the same basic features and assumptions. The generalised stressstrain relationships are derived within a framework of multi-dissipative materials that provides a consistent and formal approach when several sources of energy dissipation exist. The generalised plasticity framework
K1 =
e−αm pˆ βm
(13)
where αm and βm are model parameters. The extension suggested here is to include a dependence of the parameter βm on temperature. The following expression is proposed: βm =
57
βm eτ T /Tref
(14)
where T is the temperature difference, that is the actual temperature minus Tref , a reference temperature, and τ is a new parameter that may be obtained from experiments. It should be noted that, in this version of the model, only the microstructural level is affected by temperature. This is acceptable because the fabric of the compacted bentonite is quite dense and no irreversible strains in the macrostructure due to temperature changes are expected. If the fabric was more open, independent plastic temperature effects must be introduced in the description of the macrostructural behaviour. Figure 7 shows how the change of temperature affects the microstructural bulk modulus according to the suggested law. An increase in the microstructural stiffness with temperature is predicted. This means lower expansions when tests are conducted at higher temperature. As Figure 6 shows, the adopted expression (14) yields a satisfactory variation of swelling pressure with temperature.
4.2 Chemical effects Expansive clays contain significant amounts of active minerals. Therefore, their behaviour is generally susceptible to variations in the chemical environment. Two major effects can be identified: changes in osmotic suction and the effects of cation exchange. Both must be considered in a proper chemomechanical constitutive model. Again, the effects of chemical variables are taken into account through an adequate modification of the microstructural model. As before, an exponential law is adopted to define the elastic volumetric microstructural strain as a function of microstructural effective stresses: dεme = βm e−αm pˆ d pˆ
(15)
where αm and βm are material parameters. To incorporate the influence of geochemical variables on the behaviour of the microstructure, it is postulated that the material parameter αm is constant and that βm depends on the exchangeable cation concentrations as: βmi xi (16) βm =
Swelling pressure (MPa)
i Error bars obtained from values of tests performed at laboratory
6
3
temperature (1.6Mg/m )
4
Dry density (Mg/m3) 1.6 1.5 Test Test Model Model
where xi is the equivalent fraction of the exchangeable cation i, defined as: xi =
2
Error bars obtained from values of tests performed at laboratory
20
30
40 50 60 Temperature (ºC)
70
(17)
where CEC is the cation exchange capacity of the clay. Since xi are defined as equivalent fractions, they are subjected to the following restrictions:
3
temperature (1.5 Mg/m )
0
concentration of exchangeable cation CEC
80
Figure 6. Swelling pressure as a function of temperature for FEBEX bentonite compacted to different nominal dry densities. Experimental and modelling data (Sanchez et al., 2007).
xi = 1;
0 ≤ xi ≤ 1
(18)
i
The βmi values are parameters that control microstructure stiffness and are established for each one of the exchangeable cations. If a rough analogy is established with the diffuse double layer theory, the values of βmi are related to the hydrated radii of the cations and their valences. Finally, the microstructural volumetric strain is given by: dεme = dem = βm e−αm pˆ d pˆ −
1 −αm pˆ e dβm αm
(19)
From (19), it can be noted that cation exchange not only affects the stiffness of the microstructure but it also contributes independently to the microstructural volumetric strains. If all βmi are constant and the same for all cations (βmi = βm ), then dβm is always zero and (19) becomes
Figure 7. Changes in micro-structural stiffness with temperature.
58
(15). In this case, the influence of exchangeable cations disappears and the only geochemical variable that affects microstructural behaviour is the osmotic suction (so ). It is convenient to define a new variable: ψ = pˆ −
1 1 ln βm = p + χ sm − ln βm αm αm
A numerical simulation has been performed in which the soil was subjected to the same sequence of mechanical and chemical actions. A 1-D mesh composed of 100 elements was used for the analysis performed with the computer code CODE_BRIGHT enhanced with a chemical module. The following parameters were used: intrinsic permeability, taken as constant and equal to 5 × 10−19 m2 , the coefficient of molecular diffusion is 7.6 × 10−10 m2 /s, and the CEC is 80 meq/100 g of solid. No mechanical dispersion is considered. Arguably, the most interesting result of the experiment is the observation of positive pore pressures measured at the bottom of the sample (Figure 9). It can be noted that the same response is obtained in the computations (Figure 10). The pore pressure generation corresponds to the undrained response of the soil due to the tendency towards compression induced by the saline solution. It can be stated that pore pressures are generated because the diffusion of salts inside the sample is faster than the ability of the pore pressures to dissipate. Naturally this phenomenon depends on the relative values of intrinsic permeability and the coefficient of molecular diffusion. This a clear example of interaction between geochemical parameters and hydromechanical behaviour, successfully reproduced by the model.
(20)
that will be called the ‘‘chemically modified effective stress’’ for the microstructure, reflecting the fact that the microstructural volumetric strain depends on changes of ψ only: dεme = dem = e−αm ψ d.
(21)
Therefore, a cation exchange process that causes an increase in βm (for instance the replacement of Ca2+ by Na+ in the exchange sites of the clay) will result in a reduction of ψc and an expansion of the double layer. In fact, any reduction of p, sm or ψc will cause a double layer expansion. Therefore a reduction of ψ will be associated with microstructural wetting. Conversely, when the net effect of changes in microstructural variables p, sm , and ψc is an increase of ψ, there will be shrinkage of the double layer and it will be associated with microstructural drying. An example of application demonstrating the interaction between cation exchange and hydromechanical effects is now presented. It concerns a laboratory test carried out in the oedometer cell depicted in Figure 8 (Santamarina & Fam, 1995). In the test, the sample can only drain from the top whereas pore pressure is measured at the bottom. First the sample is subjected to a load of 100 kPa. Once consolidation is finished, the specimen is placed in contact with a KCl saline solution of 4.0 M concentration through the upper surface of the sample. The material tested is a sodium bentonite with a cation exchange capacity (CEC) between 80 and 85 meq/100 g of solid. The samples were prepared from slurry with an initial void ratio of 4.6.
Figure 9. Observed variation of the pore pressure at the bottom of a bentonite oedometer sample exposed to a 4.0 M solution of KCl. (Santamarina & Fam, 1995).
pore pressure (MPa)
0.05
0.04
0.03
0.02
0.01
0.00 0
1000
2000
3000
4000
5000
6000
7000
8000
time (min)
Figure 10. Computed variation of the pore pressure at the bottom of a bentonite oedometer sample exposed to a 4.0 M solution of KCl.
Figure 8. Schematic layout of the oedometer test with changes of chemical variables (Santamarina & Fam, 1995).
59
5
CONCLUDING REMARKS
Day, R.W. 1994. Swell-shrink behaviour of compacted clay. Journal of Geotechnical Engineering, ASCE; 120(3): 618–623. Gallipoli, D., Gens, A., Sharma, R. & Vaunat, J. 2003a. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Géotechnique 53: 123–135. Gallipoli, D., Wheeler, S.J. & Karstunnen, M. 2003b. Modelling the variation of degree of saturation in a deformable unsaturated soil. Géotechnique 53: 105–112. Gens, A. 1995. Constitutive modelling: Application to compacted soil. Unsaturated Soils. Balkema, Rotterdam. 3: 1179–1200. Gens, A. & Alonso, E.E. 1992. A framework for the behaviour of unsaturated expansive clays. Canadian Geotechnical Journal 29: 1013–1032. Gens, A., Sanchez, M. & Sheng, D. 2006, On constitutive modelling of unsaturated soils. Acta Geotechnica 1(3): 137–147. Houlsby, G.T. 1997. The work input to an unsaturated granular material. Géotechnique 47: 193–196. Jardine, R.J., Gens, A., Hight, D.W. & Coop, M.R. 2004. Developments in understanding soil behaviour. Advances on Geotechnical Engineering. The Skempton Conference Thomas Telford: London, 103–206. Josa, A., Balmaceda, A., Gens, A. & Alonso, E.E. 1992. An elasto-plastic model for partially saturated soil exhibiting a maximum of collapse. 3rd. Int. Conf. Computational Plasticity, Barcelona 1: 815–826. Khalili, N. & Loret, B. 2001. An elasto-plastic model for non-isothermal analysis of flow and deformation in unsaturated porous media: formulation. Int. J. of Solids and Structures 38: 8305–8330. Kohgo, Y., Nakano, M. & Miyazaki, T. 1993. Theoretical aspects of constitutive modelling for unsaturated soils. Soils and Foundations 33 (4): 681–687. Lloret, A., Villar, M.V., Sanchez, M., Gens, A., Pintado, X. & Alonso, E.E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique 53: 27–40. Loret, B. & Khalili, N. 2002. An effective stress elasticplastic model for unsaturated porous media. Mechanics of Materials 34: 97–116. Modaressi, A. & Abou-Bekr, N. 1994. A unified approach to model the behaviour of saturated and unsaturated soils. 8th Int. Conf. Computer Meth. and Advances in Geomech. Balkema, Rotterdam: 1507–1513. Nuth, M. & Laloui, L. 2007. Effective Stress Concept in Unsaturated Soils: Clarification and Validation of a Unified Framework, International Journal of Numerical and Analytical Methods in Geomechanics, DOI: 10.1002/nag.645. Russell, A.R. & Khalili, N. 2006. A unified bounding surface plasticity model for unsaturated soils. Int. Journal for Numer. Anal. Meth. in Geomech 30: 181–212. Sánchez, M. & Gens, A. 2005. Final Report on Thermohydro-mechanical modelling. Deliverable D19-3, Febex II Project, EC Contract FIKW-CT-2000-00016. Sánchez, M., Gens, A., Guimarães, L. do N. & Olivella, S. 2005. A double structure generalized plasticity model for expansive materials. Int. Journal for Numer. Anal. Meth. in Geomech 29: 751–787.
The paper has presented a number of developments related to the constitutive modelling of unsaturated soils under increasingly generalised conditions. In the first part, coupled hydromechanical models have been examined. By making suitable choices in the formulation of the constitutive model, it has been possible to prove its consistency with respect to a thermodynamical framework. Subsequently, the behaviour of expansive clays has been described using a double structure approach that takes explicitly into account the microstructure of the material and the interaction between the two structural levels, albeit in an approximate form. It has been shown that such an approach provides a very convenient platform to extend the constitutive mode to account for more general soil behaviour that includes both temperature and chemical effects. ACKNOWLEDGMENTS The contribution of the Spanish Ministry of Education and Science through research grant BIA2005-05801 is gratefully acknowledged. REFERENCES Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40: 405–430. Alonso, E.E., Vaunat, J. & Gens, A. 1999. Modelling the mechanical behaviour of expansive clays. Engineering Geology 54: 173–183. Bolzon, G., Schrefler, B.A. & Zienkiewicz, O.C. 1996. Elasto-plastic soil constitutive laws generalised to partially saturated states. Géotechnique 46: 279–289. Borja, R.I. 2004. Cam Clay plasticity, Part V: A mathematical framework for three-phase deformation and strain localization analysis of partially saturated porous media. Computer Methods in Applied Mechanics and Engineering 193: 5301–5338. Brackley, I.J. 1975. Swell under load. Proceedings, 6th Regional Conference for Africa on Soil Mechanics and Foundation Engineering, Durban, 1: 65–70. Collins, I.F. & Hilder, T. 2002. A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests. Int. J. Numer. Anal. Meth. Geomech. 26: 1313–1347. Collins, I.F. & Houlsby, G.T. 1997. Application of thermomechanical principles to the modelling of geotechnical materials. Proc. R. Soc. London A 453: 1975–2001. Cui, Y.J., Delage, P. & Sultan, N. 1995. An elasto-plastic model for compacted soils. Unsaturated soils. Balkema, Rotterdam, 2: 703–709. Dangla, O.L., Malinsky, L. & Coussy, O. 1997. Plasticity and imbibition-drainage curves for unsaturated soils.: A unified approach. 6th Int. Conf. Num. Models in Geomechanics, Montreal, Balkema, Rotterdam, 141–146.
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Sánchez, M., Gens, A., Guimarães, L. do N. & Olivella, S. 2008. Implementation algorithm of a generalised plasticity model for swelling clays. Computers and Geotechnics (submitted). Sánchez, M., Villar, M.V., Gens, A., Olivella, S. & Guimarães L. do N. 2007. Modelling the effect of temperature on unsaturated swelling clays. Numerical Models in Geomechanics NUMOG X. Pande & Pietruszcak (eds), Taylor & Francis, London: 57–62. Santagiuliana, R. & Schrefler, B.A. 2006. Enhancing the Bolzon-Schrefler-Zienkiewicz constitutive model for partially saturated soil. Transport in Porous Media 65(1): 1–30. Santamarina, J.C. & Fam, M. 1995. Changes in dielectric permittivity and shear wave velocity during concentration diffusion. Canadian Geotechnical Journal 32: 647–659. Sheng, D., Fredlund, D.G. & Gens, A. 2008. ‘A new modelling approach for unsaturated soils using independent stress variables. Canadian Geotechnical Journal 45(4), (in press). Sheng, D., Gens, A., Fredlund, D. & Sloan, S.W. 2008. Unsaturated soils: from constitutive modelling to numerical algorithms. Computers and Geotechnics (submitted). Sheng, D., Sloan, S.W., Gens, A. & Smith, D.W. 2003a. Finite element formulation and algorithms for unsaturated soils. Part I: Theory. Int. J. for Numer. and Anal. Meth. in Geomech. 27: 745–765. Sheng, D., Smith, D.W., Sloan, S.W. & Gens, A. 2003b. Finite element formulation and algorithms for unsaturated soils.
Part II: Verification and application. Int. J. for Numer. and Anal. Meth. in Geomech. 27: 767–790. Sheng, D., Sloan, S.W. & Gens, A. 2004. A constitutive model for unsaturated soils: thermomechanical and computational aspects. Computational Mechanics 33: 453–465. Sun, D.A., Sheng, D. & Sloan, S.W. 2007. Elastoplastic modelling of hydraulic and stress-strain behaviour of unsaturated soil. Mechanics of Materials 39(3): 212–221. Tamagnini, R. 2004. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Géotechnique 54: 223–228. Tamagnini, R. & Pastor, M. 2005. A thermodynamically based model for unsaturated soil: a new framework for generalized plasticity. C. Mancuso & A. Tarantino (eds), A.A. Balkema. Leiden: 121–134. Vaunat, J., Romero, E. & Jommi, C. 2000. An elastoplastic hydro-mechanical model for unsaturated soils. Experimental Evidence and Theoretical Approaches in Unsaturated Soils, Balkema, Rotterdam: 121–138. Wheeler, S.J. 1996. Inclusion of specific water volume within an elastoplastic model for unsaturated soil. Canadian Geotech. J. 33: 42–57. Wheeler, S.J., Sharma, R.S. & Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Géotechnique 53: 41–54. Wheeler, S.J. & Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soils. Géotechnique 45: 35–53.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A thermo-hydro-mechanical stress-strain framework for modelling the performance of clay barriers in deep geological repositories for radioactive waste L. Laloui, B. François, M. Nuth, H. Peron & A. Koliji Soil Mechanics Laboratory, Ecole Polytechnique Fédérale de Lausanne, EPFL, Switzerland
ABSTRACT: Assessing the performance of deep geological repositories for heat-generating radioactive waste requires reliable predictions of the Thermo-Hydro-Mechanical (THM) behaviour of the clay barriers (the buffer material as well as the host rock/clay). This represents an important element of the waste isolation system. In order to provide reasonable assurance that clay barriers will ensure nuclear waste isolation, it is essential to understand their behaviour under a variety of environmental conditions. The phenomena involved are complex, and adequately understanding the constitutive behaviour of clays and modelling their evolution is challenging. The stress-strain material behaviours that need to be understood and modelled include drying and wetting in nonisothermal conditions and heating-cooling in non-saturated conditions. Other aspects should be considered, such as drying induced cracks and the role of the material structure and its multi-porosity. The difficulty of some of these tasks is increased by the fact that some effects are coupled. The fundamental behaviours of clayey materials under the considered THM conditions are first identified and highlighted for deep repository experiments. We then propose a mechanical stress-strain constitutive framework to model the behaviour of clay barriers. This includes aspects such as the thermo-plastic behaviour of saturated and unsaturated materials. In the third part, we show that the proposed framework allows us to experimentally explain observed behaviours and to predict the THM behaviour of clay barriers.
1
migration into the buffer material. We therefore do not consider chemical effects. To increase the performance of the engineered barrier system (EBS), the multibarrier concept in the near-field of the waste was developed. This multiprotection generally consists of a solid waste form (e.g., vitrified high-level radioactive waste (HLW) or spent fuel), an overpack (or container) and materials placed between the overpack and the surrounding rock (backfill or buffer materials). Therefore, in many proposals for deep geological repositories (Chapman and Mc Kinley, 1987), the argillaceous materials constitute either the main barrier or an important element of the multi-barrier system. They can be either the host material1 or engineered parts of the repository (buffer materials such as compacted swelling clays, most probably bentonite). Figure 1 schematically illustrates a possible concept of the barrier system.
INTRODUCTION
In all nuclear power generating countries, spent nuclear fuel and long-lived radioactive waste management is an important environmental issue. Disposal in deep clay geological formations is a promising option to dispose of these wastes. A safety case for a geological repository for highlevel and/or long-lived radioactive waste aims at conveying reasoned and complementary arguments to illustrate and instill confidence in the performances of the disposal system. This need requires that, both in repository design and in performance assessment, all analyses and predictions about the behaviour of isolation barriers be based on robust science (Gera et al., 1996). This implies a good understanding of the fundamental behaviour of the argillaceous materials and their modelling based on the best available knowledge. In this context, predicting the short-term (up to a few years) response of clay barriers in a repository for heat-generating radioactive waste is an important task. In this paper, we suppose that during this time period, the mechanical properties of the clayey materials remain unchanged and that the efficiency of vitrification and the container prevent radionuclide
1 To maintain a general context, we use the phrase ‘‘host material’’ rather than host rock/clay.
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capacity. Several experimental results on the THM behaviour of bentonite materials that could be used in radioactive waste storage sites have been reported in the literature in the last decade. Four well-known and widely-studied bentonites are briefly presented below. The Febex bentonite extracted from the Cortijo de Archidona deposit (Almeria, Spain) is a material that has been selected in the ENRESA R& D plans as the most suitable material for backfilling and sealing the HLW repository and was tested over the last 10 years within the framework of the Febex project (ENRESA, 2000; Lloret et al., 2004; Villar, 2002, Villar et al., 2006). This clay is made of approximately 90% montmorillonite, giving it high swelling capacities upon wetting. Its liquid and plastic limits are 100% and 50%, respectively. The FoCa Clay is a sedimentary clay from the Paris Basin. This clay is supplied by the SFBD French Company. Manufacturing consists of disaggregation and gentle grinding, drying at about 60◦ C and sieving. The maximum grain size is 4 mm. The clay is largely made of an interstratified clay (50% calcium beidellite and 50% kaolinite) (Imbert et al., 2005; Olchitzky, 2002). Bentonite Kunigel V1 is a domestic bentonite produced in Japan by Kunimine Industries. More than 90% of its grains are smaller than 74 μm. The properties and behavioural features of this bentonite have already largely been investigated under the supervision of the Japan Nuclear Cycle Development Institute (JNC, 1999; Komine and Ogata, 1994). The two main constituents are montmorillonite (48%) and quartz (34%). Its liquid and plastic limits are 416 and 21%, respectively. MX-80, considered by many as the reference buffer material, is produced in the United States by the ‘‘American Colloid’’ society. The grain sizes are distributed between 10 μm and 1 mm (Tang, 2005). It is
Figure 1. The engineered barrier system: (1) steel canisters; (2) nuclear waste; (3) host material; (4) buffer material (from www.grimsel.com/febex/febex_intro_1.htm).
Clay barriers provide waste isolation mainly by restricting the contact between the groundwater and waste containers and by limiting the migration of most radionuclides released from the waste (aftercontainer failure). These two functions result from the low permeability and high retention capability of clays. Therefore, the buffer material must have several specific properties in order to ensure efficient containment with high safety for the long term. These characteristics are related to sufficient mechanical properties under isothermal, non-isothermal, saturated, and unsaturated conditions, to liquid, air and thermal conductivities, to the nuclide filtration abilities and to manufacturability of the buffer material. Such required properties are summarized in Table 1. The use of bentonite as a buffer material is the most usual solution in several national concepts. Bentonite is a clay mainly composed of smectite, which gives swelling properties due to its high water absorption Table 1.
The function of the buffer material in parallel with its required properties (JNC, 1999).
Function
Requirement
Property
Restriction of radionuclide migration
Restriction of groundwater movement
Low hydraulic conductivity (low permeability) High sorption coefficients Colloid filtration function Capability of chemical buffering
Technical feasibility of manufacturing/installation No significant impact on the engineered barriers for a specified period
Sorption of dissolved nuclides Prevention of colloid migration Buffering of changes in groundwater chemistry Possibility of filling gaps created during installation Manufacturable and placement properties Mechanical support of the overpack to ensure stability To inhibit thermal alteration of vitrified waste and buffer Stress buffering properties
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Self-sealing ability Compaction properties Strength to support the overpack in a stable position High thermal conductivity Plasticity
made of 75% montmorillonite and 15% quartz. Its liquid limit is approximately 450% while its plastic limit is around 50%. After manufacturing of the bentonite powder, all of these materials are partially wetted to reach the desired water content, and eventually mixed with additive soil (sand or graphite) in different proportions to adjust the desired properties. They are subsequently compacted with a well-defined energy. This compaction induces particular properties in the bentonite (e.g., a double structure, expansive tendency under wetting). The purposes of this keynote paper are to identify the fundamental mechanical behaviours of argillaceous materials in the context of deep repository experiments and to analyse them in a comprehensive THM stress-strain constitutive framework, named ACMEG (Advanced Constitutive Modelling for Environmental Geomechanics). Among possible failure scenarios, observed drying cracks in the material will be discussed in this framework.
2
near-field, which can be defined as the zone altered by the presence of the radioactive waste (including the buffer materials and a portion of the host material adjacent to the waste location), is subjected to complex mechanical, hydric, and thermal solicitations with a great inter-dependence (THM couplings). In this paper, we limit our analysis to processes where THM coupling is predominant. With the ‘‘intact state’’ of the host massif as the initial state with a generally anisotropic stress state, the first step is excavation. This process induces a stress redistribution due to opening, causing tension, compression and shear and leading to an Excavation Disturbed Zone (EDZ) in the host material around the excavation (Davies and Bernier, 2003). This stage is not considered in this paper. After excavation and before HLW emplacement, the galleries are ventilated. During this stage, the excavated area plays a drainage role and a consolidation process occurs in the surrounding host material. In addition, a negative pore water pressure (suction) is acting on the field material; a strong suction gradient can develop between the gallery surface and the surrounding host material. In this situation, drainage and drying in the vicinity of the ventilated excavation are likely to be associated with radial cracking in the galleries. After placing the canister and filling the gap between it and the host material with buffer material (i.e. blocks of compacted clay, initially unsaturated), the main action that affects the EBS is heating from the canister (Figure 3) and hydration from the surrounding host material. This stage can be subdivided into several expected phases:
THERMO-HYDRO-MECHANICAL PROCESSES
Figure 2 illustrates a possible layout of a deep geological repository. In the first year following the construction of the underground disposal, the
– In the very early closure stage, the thermal flux from the vitrified waste into the buffer material occurs in unsaturated conditions at a constant water content
Figure 3. Time-dependent temperature evolution at various positions within the buffer material (bentonite) and surrounding rock/clay for canisters containing four spent fuel assemblies. The bentonite is assumed to have a thermal conductivity of 0.4 W m−1 K−1 and a heat capacity of 1.2 MJ m−3 K −1 . The initial ambient temperature is 38◦ C. Canisters have a heat output of 1490 W at the time of waste emplacement in the repository (Nagra, 2002b).
Figure 2. Possible layout for a deep geological repository for Spent Fuel, High Level Waste, and Intermediate Level Waste (SF/HLW/ILW) in Opalinus Clay (Nagra, 2002a).
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(i.e. constant suction). The impact of the thermal load generated by the waste is particularly important as it will significantly affect the temperature and the stress far (more than 50 m) from the repository in the host material (Timodaz, 2007); – During early closure, the resaturation process induced by the water flux from the surrounding rock/clay mass occurs in a media in which temperature progressively increases. The buffer material is
subjected to wetting (suction decrease) and thermal swelling (and/or eventual collapse); – The THM processes progress and the buffer material reaches a saturated state while the temperature is still increasing (Figure 3); – In a later closure stage, the high temperature induces a desaturation process of the buffer material, which tends to shrink with a risk of desiccation crack occurrence. This phase is generally seen as the most critical stage for the integrity of the engineered barrier. In Figure 4 we show an example of cracks in the inner wall of the bentonite buffer annulus in which the heat-generating waste is enveloped (Graham et al., 1997). Those cracks were identified after decommissioning a large-scale test of EBS performance conducted over 2.5 years; – Finally, in the very late closure stage, when the maximum of thermal power has been emitted by the vitrified waste, temperature around the repository is slowly falling and the buffer material is re-saturated (wetting process). The thermal and hydraulic gradients are largely lower than previously and progressively vanish. When the temperature has totally decreased, irreversible thermal strains predominate. In terms of theoretical and constitutive studies of the processes encountered, the succession of different phases above clearly shows the necessity of using high-performance modelling tools to best approach the complex phenomena and interactions. Table 2 summarizes the THM processes and the modelling aspects required to treat the problems.
Figure 4. Image of cracks of inside wall of buffer annulus after removal of heater (Graham et al., 1997).
Table 2.
THM processes occurring in the life of underground nuclear waste disposal.
Stage
Processes
Modelling
Excavation
Stress redistribution EDZ formation
Ventilation of the excavation
Consolidation process in the host material; Swelling and eventual desaturation of the host material Thermal diffusion in an unsaturated medium; Hydraulic diffusion in an isothermal medium Thermal and hydraulic swelling and/or collapse of the buffer material Coupled thermal and hydraulic diffusion in a deformable media; Thermal and hydraulic swelling and/or collapse of the buffer material Desaturation of the buffer material due to thermal effects Shrinkage and risk of desiccation cracks in the buffer material Temperature decrease and wetting of the buffer material; Lower thermal and hydraulic gradient; Irreversible thermal strains
Elasto-plastic (EP) model for saturated and isothermal conditions—(EDZ aspect not considered here) Hydro-mechanical coupling in unsaturated conditions considering desiccation crack occurrence Thermo-hydraulic (TH) diffusive law coupled with an isothermal and a non-isothermal (T) EP mechanical model for unsaturated conditions TH diffusive law coupled with a THM-EP mechanical model for unsaturated conditions TH diffusive law coupled with a THM-EP mechanical model for unsaturated soil considering desiccation crack occurrence TH diffusive law coupled with a THM-EP mechanical model for unsaturated conditions considering wetting paths
Very early closure stage Early closure stage Late closure stage Very late closure stage
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3
confining stresses (similar to paths followed in underground nuclear storage) induces mainly irreversible compression strains for low over-consolidation states and reversible dilatation strains for highly overconsolidated states. For instance, Figure 5 shows the evolution of the apparent preconsolidation pressure with temperature for Boom clay (the material involved in the multi-barrier concept in the Belgian underground laboratory of nuclear waste disposal), while Figure 6 shows its mechanical response under a heating-cooling cycle at different over-consolidated states.
THM STRESS-STRAIN BEHAVIOURS OF ARGILLACEOUS MATERIALS UNDER ENVIRONMENTAL LOADINGS
Natural host materials are different in terms of mineralogical compositions and consolidation histories of buffer materials. However, natural clays exhibit THM behaviours similar to those of buffer materials. Both of these could be modelled in the following theoretical framework. All constitutive processes considered are rate independent. Very few results are available in the literature on the role of the skeleton intrinsic viscosity in THM environmental loading conditions. However, readers interested in thermo-viscoplasticity modelling of clays may refer to the paper by Modaressi and Laloui (1997). The common features of the behaviour of argillaceous materials under environmental loadings such as suction or temperature variations are their high strain irreversibility (plasticity) and the important effects of pore fluids on mechanical behaviour. The predominant THM stress-strain behaviour can be mainly characterised by the following four processes:
3.2 Hydromechanical unsaturated isothermal behaviour of clayey materials Partial saturation is also observed to significantly affect the stress-strain response of bentonite and host materials. Like most fine-grained soils, such materials
– Non-linearity and irreversibility of the strains. – Modification of the internal state through isotropic hardening. – The interaction between pore fluids and the solid skeleton through ‘‘generalized’’ effective stress. – Modification of the elastic yield limit under environmental loadings: it shrinks with increasing temperature in saturated conditions and dilates with increasing suction at ambient temperature. Such processes are expressed by a dependence of the apparent preconsolidation stress. In its geological meaning, the preconsolidation pressure is unique and constant. However, the stress yield limit that separates ‘‘elastic’’ pre-yield from ‘‘plastic’’ post-yield behaviour in isotropic or oedometric conditions varies with environmental loads (suction/temperature) and is to be considered a rheological parameter. It is evaluated as the stress value at the intersection of two linear parts of the compression curves (mean/vertical effective stress versus void ratio). It should have a specific appellation; the term apparent preconsolidation pressure, pc , is used in this paper. In this section, we present general trends of the stress-strain behaviour of clayey materials. 3.1
Thermo-mechanical behaviour of saturated clayey materials
Several results from the literature show a decrease in the apparent preconsolidation pressure with increasing temperature T (Laloui and Cekerevac, 2003). Moreover, a heating-cooling cycle under constant effective
Figure 5. Evolution of the preconsolidation pressure with temperature, Boom clay (experimental results: Sultan, 1997).
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case where the mechanical external or total stress is fixed, suction changes cause straining of the material. Figure 8a shows that the complete drying-wetting cycle of fine-grained materials is not a reversible process from the viewpoint of deformation. In parallel, Figure 8b draws the soil water retention curve corresponding to such a suction cycle, highlighting a clear capillary hysteresis in the degree of saturation versus suction relationship. Focussing in particular on the wetting process, that is decreasing suction under a given stress state, it is understood from Figure 9 that the lower the applied stress, the higher the wetting induced swelling. Indeed, the volumetric response can be interpreted as a fully reversible heave under a low applied stress (e.g., 100 kPa), whereas plastic 0.1 (a) 0 Volumetric strain v
Figure 6. Heating-cooling cycle under constant effective confining stresses at different overconsolidation ratios, Boom clay (experimental results: Baldi et al., 1991).
100
-0.1 Drying
-0.2 -0.3
Matric suction s (MPa)
80
Wetting
-0.4 60
-0.5 100
40
104 106 Matric suction s (Pa)
108
1 (b) 20
1
10
100
Degree of saturation S (-) r
0.8 1000
Apparent preconsolidation pressure p' (MPa) c
Figure 7. Evolution of the apparent preconsolidation pressure with suction for FEBEX Bentonite (after Lloret et al., 2004).
show a non-linear dependency of the apparent preconsolidation pressure on suction (Figure 7). This feature, attributed to capillary effects, signifies that the domain of elastic behaviour is larger for drier materials. In addition, the material compressibility and elastic rigidity are noted to depend on the level of saturation. The volumetric response to a direct suction loading, that is a drying or wetting cycle, is also of interest. In the
drying
0.6 wetting 0.4
0.2
0 1
100 104 Matric suction s (Pa)
106
Figure 8. Drying wetting cycle of an overconsolidated white clay under zero mechanical stress: (a) Volumetric response, (b) Saturation states—Soil Water Retention Curve (after Fleureau et al., 1993).
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σ = 14000 kPa
0.32
v
Volumetric strain ε (-)
v
σ = 5100 kPa v
σ = 100 kPa
0.24
v
0.16
0.08
Initial point
0
Wetting 10
5
10
7
10
9
Matric suction s (Pa) Figure 9. Wetting of bentonite samples under different levels of vertical stress σv (after Lloret et al., 2004). Figure 10. Thermal effect on the retention curve of FEBEX Bentonite (after Lloret et al., 2004).
compression episodes are added when the vertical stress reaches 14 MPa. The large irreversible compressions upon wetting are commonly called wetting collapse. 3.3
Thermo-mechanical behaviour of unsaturated clayey soils
The main thermal effect on the retention behaviour of fine-grained soils concerns the diminishing retention capacity with temperature increase, mainly because the interfacial tension between the water and gas phases decreases under heating (Romero et al., 2001). Figure 10 depicts such experimental evidence on FEBEX bentonite, while Tang and Cui (2005) and Romero et al. (2001) underlined the same trends for MX80 bentonite and compacted Boom Clay, respectively. This thermal effect indirectly influences the mechanical response of the host materials by changing the suction value at a given degree of saturation. It is also observed that the temperature influences the mechanical response of fine-grained soils along drying-wetting paths (swelling and/or collapse), mainly because of the thermal effect on the physicochemical interactions between clay particles. Romero et al. (2003) observed that the swelling potential of compacted Boom Clay increases with temperature, while Villar and Lloret (2004) observed a lower swelling capacity of FEBEX bentonite at 80◦ C than at ambient temperature. The coupled temperature and suction effects on the apparent preconsolidation pressure were investigated by Salager et al. (2008) along mechanical compression paths for a sandy silt. In agreement with Figures 5 and 7, this study proved that a temperature increase tends to decrease the
Figure 11. Combined effect of temperature and suction on the evolution of the apparent preconsolidation pressure of a sandy silt (Salager et al., 2008): (a) Increase with suction, (b) decrease with temperature. The normalized preconsolidation pressure is the preconsolidation pressure measured at a given temperature T and suction s over the established preconsolidation pressure at ambient and saturated conditions (T0 and s = 0). se is the air-entry suction.
isotropic yield limit, while a suction increase enhances this limit. It was observed that logarithmic functions fit well with the evolution of the apparent preconsolidation pressure pc with temperature and suction. Indeed, the decrease (or increase, respectively) with temperature (or suction, respectively) of pc appears fast for low values of the two variables and becomes asymptotic for higher values (Figure 11). In addition, an additional coupled effect of temperature and suction on this limit was observed, probably due to the thermal influence on physico-chemical properties of clay particles and the capillary meniscus.
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3.4
Double structure effect
One of the key issues that should be precisely understood for such THM phenomena is soil structure effects. The term soil structure in general corresponds to the combination of soil fabric, namely arrangement of particles, and interparticle bonding (Mitchell, 1993). These two components of soil structure characterize the compacted materials that are used as buffer materials. Meanwhile, changes in soil structure can influence, through a coupled process, the host material behaviour in the phenomenon under study. In general, materials involved in such problems have complex structures. Unlike homogenous soils, these materials exhibit a wide and often bi- or multi-modal pore size distribution. There are two extremes in conceptualizing the structure of these materials: aggregation and macro void formation. The first explains structure changes in clay during compaction stages. For compacted materials, the pores can be divided into two main groups of macro and micro pores; therefore, they can be addressed by the concept of double porosity. However, this requires a rigorous consideration of soil structure and double porosity effects in a strain-stress constitutive approach. Soil structure may influence many soil characteristics, including compressibility (Lambe, 1958), hydraulic conductivity (Tamari, 1984) and the soilwater retention curves (Brustaert, 1968) of both compacted and natural soils. Based on experimental results, mainly from mercury intrusion porosimetry (MIP), it has been shown that compacted bentonite has an aggregated structure. Figure 12 presents the pore size distribution of the FEBEX bentonite obtained by MIP tests (Lloret et al., 2003). As can be seen in the figure, these materials have a bi-modal pore size distribution corresponding to two dominant classes of inter-aggregate and intra-aggregate pores.
Figure 13. Modification of soil fabric due to suction increase (after Cuisinier and Laloui, 2004).
Moreover, pore size distribution of the material might be strongly influenced by environmental loading. Figure 13 shows the MIP results of a natural aggregated soil at different suction levels (Cuisinier and Laloui, 2004). These results represent the strong evolution of macro and micro porosity due to suction variations. We can therefore conclude that in such materials, so-called double structure soils, deformation is a combined phenomenon at both the macro and micro scales. A direct consequence of such a structure is collapse upon wetting that can be ascribed to the collapse and disintegration of aggregates due to wetting (Gens and Alonso, 1992; Lloret et al., 2003). Moreover, the strength of structural units has an important influence on the compressibility and mechanical behaviour of the material. In other words, the yield limit depends not only on the stress state and stress history, but also strongly on the soil structure. Common experimental evidence for the latter point is the extension of preconsolidation pressure in natural structured soils compared to reconstituted soil of the same mineralogy (Callisto and Rampello, 2004; Liu and Carter, 1999). It is noteworthy that in these materials, hardening (or softening) of material depends also on the degradation of structures that might happen due to different environmental loadings.
4
ACMEG—A THM STRESS-STRAIN CONSTITUTIVE FRAMEWORK TO MODEL THE BEHAVIOUR OF CLAY BARRIERS
4.1 Generalised effective stress in host materials Defining an adequate stress framework is an essential prerequisite to constitutive stress-strain modelling of host materials submitted to THM loadings. According to the effective stress principle, first stated by Terzaghi (1936), a multiphase porous medium can
Figure 12. Distribution of incremental pore volume for two compacted samples of FEBEX bentonite at different dry densities. Mercury Intrusion Porosimeter test (Lloret et al., 2003).
70
This section presents the main layout of the model with its temperature and suction extension. A more complete description can be found in François and Laloui (2008a). In an elasto-plastic framework, the total strain dε is generated by non-linear thermo-elasticity, inducing reversible strain dε e , coupled with a multi-dissipative thermo-plasticity, producing irrecoverable strain dεp . Due to the strain history dependence, the formulation is given in terms of infinitesimal increments. Reference is made here to strains and stresses in the small deformation domain. The elastic part of the deformation is expressed as:
be converted into a mechanically equivalent, singlephase, single-stress state continuum. Consequently, the constitutive equations for mechanical behaviour directly link the change in strain to a variation in a single stress averaged over a volume comprehending several constituents, each of which is likely to react internally to a global external load. Under full saturation in water, the intergranular stress in bentonite is a combination of total stress and pore water pressure, the formulation being likely to include physico-chemical interactions whenever justified (Verwey and Overbeek, 1948; Hueckel and Pellegrini, 1992). A possible generalisation to partial saturation in water is the generalised effective stress inherited from Bishop’s proposal (1959): σij
= (σij − pa δij ) + Sr (pa − pw )δij
1 −1 dεije = Eijkl dσkl − βs dT δij 3
(1)
(3)
where σij is the exterior stress, δij the Kronecker delta, pa the pore air pressure, pw the pore water pressure, and Sr (= volume of water / volume of voids) the degree of saturation. The direct dependence of the mechanical stress variable (1) on suction (s = pa − pw ) and degree of saturation is noteworthy. The main implications of the use of advanced stress variables have been investigated by Nuth and Laloui (2007). While the stress variable (1) is the unique stress entering the mechanical stress-strain relationships, later expressed by equations (4) and (5), thermodynamic (Hutter et al., 1999) and energetic (Houlsby, 1997) considerations call for a supplementary set of variables to describe the retention behaviour in parallel. The complete stress and work conjugate strain framework is then formulated as: σij εij (2) and Sr s
where compression is taken as positive. Eijkl is the mechanical elastic tensor and βs the volumetric thermal expansion coefficient of the solid skeleton. Elastic strain may be induced by total stress, suction, saturation degree variation (first term of Equation 3), or by temperature change (second term of Equation 3). Eijkl is composed of the non-linear hypo-elastic modulus. Using the concept of multi-mechanism plasticity (Mandel, 1965), the total irreversible strain increment p dεij is induced by two coupled dissipative processes: an isotropic and a deviatoric plastic mechanism. These p,iso p,dev produce plastic strain increments dεij and dεij , respectively. The yield limits of each mechanism, restricting the elastic domain in the generalised effective stress space, take the following expressions (Figure 14):
where εij is the mechanical strain variable. The sets of variables (σij , εij ) and (s, Sr ) enter the mechanical model and the retention model, respectively, developed hereafter. Coping with the particular behavioural features of unsaturated fine-grained materials reviewed in Section 3.2 raises the need for constant interaction between the two models.
(5)
4.2
fiso = p − pc riso = 0 dp fdev = q − Mp 1 − bLog rdev = 0 pc
(4)
where q is the deviatoric stress and p the mean generalized effective stress. b is a material parameter and d the distance (in the logarithmic plane) between the
Introduction to the ACMEG constitutive framework
Mathematical formulation The basic concept of the ACMEG model family is to introduce all the environmental effects mentioned above (S—partially saturated state, T—temperature, 2S—double structure effect and DC—desiccation cracks) in an elasto-plastic framework where each environmental loading can cause reversible and irreversible changes in the material state.
Figure 14. Suction (a) and temperature (b) effects on the THM yield limits.
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apparent preconsolidation pressure, pc , and the critical pressure, pcr . M is the slope of the critical state line in the (q − p ) plane and may depend on temperature. riso and rdev are the degrees of plastification of the isotropic and deviatoric mechanisms, respectively. According to bounding surface theory (Dafalias & Herrmann, 1980), this enables progressive evolution of the isotropic and deviatoric yield limits (Hujeux, 1979). The apparent preconsolidation pressure pc is shared by both yield limits, coupling the two mechanisms. Moreover, this parameter is the main hardening varip able and depends on volumetric plastic strain εv (in the sense of the Cam-Clay model family according to Roscoe & Burland (1968)), on temperature and on suction (Figure 14): ⎧ p ⎪ ⎨pc0 exp{βεv }{1 − γT log[T /T0 ]} pc = pc0 exp{βεvp }{1 − γT log[T /T0 ]} ⎪ ⎩ {1 + γs log[s/se ]}
Figure 15.
if s ≤ se
hydraulic limits, fdry and fwet , on drying and wetting paths, respectively:
if s ≥ se (6)
where pc0 is the initial preconsolidation pressure (at the initial temperature and under saturated conditions) and β the plastic compressibility modulus. γT and γs are material parameters. The flow rule of the isotropic mechanism is associated, while the deviatoric one is not; these are assumed to take the following forms, respectively:
fdry = s − sd = 0 fwet = sd shys − s = 0
p,dev dεij
=
λiso 3
=
p λdev
1 Mp
q 1 ∂q δij +α M − ∂σij p 3
(9) (10)
(7)
where sd is the drying yield limit and shys is a material parameter considering the size of retention hysteresis. If the initial state is saturated, the initial hydraulic drying limit sd0 is equal to air-entry suction se and increases when suction overtakes se as follows:
(8)
sd = sd0 exp(−βh Sr )
p
p,iso
dεii
The retention model in the ACMEG framework.
(11)
where βh is the slope of the desaturation curve in the Sr − ln s plane (Figure 15). Finally, because the air-entry suction of the materials depends on temperature and dry density, sd0 is a function of temperature and volumetric plastic strain (François and Laloui, 2008b):
where α is a material parameter. The plastic multip p pliers, λiso and λdev , are determined using Prager’s consistency equation for multidissipative plasticity (Prager, 1958; Rizzi et al., 1996). As presented earlier, the generalised effective stress concept requires evaluating the degree of saturation to fully describe the behaviour of the unsaturated soil. Therefore, the retention behaviour (the degree of the saturation/suction relationship) of materials must be modelled. This retention model considers that the desaturation process is also seen as a yielding phenomenon. As long as the soil is drying, suction increases and the degree of saturation, Sr , tends to decrease, mainly when the air entry suction, se , is reached. se is therefore considered as a hydraulic limit separating fully and partially saturated states. Under re-wetting, a hysteretic retention phenomenon occurs, represented by a second limit (Figure 15). Then, a sorption-desorption cycle activates two successive
sd = sd0 exp(−βh Sr ){1 − θT log[T /T0 ] −θe log[1 − εvp ]}
(12)
where θT and θe are material parameters describing the logarithmic evolution of the air-entry suction with respect to temperature and volumetric plastic strain, respectively. Because this retention response is governed by yielding mechanisms, the processes must be controlled by evolution laws that agree with the consistency equations, in addition to the yield functions
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origins): (i) intrinsic strain hardening, which describes the evolution of the preconsolidation pressure of saturated reconstituted soil, p∗ c0 , according to a plastic strain hardening rule similar to the Cam-clay model, (ii) primary suction effects as in reconstituted soils, (iii) pure soil structure effects and (vi) secondary suction effects in aggregated soils. The primary effects of suction on the increase of effective preconsolidation pressure are of the same nature in reconstituted and aggregated soils and are taken into account by ψ s . These effects are linked to capillary effects and depend on the geometry of the pores and the air entry value of the pore system. Similar to reconstituted soils, a reversible function is proposed to quantify the evolution of apparent preconsolidation pressure due to primary suction effects:
(François and Laloui, 2008b). Within this framework, the current degree of saturation is given by: Sr = Sr0 + Srdry + Srwet
(13) dry
where Sr0 is the initial degree of saturation. Sr and Srwet are the variations of saturation degree induced by the drying and wetting mechanisms, respectively. For very high suctions, the hydraulic conditions reach a residual state defined by the residual degree of saturation Sr,res . In this state, no more variation of the degree of saturation is possible, even if the suction increases (Figure 15). Soil structure considerations In the ACMEG constitutive framework, the influence of soil structure on the stress-strain behaviour is taken into account by making the apparent preconsolidation pressure depend not only on stress state and stress history, but also on the soil structure and suction. For this purpose, as a first requirement, a state parameter named degree of soil structure R is introduced to describe and quantify soil structure effects. This parameter is defined here as the ratio of current macro void to its initial value in the intact state. The degree of soil structure is a scaling parameter that represents the openness of the structure. Obviously, any degradation of structure due to hydro-mechanical loadings changes this parameter. Onthebasisofpore-scaleexperimentalobservations, the evolution of the degree of soil structure has been found to be reasonably reproduced by a decreasing exponentialfunctionofplasticstrain(Kolijietal., 2008): R = exp(−ωεD )
⎧ if 0 < s < s1e ⎨1; 1 s ψ = 1 + γs log(sse ); if s1e ≤ s < sref ⎩ 1 + γs log(s se ) ; if s ≥ sref
in which s1e and se are the air entry suction values of micropores and reconstituted soil, respectively, and γs and γs are two dependent material parameters. The soil structure effects and secondary suction effects on soil structure are taken into account by ψ st , a function of degree of soil structure, which controls the extension of yield limits with respect to the reconstituted reference state. At constant suction, the following evolution rule has been derived for this variable (Koliji et al., 2008): ψ st = exp[R ln ψist ]
(14)
∗
(17)
where the subscript i designates the initial value. In the presence of suction variation, however, secondary effects of suction on soil structure should be considered in ψ st . The following relation is proposed to account for additional effects of suction: s + pat nst st ψ st = ψref , ψist = 1 (18) sref + pat
where R is the degree of soil structure, ε D is a combination of volumetric and deviatoric plastic strains, and ω is the parameter controlling the rate of structure degradation. The expression of the degree of soil structure given by Equation 14 provides an experimentally based relation that establishes the link between the pore-scale structure of the soil and the macroscopic behaviour of the material. Combining the effects of suction and soil structure, a general expression of the apparent preconsolidation pressure in unsaturated structured soils reads: pc = ψ st ψ s p c0
(16)
st in which ψref is the value at the reference suction sref and the exponent nst is a material parameter. The atmospheric pressure pat in the denominator is added to avoid infinite values when the saturated state (zero suction) is the reference state. Double effects of suction on the apparent preconsolidation pressure in structured soils are illustrated in Figure 16. In this figure, the abscissa is the ratio of apparent preconsolidation pressure to saturated preconsolidation pressure in the reconstituted state (pc /p∗ c0 ). The increase of apparent preconsolidation pressure due to the intrinsic suction effect ( ψ1 ) is represented by curve a. Multiplying this curve by a
(15)
where p ∗c0 is the reference effective preconsolidation pressure in saturated reconstituted soil, and ψ st and ψ s are two functions that incorporate the effects of soil structure and suction, respectively. Equation 15 considers four sources for the evolution of the apparent preconsolidation pressure (hardening
73
Griffith’s theory (Griffith, 1924) assumes that defects are present in the material that induce large stress concentrations and lower the overall strength of the material with respect to its theoretical value. Criteria based on this theory actually reflect the failure behaviour of unsaturated (or cemented) soils when the minor net stress is tensile (Bishop and Garga, 1969; Bagge, 1985; Baker, 1981). Based on available uniaxial traction test data on clayey soils performed at various known suctions and degrees of saturation (Farrell et al., 1969; Rodriguez et al., 2007; Peron, 2008), one can establish a dependence of tensile strength on suction. An exponential law of the following form is chosen (Peron, 2008): k1 s σt = σtsat + k2 1 − exp − k2
Figure 16. Combined effects of suction and soil structure on the apparent isotropic preconsolidation pressure.
(20)
σtsat g is the tensile strength in the saturated state (s = 0), namely the saturated tensile strength. Unless the soil is cemented, the value of σtsat should not greatly differ from zero. k2 and k1 are material parameters accounting for the increase in tensile strength as suction increases. k2 has the dimension of stress, and k1 is dimensionless. The evolution of the criterion (denoted fcut ) with respect to the normalized yield surfaces fiso and fdev is sketched in Figure 17. Within the ACMEG framework, desiccation cracking is therefore the consequence of a threefold process: (1) increase of suction and effective stress, (2) constraint in the resulting shrinkage process, and (3) coupling of tensile strength with suction. During a
st ψref
reference soil structure function gives the curve b, which represents the increase in apparent preconsolidation pressure due to intrinsic suction ( ψ1 ) and pure soil structure effects ( ψ2 ) without considering suction-hardening of soil structure. The final evolution of apparent preconsolidation pressure with suction in structured soils is represented by curve c. The grey area between curves b and c ( ψ3 ) corresponds to the effects of suction on soil structure. This effect is a hardening effect for suctions beyond sref and a softening effect for suctions below it. Desiccation cracks Desiccation cracks (actually cracks that occur during drying shrinkage) are likely to form if shrinkage deformations are constrained and/or tensile stresses are generated in soil reaching its tensile strength (Corte and Higashi, 1960). Typically, these constraints can arise from (i) a frictional or other traction or displacement boundary condition or (ii) any eigen-stress concentrations within the soil sample. Intrinsic factors, such as soil texture (existence of large particles, Towner 1988) and soil structure (solid network formed by soil particles, Scherer 1997) may be the origin of constrained shrinkage in some situations. Therefore, in order to capture the possibility of desiccation crack occurrence (essentially mode I fracturing), a tensile failure criterion is integrated into the ACMEG framework. Such a criterion actually stems from Griffith’s tensile failure criterion. It is assumed that a crack is likely to appear in the medium on a drying path as soon as the minor principal stress σ3 becomes equal to this overall strength, namely the tensile strength σt : σ3 = σt
Figure 17. Tensile criteria considered in the ACMEG framework.
(19)
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initial state, simplifying their comparison. In addition, the whole history of equalization to a given level of suction and subsequent oedometric compression at a constant level of suction is retraced (Figure 19a). Simulation of wetting or drying processes from an initial suction of 138 MPa predicts a satisfactory volumetric response (Figure 19b). The magnitude of strain is observed to vary depending on the net stress applied during equalization, as shown by the comparison of wetting tests 5 and 1, under a vertical net stress of 0.1 and 5.1 MPa, respectively. Even though the global swelling trend is observed upon wetting for all tests, a punctual decrease in εv is attributed to (i) mechanical compression prior to or during equalization and (ii) seamless plastic episodes due to the initiation of minor wetting collapse. Subsequent oedometric compression tests (Figure 19c) at constant suctions from 0 (test 5) to 500 MPa (test 1) are also remarkably well predicted with the proposed framework, as a consequence of the reliability of the isotropic yield limit formulation (Equation 6). Underground confinement brings particular boundary conditions for the bentonite layers, so that their overall volume is often totally constrained. Under the effect of moisturisation, the constraint leads to inner stresses, the latter quantified by the means of swelling pressure tests. On the basis of advances brought by using the generalised effective stress, ACMEG makes it straightforward to simulate the constrained conditions and predict the generated stresses. The superposition of innovative numerical simulations (predictions for tests SP1 and SP4) with experimental points in Figure 20 shows a satisfying qualification of the stress increase trends. A close estimate of the maximum swelling pressure is then available from numerical results, even though the quantification could still be refined (Nuth and Laloui, 2007). The simulated results are also strongly dependent on the soil water retention curve shape (Equations 9 to 13).
Figure 18. Interception of stress path with tensile failure criterion during constrained shrinkage in the radial direction.
constrained desiccation phase, prescribed strains make the stress path deviate from the isotropic path normally followed during unconstrained desiccation. The stress path then tends to come closer to the tensile failure criterion. In turn, the tensile failure criterion tends to move towards higher minor effective stresses, due to its dependence on suction (this could be seen as an expression of brittleness affecting the soil as suction increases). This behaviour can be illustrated using the parameter X r , defined as ‘‘degree of shrinkage restraint,’’ and equal to the ratio of hindered strains to shrinkage strains resulting from unconstrained shrinkage. Figure 18 shows different evolutions of the minor stress during drying depending on the value of X r (from 0, unconstrained shrinkage, no crack is possible, to 1, all strains are hindered in two of the three principal directions). The trace of a possible tensile failure criterion in the s − σ3 plane, given by Equation 19, is also sketched.
5 5.1
5.2 Modelling the effect of temperature on the hydro-mechanical response of host materials In confining barriers, saturation and desaturation processes often occur in a medium affected by nuclear waste heat emission. Under such non-isothermal conditions, several couplings between capillary and temperature effects must be considered in order to understand and to predict the THM response of clay simultaneously submitted to stress, moisture and temperature changes. Figure 21 presents the retention behaviour of compacted Boom clay at two temperatures as predicted by ACMEG and as compared with experimental observations (Romero et al., 2003). This example shows the temperature effect on the retention curve. In particular, the air-entry suction is reduced with increasing temperature. Moreover, during these
MODELLING PERFORMANCES OF THE ACMEG FRAMEWORK Modelling the unsaturated behaviour of host materials
The applicability of the ACMEG framework to waste confining material is illustrated with the modelling of the complex experimental stress-strain response in unsaturated FEBEX bentonite (Lloret et al., 2004). These experimental data were preferred because most published stress paths actually start from the same
75
1000
Test 1
10
SP2 EXP SP3 EXP
Test 2
Test 3 7
10
Test 4 106
SP4 EXP
100
SP1 MOD SP2 MOD SP3 MOD SP4 MOD
10 Wetting
Initial point
8
SP1 EXP
(b)
(a)
Matric suction s (MPa)
Matric suction s (Pa)
109
1
105 104
Final point
Test 5 106 Vertical stress
108
-2
0.16
2
4
6
8 v
Experiment
12
Numerical simulation T=22˚C T=80˚C
0.08
10
(MPa)
Figure 20. Comparison of experimental swelling pressure tests on Febex bentonite and their numerical simulation using ACMEG.
Exp. test 1 ACMEG-s test 1 Exp. test 3 ACMEG-s test 3 Exp. test 5 ACMEG-s test 5
0.24
0
Vertical net stress (b)
0.32 Volumetric strain v (-)
0.1
v (Pa)
T=22˚C T=80˚C
1.1
Initial point
1
0 105
107 Matric suction s (Pa)
0.4
109
Exp. 1 Mod. 1 Exp. 2 Mod. 2 Exp. 3 Mod. 3 Exp. 4 Mod. 4 Exp. 5 Mod. 5
(c) Volumetric strain v (-)
Degree of Saturation [-]
Wetting
0.3 0.2 0.1
0.9 0.8 0.7 0.6 0.5 0.4 0.01
0.1
1
Suction [MPa]
0 -0.1 4 10
Figure 21. Comparison between experimental retention curve on compacted Boom Clay at two temperatures (22 and 80◦ C) and their numerical simulation using ACMEG model.
105 106 107 Vertical net stress v (Pa)
108
wetting-drying cycles, the porosity of the compacted Boom Clay is strongly modified by suction changes. Figure 22 shows drastic collapse upon wetting. The collapse intensity is affected not only by the external stress level, but also by the temperature condition. The evolution of these volumetric responses with suction
Figure 19. Simulations of hydro-mechanical paths in oedometric conditions; (a) stress paths, (b) volumetric response with suction changes and (c) volumetric response with respect to vertical net stress.
76
Experiment
Experiment
Numerical simulation v,net v,net v,net
= 0.085MPa
v,net
= 0.3MPa
v,net
= 1.2MPa
v,net
= 0.085MPa
Numerical simulation T= 22˚C T= 80˚C
= 0.3MPa = 1.2MPa
T= 22˚C T= 80˚C
0
s= 0.06 MPa
0.05
-0.02
Volumetric strain [-]
Volumetric strain [-]
0
-0.05
-0.1
-0.04
-0.06
-0.08 -0.15
T=22˚C -0.2 0.01
0.1
(a)
-0.1 0.1
1
Experiment
Numerical simulation = 0.085MPa v,net v,net v,net
Figure 23. Comparison between experimental oedometric compression tests on compacted Boom Clay at a suction of 60 kPa and two different temperatures (22 and 80◦ C) and their numerical simulation using ACMEG model.
= 0.085MPa v,net
= 0.3MPa
v,net
= 1.2MPa
v,net
1
Vertical net stress [MPa]
Suction [MPa]
= 0.3MPa = 1.2MPa
0.05
Volumetric strain [-]
0
-0.05
-0.1
-0.15
Figure 24. Simulation of ACMEG for oedometric compression of unsaturated aggregated silty clay at a constant suction of 500 kPa.
-0.2
T=80˚C -0.25 0.01
(b)
0.1
the interconnection between temperature, suction, and stress states. Only a unified approach can consider in a relevant manner the THM response of this kind of material.
1
Suction [MPa]
Figure 22. Volumetric strain observed for drying-wetting cycles of compacted Boom Clay under oedometric conditions. Comparison between experimental results and numerical simulations using ACMEG. a) 22◦ C and b) 80◦ C.
5.3 Modelling the behaviour of unsaturated structured material Figure 24 shows results of the model simulation for a sample of unsaturated aggregated silt during oedometric compression at a constant suction of 500 kPa. The model was found to reasonably reproduce the experimental results. Thanks to a modified equation for water properties, the model can also address increasing saturation, even at a constant suction.
is well reproduced by the ACMEG model. In addition, a temperature increase modifies the yield point along compression paths, resulting in a translation of the normally consolidated line towards lower generalized effective stress (Figure 23). All of these examples clearly indicate the necessity to consider
77
Figure 26. Experimental values of uniaxial tensile strength from Rodriguez et al. (2007) and evolution law of tensile strength with ACMEG.
Figure 25. Crack pattern obtained after drying under atmosphere with controlled relative humidity, after Rodriguez et al. (2007).
5.4
Modelling of desiccation tests
Rodriguez et al. (2007) reported an experimental and numerical study of desiccation of low plasticity silt. The experimental programme consisted mainly of desiccation tests under ambient air or controlled atmosphere. Disk-shaped slabs of the soil in a slurry state were placed on plates, grooved to create radial restraint at the base. Only water loss and vertical shrinkage were recorded during the test. For tests under controlled atmospheric conditions (simulated later), slabs were 1.6 cm tall and relative humidity was controlled with a saline solution, corresponding to a total suction of about 38 MPa. Cracking was observed, leading to the formation of the patterns shown in Figure 25. The experimental degrees of saturation at cracking were between 0.98 and 0.86; suction values extrapolated from the water retention curve were between 10 and 40 kPa. Such a drying situation is in some ways similar to that which prevails for instance during air drying of gallery walls drilled in the host clay of nuclear waste repositories. The constraint in this situation stems from the deeper intact (i.e. not dried) host material. Radial cracking is a direct consequence in the galleries. Mechanical tests were also performed: traction tests, unconfined compression tests and one determination of the water retention curve in an oedometer apparatus. For the present simulation, parameters β sat , and Kref were calibrated on the basis of a water retention curve test in oedometric conditions. The value of the
Figure 27. Simulation of nickel mining waste constrained desiccation tests, predicted evolution of minor effective stress with respect to suction.
friction angle was fixed at 25◦ prior to calibration, representative of low plasticity silts. Poisson’s ratio was fixed at 0.25. The values of d, b and α were also fixed beforehand. Parameters for suction tensile strength evolutions were calibrated from tensile strength test results. The parameter σtsat was considered fixed and equal to the experimental value given by Rodriguez et al. (2007). k1 and k2 were calibrated with experimental results (see Figure 26). On the basis of the parameters determined above, desiccation tests were simulated under a controlled atmosphere. For the simulation, the suction field was considered homogeneous within the sample. This is in
78
accordance with the authors’ claim based on boundary value problem calculations. Furthermore, strains were assumed totally constrained in the radial (horizontal) direction. Such a condition should prevail at the slab base (and was adopted by the authors themselves). Results of the simulation are presented in Figure 27. The predicted suction at cracking was 19 kPa (degree of saturation 0.98), very close to the experimental results. In this sense, the model can predict desiccation crack occurrence.
6
Corte, A. & Higashi, A. 1960. Experimental Research on Desiccation Cracks in Soil. Research report 66, U.S. Army Snow and Ice and Permafrost Research Establishment. Dafalias, Y. & Herrmann, L. 1980. A bounding surface soil plasticity model. International Symposium on soils under Cyclic and Transient Loading, Swansea, 335–345. Davies, C. & Bernier, F. 2003. Impact of the Excavation Disturbed or Damaged Zone (EDZ) on the Performance of Radioactive Waste Geological Repositories. Proceedings of a European Commission CLUSTER—Conference and Workshop, Luxembourg. ENRESA. 2000. Febex Project: Full-scale engineered barriers experiment for a deep geological repository for high level radioactive waste in crystalline host rock. Publicación técnica 1/2000. Farrell, D.A., Geacen, E.L. & Larson, W.E. 1967. The effect of water content on axial strain in a loam soil under tension and compression. Soil Science Society of America Proceedings, 31 (4), 445–450. Fleureau, J.M., Kheirbeksaoud, S., Soemitro, R. & Taibi, S. 1993. Behavior of clayey soils on drying wetting Paths. Canadian Geotechnical Journal, 30 (2), 287–296. François, B. & Laloui, L. 2008a. Thermo-plasticity in unsaturated soils, a constitutive approach. E-UNSAT 08. This conference. François, B. & Laloui, L. 2008b. ACMEG-TS: A constitutive model for unsaturated soils under non-isothermal conditions. International Journal for Numerical and Analytical Methods in Geomechanics, Submitted. Gens, A. & Alonso, E.E. 1992. A framework for the behaviour of unsaturated expansive clays. Canadian Geotechnical Journal, 29, 1013–1032. Gera, F., Hueckel, T. & Peano, A. 1996. Critical issues in modelling the long-term hydro-thermo-mechanical performance of natural clay barriers. Engineering Geology, 41, 17–33. Graham, J., Chandler, N.A., Dixon, D.A., Roach, P.J., To, T. & Wan, A.W.L. 1997. The Buffer/Container Experiment: results, synthesis, issues. Atomic Energy of Canada Limited Report, AECL-11746, COG-97–46-I. Chalk River, ON, Canada. Griffith, A.A. 1924. Theory of rupture. In Proceedings of the First International Conference on Applied Mechanics, Delft, Holland, 55–63. Houlsby, G.T. 1997. The work input to an unsaturated granular material. Géotechnique, 47 (1), 193–196. Hueckel, T. & Pellegrini, R. 1992. Effective stress and water pressure in saturated clays during heating-cooling cycles. Canadian Geotechnical Journal, 29, 1095–1102. Hujeux, J.C. 1979. Calcul numérique de problèmes de consolidation élastoplastique. PhD Thesis, Ecole Centrale de Paris. Hutter, K., Laloui, L. & Vulliet, L. 1999. Thermodynamically based mixture models of saturated and unsaturated soils. Mechanics of cohesive-frictional materials, 4, 295–338. Imbert, C., Olchitzky, E., Lassabatère, T., Danglas, P. & Courtois, A. 2005. Evaluation of a thermal criterion for an engineered barrier system. Engineering Geology, 81, 269–283. JNC. 1999. Project to Establish the Scientific and Technical Basis for HLW Disposal in Japan. Technical report support report 2.
CONCLUSIONS
We present a THM stress-strain framework for modelling the performance of clay barriers in deep geological repositories for radioactive waste. This study aims to contribute to the performance assessment of deep geological repositories for heat-generating radioactive waste. The model framework is built on the conceptual understanding of the behaviour of soils submitted to loads representing the planned in-situ scenarios. The ACMEG framework considers the main mechanisms related to the thermo-plastic behaviour of saturated and unsaturated materials. It is extended to include soil structure aspects and induced desiccation cracks. The performances of the model are illustrated through comparisons with experimental results.
REFERENCES Baldi, G., Hueckel, T., Peano, A. & Pellegrini, R. 1991. Developments in modelling of thermo-hydro-mechanical behaviour of Boom clay and clay-based buffer materials (Vol 1 and 2). EUR 13365/1 and 13365/2, Luxembourg. Bagge, G. 1985. Tension cracks in saturated clays cuttings. In Proceedings of the Eleventh International Conference on Soil Mechanics and Foundations Engineering, San Francisco, vol. 2, 393–395. Baker, R. 1981. Tensile strength, tension cracks and stability of slopes. Soils and Foundations, 21 (2), 1–7. Bishop, A.W. 1959. The principle of effective stress. Tecnisk Ukeblad, 39, 859–863. Bishop, A.W. & Garga, V.K. 1969. Drained tension tests on London Clay. Géotechnique, 19, 309–313. Brustaert, W. 1968. The permeability of a porous medium determined from certain probability laws for pore-size distribution. Water Resources Research, 4, 425–434. Callisto, L. & Rampello, S. 2004. An interpretation of structural degradation for three natural clays. Canadian Geotechnical Journal, 41, 392–407. Chapman, N.A. & McKinley, I.G. 1987. The geological disposal of nuclear waste, John Wiley and Sons. Cuisinier, O. & Laloui, L., 2004. Fabric evolution during hydromechanical loading of a compacted silt. International Journal for Numerical and Analytical Methods in Geomechanics, 28 (6), 483–499.
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Koliji, A., Vulliet, L. & Laloui, L. 2008. New basis for the constitutive modelling of aggregated soils, Acta Geotechnica, (in press). Komine, H. & Ogata, N. 1994 Experimental study on swelling characteristics of compacted bentonite. Canadian Geotechnical Journal, 31 (2), 478–490. Laloui, L. & Cekerevac, C. 2003. Thermo-plasticity of clays: An isotropic yield mechanism. Computer and Geotechnics, 30, 649–660. Lambe, T.W. 1958. The engineering behaviour of compacted clays. Journal of the Soil Mechanics and Foundation Division ASCE, 84, 1–35. Liu, M.D. & Carter, J.P. 1999. Virgin compression of structured soils. Géotechnique, 49 (1), 43–57. Lloret, A., Romero, E. & Villar, M. 2004. FEBEX II Project: Final report on thermo-hydro-mechanical laboratory tests. publicación técnica 10/2004, ENRESA. Lloret, A., Villar, M.V., Sanchez, M., Pintado, X. & Alonso, E.E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique, 53 (1), 27–40. Mandel, W. 1965. Généralisation de la théorie de Koiter. International Journal of Solids and Structures, 1, 273–295. Mitchell, J.K. 1993. Fundamentals in soils behaviour, 2nd edition, John Wiley & Sons, New York. Modaressi, H. & Laloui, L. 1997. A thermo-mechanical constitutive model for clays. International journal for numerical and analytical methods in Geomechanics, 21, 313–335. Nagra 2002a. Project Opalinus Clay: Safety Report. Nagra Technischer Bericht NTB 02–05, 360p. Nagra 2002b. Calculations of the Temperature Evolution of a Repository for Spent Fuel, vitrified high-Level Waste and Intermediate Level Waste in Opalinus Clay. Nagra Technischer Bericht NTB 01–04. Nuth, M. & Laloui, L. 2007. Effective stress concept in unsaturated soils: Clarification and validation of a unified framework. International Journal for Numerical and Analytical Methods in Geomechanics. DOI 10.1002/nag.645. Olchitzky, E. 2002. Couplage hydro-mécanique et perméabilité d’une argile gonflante non saturée sous sollicitations hydriques et thermiques. PhD Thesis. Ecole nationale des ponts et chaussées, Paris. Peron, H. 2008. Desiccation Cracking of Soils. PhD Thesis, Ecole Polytechnique Fédérale de Lausanne, Switzerland. Prager, W. 1958. Non-isothermal plastic deformation. Koninkklijk-Nederland Akademie Van Wetenschappen Te Amsterdam—Proc. of the section of sciences-B, 61, 176–182. Rizzi, E., Maier, G. & Willam, K. 1996. On failure indicators in multi-dissipative materials. International Journal of Solids and Structures, 33 (20–22), 3187–3214. Rodriguez, R., Sanchez, M., Ledesma, A. & Lloret, A. 2007. Experimental and numerical analysis of desiccation of a mining waste. Canadian Geotechnical Journal, 44, 644–658. Romero, E., Gens, A. & Lloret, A. 2001. Temperature effects on the hydraulic behaviour of an unsaturated clay. Geotechnical and Geological Engineering, 19, 311–332.
Romero, E., Gens, A. & Lloret, A. 2003. Suction effects on a compacted clay under non-isothermal conditions. Géotechnique, 53 (1), 65–81. Roscoe, K.H. & Burland, J.B. 1968. On the generalized stress—strain behaviour of ‘‘wet’’ clay. In Engineering Plasticity. Cambridge University Press, Cambridge, England, 535–609. Salager, S., François, B., El Youssoufi, M.S., Laloui, L. & Saix, C. 2008. Experimental investigations of temperature and suction effects on compressibility and preconsolidation pressure of a sandy silt. Soils and Foundations. (Accepted for publication). Scherer, G.W. 1997. Stress from re-immersion of partially dried gel. Journal of Non-Crystalline Solids, 212, 268–280. Sultan, N. 1997. Etude du comportement thermo-mécanique de l’argile de Boom: Expériences et modélisation. PhD Thesis, Ecole nationale des ponts et chaussée, Paris. Tamari, S. 1984. Relations between pore-space and hydraulic properties in compacted beds of silty-loam aggregates. Soil Technology, 7, 57–73. Tang, A. 2005. Effet de la temperature sur le comportement des barrières de confinement. PhD Thesis, Ecole National des Ponts et Chaussée, Paris. Tang, A. & Cui, Y. 2005. Controlling suction by the vapour equilibrium technique at different temperatures and its application in determining the water retention properties of MX80 clay. Canadian Geotechnical Journal, 42 (1), 287–296. TIMODAZ 2007. Thermal impact on the damaged zone around a radioactive waste disposal in clay host rocks. Deliverable 2. State of the art on THMC. Terzaghi, K. 1936. The shearing resistance of saturated soils and the angle between the planes of shear. International Conference on Soil Mechanics and Foundation Engineering, Harvard University Press, 54–56. Towner, G.D. 1988. The influence of sand- and silt-size particles on the cracking during drying of small claydominated aggregates. Journal of Soil Science, 39, 347–356. Verwey, E. & Overbeek, J. 1948. Theory of stability of lyophobic colloids—The interaction of soil particles having an electric double layer, Elsevier Publishing Company, Inc. Villar, M. 2002. Thermo-hydro-mechanical characterisation of a bentonite from Cabo de Gata: A study applied to the use of bentonite as sealing material in high level radioactive waste repositories. publicación técnica 04/2002, ENRESA. Villar, M. & Lloret, A. 2004. Influence of temperature on the hydro-mechanical behaviour of a compacted bentonite. Applied Clay Science, 26, 337–350. Villar, M.V., Perez del Villar, L., Martin, P., Pelayo, M., Fernandez, A., Garralon, A., Cuevas, J., Leguey, S., Caballero, E., Huertas, F., Jimenez de Cisneros, C., Linares, J., Reyes, E., Delgado, A., Fernandez-Soler, J. & Astudillo, J. 2006. The study of spanish clays for their use as sealing materials in nuclear waste repositories: 20 years of progress. Journal of Iberian Geology 32 (1), 15–36.
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Advances in testing techniques
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A novel suction-controlled true triaxial apparatus for unsaturated soils L.R. Hoyos, A. Laikram & A.J. Puppala The University of Texas at Arlington, Texas, USA
ABSTRACT: This paper describes a novel servo-controlled true triaxial testing apparatus that has been developed to test 7.5-cm (3-in) side, cubical specimens of unsaturated soil under controlled-suction states for a wide range of stress paths that are not achievable in a conventional cylindrical apparatus. The equipment is a mixedboundary type of device, with the specimen seated on top of a high-air-entry disk and between five flexible (latex) membranes on the remaining sides of the cube. The new cell is an upgraded, more elaborate version of the one previously reported by Hoyos (1998), featuring two independent pore-air and pore-water pressure control systems via a PCP-5000-UNSAT pressure panel. Matric suction states in the specimens are induced during testing via the axis-translation technique. The technique is implemented by utilizing the s = ua testing concept (uw = 0). The paper outlines the full development of the new cell, including details of its main components and the step-by-step assembling process. Results from a short series of constant-suction Triaxial Compression (TC) and Triaxial Extension (TE) tests are presented. The operational true triaxial apparatus will play a fundamental role in the complete characterization of unsaturated soil behavior under multiaxial stress paths that are likely to be experienced in the field.
1
as critical a role in unsaturated soil response under multiaxial stress states (Fig. 1). The present work has been largely motivated by the lack of experimental evidence of this kind. It is in the above context that a true triaxial (cubical) test cell, capable of inducing in the test specimens a wide range of simple-to-complex multiaxial stress paths under controlled-suction states, plays a fundamental role in a thorough stress-strain-strength characterization of this type of materials. This paper describes a novel servo-controlled true triaxial apparatus that has been developed to test 7.5-cm (3-in) per side, cubical specimens of unsaturated soil
BACKGROUND AND IMPORTANCE
Over the last few decades, the description of the stressstrain-strength behavior of unsaturated soils has been closely linked with efforts to isolate the relevant stress fields governing the soil’s mechanical response. The adoption of matric suction, s = (ua − uw ), and the excess of total stress over air pressure, (σ − ua ), as the relevant stress state variables, have allowed the modeling of various key features of unsaturated soil behavior via suction-controlled oedometer, triaxial, and direct shear testing (Alonso et al., 1990; Wheeler and Sivakumar, 1992; Fredlund and Rahardjo, 1993). The majority of these devices, however, allow for the application of loads along limited paths and modes of deformation, such as one-dimensional, hydrostatic or axisymmetric loading. In nature, pavement subgrades and shallow foundation soils well above the ground-water table are subject to three-dimensional stress gradients due to changes in the stress state variables (σij − ua δij ) and (ua − uw )δij , as depicted schematically in Figure 1. Therefore, accurate predictions of the stress-strain response of geosystems involving unsaturated soils require that all the constitutive relations be valid for all major stress paths likely to be experienced in the field. Moreover, matric suction has been shown to play a paramount role in unsaturated soil response under one-dimensional, isotropic and axisymmetric loading conditions. Hence, suction is also expected to play
Foundation load
Traffic load
Pavement Pavement (
1
– ua)
(ua – uw)
(
1
– ua)
(ua – uw)
(ua – uw) ( 2 – ua) (
3
– ua) (ua – uw)
(ua – uw) ( 2 – ua) (
3
– ua) (ua – uw)
Figure 1. Unsaturated soil systems subject to multiaxial stress states.
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considerably enhanced performance, which includes: (1) More testing accuracy and reliability, (2) More flexibility of operation and breadth of application, (3) More refined data acquisition and process control systems, and (4) Increased amount and quality of testing variables monitored during a typical suction-controlled testing. In general, true triaxial devices can be classified into three major categories: rigid-boundary, flexibleboundary and mixed-boundary cells (Sture, 1979; Arthur, 1988). The apparatus presented in this paper is a mixed-boundary type of cell, with the specimen seating on top of a HAE ceramic disk and between five flexible membranes on the remaining sides of the cube. The cell consists mainly of a stainless steel frame featuring six pressure cavities to accommodate one top and four lateral flexible latex membranes, and a cubical base aluminum piece at the bottom to house a 5-bar ceramic disk and four symmetrically spaced coarse porous stones, as shown in Figures 2–5.
under controlled-suction states for a wide range of stress paths that are not achievable in a conventional cylindrical apparatus. The equipment can be defined as a mixed-boundary type of device, with the specimen seating on top of a high-air-entry (HAE) disk and between five flexible (latex) membranes on the remaining sides of the cube. The new cubical cell is an upgraded, more elaborate version of the one implemented by Hoyos (1998), featuring two independent pore-air pressure (ua ) and pore-water pressure (uw ) control systems by using a PCP-5000-UNSAT pressure control panel. Suction states in the cubical specimens during suction-controlled testing are induced via axis-translation technique. The following sections describe details of the design, main components, and assembling process of the developed apparatus. Preliminary results from a short series of suction-controlled triaxial compression (TC) and triaxial extension (TE) tests are also presented. 2
PREVIOUS WORK
Hoyos (1998) reported a first attempt to test unsaturated soils under suction-controlled multiaxial loading. In order to achieve this goal, a then 30-year-old cubical apparatus was modified to test 10-cm (4-in) side, cubical specimens of silty sand under suctioncontrolled conditions. The original development of the apparatus was presented by Atkinson (1972) for multiaxial testing of rock materials. Pore-water pressure (uw ) was applied to the bottom of the specimen through a 5-bar HAE ceramic disk. Pore-air pressure (ua ) was applied to the top and four lateral faces of the specimen via an air-pressurized manifold. Test results are reported in Hoyos (1998) and Hoyos and Macari (2001). This previous device, however, presented some equipment and testing related limitations that can be summarized as follows: (1) The steel frame is highly corrosive, which resulted in occasional clogging of the 5-bar ceramic; (2) Hydraulic oil is used to pressurize latex membranes in contact with soil, with oil temperatures ranging from 28◦ C to 38◦ C; (3) Latex membranes had low durability when exposed to hydraulic oil for extended time periods; (4) Porewater temperature cannot be controlled, retarding equalization of pore fluids; and finally, (5) The device allows only for stress-controlled testing. 3
Figure 2. Cubical base aluminum piece with porous stones and grooved compartment for housing a 5-bar ceramic disk.
A NOVEL TRUE TRIAXIAL APPARATUS
3.1 General design and assembling The true triaxial apparatus described herein is aimed at overcoming all of the above limitations, yielding a
Figure 3. Sealing of previously saturated, 5-bar ceramic disk onto cubical base aluminum piece.
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Figure 6. Photograph of entire cubical test layout, including external pressure application/control system (left) and PCP5000-UNSAT pressure control panel (right).
Figure 4. Close view of cubical base aluminum piece fitted onto bottom assembly.
(a) Figure 5. Plan view of cubical base aluminum piece fitted onto bottom assembly.
Sample preparation and saturation of the ceramic disks are described in sections 3.2 and 3.3. After setting of the compacted specimen into the inner cavity of the frame, the remaining five walls are assembled to the frame. Three LVDTs per face (top and four lateral) are used to monitor soil deformations while de-aired water is used to pressurize the specimen via latex membranes. The external pressure is transmitted to the water-filled latex membranes via pressure inlet/outlet connections on the walls. Figure 6 shows a photograph of the entire test layout, including the servo-controlled external pressure application system (on the left) and the assembled cubical cell interacting with the PCP-5000-UNSAT pressure control panel (on the right). Pore-air pressure (ua ) is supplied at the bottom of the specimen via a full set of air-pressurized manifolds with nylon tubing from the PCP-5000-UNSAT pressure control panel. Pore-water pressure (uw ) can be applied and controlled at the bottom of the specimen through the 5-bar ceramic disk. Water pressure is
(b) Figure 7. Suction-controlled mechanism: (a) cubical cell interacting with PCP-5000-UNSAT panel; and (b) pore-air pressure, pore-water pressure, and flushing control systems.
also supplied via nylon tubing from the PCP-5000UNSAT pressure panel. As shown in Figure 2, a grooved compartment uniformly distributes the water
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lateral wall assemblies are then set into place. A typical 7.5-cm (3-in) side, cubical specimen is then prepared in-place using a combined pluviation-tamping compaction process, as shown in Figure 10. The specimen is prepared in approximately eight pluviated layers, with each layer compacted at a target moisture content 4% greater than standard Proctor
underneath the 5-bar disk. In this work, however, the axis-translation technique is implemented by utilizing the s = ua testing concept (uw = 0). The panel also features a flushing mechanism at the bottom assembly, as shown in Figure 7. All suctioncontrolled tests are entirely computer-driven via a data acquisition/process control system (DA/PCS). The core of the cubical cell (Fig. 6) was manufactured and check-out tested at the University of Colorado, Boulder. The PCP-5000-UNSAT pressure control panel from Geotechnical Consulting and Testing Systems (GCTS), Tempe, Arizona, was then adapted to the cubical cell at the geotechnical research laboratories of the University of Texas at Arlington to control pore-air (ua ) and pore-water (uw ) pressures. The panel has been successfully utilized in cylindrical cells, featuring both pressure/volume control cell pressure, pore/back pressure, pore-air pressure with 2 MPa (300 psi) pressure range, and 300 cc (18 in3 ) volume capacity. It also includes a full set of hydraulic servo valves, an electro-hydraulic pump, pressure transducers with 0.1 kPa (0.02 psi) resolution, and specific water volume (vw = 1 + eSr ) change transducer with 0.01 cc resolution. 3.2
Figure 8. Bottom plate of custom-made chamber housing three 5-bar disks prior to saturation.
Saturation of HAE ceramic disks
A procedure similar to that suggested by Bishop and Henkel (1962) and Fredlund (1973), to ensure proper saturation of a HAE disk, was adapted to the working conditions of the 5-bar disks in the modified test cell (Figs. 2 and 3). The same approach was successfully used by Hoyos (1998). A custom-made saturation chamber, made of high burst-resistance acrylic and capable of housing up to three HAE ceramics at the same time, was designed and utilized for saturation of the 5-bar ceramics used in this work, as shown in Figure 8. After the 5-bar ceramics are fully sealed and set into place, the inner cavity of the assembled saturation chamber is filled with distilled, de-aired water to a height of about 25 mm (1 in) above the disks. The water is poured into the cavity using a pipette to minimize the generation of air bubbles. Once the cavity is partially filled with water and the top plate of the chamber is set into place, the water film is subjected to an air pressure of 600 kPa (87 psi), as shown in Figure 9. The water is then allowed to flow through the disks under this constant pressure until air in the disks dissolves in the grooved, previously saturated compartments underneath them. 3.3
Figure 9.
Saturation process of 5-bar ceramic disks.
Preparation of cubical test specimens
Poorly graded silty sand (SM) was used for suctioncontrolled testing in this research work. After saturation of the 5-bar disk, the bottom and the four
Figure 10. In-place, combined pluviation and tamping compaction process.
86
optimum. Tamping corresponds to a compactive effort considerably less than that of standard Proctor compaction. The intention is to reproduce specimens with low preconsolidation stress values, so that, subsequently, it is relatively feasible to reconsolidate the soil to a virgin state. A custom-made, 0.25 mm (0.01-in) thick, stainless steel shaft introduced into the cubical cavity of the frame facilitates the pluviation-tamping compaction process for each layer (Fig. 10). Upon completion of the soil compaction process, the shaft is gently removed and the top assembly of the cell, as well as the remaining components and connections for external stress and suction state applications, are set into place (Fig. 6). 4
Figures 12 and 13 present the deviator stress versus principal strain response of silty sand from suctioncontrolled TC tests. In these figures, suction is shown to exert an important influence on the shear resistance of silty sand, with a considerable increase for s = 200 kPa. During TC testing, the major principal stress σ1 is increased while the intermediate σ2 and minor σ3 principal stresses reduce, such that the net (σ1 – ua)
TE (b = 1, θ = 60o)
σ2 – σ3 σ1 – σ3
θ s = 50, 100, or 200 kPa
A
The suitability of the axis-translation technique in the newly developed apparatus was first validated experimentally by conducting two drained (constant-suction) tests, each involving isotropic loading followed by axisymmetric shearing, on two identically prepared specimens of silty sand. Both tests were performed at the same constant suction s = 200 kPa and loading rate of 10 kPa/hr. The first specimen, however, was subjected to a suction state s = ua = 200 kPa(uw = 0), while the second specimen was subjected to ua = 300 kPa and uw = 100 kPa(s = 200 kPa). Test results showed no significant difference in soil response under both test conditions, hence validating the technique (Hoyos et al., 2005). In this work, four identically prepared specimens of silty sand (SM soil: 80% sand and 20% silt) were subject to a multi-stage testing scheme in which suction was kept constant at 50 or 200 kPa. A soil specimen was first brought under isotropic stress state and subsequently imposed a constant-suction, monotonic triaxial compression (TC) or triaxial extension (TE) shearing until it was apparent that the deviator stress had reached a peak value. At this point, the specimen was brought back to the initial hydrostatic condition and a new octahedral stress applied via ramped consolidation. The same TC or TE stress path was then carried out. The suctioncontrolled test scheme is depicted schematically on a deviatoric plane in Figure 11. In this work, the net octahedral stress σoct and deviator stress q are both defined in terms of total principal stresses σ1 , σ2 , and σ3 as follows: σ1 + σ 2 + σ 3 − ua 3
b=
σoct = 50, 100, or 200 kPa
SUCTION-CONTROLLED TESTING
σoct =
TC (b = 0, θ = 0o)
SS (b = 0.5, θ = 30o)
(σ2 – ua)
Figure 11.
(σ3 – ua)
Suction-controlled true triaxial testing scheme.
60
Deviator stress, q (psi)
50 40 s = 200 kPa 30 s = 50 kPa 20 10 0 -15
-10
-5
0
5
10
15
Principal strain (%)
Figure 12. 100 kPa.
Silty sand response from TC tests at σoct =
60 s = 200 kPa
Deviator stress, q (psi)
50 s = 50 kPa
40 30 20 10 0
(1)
-15
-10
-5
0
5
10
15
Principal strain (%)
1 q = √ (σ1 − σ2 )2 + (σ2 − σ3 )2 + (σ1 − σ3 )2 (2) 2
Figure 13. 200 kPa.
87
Silty sand response from TC tests at σoct =
oped apparatus is suitable for testing soils under suction-controlled conditions using the axis-translation technique. On-going testing involves a wide range of stress paths that are not achievable in a conventional cylindrical apparatus, including simple shear (SS) in a deviatoric stress plane (π -plane). The operational true triaxial apparatus will continue to play a fundamental role in the complete characterization of unsaturated soil behavior under multiaxial stress paths that are likely to be experienced in the field.
60
Deviator stress, q (psi)
50 40 30 s = 200 kPa 20 s = 50 kPa 10 0 -15
-10
-5
0
5
10
ACKNOWLEDGMENTS
15
Principal strain (%)
Figure 14. 100 kPa.
This on-going research effort has been supported by the U.S. National Science Foundation (NSF), Award # 0216545. This support is gratefully acknowledged.
Silty sand response from TE tests at σoct =
60
REFERENCES
Deviator stress, q (psi)
50 s = 200 kPa
Alonso, E.E., Gens, A., and Josa, A. 1990. A constitutive model for par-tially saturated soils. Géotechnique, 40(3), 405–430. Arthur, J.R.F. 1988. Cubical devices: versatility and constraints. Advanced Triaxial Testing of Soil And Rock, STP 977, ASTM, Philadelphia, PA, 743–765. Atkinson, R.H. 1972. A cubical test cell for multiaxial testing of materials. Ph. D. Dissertation, University of Colorado at Boulder, Boulder, CO. Bishop, A.W., and Henkel, D.J. 1962. The measurement of soil properties in the triaxial test. 2nd ed., London, England: Edward Arnold, 227 pp. Fredlund, D.G. 1973. Volume change behavior of unsaturated soils. Ph. D. Dissertation, University of Alberta, Edmonton, Alta., Canada. Fredlund, D.G., and Rahardjo, H. 1993. Soil mechanics for unsaturated soils. John Wiley and Sons, Inc., NY. Hoyos, L.R. 1998. Experimental and computational modeling of unsaturated soil behavior under true triaxial stress states. Ph. D. Dissertation, Georgia Institute of Technology, Atlanta, GA, 352 p. Hoyos, L.R., and Macari, E.J. 2001. Development of a stress/suction-controlled true triaxial testing device for unsaturated soils. Geotechnical Testing Journal, ASTM, 24(1), pp. 5–13. Hoyos, L.R., Laikram, A., and Puppala, A.J. 2005. A novel true triaxial apparatus for testing unsaturated soils under suction-controlled multi-axial stress states. CDRom Proc., 16th International Conf. on Soil Mechanics and Geotechnical Engineering, September 12–16, 2005, Osaka, Japan, pp. 387–390. Sture, S. 1979. Development of multiaxial cubical test device with pore-water pressure monitoring facilities. Rep. VPIE-79.18, Dept. Civil Eng., Virginia Poly. Inst. & State U., Blacksburg, VA. Wheeler, S.J., and Sivakumar, V. 1992. Development and application of a critical state model for unsaturated soils. Predictive Soil Mech., eds: G.T. Houlsby & A.N. Schofield, 709–728, London.
40 s = 50 kPa
30 20 10 0 -15
-10
-5
0
5
10
15
Principal strain (%)
Figure 15. 200 kPa.
Silty sand response from TE tests at σoct =
octahedral stress σoct remains constant. Therefore, the corresponding minor and intermediate principal strains were found to be expansive (−) whereas the major principal strain was compressive (+). Figures 14 and 15 present the deviator stress versus principal strain response of silty sand from suctioncontrolled TE tests. In these figures, suction is also shown to have an important effect on the shear resistance of silty sand, with a slight increase for s = 200 kPa. During TE testing, the major σ1 and intermediate σ2 principal stresses are equally increased while the minor principal stress σ3 is decreased. Consequently, the major and intermediate principal strains were found to be compressive (+) while the minor principal strain was expansive (−). 5
CONCLUDING REMARKS
Preliminary suction-controlled testing on silty sand, as described herein, has shown that the newly devel-
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A simple shear apparatus for testing unsaturated soils S. Tombolato, A. Tarantino & L. Mongiovì Dipartimento di Ingegneria Meccanica e Strutturale, Università degli Studi di Trento, Italy
ABSTRACT: The paper presents a simple shear apparatus developed to investigate shear strength of unsaturated soils. The apparatus is designed to impose a simple shear-constant volume-constant degree of saturation mode of deformation. Total vertical and shear forces are simultaneously measured by 5 pairs of biaxial load cells at the bottom surface of the sample whereas negative pore-water pressure can be measured at the top surface of the sample by 5 pairs of tensiometers. A series of tests was performed on rubber and kaolin specimens to set up the apparatus and to adjust the experimental procedure in order to achieve a uniform distribution of vertical and shear forces along the sample. Preliminary results on both saturated and unsaturated compacted kaolin samples are presented.
1
INTRODUCTION
Shear strength of unsaturated soils controls stability of artificial and natural slopes above the phreatic surface and is of major interest in unsaturated soil mechanics. A simple shear apparatus has been developed at the University of Trento to investigate shear strength of unsaturated soils. The apparatus was designed to shear the sample under constant volume and water content and, hence, under constant degree of saturation. Suction is measured at the top surface of the sample by 5 pairs of Trento high-capacity tensiometers (Tarantino & Mongiovì 2002). Total vertical and shear forces are simultaneously measured by 5 pairs of biaxial load cells at the bottom surface of the sample. The paper presents a series of preliminary tests performed on rubber and kaolin specimens to set up the apparatus and to adjust the experimental procedure in order to achieve a uniform distribution of vertical and shear forces along the sample. First results on saturated and unsaturated compacted kaolin samples are then presented to validate the apparatus. 2 2.1
Figure 1.
Ideal boundary conditions for simple shear tests.
constant degree of saturation. The only degree of freedom is then the shear strain γzy . To ensure constant volume, the specimen is laterally confined by stacked steel plates and vertically confined by the loading cap which is locked in place during shearing (Figure 2). To ensure εx = εy = εz = 0, the confinement system must be designed to be adequately stiff. The deformation of the confinement system could then be assumed to be acceptable when resulting in negligible error in the measurement of total stress. To this end, the interaction between the specimen and the confinement system was numerically analysed and its different components were designed to produce an error in the measurement of total stress lower than 5% (Tombolato 2007). To produce uniform shear strains, the specimen was bonded to the loading cap and the cell base using epoxy resin. In addition, a very low height to length ratio was adopted. The specimen is 300 mm long, 60 mm wide and 10 mm high. This was expected to minimize the in-homogeneity of stresses resulting from the non-ideal boundary conditions at
SIMPLE SHEAR APPARATUS Design criteria
The apparatus was designed to apply a simple shearconstant volume-constant degree of saturation mode of strain to a cuboidal specimen as shown in Figure 1. This mode of strain involves zero horizontal extension in the direction of shear, εy = 0, together with plain strain in the orthogonal direction, εx = γxy = γxz = 0 (simple shear), zero vertical strain, εz = 0 (constant volume), and constant water content which implies
89
3.1 Vertical force distribution during compression
Figure 2.
Vertical forces measured by the biaxial load cells during compression should be ideally uniform. Differences may arise from non-uniform soil density, and hence non-uniform soil stiffness, non-uniform stiffness of the biaxial load cells, and improper coupling between the soil specimen and the confinement system. In turn, this is associated with the unevenness of the specimen surface and the non-coplanarity of the biaxial load cells. All these effects were separately investigated through specific tests. After installation, the 10 biaxial load cells were not perfectly coplanar and the bottom surface was shown to have a step-like profile. Due to these steps not all biaxial load cells came into contact with the specimen at the same average vertical force and this clearly caused a non-uniform distribution of vertical stresses. To eliminate steps between the biaxial load cells, these were mounted on the sliding base using a dynamometric key to control the torque and the surface formed by the biaxial load cell was ground. Although the biaxial load cells and relative bolt junctions are virtually equal, stiffness is not uniform due to bending of the sliding base. Initially, two pairs of sliders were positioned at the ends of the sliding base causing the sliding base to have greater deflections at its centre. As a result, the central cells (3a and 3b) were less stiff than the lateral cells (2a, 2b, 4a and 4b) which were in turn less stiff than the cells at the edge (1a, 1b, 5a and 5b) as shown in Figure 3a where the forces recorded by the biaxial load cells are plotted against the average vertical force in a test carried out on a rubber specimen. In order to reduce bending of the sliding base, 3 pairs of sliders were added in between the 2 external pairs of sliders for a total of 10 sliders. With such a configuration, the biaxial load cells exhibited a more uniform stiffness. The beneficial effect of grinding and of the additional sliders is shown in Figure 3b, where the vertical force measured by the biaxial load cells is again plotted against the average vertical force. The figure shows a relatively simultaneous loading of the biaxial load cells and changes in local vertical force with respect to the applied vertical force appear to be more uniform. Similar compression tests were performed on soil specimens, previously compacted outside the simple shear apparatus. A test performed when the biaxial load cells had not yet been ground and with only 2 pairs of sliders supporting the sliding base is shown in Figure 4a. It can be observed that the local vertical force may vary up 50% with respect to the average value. Figure 4b shows the vertical force distribution after grinding the base and adding 3 pairs of sliders for a total of 10 sliders. It can be observed that a more uniform stress distribution was achieved and that unloading of central biaxial load cells is less
Schematic layout of the simple shear apparatus.
the ends of the specimen. To perform tests at constant water content, a system to prevent soil-water evaporation was designed. 2.2
Simple shear apparatus
The simple shear apparatus is shown schematically in Figure 2. Its main components are: – a horizontal support carrying a linear motion system; – a sliding base incorporating load cells sliding horizontally over the horizontal support; – 10 biaxial load cells 60 mm long and 30 mm wide arranged in a matrix 5 × 2 used to simultaneously measure the shear and normal forces at the base of the specimen; – stacked steel plates to prevent horizontal deformation during both compression and shearing; – a loading cap constrained to move vertically by two vertical sliders; – a piston moved by a pneumatic-cylinder to apply the vertical load during the compression stage; – two lock nuts to lock the loading cap in order to prevent vertical deformation during shearing; – a frame to carry the piston and the lock nuts; – two lateral supports mounting the two vertical slider guideways and blocking the horizontal movement of the cap during shearing; – a stepper motor to horizontally move the sliding base. 3
PRELIMINARY TESTS
A series of preliminary tests on rubber and soil specimens were performed to investigate the force distribution at the base of the specimen both during compression and shearing stages and to improve the uniformity of shear and normal force distribution.
90
2
2 5b 1b
1.5
1.6
4a 1a
vertical force (kN)
local vertical force (kN)
5a
4b
2b
1 2a
3b
0.5
P = 795 kPa
1.2
P = 493 kPa
0.8
3a
0.4
P = 287 kPa
no contact
0 2
2 0
5b
1a 1b 2a
1
local vertical force (kN)
local vertical force (kN)
P = 800 kPa 5a
1.5
4a
4b 2b
3b
3a
0.5
1.6
1.2
P = 594 kPa
0.8
P = 288 kPa
0.4
0 0
0
0.4
0.8
1.2
1.6
0
average vertical force applied (kN)
10
20
30
lenght of the sample x (cm)
Figure 3. Test on a rubber specimen. (a) with non-coplanar biaxial load cells and 4 sliders (b) with coplanar biaxial load cells and 10 sliders.
Figure 4. Test on soil specimen compacted outside the SSA. (a) with non-coplanar biaxial load cells and 4 sliders (b) with coplanar biaxial load cells and 10 sliders.
pronounced especially at high vertical forces. Despite the significant improvement, non uniformities still remained. This was attributed to inadequate coupling between the surface of the specimen and the confinement system associated with surface unevenness and nonparallelism between the matching surfaces. To improve coupling it was decided to compact the soil powder directly in the simple shear apparatus. The uniformity of stress distribution improved significantly and deviations from the average vertical force were less than 20%. Non-uniform soil density results in non-uniform soil stiffness and, hence, non-uniform distribution of vertical forces. To cope with this problem, four vertical separators were placed in the stacked plates in order to obtain five compartments, each one including one pair of biaxial load cells, where equal amounts of powder were placed. This procedure improved the uniformity of vertical stress distribution. After this last adjustment, the maximum deviation from the average vertical force was found to be equal to 10%.
3.2 Vertical and shear force distribution during shearing Preliminary shear tests at constant vertical stress were carried out on rubber specimens to test the response of the biaxial load cells during shearing. A significant difference was observed between the total horizontal force measured by the external load cell and the sum of the shear forces measured by the biaxial load cells. It was inferred that the resin squeezing out of the specimen during compression formed bridges between the sliding base and the biaxial load cells and the biaxial load cells themselves. To tackle this problem, narrow tape bands were placed to cover the gaps between the biaxial load cells and the sliding base and the biaxial cells themselves prior to spreading the epoxy resin over the biaxial load cells. The tape was 0.1 mm thick and remained incorporated into the epoxy resin layer. Since the tape is more flexible than the epoxy layer, possible interaction between the load cells will only be associated with flexural stiffness of the epoxy layer.
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4
VALIDATION OF THE APPARATUS
0.5
local shear forces (kN)
To validate the simple shear apparatus, tests were carried out on saturated kaolin specimens. Two saturated tests are presented herein. Tests were carried out on samples directly compacted in the stacked steel plates at a water content of 0.3 and vertical pressure of 300 kPa. After installing the tensiometers, the specimens were saturated under 300 kPa vertical stress and then consolidated in steps to different final vertical stresses: 590 and 820 kPa respectively. The specimens were finally sheared at constant horizontal displacement rate of 5 mm/day. The vertical force distribution at the different total vertical forces applied during consolidation and after locking the nuts is shown in Figure 5. It can be noted that at the end of the tightening process, deviations from the average vertical force were less than 7% if only the 3 central pairs of biaxial load cells are considered. Vertical forces measured by the 10 biaxial load cells during shearing are plotted versus horizontal shear strain in Figure 6 for the specimen compressed to 590 kPa vertical stress. Vertical force decreased with increase in horizontal shear strain. Deviations from the average shear force are significant only for the biaxial load cells at the ends of the specimen (1a, 1b, 5a, 5b). Before peak the maximum deviation of local vertical force from the average value is about 5% and 7% for the specimens compressed to 590 kPa and to 820 kPa respectively. A satisfactory uniformity of vertical forces was then achieved. It is interesting to note the marked change in slope exhibited by the local vertical force at shear strain of 0.2 in correspondence with the shear force peak. This seems to suggest that the peak of shear force is associated with strain localization.
local vertical forces (kN)
local vertical forces (kN)
3b
0.8
3a
2b
4a 4b
5a 5b 1a
2a
0.4
0.8
1.2
1.6
Local shear forces measured by the biaxial load cells are shown in Figure 6. All biaxial load cells show a peak at the same horizontal shear strain of 0.2. Before peak the variation of shear force versus the shear strain is very similar for cells with variations with respect to the average value less than 13% and 17% for the first and second test respectively. Data in terms of average vertical and shear force as measured by the 3 pairs of central biaxial load cells also appear to be consistent (Figure 7). For both specimens the vertical force has a marked change in slope at the same horizontal strain. This horizontal strain corresponds in both tests to the peak in the shear force. External observation of the relative position of steel plates confirmed that strains were no longer uniform after the peak in the shear force. This result is also in good agreement with experimental observations made by Airey et al. (1985) in constant volume simple shear tests performed on normally consolidated samples of kaolin. The stress paths of the effective stresses (σyy , τxy ) on the horizontal plane are shown in Figure 8. To interpret these paths, it is necessary to make an assumption
30
lenght of the samplex (cm)
Figure 5. nuts.
1.2
Figure 6. Shear local forces versus shear strain for specimens compressed to 590 kPa.
0 25
1b
shear strain, γxy
0.4
20
2b 0.1
1b
specimen compressed to 590 kPa
15
2a
4b
5a 5b
0
1.2
10
4a 0.2
0.4
1.6
5
3b
3a
1a
specimen compressed to 820 kPa
0
0.3
0 1.6
2
0.8
0.4
Vertical force distributions after tightening lock
92
1.6
400
specimens comp ressed to 590 kPa specimens comp ressed to 820 kPa
vertical force (kN)
( 'yy, yx)
200
15.5˚
0
0.8
-200
( 'xx, xy)
0.4
( 'xx, xy)
0.5
hypotetical failure circle
-400
0.4
shear force (kN)
22.3˚
( 'yy, yx)
1.2
0
200
400
600
800
1000
'yy, 'xx 0.3
Figure 8. Hypothetical circles corresponding to failure on sub-horizontal planes. 0.2
xy = 0.21
respectively. It is unreasonable that horizontal stresses increase by 152 kPa and 232 kPa respectively during shearing. On the other hand, if it is assumed that the plane of rupture was vertical, i.e. the vertical plane is the plane of maximum stress obliquity, then the angle of shearing resistance φ would be given by the following equation:
0.1
0 0.5 xy = 0.34 0.4
/ '
0.3
2 · tan ϕ +
xy = 0.32
0.2
1 1 = tan ϕ tan φ ∗
(1)
where tan φ ∗ is the stress obliquity on the horizontal plane given by:
0.1
R = tan φ ∗ =
0 0
0.4
0.8
1.2
1.6
τxy = 0.377 (φ ∗ = 20.6◦ ) σyy
(2)
shear strai n , xy
According to Equation (1), an angle of shearing resistance of 35◦ was obtained, which is also unreasonable for kaolin. It may then be concluded that failure occurs on planes that are not planes of zero extension (vertical or horizontal). To interpret the tests, an alternative assumption needs to be made for the horizontal stress. According to Oda (1975) and Wood et al. (1979) the stress ratio R mobilized on the horizontal planes ratio can empirically be obtained as:
Figure 7. Vertical force, shear and stress ratio measured by the 3 pairs of central biaxial load cells during shearing for specimens compressed to 590 kPa.
either of the failure mechanism or of the horizontal effective stress. If it is assumed that the plane of rupture is hori zontal, then the measured stress (σyy , τxy ) should lie on the failure envelope. In this case, however, the resulting horizontal stress would be equal to 552 kPa and 772 kPa for the two tests respectively, which is significantly greater than the maximum expected horizontal stress at the end of consolidation, which was estimated to be about 400 kPa and 540 kPa
R=
τxy = k tan ψ σyy
(3)
where ψ is the angle between the major principal stress and the vertical direction and k is a constant equal to
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0.387 for kaolin (Borin, 1973). The horizontal stress can then be expressed as a function of the vertical stress and R as follows:
degree of saturation of the macropores instead of the overall degree of saturation. SrM can be expressed as follows:
R2 − k 2 σxx · σyy = 1+ k
SrM =
(4)
If the Mohr circles at shear stress peak is drawn according to this criterion for the two tests, we obtain Figure 8. The two circles thus obtained can be enveloped by a straight line passing through the origin having a slope of 22.3◦ which is a reasonable angle of shearing resistance for kaolin also according to triaxial data by Dalbosco (2005) (φ = 22◦ ) and simple shear data from Airey and Wood (1987) (φ = 22◦ ). Failure planes form at an angle of 12◦ with the horizontal in both circles. The same orientation of rupture bands was detected by a polarizing microscope on longitudinal sections of soil specimens removed from the cell at peak and impregnated with resin. The Mohr circles drawn in Figure 8 are characterized by σx ∼ = σy . If it is tentatively assumed that σx ∼ = σy at the critical state, then ψ = 45◦ at the critical state according to Equations (3) and (4). In other words, the principal axes of stress and strain increment would be coincident at the critical state. Accordingly, the horizontal plane would be the plane of maximum shear stress and the angle of friction mobilized would be given by: R=
5
τxy = sin φ σyy
e − ewm ew − ewm
(7)
where e is the void ratio, ew is the water ratio, and ewm is the ‘microstructural’ water ratio, which separates the region of inter-aggregate porosity from the region of intra-aggregate porosity. Tarantino (2007) showed that ultimate shear strength of compacted unsaturated soils can be described by an equation similar to that of saturated soils with the effective stress replaced by the modified average skeleton stress σ and with ewm determined as best-fit parameter: τ = σ tan φ
(8)
For the compacted kaolin, a value ewm = 0.40 was estimated from data presented by Wheeler & Sivakumar (1995), a value confirmed by triaxial tests carried out at the University of Trento (Dalbosco 2005). The stress path interpreted in terms of σ and the associated Mohr’s circle at peak traced assuming that σx = σy are shown in Figure 9 together with the stress paths recorded in the saturated tests. The Mohr circle at peak for the unsaturated specimen appears to be tangent to the saturated envelope suggesting that shear strength recorded for the unsaturated specimen is consistent with Eq. 8.
(5)
PRELIMINARY TEST ON UNSATURATED SPECIMEN saturated tests unsaturated tests
400
One test was performed on an unsaturated specimen having initial (before shearing) water content w = 0.22 and initial degree of saturation Sr = 0.6. The effectiveness of the anti-evaporation system was checked by verifying that suction measured by tensiometers installed in the loading cap remained constant over a period of time after installation. During shearing, suction remained approximately constant which was expected as void ratio and water content did not change during shearing. Initially the test was interpreted in terms of modified average skeleton stress σ (Tarantino & Tombolato 2005):
( ''yy, yx)
22.3˚
( ''xx, xy)
hypotetical failure circle
200
0
-200
-400
σ = (σ + SrM s) tan φ
(6) 0
where φ is the saturated critical state parameter, σ is the net stress, s is the suction, and SrM is the degree of saturation of the macropores. In the modified average skeleton stress, suction is weighed by
200
400
600
800
1000
', '' Figure 9. Stress paths relative to unsaturated tests interpreted in terms of modified average skeleton stress.
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6
CONCLUSIONS
Airey, D.W. & Wood, D.M. 1987. An evaluation of direct simple shear tests on clay, Géotecnique 37 (1): 25–35. Borin, D. 1973. The behaviour of saturated kaolin in the simple shear apparatus. PhD thesis, University of Cambridge. Dal bosco, A. 2005. Studio sperimentale del comportamento meccanico di un’argilla costipata non satura e generalizzazione della teoria di stato critico ai terreni non saturi. Graduate Thesis, University of Trento. Oda, M. 1975. On the relation τ/σn = k · tan ψ in the simple shear test. Soils and Foundations, 15 (4): 34–41. Tarantino, A. & Mongiovì, L. 2002. Design and construction of a tensiometer for direct measurement of matric suction. In Proceedings 3rd International Conference on Unsaturated Soils (eds J.F.T. Jucá, T.M.P. de Campos and F.A.M. Marinho), Recife 1, pp. 319–324. Tarantino, A. 2007. A possible critical state framework for unsaturated compacted soils. Géotechnique, 57 (4): 385–389. Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Géotechnique, 55 (4): 307–317. Tombolato, S. 2007. A simple shear apparatus for testing unsaturated soils from medium to large shear strains, PhD thesis, University of Trento. Wheeler, S.J. & Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Géotechnique, 45 (1): 35–53. Wood D.M., Drescher A. & Budhu M. 1979. On determination of stress state in the simple shear apparatus. Geotechnical Testing Journal, 2 (4): 211–221.
The paper has presented an apparatus to test unsaturated soils in simple shear mode of deformation. The apparatus and the experimental procedure were set up to obtain uniform stress distribution within the specimen. Experimental data from the tests on saturated specimens are in good agreement with data available in the literature. It has been shown that failure planes are neither horizontal nor vertical and it would appear that principal axes of stress and strain increment are coincident at the critical state. For a correct interpretation of simple shear tests, it is necessary to detect rupture bands and their orientation. ACKNOWLEDGEMENTS The authors are grateful to Marco Bragagna for his support in designing and setting up the apparatus. They also wish to express their gratitude to Dr. Giacomo Mele from CNR—ISAFOM (Naples, Italy) for carrying out the photos of thin polarized sections of the resin-impregnated samples. REFERENCES Airey, D.W., Budhu, M. & Wood, D.M. 1985. Some aspects of the behaviour of soils in simple shear. In Developments in soil mechanics and foundation engineering (eds. P.K. Banerjee and R. Butterfield), Vol. 2, pp. 185–213. London:Elsevier.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A device for simultaneous measurement of acoustic and hydraulic properties in unsaturated soils L.A. George & M.M. Dewoolkar School of Engineering, University of Vermont, Burlington, Vermont, USA
C. Wei Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, China
ABSTRACT: Accurately predicting and modeling flow through unsaturated soils is difficult due to the complexities that stem from the heterogeneities inherent in soil deposits. In simulating subsurface nonequilibrium flow, it is possible to take into account the heterogeneous nature of the material by using a rate dependent, dynamic capillary pressure saturation relationship (water retention relationship). A theoretical kinetic constitutive model which describes the dynamic capillary pressure saturation relationship has been developed. This model depends on variables which can all be measured in the laboratory. All of these variables have been previously measured, except for the capillary relaxation time. The capillary relaxation time can be determined using the velocity and attenuation of low frequency acoustic waves. A device has been developed which will allow for simultaneous measurement of the acoustic velocity and attenuation as well as the hydraulic properties, including the static capillary pressure saturation relationship and the unsaturated hydraulic conductivity function. This paper describes the details of this device and some preliminary measurements.
1
capillary relaxation times and the sizes of local structures in porous media (Wei & Dewoolkar 2006; Wei & Muraleethanan 2006; Wei & Muraleetharan 2002). This paper describes the experimental equipment and procedures which will be used to verify this procedure.
INTRODUCTION
Heterogeneities in porous media occur at a range of scales, from the macro-scale to the micro-scale. Macro-scale heterogeneity can be described in numerical models using varying material properties at the element level, but intermediate scale or meso-scale heterogeneity occurs at the sub-element level. These meso-scale heterogeneities may occur either due to variations in the structure, such as clay inclusions, or the distribution of moisture content, in the case of partially saturated media. Characterization of mesoscopic heterogeneities that may occur in macroscopically homogeneous porous media is fundamental to understanding the behavior of the material, and considering the effect heterogeneities have on flow and transport could vastly improve predictive models. Acoustic techniques provide a powerful means to characterize meso-scale heterogeneity in porous media in a non-destructive manner. Several models which describe wave induced flow have been developed and applied to evaluate the details of the mesoscopic structures in porous media (Johnson 2001; White 1975), but none are used to determine the dynamic effects of capillarity. A procedure has been proposed which would explicitly evaluate the dynamic capillary effects, and has been successfully used to infer the
1.1
Acoustic characterization of mesoscale heterogeneities
When a mesoscopically or locally heterogeneous porous medium is subjected to an external disturbance, fluids in different regions respond with different pressures, resulting in local fluid flow (Pride et al. 2003). Consequently, the macroscopic capillary pressure is generally a dynamic quantity. The local flow induced by a stress wave dissipates wave energy, resulting in intrinsic wave attenuation and velocity dispersion (velocity depending upon frequency). Such acoustical signatures play a key role in determining the characteristics of local flow and dynamic capillarity. A visco-poroelastic model that is capable of characterizing the relaxation processes associated with local fluid flow has been developed (Wei & Muraleethanan 2006). Given the measured acoustical data, specifically the velocity and attenuation of the compressional wave, the model can be used to determine the characteristic time of local flow. Since local flow is governed
97
explain the development and operation of this device, developed at the University of Vermont.
by the details of local heterogeneities, the obtained characteristic times can in turn be used to infer the information on local heterogeneities, and their effects on macroscopic fluid flow through the dynamic capillary pressure saturation relationship (or water retention relationship) which is described in the next section. 1.2
2
THE EXPERIMENTAL DEVICE
The laboratory device is capable of housing a cylindrical soil sample 100 mm in diameter and up to 125 mm in height. This large sample size is necessary to allow the low frequency acoustic wave to travel through the media for a distance larger than its wavelength. The sample is confined by cell pressure in a semi-flexible Viton® rubber jacket equipped with an acoustic transmitter and receiver (see Figures 1 and 2). The rubber jacket was made flexible enough to conform to the sample under confinement, but also rigid enough to house the transducers. The transducers were placed on the side of the sample so they would not interfere with the end caps or come in contact with the pore fluid. The device is also capable of utilizing a rigid walled sample when the acoustic measurements are not needed. The acoustic equipment developed by New England Research, Inc. (NER) of White River Junction, Vermont, includes flat piezo-ceramic transducers, a waveform function generator, an oscilloscope and the data acquisition system, as seen in Figure 3. The peizoceramic crystals are mounted on titanium heads that are shaped to the radius of the sample. Canada Balsam, a non-soluble acoustic couplant, is used between the titanium head and the soil sample. An absorptive backing is mounted on the outside of the transducers to reduce reflection of the received waves within the transducer. The flat piezoceramic transducers were chosen because they can produce both shear and
Dynamic capillary pressure saturation relationship
Generally, unsaturated soil properties e.g. the capillary pressure saturation relationship and the unsaturated hydraulic conductivity function, are measured at static or steady state conditions. The capillary pressure saturation relationship describes the relationship between the capillary pressure and the level of saturation in an unsaturated porous media, it is also known as the water retention curve, soil water characteristic curve, or the pressure saturation relationship. These static properties are then used to analyze both steady-state and transient flow. An early study by Topp et al. (1967) showed that these properties are rate dependent, and the assumption that static properties can be used in a transient analysis may be incorrect. Recently, experimental studies have shown that pressure saturation relationships obtained through inverse modeling of one-step and multi-step outflow experiments were influenced by the flow rate (Schultze et al. 1997; Wildenchild et al. 2001). Other models have been developed to explain this dynamic relationship, i.e. (Hassanizadeh & Gray 1993); this model includes a material coefficient thought to depend on both saturation and the rate of saturation change, but the coefficient is impossible to measure experimentally. The coefficient has been found to vary between 104 and 107 Pa.s (Hassanizadeh et al. 2002) by analyzing experimental data reported in the literature, but this formulation has yet to be verified. A new dynamic capillary pressure saturation relationship has been developed (Wei & Dewoolkar 2006) which includes the rate dependence, describes the hereditary effect of capillarity, and is based on the characterization of local flow caused by heterogeneities. The dynamic capillary pressure saturation relationship which has been developed is formulated with commonly known and relatively commonly measured soil properties, (e.g. the static capillary pressure saturation relationship and unsaturated hydraulic conductivity function, the porosity, density, and shear modulus), along with one additional parameter, the capillary relaxation time, which can be determined using acoustic techniques (Wei & Muraleetharan 2007). In order to collect all the parameters needed to determine the dynamic capillary pressure saturation relationship, a device capable of simultaneously measuring the hydraulic and acoustic properties of the porous media is needed. The following sections
Figure 1.
98
Schematic of the device.
Figure 2.
that the deformation of the solid is small (strains less than 10−7 ). The response of the partially saturated media is thought to be frequency dependent; therefore the acoustic waves are collected over a range of frequencies. The frequency of interest is in the vicinity to 10 kHz. The confining cell is filled with mineral oil in order to protect the electronic components within the cell. Conically shaped water reservoirs are located on either end of the sample, separated from the sample by the high air entry disc on the bottom and a coarse porous stone on the top. The water reservoirs are conically shaped to aid in removal of diffused air bubbles which may pass through the high air entry disc and are modeled after the work of Lu et al. (2006). The device is capable of utilizing ceramic, metal or nylon porous discs. High air entry discs maintain the sample at a specific saturation by prohibiting air to escape from the sample. The experiments presented in this paper used high entry porous membranes (GE Cellulous Acetate Membranes), with an air entry pressure of 200 kPa and a pore size of 0.45 μm. The membrane is attached to a bronze porous plate, 3 mm in thickness to reinforce the flexible membrane (shown as the HAE disk in Fig. 1). Air pressure is supplied to the sample through the top of the sample. The air can be maintained at atmospheric pressure or can be elevated when using the axis translation technique. A differential pressure transducer is connected between the water reservoir and the air pressure supply tube, to measure the capillary pressure as described in the next section.
Photograph of the confining cell and soil sample.
3 3.1
Figure 3.
PROCEDURES Measurement of the static capillary pressure saturation relationship
The static capillary pressure saturation relationship is a relationship between the level of saturation in a soil sample and the capillary pressure at equilibrium. The relationship is determined using a controlled volume method with the option of axis translation. During a controlled volume method the saturation in the sample is changed by controlling the volume of water which is allowed to leave the sample. Water is withdrawn from the bottom of the sample at a specific rate (Lu et al. 2006; Olsen et al. 1994). The basic concept behind the axis translation technique is to control the capillary pressure (ua − uw ) by elevating the pore air pressure (ua ) and maintaining the pore water pressure (uw ), instead of the traditional method of lowering the pore water pressure and maintaining the pore air pressure. These methods were chosen because of the shortened equilibration time associated with the controlled volume method and the large range of capillary pressures
Photograph of the entire experimental set up.
compressional waves and because of the relatively small strains they produce as compared to other transducers such as bender elements. The linearization used to approximate the governing equations requires
99
possible with the axis translation technique. Other methods may also be employed using this apparatus, such as suction controlled methods. The pore air pressure is maintained at a specific pressure determined by the anticipated capillary pressures of the media being tested. The quantity of water in the sample (i.e., the saturation) is controlled by a flow pump connected to a reservoir on the bottom of the sample. When a volume of water is removed from the sample, the pump is shut off and the capillary pressures are monitored with the differential transducer. When the pressures stabilize it is assumed that equilibrium has been achieved and a point on the static capillary pressure saturation relationship is obtained. The saturation is determined by calculating the volume of water in the sample, and the capillary pressure is measured by the differential pressure transducers connected between the pore air and the lower pore water reservoir. The sample size in this apparatus is much larger than those traditionally used for measurement of the characteristic curve and a few challenges arise when using a large sample. Samples used in Tempe cells are typically approximately 50 mm in diameter and 4–5 mm in height. Generally it is assumed that the saturation distribution along the height of the sample is negligible and the saturation of the entire sample can be taken as an average calculated using the amount of water withdrawn. Since this sample is approximately 100 mm in height there could be a considerable variation in saturation over the height of the sample depending on the pore size distribution of the sample and the capillary pressure at the bottom of the sample. Several soil types are being considered in this research to minimize this variation so that the acoustic measurements are more representative of one level of saturation. The level of saturation at mid height of the sample will be calculated considering the variation in saturation and pressure that occurs over the sample, using a method similar to Liu & Dane (1995). 3.2
Measurement of the unsaturated hydraulic conductivity function
Measurement of the unsaturated hydraulic conductivity function has not yet been attempted using this apparatus. It is expected that the procedures for measuring the capillary pressure saturation relationship will have to be modified from that described in the previous section, in order to also measure the hydraulic conductivity function simultaneously. There are two possible methods which will be investigated. The first approach would use the apparatus as described above; a constant flow rate would be imposed by withdrawing water from the bottom of the sample. This withdrawal would serve to lower the saturation and determine the hydraulic conductivity. The rate of withdrawal will
have to be high enough to impose a gradient across the sample. Assuming Darcian flow, the hydraulic conductivity could be calculated from the flow rate and the imposed gradient. The second approach would require modification of the apparatus including a second high air entry disk on the top of the sample. With this modification, the methods described by Olsen, et al (1994) and Lu & Likos (2006) could be utilized. Here the same amount of water would be injected and withdrawn from the top and bottom of the sample. Simultaneously one flow pump withdraws while the other injects the same volume of water at the same rate. The pressure head difference that this flow causes across the sample would be measured by a differential pressure transducer connected to both water reservoirs, and the head loss across the porous membranes is considered negligible. The flow rate and pressure head loss could be used to calculate the hydraulic conductivity for each saturation level. Both approaches will be tested and evaluated. 3.3
Measurement of the acoustic properties
The acoustic properties are measured at the same time as the capillary pressure saturation relationship and the unsaturated hydraulic conductivity function. Compressional and shear waveforms for a range of frequencies are taken at each saturation. The compressional and shear waves are produced with the transducers, which are excited by a waveform function generator. The received wave is displayed on an oscilloscope and the data acquisition system collects the raw data. The compressional wave velocity and attenuation is determined from the compressional waveform and is used to determine the capillary relaxation time. The shear wave velocity can be determined from the shear waveform and be used to determine the shear modulus of the soil sample, if desired. 4
PRELIMINARY RESULTS
Preliminary hydraulic testing has been performed on a sand sample and the static capillary pressure saturation relationship found is shown in Figure 4. This relationship was found using the procedure outlined in section 3.1, and the capillary pressures at a point were computed using software, TrueCell (Liu & Dane 1995), which corrects for the large height of the sample. Preliminary acoustic measurements have been taken on sand samples during separate experiments from the hydraulic measurements using the device described above. Figure 5 show an example compressional waveform. The preliminary results indicate that the device is measuring the acoustic properties of the sample, without adverse effects from the jacket or end caps. The procedures which will be used to determine
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Once both the velocity and attenuation have been determined the capillary relaxation time can be calculated, and used to predict the dynamic capillary pressure function using the procedure outlined by Wei & Muraleethanan (2007). The hydraulic properties of the sample must also be measured using the procedures outlined earlier.
5
Figure 4.
CONCLUSIONS
The development of a new type of laboratory device capable of making simultaneous measurements of acoustic signatures and hydraulic properties, including the static capillary pressure saturation relationship and the hydraulic conductivity function on relatively large soil specimens was presented. The acoustic properties include the compressional wave speed and attenuation. The measurements of acoustic and hydraulic properties will be used to quantify the effects that meso-scopic heterogeneities have on non-equilibrium flow in macroscopically uniform soil deposits.
Static capillary pressure saturation relationship.
ACKNOWLEDGMENTS
Figure 5.
Example waveform.
the velocity and attenuation from the waveforms are currently being developed, but the preliminary measurements are within the range of expected values, and the trends seen in the velocity as a function of saturation is as expected and as previously shown in partially saturated limestone samples (Cadoret et al. 1995). The attenuation of these waveforms will be determined using a waveform matching procedure developed by NER, which performs time domain minimization of the measured waveforms fit to a constant Q-propagation model prediction. The waveform matching algorithm estimates the time-shift and the attenuation that is needed to convert a reference (source) pulse into a received waveform that best matches the observed waveform. The mathematical basis of the algorithm is straightforward and is just a matter of computing the effect of passage through a substance with a band limited constant Q rheology. This process is superior to traditional spectral ratio methods in that it provides information on both velocity and attenuation while providing a more robust test of model assumptions by fitting the actual waveform rather than just its power spectrum (Smith 1993).
The study presented here was supported by Vermont Experimental Program to Stimulate Competitive Research (VT EPSCoR), (grant EPS 0236976) and the Vermont Space Grant Consortium. The authors are grateful to Dr. George Pinder for his time and advice, Floyd Vilmont and Kurt Anthony of UVM for assistance in the apparatus development and Gregory Boitnott, of New England Research, Inc. for collaboration on acoustic data collection and analysis.
REFERENCES Cadoret, T., Marion, D. and Zinszner, B. 1995. Influence of frequency and fluid distribution on elastic wave velocities in partially saturated limestones. Journal of Geophysical Research 100(B6): 9789–9803. Hassanizadeh, S.M., Celia, M.A. and Dahle, H.K. 2002. Dynamic Effects in the Capillary Pressure-Saturation Relationship and its Impact on Unsaturated Flow. Vadose Zone Journal 1: 38–57. Hassanizadeh, S.M. and Gray, W.G. 1993. Thermodynamic basis of capillary pressure in porous media. Water Resour. Res. 29: 3389–3405. Johnson, D.L. 2001. Theory of frequency dependent acoustics in patchy-saturated porous media. Journal of the Acoustic Society of America 110(2): 682–694. Liu, H.H. and Dane, J.H. 1995. Improved Computational Procedure for Retention Relations of Immiscible Fluids Using Pressure Cells. Soil Science Society of America Journal 59: 1520–1524.
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Lu, N., Wayllance, A., Carrera, J. and Likos, W.J. 2006. Constant Flow Method for Concurrently Measuring SoilWater Characteristic Curve and Hydraulic Conductivity Function. Geotechnical Testing Journal 29(3): 256–266. Olsen, H.W., Willden, A.T., Kiusalaas, N.J., Nelson, K.R. and Poeter, E.P. 1994. Volume-Controlled Hydrologic Property Measurements in Triaxial Systems. Hydraulic Conductivity and Waste Contaminant Transport in Soil, ASTM STP 1142, D.E. Daniel and S.J. Trautwein, eds., American Society for Testing and Materials, Philadelphia, 482–504. Pride, S.R., Harris, J.M. and Johnson, D.L. 2003. Permeability dependence of seismic amplitudes. The Leading Edge 22: 518–525. Schultze, B., Ippisch, O., Huwe, B. and Durner, W. 1997. Dynamic Nonequilibrium During Unsaturated Water Flow, Characterization and Measurement of the Hydraulic Properties of Unsaturated Porous Media; Proc. Intern. Workshop., Riverside, CA, 22–24 October, 1997, Riverside, CA: University of California. Smith, M.L. 1993. Ultrasonic Waveform Matching, NER Application Note AN93-1, AutoLab Users Manual: New England Research, Inc. Topp, G.C., Klute, A. and Peters, D.B. 1967. Comparison of Water Content-Pressure Head Data Obtained by Equilibrium, Steady-State, and Unsteady-State Methods. Soil Science Society of America Journal 31: 312–314.
Wei, C. and Dewoolkar, M. 2006. A Continuum Theory of Nonequilibrium Two-Phase Flow through Porous Media with Capillary Relaxation, Advances in Unsaturated Soil, Seepage, and Environmental Geotechnics, Proceedings of Sessions of GeoShanghai, Shanghai, 6–8 June 2006, Shanghai: ASCE. Wei, C. and Muraleethanan, K.K. 2006. Acoustic characterization of fluid-saturated porous media with local heterogeneities: Theory and application. International Journal of Solids and Structures 43: 982–1008. Wei, C. and Muraleetharan, K.K. 2002. A continuum theory of porous media saturated by multiple immiscible fluids: II. Lagrangian description and variation structure. International Journal of Engineering Science 40: 1835–1854. Wei, C. and Muraleetharan, K.K. 2007. Linear viscoelastic behavior of porous media with non-uniform saturation. International Journal of Engineering Science 45: 698–715. White, J.E. 1975. Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics 40: 224–232. Wildenchild, D., Hopmans, J.W. and Simunek, J. 2001. Flow rate dependence of Soil Hydraulic Characteristics. Soil Science of America Journal 65: 35–48.
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A modified triaxial apparatus to reduce testing time: Equipment and preliminary results J.C. Rojas, C. Mancuso & F. Vinale Department of Geotechnical Engineering, University of Napoli Federico II, Italy
ABSTRACT: Two triaxial apparatuses capable of testing unsaturated samples under suction-controlled conditions (USPv2) have been developed at the University of Napoli Federico II with the objective of testing time reduction. Triaxial tests have been performed on reconstituted samples of a pyroclastic silty sand typical of flow slides in Campania region, Italy. Tests are addressed to evaluate the USPv2 apparatuses and to investigate the rate of loading influence on the mechanical behaviour of the material. The tests performed with two USPv2 apparatuses, modified in order to control matric suction at both the ends of the soil specimens by the axis translation technique, presents shorter equalization times with respect to the previous version of the device (USP). Isotropic compression tests have been performed under a constant suction value of 300 kPa applying different rates of loading (2, 8 and 32 kPa/h). The experimental procedures adopted and the first results obtained are presented and discussed in the paper.
1
INTRODUCTION
The mechanical laboratory testing of unsaturated soil is usually very time-consuming, causing difficulties in the application to engineering problems. In suctioncontrolled CRL (constant rate of loading) triaxial tests, the length of the drainage path and the rate of loading influences the testing time. As in saturated soil mechanics, the shorter the drainage path the shorter the time required to equalize externally applied net stresses and suctions to the values acting on the soil skeleton. In unsaturated soils, inappropriate load or deformation rates have a pronounced effect on matric suction (Cho & Santamarina 2001, Macari & Hoyos 2001, Huat et al. 2006), and may cause loss of its effects on the soil structure, and deviation of the observed behaviour from that expected in constant suction conditions. The best choice when selecting the testing rate is to select a value high enough to reduce the testing time but sufficiently low to avoid excess pore water or air pressures. Few studies in the literature address the determination of an adequate rate of loading during triaxial tests (e.g. Macari & Hoyos 2001; Huat et al. 2006), and more studies are required in order to increase understanding of the complex phenomena involved. With the purpose of reducing testing time, suction controlled triaxial apparatuses with water and air control systems at both the ends of the soil specimen have recently been developed. In these devices suction is controlled by the simultaneous application of
pore-water pressure, uw , and pore-air pressure, ua , at both ends of the specimen (e.g. Sharma 1998, Romero 1999, Barrera 2002, Schanz & Alabdullah 2007). From 1994, a triaxial device (USP) has been developed at the University of Napoli Federico II in order to test soils under unsaturated conditions (Rampino et al. 1999). In the original version of this cell, a modified version of a Bishop & Wesley (1975) apparatus and the axis-translation technique (Hilf 1956) were used, with pore-air and pore-water pressures controlled at the top and bottom of the sample, respectively. The USP device has been used during several testing campaigns to date, for example Aversa & Nicotera (1999), Bilotta et al. (2005), Vassallo et al. (2007), Casini et al. (2007), Cattoni et al. (2007) and Papa et al. (2008). A new design of the apparatus is proposed in this paper including modifications introduced to reduce testing time. Also discussed are the experimental procedures adopted during the tests and some preliminary results obtained on a moist compacted pyroclastic silty sand. 2
TRIAXIAL APPARATUSES
Two triaxial apparatuses capable of testing unsaturated samples under controlled-suction condition have been developed at the University of Napoli Federico II in association with the company Megaris. A schematic of the triaxial apparatus, named USPv2 (Unsaturated Stress Path, 2nd version), is presented in Figure 1. The cell design is based on the Bishop & Wesley (1975)
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Figure 1.
Scheme of USPv2 triaxial apparatus for unsaturated soils.
hydraulic triaxial apparatus for controlled stress path testing, with a moving pedestal (Y in Figure 1) that pushes the soil sample against a stationary internal load cell. The suction is controlled by means of the axis translation technique (Hilf 1956). The apparatus is designed to test unsaturated samples of 38 mm in diameter and 76 mm in height in both axial compression and axial extension under either controlled rate of loading or controlled rate of strain. The stress state on the tested samples is obtained by regulating the air pressure supplied by an air compressor (at a constant value of 1100 kPa) through four electro-pneumatic pressure converters (A, B, C, D in Figure 1), and controlled in feedback through the pressure transducers W and R for the pore-air and pore-water pressures, respectively, and by the pressure transducer G and the load cell M, for the cell (σc ) and deviatoric (q) stresses, respectively. The output range of pressure converters is 14 kPa to 800 kPa. The double cell technique is used to monitor the sample volume changes. An open-top inner cell (E), made of stainless steel to avoid water absorption from the measuring device itself, is used inside a conventional perspex cell (F). Pressurized air is used to provide the confining pressure above the inner cell E filled with water. The electro-pneumatic converter C controls the cell pressure and the pressure transducer G measures the cell pressure. The volume change of the specimen is monitored by the change in the volume of water
inside the inner cell. The differential pressure transducer (H) registers the pressure difference between the water level in the water bath surrounding the soil sample and the water level of an external reference double walled burette (I). To minimize water evaporation, a thin layer of silicone oil above the water surfaces of the inner cell and the reference burette is applied. The axial sample deformations are measured by means of a displacement transducer LVDT (J). The LVDT is fixed to the top of the external cell and monitors the position L moves relative to the external cell, allowing the calculation of the axial sample deformation. The electro-pneumatic converter (A) controls the axial stress: the air pressure passes through the air-water interface K and is converted to hydraulic pressure controlling the moving pedestal L and pushes the soil sample against a stationary load cell M. The submersible electric load cell (M) is placed inside the cell and used to measure the deviator load on the soil specimen. The valve N allows switching from stress to strain control thanks to a dual axial control. A stepping motor (O) driven screw pump is used for the axial strain control. The main changes introduced in the USPv2 with respect to the existing USP (Rampino et al. 1999) is the inclusion of a double drainage system to shorten testing time. The bottom pedestal (Q) and the topcap (P) in Figure 1 incorporate a combination of two different porous disks (Figure 2).
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Figure 2.
Base platen details.
These disks comprise a peripheral standard porous stone (3 mm thick porous stainless steel) connected to the pore-air pressure line and an internal HAEV disk (7 mm thick and 24 mm in diameter) connected to the pore-water pressure line. Operating with such a system suction control and the drainage of air and water is allowed at both the sample ends. The new design includes the possibility to change the base pedestal and the top cap in order to select different values of the air entry pressure of the HAEV disk. The electro-pneumatic converter D (Fig. 1) controls the sample pore-water pressure, and the pressure transducer R measures it. Changes in soil water content are obtained via measuring the water volume by means of two double walled burettes (S and T) connected to the HAEV disks (P and Q). Any change between the level of water in the reference burette (S) and in the measurement burette (T) is determined by means of the differential pressure transmitter (U). A peristaltic pump (V) is used to eliminate the air diffused in the water drainage line. The speed of the pump can be adjusted with a trim potentiometer, in order to obtain flow rates from 0.3 l/h to 1.0 l/h. The peristaltic pump acts on the drainage line flushing water through the spiral circuit carved inside the base pedestal (Fig. 2) and top cap, driving the air bubbles into the burette T and expelling them, acting as an air trap. The arrows on Figure 1 shows the water path followed during the flushing process. The pore-air pressure in the soil sample is controlled in feedback by the electro-pneumatic converter B and measured by the pressure transducer W. The tests are controlled, monitored and recorded by a data acquisition and control boards data logger connected to a personal computer. All the required pressures (i.e. axial load, cell pressure, air pressure and water pressure) are controlled through a feedback loop mechanism, the sensors M, G, W and R provide the feedback readings. The pressures are controlled to within ±1 kPa of the target value. During each testing stage the time, axial load, cell pressure, pore water pressure, air pressure, total volume change, water volume change and axial displacement are continuously recorded.
Figure 3.
Top-cap assembling.
All the electronic, pneumatic and hydraulic parts, including the pressure gauges and the valves to accomplish the test and check the operation are contained in a control box. Some measures have been introduced to allow an accurate sample positioning prior to the tests. The inner cell hinders the contact between the sample and the top-cap and connections are required between the top-cap itself, the water and air drainage. For this reason the design of top-cap has been split into a loading cup containing the porous elements and a top part hosting the joints of the water and air lines (Fig. 3). During the assembly process, the loading cup is mounted on the upper part of the sample, and the rubber membrane is positioned. Subsequently the inner cell is placed and the top cap is screwed on the top of the loading cap. On screw tightening, compressive stress is avoided using an auxiliary split collar to resist the torque and consequently to eliminate torsion acting on the soil sample. This design greatly simplifies and speeds up the test set-up.
3
MATERIALS AND METHODS
3.1 Tested soil The tested soil comes from a flow slide in Cava dei Tirreni (Italy) having the grading curve represented in Figure 4. It consists of pyroclastic sand with pumice, and corresponds to a non-plastic silty sand (SM) in the Unified Soil Classification System.
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3.2
Preparation procedure
Reconstituted samples have been selected for two reasons: (a) to minimize the samples heterogeneity and potentially obtain a more consistent set of data and (b) to allow comparison with the laboratory data for the analysis of the tests performed on a large scale prototype of slope recently developed by Pagano et al. (2008) where the same material is used. The choice to use reconstituted specimens introduces the problem of selecting an appropriate preparation method, since the behaviour of granular soils is strongly affected by the procedure selected, especially in the case of sands containing fines. Air pluviation (AP), water pluviation (WP) and moist tamping (MT) are the methods found in the literature and considered here. According to Kuerbis & Vaid (1998) WP and AP techniques result in segregation when used with silty sands as revealed by the presence of thin lenses of fine particles. In contrast to Vaid et al. (1999) some research indicates that specimens reconstituted by the MT method tend to be non-uniform compared to the WP and AP methods (Frost & Park 2003) in the case of the soil under study here the MT method
Figure 4. Table 1.
Grain-size distribution of Cava dei Terreni soil.
appeared the most appropriate due to the high content of fines (i.e. 40 %). In the Campania region (Italy), pyroclastic soils are characterized by high void ratios, ranging from 0.7 to 2.3 (Pellegrino 1967). According to this, two void ratios have been selected in this study: e = 1.30, to validate the improved triaxial apparatuses; and e = 1.66 for soil characterization. For samples of 1.30 void ratio, consolidated drained triaxial tests were carried out in order to verify the repeatability of tests, comparing data obtained with two USPv2 available at the Department of Geotechnical Engineering of the University of Napoli Federico II or by a single apparatus when similar samples under analogous testing conditions are used. Isotropic compression tests applying different constant rates of loading were performed on samples of 1.66 void ratio. Test details are presented in Table 1. The letter L (left) and R (right) identify the two USPv2 apparatuses available in the laboratory.
4
EVALUATION TESTS
In the first stage of all the tests the desired suction value is imposed by means of the air and water pressure control systems while the specimen is subjected to a low isotropic pressure (p − ua ) = 20 kPa. During equalization the variation of the water volume of the sample is measured through the twin burettes connected to the base and top of the sample. The suction equalization between the soil sample and the values imposed through the drainage lines is observed. Figure 4 shows the two curves corresponding to tests performed on samples having similar initial conditions and using the first version of the device and the USPv2 triaxial cell. The test performed with the ‘‘old’’ version of the device (Rampino et al. 1999) having the capacity to drain water only from the bottom pedestal indicates that for a suction increasing of 100 kPa equalization
Experimental program and main samples characteristics. Matric suction (ua − uw )
Net mean stress (p − ua )
Isotropic compression rate
Test
kPa
kPa
kPa/h
L-s100pn100 a L-s100pn100 b L-s100pn200 L-s150pn200 R-s100pn200 R-s150pn200 s300 (2) s300 (8) s300 (32)
100 100 100 150 100 150 300 300 300
100 100 200 200 200 100 100 100 100
2 2 2 2 2 2 2 8 32
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Initial characteristics e γd
1.30 1.30 1.28 1.30 1.28 1.28 1.68 1.68 1.68
w
kN/m3
%
11.1 11.1 11.2 11.1 11.2 11.2 9.9 9.9 9.9
28.0 28.1 28.0 28.2 28.0 28.2 28.5 28.5 28.5
Figure 5. Comparison of suction equalization stage when similar samples are used (suction variation = 100 kPa).
what has been achieved is 11/2.5 = 4.4 which is very satisfactory. Figure 6 illustrates the results obtained during some deviatoric tests performed with the L and R devices USPv2. These deviatoric stages follow appropriate equalization and isotropic compression stages under constant suction carried out increasing the net mean stress (p − ua ) at a constant rate (2 kPa/h). The shearing stage was performed at a constant suction, constant radial stress and strain controlled conditions (0.15 mm/h), slow enough to obtain drained condition. These preliminary tests performed on unsaturated pyroclastic soil shows the capacity of the systems to reproduce the experimental results since a similar sample under similar conditions shows similar results independently of the apparatus used. 5
Figure 6.
Results of drained shear tests (e = 1.30).
takes 11 days (Fig. 5). Using the triaxial with double drainage (USPv2) the equalization stage corresponding to the same suction variation just requires 2.5 days. Theoretically, introducing double end drainage should reduce equilibration time by a factor of 4. In fact,
PRELIMINARY TEST: RATE OF LOADING EFFECT
Figure 7 presents some test rsults aimed at the evaluation of the influence of rate of loading on the mechanical behaviour of pyroclastic soils. Similar samples with a constant suction of 300 kPa were loaded isotropically applying different constant rate of loading (i.e. 2, 8 and 32 kPa/h). In contrast with the observations reported in Huat et al. (2006), for the studied pyroclastic soil the higher the rate of loading the lower the sample compressibility. The observed behaviour is similar to the data reported in Crawford (1964), where different time intervals were applied during incremental loading (IL) oedometer tests performed on saturated Leda clay. The reason for such variation is that as time, t, is increased the amount of creep of the specimen is also increased. The data in Figure 7 clearly show that deformation at constant mean net stress is present in the final stage of the tests performed at 8 kPa/h and 32 kPa/h. It is worth nothing that these deformations are likely to be due to creep phenomena and not to suction variation. In fact, if a high rate of loading is used, pore water pressure increases and hence a suction decrease should be expected during the ‘‘high’’ rate of loading isotropic compression tests. If this was the case, an increase of soil compressibility with rate of loading must be expected in opposition to what has been observed during the tests. Since creep deformations should have developed during all the tests duration, it is quite obvious that for the sample s300 (2) compression effects occurred during the 185 h employed to reach the final net mean stress (i.e. (p − ua ) = 370 kPa). In samples s300 (8) and s300 (32) this phenomenon is less evident and the compressibility is lower since a significantly shorter time (46 h and 12 h, respectively) is required to reach the same isotropic compression stress. Figure 7 also
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significantly shorten the equalization stage, introducing an important improvement of the cell when testing low permeability unsaturated soils. During isotropic compression stage, the tested pyroclastic soil showed rate of loading dependent behaviour. The excess porewater pressure generated during the loading process, that may reduce the suction value, is less significant than the creep phenomena for the pyroclastic soil studied. Further studies, including isotropic compression tests at lower suction values, are necessary to generalize the observed behaviour produced by the presented testing program.
ACKNOWLEDGEMENTS The authors wish to acknowledge the support of the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTNCT-2004-506861.
REFERENCES
Figure 7. Rate of loading influence (s = 300 kPa; e = 1.68).
shows that it is possible to obtain three different values for the preconsolidation pressure dependent upon the choice of rate of loading. The water content variation at the end of the loading process is similar for samples s300 (2) and s300 (8), but lower for sample s300 (32). However, after a period of time, the water content variation of sample s300 (32) tends to reach the variation observed for the another samples.
6
CONCLUSIONS
The University of Napoli Federico II has recently improved the design of the triaxial cell USP with the objective of reducing significantly the duration of tests. This work has resulted in the design of a new triaxial cell (USPv2) capable of reducing tests duration in comparison with the previous version. The capacity to apply both fluid pressures to the top and the bottom of the sample has been demonstrated to
Aversa, S. & Nicotera, M. 2002. A triaxial and oedometer apparatus for testing unsaturated soils. Géotech Testing J 25(1): 3–15. Barrera, M. 2002. Estudio experimental del comportamiento hidro-mecánico de suelos colapsables. Ph.D. thesis. Universitat Politecnica de Catalunya, Spain. Bilotta, E., Cascini, L., Foresta, V. & Sorbino G. 2005. Geotechnical characterization of pyroclastic soils involved in huge flowslides. Geotechnical and Geological Engineering, 23:365–402. Bishop, A.W. & Wesley, L.D. 1975. A hydraulic apparatus for controlled stress path testing. Géotechnique, 25(4): 657–670. Casini, F., Vaunat, J., Callisto L. & Desideri, A. 2007. Comportamento meccanico di un limo parzialmente saturo utilizzato per una sperimentazione in centrifuga. Incontro Annuale dei Ricercatori di Geotecnica. Fisciano, 4–6 luglio 2007. Cattoni, E., Cecconi, M. & Pane V. 2007. Geotechnical properties of an unsaturated pyroclastic soil from Roma. Bull Eng Geol Environ 66: 403–414. Cho, G.C. & Santamarina, J.C. 2001. Unsaturated Particulate Materials—Particle-Level Studies. J. Geotech. and Geoenvir. Engrg. 12(1): 84–96. Crawford, C.B. 1964. Interpretation of the consolidation test. Journal of the Soil Mechanics and Foundations Division, ASCE, 90: 87–102. Frost, J.D. & Park, J.Y. 2003. A critical assessment of the moist tamping technique. J. Geotechnical Testing, 26(1): 57–70. Hilf, J.W. 1956. An investigation of pre-water pressure in compacted cohesive soils. Ph.D. dissertation, Tech. Memo. No.654, U.S. Dep. of the Interior, Bureau of Reclamation, Design and Construction Div., Denver.
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Huat, B.B.K., Ali, F.H.J. & Choong, F.H. 2006. Effect of loading rate on the volume change behaviour of unsaturated residual soil. Geotechnical and Geological Engineering 24: 1527–1544. Kuerbis, R. & Vaid, Y.P. 1998. Sand sample preparation—the slurry deposition method. Soils and Foundations, 28(4): 107–118. Macari, E.J. & Hoyos, L.R. Jr. 2001. Mechanical behaviour of an unsaturated soil under multi-axial stress states. Geotechnical Testing Journal 24(1): 14–22. Pagano, L., Zingariello, M.C. & Vinale, F. 2008. A large physical model to simulate flow-slides in pyroclastic soils. First European Conference on Unsaturated Soils. Durham, UK, 2–4 July 2008. Papa, R., Evangelista A., Nicotera, N.V. & Urcioli G. 2008. Mechanical properties of unsaturated pyroclastic soils affected by fast landslide phenomena. First European Conference on Unsaturated Soils. Durham, UK, 2–4 July 2008. Pellegrino, A. 1967. Proprietà fisico-meccaniche dei terreni vulcanici del napoletano (in italian). VIII Convegno Nazionale di Geotecnica, Cagliari, Italy.
Rampino, C., Mancuso, C. & Vinale, F. 1999. Laboratory testing on an unsaturated soil: equipment, procedures, and first experimental results. Can. Geotech. J. 36: 1–12. Romero, E. 1999. Characterisation and thermo-hydromechanical behaviour of unsaturated Boom clay: an experimental study. Ph.D. thesis. Universitat Politecnica de Catalunya, Spain. Sharma, R.S. 1998. Mechanical behaviour of unsaturated highly expansive clays. Ph.D. thesis, University of Oxford, UK. Schanz, T. & Alabdullah, J. 2007. Testing unsaturated soil for plane strain conditions: A new double wall biaxial device. In Schanz (ed.) Experimental Unsaturated Soil Mechanics. SpringerProceedingsinPhysics112:169–178. Vaid, Y.P., Sivathayalan, S. & Stedman, D. 1999. Influence of specimen-reconstituting method on the undrained response of sand. Geotechnical Testing Journal, 22(3): 187–195. Vasallo, R., Mancuso, C. & Vinale, F. 2007. Effect of net stress and suction history on the small strain stiffness of a compacted clayey silt. Can. Geotech. Journal 44: 447–462.
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A large physical model to simulate flowslides in pyroclastic soils L. Pagano, M.C. Zingariello & F. Vinale Department of Geotechnical Engineering, University of Naples Federico II, Italy
ABSTRACT: This paper describes a large physical model built at the University of Naples Federico II. The equipment has been developed to study those factors affecting flowslides in pyroclastic soils. The physical model is presented along with procedures adopted up to now during the first tests; typical results concerning changes in weight of the sample, soil suction and volumetric water content are plotted and discussed.
1
INTRODUCTION
In the Campania region the number of rain induced flowslides has significantly increased in the last decades. Flowslides involve pyroclastic soil layers no thicker than 2 meters inclined between 30◦ –45◦ , mantling carbonaceous and tuffaceous slopes close to the Vesuvius volcano and the volcanic area of the Campi Flegrei Soils involved are non plastic silty sands with high porosity (ranging between 60–80%). The high porosity, the lack of electrochemical forces between soil particles and conditions at saturation or near saturation are considered to be the main factors determining soil liquefaction upon failure (Olivares & Picarelli, 2003). As a consequence, the sliding mass accelerates significantly, transforming into a rapid flowslide. The high kinetic energy associated to the soil mass is what mainly causes damages to buildings and infrastructures, along with casualties. In the last years the increasing of risks has stimulated studies aimed at deeply investigating the slide triggering factors. Some of these factors, such as the layer thickness, the slope inclination and the soil porosity, do not change significantly during a rain event and are typically used to build up susceptible maps of areas where flowslides are likely to be generated. Other factors, such as soil suction and water content, may vary significantly during a rain event; since a slide trigger is determined by their changes, they are now going to be used, along with the rain itself, in early warning systems. The above mentioned factors may be investigated either theoretically, by using mathematical models solved through numerical approaches, or experimentally, by reproducing such phenomena in laboratory in quite controlled conditions. This latter approach inspired the development at the Department of Geotechnical Engineering of University of Naples
of a physical model to simulate flowslides. The work has been made possible thanks to the financial support of Società Autostrade Meridionali. The model is much larger than other ones developed in the past (Olivares & Damiano, 2005) in order to permit extending experimental results directly to site conditions, without dealing with typical troubles related to scaled tests. The paper describes the physical prototype in all its components and presents the first experimental results. 2
TESTING DEVICES AND EXPERIMENTAL PROCEDURE
Since the slide velocity represents a crucial matter in the hazard evaluation, the prototype design was conceived to investigate how different factors influence not only the slide triggering but also the slide postfailure behaviour. According to these aims, the core of the physical prototype is made up of two parts supported by a steel frame: the upper one, where the flowslide is generated (Fig. 1, tank A); the lower part, located downstream of the upper one, where the postfailure behaviour may be observed. This in order to identify if the kinematics is that of a slow-dry flowslide or that of a rapid one (Fig. 1, tank B). The two tanks may also be inclined differently each other (Fig. 2), to make possible studying geometries where the inclination that regulates the slide trigger differs from that governing the post-failure behaviour. Inclination is provided by two couple of hydraulic rams, pressurized by a plunger. A first couple or rams connects part B to the steel plinth and may incline both parts up to 45◦ with respect to the horizontal plane; the second couple of rams connects the part A with the part B and may incline the former with respect to the latter. In this way, inclination of the sample may reach 70◦ , or may be reduced down to 0◦ , thanks to the
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Figure 1.
Figure 2.
Figure 3.
Plan view of conveyer belt around the apparatus.
Figure 4.
A schematic section of the whole set of apparatus.
Figure 5.
Bucket carrier.
Physical model scheme.
Traveling pluviation system.
particular position at rest of the rams allowing them to be shortened or enlarged. Both tanks A and B are 3 × 3 m in plant. The whole structure has been designed to be loaded by 12 t, so that samples up to 0.7 m thick may be tested. In the tests carried out up to now the samples have been fully restrained at the lower boundary, where also free drainage has been ensured through a geosyntetic sheet. The soil has been glued (on the base of tank A) at the bottom contact, in order to make the sliding mechanism fully regulated by the soil friction angle. The bottom of the tank A has been left impervious during the tests. Downstream of the part B a third tank collects and stores the mud after the slide has occurred (Figs. 3 and 4). In order to put in place samples characterized by high porosity, a pluvial deposition system has been designed. To obtain an uniform pyroclastic fall the soil needs to be preliminary disaggregated and dried. The whole deposition system is therefore made of various components, which are outlined below in the same sequence as they are usually used during sample making procedure: – a vibrating sieving, used to break soil particles aggregates, typically forming in the drying stage due to soil suction increase;
– a oven 8 m long and 0.8 m large, up to which soil is raised through a buckets carrier (Fig. 5); soil runs through the oven on a conveyer belt; the oven air temperature may be raised up to 150◦ C; – a hopper of around 3 m3 of volume of the same width as the part A; the hopper puts in place the soil on part A (Figs. 3 and 4) after has collected it from the oven; the hopper climbs vertically along four tracks and runs horizontally above part A along two beams; the hopper velocity may be set automatically as well as the start and the end of the hopper run; the hopper produces the pyroclastic fall through the opening; to influence the soil density both the fall height and the opening width may be regulated automatically. The rain is produced in very small drops falling on the sample surface. The water is nebulized to reduce erosion of the sample surface during the test (actually, erosion is reduced by vegetation which protects the soil surface). The rain comes out from four nozzles located at the end of the four arms overhanging the part A
112
Figure 6.
Figure 7.
Rain simulation system.
A detail of the load cell.
inward (Fig. 6). Rain intensity may be controlled and varied in the range from 20 to 200 mm/h. During a test the typical measurements carried out are: – – – –
changes in weight of the sample; surface displacements; water content; soil suction.
Some of monitoring instruments are part of the physical model and have been designed along with it; other ones are ‘‘external’’, and consist of devices suitable to monitor the behaviour of a real slope The instruments which are part of the model consist of: – four load cells (Fig. 7), installed as support of part A; each cell measures continuously in time the six reaction force components; as a result, changes in weight of the part A may be obtained; such changes may be used to derive the sample unit weight during the soil deposition, the changes in the water mass stored by the sample during the test (as a result of the rain, seepage processes and run off), the losses of soil mass associated to the occurrence of landslides or limited earth flows; – a 2D laser scanner device (Figs. 8, 9), that acquire with the triangulation technique the position of the sample surface, with a depth of scanning of few centimeters; the scanner is moved parallel to the sample surface by a mechanical system; measure accuracy (less that ±0.5 mm) is fully satisfactory, while the time period needed to scan the entire sample surface is significant (about six minutes), and makes such technique only suitable to characterize the pre-failure stages; – a Particle Image Velocimetry (P.I.V.) technique based on the interpretation of images taken by a videocamera pointing normally to the sample surface at a distance of about three meters; results are in terms of sequence of two-dimensional velocity fields; these measures are characterized by a good time resolution (up to 25 images per second may be acquired and interpreted) but by a poor accuracy
Figure 8. Plan view of the laser scanner supported by the moving system.
Figure 9.
Laser scanner apparatus.
(approximately 20 mm); however the P.I.V. technique integrates to some extent the laser scanner technique: it is suitable to monitor the failure and post-failure stages, when the occurrence of rapid movements requires high time resolution and the significance of displacements makes poor accuracy acceptable. The external instruments are used to characterize the sample hydraulic behavior; they consist of tensiometers and TDR probes to measure soil suction and water content, respectively. They are installed during the deposition process at three or four different depths.
3
EXPERIMENTAL PROCEDURES
The soil tested is a volcanic ash, made of non plastic silty sand with gravel (see Fig. 10); it is the same soil involved in a significant rapid flowslide of 33000 m3
113
4
PRELIMINARY RESULTS
During each test the sample hydraulic response has been characterized by measuring evolution of the sample weight, soil suction (approximately 20 measurement points) and soil volumetric water content (4 measurement points). Typical trends of such quantities are plotted in Figures 11, 12, 13.
0.9 0.7 Weight changes (kN)
occurred on 4th March, 2005 and affected a slope inclined of 37◦ close to the Nocera town (Salerno). In the 10 tests carried out up to now, samples 40 cm thick have been reconstituted, with soil porosity ranging between 60% and 70% (see Tab. 1). The samples have been put in place taking the part A horizontally; once put in place, the sample has been wetted about a week, to decrease suction until to reach the suction level wished at the beginning of the test. The sample has been inclined only before the start of the test. Inclinations ranging between 32◦ and 40◦ have been adopted for the samples (part A). Part B has instead been slightly inclined (10◦ ), in order to make more easy to identify the post-failure behaviour, by maximizing differences in the time needed to cover the trench between a rapid flowslide and a slow-dry one. Up to now, layer thickness, rain history (rain intensity = 30 mm/h) and inclination of the tank B have been kept constant, while the initial state in terms of soil porosity and soil suction, along with the sample inclination, have been varied.
0.5 0.3 0.1 -0.1 0
50
100
150
200
250
300
350
400
450
-0.3 -0.5 Time (min)
Figure 11. Sample weight changes measured by load cells (the weight at the start of the test is assumed as zero reference).
Tensiometer vertical position HOPPER
5 2 1
Side direction
15
4
12
14
11
3
sample surface
13
-2.00
35.0 20
70
120
170
220
Ten_13
30.0
0.00
-u w (kPa)
20.0 4.00 15.0 6.00 10.0
Figure 10.
8.00
5.0
10.00
0.0
Slide
Rain intensity (mm/h)
Development with time of soil suction at three
Sample characteristics. Slope
w
n
TDR probe s ve rtical pos ition
Sr
HOPPE R
S ide dire ction 1
Test
Ten_15
Time (min)
Soil grading. Figure 12. points.
Table 1.
Ten_14
Rain intensity (mm/h)
25.0 2.00
◦
%
%
2
3
4
s a mple s urfa ce
%
0.60
35 .0
0.50
30 .0
31.09 33.21 31.38 25.83 – – 41.89 36.35 39.21 26.58
66.72 70.73 70.02 68.33 – – 62.24 66.22 62.83 67.91
41.10 36.43 35.62 31.74 – – 67.59 49.34 64.71 33.29
25 .0
0.40
20 .0 0.30 15 .0 0.20
10 .0
0.10
5.0
0.00
Rain inte ns ity (mm/h)
32 35 32 35 37 – 37 40 35 37.5
Volumetri c water content
TDR 1
1 2 3 4 5 6 7 8 9 10
TDR 2
TDR 3
TDR 4
S lide
Ra in inte ns ity (mm/h)
0.0 20
70
120
170
220
Time (min)
Figure 13. Development with time of volumetric water content at four points.
114
Increments in weight of the sample during the test (Fig. 11) indicate that the sample stores water. It is important to note that the small drops in weight correspond to lost in run off water from the sample surface and empting of tubes when the rain has been stopped in order to make possible working with the laser scanner. Storing water capability under constant rain intensity however reduces with time, as indicated by the decreasing of the derivative of the curve. This effect is manly due to the progressive reduction of soil suction within the sample (Fig. 12). This reduction lowers the hydraulic gradients (driving the water drops within the sample) acting at the sample top surface between the exterior and the interior of the sample. In the initial stages, an additional contribution to the same effect is provided by the time needed for the seeping water to reach downstream the draining boundary. As well known, soil permeability increases during the wetting process. In the initial stages, while the water does not yet drain through the permeable boundary, soil permeability increments should enhance water adsorption. However Figure 11 indicates that permeability effects are not so relevant as that produced by the gradient reductions. Consistently to what expressed by Figure 11, initially the rain appears to the naked eye fully adsorbed by the sample surface and, then increasingly rejected by it, with enhancing run off. The tensiometers (Fig. 12) (installed at the three different depths of 10, 25, 40 cm from the sample surface) along with TDR probes (installed at a depth of 25 cm), indicate the arrive of the saturation front (i.e. suction goes to zero as show in Fig. 12 and volumetric water content goes to zero in Fig. 13). Since the rain intensity adopted is significant the wetting front correspond to a saturation front that lowers soil suction to the null value. The flowslide trigger is clearly indicated by the load cells with an abrupt decrease in the sample weight (Fig. 11). The size of the weight drop is related to the quantity of soil lost in the landslide.
On the other hand, the flowslide trigger is anticipated by soil suction and water content changes. Suction at the bottom of the sample goes down to zero before the triggering time (see tensiometer N. 13 in Fig. 12). In this kind of test, where the sample inclination is slightly less than the soil friction angle, triggering is caused by positive pore pressures developing at the bottom of the sample.
5
CONCLUSION
In this work a physical model to simulate rain induced flowslides has been presented, explaining how such device allows one in taking into account the main factors affecting such phenomena. In the paper the experimental procedures adopted up to now have been illustrated. The apparatus may be used also differently to study the influence of factors such as static and hydraulic boundary conditions differing from those adopted, samples thicker, presence of vegetation. First results have evidenced the effectiveness of load cells in indicating, through changes in the sample weight, the history of test in terms of water mass adsorbed and losses by the sample. Tensiometers and TDR measures may be used to characterize the hydraulic behavior and to estimate the time after which the landslide may trigger.
REFERENCES Olivares L. & Damiano E. 2007. Postfailure Mechanics of Landslides: Laboratory Investigation of Flowslides in Pyroclastic Soils. J. Geotech. and Geoenvir. Engrg., 133(1): 51–62. Olivares L. & Picarelli L. 2003. Shallow flowslides triggered by intense rainfalls on natural slopes covered by loose unsaturated pyroclastic soils. Géotechnique, 53(2): 283–288.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Climatic chamber to model soil-atmosphere interaction in the centrifuge J. Tristancho & B. Caicedo Universidad de los Andes, Bogotá, Colombia
ABSTRACT: The behaviour of geotechnical structures located close to the surface of the ground, e.g. shallow foundations, retaining walls, embankments, slopes and pavements is highly affected by water content and pore pressure of the soil located near the surface where it is in contact with the atmosphere. The objective of this paper is to describe the design, construction and instrumentation of a climatic chamber used to simulate the tropical atmospheric variables for small scale models in centrifuge.
1
INTRODUCTION
Compressible soils of lacustrine origin in Bogotá region and other sites around the world show high deformations originating from the interaction between the soil and the atmosphere. These deformations can produce settlements (compaction) or swelling (expansion). These problems are of such magnitude that according to Jones & Holtz (1973), the economic losses produced by expansive soils surpass the sum of the losses originated by earthquakes, floods and hurricanes. Nowadays, a phenomenon of drying accompanied by cracking of soils and expansive soil appearance has been observed in Bogotá (Colombia). As a consequence a great amount of construction and infrastructure constructed in the city and its suburbs may be expected to undergo problems of unpredictable settlements. The drying and later expansion of soils in Bogotá and elsewhere takes place by a complex interaction between soil and atmosphere. This phenomenon is associated with the heat and water transference that affects, in a nonlinear way, the deformation of the soil. For this physical problem, centrifuge modeling is an appropriate tool to study the effects of multiannual climatic conditions in geotechnical structures since centrifuge modeling allows acceleration of the time of the physical process. This paper contains a brief description of climatology, its main variables and the method of how the climatic simulation was implemented in the geotechnical centrifuge. The objective of this project is to simulate the main atmospheric variables (for tropical and subtropical countries) according to the scale laws that govern centrifuge modelling. Bolton (2002) proposed that the control of atmospheric boundary conditions as one of the major
challenges in centrifuge modelling. Since 2003 the University of los Andes, Bogota has been working on the design of a new device to control the atmospheric boundary conditions in the centrifuge. 2
THE CLIMATE
The climate is the long term effect of the solar radiation on the earth surface. Climate and its parameters can be characterized for long periods of time (generally greater than 30 years), the weather can be characterized instead for short windows of time. The physical variables measured to determine the weather conditions at a certain site are (Holton, 1992): – Insolation: A measurement of the solar energy entrance to the atmosphere. – Air temperature: Direct consequence of the solar radiation. – Atmospheric pressure: Pressure exerted by the atmospheric mass in the earth’s surface. – Wind speed: Horizontal air movement with respect to the earth surfaces, caused by the atmosphere differential pressure. – Rain intensity: The earth’s water is in constant process of transformation and movement. – Humidity: Relation between the dry air and water vapour that exists in the atmosphere. The main objective of the new device is to simulate the typical meteorological parameters present in the Bogotá region. Therefore the simulation of extreme climatic parameters such as snow, hail or very strong winds are outside the scope of this project. Table 1 summarizes the characteristic averages (maximum, minimum and average) of the principal meteorological variables for Bogotá’s region based on the information provided by the weather station of the
117
‘‘El Dorado’’ Airport and the IDEAM (Institute of hydrology, meteorology and environmental studies from Colombia). Each variable is modelled by independent pieces of equipment which were integrated to perform the complete simulation. The following sections present a description of the testing equipment used to reproduce each climatic parameter. 2.1
Wind, air temperature and humidity
Temperature and humidity are the fundamental variables used to determine the weather state of a site (Wang, 1999). The existing relation between temperature, humidity and atmospheric pressure, is complex and is known as psychrometry (Wang, 1999). A Climatic Simulation Chamber (CSC) located on the upper part of the soil container is designed to control these weather parameters. The principle of operation is based on heat transfer for convection, an effective method for heat transfer (Lienhard, 2004). The relative humidity is controlled by means of the extraction of moisture by condensation (dew point) and humidification by dispersion. Figure 1 shows the internal structure of the Climatic Simulation Chamber (CSC). The air that is inside the Table 1.
Climatic variables for Bogotá: IDEAM.
Variable
Max.
Min.
Average
Insolation (MJ/m2 day) Air temperature (◦ C) Atmospheric pressure (Bar) Wind speed (m/s) Rain intensity (mm/year) Relative humidity (%)
16.75 20
14.65 0
15.7 12 0.75 2.2 1250 70
Figure 1.
container moves towards the chamber driven by three axial discharge fans. Later the air passes through a dehumidifier prism, based on the psychrometric process of latent heat elimination by condensation. The dehumidifier prism was constructed using the Peltier effect (Tellurex, 2003), which reduces the temperature in the plate receiving condensation (a lower temperature than the dew point). The condensed water generated by the loss of latent heat is canalized by gravity to a closed deposit, and monitored by an ultrasonic level sensor. The air is then canalized to the heating prism that increases its temperature using again the Peltier effect. The use of thermoelectric devices (Peltier plates) facilitates the design of the power unit and the control system. An additional advantage of the use of the Peltier boards in two prisms (dehumidifier and heater) is the possibility of inverting its functions: allowing two heaters or two dehumidifiers working simultaneously to enhance the power of the chamber. Once the humidity and temperature of the air are adjusted, the air is driven by means of three fans towards the container inside. The Peltier plates are attached to a heat dissipater and exposed to the outside to allow a more efficient heat transfer (Tellurex, 2003). The fans installed are capable of generating a wind speed the order of 7.2 m/s (Approx. 26 km/h). The system at full load is able to make the complete air interchange on the model every 2 sec. The calculation of the power needed by the CSC is based on the day-night cycles typical of Bogotá. Cycles from 0 to 20◦ C and HR (Humidity Relative) of 79% represents an energy change of 145 kJ for the air inside the chamber (approx. 10 Kg of air). The CSC has 10 Peltier plates of 80 W each one. The entire time needed for heat addition is 182 sec. One day at prototype using 20 g corresponds to 216 sec according to scaling law in the centrifuge.
Internal structure and operational functions of the Climatic Simulation Chamber (CSC).
118
radiation (without the typical indirect effect of warming). Taking into account the power needed to simulate sun radiation respecting scaling laws in the centrifuge it would be necessary to use optic technologies to concentrate the light. Another effect is the influence of the electromagnetic radiation of the solar light on the soil. Due to these technological constraints, the present version of the CSC does not have the capability to simulate sun radiation.
2.50 LEDs app roach Solar Irradiance (sea level)
Irradiance [W/m²μm]
2.00
1.50
1.00
0.50
0.00 0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
Wavelength [μm]
Figure 2. Solar radiation at the sea level and modeling approach.
The atmospheric pressure was not taken into account for the modelling due to technical difficulties in making changes on the pressure inside the container. The development of systems to control the pressure in centrifuges can help to increase the mechanical and electrical efficiency of the machine as well as to improve modelling (Craig et al., 1991).
2.2
Solar radiation
The sun is the fundamental source of energy for the climate. The transference of energy from the sun to the ground occurs by radiation (Holton, 1992). Solar radiation is produced by electromagnetic waves having different wavelengths (visible, infrared and ultraviolet light). Figure 2 shows the solar spectrum for sea level (dark line). Modelling of solar radiation can be performed by means of light sources. Each source of light has its own characteristic spectrum: the illumination lamps are optimized for the visible light; the greenhouse lamps have a spectrum with a high level of infrared and some parts of the visible spectrum but without ultraviolet light (spectrum with high efficiency in plant photosynthesis); ultraviolet lamps are used in disinfection and finally infrared lamps are used in medicine. To obtain the best approximation to the solar light it is necessary to create a lamp composed of several types of light. A new method of lighting is based on high power Light Emitting Diodes (LEDs). Every LED has a determined wavelength (i.e. colour) and power. By means of optimization software and by changing the number of LEDs, it is possible to achieve a combination shown in Figure 2 (gray line). The obtained approach is near 75% of the real spectrum of the sun. The mean total radiation at Bogotá is 15.7 MJ/m2 day (approximately 182 W/m2 for one day of 12 hours of light). According to the laws of scaling in centrifuge it would be necessary to generate a power in the model of 1.3 kW. This value of radiation is huge considering that it must be effective
2.3
Rain
Rainfall is one of the mechanisms by which soil is humidified the soil and is a very important factor in the determination of water tables, saturation of soils and erosive processes (Craig et al., 1991). The typical size of a water drop is 4 mm. According to the laws of scaling the approximate diameter of a drop must be of 20 μm at 20 g. Systems of nebulization for greenhouses were used in this work to simulate the size of the drops which have on average a diameter less than 50 μm depending on the pressure. The control system is based on a pressurized line of water with 12 sprinklers, controlled by an electro valve. The rain is generated by opening of the electro valve and controlling the rainfall over specific times. 2.4
Other variables
During testing heat transference appears between the container and the atmosphere. This loss of heat can be significant (Lienhard, 2004). Good performance of the CSC in controlling the climatic variables during testing depends on the limitation of this additional load. With this energetic condition, the design of a new container that allows a minimum loss of heat was carried out (adiabatic container). Metals have high coefficients of thermal conductivity, thus a new material is needed to replace the steel casing. Materials based on fibre-glass present good features in terms of strength, stiffness and low thermal conduction but their high hardness made them inappropriate for this application (Lienhard, 2004). The selected material is a phenolic resin with cotton fibre, used commercially as a dielectric but also has a high mechanical resistance, a good workability and low absorption. This material combined with a metallic external structure is retained for the container design. The container is designed to support pressures up to 0.5 MPa without any significant deflection in order to respect adequate conditions for plane strain models. Figure 3 shows the results of the finite element simulation (FEM) of the final design. The accumulated maximum deflection obtained is 0.5 mm at 1 MPa internal pressure. The basket has a total mass of 65 kg and a total capacity of 0.09 m3 . The maximum heat flux is 0.02 W/cm2 .
119
Step motor X axis
Step motor Y axis
Laser displacement
Additional
sensor
Sensors
Figure 4.
Three-dimensional laser profilemeter.
Figure 3. FEM analysis of the basket for maximum deformation (Pressure of 0.5 MPa).
3
CSC
INSTRUMENTATION
The control system set inside the CSC is a closeloop system (Ogata, 2004). All the variables that are controlled are measured. The CSC has the following instrumentation: – – – – –
Three-dimensional
Basket
laser profilemeter 550mm
2 Relative humidity sensors 3 Contact thermometers 1 Infrared thermometer 1 Pressure sensor 1 Wind velocity sensor
664mm 550mm
The interaction between the atmosphere and the soil induces water migration and volumetric changes. These volumetric changes generate heave or settlement causing cracks to appear at the soil surface. A positioning table of two degrees of freedom with a non-contact laser sensor is used to perform the displacement measurements during flight (Doebelin, 1993). The surface level is measured for different positions of the laser sensor and the measurements are carried out periodically to determine the evolution of the soil surface movements. Figure 4 shows the final design for the three-dimensional laser profile-meter. The positioning table has a longitudinal precision of 0.1 mm and transverse precision of 10 μm and effective stroke of 430 mm and 230 mm. In addition to the displacement sensor, the following sensors are installed: – Infrared thermometer: with this sensor is possible to generate thermal maps of the surface – Relative humidity sensor – Contact thermometer (air temperature) – Wind velocity sensor
Figure 5. trifuge.
Climatic modelling system for geotechnical cen-
The total assembly of the designed system for the physical modelling of the soil-atmosphere interaction in centrifuge is presented in Figure 5.
4
CONCLUSIONS
Climatic conditions in tropical countries have a strong influence on civil engineering constructions. All weather parameters affect the soil in a non-linear way that makes numerical modelling difficult. Centrifuge modelling instead could be a useful way to study soil atmosphere interaction in these situations. The climatic chamber presented in this paper is a first approximation to simulate geotechnical problems related with weather since the chamber reproduces the atmospheric parameters at the soil surface. However additional works are necessary to enhance the capacity of the chamber.
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The centrifuge accelerates processes like wetting and drying therefore important future effort in the development of control systems is needed to reproduce cyclic behaviour. The simulation of sunlight radiation needs light concentration in order to respect the scaling laws in centrifuge. REFERENCES Bolton, M. 2002. An atmospheric chamber for the investigation of the effect of seasonal moisture changes on clay slopes. Physical modeling in Geotechnics: ICPMG’02, Tokyo 765–770. Craig, W., Bujang, B. & Merrifield, C. 1991, Simulation of Climatic Conditions in Centrifuge Model Tests. Geotechnical Testing Journal, GTJODJ, Vol. 14, No. 4, 406–412.
Doebelin Ernest. 1993. Diseño y aplicaciones de sistemas de medición. DIANA (ed.). Holton, J.R. 1992. An introduction to dynamic meteorology. Academic Press (ed.). Jones, D. & Holtz, W. 1973. Expansive soils-the hidden disaster. Civil Engineering, pp. 49–51. Lienhard, J. 2004. A Heat Transfer TextBook. PHLogiston Press (ed.). pp. 141–171. Ogata, K. 2004. Ingeniería de Control Moderna. Prentice Hall. Tellurex Corporation, 2003. A guide to temperature Control of thermoelectric systems. Tellurex. Vargas, J. 2003. Modelación Física en Centrífuga, de un Muro Pantalla Apuntalado en Suelos Blandos de Bogotá, Universidad de los Andes. Wang, S.K. & Lavan, Z. 1999. Air-Conditioning and Refrigeration. Mechanical Engineering Handbook. Frank Kreith (ed.). pp. 11–13. White, Frank. 2001. Fluid Mechanics. McGrawHill.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Experimental determination of unsaturated hydraulic conductivity in compacted silt J.J. Muñoz, V. De Gennaro & E. Delaure Ecole des Ponts (Université Paris-Est, Navier Inst. – CERMES), Paris, France
ABSTRACT: Experimental data of unsaturated hydraulic conductivity were determined in aeolian silt taken from Jossigny, east Paris. This test was performed by means of the instantaneous profile method (Daniel 1982). An infiltration column of 50 mm in diameter and 200 mm height was used. The soil was statically compacted by means of the double piston method. The suction profiles were measured with four home-made high capacity tensiometers located at different heights. The tangent of the suction isochrones permits the determination at each point of the hydraulic gradient i = ∂ψ/∂z, with ψ being the water potential or suction head. Consequently, the variation of hydraulic conductivity as a function of suction has been determined. A reduction of two orders of magnitude of unsaturated hydraulic conductivity was determined. 1
INTRODUCTION
In order to determine the hydraulic conductivity in unsaturated soil, more complex experimental methods are required than in saturated soils. As in saturated soils, these methods can be performed in transitory or stationary conditions. Existing techniques to determine the permeability of unsaturated soils can be broadly categorized in three main methodologies. The first one, the so-called Gardner’s method (Gardner 1956), proposes the use of the Richards’s cell (Richards 1931). This method determines the hydraulic conductivity in transitory conditions. It consists in measuring the time evolution of the water volume that moves out of the sample due to a gas pressure increment, which in turns means a suction increment, as the suction s = pg − pw where pg and pw are the gas pressure and the water pressure, respectively. The second method, the so-called Corey’s method (e.g. Green & Corey 1971), determines the hydraulic conductivity in stationary condition. A constant suction is applied to the sample by means of axis translation technique. Positive gas pressure (pg ) and water pressure (pw ) are applied at the bottom of sample, where pg − pw > 0. The same pressure increment is applied to both gas and water at top of sample pg = pw . The gas pressure and water pressure are respectively pg + pg and pw + pw at top of sample, and pg and pw at bottom of sample. A constant value of suction is applied in whole sample. The hydraulic conductivity is determined from the water volume evolution measured during a given time interval due to gradient of pressure applied at each fluid.
Finally, the third method, also known as the instantaneous profile method (Daniel 1982), consists in measuring the variation of the suction profile within an infiltration column as a function of time during the infiltration process. The suction measurements can be performed by means of tensiometers or psychrometers, depending of the expected suction range. The knowledge of the water retention curve (WRC) of the soil allows the determination of the water content profile from the suction profiles and its correlation with the corresponding hydraulic conductivity. In this paper, the determination of the hydraulic conductivity of compacted unsaturated silt by means of the instantaneous profile method will be presented. 2
MATERIAL
The laboratory test was performed on aeolian silt taken from the eastern region of Paris, near to Jossigny village. Jossigny silt can be classed as low plasticity soil in the Casagrande chart. The clay minerals contained in Jossigny silt are illite, kaolinite and inter-stratified illite-smectite (Cui & Delage 1996). The geotechnical properties of Jossigny silt are given in Table 1. The WRC of the Jossigny silt was determined in confined conditions with a suction-controlled oedometer by means of axis translation technique following a wetting path (Casini et al. 2007; Figure 1). No significant swelling properties have been observed on wetting. Experimental data of WRC were fitted adopting the expression proposed by Van Genuchten (1980).
123
Table 1. Geotechnical properties of Jossigny silt (after Cui & Delage 1996). wL
wP
(%)
(%)
37
19
IP
18
%
%
γs
80 μm
kN/m3
34
4
27.2
Suction [kPa]
1000 100 10 1 0.1
Experimental data Van Genuchten 0
0.2
0.4 0.6 Degree of Saturation
0.8
1
Figure 1. Water retention curve in wetting path of Jossigny silt (data after: Casini et al. 2007).
1 −λ s 1−λ Sl = Srl + (Sls − Srl ) 1 + P
(1)
where Sls = 1.0 is the maximum saturation, Srl = 0.0 is residual saturation, s is the suction [kPa], P = 8.67 kPa and λ = 0.217 are the soil parameters. The soil was oven-dried at 40◦ C. Afterwards, soil aggregates were mechanically broken up to pass an 800 μm sieve. The dry soil powder was wetted to a water content of 12.5%, equivalent to an initial suction of 400 kPa. Subsequently, the wetted soil was stored in an airtight container for 24 hours in order to homogenize the soil moisture. The soil was then statically compacted in an infiltration column of 50 mm in diameter and 200 mm height at a dry unit weight of γd = 14.5 kN /m3 . The double piston technique was used in the compaction process (Cui & Delage, 1996).
3
Figure 2. Suction measurements with four tensiometers installed in the infiltration column.
Suction is measured by means of a saturated high air entry value ceramic porous stone (capillary pressure threshold equal to 1500 kPa). The tensiometers were saturated in a saturation cell filled with de-mineralized and de-aired water. A positive pressure of 2000 kPa was applied by means of a pressure-volume control system (GDS) during 24 hours. The calibration curve of the tensiometers was determined by means of the applied positive pressure and the electrical signals of the strain gauge. The water content profiles of each suction isochrone were determined by means of the water retention curve (equation 1). For a given time t, the determination of tangents of one suction isochrone gives at every point the hydraulic gradient (2).
EXPERIMENTAL METHOD
The time evolution of suction profile during the infiltration process was measured inside of an infiltration column of 50 mm in diameter and 200 mm height (Cui et al. 2001). Suction measurements were performed by means of four homemade high capacity tensiometers (Mantho 2005; Cui et al. 2007), placed at 40, 80, 120 and 160 mm from the base of the column (Figure 2).
i=
∂ψ ∂z
(2)
where i is the hydraulic gradient, ψ the water potential or suction head and z is the height. The water volume (V ) infiltrated between two instants t and t + t at a given point, was deduced from
124
⎛ H ⎞ H V = A⎝ θt+ t dz − θt dz ⎠ zi
Water pressure [kPa]
the difference between the water content isochrones corresponding to both instants, that is:
(3)
zi
where: A is the sectional area of the column, w is the water content, H is the total height of the column and zi is the current height considered. The water flux q between time t and t + t was computed as indicated in equation (4).
H
θt+ t dz −
zi
q=A
H
0 -50 -100 -150 -200 -250 -300 -350 -400 -450 0
12
θt dz
t
(4)
60
72
Figure 3. Time evolution of suction measured at four different elevations during equalization phase (48 hours) and subsequent wetting phases.
The unsaturated hydraulic conductivity K was calculated from the ratio between the water flux and the hydraulic gradient following Darcy’s law. An average value of hydraulic gradient between two distinct time increments was considered, as shown in the following equation:
0 -50 Water pressure [kPa]
1 2q K= A (it + it+ t )
36 48 Time [hours]
Tensiometer 6 (z = 40 mm) Tensiometer 7 (z = 80 mm) Tensiometer 9 (z = 120 mm) Tensiometer 10 (z = 160 mm)
zi
24
(5)
-100 -150 -200 -250 -300 -350 -400 -450 48
4
EXPERIMENTAL RESULTS
Figure 3 shows the time evolution of suction measured at four different elevations during the equalization phase. Forty eight hours were required for suction equalization in the 350 kPa–400 kPa suction range, until reach a uniform suction profile. Suction equalization was followed by subsequent wetting up to full saturation. Figure 4 shows the details of the time evolution of suction during the wetting phases shown in Figure 3. The advancing front of water saturation is clearly depicted from the tensiometers measurements. More than three hours were required to reach almost full water saturation (i.e. nearly zero suction values) on the top of the soil column at an elevation z = 160 mm (tensiometer 10, Fig. 4). Figure 5 shows both the isochrones of suction (Fig. 5a) and the isochrones of water content (Fig. 5b), determined after 0.46, 0.94, 1.83, 3.08 and 7.0 hours of water infiltration. The suction distribution with the elevation has been computed by means of the equation (6): s = s0
1 −β z 1−β 1− 1+ α
(6)
49
50 51 Time [hours]
52
53
Tensiometer 6 (z = 40 mm) Tensiometer 7 (z = 80 mm) Tensiometer 9 (z = 120 mm) Tensiometer 10 (z = 160 mm)
Figure 4. Time evolution of suction measured during the infiltration phase.
where z is the column elevation and so is the initial suction. The parameters α and β have been determined adopting the minimum square method in order to fit the measured suction profile. The isochrones of water content were determined from suction isochrones using the water retention curve shown in Figure 1 and equation (1). It is worth noting that important suction changes occur within the first 1.83 hours up to an elevation of 120 mm. In this zone the mass transfer occurs mainly in the liquid phase, whereas above 120 mm the likely mechanism of mass transfer is related to the water vapour. Since the former is generally quicker than the latter suction changes in the upper part of the column are recorded later on, after 3.08 hours of elapsed time. For this condition the corresponding change of water content is of about 2% (Fig. 5b). Condition of almost full water saturation along the whole column height
125
Height [mm]
200
200
160
160
120
120
80
80
40
40
0
Initial state t = 0 sec Tensiometer (t = 0.46 hours) t = 0.46 hours Tensiometer (t = 0.94 hours) t = 0.94 hours Tensiometer (t = 1.83 hours) t = 1.83 hours Tensiometer (t = 3.08 hours) t = 3.08 hours Tensiometer (t = 7.0 hours) t = 7.0 hours
0 0
100
200 300 Suction [kPa]
400
0.3
a)
0.2 0.1 Water content
0
b)
Figure 5.
Water infiltration test: (a) isochrones of suction and (b) isochrones of water content.
1
1E-006
Relative permeability K/Ksat
Hydraulic conductivity [m/s]
Saturated hydraulic conductivity
1E-007
1E-008
Y = 8.5187E-08*X-0.591 R2 = 0.992 1E-009 1000
100
10
1
0.01
0.001
0
0
Suction [kPa] Unsaturated hydraulic conductivity Saturated hydraulic conductivity
Figure 6.
0.1
0.2 0.4 0.6 0.8 Degree of saturation
1
Hydraulic conductivity Fit
Hydraulic conductivity as a function of suction.
Figure 7. Relative hydraulic permeability as a function of degree of saturation.
(i.e. almost null suction values) is attained for an elapsed time of 7.0 hours. The variation of the hydraulic conductivity as a function of suction is shown in Figure 6. In this work the gradients were obtained graphically from Figure 5. Eight data points were obtained taking the average gradients between two isochrones at every height (40, 80, 120 and 160 mm. Also the gradients could be obtained differentiating equation (6).
The saturated hydraulic conductivity was determined by applying a positive pressure at the base of the column by means of a pressure-volume controller GDS® . The corresponding value was 3.67 × 10−7 m/s. The evolution of the hydraulic conductivity with suction (i.e. saturation) seems to reflect the general findings observed in saturated and partially saturated
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soils. Note that these results suggest a reduced effect of the hydraulic gradient and the general reliability of Darcy’s law when coupled with the instantaneous profile method. This is not necessarily the general trend observed when important microstructural changes are associated with suction changes, as in the case of high swelling soils (e.g. Cui et al. 2001). Finally, Figure 7 shows the variation of the relative permeability computed as a function of degree of saturation. Data on relative permeability were fitted by equation (7). Kr =
β n Sl 1 − 1 − Slλ
(7)
where Sl is the degree of saturation. The parameters λ = 0.138, β = 2.0E − 04 and n = 0.55 have been determined adopting the minimum square method in order to fit the relative hydraulic conductivity.
5
CONCLUSIONS
An infiltration test was conducted on remoulded silt statically compacted in an undeformable column. The results were analysed using the instantaneous profile method (Daniel 1982). The suction profiles were derived from the suction measurements obtained by means of four high capacity tensiometers equally spaced along the column height. The reliability of suction tensiometers was successfully verified. A saturated permeability of 3.67 × 10−7 m/s was found considering constant head condition and stationary flow. The variation of the unsaturated hydraulic conductivity derived following Daniel’s method showed an increase of soil hydraulic conductivity for decreasing values of suction, as is often observed in partially saturated conditions. For suction values of 400 kPa a hydraulic permeability of 3.11E−09 m/s was obtained. Note that this unsaturated hydraulic conductivity is two orders of magnitude smaller than the saturated permeability (1.18E+02). Within the explored suction range, from 0 kPa to 400 kPa (i.e. Srw varying between 100% and 33%), results obtained on Jossigny silt indicate reduced
effects of the hydraulic gradient and the applicability of Darcy’s law. This might not be the case when higher suction levels are considered, as possible influence of microstructural changes could be involved in the assessment of the hydraulic properties. ACKNOWLEDGEMENTS The financial support of EU RTN ‘‘MUSE’’— Mechanics of Unsaturated Soils for Engineering, RTN—Marie Curie Actions) is kindly acknowledged. Authors wish to thank Prof. Y.J. Cui for providing the suction probes used during this study. REFERENCES Casini, F., Muñoz, J.J., Lourenço, S., Vaunat J. & Pereira, J.M. (2007). Technical Report: Results of the first centrifuge campaign al LCPC facilities, Nantes, France. Cui, Y.J. & Delage, P. (1996) Yielding and plastic behaviour of an unsaturated compacted silt. Géotechnique 46, N◦ 2, pp. 291–311. Cui, Y.J., Loiseau, C. & Delage, P. (2001). Water transfer through a confined heavily compacted swelling soil. In Proc. 6th Int. Workshop on Key Issues in Waste Isolation research-KIWIR, ENPC Paris), 43–60. Cui Y.J., Tang A.M., Mantho A. & de Laure E. (2007). Monitoring field soil suction using a miniature tensiometer. Geotechnical Testing Journal, vol. 31 (1), doi:10.1520/GTJ100769. Daniel D.E. (1982). Measurement of hydraulic conductivity of unsaturated soils with thermocouple psychrometers. J. of Soil Science Society of America, 20 (6): 1125–1129. Gardner, W.R. (1956). Calculation of capillary conductivity from pressure plate out-flow data. Soil Science Society of America Proceedings 20, 317–320. Green, R.E., & Corey, J.C. (1971). Calculation of hydraulic conductivity: a further evaluation of some predictive models. Soil Science Society of America Proceedings, 35: 3–8. Mantho, A.T., (2005) Echanges sol-atmosphère application à la sécheresse. PhD. Thesis, Ecole Nationale des Ponts et Chaussées, Paris, France. Richards L.A. (1931). Capillary conduction of liquids through porous mediums. Physics, 1 (5), 318–333. Van Genutchen, M.T. (1980). A close-form equation predicting the hydraulic conductivity of unsaturated soils. Journal Soil Science Society of America 44, pp. 892–898.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Testing for coefficient of permeability of a sandy soil in the residual state zone N. Ebrahimi-Birang Department of Civil and Geological Engineering, University of Saskatchewan, Saskatoon, SK, Canada
D.G. Fredlund Golder Associates Ltd., Saskatoon, SK, Canada
L. Samarasekera Department of Civil and Geological Engineering, University of Saskatchewan, Saskatoon, SK, Canada
ABSTRACT: A series of evaporation tests were conducted in an environmentally controlled room in order to determine the unsaturated coefficient of permeability function for Beaver Creek sand in the residual state zone. Two boundary conditions were applied at the top of the evaporation column; namely, i) ‘‘radiation and wind’’ treatment, and ii) ‘‘wind’’ treatment. The results of the tests indicated that the ‘‘wind’’ treatment was more suitable method for the determination of the unsaturated coefficient of permeability function in the residual state zone. Further tests also revealed that the steady state conditions that appeared to be reached in a fairly short period of time (i.e. 3 to 4 days) might be an ‘‘apparent steady state’’ condition.
1
INTRODUCTION
An understanding of the permeability function for an unsaturated soil is required in modeling the unsaturated seepage problems. Estimation methods have often been used to determine the permeability function. Most of the available estimation methods show a continuous decrease in unsaturated coefficient of permeability, kw , with increasing suction (or decreasing water content). A continuous decrease in the kw with an increase in soil suction can cause numerical instability because of the high nonlinearity and the computing difficulties associated with extremely small numbers. More importantly, an unlimited decrease in the value of kw fails to simulate actual water flow conditions since other moisture transfer mechanisms may cause moisture flow at relatively high soil suctions (Wilson et al. 1994, Gitirana Jr. & Fredlund 2003). Ebrahimi-Birang et al. (2004) suggested a lower limit of 10−14 m/s for kw . Due to restrictions associated with experimental measurements, the unsaturated permeability behaviour of soils remains largely unknown in and beyond the residual state zone. Amongst the methods that have been used for the measurement of the unsaturated coefficient of permeability, the evaporation method can be used to measure small coefficients of permeability in the residual state zone.
The primary objective of this research project was to measure the unsaturated coefficient of permeability in and beyond the residual state zone and also to investigate the mechanism of flow in a porous media when using an evaporation test. During the steady state evaporation method some interesting results were observed. The presentation and discussion of these results are the scope of the current paper. 2
BACKGROUND
The evaporation method to simultaneously measure the soil-water characteristic curve and permeability function was first introduced by Wind (1968). The method was a transient method and involved iterative calculations. Arya (2002) provided information regarding the modifications, commercial equipment, procedure and calculations associated with determining the unsaturated coefficient of permeability. The advantages and disadvantages of the method were also presented. Mehta et al. (1994) used the steady state evaporation method to determine the unsaturated coefficient of permeability. Recently Fujimaki & Inoue (2003) applied the method with some modifications. The principle of the method is based on the assumption that the evaporation rate will start from the maximum
129
rate (i.e. potential evaporation) when the soil column is saturated and will reduce with time and stay constant as the rate of the evaporation reaches the constant inflow rate which is applied from the bottom of the column. The inflow rate is always less than the potential evaporation rate. The test must be run in an environmentally-controlled room. In other words, the potential evaporation must be constant throughout the test. Equation 1 is used to calculate the coefficient of permeability. It must be noted that the soil-water characteristic curve must be measured separately. Research results have shown that steady state conditions appear to be reached within 2 to 3 days for a sandy soil.
k(ψ) =
q−
aτ Dva ρv∗ ρw Rv T ∂ψ ∂z
exp Rψv T ∂ψ ∂z
(1)
−1
where q = ql + qv , ql and qv = the liquid-water and water-vapour fluxes respectively, cm/s; z = depth, cm; a = the air-filled porosity, cm3 /cm3 ; τ = the tortuosity factor; Dva = the diffusion coefficient of water vapour in free air, g/(cm2 · s); ρv∗ = saturated water vapour density; ρw = the density of water, g/cm3 ; Rv = gas constant for water vapour, 4697 cm/K; T = temperature, K; and ψ = soil suction. 3
EXPERIMENTAL PROGRAM
The soil-water characteristic curve for Beaver Creek Sand and details of the evaporation tests procedure are presented in the following sections. 3.1
Soil used
The Beaver Creek sand was used in this research study. The sand was air dried, passed through the sieve #10 (2 mm) and washed thoroughly in order to minimize the amount of salt. Then the properties of the soil were measured. Table 1 summarizes some of the properties of the Beaver Creek Sand. The soil will be referred to as ‘‘Sand’’ throughout the paper. 3.2
SWCC
Hanging column method, Pressure plate (Tempe Cell and Fredlund Cell) and Chilled Mirror Dewpoint Table 1.
Properties of Beaver Creek sand.
Soil properties
Beaver Creek sand
Sand Silt and Clay Specific gravity
99.5 % 0.5 % 2.65
technique (WP4-T apparatus) were used to measure the soil-water characteristic curve of the sand for entire range of suction from zero to 1,000,000 kPa. The equation proposed by Fredlund & Xing (1994) was used to fit the experimental data. Figure 1 shows the experimental data and fitting SWCC for the sand. The air entry value for the sand was 1.7 kPa and residual suction state was reached at about 5 kPa. 3.3 Evaporation test The soil column design, preparation of soil specimens and the evaporation test procedure are presented in the following sections. 3.3.1 Soil column Figure 2 shows a schematic diagram of the soil column used in this study. The column is made of a Plexiglass tube with an inside diameter of 70 mm and a length of approximately 160 mm. Several holes were drilled along the column for the installation of the thermocouples. Eight thermocouples could be installed horizontally at different depths. These depths were: 4.5, 14.5, 24.5, 34.5, 49.5, 72, 112.5, and 147 mm. Some ports were also drilled around the perimeter of the tube to retrieve water content and electrical conductivity samples. The sampling ports in the top 40 mm of the column were smaller (5 mm in diameter) allowing sampling in closer proximity. There were three sampling ports for each depth in the top section of the column. The ports in the lower part of the column had a diameter of 10 mm. Soil samples could be taken from 16 different depths (i.e. 5.5, 10.3, 15.4, 20.5, 25.6, 30.7, 35.8, 40.9, 50.5, 60.4, 70.3, 80.5, 90.5, 100.5, 110.5, 120.5, 130.5, and 140.5 mm). The sampling ports were plugged using rubber stoppers during the test. A heat insulation jacket was used to prevent horizontal heat transfer in the upper part of the column. A porous plate with low air entry value was placed on a grooved pedestal. The column was attached to the pedestal using five bolts and nuts. 3.3.2 Preparation of the soil sample The air-dried sand was mixed with a given amount of water to produce a gravimetric water content of 17%. The soil was left in a plastic container with a tight lid for a day. A Plexiglass tube with a diameter equal to that of the soil column was taped to the column to increase its height. The soil was placed into the column. In order to create a uniform soil, a vertical force was applied on top of the soil through a load cap. Extra soil was trimmed from top of the column. The column was slowly placed on the pedestal and fastened using the bolt and nuts. It should be noted that samples for the SWCC tests (section 3.2) were prepared using a similar procedure. However, the soil
130
Hanging column
Gravimetric water content (%)
30 25 Vapour pressure method method
Tempe Cell and Fredlund SWCC apparatus
20 15
Fredlund and Xing equation 10 Experimental data 5 0 0.1
1
10
100
1000
10000
100000
1000000
Soil suction (kPa)
Figure 1.
Soil-water characteristic curve of Beaver Creek sand.
70 mm
Relay
Electric Fan
Rubber stoppers
150 mm
Sampling ports
Heat insulation jacket
Thermocouples
70 mm
150 mm
Rubber stoppers
Sampling Thermocouples ports
Heat insulation jacket
Bulb
O-rings
GDS Data Logger Porous plate Grooved pedestal
Electronic Balance
O-rings Figure 3.
Porous plate
Grooved pedestal
Figure 2. Schematic diagram of the soil column used in the evaporation test.
samples were extruded into stainless steel rings for the SWCC test. 3.3.3 Test procedure The soil column was placed on an electronic balance (Fig. 3). Thermocouples were horizontally installed
Schematic diagram of the evaporation tests.
through rubber stoppers at specified depths along the column. The thermocouples were attached to a CR1000 Campbell Scientific data logger to monitor temperature during the test. The temperature of the ambient air above the soil column was also monitored using two thermocouples. The soil column was saturated by applying slow flow of distilled water from the bottom of the column. After saturation, the top of the soil was covered with a plastic sheet. The system was left overnight to reach equilibrium. A fiberglass tube was cut and placed around the top part of the column. Two pieces of Velcro were used to tighten the fiberglass around the column. A syringe pump (GDS apparatus) was attached to the column from the bottom through a plastic tube and a needle. The pump was programmed
131
4
2560 Weight of the column (g)
2540 2520 2500 2480 2460 2440 2420 2400 0
1
2 3 4 Elapsed time, day
5
6
Figure 4. Change in the weight of the column for ‘‘wind and radiation’’ treatment.
Temperature, ˚C 20
22
24
26
28
30
0 20 Depth (mm)
to apply a specified amount of distilled water into the column (0.36 cm3 /hr). The bottom porous plate had an air entry value of 1.8 kPa. The evaporation test was initiated by removing the plastic cover. An electric fan was used above the column to promote the evaporation. The weight of the soil column was recorded during the test using an electronic balance connected to a computer. The readability of the balance was 0.01 g. The evaporation tests were conducted using two types of top boundary conditions; namely, i) ‘‘radiation and wind treatment’’ and ii) ‘‘wind’’ treatment. In the ‘‘radiation and wind treatment’’ an attempt was made to keep the temperature constant and equal to the room temperature along the soil column using a lamp and a relay. All tests were conducted in an environmentallycontrolled room. The room temperature was about 25.5◦ C and the relative humidity was about 26%. To minimize the effect of the radiation on evaporation, all lights were turned off during the test. The temperature and relative humidity in the room were also recorded using a hygrometer.
RESULTS AND DISCUSSIONS
40 T = 25.4°C
60
t = 100 min
80
t = 2830 min
100 120
4.1
Weight of the column
140 160
Figure 4 shows the change in the weight of the column during the evaporation test for the ‘‘wind and radiation’’ treatment. Steady-state conditions appear to have been reached after 3 to 4 days. A similar result was obtained for the case of the ‘‘wind’’ treatment. Further investigations have shown that this condition may not be a ‘‘true steady state’’ condition (see section 4.4). Further study is required with regard to ‘‘true steady state’’ conditions.
19
21
23
25
0 20
Temperature profiles
t = 7000 min
40 60
t = 400 min
80 100 120
Figure 5 shows temperature profiles during early stages of the evaporation and after what appears to be ‘‘steady state’’ conditions. Temperature gradients are greater for the case of the ‘‘wind treatment’’. For the case of the ‘‘radiation and wind’’ treatment the temperature profile did not change substantially after ‘‘apparent steady state’’ conditions were reached. As can be seen in Figure 5a, the attempt to control temperature seems to be successful. The temperature gradients appear to be small. Further investigation is needed to determine the effect of temperature gradient on the flow through the soil. 4.3
t = 100 min
Temperature, °C 17
Depth (mm)
4.2
t = 2830 min 5a. “Radiation and wind” treatment
Water content profiles
Water content profiles are shown in Figure 6 for both cases. For the case of the ‘‘radiation and wind’’
140 160 t = 7000 min
t = 400 min
5b. “Wind” treatment
Figure 5. Temperature profiles for a) ‘‘radiation and wind’’ treatment, b) ‘‘wind’’ treatment.
treatment it can be inferred that the coefficient of permeability cannot be determined for water contents below 5%. The corresponding suction for a water content of 5% is about 5 kPa (see Fig. 1). However, the water content profile for the ‘‘wind’’ treatment shows that it is possible to determine the corresponding coefficient of the permeability for water contents below 5%.
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Gravimetric water content (%) 0
5
10
Time (min) 15
20
0
0
0 Decrease in weight (g)
20
Depth (mm)
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
40 60 80 100 120 140 160
20 40 60
Removing a layer of Soil from the surface
80 100 120 140 160
6a. “Radiation and wind” treatment
Figure 7. Weight of the column versus time for the ‘‘wind’’ treatment.
Gravimetric water content (%) 0
5
10
15
20
25
0
EC (ds/m) 0
40
80 100 120 140 160
Figure 6. Water content profiles for a) ‘‘radiation and wind’’ treatment b) ‘‘wind’ treatment.
Steady state condition
Equation 1 can be used along with the soil-water characteristic curve and the water content profile to calculate the coefficient of permeability provided a ‘‘true steady state’’ condition is reached. Further tests must be conducted to determine if the observed steady state condition was truly a steady state condition. The evaporation test with the ‘‘wind’’ treatment was continued for a longer time after reaching an apparent steady state condition. The results of the change in the weight of the sand column are shown in Figure 7. After initiating the evaporation process, the weight of the column started to decrease. Then the weight remained constant for a couple of days (i.e. the steady state condition appeared to be reached). After a day or so the weight of the column started to increase indicating that the outflow rate (evaporation rate) was becoming less than the inflow rate. In other words the evaporation rate was still decreasing. There are two possible reasons for the increase of the weight: i) accumulation of the salts in the top layer of the soil and/or ii) break in the liquid-water continuity between the top and bottom of the column. These two reasons are discussed in the following sections. 4.4.1 Salts accumulation Measurement of the salt profile after reaching the apparent steady state condition showed that the
0.4
0.6
0.8
1
1.2
1.4
20 40 60 80 100 120 140 160
6b. “ Wind” treatment
4.4
0.2
0
60
Depth (mm)
Depth (mm)
20
Figure 8. Electrical conductivity profile for the ‘‘radiation and wind’’ treatment (soil:water = 1:5).
electrical conductivity, EC, of the soil in a thin layer of the soil surface was much higher than the EC for the bottom layers (Fig. 8). Electrical conductivity was measured for the samples with soil to water ratio of 1 to 5. It is possible that this may be related to the reason why the weight starts to increase. If so, then the ‘‘steady-state condition’’ should resume by removing a thin layer of the soil from top of the column. As can be seen in Figure 7 this did not happen and the weight of the column continued rising at the same rate. 4.4.2 Break in the hydraulic continuity of liquid water To examine the hydraulic continuity of the liquid water throughout the soil column, a separate evaporation test was conducted. A soil column was prepared in a similar manner as before except that the porous plate with an air entry value of 100 kPa was used. The inflow rate was also increased to 0.9 cm3 /hr. After the apparent steady state condition passed and the weight of the column started to increase, the inflow rate was reduced to zero. As was expected a decrease in the weight of the column was observed after stopping the inflow rate as shown in Figure 9. The slope of the weight change line corresponds to a rate of evaporation of 0.0101 cm3 /min. The rate of evaporation did not change when compared with the rate before reducing the inflow rate to zero. This may be attributed to
133
Time (min) 0
500
1000
1500
2000
2500
3000
3500
Decrease in weight (g)
0 5 w = 0.0101t + 0.2718 RR22= 0.9999
10 15 20 25 30 35 40
Figure 9. Decrease in the weight of the column (evaporation) versus time after reducing the inflow rate (inflow rate = 0).
Gravimetric water content (%) 0
5
10
15
20
25
Depth (mm)
0 20 40
Porous plate (AEV = 1.8 kPa) Inflow rate = 0.36 cm3/hr
60
Porous Plate (AEV =100 kPa) Inflow rate = 0.9 cm3/hr
80 100 120 140
REFERENCES
160
Figure 10. Water content profiles for two different conditions at the bottom of the column.
the fact that there was no hydraulic continuity of liquid water between the top and bottom of the soil column. Plotting the water content profiles for the two different cases provides further evidence that it is possible that the liquid water was not hydraulically connected between the top and bottom parts of the column (Figure 10). The two cases created the same water content profile at the top of the soil while the bottom parts were different due to the change in inflow rate and the bottom plate. In other words, the top portion of the column was solely controlled by the ambient conditions. 5
was promoted with an electric fan above the soil column. While controlling of the temperature seemed to be successful, the water content profiles indicated that the ‘‘radiation and wind’’ treatment might not be a suitable method in order to measure the coefficient of permeability for the range of water content below 5%. On the other hand, the results for the ‘‘wind’’ treatment were encouraging. Continuing the evaporation test for a long time showed that the ‘‘true steady state’’ condition may not have been reached during the short run of the evaporation tests. Two hypothesis were examined for the reason why the steady state condition may not have been attained; namely, i) accumulation of the salt in the surface of the soil and reducing the evaporation as a result, and ii) break in the hydraulic continuity of the liquid water between the bottom and top of the soil. Further investigation showed that the latter reason may provide the best explanation. Further tests are currently being conducting where the water table will be held constant within the soil column at a shallow depth. Hopefully, ‘‘hydraulic continuity’’ will be maintained between the top and bottom of the column.
SUMMARY AND CONCLUSIONS
A series of the evaporation tests were conducted on a sand column in an environmentally controlled room. The aim was to reach steady-state conditions during the evaporation tests and to determine the permeability function in the residual state zone. Two boundary condition treatments were tested, i) ‘‘radiation and wind’’ treatment, and ii) ‘‘wind’’ treatment. In the case of the ‘‘radiation and wind’’ treatment, an attempt was made to control the temperature of the soil column using a relay and lamp system. In both cases the evaporation
Arya, L.M. 2002. Wind and hot air methods. In J.H. Dane & G.C. Topp (eds), SSSA Book Series: 5, Methods of Soil Analysis, Part 4—Physical Methods: 916–926. Madison, Wisconsin: Soil Science Society of America Inc. Ebrahimi-Birang, N., Gitirana, Jr. G.F.N., Fredlund, D.G., Fredlund, M.D. & Samarasekera, L. 2004. A lower limit for the water permeability coefficient. Proceedings of the 57th Canadian Geotechnical Conference: 12–19, 24–27 October 2004. Quebec city, Canada. Fredlund, D.G. & Xing, A. 1994. Equations for the soil water characteristic curve. Canadian Geotechnical Journal 31(3): 521–532. Fujimaki, H. & Inoue, M. 2003. A flux-controlled steadystate evaporation method for determining unsaturated hydraulic conductivity at low matric pressure head values. Soil Science 168(6): 385–395. Gitirana, Jr., G.F.N. & Fredlund, D.G. 2003. From experimental evidences towards the assessment of weather-related railway embankment hazards. Keynote address, Proc. of the International Conference on ‘‘From Experimental Evidences Towards Unsaturated Soil Practice’’, Sept. 18–19 Weimar, Germany. Mehta, B.K., Shiozawa, S. & Nakano, M. 1994. Hydraulic properties of a sandy soil at low water contents. Soil Science 157(4): 208–214. Wilson, G.W., Fredlund, D.G. & Barbour, S.L. 1994. Coupled soil-atmosphere modeling for soil evaporation. Canadian Geotechnical Journal 31(2): 151–161. Wind, G.P. 1968. Capillary conductivity data estimated by a simple method. In P.E. Rijtema & H. Wassink (eds), Proc. Wageningen Symp. on Water in the Unsaturated Zone, Paris, June 1966, Vol. 1: 181–191 Int. Assoc. of Scientific Hydrol., Gent/Brugge/UNESCO.
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Preparation of unsaturated soils by oedometric compression B. Caicedo, J.C. Ulloa & C. Murillo Universidad de Los Andes, Bogotá D.C., Colombia
ABSTRACT: The study of unsaturated soils for laboratory tests or physical modeling requires a well controlled preparation method. Usually the procedures for unsaturated soil preparation include different compaction methods controlling water content and voids ratio. However the traditional compaction techniques using blows or kneading reduces the possibility of controlling the stress path during soil compaction. Although a uniaxial compression process allows soil preparation under controlled vertical stress, the whole stress path remains unknown. This paper describes a fully instrumented oedometric apparatus that allows the measurement of vertical and horizontal stress as well as the suction and water content during the oedometric compression test. This new oedometric apparatus is used to prepare unsaturated soils made of mixtures of sand and kaolin. The sensors on the oedometric cell allow the measurement of suction and water content during soil preparation. The results obtained confirm the satisfactory operation of the oedometer and show that this apparatus could be an important tool to investigate the anisotropic response of the unsatrated compacted soils.
1
INTRODUCTION
The increasing interest in physical modelling of unsaturated soils has heightened the need for soil preparation techniques suitable to predict the behaviour of soils during modelling. Of particular interest is the prediction of the expansive or collapse behaviour of soils prepared using different compaction techniques. Studies have been carried out in order to establish controlled methodologies to reproduce intermediate unsaturated soils. These procedures can be grouped into two main techniques: (i) the inclusion of a cementing material in sandy soils (Abdulla et al. 1994, Dupas et al. 1979, Ismail et al. 2000) and (ii) mixtures of clay and sand compacted by uniaxial compression (Brandon et al. 1991, Kimura et al. 1994, Boussaid et al. 2005, Murillo et al. 2006). However these methods suffer from some limitations mainly concerning the possibility of controlling the stress path during compaction. In fact, traditional compaction techniques using blows or kneading make impossible any knowledge of the stress path during compaction. Although uniaxial compression allows soil preparation under controlled vertical stress, the whole stress path remains unknown. Compacted materials are fundamentally unsaturated soils having expansive or collapsible behaviour which is strongly dependent on their negative pore water pressure and their stress history. These soils have been traditionally studied using a set of suction controlled triaxial and oedometric tests. During
these tests soils are submitted to different stress paths and different cycles of drying and wetting in order to analyze their compressibility behaviour. Since these tests are suction controlled tests, the time necessary to characterize the soil takes several weeks or months. As an alternative suction monitored apparatus (triaxial or oedometer) allows the characterization of unsaturated soils in a fraction of time compared with suction controlled apparatus (Blatz and Graham 2003, Jotisankasa et al. 2007). The main objective of this paper is to present a method to investigate the stress—strain—suction paths during the preparation of unsaturated soils by vertical stress compaction. For this purpose this paper presents a new oedometer apparatus having the capability to measure the horizontal stress, suction and water content during compaction. Tests on samples made of a mixture of sand and kaolin are carried out in order to verify the performance of this new oedometer apparatus, however the results in this paper focus on kaolin. 2 2.1
MATERIAL AND EQUIPMENT Material properties
The materials used for the tests are different mixtures of sand and clay. The sand is rounded, well graded silica sand having a specific gravity of 2.45. The clay is kaolin having liquid limit w1 = 55, plasticity index Ip = 29, and a specific gravity of 2.8. The mixtures
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are obtained by combining different dry masses of silica sand and kaolin with water. Previous standard compaction tests were performed in order to measure the optimum water content and the maximum dry density of the samples. Table 1 shows the sand and clay proportions of the mixtures and the proctor standard results: water content, dry density and void ratio at the optimum water content. 2.2
New suction monitored oedometer apparatus
Figure 1 shows the oedometric cell used for the testing. The cell was designed to measure the stress-strain and suction-water content paths during Table 1.
Soil properties.
Sample
Sand %
Kaolin %
wopt %
ρd kN/m3
E
1 2 3
88 65 0
12 35 100
12 13 29
18.5 18.8 14.5
0.258 0.269 0.482
Figure 1.
Modified oedometric cell.
vertical compression. The modifications to perform the path measurements include: – A capacitive cylindrical water content sensor installed in the centre of the sample (Figure 2). – Three psychrometers to independently measure the suctions. – A linear variable differential transducer (LVDT) to measure the vertical displacement. – A load cell to measure the vertical load. – Three miniature load cells to measure the horizontal stress. The psychrometers are monitored using a Campbell Scientific CR7 data acquisition and control system. The displacement and loads were measured using an Advantech ADAM data acquisition system. The oedometric cell is installed on a Wykeham Farrance press in order to perform oedometric tests with controlled strain rate.
3
TESTING PROGRAMME
Two tests were carried out for each mixture. One of these tests was performed at the optimum water content and compacted up to 9 kN vertical load (2.62 MPa vertical stress). On the other test the soil is mixed at 70% of the optimum water content and compacted up to 3 kN vertical load (0.90 MPa vertical stress). The vertical compression test was performed having one unloading/reloading stage and the oedometric test was a constant rate of displacement test. This type of test allows the continuous measurement of the vertical and horizontal stresses as well as the water content and suction. Increase in water content is allowed after the unloading—reloading process by opening the bottom saturation valve and applying 20 kPa water pressure. During this process the loading piston remains at the same position as at the end of the compression stage; therefore the expansive or collapse behaviour appears as the vertical load increases or decreases.
4
RESULTS AND DISCUSION
4.1 Results for kaolin with high compaction stress Figures 3 to 9 show the results of the sample comprising 100% kaolin and compacted up to 2.62 MPa. On these figures the different phases during the test are identified by the points A to D:
Figure 2.
– Initial state – Loading – Unloading – Wetting
Capacitive water content sensor.
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point A point B point C point D
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Figure 4.
The oedometric cell has a set of miniature load sensors that allows the measurement of the horizontal stress. Figure 3 shows measured vertical and horizontal stresses and it appears there is different behaveiour depending on the direction of loading. The first stage (A-B) corresponds to the loading stage; this stage could be characterized by two linear stages that probably correspond to an overconsolidated stage and a normally consolidated stage. During unloading (B-C) the horizontal stress at first remain constant and then decreases. When the vertical stress reaches zero a horizontal stress of 200 kPa is measured. The reloading path (C-B) is almost linear, corresponding to elastic behaviour. Finally, during wetting, a small decrease in vertical stress and a more importantly an increase in the horizontal stress are apparent. These results show an important anisotropic behaviour since it appears to show a small collapse in the vertical direction and expansion on the horizontal direction. One of the main advantages of measuring the horizontal stress during loading is the possibility of calculating the p-q path. Figure 4 shows the p-q path during loading, unloading, reloading and wetting. This figure shows a number of features: non-linear behaviour during loading, mainly at low stress levels, then approximate linear behaviour for high levels of stress. During unloading and reloading the p-q path is fairly linear but shows a hysteresis. During wetting, the deviatoric stress decreases and the isotropic stress remains almost constant. Figure 5 shows the relationship between axial strain and deviatoric stress. As the test starts with the soil in a loose state, the initial part of the loading stage (A–B) shows a large axial strain without a significant increase in deviatoric strain; however for small strain (ε1 < 0.01) the deviatoric stress grows at higher rate than in the second part of the loading stage corresponding to intermediate strains (0.01 < ε1 < 0.1). This higher slope could be the trace of an initial elastic domain. After unloading (point C) a negative deviatoric stress is measured which is the consequence of combining
p-q path.
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Figure 3.
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Figure 5. stress.
Relationship between axial strain and deviatoric
zero axial stress with positive horizontal stress. Finally on wetting a reduction in deviatoric stress appears with any change in axial strain. Figure 6 shows the relationship between specific volume and mean stress. This figure appears to show a clear elastic domain in the first part of the loading stage. As compression starts with the soil in a loose state, this elastic domain is the consequence of an overconsolidated behaviour due to the initial suction. This initial elastic domain is characterized by a line parallel to the unloading reloading stage (B–C). After this initial elastic phase the specific volume reduces at higher rate, during which the degree of saturation of the sample grows and the suction reduces. During wetting an insignificant change in mean stress is recorded therefore on Figure 6 points B and D are superimposed. Figures 7 and 8 show the evolution of suction during testing. Figure 7 shows the relationship between the suction and the volumetric water content θw , and Figure 8 shows the relationship between suction and isotropic stress. As observed on these figures, the new oedometric cell allows the measurement of the suction curve during compression.
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A
2.8 2.6
V
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2.4
Wetting Initial state Unloading reloading
2.2
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Figure 9. p − q − s path during oedometric compression. 250
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domains, an initial elastic domain where the deviatoric stress shows a more important increment as a function of isotropic stress and a normally consolidated domain where the deviatoric stress grows slowly almost for the intermediate strains (0.01 < ε1 < 0.1). This initial compression shows the highest evolution in suction value. During unloading (B-C), the stress path shows a reversible behaviour with minor change in suction value. Finally during wetting a major decrease in suction is evident, as well as an increase of the isotropic stress and a reduction of the deviatoric stress.
A
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Figure 10. Vertical and horizontal stress for low compaction stress material.
Figure 7. Relationship between suction and volumetric water content. 8000
400 v
w
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h
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p (kpa) Figure 8.
Relationship between suction and isotropic stress.
Finally it is possible to draw the oedometric compression test on a p−q−s plot (Figure 9). On this curve it is possible to observe all the features described using Figures 3 to 8. The initial state (point A) is characterized by a high suction value and zero p − q stress. The high suction value creates an overconsolidated soil. The loading stage (A-B) is characterized by two
4.2 Results for kaolin with low compaction stress Figures 10 to 12 show the results of the sample comprising 100% kaolin and compacted up to 0.9 MPa. In this tests the reloading phase progresses up to point B2 . This test shows differences to the test carried out with a high compaction stress, mainly in the wetting stage. In fact, on wetting the vertical stress reduces although the horizontal stress remains almost constant (Figure 10). As a consequence for this low compaction stress the collapse behaviour is noticeable on the p-q
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1000
q kpa
800
The results obtained indicate the apparatus to be responding well in the tests and shows that this kind of apparatus may be an important tool to investigate the anisotropic response of unsaturated compacted soils. The measurement of all the variables involved during the compression of an unsaturated soil allows a better understanding of the preparation of expansive or collapsing soils by static compression. Complementary work is necessary to analyze and model the whole behaviour of compacted soils focusing on their anisotropic response.
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p (kpa) Figure 11.
REFERENCES
p-q path for low compaction stress material.
A
2.8
V
2.6 2.4 B1
2.2 C
D
2 1
10
100
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1000
p (kpa) Figure 12. Relationship between specific volume and isotropic stress, low compaction stress.
path (Figure 11), and on the curve relating the specific volume and the isotropic stress (Figure 12). 5
CONCLUSIONS
This paper presents some details of a suction monitored oedometer to investigate the stress—strain and suction—water content paths during vertical compaction.
Abdulla W.A., Goodings D.J. 1994. Study of sinkholes in weakly cemented sand. Centrifuge 94, Leung, Lee and Tan (eds) Balkema, Rotterdam. Blatz J.A., Graham J. 2003. Elastic—plastic modelling of unsaturated soil using results from a new triaxial tests with controlled suction. Géotechnique 53. No 1. Boussaid K., Thorel L., Garnier J., Ferber V., David J.P. 2005. Comportement mécanique de sols intermediaries reconstitutes: Influence de la teneur en eau et du percentage d’argile. Congrès fancais de mécanique, Troyes, France. Brandon T.L., Clough G.W., Rahardjo P.P. 1991. Fabrication of silty sand specimens for large and small scale tests. Geotechnical testing Journal, Vol. 14 No 1. Dupas J.M., Pecker A. 1979. Static and dynamic properties of sand—cement. ASCE Journal of Geotechnical Engineering Vol. 105, GT3. Ismail M.A., Joer H.A., Randolph M.F. 2000. Sample preparation technique for artificially cemented soils. ASTM Geotech. Testing J., 23(2), 171–177. Jotisankasa A., Ridley A., Coop M. 2007. Collapse behavior of compacted silty clay in suction—monitored oedometer apparatus. Journal of Geotechnical and Geoenvironmental Engineering. ASCE, 133(7), 867–877. Kimura T., Takemura J., Hiro–Oka A., Okamura M. 1994. Mechanical behaviour of intermediate soils. Centrifuge 94. Singapore, Leung et al. (Ed), Balkema. Murillo C. 2006. Caraterización Geotécnica en Centrífuga de Macizos Multicapa de Suelo Parcialmente Saturado usando Ondas de Superficie. PhD. Thesis Universidad de los Andes, Bogotá Colombia.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Influence of sample height on the soil water characteristic curve C.N. Khoury & G.A. Miller School of Civil Engineering & Environmental Science, University of Oklahoma, Norman, Oklahoma, USA
ABSTRACT: The Soil Water Characteristic Curve (SWCC), one of the fundamental relations to describe unsaturated soil, has been studied extensively; however, not much emphasis has been placed on the effect of sample geometry on the SWCC. The study described in this paper was originated to evaluate the effect of sample height on the SWCC for various soils with the intent of optimizing testing efficiency. A custom made device was built to obtain the SWCC (wetting/drying paths) using automated pore-water pressure and pore-air pressure controllers. Specimens with two heights, 25 mm and 6.35 mm and having a diameter of 63.5 mm, were compacted with similar initial dry density and moisture content. Samples were saturated and then subjected to drainage approaching residual saturation followed by wetting back to a zero suction state. Experimental results thus far demonstrate that the SWCC primary drainage and wetting curves compare favorably for different sample heights. However, an essential distinction in equilibrium time was observed. As expected, tests with smaller sample heights reached equilibrium much faster than larger sample heights. Preliminary results indicate that a 75% reduction of sample height reduced equilibrium time by about 50%. Implications of reducing the sample height are discussed and some general improvements in SWCC testing with the custom made device are presented.
1
INTRODUCTION AND BACKGROUND
The Soil Water Characteristic Curve (SWCC) expresses the relationship between water content and suction in a soil. It is an important relationship in unsaturated soil, and thus obtaining SWCCs experimentally is a crucial yet time consuming endeavor. Extensive research on the SWCC and its importance to unsaturated soil behavior is reported in the literature (e.g. Barbour 1998, Fredlund & Rahardjo 1993, Fredlund et al. 1996). Various test procedures and equipment have been developed to investigate the SWCC (e.g. Olson & Langfelder 1965, Fredlund & Xing 1994, Kawai et al. 2000) such as the filter paper method, pressure plate, Tempe Cell, and many others. However, it seems little research has been conducted to study the effect of sample geometry on the SWCC. Since laboratory testing generally requires significant time to generate a SWCC, there are major advantages to reducing the sample dimensions, particularly the sample height. For example, very little experimental data are available in the literature showing hysteretic behavior of the SWCC; most reported data represent a single branch of the SWCC, typically the primary drainage curve. Probably, time required for completing the SWCC test is the main reason for the lack of reported hysteretic
data; thus, reducing testing time will encourage more extensive testing to fully define hysteretic behavior of the SWCC. This was precisely the motivation for the current authors to pursue this study. This paper presents results of a study to investigate the effect of sample height on the SWCC for a silty soil. The goal was to optimize the testing geometry while shortening the equilibrium time. A preliminary set of experimental results are presented for sample heights of 25.4 mm and 6.35 mm; resulting SWCCs include primary drying and wetting curves. Results clearly demonstrate the time advantage to be gained by reducing sample height. 2
TEST PROCEDURE
The Soil Water Characteristic Curves were experimentally obtained using a custom made test cell built at the University of Oklahoma. Schematic and photographic views of the test cell are shown in Figure 1. The pore-water pressure was digitally controlled using a commercially available high precision motorized piston pump and transmitted to the soil via a high air entry porous disc (HAEPD). A similar pump having a larger piston volume was used to control the air
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size distribution similar to that of fine silt with sand having about 30% fine sand (0.075–0.25 mm), 62% silt (0.002–0.075 mm), and 8% clay size material (≤0.002). A series of tests was conducted to determine the effect of soil sample height on the SWCC. The sample heights tested in this study were 25.4 mm and 6.35 mm with a diameter of 63.5 mm. Each sample was prepared in an identical manner to achieve nominally the same initial void ratio (0.60) and gravimetric moisture content (17.2%) in the test specimens. Samples were compacted into the test cell on top of the pre-conditioned high air entry porous stone using volume-based moist tamping. The test cell was then flooded with water and water was pushed under low pressure through the sample by increasing the air pressure (ua ) above the water in the cell. This process continued until a minimum of three pore volumes of water had flowed through the sample to remove entrapped air. Following saturation, the drying (drainage) and wetting cycles were initiated. The drying curve is obtained by applying ua in increments to obtain different values of matric suction; the amount of pore water volume expelled out of the soil sample is automatically recorded in the system to estimate the gravimetric water content corresponding to each increment of suction. Equilibrium was assumed to occur when negligible water volume (i.e. less than 1% change over a period of 4 hours) occurred for each suction increment. For each height, samples were subjected to wetting and drying cycles under zero net normal stress to obtain the primary drying and primary wetting curves.
GDS Digital Air Pressure Controller
Test Cell
Porous stainless steel top platen Soil sample High air entry porous disc (HAEPD) GDS Digital Water Pressure Controller
Figure 1.
Schematic and photographical view of test cell.
120 100 Sil-Co-Sil (SCS) 250
% Passing
80 60 40 20
3
TEST RESULTS AND DISCUSSIONS
0 1
0.1
0.01
0.001
Particle Diameter (mm)
Figure 2.
Grain size distribution for tested soils.
pressure in the cell. These pumps can accurately control pressure and volume changes to a resolution on the order of 1 kPa and 1 mm3 , respectively. The experimental apparatus allowed for continuous control and measurement of the pore-air pressure and pore-water pressure throughout testing. A porous stone with a relatively low air entry value was used (i.e. 3 bar) to gain maximum efficiency with respect to water transmission into and out of the soil. A commercially available ground silica, Sil-Co-Sil 250 (SCS-250) manufactured by U.S. Silica Company was used as the test soil. The grain size distribution of the SCS-250 is given in Figure 2. As shown, the test soils have a grain
Plots of the Soil Water Characteristic Curves (SWCC) in terms of matric suction (ua − uw ) versus gravimetric water content for tests having heights of 25.4 mm and 6.35 mm are presented in Figure 3 and Figure 4, respectively. Each data point in these figures represents an increment of suction and corresponding measurement of water volume change at equilibrium. Equilibrium was assumed to occur when negligible water volume change occurred for each suction increment. In Figure 5 an example of water volume change versus time for primary drainage of the 25.4 mm sample height is shown; water volume changed fairly rapidly following application of an increment of suction followed by a more gradual change until equilibrium was observed. In Figure 6, a comparison of the primary drainage and primary wetting curves for each (25.4 mm and 6.35 sample height) test is shown. In examining Figure 6 it is apparent that the SWCCs for both sample heights were practically the same.
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0
Water Volume Change (cc)
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Figure 3.
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Figure 5. Water volume change versus time for primary drainage during testing for 25.4 mm height.
SWCC for the sample of 25.4 mm height.
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SWCC for the sample of 6.35 mm height.
Figure 6. SWCC comparison for the two sample heights (25.4 and 6.35 mm).
Figure 7 shows a comparison of water volume change versus total test time for both sample heights. The total time for testing, including primary drainage and primary wetting curves for the 25.4 mm height was about 30 days compared to 15 days for the reduced sample height (6.35 mm). It can be noted that the time required to complete testing was reduced by about 50% when the sample height was reduced from 25.4 mm to 6.35 mm. Results indicate that a reduction in sample height can be an effective way of achieving considerably faster equilibrium test times. However, other considerations remain when reducing the test specimen height, such sample uniformity, and minimum vertical deformations required for accurate measurements on the specimen under vertical loading (i.e. for a given strain shorter heights mean smaller displacements). The reduction in testing time gained by reducing the sample height was a major achievement in that it allowed researchers at the University of Oklahoma to efficiently obtain in a reasonable time frame a complete set of SWCCs including the hysteretic behavior;
0
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Figure 4.
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Figure 7. Water volume change versus time for both 25.4 mm to 6.35 mm sample height.
this included primary drying, primary wetting, secondary drying and scanning curves (Fig. 8). This is part of an on-going study of the coupled mechanicalhydraulic behavior of unsaturated soils.
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produced for two different sample heights. By reducing the sample height by 75%, the time required to complete a SWCC was reduced by about 50%. Furthermore, there was virtually no difference in the SWCCs produced using different samples heights.
120 100
ua-uw (kPa)
80 60
REFERENCES 40 20 0 0.1
0.2
0.3
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Gravimetric Water Content
Figure 8. 200 kPa.
4
SWCC showing hysteresis for normal stress of
CONCLUSIONS
Experiments were conducted in a specially fabricated testing cell and used to examine the effect of sample height on the SWCC relationship in an unsaturated silty soil. The soil water characteristic curves, including primary drainage and wetting curves were
Barbour, S.L. 1998. Nineteenth Canadian Geotechnical Colloquium: The soil-water characteristic curve: a historical perspective, Canadian Geotechnical Journal, Vol. 35, pp. 873–894. Fredlund, D.G. and Rahardjo, H. 1993. Soil mechanics for Unsaturated soils. John Wiley & Sons Inc., New York. Fredlund, D.G. and Xing, A. 1994. Equations for the soil-water characteristic curves, Canadian Geotechnical Journal, Vol. 31, pp. 521–523. Fredlund, D.G., Xing, A., Fredlund, M.D. and Barbour, S.L. 1996. The Relationship of the Unsaturated Soil Shear Strength Functions to the Soil-Water Characteristic Curve, Canadian Geotechnical Journal, Vol. 33, pp. 440–448. Kawai, K., Karube, D. and Kato, S. 2000. The Model of Water Retention Curve Considering Effects of Void Ratio, In: Rahardjo, H., Toll, D.G., Leong, E.C. (Eds.), Unsaturated Soils for Asia, Balkema, Rotterdam, pp. 329–334. Olson, R.E. and Langfelder, L.J. 1965. Pore-Water Pressures in Unsaturated Soils, Journal of Soil Mechanics and Foundation Div., Proc. ASCE, Vol. 91, SM4, pp. 127–160.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Observations of unsaturated soils by Environmental Scanning Electron Microscopy in dynamic mode S.D.N. Lourenço, D.G. Toll & C.E. Augarde School of Engineering, Durham University, Durham, UK
D. Gallipoli Department of Civil Engineering, University of Glasgow, Glasgow, UK
A. Congreve & T. Smart Department of Chemistry, Durham University, Durham, UK
F.D. Evans Controls Testing Equipment Ltd, Wykeham Farrance Division, Tring, Hertfordshire, UK
ABSTRACT: The Environmental Scanning Electron Microscope (ESEM) allows observation of hydrated samples in their original state. Imaging can be done at a constant vapour pressure and temperature or in dynamic conditions to observe a sample response to changes of water vapour pressure and/or temperature. This paper focuses on the use of the dynamic ‘mode’ for unsaturated soils studies. Examples are presented on the hydraulic and structural response of kaolin and silica microspheres to cycles of relative humidity at constant temperature. Qualitative observations were made throughout the cycles and focused on the particle level phenomena (e.g., meniscus shape) and mesoscale phenomena (e.g., particle re-arrangements and emptying and filling of pores). Some quantification was also possible: the contact angle between the air-water and water-solid interfaces was measured. Other applications of the ESEM technique to unsaturated soils and limitations are discussed.
1
INTRODUCTION
The Environmental Scanning Electron Microscope (ESEM) allows hydrated samples to be observed in their original state, unlike the conventional Scanning Electron Microscope (SEM) where samples dry during observation. The ESEM, therefore, provides an essential tool for the study of unsaturated soils, since the arrangements of water within the soil can be observed. ESEM imaging has normally been done in static ‘mode’, under constant relative humidity and constant temperature (i.e. under a constant total suction), to observe a specimen in that particular state. However, it is also possible to use the ESEM in a dynamic ‘mode’ to observe a sample response to changes of relative humidity and/or temperature (i.e. to a change of total suction). This allows the possibility of using the ESEM for ‘‘testing’’ rather than just ‘‘observing’’. Dynamic testing can be carried out in situ,
i.e. without removing the sample from the microscope chamber. There is a need to start developing techniques for ‘‘testing’’ at particle level. The particular techniques to be used will depend on: • the accuracy required: whether measurements (quantitative) or estimations (qualitative) are obtained • the parameter to be measured: stress, strain, suction, water content • particle size scale: mm (sand) to μm (clay) • number of particles to be tested: single particle to particle contact or group of particles. This paper investigates the use of ESEM for unsaturated soil testing. It focuses on dynamic tests where relative humidity is changed at constant temperature in order to change the value of total suction imposed on the sample. Examples are presented for kaolin as well as for samples made of artificial microspheres (around
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6 μm diameter) and the limitations of the technique are also discussed. 2
PREVIOUS WORK
A range of visualisation techniques have been used to study the fabric of unsaturated soils. These include optical microscopy and video methods, X-ray computed tomography (CT), scanning electron microscopy and more recently environmental scanning electron microscopy. Cho and Santamarina (2001) studied samples made of 1.6 mm glass beads and observed the meniscus strain at failure for different rupture modes (shear, extension and rotation). Tests were conducted at the particle-to-particle level by using optical microscopy. Strain was measured directly from the images while water content was estimated for cubic packing. Reinson et al. (2005) observed the drying process of 12 mm glass beads to determine the unsaturated hydraulic conductivity and the soil water retention curve. Observations were made by digital videography in grouped glass beads to capture the meniscus formation and to track the movement of a dye tracer. Suction was estimated by using the Laplace equation based on the observations for a cubic packing arrangement. Computed tomography was used by Wong and Wibowo (2000) to estimate the 3D spatial distribution of porosity, air and water saturation during water flow in a silty sand soil column. Wildenschild et al. (2002) showed that the air-water interfaces in sands could be observed by CT while Cnudde et al. (2006) reviewed the potential to use CT in geo-disciplines. The conventional SEM uses high vacuum to obtain good resolution images. As a result, imaging of wet samples is not possible and special sample preparation procedures are needed. In unsaturated soils, the SEM has traditionally been used for fabric studies, mostly to observe the orientation and packing of particles (e.g. Delage and Lefebvre, 1984; Gasparre et al., 2007). The conventional SEM was later improved to the Environmental SEM, which permits observation of hydrated samples in their original state (e.g. Donald, 2003; Redwood et al., 2005). This increased versatility allowed application of the ESEM to various research fields including, for example, the study of colloids (e.g. Donald et al., 2000). In rock and soil mechanics, the studies conducted so far using the ESEM have focused on: wettability of reservoir rocks in petroleum engineering (e.g. Combes et al., 1998; Buckman et al., 2000; Skauge et al., 2006); hydraulic behaviour of mine marls (Sorgi and De Gennaro, 2006; Sorgi and De Gennaro, 2007); hydration of geopolymer concrete (Zhang et al., 2005). In unsaturated soils, the ESEM was used in the static ‘mode’ to observe the structure of bentonites by Musso et al. (2003), Baker
et al. (1995) and Agus and Schanz (2005). Montes-H. (2004) and Montes-H. et al. (2005) seem to have been the first to use the ESEM for dynamic studies in unsaturated soils. They imposed wetting-drying cycles on bentonite MX80 aggregates while monitoring the structural changes and volume variations. The swelling-shrinkage was measured by a coupled digital image analysis program. Due to the aggregated nature of the material the scale of observation was relatively large (20 μm) and the study was conducted more at a mesoscale rather than at a microscale. Regarding the fabric changes, it was possible to observe cracking and swelling of the aggregates and to quantify the swellingshrinking potential by measuring volume changes. The authors, however, do not report any details about the water menisci, which are present at the interparticle contacts. 3
ESEM WORKING PRINCIPLE
The conventional SEM works by emitting an electron beam towards a conductive sample in high vacuum conditions. Secondary electrons are released from the sample, collected by a detector and amplified to produce an image. The conductive coating of the sample (usually made of gold) improves the image quality and the vacuum ensures the effective operation of the electron gun. In the presence of water vapour inside the microscope chamber, the emitted secondary electrons collide with the water molecules generating positive ions that are directed towards the sample. This causes overcharging of the sample surface and the consequent loss of image quality. In the ESEM a high vacuum condition is ensured only in a limited zone surrounding the electron gun while the relative humidity around the sample stays relatively high. This working mode ensures imaging of hydrated samples in their natural state. Further details about the physical principles governing the operation of the ESEM can be found in Donald (2003) and Stokes (2003). The ESEM is able to induce changes of relative humidity, i.e. water condensation in the sample or evaporation from the sample, by controlling the values of water vapour pressure and temperature. The temperature is controlled by means of a Peltier cooling stage, which can impose temperatures up to 20◦ C (however temperatures are usually kept at low values between 2◦ C and 6◦ C during tests) while the value of vapour pressures can be increased up to 2.339 kPa. The control of relative humidity (RH) inside the microscope chamber is based on the phase diagram of water. Fig. 1 shows the boundary of this diagram separating the region in which vapour pressure at equilibrium is saturated (RH = 100%) from the region where vapour pressure at equilibrium is not saturated (RH < 100%).
146
water vapour pressure (kPa)
2.5 2 1.5
liquid
evaporation 0.5 saturation vapour pressure - 100% RH
0 0
Figure 1.
4
vapour
1 condensation
5
10 15 temperature (degC)
20
Phase diagram of water.
DYNAMIC TESTING OF UNSATURATED SOILS BY ESEM
As discussed previously, changes in the relative humidity of the pore air can be induced by changing both temperature and water vapour pressure. However, when testing soils, it is preferable to keep the temperature constant and change the water vapour pressure because many soils exhibit a temperature dependent behaviour (e.g. bentonites). 4.1
Examples of tests
Dynamic experiments relevant to unsaturated soils conducted in a FEI XL-30 model have been performed as follows: 1. Clay aggregates under changes of RH Dry Speswhite kaolin was placed in the ESEM chamber in dry conditions and subjected to an increase of relative humidity from 93% to 96% at a constant temperature of 5◦ C. The sequence in Fig. 2 shows an aggregate composed of clay platelets being enclosed in a water film as relative humidity increased from 93% to 96%. In Fig. 2c the clay platelets can still be seen through the water film. Note that both Figs. 2b and 2c refer to the same imposed relative humidity of 96%. The differences between these two images are therefore attributable to the fact that in Fig. 2b equilibrium had not yet been achieved under the imposed value of relative humidity. 2. Microspheres (6 μm) under changes of RH Fig. 3 shows a wetting sequence of three silica microspheres (6 μm diameter) subjected to an increase of relative humidity from 80.1% to 82.3% at a constant temperature of 5◦ C. The water phase is neatly distinguished from the spheres, including the shape of the menisci (concave)
Figure 2. ESEM micrographs of kaolin aggregates at increasing RH.
and its radius. As relative humidity increases the meniscus curvature decreases from a concave shape but without becoming convex (Fig. 3a to Fig. 3b) until it ‘‘bursts’’ in Fig. 3c. Contact angles between the water-solid interface and the air-water interface can be measured directly and are in the range 20◦ –30◦ . Again, the differences between Figs. 3b and 3c (both at the same value of relative humidity) are due to the fact that these figures refer to two different instants in time during the transient phase. 3. Fabric deformation under changes of RH
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Figure 4. ESEM micrographs of silica spheres after a wetting-drying sequence. Arrows in (b) indicate displacement of the spheres.
Figure 3. ESEM micrographs of silica spheres at increasing RH. The spheres, water menisci are identifiable and the contact angle (θ) measurable in (b).
Observations were carried out to detect displacements of the silica microspheres during cycles of relative humidity. All tests were carried out at a temperature of 5◦ C. The sequence in Fig. 4 shows interparticle movements occurring as the microspheres were submitted to the wetting-drying cycle. Distances and directions of movements are measurable and are indicated in Fig. 4b (for the case of the bottom spheres the movement was 90% corresponds about to 1.5% RH changes. These steps are rather coarse and evaporation or condensation can therefore occur too fast leading to a loss of important information during the wetting/drying process. For fabric studies, care must be taken due to different water vapour pressure and temperature conditions between the ESEM chamber and the room. Errors could lead to changes in the fabric as the sample is moved into the ESEM chamber. 5
CONCLUSIONS
This study has demonstrated the potential usefulness of the Environmental Scanning Electron Microscope (ESEM) for unsaturated soils. In the examples shown, water menisci are neatly distinguished from the solid surfaces and details such as the meniscus curvature and contact angle are easily traced and quantifiable. The ESEM allows observation of the effect of changes in total suction on the fabric of unsaturated soils. The ESEM has the capability of conducting dynamic experiments where the total suction imposed to the sample can be varied by changing the relative humidity and temperature inside the microscope chamber. The analysis of images from the ESEM allows the direct measurement of contact angle during wettingdrying cycles. Moreover, published studies have also shown that stress-strain testing inside the ESEM is possible. One limitation of ESEM is however the impossibility of obtaining direct measurements of water content inside the sample. Despite this, the potential of this technique for the study of the engineering behaviour of unsaturated soils is considerable. ACKNOWLEDGEMENTS The authors thank David Beamer (FEI Instruments), Helen Riggs (Durham University) and Dr Jim Buckman (Heriot-Watt University) for helping with the ESEM observations. This research is supported by the Engineering and Physical Sciences Research Council (UK) and Wykeham Farrance Ltd. The support from the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTN-CT-2004–506861 is also acknowledged.
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REFERENCES Agus, S.S., Schanz, T. (2005). Effect of shrinking and swelling on microstructures and fabric of a compacted bentonitesand mixture. Proc. Int. Conf. on Problematic Soils (2) 543550. Baker, J.C., Grabowska-Olszewska, B., Uwins, P.J.R. (1995). ESEM study of osmotic swelling of bentonite from Radzionkow (Poland). Applied Clay Science 9, 465–469. Buckman, J.O., Todd, A.C., Hill, P.I. (2000). Observations on a reservoir rock wettability using an environmental scanning electron microscope. Microscopy and Analysis 14, 2, 35–37. Cho, G.C., Santamarina, J.C. (2001), Unsaturated particulate materials— particle level studies. J. Geotech. Geoenv. Eng. 127, 1, 84–96. Cnudde, V., Masschaele, B., Dierick, M., Vlassenbroeck, J., Van Hoorebeke, L., Jacobs, P. (2006). Recent progress in X-ray CT as a geosciences tool. Applied Geochemistry 21, 5: 826–832. Combes, R., Robin, M., Blavier, G., Aidan, M., Degreve, F. (1998). Visualization of imbibition in porous media by environmental scanning electron microscopy: application to reservoir rocks. J. Petroleum Sc. and Eng. 20, 133–139. Donald, A.M., He, C., Royall, C.P., Sferrazza, M., Stelmashenko, N.A., Thiel, B.A. (2000). Applications of environmental scanning electron microscopy to colloidal aggregation and film formation. Colloids and Surfaces A: Physicochemical and Eng. Asp. 174, 37–53. Donald, A.M. (2003). The use of environmental scanning electron microscopy for imaging wet and insulating materials. Nature Materials 2, 511–516. Gasparre, A., Nishimura, S., Coop, M.R., Jardine, R.J. (2007). The influence of structure on the behaviour of London Clay. Geotechnique 57, 1, 19–31. Lampenscherf, S., Pompe, W., Wilkinson, D.S. (2000). Stress development due to capillary condensation in powder compacts: a two-dimensional model study. J. Am. Ceram. Soc., 83 6, 1333–1340. Montes-H., G. (2005). Swelling—shrinkage measurements of bentonite using coupled environmental scanning electron microscopy and digital image analysis. J. Colloid and Interface Sc. 284, 271–277. Montes-H., G., Geraud, Y., Duplay, J., Reuschle, T. (2005). ESEM observations of compacted bentonite submitted to hydration/dehydration conditions. Colloids and Surfaces A: Physicochem. Eng. Aspects 262, 14–22. Molenkamp, F., Nazemi, A.H. (2003). Interactions between two rough spheres, water bridge and water vapour. Geotechnique 53, No. 2, 255–264.
Musso, G., Morales, E.R., Gens, A., Castellanos, E. (2003). The role of structure in the chemically induced deformations of FEBEX bentonite. Applied Clay Sc. 23, 229–237. Redwood, P.S., Lead, J.R., Harrison, R.M., Jones, I.P., Stoll, S. (2005). Characterization of humic substances by environmental scanning electron microscopy. Env. Sc. and Tech. 39, 7, 1962–1966. Reinson, J.R., Fredlund, D.G., Wilson, G.W. (2005). Unsaturated flow in coarse porous media. Can. Geotech. J. 42, 252–262. Schenk, M., Futing, Reichelt, R. (1998). Direct visualization of the dynamic behavior of a water meniscus by scanning electron microscopy. J. App. Phys. 84, 9, 4880–4884. Skauge, A., Spildo, K., Hoiland, L., Vik, B. (2006). Theoretical and experimental evidence of different wettability classes. J. Petroleum Sc. and Eng. (in press). Sorgi, C., De Gennaro, V. (2006). Observations at the Environmental SEM of the water influence in the behaviour of marls. Proceedings Journ. Nat. de Geotech. et de Geol. de l’Ing., Lyon, France, pp. 9 (in French). Sorgi, C., De Gennaro, V. (2007). ESEM analysis of chalk microstructure submitted to hydromechanical loading. Comptes Rendus de l’Academie des Sciences—serie Geoscience (accepted) (in French). Stokes, D.J. (2003). Recent advances in electron imaging, image interpretation and applications: environmental scanning electron microscopy. Phil. Trans. R. Soc. Lond. A 361, 2771–2787. Stokes, D.J., Donald, A.M. (2000). In situ mechanical testing of dry and hydrated breadcrumb in the environmental scanning electron microscope (ESEM). J. Mat. Sc. 35, 599–607. Zhang, Y.S., Sun, W., Li, J.Z. (2005). Hydration process of interfacial transition in potassium polysialate (K-PSDS) geopolymer concrete. Mag. Concrete Res. 57, 1, 33–38. Weeks, B.L., DeYoreo, J.J. (2006). Dynamic meniscus growth at a scanning probe tip in contact with a gold substrate. J. Phys. Chem. B 110, 10231–10233. Wildenschild, D., Hopmans, J.W., Vaz, C.M.P., Rivers, M.L., Rikard, D. and Christensen, B.S.B. (2002). Using X-ray computed tomography in hydrology: systems, resolutions and limitations. J. Hydrology 267, 285–297. Wong, C.K., Wibowo, R. (2000). Tomographic evaluation of air and water flow patterns in soil column, Geotech. Test. J. GTODJ 23, 4, 413–422.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Recent advances in ESEM analysis of partially saturated geomaterials C. Sorgi INERIS, Verneuil-en-Halatte, France (now RATP, Paris, France)
V. De Gennaro Ecole des Ponts (Université Paris-Est, Navier Inst. – CERMES), Paris, France
H.D. Nguyen Ecole des Ponts (Université Paris-Est, Navier Inst. – CERMES), Paris, France INERIS, Verneuil-en-Halatte, France
P. Delalain INERIS, Verneuil-en-Halatte, France
ABSTRACT: The Environmental Scanning Electron Microscope (ESEM) allows the observation of microstructural changes of geomaterials in their natural state, under controlled conditions of temperature and pressure. Unlike the traditional Scanning Electron Microscopy (SEM), ESEM technology does not require any preliminary treatment of the observed samples (i.e. previous dehydration and eventually conductive coating) reducing possible procedure compliances. Although ESEM applications are nowadays recurrent in many research fields related to materials science, this investigation tool is still seldom used in geomechanics. In this paper we discuss some aspects associated with this technology when used for partially saturated geomaterials. Examples of applications on chalks are presented and some perspectives on the development of this instrument in relation with geomechanical applications are discussed.
1
INTRODUCTION
It is now well recognized that the characterization of a geomaterial’s microstructure and the analysis of its evolution under the effect of applied loadings and/or environmental conditions can provide valuable information for the interpretation and the prediction of mechanical behaviour. The objective of this paper is to present some recent developments and examples of application of the Environmental Scanning Electron Microscope (ESEM) for the study of the microstructure of geomaterials and its relationship with the macroscopic behaviour. So far the observation and the microstructural analysis of geomaterials have been conducted successfully with the Scanning Electron Microscope (SEM); a synthesis of the results obtained in this area of investigation has been presented recently by Mitchell & Soga (2005). Undoubtedly attractive, this technique however requires a preliminary preparation of the samples, submitted to high vacuum during the observation, consisting of dehydration and gold coating to improve the interaction between the electrons and the matter. Sample preparation procedure may have a major impact on
the structure of the material, particularly in clays, for which the dehydration process can harm the integrity of the initial microstructure of the soil sample and lead to important modifications because of shrinking due to drying (e.g. Tessier & Berrier 1978, Delage et al. 1982). Also, this situation prevents the observation of materials at their natural moisture content. In order to demonstrate the potential of the ESEM to investigate behaviour of geomaterials we will focus our investigation on a chalk from the shallow mine of Estreux, located near Valenciennes (France, North department). This chalk is the object of an ongoing research programme conducted by INERIS, devoted to the study of water-rock interaction mechanisms and ageing processes in geomaterials, in relation to the risk assessment of sudden collapses and subsidence originated by the breakdown of shallow abandoned mines. 2
MATERIAL CHARACTERISATION
Under the effect of environmental agents (e.g. temperature, pressure) microstructural evolutions in
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geomaterials often occur. These evolutions can affect the integrity of the solid skeleton and eventually change the mechanical behaviour of the material at the macroscopic scale. The result of these microscopic processes is often identified with the progressive ‘‘ageing’’ of the microstructure and is mainly related to the interaction between the solid skeleton and the fluids which saturate partially or completely the porous network. The intrinsically dynamic nature of these processes is at odds with the static character of SEM imaging. It is thus clear the interest that ESEM can present, allowing observation of samples in their natural state (i.e. saturated, partially saturated or dry) and under variable environmental conditions (temperature, pressure, moisture content), by letting the vapour reside inside the observation chamber (Danilatos 1998). Some phenomena observed during wetting and drying processes in chalk are presented herein.
100 Hr = 83.5% ( s = 24.9 MPa)
10
SUCTION, s :MPa
Hr = 98.2% ( s = 2.5 MPa)
1 Hr = 99.8% ( s = 1.5 MPa)
0.1
Dry path Wetting path Initial state
0.01
0.001 0
Figure 1.
2.1
Hr = 97% ( s = 4.2 MPa)
0.2
0.4 0.6 DEGREE OF SATURATION, Srw
0.8
1
Water retention curve of Estreux chalk.
Physical properties of Estreux chalk
The chalk used in this work originates from the Estreux abandoned underground mine in Northern France. The mine is located 15 km East of Valenciennes (France). Estreux chalk is a gluconite rich chalk. Glauconite is an allumino-silicate of iron, potassium and sodium. Its mineral composition is close to the illite, although glauconite is not hydrated, with the additional presence of sodium and strong isomorphism by substitution of aluminium atoms with Fe2+ and Fe3+ iron atoms (Amouric 1990). Glauconite is often present in chalk deposits in northern France (Masson 1973). The porosity of Estreux chalk is of about 37%, its specific gravity is Gs = 2.74 and the average water content is equal to 20.7% when the rock is water saturated. At microstructural level the solid matrix is made up of small micrometric grains which are principally fragments of coccolithes. Sometimes intact coccolithes also occur. The chalk is then principally made up of calcite (i.e. calcium carbonate CaCO3 ), which often constitutes also the cementing agent at the intergranular contacts. Microfossils and mineral impurities are also frequently observed.
the atmospheric pressure pa ) and the water pressure pw , as st = pa − pw = −
ρw pv RT ln Mv pvs
(1)
where ρw is the water density, Mv the molar mass of the water vapour, R the universal constant of an ideal gas (8.314 Jmol−1 K−1 ), T the absolute temperature, pv the vapour pressure and pvs the pressure of the saturating vapour at temperature T (hr = pv /pvs ). It is well known that any change in total suction induces a change in the degree of water saturation Srw as quantified via the Water Retention Curve (WRC) of the material. The WRC of Estreux chalk is presented in Figure 1 (De Gennaro et al. 2006). As can be observed, important changes in Srw occur when suction varies between 1 and 2 MPa, causing nearly complete material desaturation. This occurs when the corresponding relative humidity reduces from 100% to 98.2%. Since similar changes of hr are possible in the underground mine, the relative humidity may have a significant effect on the state of saturation of the material.
2.2 Retention properties of Estreux chalk Estreux chalk samples were completely saturated when extracted; mine temperature was 11◦ C and the relative humidity hr ∼ = 100% (owing to the 2% accuracy of the hygrometry resistive sensors). It should be noted that relative humidity inside the mine can vary seasonally between 80% and 100% (Sorgi 2004). Based on Kelvin’s law, the change in relative humidity modifies the total air-water suction st , the difference between the water vapour pressure (assumed equal to
3
ESEM ANALYSIS
Changes in Srw can be reproduced with the ESEM controlling sample temperature and pressure following the state diagram of water (Fig. 2), being simultaneously correlated to the corresponding microstructural evolutions. A further step of the analysis consists of the investigation of the microstructure while the material is
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hr = 100% 95 % 85%
1400 LIQUID
PRESSURE (Pa)
1200 1000
60%
A≡D
800
50%
600 B 400 C
200
GAS
0 0
2
4
6
8
10
12
14
TEMPERATURE (°C)
Figure 2.
State diagram of water.
subjected to a micromechanical loading under constant or variable relative humidity by means of ESEM micromechanical in situ tests. In this study a FEI Quanta 400® ESEM equipped with a Deben® microtesting facility has been used as a tool for the microstructural and micromechanical characterization of chalk. Three types of observations are presented: (i) the observation of changes in microstructure under wetting, (ii) the observation of samples submitted to saturation/desaturation cycles starting from their natural state of saturation and (iii) the observation of samples submitted to unconfined compression microtests under variable states of water saturation.
(a)
3.1 Sample preparation Samples were extracted from available blocks of Estreux chalk retrieved from the underground mine, sealed and stored in a thermo regulated chamber. This ensured the preservation of in situ conditions in terms of water content and saturation. Observations (i) and (ii) were conducted on chalk plugs having a square section (about 10 mm side) and a thickness varying from 2 mm to 4 mm. Samples were fixed on the observation stage by means of carbon conductive glue. The small plug thickness allowed for a uniform temperature distribution within the sample. Temperature was controlled using a thermo-electric cooler (Peltier’s effect). The corresponding value of the pressure in the observation chamber was used to define the level of hygrometry hr based on the state diagram of water (Fig. 1). 3.2
Microstructural changes under wetting
The changes in microstructure under wetting when passing from hr = 97% (chalk in its natural state at sampling with w = 20.7%) to hr = 100% are observed by comparing Figures 3a and 3b. A reference network has been superimposed on the micrograph and
(b) Figure 3. Modifications of the porous network in chalk during wetting: (a) initial state, (b) intermediate state before complete saturation.
the boundary of one characteristic pore has been plotted. Since the condition in the chamber corresponds to hr = 100% (p = 705 Pa, T = 2◦ C), hydration takes place as time passes. In Figure 3b, the same pore is visualised after the in-situ hydration. As can be seen, hydration produces a progressive enlargement of the pore boundaries due probably, but not exclusively, to the loss of capillary bridges between the grains. Progressive saturation of smaller pores is also observed on the left side of the photo in Fig. 3b. This observation still remains rather qualitative, though it provides a qualitative picture of the ongoing phenomena. It should be emphasized that
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(a) 1st wetting
(b) 1st drying
(c) 2nd wetting (start)
(d) 2nd wetting (end)
Figure 4. (a) & (b) fracture opening in chalk specimen during drying; (c) & (d) fracture closing following the second saturation.
pore enlargements are certainly amplified by the specific condition reproduced in the ESEM environment, namely the absence of any external loading and the observation of the external surface of the sample. It is expected that the extent of this phenomenon could reduce for the inner (invisible) pores. 3.3
Saturation-desaturation cycles with ESEM
A series of tests was carried out on samples submitted to saturation-desaturation cycles following the path indicated in Figure 2. During these tests a constant temperature condition was chosen (T = 2◦ C). Relative humidity was modified changing the level
of vacuum inside the chamber between 705 Pa and 346 Pa, corresponding to an hr varying between 100% et 50% (path A-B-C-D Fig. 2). Observations were conducted at 1500 magnification starting from the saturated state (i.e. hr = 100%). During the pressure changes images were captured every 2 minutes and later mounted as a video clip. The observed zone was characterised by the presence of a rigid inclusion (crystal) embedded in the chalk porous matrix (Fig. 4a). The analysed cycles included: Phase 1: saturation & stabilization; sample was left 90 minutes at T = 2◦ C and p = 705 Pa, hence hr = 100% (Fig. 2). The reference image is captured after 90 minutes of elapsed time.
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3.4 Micromechanical in situ testing The combined use of the ESEM technique and a micromechanical testing apparatus was investigated by means of unconfined compression tests. A loading module Deben MICROTEST® allowed the application of a maximum compression load of 5000 N at a constant strain rate of 1 × 10−5 s−1 . A specific set up was developed to carry out micromechanical tests under controlled total suction (i.e. controlling the level of relative humidity during the tests). Cylindrical samples approx. 8 mm in diameter and 15 mm in height were used. Samples were obtained by means of highprecision coring. Upper and lower base parallelism was ensured by means of a high-precision slicer having the accuracy of the order of 1 μm. A first series of preliminary micromechanical tests was conducted on samples saturated, partially saturated and dry in order to verify the agreement between the micromechanical
12 DRY CHALK 10
UCS (MPa)
Phase 2: desaturation; pressure is decreased instantaneously down to 599 Pa (hr = 85%, path A-B-C in Fig. 2). Sample is left to stabilize during 60 minutes. Phase 3: 2nd saturation; the pressure inside the chamber is increased up to 705 Pa (Fig. 2, path CD) and sample is left to stabilize during 60 minutes at hr = 100%. During the first phase of saturation (Phase 1) the initial condition corresponding to full water saturation was reproduced inside the samples (Fig. 4a). The successive drying process (Phase 2) induced a fracture opening at the contact between the crystal and the chalk matrix (indicated by an arrow in Fig. 4b). The presence of this fracture wasn’t observed at the beginning of the test (Fig. 4a). This phenomenon seems to be associated with the changes in suction induced by wetting and drying cycles, admitting that capillary effects could be at the origin of this microstructural modification (swelling/shrinkage of the material). In other words, wetting would have brought to fracture closing whereas drying caused chalk matrix shrinkage around the crystal inducing fracture opening. Fracture opening could then be the consequence of increasing capillary bridges (hence air-water interfaces) inside the chalk matrix during drying. In opposition to this mechanism, wetting decreased the number of air-water menisci between the chalk matrix and the crystal leading to a progressive fracture seal (Figs. 4c, 4d). If related to material ageing, the evolution of this phenomenon with time following consecutive wetting and drying cycles could help in assessing the microstructral feature associated with material degradation. This type of observation could also be assisted by advanced techniques of 2D and 3D image analysis, allowing for a more quantitative characterisation of the morphological modifications induced by changes in water saturation (e.g. Sorgi & De Gennaro 2007).
8 6 PARTIALLY SATURATED CHALK (s = 4.2 MPa)
4 2
SATURATED CHALK
0 0
1 2 AXIAL STRAIN (%)
3
Figure 5. ESEM in situ unconfined compression tests on dry and water saturated chalk.
test results and the laboratory test results performed on samples having standard dimensions. Preliminary results of unconfined compression microtests are presented in Figure 5 which indicates tests results on dry samples to show good reproducibility. The linear slopes of the compression curves (eventually after a first tightening phase) allow the quantification of the Young’s modulus at various states of saturation. It is worth noting that the Young’s modulus for dry chalk was Edry = 1.1 GPa, as compared with that of saturated chalk Esat = 0.71 GPa. The ratio Edry /Esat = 1.6 is the same obtained from other researchers by means of standard laboratory unconfined compression tests (e.g. Raffoux & Ervel 1980). At a suction level so = 4.2 MPa the value of Young’s modulus Eo is between Edry and Esat ; a value of 0.78 GPa. Concerning material strength, the comparison between the Unconfined Compression Strength (UCS) values obtained at saturated and dry states gives a ratio UCSdry /UCSsat ∼ = 2 in agreement with available data on North French chalk (e.g. Bonvallet 1979). Results from the sample tested under constant suction equal to 4.2 MPa (i.e. Sr ∼ = 97%, Fig. 1) show that higher suction levels strengthen the rock by means of additional bonding due to capillary effects. This seems in good agreement with the general pattern of behaviour observed for this chalk in oedometric compression tests under controlled suction conditions (Nguyen et al. 2007). Also of note is that Nguyen et al. (2007) also found a ratio of 2.1 between the yield stress in dry and saturated conditions, close to the ratio UCSdry /UCSsat ∼ = 2 found during ESEM micro-testing. Also, the ratios between the yield stress at a suction level of 4.2 MPa and that at saturated
155
3
2.5
UCS (MPa)
2
1.5
1
0.5
0
Figure 6.
0
0.5
1 1.5 AXIAL STRAIN (%)
2
Failure pattern during ESEM in situ unconfined compression test on water saturated chalk.
and dry state were 1.5 and 0.7, respectively. Similar ratios obtained by micromechanical testing using ESEM were equal to 1.5 and 0.75, showing a notable agreement with the oedometric tests results. Finally, Figure 6 shows some preliminary results of ESEM in situ testing with simultaneous visualisation of the deformation pattern and the failure mode. The direction of compression is vertical, as indicated on the ESEM image (A). At peak strength (image B) the sample surface is still apparently unchanged. At about 0.9% axial strain, in the softening regime, a pseudovertical fracture is visible (image C) followed by a progressive opening in the post-peak phase (images D and E). The aim of these preliminary tests was to explore the possibility to have a characterisation of the local strain field during hydro-mechanical loading using ESEM. Some possible developments like Digital Image Correlation (DIC) technique (e.g. Vales et al. 2007) could be envisaged to aid a quantitative characterisation of the local deformation at microstructural (few hundreds μm) and mesostructural (some mm) levels.
4
2.5
CONCLUSIONS
In this paper some basic applications of the ESEM for the microstructural characterisation of partially saturated geomaterials have been presented. The ESEM allows the observation of microstructural changes of geomaterials in their natural state, under controlled conditions of temperature and pressure. Change in saturation can be easily reproduced in
the observation chamber by means of a thermo-electric cooler based on the Peltier’s effect. This allows for an analysis of the microstructural modifications induced by the saturation/desaturation cycles in the absence of mechanical loading. Suction controlled in situ tests are also possible. The validation of a specific experimental technique is in progress. Further developments are needed to characterize quantitatively the effects of the mechanical and physico-chemical processes associated with the waterrock interaction. In the specific case of the carbonated rocks these developments could improve characterization of some fundamental processes like dissolution, precipitation, crystallization and solid transport under stress, often at the origin of the degradation mechanisms of the rock under the effect of environmental and mechanical agents. ACKNOWLEDGEMENTS The results on Estreux chalk have been obtained during the French National Project BCRD coordinated by INERIS. The collaborations of Mr. P. Delalain (INERIS) and Mr. J.M. Taulemesse (Ecole des Mines d’Alès) are kindly acknowledged. REFERENCES Allais L., Bornert M., Bretheau T. & Caldemaison D. 1994. Experimental characterization of the local strain field in a heterogeneous elastoplastic material. Acta Metallurgica et Materallia, 42 (11): 3865–3880.
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Amouric M. 1990. La transformation gel—smectite— glauconite. Matériaux Agileux: Structure, Propriétés et Applications—SFMC (A. Decarreau, editor): 451 461 Danilatos G.D. 1998. Foundations of environmental scanning electron microscopy, Advances in Electronics and electron physics, 71: 109–250. De Gennaro V., Sorgi C. & Delage P. 2006. Water retention properties of a mine chalk. Proc. 4th International Conference on Unsaturated Soils (UNSAT 2006), Phoenix (USA): 1371–1381. Delage P., Tessier D. & Marcel-Audiguier M. 1982. Use of the Cryoscan apparatus for observation of freeze-fractured planes of a sensitive Quebec clay in scanning electron microscopy. Canadian Geotech. J., 19: 111–114. Masson M. 1973. Pétrophysique de la craie. Bulletin des Laboratoires des Ponts et Chaussées, Spécial V: 23–48. Mitchell J.K. & Soga K. 2005. Fundamentals of Soil Behavior, 3rd Edition, John Wiley & Sons, Hoboken, NJ: 577 pp. Nguyen H.D., De Gennaro V., Sorgi C. & Delage P. (2007). Retention and compressibility properties of a partially saturated quarry chalk. Proc. 1st European Conf. on Unsaturated Soils (E-UNSAT), Durham (UK). Raffoux, J.F. & Ervel, C., 1980. Stabilité générale de la carrière souterraine d’Estreux. Rapport CERCHAR, 8 pp.
Sorgi C. (2004). Contribution méthodologique et expérimentale à l’étude de la diminution de la résistance des massifs rocheux par veillissement. BCRD Rapport Final (2001–01111) INERIS-DRS: 132 pp. Sorgi C. & De Gennaro V. 2007. ESEM analysis of chalk microstructure submitted to hydromechanical loading. C.R. Géosciences 339: 468–481. Stockes D.J. & Donald A.M 2000. In situ mechanical testing of dry and hydrated breadcrumb in the environmental scanning electron microscope (ESEM). Journal of Materials Science, 35: 599–607. Tessier D. & Berrier J. 1978. Observation d’argiles hydratées en microscopie éléctronique à balayage. Importance et choix de la technique de preparation. Proc. 5th Int. Work.—Meet. on Soil Micromorphology: 117–135. Tovey D. & Wong K. 1973. The preparation of soils and other geological materials for the SEM. Proc. Int. Symp. on Soil Structure: 59–67. Valès F., Bornert M., Gharbi H., Nguyen Minh D. & Eytard J.C. 2007. Micromechanical investigations of the hydro-mechanical behaviour of argillite rocks by means of optical full field strain measurement and acoustic emission techniques. Proc. 11th ISRM Congress, Lisbon, July 2007: in press.
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Study of desiccation crack evolution using image analysis S. Costa & J. Kodikara Department of Civil Engineering, Monash University, Australia
N.I. Thusyanthan Schofield Centre, Department of Engineering, University of Cambridge, UK
ABSTRACT: Desiccation cracking can be heavily detrimental on the performance of clay soils in various engineering applications. Typical engineering applications include compacted clay barriers in waste containment, dam cores, canal liners and road pavements. The evolution of desiccation cracks has not been clearly understood and explained. A series of laboratory tests were conducted using Merri-Creek clay. The evolution of cracks was captured by automated digital photography. It was revealed that under the conditions tested, the cracks occurred sequentially subdividing the overall surface area into cells. The relationship between desiccation rate, average cell area, thickness of the specimen and crack initiation are examined and discussed.
1
INTRODUCTION
Clay soils undergo shrinkage cracking during desiccation. Cracks can be a major unwanted feature in a number of geoengineering applications as well as in some other disciplines. For instance, in geoengineering shrinkage cracking is significant in earth embankments, slopes, foundations and roads. In agricultural engineering, cracks can stimulate the water and solute flow through soil in irrigated land. Clay liners are commonly used for lining and covering waste landfills in geo-environmental engineering. Shrinkage cracks can highly compromise the primary function of these clay liners by promoting water and leachate migration. A substantial amount of research work has been conducted in materials engineering on this issue to study the glazing and thermal fracturing in ceramics (e.g. Chiu & Cima, 1993) and printing, painting & washing (e.g. Deegan et al. 1997). Despite the significance of cracking on these applications, the essential understanding of soil shrinkage crack evolution and propagation is still far from satisfactory. The majority of previous research has been qualitative and behavioural (Corte & Higashi 1960, Muller 1998, Kodikara et al. 2000). Many researchers have work on the final state of the cracking process (Morris et al. 1991, Konrad & Ayad 1997, Kodikara et al. 2000). Nahlawi and Kodikara (2006) presented results of cracking tests, where they measured the onset of the first crack, cracking water content and subsequent crack evolution. A similar study was undertaken by Lakshmikantha et al. (2006). In contrast, using time-lapse video technology, it was
possible to capture the complete process of shrinkage cracking in laboratory test specimens. Results are presented in image format as well as in video clips. These videos will be uploaded to a web link in near future.
2
LABORATORY CRACKING TESTS
Merri-Creek clay was used in the experiments. MerriCreek clay is found in Northeastern Melbourne. This very heavy and sticky grey to black clay soil has been used by other researchers (e.g., Chan et al. 2007) and its basic properties includes: LL = 74%, PL = 33%, PI = 41%, Linear shrinkage = 13%. The Merri-Creek clay used for the tests was processed for commercial use and contained a considerable amount of tiny plant roots. This clay is commonly used for construction of cricket pitches in Melbourne, including the Melbourne Cricket Ground. 2.1 Merri-Creek clay A series of tests were conducted with Merri-Creek clay. The unprocessed clay samples were lightly crushed using a rubber hammer and sieved through a 1.45 mm sieve. The plant roots were removed as much as possible for the soil samples. The initial moisture content of soil was determined using the oven drying method. The material that passed a 1.45 mm sieve was mixed with water to its liquid limit (74%), and stirred well until it attained a visibly homogeneous state. The prepared clay mixture was placed in a plastic tray, which was then placed into two polythene bags and was
159
sealed for moisture leakage. The tray was kept in a cool, damp place for 48 to 72 hours allowing the clay paste to gain adequate moisture homogenization. Circular glass containers of 140 mm diameter were used to make the specimens. An air vibrator was used while preparing the specimen in order to remove entrapped air. Then the glass container was placed on an electronic balance which was connected to a computer. This system automatically measured and stored the weight of the specimen every 30 minutes. Specimens were dried using flood lamps each of 500 watts. Four lamps were placed above, surrounding the specimen at a distance of 50 cm. A digital camera, which was operated by a computer, was positioned directly above the specimen. The camera was programmed to take photos at 30 second intervals and the data were automatically saved in the computer. The tests were conducted at varying lamp distances (35, 50 & 75 cm) as well as with varying specimen thicknesses (5, 10 & 20 mm). Although the tests were not performed in a temperature or humidity controlled environment, both surrounding temperature and relative humidity were reasonably constant at 50◦ C and 20% respectively owing to the constant heat emitted by lamps. 3
RESULTS
It is interesting to observe that all specimens produced predominantly sequential, orthogonal crack patterns (Figs 1 & 2), leading to subdivision of the crack area into smaller cells.
(a)
(c) Figure 2. Crack pattern for 35, 50 & 75 cm lamp distances (a, b & c respectively) for 20 mm thick specimen. Table 1.
(b)
(c) Figure 1. Crack patterns for 5, 10 & 20 mm thick specimens (a, b & c respectively) at 50 cm lamp distance.
Statistical features of clay specimens.
Lamp distance cm
Thickness of the specimen mm
Desiccation rate g/hr · cm2
Average cell area mm2
35
5 10 20 5 10 20 5 10 20
0.1939 0.0884 0.0574 0.1196 0.0420 0.0252 0.0677 0.0298 0.0220
224 217 296 113 326 481 134 294 362
50
75
(a)
(b)
For the clay cracking shown in Figures 1 & 2 the number of cracked cells and the average cell area are found to be dependent on the specimen thickness and the lamp distance (or the desiccation rate). As the thickness of the specimen increases, number of cracked cells decreases, in turn increasing the average cell area. Similarly, an increased desiccation rate (or decreased lamp distance) will result in an increase of number of cracked cells and a decrease in the average cell area. Some statistical features of cracked specimens are given in Table 1. An exceptional situation can be seen at 35 cm lamp distance, where for 5 mm thick specimen, the average cell area is larger than that for the 10 mm thickness. The desiccation rates for each test condition were computed on the basis of the automatic weight measurements during drying.
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4
DISCUSSION 3
3
4.1
8
8
The average cell area of the final crack pattern was dependent on the desiccation rate and the thickness of the specimen. It can be seen from Table 1, that the desiccation rate increases when the lamp distance decreases or the clay thickness decreases. In general, the higher the desiccation rate, the lower the average cell area. At higher desiccation rates, more cracks are needed to release the rapid increase of stress in the specimen, subsequently reducing the crack spacing and the size of the cells. With a low desiccation rate, the specimen has enough time to release the stress increment with a few slowly opening cracks.
10
4
10
5
2
2 1
6
1
9
(a)
4.3
3
3
7
Generally, the evolution and propagation of shrinkage cracks cannot be categorized as purely orthogonal or non-orthogonal patterns. The final state of the crack pattern is generally a mixture of orthogonal, non-orthogonal, simultaneous and sequential cracks (Kodikara et al. 2000). However, crack patterns in all the clay specimens contained almost all orthogonal, sequential cracks where subdivision was the dominant feature in propagation. Figure 3 highlights some of the main features of cracking process. Onset of cracking is dependent on tensile stress distribution was well as the flaw distribution within the material. As theorized by Kodikara and Choi (2006), the maximum stress is likely to occur at the middle of a layer or cracked cell, if cracks have already formed, otherwise predominantly uniform stress conditions might prevail, as applicable to initial cracking. However, the exact location of crack formation will depend on the existence of a flaw that can be propagated with the prevailing stress level at
7
8 10
8 4
10
5
4
5 2
2
6 9
1
6 9
(d)
Specimen thickness
Crack evolution
6 9
(b)
1
The decrease of the average cell area with reducing specimen thickness has been presented by several previous researchers (Nahlawi & Kodikara 2006, Lakshmikantha et al. 2006). The exceptional behaviour (noted in the previous section) of the 5 mm thick specimen at 35 cm lamp distance is being further investigated using thinner specimens. Kodikara et al. (2007) theorized that the spacing between cracks decreases when the specimen thickness decreases up to a certain critical thickness, below which the spacing between cracks becomes larger, increasing the area of the cells. It may be possible that this behaviour is relevant for interpreting the current experimental results, or it may be one-off result dependent on the specific conditions of testing.
4
5
(c)
4.2
7
7
Desiccation rate
3
3
7
7
8 10
8 4
10
2 1 (e)
4
5
5
2
6 1
9
6 9
(f)
Figure 3. Evolution and propagation of shrinkage cracks in 5 mm thick clay specimen at 75 cm lamp distance.
that location. Therefore, the initial cracking is generally associated with edge cracking, where the material can be weakly attached to the container. However, it is possible for several cracks to initiate simultaneously because the stress conditions are relatively uniform at the beginning. Thereafter, cracks can occur somewhere in the vicinity of the centre of a layer or cracked cell, although theoretically, the tensile stress development would likely to be a maximum at the centre. Numbers 1, 2, & 3 in Figure 3(a) refers to the onset of first three cracks respectively. Once a crack is open, it tends to spread in both directions until it intersects another crack or the boundary. It is hardly seen that two cracks meet at an angle of 120◦ to form one crack, or an existing crack bifurcates to form a 120◦ nucleation. This can be identified by following the crack no. 1, 2, 3, 4 & 5 in Figure 3(a) to (f). Crack no. 7 & 8 in Figures 3(c) & (d) are examples for subdivision. Instead of subdivision, only rarely do cracks appear to bifurcate to form new cracks. In Figure 3, crack no. 9 appears to bifurcate into two cracks. A certain few cracks appear to start from one point simultaneously and propagate in three directions making approximately 120◦ angles among them. Crack no. 6 in Figures 3(b) to (f) is an example of
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4.4
Percentage crack length / (%)
The distribution of cumulative crack length over the drying period illustrates a similar behaviour for specimens with same thickness at different lamp distances. Figure 4 shows the increase in crack length as a percentage of the final crack length for 5 mm thick specimens as the drying progressed. All the specimens were prepared at their liquid limit (74%). The specimen under highest desiccation rate (lamp distance = 35 cm) starts cracking first as expected. These results show that the average cracking water content (as determined from overall weight measurements) is also higher when the first crack occurred. However, the actual cracking water content may be different and was not measured in these tests. Once the cracks are initiated, they grow rapidly to the final state where the crack length becomes stabilized. When desiccation rate is low, cracks open up reasonably late, but continue to grow until the soil is almost fully dried. Using the photos taken at various time intervals, the frequency of crack initiation was analyzed within each hour. A typical distribution is shown in Figure 5. Almost all the cracks have opened up within the initial stage of drying. This distribution shows the likely distribution of flaws that were propagated at various moisture contents. In other words, it represents the flaw distribution with associated fracture stress given by the corresponding moisture content. This analysis
120.00
75cm
100.00
50cm
80.00 60.00
35cm
40.00 20.00 0.00 10
20
60
50
40
30
20
10
0 0
1
2
3
4
5
6
Time/(hr)
Figure 5. Number of cracks initiated during the first few hours of the drying of 5 mm thick specimen at 75 cm lamp distance.
Crack initiation
0
No. of cracks initiated within the hour
such a formation. However, closer examination of these crack formations reveals that these can very well be explained by the presence of certain flow orientations and the influence of stress relief caused by other already formed cracks. In this regard, the crack formation observed in these tests can be considered to form generally orthogonal patterns. This is very common when cracks propagate in subdivision, as a requirement of the prevailing stress regimes influenced by formed cracks. An example is shown in Figures 3(b) to (f) by crack no.10.
30
40
50
60
70
80
Water Content / (%)
Figure 4. Variation of percentage crack length with average water content of a 5 mm thick layer—the legend shows the lamp distance.
Figure 6. Displacement vectors of a cracked specimen generated using PIV analysis.
can be extended further to develop detailed flaw distributions as well as flaw orientations that are required for numerical modelling of crack evolution. 4.5 Strain analysis Particle Image Velocimetry (PIV) is becoming a powerful tool in the study of failure mechanisms and material failure parameters in geomechanics (White et al. 2003, Thusynathan et al. 2007). This paper presents some preliminary results of the application of this technique to study desiccation crack evolution. Figure 6 shows the displacement vectors of a cracked specimen of Merri-Creek clay analyzed using the PIV technique. The PIV image software developed at the University of Cambridge, UK (White, 2002, Take, 2003) was used here. It is clear that despite the large deformations cracked cells have experienced, it is possible to track their strains and displacements provided that additional texture is provided to the cracking surface. In this instance, fine white sand was randomly distributed on the clay surface at the beginning to provide sufficient textural properties for image tracking by the software.
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Cracks
Figure 7.
Cracks analyzed with PIV technique.
PIV can produce plots of strain contours which distinguish the strain localization prior to the crack initiation. For example, analysis focused on the initiation of a selected single crack in the specimen shown in Figure 7. Plots generated from a preliminary analysis are shown in figure 8a–c. Initially, soil was undergoing almost uniform strain over the entire region as shown in Figure 8a. Strain localization close to the top right and left corners of the region before the crack initiation can be seen in Figure 8b. The grayscale code on the right of the each figure refers to the value of strain in pixels as the images were not calibrated. In Figure 8c, the crack has already opened increasing the maximum strain from 1.8 to 18.
5
(a)
Cracks
(b)
CONCLUSION
This paper presents the results of laboratory cracking tests undertaken on a reactive clay. The evolution of crack patterns was studied using image analysis, and time-lapse videographs were produced giving a complete picture of crack evolution. Tensile stress distribution within the material and the flaw distribution govern the crack evolution. The spacing between cracks or the average cell area decreased the increasing of either the desiccation rate and (or) the specimen thickness. In line with previous observations on desiccation cracking, clay specimens cracked mainly orthogonally by sequential subdivision after the crack initiation, which was associated with some simultaneous cracking, influenced by flaw and tensile stress distributions. Preliminary analyses were undertaken using Particle Image Velocimetry (PIV) technique in order to capture the development of strain prior to crack initiation. This technique will further be used in future experiments for further studies.
ACKNOWLEDGEMENTS The support given by ARC Discovery Scheme is gratefully acknowledged. Thanks are also rendered to Drs White and Take and Cambridge University for providing PIV software.
Cracks
REFERENCES
(c)
Figure 8a–c. opening.
Plots of strain build-up around the crack
Chiu, R.C. and Cima, M.J. 1993. Drying of granular ceremic films: II, Drying stress and saturation uniformity. J. American Ceremic Society, 76(11), 2679–2777. Corte, A. and Higashi, A. 1960. Experimental research on desiccation crack in soil. U.S. Army Snow Ice and PermafrostResearch Establishment. Research report No.66. Corps of Engineers. USA.
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Deegan, R.D., Bakajin, O., Dupont, T.F., Huber, G., Negal, S.R. and Witten, T.A. 1997, Capillary flow the cause of ring stains from dried liquid drops, Nature, 389, 827–829. Chan, D., Kodikara, J.K., Ranjith, P.G. and Choi, X. 2007. Data analysis and laboratory investigation of the behaviour of pipes buried in reactive clay, 10th AustraliaNew Zealand Conference on Geomechanics, Brisbane, Australia. Kodikara, J.K., Barbour, S.L. and Fredlund, D.G., Choi, X. 2007, Theoretical analysis of desiccation cracking of a long soil layer, under review. Kodikara, J.K. and Choi, X. 2006. A simplified analytical model for desiccation cracking of clay layers in laboratory tests, Proceedings of UNSAT2006 Conference, Edited by G.A. Miller, C.E. Zapata, S.L. Houston and D.G. Fredlund, ASCE Geotechnical Special Publication, Unsaturated Soils Vol. 2, pp. 2558–2567. Kodikara, J.K., Barbour, S.L. and Fredlund, D.G. 2000. Desiccation cracking of soil layers, Proceedings of Asian Conference on Unsaturated Soils: From Theory to Practice, A. A. Balkema, pp. 693–698. Konrad, J-M. and Ayad, R. 1997. Desiccation of a sensitive clay: field experimental observations, Canadian Geotechnical Journal, 34, 929–942. Lakshmikantha, M.R., Prat, P.C. and Ladesma, A. 2006. An experimental study of cracking mechanisms in drying
soils, Proceedings of 5th International Conference on Environmental Geotechnics, Thomas Telford, London. Lee, S.L., Lo, K.W. and Lee, F.H. 1982. A Numerical model for crack propagation in soils, Proceedings of the International Conference on Finite Element Methods, Shanghai, China, pp. 412–418. Morris, P.H., Graham, J. and Williams, D.J. 1992. Cracking in drying soils, Canadian Geotechnical Journal, 29, 263–277. Muller, G. 1998. Experimental simulation of basalt columns, J. Volcanology and Geothermal Research, 86, 93–96. Nahlawi, H., and Kodikara, J.K. 2006. Laboratory experiments on desiccation cracking of thin soil layers, Journal of Geotechnical and Geological Engineering, GEGE2281, Springer Netherlands, Vol. 24, No. 6, pp. 1641–1664. Take, W.A. 2003. The influence of seasonal moisture cycles on clay slopes, PhD dissertation, University of Cambridge, UK. Thusyanthan, N.I., Take, W.A., Madabhushi, S.P.G. and Bolton, M.D. 2007. Crack initiation in clay observed in beam bending, Géotechnique, Vol. 57, No. 7, 581–594. White, D.J. 2002. An investigation into the behaviour of pressedin piles. PhD dissertation, University of Cambridge, UK. White, D.J., Take, W.A. & Bolton, M.D. 2003. Soil deformation measurement using particle image velocimetry (PIV) and photogrammetry, Géotechnique, 53, No. 7, 619–631.
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Theoretical analysis of the effect of temperature, cable length and double-impedance probe head on TDR water content measurement A. Tarantino & A. Pozzato Dipartimento di Ingegneria Meccanica e Strutturale, Università degli Studi di Trento, Italy
ABSTRACT: The TDR method for volumetric water content determination is based on the measurement of the soil apparent permittivity from travel time analysis of a reflection waveform. This is in turn related to water content through a calibration curve. Methods for travel time determination and calibration equations have been developed in the laboratory under conditions that often differ from those in the field, where longer cable are used and temperature fluctuations are significant. This paper presents a theoretical analysis of the effect of temperature, cable length, and double-impedance probe head on signal travel time. This is made by solving the transmission line equations in the frequency domain and by obtaining the time domain waveform by inverse Fast Fourier Transform. It is shown that multiple reflections associated with double-impedance probes may significant affect TDR travel time-based water content determination.
1
INTRODUCTION
Water content measurement in the laboratory and the field is a key to understanding the hydraulic and mechanical behaviour of unsaturated soils. The method based on Time Domain Reflectometry (TDR) may be considered as the most accurate and versatile technique. TDR measurement involves a fast rise-time step pulse generator, a coaxial cable, a two or three-rod probe inserted into the soil, and a sampling oscilloscope. The step pulse is launched into the transmission line, travels along the coaxial cable and probe rods. It is then reflected at the end of the rods and travels backward along the rods and coaxial cable. The time taken to the pulse to travel forth and back the probe rods depends on the volumetric water content of the soil but also on soil dry density, clay content, temperature, soil conductivity, cable length and rise-time of step pulse. Reviews of TDR technique for water content measurement can be found in O’ Connor & Dowding (1999), Gardner et al. (2001), Noborio (2001), Dane & Topp (2002), Jones et al. (2002), Robinson et al. (2003), Tarantino et al. (2008). Conventional interpretation of TDR measurement consists of determining the pulse travel time along the rods and relating it to the volumetric water content through a suitable calibration curve. This can be the Topp’s equation (Topp et al. 1980) or Ledieu’s equation (Ledieu et al. 1986) or a soil specific calibration curve. Conventional interpretation of TDR measurement lies on the assumption that travel time is only affected by volumetric water content and is independent of
other factors such as temperature, cable length. This assumption is clearly a source of error in water content measurement especially in the field, where long cable are often used and temperature fluctuations are significant particularly in surface installations. The paper presents a theoretical analysis to assess the effect of temperature and cable length on TDR signal travel time and, hence, on water content measurement. In addition, the effect of multiple reflections occurring at the probe head is analysed. Probe heads of current commercially available probes are formed by two series impedances which cause the waveform to first descend and then ascend when the signal travels along the probe head. This form of the wave at the interface between cable and soil is somehow different from the classical ‘single rising limb’ form (single-impedance head) reported in the literature (Heimovaara & Bouten 1990). A question that might be asked is whether the methods for travel time determination developed for single-impedance heads still hold for double-impedance heads. The theoretical analysis was carried out by solving the transmission line equations in the frequency domain and then obtaining the time domain waveform by inverse Fast Fourier Transform. Soil permittivity was represented by a four-component mixing model and free and bound water were assumed to have frequency-dependent complex dielectric permittivity. The cable was modelled by assuming that its permittivity is complex and frequency-dependent. The analysis is here limited to soils having pore water with low electrical conductivity and negligible
165
amount of bound water (soils having low cation exchange capacity). 2
SIMULATING TDR WAVEFORMS
2.1
Uniform transmission line
Let us consider an equivalent circuit for a uniform transmission line as shown in Figure 1. The line is terminated with an independent voltage source VS at z = 0 and a source impedance ZS and with a load impedance ZL at z = l (ZL = ∞ for the open-ended TDR probe). Electromagnetic wave propagation inside the uniform transmission line is described by the line current I and the voltage V between the conductors. If V and I are time-harmonic cosine functions with angular frequency ω and the symbolic representation of sinusoidal signal is adopted, the following transmission line equations can be obtained (Kraus & Fleisch 1999): ⎧ + −γ z+jωt + V0− eγ z+jωt ⎪ ⎨ V (t, z) = V0 e (1) V+ V− ⎪ ⎩ I (t, z) = 0 e−γ z+jωt − 0 eγ z+jωt Z Z where t is the time, z is the position along the line, and V + and V − are complex constants to be determined for given boundary conditions. The two complex terms in each equation denotes travelling waves in positive and negative direction respectively. The propagation constant, γ , and the characteristic impedance of the line, Z, are the two complex parameters governing the propagation of electromagnetic waves along the transmission line and can be expressed for the case of non-ferromagnetic materials as follows: γ =
jω ∗ εr ; c
Zp Z= √ ∗ εr
(2)
where c is the speed of an electromagnetic wave in free space (c = 3 · 108 m/s), εr∗ is the equivalent permittivity of the medium between the inner and outer conductor, and Zp the characteristic impedance in vacuum, which is only a function of the crosssectional geometry of the transmission line and can ZS Vs
+
+ V(0) Characteristic impedance, Z
z=0 Figure 1.
Uniform transmission line.
ZL
z=l
be assumed, as a first approximation, to be equal to the characteristic impedance in air. The boundary conditions for the uniform transmission line shown in Figure 1 can be written as follows: V (0) = VS − ZS I (0) (3) V (l) = ZL I (l) By combining the second of these boundary conditions with Equation 1, we can obtain the impedance that the oscilloscope sees at z = 0 (Kraus & Fleisch 1999): Z(0) = 2.2
V (0) ZL + Z tan h(γ l) =Z Z + ZL tan h(γ l) I (0)
(4)
TDR multi-section transmission line
The equivalent circuit for the TDR system is shown in Figure 2. It includes a multi-section transmission line consisting of a cable, a probe head split in two sub-sections, head 1 and head 2, and a probe. Each section of the transmission line is characterised by an impedance Z, a propagation constant γ , and a length l. The solution for the multi-section transmission line can be obtained by writing Equation 1 for each section of the line and by considering the continuity constraints at the discontinuities between the terminations of each section and by imposing the boundary conditions at z = 0 and z = l given by Equation 3. Rather than simultaneously solving Equation 1 for each section of the line, we will use the explicit procedure suggested by Lin (2003a, 2003b), which involves determining the input impedance at the end of the line and transforming the impedance successively to the subsequent discontinuity until the source is reached at z = 0: Z(4) = ZL Z(3) = Zprobe
Z(4) + Zprobe tan h(γprobe · lprobe ) Zprobe + Z(4) tan h(γprobe · lprobe )
Z(2) = Zhead2
Z(3) + Zhead2 tan h(γhead2 · lhead2 ) Zhead2 + Z(3) tan h(γhead2 · lhead2 )
Z(1) = Zhead1
Z(2) + Zhead1 tan h(γhead1 · lhead1 ) Zhead1 + Z(2) tan h(γhead1 · lhead1 )
Z(0) = Zcable
(5)
Z(1) + Zcable tan h(γcable · lcable ) Zcable + Z(1) tan h(γcable · lcable )
The impedance Z(0) obtained from Equation 5, which is the impedance that the oscilloscope sees at z = 0, controls the voltage V (0) in the frequency
166
suggested by Heimovaara (1994) and Jones & Or (2001), provided the input function was zero padded with the addition of a number of zero samples equal to 4 N/8 N. To verify that the FFT of the sampled input function after zero-padding was not affected by noise, we compared the discrete Fourier transform with the continuous Fourier transform of the input function obtained from the Fourier integral (Brigham 1974). The following expression for the input function in the frequency domain was derived:
Cable Head 1 Head 2 Probe ZS Z(0) Z(1) Z(2) Z(3) Z(4) Vs
+ Zcable V(0) γcable lcable
+
Zhead1 γhead1 lhead1
l1 z=0
Figure 2.
l2 z=z1
Zhead2 γhead2 lhead2
Zprobe γprobe lprobe
l3 z=z2
ZL
l4 z=z3
z=l
Multisection transmission line.
V
H( f ) = V0 V0
j −j2π f T e−j2π f t1 − e−j2π f t0 e + 2 (t1 − t0 )(2πf ) 2πf
(7)
where f is the frequency and V0 the voltage amplitude. t0
Figure 3.
Δt
t1
T
t
ΔT
3
Ideal input step function.
domain sampled by the oscilloscope at z = 0 (Lin 2003a, 2003b): V(0) = Vin +
Z(0) − ZS · Vin Z(0) + ZS
(6)
where Vin is the incident waveform in the frequency domain (Vin = Vs /2). 2.3
Numerical modelling of TDR reflection waveform
According to Lin (2003a, 2003b), the TDR waveform can be obtained by standard spectra analysis that involves (i) transforming the incident step input in the frequency domain to determine Vin ; (ii) determining the frequency response of the output V (0) using Equations 5 and 6 and (iii) transforming the frequency response back into the time domain. The Fourier and Inverse Fourier Transforms were performed using the Fast Fourier Transform (FFT) and inverse FFT (IFFT) algorithm. Appropriate zero padding and suitable window size were selected. 2.4
Input function
We considered the ideal input step function shown in Figure 3, where T = T − t0 is the pulse length and t = t1 − t0 is the pulse rise time ( t = 200 ps). We assumed that the pulse length T is finite, with T greater than the time required for complete reflections of waves traveling forth and back the TDR probe. When transforming the sampled input function into the frequency domain by FFT, we found that it was not necessary to introduce any algorithm as earlier
TRANSMISSION LINE PARAMETERS
The propagation constant, γ , and the characteristic impedance, Z, are the parameters governing the signal propagation through each section of the line. According to Equation 2, these parameters depend on the dielectric permittivities of the media filling the sections of the transmission line. These permittivities are discussed in the following sections. 3.1 Soil permittivity The permittivity of the soil εm∗ was described by the four-component complex dielectric mixing model presented by Heimovaara et al. (1994): ρd √ ∗ εm∗ = εs + (θ − δρd As ) εfw ρs √ ρd ∗ + δρd As εbw + 1− −θ εa (8) ρs where εs and εa are the permittivities of soil solids ∗ ∗ and air respectively, εfw are the equivalent and εbw permittivities of free and bound water respectively, ρd is the bulk dry density of the soil, ρs is the average density of the solid phase, the product δρd As represents the volumetric bound water content, with As and δ being the specific surface of the soil and thickness of the bound water layer respectively. ∗ The equivalent permittivity of free water εfw was assumed to be described by a Debye-type equation (Hasted 1973): ∗ εfw = εfw,∞ +
167
−j
εfw,s (N , T ) − εfw,∞ 1 + j ffw,relf(N ,T )
σfw,dc (N , T ) 2πf ε0
(9)
Table 1. Debye parameters for free water at N = 0.05 (moderately saline water). T (◦ C)
σfw,dc (S/m)
εfw,s –
ffw,rel (GHz)
εfw,∞ –
0 20 40
0.28 0.47 0.69
86.8 79.2 72.3
9.0 17.1 27.5
4.2 4.2 4.2
where f is the frequency, ffw,rel is the relaxation frequency, εfw,s the static permittivity, εfw,∞ the permittivity at infinite frequency (refractive index), ε0 is the permittivity in free space, σfw,dc the direct current electric conductivity. The parameters εfw,s , ffw,rel , and σfw,dc depend on temperature T and normality N of the aqueous solution according to the relationships given by Stogryn (1971). Table 1 show the values of the free water dielectric parameters for three different temperatures T for the case of an aqueous solutions having N = 0.05 (moderately saline water). A similar Debye relationship was used to represent the equivalent permittivity of bound water. Since the relaxation frequency of bound water is well below the TDR bandwidth (Tarantino et al. 2008), the Debye ∗ permittivity of bound water εbw was simplified to: ∗ εbw = εbw,∞ − j
σbw,dc 2π f ε0
(10)
where εbw,∞ and σbw,dc were assumed to be temperature-independent. We assumed εbw,∞ = 5 and σbw,dc = 15 S/m according to Heimovaara et al. (1994). The permittivities of soil solids and air were assumed to be real and frequency independent (εs = 5, εa = 1). 3.2
Cable permittivity
The permittivity of the cable was modelled according to Lin & Tang (2007), who presented the following expressions for the propagation constant, γ , and the characteristic impedance, Z: j2π f √ αR εcable 1 + (1 − j) γcable = c f Zp,cable αR 1 + (1 − j) Zcable = √ εcable f
(11)
(12)
where εcable is the dielectric permittivity of the medium filling the cable assumed to be real and frequencyindependent, and the αR is the resistance loss factor
representing the combined effect of geometric factors and surface resistivity. We determined the parameters εcable , αR , and Zp,cable with reference to the cable RG58A/U connected to the TDR probes manufactured by Campbell Scientific. These parameters were determined by fitting the frequency-dependent nominal attenuation (dB/m), the nominal velocity of propagation, and the nominal impedance reported in the cable datasheet. We obtained αR = 130 sec−0.5 , εcable = 1.62, and Zp,cable = 63.6. 3.3 Head permittivity We assumed that the head permittivity was real and frequency-independent. For sake of simplicity, we assumed that the head permittivity was equal to the cable permittivity (εhead = 1.62). 4
EFFECT OF DOUBLE-IMPEDANCE PROBE HEAD
To investigate the effect of the double-impedance probe head, we considered different combinations of Zhead1 and Zhead2 (Table 2). For each impedance combination, we simulated the waveform in water, air, and soil at different volumetric water contents. The waveform in air and water was used to calibrate the probe according to Heimovaara (1993). The water content was then derived from travel time analysis using Ledieu’s calibration and compared with the theoretical value used to generate the waveform. To isolate the effect of multiple reflections occurring at the double-impedance head, we assumed that both cable and soils were non-dissipative (αR = 0, As = 0, σfw,dc = 0). The waveforms obtained by considering a single impedance probe head are reported in Figure 4(a) (combinations No. 1 and 2 in Table 2) whereas the waveforms obtained by considering a double-impedance probe head with different values of Zhead1 and Zhead2 are reported in Figure 4(b) (combinations No. 3 to 5 in Table 2). It can be observed that the waveform can change significantly if there is a high impedance mismatch between the two head sub-sections. Table 2. Combinations of impedances of probe head sub-sections. No.
Cable L(m)
Head1 L(m)
Zp()
Head2 L(m)
Zp()
1 2 3 4 5
0.08 0.08 0.07 0.07 0.07
– – 0.01 0.01 0.01
– – 28 6 6
0.02 0.02 0.02 0.02 0.02
57 285 57 171 57
168
0.7
0.5
0.6
No.1
0.5
No.2
0.4
0.3
'MEASURED'
reflection coefficient, ρ
0.4
0.2 0.1
(a)
0 0.1
0.3
0.2
combination No.1 No.2 No.3 No.4 No.5
0.2 0.3
0.1
0.4 0.5 9
10
11
12
13
14
15
16
0
t [ns]
0
0.5 0.4
No.3
0.3
No.4
reflection coefficient, ρ
0.2
0.3
0.4
0.5
IMPOSED
Figure 5. Comparison between ‘measured’ water content and water content used to generate the waveform for different combinations of head sub-section impedances.
No.5
0.2
0.1
0.1 0 0.1
0.4
(b)
0.2 0.3 0.4
0.6
'MEASURED'
0.5 ρd=1.5 g/cm3; ρs=2.65 g/cm3
0.7 0.8 9
10
11
12
13
14
15
16
0.3
t [ns]
cable length 1m
0.2 Figure 4. Waveforms in water. (a) single-impedance probe head; (b) double impedance probe head.
10 m 50 m
Finally, the ‘measured’ water content is compared with the water content used to generate the waveform (Fig. 5). For the two single-impedance combinations (No. 1 and 2), the ‘measured’ water contents are close to each other and close to the values used to generate the waveform. However, deviations from the ‘true’ water content may be significant for the case where the probe head has two sub-sections having high impedance mismatch. 5
0.1 0.1
0.3
0.4
IMPOSED
Figure 6. Comparison between ‘measured’ water content and water content used to generate the waveform for different cable length.
considering in Equation 11 an equivalent resistance loss factor αR∗ determined as follows:
EFFECT OF CABLE LENGTH
The effect of cable length on signal travel time was investigated by considering a dissipative cable (αR = 130 sec−0.5 ). We investigated the cable lengths lcable = 1, 10, and 50 m. The different cable lengths were simulated by con∗ sidering a single fictitious length lcable = 1 m and
0.2
αR∗ = αR
lcable ∗ lcable
(13)
This approach was adopted because the time domain window becomes extremely large for excessive cable length and the Fourier Inverse Transform becomes problematic.
169
Since the cables acts as a low-pass filter, the case of dissipative soil was considered. In particular, we assumed As = 66.7 m2 /g, ρd = 1.66 g/cm3 , ρs = 2.71 g/cm3 and the free water parameters corresponding to N = 0.05 and T = 20◦ C (Table 1). These values of As , ρd , ρs are those used to simulate the waveforms measured in the clayey silt reported by Pozzato et al. (Ibid.). For each cable length, the waveform in air and water was used to calibrate the probe according to Heimovaara (1993). The water content derived from travel time analysis using Ledieu’s calibration was then compared with the theoretical value used to generate the waveform. Results from this analysis are shown in Figure 6. It can be observed that for a soil moderately dispersive (σfw,dc ∼0.5 S/m), the effect of cable length is not significant. This may not be the case for pore-water with high electrical conductivity and significant amount of bound water (soils having high cation exchange capacity).
6
The effect of temperature was investigated by considering a non-dissipative cable, a zero-length probe head, and As = 0. In this way, the signal losses are only associated with electrical conductivity of free water. We considered three different temperatures (T = 0, 20, and 40◦ C) and a moderately saline pore-water (Table 1). The waveform in air and water at T = 20◦ C was used to calibrate the probe according to Heimovaara (1993). The water content was then derived from travel time analysis using Ledieu’s
'MEASURED'
0.4
0.3
temperature 0 °C 20 °C 40 °C
0.1 0.1
0.2
7
CONCLUSIONS
The paper has presented a theoretical analysis to investigate sources of error in TDR water content measurement. It has been shown that double impedance probes may considerably affect the measurement for the case where sub-section head impedances are significantly different. For non-dispersive soils characterised by porewater with low electrical conductivity and negligible amount of bound water (low cation exchange capacity), temperature and cable length do not appear to have significant effect. REFERENCES
EFFECT OF TEMPERATURE
0.2
calibration and compared with the theoretical value used to generate the waveform. Again, it can be observed (Fig. 7) that for a soil moderately dispersive (σfw,dc ∼0.5 S/m), the effect of temperature is not significant.
0.3
0.4
IMPOSED
Figure 7. Comparison between ‘measured’ water content and water content used to generate the waveform for different combinations of T and N .
Brigham, E.O. 1974. The fast Fourier transform. PrenticeHall, Inc., Englewood Cliffs, N.J. Dane, J.H. & Topp, G.C., eds. 2002. Methods of soil analysis. Part 4-Physical Methods. SSSA Books Ser. 5. SSSA Madison, WI, USA. Gardner, C.M.K., Robinson, D.A., Blyth, K. & Cooper, J.D. 2001. Soil water content measurement. In K. Smith & C. Mullins (eds), Soil and Environmental Analysis: Physical Methods (Second Edition): 1–64. Marcell Dekker, Inc., 270 Madison Ave, New York. Jones, S.B., Wraith, J.M. & Or, D. 2002. Time domain reflectometry measurement principles and applications. Hydrol. Process. 16: 141–153. Hasted, J.B. 1973. Aqueous dielectrics. London: Chapman and Hall. Heimovaara, T.J. 1993. Design of triple-wire time domain reflectometry probes in practice and theory. Soil Sci. Soc. Am. J. 57: 1410–1417. Heimovaara, T.J. 1994. Frequency domain analysis of TDR waveforms 1. Measurement of the complex dielectric permittivity of soils. Water Resources Research. 30(2): 189–199. Heimovaara, T.J. & Bouten, W. 1990. A computer-controlled 36 channel time domain reflectometry system for monitoring soil water contents. Water Resour. Res. 26: 2311–2316. Heimovaara, T.J., Bouten, W. & Verstraten, J.M. 1994. Frequency domain analysis of time domain reflectometry waveform. 2. A four-component complex dielectric mixing model for soils. Water Resour. Res. 30(2): 201–209. Jones, S.B. & Or, D. 2001. Frequency-Domain methods for extending TDr measurement range in saline soils. Symposium and Workshop on TDR for Innovative Geotechnical Applications. Available at http://www.iti.northwestern. Kraus, J.D. & Fleisch, D.A. 1999. Electromagnetics with applications. McGraw-Hill.
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Lin, C.P. 2003a. Analysis of nonuniform and dispersive time domain reflectometry measurement systems with application to the dielectric spectroscopy of soils. Water Resour. Res. 39 DOI:10.1029/2002 WR001418. Lin, C.P. 2003b. Frequency domain versus travel time analyses of TDR waveforms for soil moisture measurement. Soil Sci. Soc. Am. J. 67: 720–729. Lin, C.-P. & Tang, S.H. 2007. Comprehensive wave propagation model to improve TDR interpretation for geotechnical applications. Geotech. Testing J. 30(2): 90–97. Ledieu, J., De Ridder, P., De Clerck, P. & Dautrebande, S. 1986. A method of measuring soil moisture by time domain reflectometry. Journal of Hydrology. 88: 319–328. Noborio, K. 2001. Measurement of soil water content and electrical conductivity by TDR: a review. Computers and Electronics in Agriculture. 31: 213–237. O’ Connor, K.M. & Dowding, C.H. 1999. Geomeasurements by pulsing TDR cables and probes. CRC Press.
Pozzato, A., Tarantino, A., McCartney, J. & Zornberg, J. (Ibid). Effect of dry density on the relationship between water content and TDR-measured apparent dielectric permittivity in compacted clay. This conference. Robinson, D.A., Jones, S.B., Wraith, J.M., Or, D. & Friedman, S.P. 2003. A review of advances in dielectric and electrical conductivity measurement in soils using TDR. Vadose Zone Journal 2: 444–475. Stogryn, A. 1971. Equations for calculating the dielectric constant of saline water. IEEE Trans Microwave Theory Tech 19: 733–736. Tarantino, A., Ridley, A.M. & Toll, D.G. 2008. Field measurement of suction, water content, and water permeability. Geotechnical and Geological Engineering. In press. Topp, G.C., Davis, J.L. & Annan, A.P. 1980. Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resour. Res. 16: 574–582.
171
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Effect of dry density on the relationship between water content and TDR-measured apparent dielectric permittivity in compacted clay A. Pozzato & A. Tarantino Dipartimento di Ingegneria Meccanica e Strutturale, Università degli Studi di Trento, Italy
J. McCartney & J. Zornberg University of Texas, Austin, TX, US
ABSTRACT: The paper presents an experimental investigation of the effect of dry density on dielectric apparent permittivity. It was observed that the effect was not significant, but not negligible for sensitive applications. It is shown that the effect of dry density can be successfully modeled using a three-phase ‘refractive index’ model. It is also shown that Topp’s equation can accurately predict water content provided bulk electrical conductivity is accounted for.
1
INTRODUCTION
The volumetric water content, θV , is a key variable in unsaturated soil mechanics and needs to be measured both in the laboratory and the field. Time domain reflectometry (TDR) is a technique that can be successfully used for this purpose. This technique is based on the measurement of the dielectric permittivity of the soil, Ka , which is in turn related to the volumetric water content through a suitable calibration curve. An empirical calibration curve was presented by Topp et al. (1980) suggesting a unique relationship between Ka and θV . However this curve was developed for agriculture soils which have dry densities typically lower than compacted soils used in geotechnical engineering. The purpose of this study is to investigate the effects of dry density on the Ka − θV relationship.
To prepare the samples for calibration, dry soil was placed in a motorized mixer and sprayed with a predetermined amount of demineralised water while continuously mixing the soil. Samples were prepared at water contents ranging from 9.7% to 17.7%. The moistened soil was stored for at least two days to allow moisture equilibration. A PVC mold having a diameter of 103 mm was used to compact the soil. The soil was compacted in six layers 19.4 mm thick using a drop hammer to obtain
2.2
2
MATERIAL AND SPECIMEN PREPARATION
A low plasticity compacted clay (RMA soil) was selected for use in investigating the impact of density on the TDR calibration. The soil has a plastic limit wP = 0.12, liquid limit wL = 0.27 and hygroscopic water content wH = 0.02. The grain size distribution showed it to have 0.24 clay fraction, 0.36 silt fraction, and 0.4 sand. The specific gravity of the soil is 2.71, and the saturated hydraulic conductivity is about 5 ∗ 10−6 m/sec. The maximum dry density, ρd , obtained using the standard Proctor compaction effort is 1.9 g/cm3 , and the optimum water content, wC was 12.9% (McCartney 2007).
d
2
[gr/cm^3]
1.9 1.8
proctor standard compaction rd = 1.4 gr/cm3 rd = 1.5 gr/cm3 rd = 1.7 gr/cm3
ZAV
(S =
2.1
S= S=
S=
100
%)
70% 60%
50%
1.7 1.6
S=
40%
1.5
S= 1.4
30%
1.3 9
10
11
12
13
14
15
16
17
wC [%]
Figure 1. Samples prepared for TDR calibration (the standard Proctor compaction curve is shown for reference).
173
specimen 116.4 mm high. Each layer was compacted which a same target dry density. Three series of samples were prepared, each with a different dry density. The dry densities and the gravimetric water content of the samples used in the TDR measurements are shown in Figure 1. 3 3.1
cable
Voltage, mV
2400
1600 TRANSIT TIME
1200
400
TDR installations
Three types of measurements were performed; measurements in demineralised water and air, in layers of water and air, and in compacted soil. For measurement in soil, the TDR probe was inserted centrally into the cylindrical specimen still in the mould (Figure 2). For measurement in water and in layers of air and water, the probe was inserted centrally in a container of the same size as the mould. The measurements were performed in a temperature-controlled laboratory (22 ± 1◦ C).
w ave guide
soil
PVC cylinder
end of waveguide
start of waveguide
2000
800
Instrumentation
116.4 mm
2s
103 mm Figure 2.
reflections in cable tester
2800
EXPERIMENTAL PROCEDURE
The TDR system used in this study consists of an electromagnetic step pulse generator with a fast rise time, a time equivalent sampling oscilloscope, and a trifilar waveguide. A commercially available TDR system was used in this study (MiniTrase). The oscilloscope and the step pulse generator were incorporated into the MiniTrase (6050X3) and the waveforms were collected via serial port with the TraseTerm software. An uncoated, 8-cm buriable probe (Model 6111, Soil Moisture Equipment Corp., Santa Barbara, CA) was used in this study. The probe had three 3 mm stainless steel rods having spacing, s, of 12.5 mm. A 3 m of low-loss RG-58 coaxial cable was used. 3.2
3200
Probe installation in the compacted soil.
start of incident pulse
0 0
4
8
12
16
20
24
t [ns]
Figure 3.
Complete reflection waveform.
3.3 TDR measurement A typical reflection waveform with a large time window, obtained from measurement in water, is shown in Figure 3. At t = 2ns, the voltage step pulse launched into the transmission line is recorded by the oscilloscope. The oscillations following the rising step are perhaps aberrations due to the internal circuit and reflection from the front panel. The signal becomes stable while travelling down the cable. At t = 15ns, a drop in voltage amplitude is detected when the signal enters the probe. This is associated with the impedance mismatch between the probe and the cable. A voltage rise is then observed at t = 18ns when the signal reaches the end of the rods (open-ended termination). Finally, multiple reflections occurs until a steady state is attained (not shown in the figure). The time required for the step pulse to travel along the waveguide is used to measure the apparent dielectric permittivity of the soil. The higher is the water content, the higher is the soil bulk permittivity and, hence the lower is the velocity at which the wave propagates into the guide (Robinson et al. 2003). The portion of the waveform of interest for travel time determination (box in Fig. 3 ) is shown in Figure 4. In the same figure, the waveforms in air and soil are also shown. The initial dip and the following bump are associated with the transit of the signal through the probe head. The time corresponding to the second ascending limb is associated with signal reflection at the end of the probe (Figure 4). In Figure 4 it can be observed that the waveforms are shifted with respect to time and voltage. This instrument response is surprising. The time at which the signal enters the probe after traveling along the cable should always be the same. Nonetheless, if the waveforms are ideally superposed, one would observe that the first descending limb (valley) is equal for
174
4000 air
3600
0.8
2800
reflection coefficient,
Voltage, V
3200 soil DVc-p
2400
water
2000 1600
DVc-p
DVc-p
air
Dt AIR
0.6
water
0.4
Dt*
0.2 0
baseline -0.2
tangent
1200 -0.4
6
7
8
9
10
11
12
8
t [ns]
Figure 4.
Dt WATER
t IN
800
8.5
9
9.5
10
10.5
t FIN 11
11.5
12
t [ns]
Figure 6. form.
Waveforms in air, water, and soil.
The Heimovaara interpretation of a TDR wave-
reflection coefficient
0.2 moving apex a
0.1
w
0 –0.1 –0.2
ascending limb dip in probe head
66% air 33% air ~3% air
Figure 5. Waveforms measured as the probe is moved from air to water as surrounding medium.
all waveforms whereas the subsequent first ascending limb (bump) is different. This suggests that the bump cannot be taken as a reference for the beginning of the rods as suggested by other authors (e.g. Or et al. 2002). To better understand the nature of the bump located after the first valley of the waveform, a series of measurements was carried out with the probe inserted vertically downward into a low permittivity layer (air) over a high permittivity layer (water). The waveforms collected with the probe sequentially dipped into water are presented in Figure 5. The apex of the bump is observed to move forward in time as the probe is removed from water. This confirms that the bump depends on the permittivity of the medium surrounding the rods and it cannot be taken as reference for the beginning of the rods. This has been demonstrated by Robinson et al. (2003). A different approach should be therefore developed to identify the beginning of the rods. It would be expected that the beginning of the rods lies somewhere along the first descending limb.
the signal enters the rods. The signal is represented in term of reflection coefficient, ρ. The time tIN is the time at which the signal enters the head of the probe. The time tFIN , obtained by the intersection between the line tangent to the second ascending limb is the time at which the signal is reflected at the end of the probe. The time t ∗ , which is the time taken by the signal to travel along the probe head to reach the beginning of the rods, and the effective length of the rods L∗ are determined by calibration in air and water. It is assumed that the reflection in water is the slowest, while the reflection in air is the fastest, providing bounds on the possible travel times. The relationship between the apparent permittivity Ka and the propagation velocity vP of the signal along the rods can be written as follows: vP =
tFIN
L∗ c = √ − tIN − t ∗ KA
(1)
where c is the speed of light in vacuum and (tFIN − tIN − Dt ∗ ) determines the value of DT. By combining measurements in air (Ka = 1) and water (Ka = 79.1), the values for t ∗ and L∗ equal to 0.136[ns] and 0.0792[m], respectively, were obtained. The time at which the signal enters the rods, (tIN + Dt ∗ ), was found to be very close to the first waveform valley. We therefore assumed this time could alternatively be taken as reference for the beginning of the rods. 4.2 Waveform interpretation
4 4.1
WAVEFORM INTERPRETATION Calibration
The approach suggested by Heimovaara (1993), shown in Figure 6, was used to determine the time at which
Two methods were considered to calculate the transit time from the reflected waveform. In method 1, the time tIN and tFIN were taken as shown in Figure 6, and the apparent permittivity was calculated by considering the values of L∗ and t ∗ derived from Equation 1. In method 2, the length of the rods L∗ was assumed to
175
be equal to the physical length (0.08 m). In this case, the time t ∗ was set to zero and tIN is taken at the first waveform valley.
5
The two methods are essentially equivalent. It may be concluded that, for this TDR system, the time associated with the first waveform valley can be successfully used to identify the beginning of the rods, for cases when TDR measurements in water and air are not available. The relationship between the apparent permittivity and the volumetric water content for the three series of samples, which are characterized by nominal dry densities of 1.4, 1.5, and 1.7 g/cm3 respectively, is shown in Figure 8. Topp’s equation (Topp et al. 1980) is also plotted as a reference (dotted line). It can be observed that the higher the dry density ρ d , the higher the apparent permittivity Ka at a given θV . This is expected because when ρ is increased, the air (Ka = 1) is replaced by solids having higher dielectric permittivity (Ka ∼ 5). Overall, all data are located above Topp’s equation.
RESULTS
A comparison between the two procedures used to determine Ka value is shown in the Figure 7. 14 13
Ka (method 1)
12 I1I
11 10
6
9
DISCUSSION
8
To assess the effect of dry density on dielectric permittivity, the three-phase Litchteneker ‘refractive index’ mixing model was considered:
7
√ 7
8
9
10 11 12 Ka (method 2)
13
14
Figure 7. Comparison of the two procedures used to obtain Ka.
ation ( as re 1980) feren ce
14
Topp ´s Eq u
13
12 rd = 1.7 g /cm3
Ka
11
10
rd = 1.5 g /cm3
rd = 1.4 g /cm3 8
7 0
0.05
0.1
0.15
0.2
0.25
0.3
qV measured
Figure 8. Ka versus θv for the three different dry densities (Ka determined using method 1).
ρREFd + ρd Ks − 1 + ϑ Kw − 1 ρs (2)
where K denotes the real part of the apparent permittivity, Ks and Kw are the permittivity of solids and water, respectively, ρs is the density of solids, ρREFd is a reference bulk dry density and ρd is the variation of dry density with respect to ρREFd . The real part of the apparent permittivity K was used in place of the apparent permittivity Ka to denote the fact that Equation 2 is written by assuming that the complex part (which reflects the electrical conductivity) is negligible. This model has been found to satisfactorily capture experimental data for the case of soils having low clay content and/or low specific surface (Roth et al. 1990; Robinson et al. 1999). The Equation 2 can be written as follows: √
9
K − 1=
K =
ρ KREFd + Ks − 1 ρs
(3)
where KREFd is the permittivity for ρd = 0. We assumed ρREFd equal to 1.5 g/cm3 because KREFd calculated using Equation 2 equals KTOPP for this value of ρREFd (Tarantino et al. 2008). In Figure 9, the measured apparent permittivities corrected by the factor ρ(Ks0.5 − 1)/ρs are plotted versus the volumetric water content θV together with the uncorrected data. It can be observed that corrected
176
3.8 3.6
(Ka') ^ 0.5
3.4 3.2 3 2.8
Topp's equation K'a
2.6
K'a , corrected for r effect D
2.4
qV measured 0.15
0.2
0.25
0.3
Figure 9. Apparent permittivity Ka data corrected for the effect of dry density.
a period of time of only 24 ns, which is not enough to measure the reflection coefficient at t ∼ ∞. To extrapolate the recorded waveform to higher times, we simulated the waveform according to the approach presented by Lin (2003) for multi-section transmission lines as described by Tarantino and Pozzato (Ibid.). For sake of simplicity, an ideal input function was considered. The specific surface As , was estimated from hygroscopic water content according to Dirksen and Dasberg (1993) assuming that a monomolecular layer of water envelops the clay particles. A value of 67 m2 /g was thus obtained. The measured and simulated waveforms are shown in Figure 11. We tentatively assumed the following values for the permittivity of free water, bound water and
a)
0.3 reflection coefficient,
data have significant lower dispersion suggesting that the ‘refractive index’ model adequately captures the effect of dry density. Nonetheless, data are located above Topp‘s equation. We checked whether bulk electrical conductivity could explain this discrepancy. In fact, a relative high electrical conductivity tends to increase dielectric permittivity as shown by the equation of apparent permittivity for a sinusoidal plane wave (Von Hippel, 1954):
0 –0.1 –0.2
10% of risetime
–0.3
tR~0.4ns
reflection coefficient,
0.1 0 –0.1
90% of risetime
–0.2
10% of risetime
–0.3 –0.4
tR~0.6ns
–0.5 8.5
9
9.5
10
10.5
11
11.5
12
t [ns]
Figure 10. Determination of risetime, tR , from the TDR waveform using the 10%–90% values in water (a) and soil (b).
measured waveform (r D = 1.67gr/cm3, w= 11.94%, qV = 19.9%) simulated waveform
0.2
(5)
where tR can be obtained according to the construction shown in It was observed that the effective frequency decreases from about 800 MHz to 550 MHz from water to soil respectively. This signal dispersion is due to a non-negligible electrical conductivity. Lower frequency waves are slowed down (see Equation 4, producing less steep second ascending limb. According to Topp et al. (1988), the bulk electrical conductivity, σa , can be calculated from reflection at t ∼ ∞. Unfortunately, waveforms were recorded by the Trase over
0.1
8
reflection coefficient,
ln(0.9/0.1) 2π · tR
ascending limb
b)
fEFF =
90% of risetime
0.2
–0.4
ε εa = (1 + 1 + ((εRELAX + σ/2πfEFF ε0 )/ε )2 ) 2 (4) where εa is the measured apparent permittivity, ε and ε are the real and imaginary part of the soil dielectric permittivity, respectively, εo the dielectric permittivity in the vacuum, σ is the bulk electrical conductivity and fEFF is the effective frequency in Hz. The effective frequency fEFF of the signal propagating in water and soil was calculated according to Strickland (1970) as follows:
0.4
0.1
0 –0.1 –0.2 –0.3 –0.4 8
8.5
9
9.5 t [ns]
10
10.5
11
Figure 11. Measured (ρs = 2.71 g/cm3 , ρD = 1.67 g/cm3 , θV = 0.2) and predicted waveform for soil (As = 66.7, εfw = 80.2, εs = 5, σbw = 15 S/m, σfw = 1.1 S/m).
177
0.3
3.8 t
3.6 3.4
0.1
3.2
0
(Ka') ^ 0.5
reflection coefficient
0.2
0.1 0.2
3 2.8 Topp's equation K'a
2.6
0.3
2.4 20
30
40
50
60
K'a, corrected
t [ns]
2.2
Figure 12. Simulated reflection coefficient from the plotted reflection at t ∼ infinite.
2 0.1
solids, εfw = 80.2, εfw = 5, and εs = 5, respectively, and σfw = 1.1 S/m and σbw = 15 S/m for the electric conductivity of free water and bound water, respectively. The entire simulated waveform was plotted and the value of the reflection coefficient was determined as equal to ∼0.2 (Figure 12). The bulk conductivity, σa , was calculated according to Topp et al. (1988): 1 ε0 cZ0 1 − ρ∞ 1 ε0 cZ0 2V0 σ = −1 ≡ 1 + ρ∞ Zc L VF Zc L (6) where ε0 is the permittivity of free space (8.854 · 10−12 F m−1 ), c is the speed of light in a vacuum (3 · 108 m s−1 ), L is the probe length (0.08 m), ρ∞ the reflection coefficient at infinite time (∼0.2), V0 is the voltage entering the head of the probe, VF the final voltage recorded by the oscilloscope after all multiple reflections had taken place, Zc is the characteristic impedance of the cable tester (50 W), and Z0 is characteristic impedance of the probe (220 W). A value of 1dS/m was obtained. To account for the effect of electrical conductivity on apparent permittivity, the empirical approach proposed by Wyseure et al. (1997) was considered: Ka = K + 1.432σ
(7)
where σ is the electrical conductivity in dS/m. If Equation 7 is substituted in Equation 3, the following equation is obtained: KTOPP =
√ 2 Ks − 1 Ka − ρd − 1.432 · σ ρs (8)
The values of Ka measured using TDR and the values corrected to account for the combined effect of
0.15
0.2
0.25
0.3
qV measured
Figure 13. Apparent permittivity Ka as result of the correction in term of dry density and bulk electrical conductivity.
ρd and σ (KTOPP in Equation 8) are plotted against volumetric water content θV . It can be observed that the corrected data collapse on Topp’s calibration curve. This demonstrates again that deviations from Topp’s equation occur for dry densities and bulk electrical conductivities outside the range investigated by Topp et al. (1980). Nonetheless, simple corrections could be introduced to account for these deviations.
7
CONCLUSIONS
An experimental investigation of the effect of dry density on dielectric apparent permittivity was carry out in this study. It was observed that the effect was not significant, but not negligible for sensitive applications. The effect of dry density was successfully modeled using a three-phase ‘refractive index’ model. Nonetheless, the measured permittivity corrected for dry density was still underestimated by Topp’s equation. We observed a decrease in effective frequency when measuring the waveform in the soil and we inferred the soil had non-negligible electrical conductivity. Since the waveform was recorded over a short period of time that was insufficient to reach steady-state conditions, the waveform was simulated to capture the reflection coefficient that would have been recorded at infinite time. This made it possible to estimate the bulk electrical conductivity and to further correct the measured Ka using an empirical equation. Topp’s equation was shown to match the corrected data.
178
REFERENCES Dirksen, C. and Dasberg, S. (1993). Improved calibration of time domain reflectometry soil water content measurements. Soil Sci. Soc. Am. J., 57: 660–667. Heimovaara, T.J. 1993. Design of triple-wire time domain reflectometry probes in practice and theory. Soil Sci. Soc. Am. J., 57: 1410–1417. Lin, C.P. (2003a). Analysis of nonuniform and dispersive time domain reflectometry measurement systems with application to the dielectric spectroscopy of soils. Water Resour. Res. 39. McCartney, J.S. (2007). Determination of the Hydraulic Characteristics of Unsaturated Soils using a Centrifuge Permeameter. Ph.D. Dissertation. The University of Texas at Austin. Or, D., VanShaar, T., Fisher, J.R., Hubscher, R.A. and Wraith, J.M. 2002. WinTDR99—Users guide. Utah State University – Plants, Soils & Metereology, Logan, UT. Robinson, D.A., Gardner, C.M.K. and Cooper, J.D. (1999). Measurement of relative permittivity in sandy soils using TDR, capacitance and theta probes: comparison, including the effects of bulk soil electrical conductivity. Journal of Hydrology, 223: 198–211. Robinson, D.A., Schaap, M., Jones, S.B., Friedman, S.P. and Gardner, C.M.K. (2003b). Considerations for Improving
the Accuracy of Permittivity Measurement using Time Domain reflectometry: Air-water calibration, effects of cable length. Soil Sci. Soc. Am. J., 67: 62–70. Roth, K., Schulin, R., Flühler, H. and Attinger, W. (1990). Calibration of TDR for water content measurement using a composite dielectric approach . Water Resources Research, 26 (10): 2267–2273. Strickland, J.A. (1970). Time-domain reflectometry measurements. Tektronix Inc., Beaverton, Oregon: 11–13. Tarantino, A., Ridley, A.M. and Toll, D. (2008). Field measurement of suction, water content and water permeability. Geotechnical and Geological Engineering, in press. Tarantino, A. and Pozzato, A. (Ibid). Limitations of travel time interpretation of reflection waveform in TDR water content measurement. Topp, G.C., Yanuka, M., Zebchuk, W.D. and Zegelin, S. (1988). Determination of Electrical conductivity using TDR: soil and water esperiments in coaxial lines.. Water Resources Research, 24(7): 945–952. Topp, G.C., Davis, J.L. and Annan, A.P. (1980). Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resour. Res., 16:574–582. Wyseure, G.C.L., Mojid, M.A. and Malik. (1997). Measurement of volumetric water content by TDR in saline soils. European. Journal of Soil Science, 48: 347–354.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Spatial Time Domain Reflectometry (Spatial TDR) – Principles, limitations and accuracy R. Becker IMKO Micromodultechnik GmbH, Ettlingen, Germany
A. Scheuermann Institute for Soil Mechanics and Rock Mechanics, University of Karlsruhe (TH), Germany
S. Schlaeger Schlaeger Mathematical Solutions & Engineering, Horn, Bad Meinberg, Germany
C. Huebner University of Applied Sciences, Mannheim, Germany
N. Wagner Institute of Material Research and Testing (MFPA) at the Bauhaus University Weimar, Germany
ABSTRACT: Monitoring of transient soil moisture profiles yields valuable insight into soil hydraulic processes. A recently developed reconstruction algorithm allows deriving water content profiles along extended moisture probes from Time Domain Reflectometry (TDR) signals. Based on inverse modelling of the wave propagation along a transmission-line the algorithm calculates electrical parameter distributions. The method named Spatial TDR will be explained and the accuracy as well as the spatial and temporal resolution defining the possibilities and limitations of the procedure will be presented on practical examples.
1
INTRODUCTION
Many applications in geotechnical engineering, hydrology and agriculture require determining the transient water content profile characterizing soil hydraulic processes in unsaturated soils. However the monitoring of a sufficient number of soil moisture profiles can be costly, laborious and extraordinary invasive, especially if the profiles are determined point-wise by a large amount of single probes buried in soil. A recently developed reconstruction algorithm (Schlaeger 2005) allows computing complete soil water content profiles along elongated single moisture probes from time domain reflectometer (TDR) measurements in a short time. This method leads to a reduction of the number of probes accompanied by a higher spatial resolution of moisture profiles. The whole technology of soil moisture profile retrieval—including measurement devices and probes, reconstruction algorithm and calibration procedure—has been named Spatial TDR (Becker 2004, Huebner et al. 2005). This method is being developed and applied by the Soil Moisture Group (SMG),
an interdisciplinary research group at the University of Karlsruhe. This article gives a brief introduction into the fundamentals of TDR before the basic concept of STDR is explained with the emphasis on its algorithm and the initial probe calibration by way of a coated 3-rod-probe. The theoretical accuracy of the measured moisture profiles is assessed by means of electromagnetic (EM) field simulations. Laboratory and large-scale experiments were realized to evaluate the method and to compare the reconstructed water content profiles with comparable information of the real soil.
2 2.1
MEASUREMENT METHOD Dielectric properties of soils
Soil as a typical porous medium consists of three phases: solid particles (clay minerals and granulates) pore air and pore water in different forms of bounding (cf. Fig. 1). The fractions of the soil phases vary both in space—due to composition and density of
181
pulse generator voltage
oscilloscope
coaxial cable
length l
two wire transmission line (metallic fork)
incident signal reflected signal sum signal two wire line travel time
soil
time
Figure 2. Basic TDR set-up and signals. Oscilloscope and pulse generator are usually integrated in a single TDR device.
Figure 1. Dielectric (permittivity) and electric (resistivity) properties of the soil phases.
soil—and time—due to changing of water content and temperature. For the determination of the water content, one utilizes the fact that the effective relative dielectric permittivity of the soil depends on the fractions of the soil phases (Robinson 2004). The relation between water content and effective permittivity can be performed using specific laboratory calibration with gravimetric sampling. (e.g. Topp et al. 1980). Alternatively empirical, semi-empirical and theoretical mixing rules can be used as a relationship between dielectric properties of the soil and its water content (Tuncer et al. 2002). For highly conductive soils—e.g. for fine grained soils with clay contents—general empirical calibration equations fail due to the strong frequency dependency of the effective dielectric permittivity, whereas soil and probe specific calibration function or theoretical models can provide a satisfactory estimate of the water content (Cosenza & Tabbagh 2004, Kupfer et al. 2007). 2.2
Time Domain Reflectometry (TDR)
A TDR instrument, which consists of a pulse generator and an oscilloscope, emits a voltage step pulse VI(m) (t) via a feeding cable into a waveguide (e.g. a moisture probe) buried in the soil. When the propagating electromagnetic (EM) wave hits the transition between cable and probe it is generally split due to impedance discontinuity. One part is reflected and traveling back and the rest of the signal is transmitted into the waveguide, interacting with the surrounding soil. When the pulse reaches the probe end it is reflected again. Hence the incident signal VI(m) (t) (input, measured) excites the system under test (SUT, probe/soil) which reacts with voltage reflections whose superposition V0(m) (t) (output, measured) is sampled by the TDR instrument as a sum of both signals (schematic description in Fig. 2).
Figure 3.
Flat band cable as moisture probe.
The elapsed time between first and second main reflection is the pulse travel time along the SUT. This travel time can be transformed into average soil moisture or water content by appropriate calibration functions and/or mixing rules. This is the common evaluation procedure for TDR measurements.
2.3 Moisture probes (transmission line) The length of standard, non-insulated metallic forks as transmission lines are restricted to about 30 cm because of high electrical attenuation. For longer investigation areas insulated 2- or 3-wire transmission lines as rod-probes (cf. Becker 2004) or insulated flat band cables are used (Huebner et al. 2005). Such insulated flexible flat band cables are proposed for the use as elongated moisture probes with lengths of more than 0.5 m. In the past several cables with different geometries have been developed and manufactured, from simple concentric insulation to sophisticated multiwire structures with unilateral sensitivity. The flat band cable used in the most experiments within the SMG is shown in Figure 3. The cable consists of three copper wires covered with polyethylene insulation. The sensitive area around the cable extends approximately 3 to 5 cm. For the near surface observation of moisture profile changes 3-rod-probes are frequently used which are described in the next chapter.
182
Figure 5. The simplified moisture probe model consisting of bulk electronic parts. Above: coated 3-rod-probe as an example for a moisture probe (TDR waveguide); below: infinitesimal section of an equivalent circuit of the transmission line.
Figure 4. TDR-signals measured at a flat band cable, half of the cable is located in saturated soil.
3 3.1
propagation of a voltage pulse V (x, t) along the buried waveguide:
SPATIAL TDR PROCEDURE
∂ ∂2 + L(x)G (x) ∂t ∂t 2 ∂2 ∂L(x)/∂x ∂ V (x, t) = 0 − + L (x) ∂x ∂x2
L(x)C (x)
The inverse problem
The measured TDR signal contains far more than the travel time of the reflected electromagnetic signal. The reflectogram, especially the part between first and second main reflections at the probe’s beginning and end, is a finger print of the dielectric profile along the waveguide, which is mainly ruled by the water content. Figure 4 shows TDR signals measured with a flat band cable as sensor up to the half of the length located in saturated soil. Unfortunately the moisture distribution cannot be calculated directly from the TDR signal but has to be estimated indirectly. The basic idea of STDR is to transform the measured output signal V0(m) (t) into the soil moisture profile θ (x) along the probe by means of inverse modeling. The essence of this approach is to simulate the propagation of the TDR signal along the waveguide in time domain by employing a numerical model (forward problem) based on the telegraph equations. This simplified model assumes that the relevant properties of the transmission-line can be described by bulk electronic parts like resistors, inductors, and capacitors (Figure 5). Among the conditions for this electronic circuit model to hold the most important are: wave modes other than the transversal-electromagnetic (TEM) mode and frequency dependence of transmission-line properties may be neglected. The first condition requires a wellbehaving waveguide with little distortion on the signal propagation, the second is only met, if the losses in the SUT are not too large. Schlaeger (2005) derived the following wave equations from the circuit model for describing the
(1)
Capacitance C (x) and effective conductance G (x) are influenced by the soil water content distribution θ(x) along the waveguide. Inductance L (x) is a function of the transmission-line only and constant and known for coaxial cable and moisture probe. The spatial derivative of L (x) in (1) describes the change of inductance between coaxial cable and probe. Resistance R along the waveguide has been neglected. All parameters are given per unit length. Strictly spoken the equivalent circuit of Figure 4 is not totally correct, because the conductor G should be enclosed by two capacitors due to the rod coating. Therefore G is not the real ionic conductance of the soil but a kind of correcting parameter in the determination of C . According to former results we assume that this simplification does not have a large influence on the results. Equation (1) is solved numerically with appropriate initial and boundary conditions to simulate a TDR measurement V0(s) (t) for given C (x) and G (x). The result of the simulation is compared to the TDR measurement V0(m) (t). An optimization algorithm is used to modify the electrical parameters C (x) and G (x) until the simulated TDR reflectogram V0(s) (t) matches the measurement V0(m) (t)sufficiently well. The final parameter distributions resulting from the simulation are the best estimates of the electric properties along the probe in soil.
183
3.2
Empirical relationship between capacitance and effective conductance
The wave equation (1) needs two parameter distributions C (x) and G (x). These parameter distributions could be found simultaneously by inverse modeling, if two independent TDR measurements were available for the same moisture probe, which is best possible with probes connected from both sides (double sided). Those kinds of probes can be constructed using flat band cables, which are frequently in use for monitoring purposes with elongated probes in earth structures like dikes (cf. Scheuermann et al. 2008, Huebner et al. 2005). In case of single sided probes it is reasonable to assume a relationship between C (x) and G (x), since both parameters are linked by soil moisture: higher water content leads to higher dielectric permittivity and higher conductivity. The following relationship is proposed:
1/C (ε) = 1/(ε · C1 ) + 1/C2
(3)
The rods of the 3-rod-probe presented here consist of stainless steel cores of 6 mm diameter with a 1 mm thick PVC coating. The rods are 30 mm apart. They are screwed into the probe head which connects them to a 50 Ohms coaxial cable. According to the equations (1) and (3) it is necessary to get the three parameters C1 , C2 and L for the rod probe. This can be done empirically by TDR pulse propagation velocities vi = v (εi ) measured for two different media with well known dielectric permittivities ε 1 and ε 2 , respectively. The pulse propagation velocity along the coated probe rods is: v(ε) = 1/ L · C (ε)
G (C ) G∞ · (1−exp(−(C −C0 )/Cd ), if C ≥ C0 , = 0, if 0 ≤ C ≤ C0 . (2) The parameters G∞ , C0 and Cd can be determined by soil and probe dependent calibrations.
3.3
as a probe specific calibration which can be easily solved for ε with the constant capacitances C1 and C2 :
The pulse velocity is determined empirically by measuring the time between the two main reflections in the TDR reflectogram. Combining equation (4) with (3) for the two materials one yields: C1 = (ε2 − ε1 )/(ε2 ε1 (v12 − v22 ) · L ) C2
From capacitance to dielectric permittivity
To derive the volumetric water content profile θ (x) the dielectric permittivity profile ε(x) of the soil/water/air mixture has to be extracted from the capacitance profile C (x) first. For the design of a simple moisture probe (cf. Figure 6) it is possible to find analytically a convenient parametric form for C (ε)
(4)
= (ε2 −
ε1 )/((ε2 v22
−
ε1 v12 )
and
·L)
(5)
The rod impedance Z can be used to get L : Z(ε) =
L /C (ε)
(6)
The impedance mismatch between coaxial cable and probe rods leads to a partial reflection of the incident excitation pulse. The amplitude of incident and reflected signal are denoted by AI and AR , respectively. Then the reflection coefficient yields: r(ε) = AI /AR = (Z(ε) − Z0 )/(Z(ε) + Z0 )
(7)
which can be determined experimentally from TDR measurements. Z0 = 50 Ohms is the impedance of the coaxial cable. The combination of the equations (5) and (6) yields: Figure 6. Capacitance C of a 3-rod-probe as a function of the soil’s dielectric permittivity ε. (a) segment of three parallel rods encompassed by soil; light gray: PVC coating; dark gray: metallic core; (b) equivalent circuit. C1 , C2 : constant capacitance parameters determined by the probe’s geometry and material.
L = (1 + r(ε))/(1 − r(ε)) · Z0 /v(ε)
(8)
The equations (5) and (7) are sufficient to determine the dielectric parameter ε of the soil from TDR signals when a coated rod-probe is used (cf. Fig. 6).
184
3.4
From dielectric permittivity to water content
The second step performs the transition from dielectric permittivity to water content based on the phase fractions of the soil solid particles, water and air. An empirical relationship between ε and θ often used in TDR applications was found by Topp (1980). For the presented example a more simple but also less general empirical formula was found derived from laboratory experiments with a loamy sand: θ(ε) = 30.1 · ε 0.31 − 41.1(%vol)
4
Figure 7 displays the TDR reflectograms simulated with MWS and reconstructed by the Spatial TDR algorithm. The predefined and reconstructed soil moisture profile for the sequence wet/moist/dry is shown in Figure 8. Two cases were realized: one with and the other without consideration of ionic conductivity σ (lossy and lossless case). Although the difference between simulated and measured TDR reflectogram is very small, the deviation in the moisture profile can be quite large.
(9)
ACCURACY OF SPATIAL TDR
4.1 Electro-dynamic simulation To test the Spatial TDR method with 3-rod-probes several TDR reflectograms were simulated with Microwave Studio (MWS), an EM simulation tool based on the full wave solution of Maxwell’s equations. In the numerical model the 3-rod-probe is embedded in a three layer material, whose dielectric permittivity and ionic conductance can be modified. A step pulse of 1 Volt amplitude and 1 GHz bandwidth is fed into the probe. The simulated TDR reflectograms are used for three purposes: 1. determination of the probe parameters according to (4) and (6), 2. determination of the empirical C − G -relationship (7), and 3. generation of test reflectograms to assess the quality of the Spatial TDR algorithm.
4.2
Figure 7. TDR reflectograms simulated by MWS and the corresponding signal approximations resulting from the reconstruction algorithm. Material sequence wet/moist/dry. Energy losses due to ionic conductance lead to a strong falling trend of the TDR signals.
Numerical investigations
To assess the quality of the algorithm which determines the water content profile from a TDR reflectogram by inverse parameter estimation, the MWS is fed with three soil layers of different moisture. Table 1 shows the applied soil parameters. Each simulated reflectogram together with the excitation pulse was fed into the Spatial TDR algorithm and a reconstruction process was conducted to retrieve the soil moisture profiles, which should match the predefined one as close as possible.
Table 1.
Material parameters used in Microwave Studio. Moisture state
‘dry’ ‘moist’ ‘wet’
θ (%vol)
ε (−)
σ (mS/m)
0.5 8 13.5
2.9 4.9 6.8
0 14 23
Figure 8. Moisture profile, sequence wet/moist/dry, predefined in the MWS model and reconstructed by means of the Spatial TDR algorithm.
185
transient soil moisture profiles under irrigation with high spatial and temporal resolution (Becker 2004, Scheuermann et al. 2008).
5 5.1
Figure 9. Spatial TDR application to a real soil moisture profile. Measured and reconstructed TDR reflectograms for short and long coaxial cable as connecting cable.
Figure 10. Spatial TDR application to a real soil moisture profile. Material sequence dry/moist/wet. Reconstruction results compared to volumetric water content of soil samples determined by oven drying. Differences up to 3%vol are due to imperfect calibration of the real 3-rod-probe.
4.3
SPATIAL AND TEMPORAL RESOLUTION OF SPATIAL TDR Sensitivity of TDR Probes
A simplification frequently utilized in TDR applications is the use of an idealized equivalent circuit (c. f. Fig. 5) for the sensor without consideration of losses due to the skin-effect or radiation from the sensor as well as the assumption of a homogeneous sensitivity distribution along the sensor (Heimovaara et al. 2004, Huebner & Kupfer 2007). In addition, a frequently arising problem in various applications is the direct contact between sensor and surrounding material. For these reasons the sensitivity of a flat band cable as moisture probe was investigated with 3D electromagnetic finite element modeling under consideration of the frequency-dependent complex dielectric permittivity (Wagner et al. 2007). One main result of this investigation is that coupling problems caused by air or water gaps lead to dramatic travel time distortion even for very small gaps. An air filled gap with a thickness of 0.25 mm on both sides of a flat band cable sensor already leads to the drastic underestimation of water content of approximately 36%. In contrast a drastic overestimation occurs in the case of a water filled gap for the same gap size. Therefore, an accurate installation of the moisture probes is stringently necessary for the quantitative in situ water content determination.
Laboratory investigation
To test Spatial TDR in laboratory a box with three chambers of 0.2 m length each was prepared in accordance to the MWS numerical model and filled with soil of predefined moisture (see Table 1). A 3-rod-probe of 0.6 m length (Figure 4) was installed such that it crossed all chambers. TDR measurements were performed with a Tektronix metallic cable tester 1502B. A comparison between measured and reconstructed TDR-signals for different lengths of the connecting coaxial cables is given in Figure 9. With each material sequence four soil samples of known volume were taken from each chamber. Their volumetric water content was determined by oven drying. Figure 10 shows the result for the material sequence dry/moist/wet. The overall accuracy of Spatial TDR with coated rod probe is sufficient for many applications in soil science. A lysimeter experiment with 1 m3 loamy sand showed that the method is capable of tracking
5.2
Laboratory and in situ comparison
An experiment for the investigation of transport of volatile organic compounds in a medium grained sand (grain size 0.2 to 1 mm) was conducted under different moisture conditions to verify the spatial variations of the water content distribution. For the Spatial TDR measurements flat band cable connected from both sides were used. Figure 11 shows the temporal process of redistribution of water after a one hour lasting irrigation from top. Graph d) of Figure 11 shows a comparison of the volumetric water content between the reconstruction and results from the oven-drying technique at 105◦ C. An average uncertainty of ±2.3% was determined. Figure 12 shows the result of Spatial TDR measurements in a full-scale dyke model (cf. Scheuermann et al. 2008) in comparison with water pressure measurements conducted at the water-proof base of the dyke.
186
correct installation of probes in soils plays a decisive role for the accuracy of the measurement results. The examples show clearly the functional capability of Spatial TDR for the measurement of water content distributions. REFERENCES
Figure 11. a)—c) Redistribution of the moisture profile after an irrigation to the steady state (dashed line) and d) comparison with gravimetric measurement of several soil samples (∗).
Figure 12. Saturation distribution inside a dyke as result of Spatial TDR measurements.
The measured phreatic line and the location of the transition from the wet to the dry zone correspond very well. Underneath the phreatic line in the ‘saturated’ zone different values below full saturation can be recognised indicating a fairly high residual rate of air remaining in the pores. This observation was also verified by independent measurements during the steady state condition. The changes in water content are reconstructed with a spatial accuracy of about 3 cm and an average deviation of ±2% compared to independent water content measurements.
6
CONCLUSION
Spatial TDR is a new innovative method for the investigation of moisture distributions in porous materials with high resolution in space and time. However the accurate use of Spatial TDR requires calibration procedures both for the probe and the soil. Furthermore the
Becker, R. 2004. Spatial Time Domain Reflectometry for Monitoring Transient Moisture Profiles. Ph.D. thesis, Inst. for Water and River Basin Management, Univ. of Karlsruhe. Cosenza, P. & Tabbagh, A. 2004. Electromagnetic determination of clay water content: role of the microporosity. Applied Clay Science, 26 (1–4):21–36. Heimovaara, T.J., Huisman, J.A., Vrugt, J.A. & Bouten, W. 2004. Obtaining the spatial distribution of water content along a TDR probe using the SCEM-UA bayesian inverse modelling scheme. Vadose Zone J. 3:1128–45 Huebner, C. et al. 2005. Advanced measurement methods in TDR for soil moisture determination. In K. Kupfer (ed.), Electromagnetic Aquametry: 317–347. Springer. Huebner, C. Kupfer, K. 2007. Modelling of electromagnetic wave propagation along transmission lines in inhomogeneous media. Meas. Sci. Technol. 18:1147–1154. Kupfer, K., Trinks, E., Wagner, N. Huebner, C. 2007. TDR measurements and simulations in high lossy bentonite materials, Meas. Sci. Technol. 18:1118–1136. Robinson, D.A. 2004. Calculation of the Dielectric Properties of Temperate and Tropical Soil Minerals from Ion Polarizabilities using the Clausius-Mosotti Equation. Soil Sci. Soc. Am. J. 68:1780–1785. Scheuermann, A. et al. 2008. Spatial Time Domain Reflectometry (Spatial TDR)—On the use in geotechnics and geohydraulics. First European Conference on unsaturated soils; Proc. intern. symp. Durham, 2–4 July. Schlaeger, S. 2005. A fast TDR-inversion technique for the reconstruction of spatial soil moisture content. Hydrol. Earth Sys. Sci. 9:481–492. Topp, G.C., Davis, J.L. & Annan, A.P. 1980. Electromagnetic determination of soil water content: Measurement in coaxial transmission lines. Water Resour. Res. 16 (3):574–582. Tuncer, E., Serdyuk, Y.V. & Gubanski, S.M. 2001. Dielectric mixtures—electrical properties and modelling. IEEE Transactions on Dielectrics and Electrical Insulation 9:809–828. Wagner, N., Trinks, E. & Kupfer, K. 2007. Determination of the spatial TDR-sensor characteristics in strong dispersive subsoil using 3D-FEM frequency domain simulations in combination with microwave dielectric spectroscopy. Meas. Sci. Technol. 18:1137–1146.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Spatial Time Domain Reflectometry (Spatial TDR) – On the use in geohydraulics and geotechnics A. Scheuermann, A. Bieberstein & Th. Triantafyllidis Institute for Soil Mechanics and Rock Mechanics, University of Karlsruhe (TH), Germany
C. Huebner University of Applied Sciences, Mannheim, Germany
R. Becker IMKO Micromodultechnik GmbH, Ettlingen, Germany
S. Schlaeger Schlaeger Mathematical Solutions & Engineering, Horn, Bad Meinberg, Germany
N. Wagner Institute of Material Research and Testing (MFPA) at the Bauhaus University Weimar, Germany
ABSTRACT: Time Domain Reflectometry (TDR) is a widely-used tool for the point-wise determination of water contents in soils, especially in hydrology and soil-physics. Another well-known field of application of TDR is the observation of deformation processes in soils or rocks. The development of Spatial TDR offers new fruitful possibilities in geohydraulics and geotechnics. With Spatial TDR it is possible to determine physical properties of the soil along elongated transmission lines. The paper presents completed and ongoing research projects in which the determination of the spatial and temporal evolution of state variables like water content and pressure play an important role.
1
INTRODUCTION
The hydraulic and the mechanical behavior of unsaturated soils depend on several state variables. Firstly water content and suction should be named, which are both connected to each other via the soil water retention curve. Others are the soil density and the stresses involving deformations preferentially along shear zones. For the safety assessment of earth structures the experienced geotechnical engineer has to rely on quantitative information on the spatial as well as temporal evolution of these state variables. The electromagnetic measurement method Time Domain Reflectometry (TDR) offers different helpful solutions for the observation of these state variables. The most well known application of TDR is the measurement of water content at a single point, for example for the monitoring of landfill covers (e.g. Schofield 2001). Furthermore, water content measurements with TDR on a field scale are used for intensive sampling
(e.g. Long et al. 2002) and also for the determination of soil hydraulic properties (e.g. Heathman & McAfee 2006). TDR is also well-known in geotechnical monitoring for the shear zone localization, e.g. in rock masses (Dowding et al. 1989) as well as in landslides (Kane et al. 2001). In this regard the accuracy of the so-called TDR extensometers is better than ±0.5 mm. With the development of Spatial TDR, for the first time it is possible to determine the spatial distribution e.g. of water contents for practical purposes along elongated transmission lines. An introduction to the Spatial TDR procedure is given in Schlaeger (2005) and Becker et al. (2008). In this paper the use of Spatial TDR as a monitoring system for dams and dykes is presented first. Another major application is the measurement of moisture in small catchment areas in order to improve flood forecasting. Finally, a novel application of TDR is presented to determine the spatial distribution of mechanical pressure along transmission lines.
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2 2.1
MONITORING OF DAMS AND DYKES Full-scale dyke model
The transient seepage through dykes due to a hydraulic stress depending on the initial moisture condition was investigated on a full-scale dyke model (Fig. 1). The dyke is built up homogeneously with sand (grain size 0.2–2 mm) and has a waterproof sealing consisting of plastic sheeting as a base, so that the water within the dyke body flows to a drain at the toe of the landside slope. In order to simulate flood events, a basin is included in the construction. The dyke is equipped with pore water gauges at the base for measuring the hydraulic head and with flat band cables for measuring the spatial water content distribution using Spatial TDR (cf. Fig. 2). The TDRsystem consists of 12 flat band cables from 1 to 3 m in length, which are installed vertically inside the dyke. They are connected with coaxial cables at both ends to a multiplexer and a TDR device in a box on the crest of the dyke. The data collection and controlling equipment (PC) of the multiplexer and the TDR device are placed in a measuring container at the toe of the landside slope (Figs. 1, 2). 2.2
Measurement results
Different physical flood simulation tests were carried out on the dyke model (Scheuermann & Bieberstein 2006). Figure 3 shows water content measurements
Figure 1. Full-scale dyke model at the Federal Waterways and Research Institute in Karlsruhe during a flood simulation test in December 2000 (steady state of seepage condition).
Figure 2. Setup of measuring devices with positions and length of the flat band cables and positions of piezometer gauges on the base of the dyke model.
Figure 3. Distributions of saturation during a flood simulation test on the full-scaled dyke model.
as distributions of saturation indicating different hydraulic situations during the transient hydraulic process of water infiltration. The positions and lengths of the flat band cables are shown as dots and the values beside the dots show the measured saturation at these locations (cf. Fig. 2). For better clarity the water content distributions are interpolated over the cross-section of the dyke. These kinds of measurements during the experiment are available at a temporal resolution of 15 min. On the basis of these experiments, it was possible to demonstrate the influence of initial water content distributions on the transient seepage through dykes. However, with this system it is also possible to measure small changes in the distribution of the water content. Since 2000, water content has been measured on the dyke model almost continuously with Spatial TDR. Apart from any sprinkler irrigation during the summer time to water the grass cover, the water content changes are mainly influenced by precipitation and evapotranspiration. Depending on these hydraulic boundary conditions it is possible to use the dyke as a lysimeter to characterize and investigate the water balance processes. Figures 4 and 5 show the moisture situation inside the dyke with the precursory precipitation events as well as the discharge measured near the drain at the downstream slope. As can be seen from Figures 4 and 5, the water content distributions show distinctive differences not only concerning the mean saturation (given in the graphs), but also concerning the distribution of the water inside the dyke. In particular it should be mentioned that during long periods with precipitation that occurred several times in March 2001 (see Fig. 5) the water
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Figure 6. Plan of the measurement site at the river Unstrut in Thuringia, Germany.
Figure 4. Moisture distribution inside the dyke on the 31st May 2002 with precursory meteorology over 16 days.
Figure 5. Moisture situation inside the dyke on the 26th March 2001 with precursory meteorology over 16 days.
content primarily increased within a certain depth from the dyke surface, forming an area in the middle of the dyke cross-section, which is almost unchanged with respect to the water content compared to the rather dry situation shown in Figure 4. One explanation for this observation is the lateral movement of water in the wet zone, which occurs frequently in combination with fingering effects. During a precipitation experiment, observations were made indicating such phenomena (Scheuermann & Bieberstein 2007). 2.3
Monitoring system for real dykes
The long-term measurements on the full-scale dyke model have proven that the preliminary hydrological and meteorological events lead to a water content
distribution inside the dyke, which is characteristic for the previous hydrologic events. Furthermore, the investigations on the dyke model have shown that the transient seepage is influenced considerably by the initial moisture content inside the dyke. Due to these findings, it confirms that Spatial TDR can be used to develop a monitoring system for river dykes, which can also be adapted to other embankments or earth structures like slopes. In cooperation with the Institute of Material Research and Testing (MFPA) at the Bauhaus University in Weimar, two measurement systems have been installed in real dykes along the river Unstrut and the river Elbe. Along the river Elbe one dyke section is monitored on 6 cross-sections over a distance of 250 m. The smaller measuring location on the Unstrut (cf. Fig. 6) can be used as a reference object, since flood events can be artificially initiated using a water retaining structure. This project is being carried out within the national research program ‘‘Risk management of extreme flood events—RIMAX’’.
3
MOISTURE SENSING IN HYDROLOGY
3.1 Lysimeter investigations Especially in small catchments, the development of flooding depends on the initial moisture situation within the catchment area due to a reduced storage capacity of the soil. The moisture distribution in the top few decimeters is decisive for surface runoff generation. To investigate the development of water content distribution near the top surface 3-rod-probes were developed and tested using Spatial TDR (Becker 2004, Becker et al. 2008). In order to test the suitability of Spatial TDR for the observation of the small-scale variability of water content distributions, infiltration experiments were conducted in a lysimeter (Fig. 7).
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The soil used for the experiments was a silty sand with a saturated hydraulic conductivity of kf ≈ 10−5 m/s. The artificial precipitation was achieved using a spray nozzle bar. For comparative purposes additional moisture measuring devices were included in the lysimeter. Figure 8 shows the results of water content profile measurements at two different 3-rod-probes during an infiltration experiment. Since deliberate inhomogeneities were included in the sample in the lysimeter the moisture profiles show different temporal evolutions. At time step 0 both moisture profiles show disturbances, most probably due to differences in the density within the soil sample. These disturbances were persistent over the whole experiment. The graph
on the right in Figure 8 shows a more or less continuous infiltration of water into the sample. The moisture front passed the end of the probe after 180 min. In contrast, the temporal evolution of the moisture profile on the left of Figure 8 shows completely different temporal behavior. After 60 min. the infiltration seemed to stop at a depth of about 10 to 12 cm. After 180 min. the profile evolution indicated horizontal water movement. Only the combination of measurement results from several probes provides a good basis for the assessment of water movements.
Figure 7. Lysimeter holding 1 m3 of soil. 1: tubular steel frame, 2: soil; 3: probe connecting coaxial cables; 4: probe multiplexer; 5: spray nozzle bar; 6 and 7: additional smallscale moisture measuring devices.
Figure 9. Interpolated soil moisture distribution on two different measurement dates registered at 46 2-rod-probes. Dark grey: wet, light grey: dry condition. A cross-section along the black line is given in Figure 10.
Figure 8. Water content profiles measured at two 3-rodprobes during an. infiltration experiment lasting 360 min.
Figure 10. Water content distribution in the cross-section along the black line shown in Figure 9.
3.2 In situ application A first in situ application of the system was carried out at the Goldersbach catchment near Tübingen (Figs. 9 and 10). In this case 46 2-rod-probes were installed. The aim of this application was to measure the extension of a saturation zone both horizontally as well as vertically. An ephemeral creek divides the measurement site, which is dominated by podzolic soils.
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The TDR measurements were reconstructed yielding water content profiles along the 60 cm long 2-rodprobes. For a quasi three-dimensional soil moisture distribution, the results were interpolated between the probes. Figure 9 shows a two-dimensional map of the average moisture for a dry (A) and wet (B) condition. The growth of the zone of high average water content is evident. An example of a vertical cross-section through the soil is given in Figure 10. A wet zone in the deeper soil regions can be clearly seen.
4 4.1
MEASUREMENT OF PRESSURE PROFILES
Figure 12. Measured and reconstructed TDR reflections for profile measurements of buckled steel strips.
Laboratory experiments
Many applications in geotechnical engineering require the knowledge of total pressure distributions. A novel sensor makes it possible to determine pressure profiles from Spatial TDR data. The design of the sensor is based on a rubber-insulated transmission line. Due to mechanical forces, the distance between the conductors of the transmission line is changed, which leads to a spatial distribution of the capacitance and inductance of the sensor properties. The resulting partial reflections of an incident step pulse are used to reconstruct the physical parameter distributions. Detailed information on the reconstruction algorithm are given in Scheuermann & Hübner (2008). The reconstruction procedure was validated in a simplified laboratory experiment. Steel strips (20.5 mm in width and 1.1 mm thick) were used as conductors for a 102 cm long transmission line (see Figure 11). The TDR signal was launched at a distance of 1 cm from the end of the strips into the transmission line. In this way, the actual length available during a TDR-measurement was reduced to 101 cm. The steel strips were bent at regular intervals of 25 cm. Thus four areas were adjusted at a more or less constant distance. The transmission line was calibrated by means of TDR measurements with even steel strips, in order to obtain a calibration function between conductor distance and capacitance. The results of the test were verified by numerical calculations (Scheuermann & Hübner 2008).
Figure 13. Measured and reconstructed distances between the conductors for the profile measurement.
The validation of the reconstruction algorithm is conducted with TDR-measurements, which are recorded for different profiles of the steel strip distances. Figure 12 shows an example of a measured reflected signal (solid line) of a profile and its reconstruction (dashed line). The calibration function mentioned is used to determine the distance between the conductors from the inversely adjusted capacitance profile (cf. Fig. 13). When compared, the reconstructed and measured distance profiles agree satisfactorily. The overshoot at steep edges and other deviations can be attributed to the spatial resolution of 2.5 cm of the algorithm, timing/amplitude errors in the TDR instrument, end capacitance effects and other non-ideal properties of the transmission line. 4.2 Prototype development
Figure 11. sion line.
Bent steel strips as inhomogeneous transmis-
A prototype sensor for geotechnical applications has been developed and investigated. It consists of two
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Figure 14.
to minimize outer influences on the electromagnetic field (cf. Fig. 14). The aim of the investigations with the prototype design is to demonstrate the general use of this measurement technique under real conditions. In order to prove the spatial sensitivity for the localisation of pressure changes, simple experiments were conducted with a sensor of the prototype design 113 cm in length. For this purpose, the sensor was placed in a loading frame. The sensor was loaded at four different positions using flat weights and rigid polystyrene blocks to distribute the load over a specific section (20 cm). The step-wise load at the different positions was achieved with weights of 10 kg each. After each load step TDR measurements were conducted from both sides of the sensor, which increases the information content of a measurement for each load condition. Figure 15 shows the evolution of the TDR traces for every load condition of the loading phase. The initial condition without load (0 0 0 0) forms the upper border of the graph. With every load step the TDR trace changes due to the changing capacitance respectively due to the changing impedance. The resulting difference forms an area which is highlighted in a grey colour (cf. legend top right). The photo shows the load conditions 10 30 20 10. The top graph shows the TDR measurements from position 1 and the graph in the middle the measurements from position 4. The bottom graph shows the differences of the superposed TDR traces compared to the initial condition. The evolution of the TDR traces shows clearly the changes of the conductor distance due to the mechanical load. In contrast to the distinct changes in the distances on the profiled transmission line presented above, the changes in the distance are smoother, which can be also seen in the evolution of the TDR traces. In particular, the presentation of the differences implies a parabola like distribution of the distances below the polystyrene blocks at each load position.
Diagram of the prototype sensor.
5
Figure 15. Stepwise loading test with the long prototype sensor: photo: load configuration 10 30 20 10 (for illustration purposes) above: TDR traces measured from left end (near position 1) middle: TDR traces measured from right end (near position 4) below: differences of the superposed TDR traces relative to the initial condition (0 0 0 0).
steel-strips (15 mm in width and 0.4 mm thick) with rubber foam (approx. 9.7 mm thick) as dielectric material. At the free surfaces of the steel strips (above and below the sensor) 6.9 mm thick rubber sealings are fastened with glue serving as electric insulation in order
CONCLUSIONS
The applications of Spatial TDR presented clearly show the wide applicability of this new method. The great advantage of Spatial TDR is its high resolution both in space and time, which is required for monitoring purposes, especially for transient processes. Hence Spatial TDR is applicable on different scales, from a laboratory scale of several decimeters (cf. Becker et al. 2008) up to a field scale of several meters (Scheuermann & Bieberstein 2006). In this respect it should be emphasized that— besides the reconstruction algorithm—Spatial TDR includes hardware components like multiplexers, probes and additional electronic devices and the
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corresponding controlling software (cf. Becker 2004, Hübner et al. 2005). Although the observation of the unsaturated water movement is still the major field of application, other applications—especially in geotechnics—are under development, such as the measurement of pressure distribution.
REFERENCES Becker, R. 2004. Spatial Time Domain Reflectometry for Monitoring Transient Moisture Profiles. Ph. D. thesis, Inst. for Water and River Basin Management, Univ. of Karlsruhe. Becker, R., Scheuermann, A., Schlaeger, S., Hübner, C. & Wagner, N. 2008. Spatial Time Domain Reflectometry (Spatial TDR)—Principles, limitations and accuracy. First European Conference on unsaturated soils; Proc. First European Conference on Unsaturated Soils, Durham. Dowding, C.H., Su, M.B. & O’Connor, K. 1989. Measurement of rock mass deformations with grouted coaxial antenna cables. Rock Mechanics and Rock Engineering, 22:1–23. Heathman, G.C. & McAfee, J. 2006. Measuring soil hydraulic properties using dielectric sensors. TDR 2006, Purdue University, Proc. https://engineering.purdue.edu/ TDR/Papers. Huebner, C., Schlaeger, S., Becker, R., Scheuermann, A., Brandelik, A., Schaedel, W. & Schuhmann, R. 2005. Advanced measurement methods in Time Domain
Reflectometry for soil moisture determination. In Klaus Kupfer (ed.), Electromagnetic Aquametry: 317–347. Springer. Kane, W.F., Beck, T.J. & Hughes, J.J. 2001. Applications of Time Domain Reflectometry to landslide and slope monitoring. TDR 2001, Proc. http://www.iti.northwestern.edu/ tdr2001/proceedings. Long, D.S., Wraith, J.M. & Kegel, G. 2002. A heavyduty Time Domain Reflectometry soil moisture probe for use in intensive field sampling. Soil Sci. Soc. Am. J. 66:396–401. Scheuermann, A. & Bieberstein, A. 2006. Monitoring of dams anddikes—watercontentdeterminationusingTimeDomain Reflectometry (TDR). 13. Danube European Conference on Geotechnical Engineering: Ljubljana, Slovenia, Mai 29–31, 2006, ISBN 961-90043-8-8, 2: 493–498. Scheuermann, A. & Bieberstein, A. 2007. Preferential water movement in homogeneous soils. Proc. Int. Symposium on Mechanics of Unsaturated Soils, March 7–9, Weimar, 461–473. Scheuermann, A. & Hübner, C. 2008. On the feasibility of pressure profile measurements with Time Domain Reflectometry (TDR). IEEE Trans. Instr. Meas. (accepted). Schlaeger, S. 2005. A fast TDR-inversion technique for the reconstruction of spatial soil moisture content. Hydrology and Earth System Sciences 9: 481–492. Schofield, T.G. 2001. Long-term stability of Time Domain Reflectometry measurements in a multi-layer field experiment. TDR 2001, Proc. http://www.iti.northwestern.edu/ tdr2001/proceedings.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Water content dynamics in unsaturated soils – Results of experimental investigations in laboratory and in situ A. Scheuermann Institute for Soil Mechanics and Rock Mechanics, University of Karlsruhe (TH), Germany
ABSTRACT: The unsteady movement of water frequently involves so-called ‘‘dynamic effects’’. So far, most investigations regarding these effects have been mainly focused on the drainage processes starting from full saturation, which represents only one aspect concerning questions on dynamic effects. The contribution presents measurements obtained during laboratory and in situ experiments revealing new aspects of these effects in conjunction with infiltration and alternating hydraulic stresses.
1
2
INTRODUCTION
Dynamic effects in connection with multi-phase or unsaturated water flow have been observed many times in experimental investigations, which generally arise as temporarily delayed changes in the water content (Topp et al. 1967) or in the outflow (Hollenbeck & Jensen 1998). However, most of the experiments conducted were not designed especially to investigate these effects. They were carried out in order to verify Richards’ equation (Biggar & Taylor 1960), to investigate the soil properties affecting soil water characteristics (Elzeftawy & Mansell 1975) or to determine the parameters describing the soil water characteristic curve (Wildenschild et al. 2001). An overview of experiments showing dynamic effects is given by Hassanizadeh et al. (2002). These experimental investigations clearly show that dynamic effects are significant in both granular and fine-grained soils in drainage and infiltration. However, in the literature (cf. Wildenschild et al. 2001, Hassanizadeh et al. 2002) the mechanisms discussed as being the cause of these dynamic effects are focussed mainly on drainage. The possible mechanisms for the occurrence of dynamic effects during infiltration or even for cyclic hydraulic conditions, i.e. the alternate infiltration and drainage of water, have not been investigated in detail so far. In the following, measurement results are presented, which were observed in the laboratory using column test apparatus. In situ experiments on a full-scale dyke model are also shown.
SOIL USED IN THE EXPERIMENTS
The soil used in the experiments was a well graded sand with grain sizes between 0.2 and 2 mm. The densities of the sand in both experiments were similar corresponding to a density index Dr = (nmax − n)/ (nmax −nmin ) ≈ 0.6 with porosity n of the material, the maximum being nmax and the minimum nmin . Based on this density index, the pore constriction size distribution of the sand was calculated using a numerical method (cf. Scheuermann et al. 2008). Both the grain size and the pore constriction size distributions are shown in Figure 1. With regard to the well graded distribution of the grain size as well as the distribution of the pore constriction size, the soil water retention curve of the sand
Figure 1. Grain size and pore constriction size distribution of the well graded sand used for the experiments.
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Figure 2. Primary drainage und main wetting curve of the sand with fitting curves using the model acc. to Mualem (1976). Figure 4. Diagram of the column test apparatus with the measuring devices used.
Figure 3. Unsaturated hydraulic conductivity of the sand ac-cording to the model of Mualem (1976).
shows a distinct transition from a saturated to an unsaturated condition (see Figure 2). The corresponding air entry value |ψAEV | of the sand is about 1 kPa. Figure 2 shows the primary drainage and the main wetting curves of the sand measured in the laboratory under a state of equilibrium using a Buchner funnel set-up. In addition a fitting curve is included with the parameterization according to Mualem (1976). The saturated hydraulic conductivity of the sand is kf = 2.1 · 10−4 m/s. The correspond-ing evolution for the unsaturated condition is shown in Figure 3 (based on the primary drainage curve).
3
COLUMN TEST APPARATUS
3.1 Experimental set-up and instrumentation In order to determine the soil hydraulic parameters depending on the density, the soil water retention curve and the unsaturated hydraulic conductivity, a column test apparatus was developed to carry out multi-step inflow and outflow experiments under de-fined stress conditions on samples 40 cm in height and 19 cm in diameter (cf. Scheuermann et al. 2003). Figure 4 gives
a diagram of the experimental set-up of the column test apparatus. The soil sample is located in a plastic-bag, which is embedded in a pipe of fiber glass. The plastic-bag is sealed with closing plates at both ends. In order to induce a hydraulic stress on the sample, a filter of sintered porous glass is installed in the lower plate. In contrast, the upper plate has a small opening to ensure atmospheric boundary conditions at the opposite end of the sample. As a result of this arrangement, the fiber glass pipe is unsupported and it floats, only held by the friction between the plastic-bag and the pipe. The interface between the plastic-bag and pipe is lubricated with Vaseline in order to reduce the friction and to allow the sample to deform axially with as little hindrance as possible (oedometric-like condition). In order to vary the density of the material, the sample is mechanically loaded using a hydraulic pump using the steel frame as a reaction. A position encoder records the deformation of the sample. For the purpose of the experiment, the hydraulic stress is imposed on the lower closing plate by means of a hanging water column. An overflow connected to a water reservoir is used to keep the hydraulic stress constant (cf. Figure 4). The column is equipped with different measuring devices, including four tensiometers installed in order to measure the matric suction at four different points along the column. For this reason, small windows are located in the pipe. Furthermore, two flat band cables are placed between the pipe and the plasticbag, which make it possible to measure the spatial distribution of the water content in the soil using a newly developed measuring method called ‘Spatial TDR’ (see Becker et al. 2008, Scheuermann et al. 2008). A detailed description of any further equipment is given in Scheuermann et al. (2003). With the above mentioned measuring devices continuous observation of both the matric suction and the water content is
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possible, thus describing the transient changes of the hydraulic conditions inside the soil sample.
Table 1. Mechanic load, deformation and stored water after each hydraulic cyle.
3.2
Hydraulic cycle
Mech. load kPa
Deformation mm
Stored water ml
1 2 3 4
0 100 200 300
0 6 2 1
580 560 350 350
Performing the experiment
The following experiment differs firstly from conventional multi-step experiments regarding the conditions and secondly from the experiment originally planned using this set-up. Thus the test started with infiltration under quite dry initial conditions of θi ≈ 3 vol-% roughly corresponding to the residual water content θr (cf. Figure 2). Furthermore, the density of the sand was initially too high to compact the sample normally with increasing mechanical loads. Only small deformations were observed. In this way an experiment was performed, whereby the sample was hydraulically stressed in cycles with repeated infiltration and drainage phases. Below the performance of the experiments is illustrated taking as an example the last (4th) hydraulic cycle, which was carried out with a mechanical load of 300 kPa (cf. Table 1). The corresponding time-variations of the experiment (with a hydraulic cycle consisting of infiltration followed by drainage) is given in Figure 5. In the upper diagram the imposed steps in hy-draulic stress are shown. The reference level is at the top edge of the lower closing plate. As can be seen, the infiltration path as well as the drainage path were carried out in four steps each consisting of 2 kPa beginning with an initial matric potential of −4 kPa. A new hydraulic stress was set before the state of equilibrium was reached. In the second graph the cumulative discharge is shown. The mean volumetric water content measured with the TDR sensors (symbols) and calculated from the discharge (line) is plotted in the third graph in Figure 5. It can be seen, that there is a difference in the values of up to 3 vol-%. One reason for this discrepancy is the fact that the lower part of the sample (ca. 5 cm) was not observed by the sensor. The last four graphs show the time-variation of the matric suction measured with the tensiometers. The positions of each tensiometer are given in the graph. Altogether four identical hydraulic cycles (infiltration and drainage with four steps each with 2 kPa) were carried out with four different mechanical loads. Two experiments were carried out every day; thus there was a break over night between the second and the third experiments. After each hydraulic cycle a certain amount of water was stored in the sample as can be seen from the graph for the cumulative discharge in Figure 5. This water could not flow out of the sample, since the outlet was closed during the break, when the new mechanic load was also adjusted. The volume of water stored after each hydraulic cycle is given in Table 1 together with the deformations for each mechanical load. The same observation can be seen
Figure 5. Time-variation curve of the measured values of the last (4th) hydraulic cycle with a mechanical load of 300 kPa.
in Figure 6, in which the temporal evolution of the mean volumetric water content for each experiment is presented. After each hydraulic cycle, the mean hydraulic water content throughout the sample increased. Furthermore, it can be seen from the graph that the final condition of each experiment corresponded to the initial condition of the next one. This also means that
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Figure 6. Time-variation of the mean volumetric water content along the soil sample measured at different load stages.
the mechanical load increased in stages had no influence on the water content measurements. Below these results are presented in detail and discussed in relation to the observed dynamic effects. 3.3
Figure 7. Water content profiles at different time steps of the 4th hydraulic cycle during infiltration (left) and drainage (right) with readings of the water level measured with tensiometers.
Results and discussion
Figure 7 shows the profiles of volumetric water content for the different time steps of the 4th hydraulic cycle during the experiment (cf. Figure 6 and Table 1) for the phases of infiltration (left) and drainage (right). The time of measurement and the appropri-ate level of the hydraulic zero potential (z-coordinate in regard to the lower boundary of the sample) is indicated in each legend. The zero potential is derived from the tensiometer readings and corresponds to the water level under the assumption that there is a state of equilibrium. It indicates the situation under transient conditions when matric suc-tion is lost. A comparison between the water content profiles for the infiltration and the drainage shows, that completely differing pore water pressure conditions can be observed for similar water content distributions. For example, during infiltration a zero potential and thus a loss of matric suction can be measured even for small volumetric water contents (cf. water content profile for t = 59 min.). However, for a similar water content distribution at t = 107 min. in the drainage phase, there is still an area with a fairly high volumetric water content above the level of hydraulic zero potential. This observation is not only caused by the hysteresis of the soil water retention curve. Another reason can be found in effects caused by the transient or dynamic conditions, prevailing during the experiment. Figure 8 shows a synoptical description of the overall conditions of the 4th hydraulic cycle at tensiometer 2 (z = 18 cm) during the experiment. In the graph on the top left, the cumulative discharge is shown. In this regard it should be mentioned that the
Figure 8. Multi-step-inflow and outflow-experiment of the 4th hydraulic cycle: Time-variation curve of recorded measure-ments at tensiometer 2 (2nd from below, cf. Figure 4).
time axis runs from right to left. The hydraulic potentials as lower boundary conditions are highlighted in grey (cf. data in the bend of the diagram at the bottom on the left).
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The matric potential readings at tensiometer 2 are presented in the central graph on the left. Here both negative and positive pore water pressures are included in the graph. The corresponding water con-tents at this location are presented in the lower graph on the right. A mean volumetric water content is calculated from the Spatial TDR measurements over a range of 2 cm on the elevation of tensiometer 2. By combining the matric suction readings and volumetric water contents, the graph in the centre on the right with the white background can be taken as a kind of soil water retention curve, whereby ‘a kind of ’ merely highlights the fact that also positive matric potential readings are included here. Finally the graph shows the relationship between pore water pressure and water content as a closed hysteresis loop. For comparative purposes the quasi-static soil water retention curve from Figure 2 is included in the graph. As can be seen from the graph, neither result can really be compared with the other. For example, the primary drainage curve (grey triangles) is located above the transient drainage curve (black rhombuses). Earlier experimental investigations (cf. Hassanizadeh et al. 2002, Mohamed & Sharma 2007) have shown, that the curve for dynamic conditions should be located above the quasi-static curve and not conversely. The reason for this contradiction lies on the one hand in the densities of the samples. The quasi-static water retention curve was measured with a density index Dr ≈ 0.95 under very dense conditions, whereas the density index of the sample in the column was Dr ≈ 0.6. On the other hand, the quasi-static drainage curve was determined starting at full saturation. The highest saturation during the transient experiment in the column was circa 80%. Nevertheless, the infiltration curve especially shows distinctive devolution influenced by the tranient or dynamic boundary conditions. The loss of negative matric potential happens at a volumetric water content of circa θ = 17 vol-%, which corresponds to a saturation of not even S = 50%. For this reason, the soil water retention curve of the column experiment is located considerably below the quasi-static curve. Another impressive effect caused by dynamic—and in special cases cyclic—hydraulic boundary conditions is given in Figure 9. It shows the soil water retention curves for all hydraulic cycles conducted with in column test apparatus. As can be seen from the graph, the soil water retention curves reflect the same cumulative response as indicated by the stored water volume (cf. Table 1) or by the mean volumetric water contents of Figure 6. The volumetric water content of the 1st hydraulic cycle is particularly surprising, when the negative matric potential was lost. At circa θ = 9 vol-% it does
Figure 9. Step-wise increase in the water content inside the soil sample with repeated infiltration of water (measurements at tensiometer 2).
not even correspond to a saturation degree of S = 25%, and the highest volumetric water content measured in this experiment was roughly θ = 18 vol-% (S = 50%). Although these degrees of saturation are quite small, it is perfectly conceivable that positive matric potentials could occur, since both the air and water phases form continuous phases during these degrees of saturation. Both values (water content at loss of suction and maximum water content) increased from cycle to cycle with repeated infiltration and drainage of the sample, indicating an accumulation of water. Under the supposition that the hydraulic boundary conditions remain constant, it can be expected that with additional hydraulic cycles a limit cycle would be reached, leading to a constant hysteresis loop. This kind of pumping effect was also qualitatively ob-served in column experiments with clayey material (Delov & Diankov 1998). One possible explanation for this observation is based on the sintered porous glass plate at the lower end of the sample. The saturated hydraulic conductivity of the glass plate at kf = 2.5 · 10−6 m/s is roughly 100times smaller than the hydraulic conductivity of the sand. Nevertheless, in a dry condition the sand strives to soak up water. If during infiltration a degree of saturation is reached, which is high enough to transport the water upwards for the existing hydraulic gradients, the water content should stay constant. It can be expected that primarily small pore-channels will be activated in such a process. The subsequent drainage of the sample leads to an incomplete desaturation of the sand and some pores remain filled with water. During subsequent infiltration under the existing conditions (hydraulic gradient and initial saturation of the sample) further porechannels are activated and more water can flow into the sample.
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This explanation is just a hypothesis for the observation presented, which needs to be verified in controlled experimental investigations. Nevertheless, the observations in the column experiments demonstrate a new aspect concerning dynamic effects. Even if the absolute values of the water con-tent measurements may be inexact, the relative changes are given and they are significant. Confirmation of these observations is given in the next section, in which measurements in a full-scale dyke model are presented.
4
FULL-SCALE DYKE MODEL
Physical flood simulation tests were carried out in a full-scale dyke model. The dyke was built up with the same sand used for the investigations with the column test apparatus and with a similar density. Figure 10 shows the positions and lengths of the flat band cable used as TDR-sensors inside the dyke cross-section. Tensiometers are installed at different depths along the first sensor from the crest of the down-stream slope side (see crosses in Figure 10). A de-tailed description of the dyke model and its instru-mentation is given in Scheuermann et al. (2008). The readings of the water content measured with Spatial TDR and the recorded matric potentials were analyzed in the same manner as for the experiments with the soil column. Figure 11 presents the corresponding relationship between the volumetric water content and the matric potential. As can be seen from the graph, the volumetric water content, at which the matric suction is lost, increases with the height of the observation point. The measurements were conducted during the transient seepage through the dyke. The velocity of the moving phreatic surface during infiltration decreases with increasing in-filtration. The closer the phreatic surface is situated to the stationary condition, the slower is the velocity. Thus, the differences in the soil water retention curves measured in situ must be caused by the different velocities of the phreatic surface. These independently measured observations verify the results from the laboratory investigations in the soil column.
Figure 11. Measurements of matric potential during a flood simulation experiment on a full-scale dyke model.
5
OUTLOOK
The experiments presented were not originally designed for investigating dynamic hydraulic effects. However, the observations clearly show several phenomena resulting from the particular dynamic conditions. Thus it could be seen that, during the transient infiltration of water, matric suction may be lost even at very small water contents. This phenomenon depends on the velocity of the infiltration, as could be seen from the results when in the dyke model. A new aspect with regard to dynamic effects is the cumulative storage of water during cyclic hydraulic boundary conditions. The velocity of the in-filtrating water is only one influencing factor for this phenomenon. Another might be the availability of water during infiltration. The observations presented in this paper were only possible with the help of the new measuring method, Spatial TDR. In future laboratory experiments and large-scale experiments this method will also be used for the targeted investigation of hydraulic dynamic effects. REFERENCES
Figure 10. Set-up of measurement devices with positions and lengths of the flat band cables and positions of tensiometers.
Becker, R., Scheuermann, A., Schlaeger, S., Huebner, C. & Wagner, N. 2008. Spatial Time Domain Reflectometry (Spatial TDR)—Principles, limitations and accuracy. First European Conference on Unsaturated Soils; Durham.
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Biggar, J.W. & Taylor S.A. 1960. Some aspects of the kinetics of moisture flow into unsaturated soils. Soil Sci. Soc. Am. Proc. 24: 81–85. Delov, K. & Diankov, Z. 1998. Einfluss des Lufanteiles auf die Hysteresisparameter bei der Bodenbewaesserung. Dresdner Wasserbauliche Mitteilungen, Inst. f. Wasserbau und Techn. Hydrom., TU Dresden, 13: 391–400. Elzeftawy, A. & Mansell, R.S. 1975. Hydraulic conductivity calculations for unsaturated steady-state and transientstate flow in sand. Soil Sci. Soc. Am. Proc. 39: 599–603. Hassanizadeh, S.M., Celia, M.A. & Dahle, H.K. 2002. Dynamic effect in the capillary pressure-saturation relation-ship and its impacts on unsaturated flow. Vadose Zone J. 1: 38–57. Hollenbeck, K.J. & Jensen, K.H. 1998. Experimental evidence of randomness and nonuniqueness in unsaturated outflow experiments designed for hydraulic parameter estimation. Water Resour. Res. 34: 595–602. Mohammed, M.H.A. & Sharma, R.S. 2007. Role of dynamic flow in relationships between suction head and degree of saturation. J. of Geot. and Geoenviron. Engin. 133: 286–294.
Mualem, Y. (1976). Hysteretical models for prediction of the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12(6): 1248–1254. Scheuermann, A., Bieberstein, A., Triantafyllidis,Th., Huebner, C., Becker, R, Schlaeger, S. & Wagner, N. 2008. Spa-tial Time Domain Reflectometry (Spatial TDR)—On the use in geotechnics and geohydraulics. Proc. First European Conference on Unsaturated Soils, Durham. Scheuermann, A., et al. 2003. Column test apparatus for the inverse estimation of soil hydraulic parameters under de-fined stress condition. ISBN 3-540-21121-7, Springer, Ber-lin, 33–44. Topp, G.C, Klute, A. & Peters, D.B. 1967. Comparison of water content-pressure head data obtained by equilibrium, steady-state, and unsteady-state methods. Soil Sci. Soc. Am. Proc. 31: 312–314. Wildenschild, D., Hopmans, J.W. & Šim˚u,nek. 2001. Flow rate dependence of soil hydraulic characteristics. Soil Sci. Soc. Am. J. 65: 35–48.
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A new high capacity tensiometer: First results J.C. Rojas, L. Pagano, M.C. Zingariello & C. Mancuso University of Naples, Federico II, Italy
G. Giordano & G. Passeggio INFN, Naples, Italy
ABSTRACT: A high capacity tensiometer has been developed at the University of Napoli Federico II that allows substitution of the High Air Entry Value (HAEV) filter and, hence, the variation of the probe measurement range and response time. The device has been also designed to allow initial saturation without removal from the high vacuum temperature-controlled pre-conditioning chamber. Regardless of the HAEV filter (5 bar and 15 bar), the probe has been saturated under a saturation pressure of 800 kPa and then calibrated applying positive pressure values. To evaluate the performance of the tensiometer free evaporation tests, prolonged high suction measurements and pressure reversal tests were carried out. The tensiometer layout, the pre-conditioning setup and the saturation process are described in the paper. The results obtained during some preliminary tests are also presented and discussed.
1
INTRODUCTION
In recent years, several designs of high capacity tensiometers have been presented in the literature. According to the original proposal from Ridley & Burland (1993), all these devices use a fixed high air entry value (HAEV) filter to protect the water reservoir against de-saturation (Fig. 1). This introduces however two contrasting requirements: (a) the need to maximize the air entry value (AEV) of the filter, in order to extend as much as possible the suction measured, and (b) the need to limit the AEV of the filter in order to reduce the response time of the tensiometer. In addition, the need for high pressurization during the saturation of the HAEV filter and water reservoir (i.e. 4 MPa after Ridley & Burland 1999),
Figure 1. 1995).
Model of mini-tensiometer (Ridley & Burland
makes unfeasible the use of high sensitivity thin diaphragms due to the possibility of them yielding during pressurization. This paper discusses the above two problems, presenting a new high capacity tensiometer developed at the University of Napoli Federico II (UNINA). The design of the new tensiometer addresses the contrasting requirements associated with the functioning and pre-conditioning of the probe. Also discussed are the performance of the probe when a saturation pressure of 800 kPa is used and ceramic filters of 5 and 15 bar AEV are adopted. 1.1 Cavitation When water is subjected to a pressure lower than its vapour-saturation value, it usually transforms into vapor (causing cavitation). However, in a tensiometer, if pure water is used to saturate the HAEV and water reservoir, and hydrophilic materials are adopted to build a very smooth measuring chamber, cavitation may occur only in appropriate circumstances far beyond thermodynamic equilibrium. As a matter of fact, the maximum tension that pure water can stand ranges from 200 MPa, as measured by Imre (2002), to 400 MPa, as theoretically predicted by Tabor (1979). Under a tension of 200 MPa the pure water is not in equilibrium but can remain in this metastable condition for a long time. To explain this fact it is worth recalling that cavitation is a non-equilibrium process triggered at a
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cavitation nucleus, that brings an unstable system to a new equilibrium condition through a process of phase transition by heterogeneous density fluctuations. Cavitation may be triggered at the site of microscopic heterogeneities in the liquid, such as suspended dirt particles, gas micro-bubbles, etc. (i.e. heterogeneous nucleation), or it may arise randomly in the liquid itself (i.e. homogeneous nucleation) if the required conditions of pressure and temperature exists. In nature and in technical applications heterogeneous nucleation is the most common trigger of cavitation. If sufficient numbers of ‘‘nucleation sites’’ of sufficient size are present, when a liquid is subjected to a pressure reduction the liquid will become vapor and cavitation rapidly occurs. On the contrary, if no nucleation site is present, the depressurization of the liquid may lead to a metastable state down the theoretical isotherm, since imperfections may cause instability and transition to the vapor phase. In the particular case of high capacity tensiometers, even if pure water is used, a weakness will still exist in the microscopic bubbles of gas present in crevices at the water-solid contact (Brennen 1995) (i.e. at the contact between the water and the reservoir), and inside the water filling the pores of the HAEV filter. To understand how this weakness may be reduced, the crevice model proposed by Harvey et al. (1944) may be helpful. As a matter of fact, this model establishes that if a small volume of gas is trapped in minute crevices at the contact between the water and a solid, the application of an appropriate water tension may cause the expansion of the gas until the bubble stability is lost and uncontrollable expansion occurs. In this situation it is likely that the bubble will move from the solid-liquid surface into the liquid and will dissolve if a new pressurization stage is applied (Atchley & Prosperetti 1989). A higher water tension is now necessary to cause the expansion of the micro-bubble that remains within crevice (Harvey et al. 1944), though, in water, microbubbles of air seem to persist almost indefinitely and are almost impossible to remove completely (Brennen 1995). All the above suggests that subjecting a high capacity tensiometer to cycles of high depressurization and high pressurization may improve its saturation, reducing the size of heterogeneous cavitation nuclei by extracting ‘‘air fractions’’ from the cavities and dissolving them in the water. Trevena (1982) summaries the experimental results reported in the literature regarding the effects of time in cavitation. Their conclusions can be outlined as: a) if the nucleation site is the solid surface, the breaking tension decreases as the pressure rate increases with time; b) when the cavitation starts in the liquid itself, the breaking tension increases as the stressing rate increases; c) the longer the time of pressurization the greater is the tension needed for cavitation; d) the breaking tension increases steadily as the number of
cycles of cavitation and pressurization increases until it levels-off at an upper limit. 1.2
Direct suction measurement: previous studies
As mentioned, many studies considering direct suction measurements with high capacity tensiometers have been published. Table 1 summarizes some basic information on the type of HAEV filter, assembly method, etc. used by various Authors. All these studies seem to indicate that the design of a tensiometer is crucially important as it influences its robustness, sensitivity, ease of saturation, speed of response, and cavitation resistance (Take & Bolton 2003). Equally clear is that the design of appropriate saturation setups and procedures is also critical. With reference to the probe design, previous experience recognizes the important role of the water reservoir volume, as this is in direct contact with the internal area of the diaphragm. In particular it is generally recognized that the use of water reservoirs as small as possible will reduce the probability of cavitation (Ridley & Burland 1993; Marinho & Pinto 1997). In particular, Guan & Fredlund (1999) suggested that there is a cavitation tension for a particular pre-pressurization procedure and a particular suction probe. Ridley & Burland (1999) found, on the contrary, that for a thoroughly saturated suction probe the stress required to cause a tension breakdown in the reservoir water is uniquely related to the AEV of the filter. Most of these probes can stand very high values of suction but, as Take & Bolton (2003) mentioned, there are many applications where small suction values (i.e. 300 kPa) are of interest. This implies the requirement for sensitive lower-pressure-range devices that are likely to be damaged when a high pressure is applied. According to the previously described crevice model, Tarantino & Mongiovì (2001) observed that saturation of the ceramic filter is achieved mainly through cycles of cavitation and subsequent pressurization, and that an inadequate initial saturation simply increases the number of cycles required to obtain a satisfactory performance of the probe. Contrarily, Guan & Fredlund (1999) indicated that repeated cavitation of the sensor appeared to reduce the maximum sustainable tension. Finally, Chiu et al. (2005) and Lourenço et al. (2006) show unclear evidence to support the hypothesis of an increase of cavitation suction with cycles of cavitation and pressurization. In summary, after Marinho & Chandler (1994), the main requirements to avoid cavitation in the measurement system and improve the ability to measure negative water pressure seems to be: a) water and all surfaces within the measurement system must be pure and clean (Henderson & Speedy 1980), b) the surfaces in contact
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Table 1.
Saturation process data used in previous studies.
Tensiometer
Filter AEV (bar)
Assembly
Vacuum saturation
Pre-pressurization pressure (kPa)
Pre-pressurization cycles
Ridley & Burland (1999) Guan & Fredlund (1997) Tarantino & Mongiovì (2002) Meilani et al. (2002) Take & Bolton (2003) Chiu et al. (2005) He et al. (2006) Lourenço et al. (2006) Mahler & Diene (2007)
15 15 15 5 3 5 5 15 5, 15
dry under water dry dry oven dried dry dry or saturated dry dry
yes (60 min) no yes no yes (20 min) yes (60 min) no yes yes (15 h)
4000 (24 h) 12000 (1 h) 4000 (24 h) 800 (4 days) 1000 (1 h) 700 (24 h) 2000 (1 month) 800 (72 h) higher than filter AEV
no yes (6 cycles) no no yes no no no yes
with the water system must be as smooth as possible to avoid or reduce the number and size of crevices, c) the system should be air-evacuated by vacuum application prior to the pre-pressurization in order to remove the maximum amount of air entrapped into the crevices (Jones et al. 1981), d) pre-pressurization of the system to high pressure is required in order to dissolve all the free air (Harvey et al. 1944), e) the HAEV disk must be brought to a low initial moisture content prior to the application of initial saturation, as this has been demonstrated a crucial factor for the saturation of the disk itself (Take & Bolton 2003). All these factors should be considered in the design of a saturation setup and saturation procedure adopted for any probe.
2
THE UNINA PROBE
A high capacity tensiometer has been developed at the University of Naples Federico II using a design layout similar to that initially proposed at the Imperial College of London (Ridley & Burland 1995) but including some variants to allow the substitution of HAEV disk without changing the whole probe. This measure has been adopted in order to easily tune the measurement capacity of the tensiometer and its response time to the particular application under study. The UNINA probe (Fig. 2), utilizes a circular clamped-edge diaphragm. The strain-gauged diaphragm is 6 mm in diameter and 0.4 mm in height. The strain gauge has a rosette-like design with the radial strain gauges next to the rim and tangential strain gauges adjacent to the radial ones, generating the highest sensitivity when combined in a Wheatstone bridge. The circular trim diameter of the strain gauge covers a considerable area of the micro diaphragm. To produce the maximum allowable output signal the strain gauge is bonded to the non-pressurized side of the diaphragm. The novel piece is an interchangeable filter cap containing a HAEV ceramic disk of 7.4 mm in diameter
Figure 2.
UNINA high capacity tensiometer.
and 6.0 mm in height. The operating range is determined by the filter’s AEV (e.g. 5 or 15 bar), allowing a single unit to operate in different suction ranges by changing the filter. The water reservoir between the ceramic disk and the strain-gauged diaphragm has a volume of approximately 3 mm3 . Two stainless steel housings are used (Fig. 2), one to hold the diaphragm, and another one to provide a support and isolate the electrical connectors. A vented waterproof sheating ensures atmospheric pressure is maintained in the back of the strain-gauged diaphragm and isolates the electronic parts from water and dust. The strain-gauge measurements are acquired through a bridge amplifier static strain indicator and stored in a digital data logger. The recorded data (i.e. up to 1 per second of observation) are stored on a memory card and transferred by a USB port to a PC. The strain gauge is connected to the acquisition system through appropriate input terminals. An undefined full-bridge circuit is used as input, selected on the basis of the net output of the active strain gauges without mathematical corrections for either bridge configuration or nonlinearity being applied. Operating in this way, the nonlinearity errors will have to be determined by direct calibration against a previously calibrated transducer. Table 2 shows the design parameters that characterize the UNINA probe, determined assuming 2000 kPa as the maximum
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Table 2. Characteristics corresponding to a maximum applied pressure of 2000 kPa. Parameter
Symbol
Critical magnitude
Units
Radial strain Total gage output Sensitivity Deflection Radial stress
εR Eo – Yc σR
3.8 × 10−4 0.125 0.28 2.1 × 10−3 54, 210
– mV/V μV/kPa mm kPa
pre-pressurization pressure. The maximum radial strains in the diaphragm are well-suited with the reference of the strain gauge manufacturer (i.e. >−2 × 10−3 ). The maximum expected deflection is very little compared with the water reservoir depth (0.1 mm) and therefore the design ensures the free deformation of the diaphragm. Also, the maximum radial stress remains below the yielding stress for the stainless steel.
3
Figure 3.
Saturation system.
Figure 4.
Tensiometer calibration curve.
SATURATION SYSTEM
As the initial saturation procedure of high capacity tensiometers has been demonstrated to be very important, a saturation system (Fig. 3) has been designed to saturate and calibrate the UNINA probe. The apparatus consists of two chambers (c1 and c2), a vacuum generator (g), a vacuum gauge (m), two heaters (h1 and h2), and five valves (v1–v5). Initially valve v1 is opened to drive distilled water into the chamber c1. The water is then de-aired keeping all the valves closed except valve v2 and applying a relative pressure of −95 kPa to the chamber c1 through a pressure p1 = 600 kPa applied to the vacuum generator g. The water is de-aired for at least 3 hours. The tensiometer T is then screwed into the chamber c2. To dry the tensiometer, the heaters h1 and h2 are switched on to bring the tensiometer chamber to constant temperature of 70◦ C. Opening the valve v3 vacuum is applied to the chamber c2. After 16 hours the heaters are switched off and valve v5 is opened to slowly introduce water into the chamber c2 (and, hence, into the HAEV filter and water reservoir) while under vacuum. Four hours after, the vacuum is released and further time is allowed for saturation of the filter and water reservoir under atmospheric pressure. The valve v4 is then opened and the valves v3 and v5 closed in order to pressurize the chamber c2 at a pressure p2 = 800 kPa and to force any residual amount of air into solution. The pressurization stage is applied for 72 hours. It is important to note that a maximum pressure of 800 kPa has been applied during saturation, independently of the AEV used. A weakness of the saturation system is the absence of an interface membrane between air and water in
the pre-pressurization chamber, allowing potential air diffusion. The tensiometer is finally calibrated inside the chamber c2 varying the pressure p2 from 0 to 800 kPa. During cyclic pressure loading the probe shows a linear response without appreciable hysteresis (Fig. 4). The calibration curve in the negative pressure range was extrapolated from the calibrated positive range. As Tarantino & Mongiovì (2002) observe, sensitivity resulting from calibration is not so different from the expected value, 0.25 μV/kPa and 0.28 μV/kPa (Table 2), respectively. 4
EVALUATION TESTS
To check the performance of the tensiometer some evaluation tests have been conducted in a 22◦ C constant temperature room. 4.1 Comparison measurements against known suction values Comparisons of the tensiometer measurements against known values of suction were conducted to verify its
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4.2
Figure 5.
Long time suction measurements on soil samples.
time response, its ability to stand high suctions for a long time and to roughly verify the calibration data. The data presented in Figure 5 were obtained using a 15 bar filter. Similar results were obtained when a 5 bar filter was used. The equilibration time of the tensiometer was examined using silty-sand. Matric suctions of 200, 250 and 350 kPa were generated in different samples of this material using a modified Wisa oedometer working under the axis translation technique. Matric suction of the sample was then measured dismounting the oedometer, putting the sample to the atmospheric pressure and using the UNINA probe. A thin layer of the soil paste was used to improve contact between the soil sample and the miniature tensiometer. During the tests the samples remained isolated to avoid large suction changes associated with environmental conditions. The observed trend of matric suction with time may be subdivided into three parts and explained following Guan & Fredlund (1999). In Part I, a sudden increase of readings is observed to reach suction values slightly less than those expected on the basis of the suction applied by the axis translation technique. Afterward, in Part II of the tests, a slow process of suction equalization is observed. In Part III, following a period in which the suctions are almost constant at the expected values, slow increases in the tensions are observed. These are mainly attributed to moisture losses due to evaporation from both the samples and the suction probes during the measurements. The measurements performed on the sample preconditioned to a suction of 350 kPa present some cyclic variations. It is worth noting that large variations are observed during days I, II, V and VI, while no variations were registered in days III and IV corresponding to Saturday and Sunday, respectively. This seems to suggest that the observed variations are related to small temperature changes in the controlled temperature room during working days. The tests were stopped when the probe measured constant suction for a time long enough to validate the capacity of the probe to withstand high suction for a long time.
Evaporation tests
Evaporation tests were performed to determine the maximum measurable suction. The maximum suction values registered are 450 kPa (Fig. 6a) and 720 kPa (Fig. 6b) when 5 bar and 15 bar filters were used respectively. For the 5 bar filter the maximum value registered was approximately the expected one (i.e. ≈500 kPa). This implies that the saturation process for this AEV seems to have worked properly. However, the maximum suction obtained for the 15 bar filter was almost one half of the expected value, but very near to the pre-pressurization pressure applied during the saturation process (i.e. 800 kPa). It is worth noting that Figure 6 indicates that, on cavitation, the pressure increases to −100 kPa, indicating good accuracy of the probe’s calibration. Table 3 presents the values of suction measured at cavitation when the 15 bar filter is used. According to Tarantino & Mongiovì (2001), the data in Table 3 seem to indicate that an enhanced saturation of the ceramic filter is achieved through cycles of cavitation and subsequent pressurization. Moreover, according to Trevena (1982) the upper limit of the tensiometer is of about 645 kPa. Obviously, if a probe is saturated at its upper limit the cycles of cavitation will not improve the probe’s performance. However higher pre-pressurization pressures may improve its response. Then, analogous to observations by Atchley & Prosperetti (1989) in their crevice model of bubble
Figure 6.
209
Cavitation tests: maximum measurable suction.
Table 3.
(Fig. 7a). However, if the probe had not been properly saturated, the offset decreased after every reversal (Fig. 7b).
Tension breakdown values using 15 bar filter.
Test
Tension breakdown (kPa)
1st 2nd 3rd 4th 5th 6th 7th
330 481 566 647 646 720 635
5
CONCLUSIONS
A new high capacity tensiometer has been developed at University of Naples Federico II. The novel design of the probe allows the substitution of the HAEV filter without changing the whole probe. The objective was to study the behaviour of the UNINA probes when they had been saturated under a reduced pressure (i.e. 800 kPa), well below the maximum allowable prepressurization pressure (i.e. 2000 kPa). The response of the new high capacity tensiometer when a 5 bar filter was used was found to be excellent during free evaporation tests, cyclic evaporation tests and equilibration time tests. On the other hand, the 800 kPa pressure applied during the saturation stage was not enough to properly saturate the 15 bar filter. The maximum suction registered seems to be approximately equal to the minimum of either the pre-pressurization pressure used or the AEV of the filter.
REFERENCES
Figure 7.
Response of the probe to suction reversals.
nucleation, the maximum cavitation suction depends on the past history of the tensiometer. Contrarily to the observations in Berthelot tube tests, the tension breakdown value seems not to be affected by the rate at which the tension increases (Fig. 6a, b). 4.3
Cyclic evaporation tests
The probe’s ability to register rapid suction changes was examined using cyclic evaporation tests. Figure 7 shows several evaporation cycles, consisting in free evaporation stages up to prescribed suction values (i.e. lower than the nominal filter’s AEV) and stages in which the atmospheric pore water pressure was applied by immerging the tensiometer tip in water. A probe’s response to reversals of suction was found to be excellent for properly preconditioned probes
Atchley, A.A. & Prosperetti, A. 1989. The crevice model of bubble nucleation. J. Acoustical Society of America 86(3): 1065–1084. Brennen, C.E. 1995. Cavitation and bubble dynamics. Oxford University Press. Chiu, C.F., Cui, Y.J., Delage, P., De Laure, E. & Haza, E. 2005. Lessons learnt from suction monitoring during centrifuge modeling. Proc. intern. symp. on advanced experimental unsaturated soil mechanics EXPERUS 2005. Trento, Italia, June 27–29: 3–8. Guan, Y. & Fredlund, D.G. 1997. Use of the tensile strength of water for the direct measurement of high soil suction. Canadian Geotechnical Journal 34: 604–614. Guan, Y. & Fredlund, D.G. 1999. Use of the tensile strength of water for the direct measurement of high soil suction: Reply. Canadian Geotechnical Journal 36: 181. Harvey, E.N., Barnes, D.K., McElroy, W.D., Whiteley, A.H., Pease, D.C. & Cooper, K.W. 1944. Bubble Formation in Animals. J. Cellular and Comparative Physiol. 24(1): 1–22. Henderson, S.J. & Speedy, R.J. 1980. A Berthelot-Bourdoon tube method for studying water under tension. J. of Physics E: Scientific Instrumentation 13: 778–782. Imre, A.R., Maris, H.J. & Williams, P.R. 2002. Liquids Under Negative Pressure, NATO Science Series. Jones, W.M., Overton, G.D.N. & Trevena, D.H. 1981. Tensile strength experiments with water using a new type of Berthelot tube. J. of Physics D: Applied 14: 1283–1291. Lourenço, S.D.N., Gallipoli, D., Toll, D.G. & Evans, F.D. 2006. Development of a commercial tensiometer for triaxial testing of unsaturated soils. In Miller et al. (eds.).
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ASCE Geotechnical Special Publication No. 147(2): 1875–1886. Mahler, C.F. & Diene, A.A. 2007. Tensiometer development for high suction analysis in laboratory lysimeters. In Schanz (ed.), Experimental unsaturated soil mechanics; Springer proceedings in physics No. 112: 103–115. Marinho, F.A.M. & Chandler, R.J. 1994. A new instrument for the measurement of soil moisture suction: Discussion. Geotechnique 44(3): 551–556. Marinho, F.A.M. & Pinto, C.d.S. 1997. Soil suction measurement using a tensiometer. In Almeida (ed.), Recent developments in Soil and Pavement Mechanics 1: 249–254. Rotterdam: Balkema. Meilani, I., Rahardjo, H., Leong, E. & Fredlund, D.G. 2002. Mini suction probe for matric suction measurements. Canadian Geotechnical Journal 39: 1427–1432. Ridley, A.M. & Burland, J.B. 1993. A new instrument for the measurement of soil moisture suction. Géotechnique 43: 321–324. Ridley, A.M. & Burland, J.B. 1995. Measurement of suction in materials which swell. Applied mechanics reviews 48(10): 727–732. Ridley, A.M. & Burland, J.B. 1999. Use of the tensile strength of water for the direct measurement of high soil
suction: Discussion. Canadian Geotechnical Journal 36: 178–180. Tabor, D. 1979. Gases, liquids and solids. Cambridge University press. Take, W.A. & Bolton, M.D. 2003. Tensiometer saturation and the reliable measurement of soil moisture suction. Geotechnique 53(2): 159–172. Tarantino, A. & Mongiovì, L. 2001. Experimental procedures and cavitation mechanisms in tensiometer measurements. Geotechnical and Geological Engineering 19: 189–210. Tarantino, A. & Mongiovì, L. 2002. Design and construction of a tensiometer for direct measurement of matric suction. In Jucá, de Campos & Marinho (eds.) Unsaturated Soils; Proc. 3rd inter. conf., Recife, 10–13 March 2002: 319–324. Lisse: Balkema. Tarantino, A. 2004. Direct measurement of soil water tension. In Jucá, de Campos & Marinho (eds.) Unsaturated Soils; Proc. 3rd inter. conf., Recife, 10–13 March 2002, 3: 1005–1017. Lisse: Balkema. Trevena, D.H. 1982. Time effects in cavitation experiments. J. Phys. D: Applied Physics 15: L111–L114.
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Evaluation of suction measurement by the tensiometer and the axis translation technique S.D.N. Lourenço, D.G. Toll & C.E. Augarde School of Engineering, Durham University, Durham, UK
D. Gallipoli Department of Civil Engineering, University of Glasgow, Glasgow, UK
F.D. Evans Controls Testing Equipment Ltd, Wykeham Farrance Division, Tring, Hertfordshire, UK
G.M. Medero Department of Civil Engineering, Heriot-Watt University, Edinburgh, UK
ABSTRACT: The axis translation technique is a well-established method for imposing values of suction in unsaturated soil samples. High-suction tensiometers are more recently developed devices used for measuring pore water pressures in soils, including negative pore water pressures (i.e. suctions) below absolute zero. Both these techniques are comparable in terms of the suction range in which they operate. In this work a tensiometer has been used to measure suction values imposed by the axis translation technique in kaolin samples inside a pressure plate and a triaxial cell. The tensiometer has been kept in contact with the soil sample to track pore water pressure variations throughout the duration of the tests. The suctions measured by the tensiometer have been compared to those imposed by the axis translation technique and it was found that the suction measured by the tensiometer was always smaller than that imposed. Two scenarios are proposed to explain this. The first scenario considers the presence of water inside and below the high air entry value ceramic plate whereas the second one hypothesises the lack of equilibrium in terms of soil water content when suction is measured. The latter scenario seems to be supported by the evidence in the literature of equilibration times for pressure plate tests that are significantly longer than those reported for the present testing programme. Implications of both scenarios for laboratory testing are discussed.
1
INTRODUCTION
The axis translation technique (Hilf, 1956) is commonly used in unsaturated soil mechanics for imposing matric suctions in samples. In this technique, the pore air pressure and the pore water pressure are raised by the same amount so that the matric suction (given by their difference) is kept constant. In this way, the pore water pressure can become positive, thus avoiding water cavitation inside the experimental set up. The technique is employed in the pressure plate device, which consists of a high air entry value ceramic plate saturated by water and acting as a separation filter between the air above and the water below. Soil samples are placed on the ceramic plate and the suction is imposed by controlling independently both the air pressure and the water pressure on the two sides of the plate. The range of suction over which the technique
can be applied depends on the air entry value of the ceramic plate (usually between 500 kPa and 1500 kPa) and the capacity of the compressor controlling the air pressure. High-suction tensiometers (Ridley and Burland, 1993) are relatively new devices used for the direct measurement of pore water pressures in soils, including negative pore water pressures below absolute zero. Tensiometers are usually employed under conditions where the air pressure is atmospheric and the matric suction is given by pore water under tensile stress, which is directly measured by the tensiometers. High suction tensiometers can be schematically divided into three parts (Figure 1): a miniature water reservoir, a pressure transducer measuring the water pressure inside the reservoir and a high air entry value porous stone acting as a separation filter between the reservoir on one side and the soil on the other side.
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reservoir
transducer
porous stone Figure 1. Schematic of the tensiometer used for this research (Lourenço et al., 2006).
Work done by Guan (1996) and reported in Guan and Fredlund (1997) used a modified pressure plate to perform a standard drying test by increasing pore air pressure in an initially saturated sample to impose a given value of suction (water pressure was at atmospheric pressure). Subsequently, the air pressure was instantaneously released to atmospheric pressure while a high suction tensiometer, placed in contact with the soil, simultaneously measured the corresponding drop in pore water pressure. This procedure was used to assess the accuracy of the tensiometer calibration over the negative range of pressures. The authors observed that the suction measured by the tensiometer was less than the suction imposed via the pressure plate. The same was observed by Lourenco et al. (2006) in similar tests. The tests conducted by Guan and Fredlund (1997) had a unique feature: water in the compartment below the porous stone of the pressure plate was flushed out before the air pressure decrease. No details are provided but it is believed that this was to avoid water flowing from the water compartment to the sample and therefore to avoid a further decrease of suction during the air pressure decrease. It is the purpose of this paper to evaluate the suction measurement of samples prepared at the same initial conditions by the tensiometer and the pressure plate. In this work, a conventional pressure plate sold commercially by Soil Moisture Corporation as well as a triaxial cell, whose pedestal was fitted with a high air entry value ceramic plate, were used. In the pressure plate the compartment below the ceramic plates was always full of water. In the triaxial cell, the compartment could be full or empty of water (but with the ceramic plates always saturated) (Figure 2). In the following part of this paper, the working principle of both the tensiometer probe and the axis translation technique will be initially reviewed in more detail including limitations and terminology. Then the procedures and results of the testing programme will be shown and the implications for laboratory testing of unsaturated soils will be discussed.
Figure 2.
2
Experimental set-up.
DIRECT SUCTION MEASUREMENT VERSUS AXIS TRANSLATION TECHNIQUE
The axis translation technique imposes a value of suction by raising the air pressure above atmospheric value with the water phase kept either at atmospheric or at a given positive value smaller than the air pressure. This forces water to move from (or into) the soil through the ceramic plate. Water will move to or from the compartment below the plate depending on whether the imposed suction is smaller or higher than that initially present in the soil sample. Once equalisation is achieved, no more transfer should occur and the water content in the sample should remain constant at the equilibrium value corresponding to the imposed suction (Figure 3). The tensiometer measures directly the water tensile stress existing in the soil pores. After the porous stone of a tensiometer is placed in contact with a soil sample with a negative pore water pressure, an initial equilibration phase takes place whereby a small volume of water is sucked out from the reservoir through the porous stone into the soil producing a deformation of the transducer diaphragm in the direction of the soil. This deformation is transferred to a strain gauged diaphragm from which pressure can be measured. Once this transfer ends, all water inside the tensiometer as well as in the soil will have the same value of negative pressure. The volume of water transferred from the reservoir to the soil is small enough so that it can be considered negligible, and therefore the water content of the sample is not affected. The working principle for both the axis translation technique and the tensiometer are schematically illustrated in Figure 3.
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Figure 3. Working principle for the tensiometer (above) and pressure plate (below).
One of the main limitations of the pressure plate device is related to the presence of air diffusion through the ceramic plate (e.g. Padilla et al., 2006), which needs to be accounted for when the change in water content of the sample is measured by means of volume gauges connected to the water compartment below the ceramic plate. For the tensiometer, the range of measurable suctions is primarily limited by the occurrence of cavitation inside the probe, which is in turn governed by the degree of saturation of the porous stone and reservoir (e.g. Guan and Fredlund, 1997; Lourenco et al., 2006). Suction measurements by the tensiometer also appear to be sensitive to temperature as shown by Toker et al. (2004).
3
TESTING PROGRAMME, EQUIPMENT AND MATERIAL
in contact with the sample to track pore water changes throughout the test. A kaolin slurry was prepared at a water content of 200% and was deposited directly on the previously saturated ceramic plates inside the triaxial cell and the pressure plate. In order to avoid spreading, the slurry was placed in a cylindrical mould (diameter 38 mm) with open top and bottom ends. The tensiometer was then set directly on the top surface of the kaolin slurry and a plastic mesh was also used to keep the tensiometer in the right position during the test, i.e. to avoid it falling or tilting. The tensiometer used in this work has a nominal measuring capacity of 1000 kPa in both the positive and negative ranges. The tensiometer was previously saturated and calibrated according to procedures described in Lourenço et al. (2006). Suction was imposed in the sample inside the pressure plate by quickly raising the air pressure to the required value while pore water pressure was maintained at the atmospheric value. As soon as the air pressure was raised, the tensiometer (placed on the top of the sample) recorded a positive excess pore water pressure, which subsequently started to dissipate. Once the pore water pressure read by the tensiometer dropped back to zero, it was assumed that equilibrium was achieved throughout the sample. The air pressure was then reduced to the atmospheric value and the corresponding negative pore water pressure generated inside the sample was measured by the tensiometer. Increasing values of suction were applied and measured on the sample in a sequence up to a maximum value of 500 kPa corresponding to the air entry value of the ceramic plates in both the triaxial cell and the pressure plate. The tests performed in the pressure plate and in the triaxial cell differed in one respect. In the triaxial cell, after pore water pressure equalized at 0 kPa and before releasing the air pressure to zero, water was flushed out below the ceramic plate by air circulation. Once the air pressure was dropped and the reading from the tensiometer was taken, water was restored below the ceramic for the application of the next suction stage. In the pressure plate, water at atmospheric pressure was present in the compartment below the ceramic plate throughout the entire test.
4
If a given suction is imposed in a soil sample by using the axis translation technique, one would expect that an equal value of suction would be read by a tensiometer when placed in contact with the same sample. In order to verify this, tests were conducted by imposing given values of suction on Speswhite kaolin samples in the pressure plate while a tensiometer was placed
RESULTS AND DISCUSSION
Figure 4a shows the results for the test performed in the pressure plate. Inspection of Figure 4a indicates that, after the air pressure was increased to 187.6 kPa, the pore water pressure measured by the tensiometer instantaneously increased by 170 kPa and then progressively dissipated back to zero. After equilibrium was achieved, air pressure was reduced to zero
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a)
400
pressure (kPa)
200
Table 1. Difference between the imposed and measured suctions for each test.
ua =396.5 kPa ua =187.6 kPa
0 uw =-149.2 kPa
-200
uw =-278.5 kPa -400 0
100 time (min)
150
200
Device
Difference (%)
T14 T17 T31 T35 T36 T38 T39 T40
Pressure plate Pressure plate Triaxial cell Triaxial cell Triaxial cell Triaxial cell Triaxial cell Triaxial cell
20.4–30.5 12.5–18.2 10.5–11.0 4.6–10.5 12.5–16.25 14.2–17.2 4.3–6.0 4.3–4.6
600 400 400
ua
200
measured suction (kPa)
pressure (kPa)
b)
50
Test nr
0 uw
-200 -400 -600 0
2000
4000
6000
8000
time (min)
expected pressure plate triaxial cell
300 200 100 0 0
Figure 4. Axis translation tests with uw measured with the tensiometer. (a) Test T14 conducted in the pressure plate and, test T40 conducted in the triaxial cell.
and this induced a reduction of the pore water pressure from zero to −149.2 kPa, i.e. a reduction about 20% smaller than the corresponding reduction in air pressure. Subsequently, the air pressure was increased again to a higher level of 396.5 kPa and, after dissipation of the excess pore water pressure from 160 kPa, was reduced again to zero. Also in this case, the corresponding reduction of pore water pressure from zero to −278.5 kPa was about 30% smaller than the corresponding reduction of air pressure. For the case of Figure 4b, the air pressure was increased in 4 stages to 99.6 kPa, 200 kPa, 299.4 kPa, and 400 kPa. The measured water pressures were 95.7 kPa, 191.4 kPa, 284.9 kPa, and 381.6 kPa, respectively. Comparing to Figure 4a, the imposed and measured suctions are smaller. Table 1 shows for each test the difference, in percentage, between the applied suction and measured suction. This difference was seen to vary throughout the air pressure releases. For instance, for test T14 in Figure 4a for the first air pressure release the ratio 149.2/187.6 gives 20.4%. In the second release this ratio gives 30.5%. Therefore during each air pressure release this difference became greater. Results from all tests are shown in Figure 5 where the suction imposed by the axis translation technique is plotted against the suction measured by the
Figure 5.
100 200 300 imposed suction (kPa)
400
Imposed versus measured suctions for all tests.
tensiometer. The difference between the measured and imposed suction were larger when the pressure plate was used. Previous work by Guan and Fredlund (1997) showed similar results, with the suction measured by the tensiomer smaller than the suction imposed by the axis translation technique by a margin ranging between 0.5% to 8.5%. Figure 6a shows an expanded view of the final part of the test shown in Figure 4a. It can be seen that, after the instantaneous initial drop in pore water pressure, the pore water pressure slowly rises over a period of about 20 minutes until it stabilises at a value of approximately −73 kPa. A similar result is shown in Figure 6b, which presents part of a test carried out in the triaxial cell where the pore water pressure recorded by the tensiometer, after an initial instantaneous drop, rises under constant air pressure and stabilises at a value of −335 kPa. This was a common feature of behaviour observed in all tests where the air pressure was maintained at zero for some time, after reducing it from the imposed value of suction. This result might be a consequence of the availability of free water inside the ceramic plate or below it. This water is sucked into the sample under the action of the negative pore water pressures generated by the air pressure drop, thus increasing water content and reducing soil suction.
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pressure (kPa)
a)
400
ua = 396.5 kPa
200
0
-200 uw = -278.5 kPa -400 125
150
175
200
b)
800
pressure (kPa)
time (min)
400
ua =599.4 kPa
0 -400 uw =-473.5 kPa
uw =-335 kPa
-800 0
200
400
600 800 time (min)
1000
1200
Figure 6. Kaolin response after releasing the air pressure. a) Suction measured by the tensiometer continuously decreasing and, b) stabilizing at a 335 kPa.
A consistent result emerging from this work, as well as previous work by Guan (1996), is that the instantaneous pore water pressure decrease recorded by the tensiometer is generally smaller than the imposed drop of air pressure (Figure 6a and Figure 6b). Two possible explanations are provided here to interpret this result. One possibility is that, despite the air pressure drop being applied almost instantaneously, some water is still sucked back into the sample, which limits the magnitude of the measured pore water pressure reduction. This explanation seems consistent with the observation that pore water pressure reductions tending to be proportionally smaller for tests carried out in the pressure plate, where water is permanently present below the ceramic plate, than for tests carried out in the triaxial cell, where water below the ceramic plate is flushed out before each air pressure drop. A second possibility is that the water content in the soil sample had not yet come to equilibrium, despite the pore water pressure having done so. Equilibrium was assumed to be achieved at each imposed value of suction when the tensiometer read a value of zero pore water pressure. After this condition was attained, the air pressure was decreased and the corresponding negative pore water pressure drop was measured by the tensiometer. However, although the pore water pressure is equal to zero throughout the specimen, it is
possible that water content is still reducing inside the sample due to a slow rearrangement of water menisci at the interface between gas and liquid phases inside the pores. Such a hypothesis seems to be supported by the observation that pressure plate tests published in the literature (where the achievement of equilibrium is based on the measurement of the sample mass during equalisation) usually require significantly longer time than the tests reported in this work (where the achievement of equilibrium is based on the dissipation of the excess pore water pressures measured by the tensiometer). For example, the tests shown in Figure 4a and Figure 4b, both of which involved imposing more than one suction value to the sample, took overall 4 hours and 5 days respectively. Tinjun et al. (1997) and Vanapalli et al. (1997) reported equalisation times for clay samples of 5–8 days and 6–7 days respectively for each imposed value of suction in the pressure plate. However, both authors did not measure the sample’s mass, equilibrium conditions were ensured when the outward flow of water from the sample stopped. If the above hypothesis were true, the dissipation of pore water pressure to zero would not be enough to conclude that a given suction ‘is imposed’ on the sample, as assumed by Guan and Fredlund (1997) and Lourenço et al. (2006). Hence, the difference between the measured and imposed suction is simply due to lack of equilibrium in terms of water content. The tensiometer would be expected to measure suctions closer to the imposed ones if longer periods of time are waited during equalisation. A testing program is on the way to confirm this. 5
CONCLUSIONS
This paper presents a series of measurements performed by high suction tensiometers on kaolin samples, which were previously subjected to different suction levels by using the axis translation technique. It was found that the suction measured by the tensiometers was always smaller than that imposed by the axis translation technique. Two different hypotheses have been put forward to justify such discrepancy. One possibility is that the smaller measured suctions are due to the absorption of water by the sample from the ceramic plate and/or the compartment below it. However, another possibility is that for each imposed value of suction equilibrium conditions had only been achieved in terms of pore water pressure but not water content. This idea is suggested by comparison with published data on the equilibrium times for pressure plate tests, which have required longer times. This might be explained by considering that water menisci at the interface between the gas and liquid phases inside soil pores take longer to re-arrange in a stable configuration after the pore water pressure has come to
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equilibrium. Should this hypothesis hold, then it would not be correct to assume achievement of equilibrium based on the pore water pressure read by the tensiometer but equilibrium should be assessed on the basis of subsequent sample mass measurements during the equalisation phase. Further testing is currently being undertaken to confirm or refute such a hypothesis. ACKNOWLEDGEMENTS This research was funded by the Engineering and Physical Sciences Research Council of the United Kingdom through a CASE research grant, with additional financial support from Controls Testing Equipment Ltd. Support from the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTN-CT-2004-506861 is acknowledged. Technical support was given by Mr. C. McEleavy and Mr. S. Richardson. REFERENCES Guan, Y. 1996. The measurement of soil suction, PhD Thesis, University of Saskatchewan, pp. 331. Guan, Y., Fredlund, D.G. 1997. Use of the tensile strength of water for the direct measurement of high soil suction, Can. Geotech. J. 34: 604–614. Hilf, J.W. 1956. An investigation of pore water pressure in compacted cohesive soils, US Bureau of Reclamation, Tech. Mem. 654, Denver: US Bureau of Reclamation.
Lourenço, S., Gallipoli, D., Toll, D.G., Evans, F. 2006. Development of a commercial tensiometer for triaxial testing of unsaturated soils, Geotechnical Special Publication (ASCE) No. 147, Vol. 2, 1875–1886. Lourenço, S.D.N., Gallipoli, D., Toll, D.G., Evans, F., Medero, G. 2007. Determination of the Soil Water Retention Curve with tensiometers, Weimar, Germany, Experimental unsaturated soil mechanics, T. Schanz (Ed.), Springer, 95–102. Oliveira, O.M., Marinho, F.A.M. 2006. Study of the equilibration time in the pressure plate, Geotechnical Special Publication (ASCE) No. 147, Vol. 2, 1865–1874. Padilla, J.M., Perera, Y.Y., Houston, W.N., Perez, N., Fredlund, D.G. 2006. Quantification of air diffusion through high air-entry ceramic disks, Geotechnical Special Publication (ASCE) No. 147, Vol. 2, 1852–1863. Ridley, A.M., Burland, J.B. 1993. A new instrument for the measurement of soil moisture suction, Geotechnique 43, No. 2, 321–324. Tinjun, J.M., Benson, C.H., Blotz, L.R. 1997. Soilwater characteristic curves for compacted clays, ASCE J. Geotech. Geoenv. Eng. 123, 11, 1060–1069. Toker, N., Germaine, J., Sjoblom, K., Culligan, P. 2004. A new technique for rapid measurement of continuous soil moisture characteristic curves, Géotechnique 54, 3:179–186. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E. 1999. The influence of soil structure and stress history on the soil-water characteristics of a compacted till, Geotechnique 49, 2, 143–159.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A system for field measurement of suction using high capacity tensiometers J. Mendes, D.G. Toll & C.E. Augarde School of Engineering, Durham University, Durham, UK
D. Gallipoli Department of Civil Engineering, University of Glasgow, Glasgow, UK
ABSTRACT: This paper presents a new system to measure suction in the field using high capacity tensiometers recently developed through collaboration between Durham University and Wykeham Farrance Limited. The system comprises a borehole probe locator where five tensiometers can be inserted allowing the measurement of suction at different depths. Since the tensiometers are left in place, rather than being used for a single ‘‘spot’’ measurement, suctions can be observed continuously with the aid of a logger and a computer. This enables the measurement of variations of suction due to seasonal changes and the observation of the immediate response to a rainfall event. Two borehole probe locators have been installed at different points in an embankment to measure suction in the fill material. The instrumented embankment was built for research purposes at Nafferton farm, near Newcastle, UK, as part of a cooperative project (BIONICS) investigating the biological and engineering impacts of climate change on slopes. The paper describes the installation and some preliminary observations obtained using the system.
1
INTRODUCTION
Field measurements of suction in unsaturated soils have been made using different approaches: directly (using tensiometers) or indirectly (using techniques such as porous blocks) or by collection and measurement of suction in recovered samples. A direct approach is always to be preferred as the measurement is made in situ and avoids errors in defining indirect relationships (e.g. between suction and resistivity or thermal conductivity). It also avoids concerns that the quality of the suction measurement on recovered samples may be jeopardized because measurements are made in a different stress or water content condition. Conventional tensiometers have been widely used for direct measurement of suction in the field, but they have a cavitation limit of −100 kPa. On the other hand, high capacity tensiometers (i.e. tensiometers capable of measuring pore water pressures lower than −100 kPa) have been mainly used for the measurement of suction in the laboratory rather than in the field. This paper describes the use of a commercial high capacity tensiometer, manufactured by Wykeham Farrance Limited, for the measurement of suction in the field. This tensiometer has been developed through collaboration between Wykeham
Farrance Limited and Durham University and can measure water pressures directly down to −1.2 MPa or even lower (Lourenço et al., 2006). Like other high capacity tensiometers that can be found in the literature (e.g. Ridley & Burland, 1993), the design of the Wykeham Farrance—Durham University tensiometer includes a high air entry value porous filter, a water reservoir and a pressure transducer (see Figure 1).
Figure 1. Wykeham Farrance—Durham University high capacity tensiometer (after Lourenço et al., 2006).
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Previous field observations using high capacity tensiometers (Ridley et al., 2003) have used ‘‘spot’’ measurements where the tensiometer has been placed in contact with the soil to take a suction reading at a particular time, i.e. the tensiometer was not left in place to take continuous readings with time. Cui et al. (2008) have used high capacity tensiometers for the continuous measurement of suction but their system does not allow installation of multiple tensiometers at different depths at the same location. The system reported in this paper provides multiple tensiometers at different depths as well as the possibility of taking continuous readings with time from each tensiometer. In the proposed system, the tensiometers can also be easily removed if required for re-saturation or replacement. A total of ten high capacity tensiometers have been installed to observe the variation of soil suction with depth at two different locations in an experimental embankment. The embankment is located at Nafferton farm, near Newcastle, UK and has been built as part of a cooperative project (BIONICS) aimed at investigating the biological and engineering impacts of climate change on slopes. The paper describes the installation of the tensiometers in the BIONICS embankment and reports on some preliminary observations of suction using the system.
2 2.1
THE EQUIPMENT Design of the high capacity tensiometer
The operation of the Wykeham Farrance—Durham University tensiometer is based on the same general principles as other versions of high capacity tensiometer proposed in the literature. The device measures soil suction through a high air entry value filter connected to a small water reservoir, which is in contact with a pressure transducer. The tensiometers used in this work were saturated prior to calibration inside a high pressure vessel (Figure 2). The tensiometers were fixed inside the vessel, which was then filled with de-aired water and pressurized to about 1000 kPa. The tensiometers were left exposed to this pressure for a period of two weeks which is assumed to be enough for the first saturation while for subsequent re-saturations 24 hours should be enough (depending how dry the tensiometer is). In this work, however, the tensiometers were re-saturated for a longer period of two weeks given that site visits took place fortnightly. Calibration was performed by submerging the tensiometers inside a triaxial cell and reading the voltage from the tensiometers at different values of (positive) cell pressure. The ability to calibrate in the positive range and extrapolate to the negative range has been verified by Lourenço
Figure 2. Saturation vessel with a set of 5 Wykeham Farrance—Durham University field tensiometers.
et al. (2007) for the Wykeham Farrance—Durham University tensiometer and confirms the observations by Tarantino & Mongiovi (2003) for another type of high capacity tensiometer. High capacity tensiometers are limited by cavitation and air entry. Although tensiometers can sustain high suctions for short periods, they may not be able to sustain these suction values when installed in the ground for a long periods (usually, after two to three weeks the tensiometer cavitates, if a value much greater than −100 kPa is continuously read as observed from other laboratory tests). Therefore, any reliable system for the field measurement of suction has to account for the possibility of cavitation occurring in the tensiometers and it must allow removal of the probes so they can be re-saturated and re-installed whenever necessary. Some minor modifications were made to the original version of the Wykeham Farrance—Durham University tensiometer to adapt it to field conditions. The electrical cable that connects the tensiometer to the logger was covered with nylon tubing (10 m long by 8 mm diameter) to provide a stronger, stiffer connection that would allow the tensiometer to be pushed in (without buckling) during installation and pulled out during removal. The nylon tubing had the dual purpose of protecting the electrical cable from damage. The edges of the tensiometers were also smoothed for easy removal and installation.
2.2 Borehole probe locator The borehole probe locator included five suction stations at depths of 0.5 m, 1 m, 1.5 m, 2 m and 3 m, with each suction station fitted with a high capacity tensiometer. The borehole probe locator consisted of a PVC pipe 3 m long with an
220
outer diameter of 90 mm and an inner diameter of 70 mm. Five guide tubes were inserted inside the borehole probe locator to individually connect each suction station to the surface. These guide tubes were made from flexible hose with an inner diameter of 19 mm. A small tapered aluminium cylinder was fitted at the end of each hose reducing the inner diameter from 19 mm down to 14 mm (this is about the same as the external diameter of the tensiometer). The aluminium fitting helped to hold the tensiometer in place and prevented movement of soil into the hose. Such a design enabled the tensiometers to be removed and inserted individually whenever necessary (see Figure 3). Due to the small inner diameter (70 mm) of the borehole probe locator the exit angle of the suction stations had to be 45◦ with the exception of the suction station located at the bottom which was vertical (see Figure 3). The top of the borehole probe locator was sealed with foam and silicone to avoid any infiltration of water or other kind of material from the surface.
3
INSTALLATION AND USAGE
Figure 3. Borehole probe locator (a) with enlarged views of the suction stations on the side (b) and bottom (c).
Figure 4. Plan view of BIONICS embankment and borehole probe locators (after Glendinning et al., 2006).
3.1 The BIONICS embankment The objective of the BIONICS project is to investigate what could happen to infrastructure embankments in the UK when subjected to climate change. As part of the project, an experimental embankment has been built in four panels (Figure 4) separated by vertical impermeable membranes and constructed by using different compaction efforts. Panels A and D are poorly compacted (intended to represent old rail embankments constructed in Victorian times) while panels B and C are well compacted (representing modern embankments). The compactive effort has two roles in the suction measurement: (i) changes in void ratio can affect the
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3.3
Figure 5. Cross section of the BIONICS embankment and borehole probe locator showing suction station depths.
water retention properties of the soil, and (ii) the permeability will also be affected (which will influence infiltration, evaporation and internal flow throughout the fill material). Current measurements of suction have been obtained during natural rainfall conditions. In the near future, a climate control system will be used to impose expected future climate patterns on the embankment. 3.2
Equipment at the embankment
One borehole probe locator was installed in the poorly compacted panel A while the second was installed in the well compacted panel B (see Figure 4). Both were located close to the south facing slope of the embankment at about 1 m from the edge of the crest (see Figure 5). Boreholes were drilled in the embankment to a depth of 3 m with a diameter of 110 mm, which is slightly larger than the outer diameter of the borehole probe locators of 90 mm. The borehole probe locators were subsequently lowered into the embankment while the suction stations were sealed using plugs with a similar shape and dimension as the tensiometers to avoid soil particles from the fill material entering the guide tubes. A period of two weeks was allowed to elapse to promote the natural closure of the borehole walls around the probe locator. During this time the plugs were kept in place to avoid entry of fill material inside the guide tubes. Subsequently the plugs were replaced with the tensiometers, which were firmly pushed into place (using the stiff nylon tube around the electrical cable) to ensure good contact between the tensiometer and the soil. Each tensiometer was fitted with an 11 m long electrical cable connected to a data logger inside a waterproof steel box placed on the top of the embankment between the two borehole probe locators. The data logger was connected to a computer in a field hut near the embankment for direct real-time downloading of data.
Maintenance of tensiometers
As discussed previously, cavitation is a possible problem for tensiometers operating over long periods of time. Regular fortnightly visits were therefore made to the site in order to verify the correct functioning of the equipment. If a tensiometer cavitates, it can be removed from the suction station and replaced by a plug. The tensiometers should not be allowed to dry so the saturation vessel is taken to the field (filled with de-aired water) to transport back the cavitated tensiometer (s); in this way a long re-saturation is avoided and after two weeks it is possible to re-install the tensiometer back in its position.
4
IN-SITU OBSERVATIONS
Preliminary suction measurements in the embankment are available from May to July 2007. Figures 6 and 8 show measurements for the well compacted panel and the poorly compacted panel respectively. Values of daily rainfall are also shown as spikes in Figures 6 and 8 for the period May to June 2007 (the record of daily rainfall for the month of July 2007 was not yet available at the time of submission of the manuscript). Note that the tensiometer for the 3 metre deep suction station in the poorly compacted panel has yet to be installed; therefore, there are only four recorded values down to 2 metres depth. It can be observed from the two figures that during the initial drier period (May) both panels had values of suction that increased with depth. However, that trend has changed for the poorly compacted panel during the wetter period (June-July). The well compacted panel shows greater suctions (20–40 kPa at 3 m) whereas in the poorly compacted panel suctions are less than 5 kPa and generally pore water pressures are positive (in the wetter period since June).
Figure 6. Pore water pressure records for the well compacted panel suction (SS indicates suction station at different depths). Vertical spikes show daily rainfall.
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Pore water pressure (kPa) –35 0 0.5
–30
–25
–20
–15
–10
–5
0
5
10
15
13/06/2007 after heavy rainfall
Depth (m)
24/05/2007 1 1.5 26/06/2007 2 31/07/2007 2.5 3
Figure 7. Well compacted panel pore water pressure profiles for different weather conditions.
pressures approaching zero within the top 1 m (and becoming positive at 1 m). In the well compacted material the tensiometers do not show rapid responses to rainfall events, although there is a general increase in pore water pressure (reduction in suction) with time. This could be because of the lower permeability of the well compacted material is restricting infiltration, perhaps suggesting there is greater runoff from this section (runoff is not yet being measured so there are no measurements to corroborate this). It seems that it is taking some time for infiltration to slowly wet the fill material (see Figure 6) gradually decreasing the value of suction over time. 4.2
Figure 8. Pore water pressure records for the poorly compacted panel suction (SS indicates suction station at different depths). Vertical spikes show daily rainfall.
The tensiometers in the poorly compacted panel can be seen to respond almost immediately to weather changes (see Figure 8), especially during the second half of June. Note that the gaps in the curves of Figures 6 and 8 correspond to periods when data are missing because either the tensiometers were temporarily removed from the site or a mains power cut occurred causing the computer and logger to shut down. To avoid loss of data, a backup uninterruptible supply has recently been installed to power the computer in the occurrence of electrical cuts.
Poorly compacted panel
The pore water pressure readings for the poorly compacted panel (see Figure 8) within the top 1 m show a similar pattern to those for the well compacted panel. As in the well compacted panel the pore water pressure at 0.5 m is close to zero (or with small positive values). Pore water pressures at 1 m were initially around −5 kPa but have increased with time and by July show positive pore water pressures approaching 10 kPa. Initially in May, pore water pressures in the poorly compacted panel showed a reduction with depth to around −20 kPa at 2 m depth, quite similar to the well compacted panel (cf. Figures 9 and 7). However, after the rainfall events of 11–16 June, the responses of the poorly compacted panel changed and small suctions or positive pore water pressures were recorded at 1.5 and 2 m depth (see Figure 8). The reaction of the tensiometers to rainfall is clearly observed during the period 13 to 26 June. It can be seen that during this period there was a decrease on the pore water pressure measured in the shallow zone (0 to 1 m) when it rained, while the deeper tensiometers showed quite significantly increased pore water pressures, recovering to former pore water pressure values when there was less rainfall (see Figure 8). These overall trends can also be seen in the pore water pressure
Pore water pressure (kPa) -35 -30 -25 -20 -15 -10 -5 0 5 10
15
20
25
0
Well compacted panel
31/07/2007
The pore water pressure records for the well compacted panel (see Figures 6 and 7) show a value close to zero at 0.5 m. At 1 m the initial pore water pressure was −20 kPa but has increased with time to just above zero. Below 1 m, pore water pressures reduce with depth but the values of pore water pressure have been gradually rising with time (see Figure 6). The changes in pore water pressure profiles can be seen in Figure 7. This shows a progressive wetting up, since the initial readings in May; with pore water
0.5 24/05/2007 Depth (m)
4.1
1 1.5 2 2.5 28/06/2007 3
13/06/2007 after heavy rainfall
Figure 9. Poorly compacted panel pore water pressure profiles for different weather conditions.
223
be seen that the tensiometers in the switched positions gave consistent (if not identical) readings. After this test, from 26 July, both tensiometers were returned to their initial position recording similar values with those recorded previous to the shift in the position. The lack of identical readings could suggest some shift in zero values for the tensiometers. This is now being investigated by regularly removing the tensiometers (every two weeks) and immersing them in a container of water to check the zero values.
Figure 10. siometers.
5
Scattering caused by poor saturation of ten-
Figure 11. Shift in position of tensiometers at 0.5 m and 3 m in the well compacted panel.
profiles in Figure 9. It is expected that further measurements will help to provide explanations for this seemingly anomalous behaviour. 4.3
Tensiometer issues
Figure 10 shows an enlarged view of the readings plotted in Figure 6. A high degree of scattering is observed in the values measured by the tensiometer at 2 m depth, much worse than the scatter seen from other tensiometers (this scattered data was removed from Figure 6). This large fluctuation was overcome by re-saturating the tensiometer, suggesting that the tensiometer was initially not well saturated. This confirms the importance of tensiometer saturation in ensuring good quality readings. It can be observed from Figure 6 that after the re-saturation this same tensiometer showed less scatter and behaved similarly to other tensiometers. In order to check the reliability of the equipment, two tensiometers in the well compacted panel were changed in position for a period of 2 weeks (the tensiometer that was initially in the suction station at 0.5 m was swapped with tensiometer that was initially in the suction station at 3 m). From Figure 11 it can
CONCLUSIONS
The paper presents a system to measure suction in the field using Wykeham Farrance—Durham University tensiometers. The wide measuring range of the tensiometers (up to −1.2 MPa) allows usage of the proposed system in most natural and manmade earth structures. A borehole probe locator has been designed and installed. This allows the user to easily remove tensiometers for their re-saturation whenever necessary, overcoming one of the major limitations associated with the use of high capacity tensiometers in the field. The proposed borehole probe locator also allows readings at different levels in a single borehole, permitting observations of the variation of suction with depth. Two borehole probe locators have been installed in the BIONICS embankment with the intention of measuring suction in two different areas constructed by using different compactive efforts. This has allowed the observation of the variation of suction with depth in both areas and the suction changes to rainfall events. Preliminary results (from three months of monitoring) show that there are different patterns of suction measurements from the tensiometers installed in the well compacted part of the embankment compared to those installed in the poorly compacted part. It has been observed that tensiometers installed in the poorly compacted part of the embankment react rapidly to rainfall. The well compacted panel instead shows a slower change of suction and does not respond rapidly to rainfall. To check the validity of measurements, two tensiometers were swapped in position. The values measured by the two tensiometers at the same depth were consistent but not identical. This suggests there may have been some shift in the calibration zero, which is now being investigated. ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from Engineering and Physical Sciences Research Council (EPSRC) for the BIONICS project (Grant
224
GR/S87430/01). The support from the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTN-CT-2004–506861 is also acknowledged. Thanks are also due to Dr. Paul Hughes from Newcastle University and the laboratory technicians at Durham University: Mr. McEleavey and Mr. Richardson for assistance with the experimental work. REFERENCES Cui, Y.J., Tang, A., Mantho, A.T. & De Laure, E., 2008. Monitoring Field Soil Suction Using a Miniature Tensiometer, Geotechnical Testing Journal 31 (1), (available online). Glendinning, S., Rouainia, M., Hughes, P. & Davies, O., 2006. Biological and engineering impacts of climate on slopes (BIONICS): The first 18 months, In Proc. 10th IAEG Congress, Nottingham, Paper 348 (on CD).
Lourenço, S.D.N., Gallipoli, D., Toll, D.G., Augarde, C.E., Evans, F.D. & Medero, G.M., 2007. Calibration of high suction tensiometers, submitted to Géotechnique August 2007. Lourenço, S.D.N., Gallipoli, D., Toll, D.G. & Evans, F.D., 2006. Development of a commercial tensiometer for triaxial testing of unsaturated soils. In Proc. 4th International Conference on Unsaturated Soils, Carefree, USA, Geotechnical Special Publication No. 147, ASCE, Reston. Vol. 2, 1875–1886. Ridley, A.M. & Burland, J.B. 1993. A new instrument for the measurement of soil moisture suction, Géotechnique 43 (2), 321–324. Ridley, A.M., Dineen, K., Burland, J.B. & Vaughan, P.R., 2003. Soil matrix suction: some examples of its measurement and application in geotechnical engineering, Géotechnique 53 (2), 241–253. Tarantino, A. & Mongiovi, L., 2003. Calibration of tensiometer for direct measurement of matric suction, Géotechnique 53 (1), 137–141.
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Engineering behaviour Water retention behaviour and hydraulic properties
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Water retention properties of Boom clay: A comparison between different experimental techniques T.T. Le, P. Delage, Y.J. Cui & A.M. Tang Ecole des ponts – CERMES (I. Navier, Université Paris-Est), Marne la Vallée, France
A. Lima, E. Romero & A. Gens Department of Geotechnical Engineering and Geosciences, Universitat Politècnica de Catalunya, Barcelona, Spain
X.L. Li EURIDICE, c/o SCK-CEN, Mol, Belgium
ABSTRACT: The water retention properties of Boom clay samples extracted at a depth of 223 m have been determined in ENPC Paris and UPC Barcelona using different experimental techniques. Boom clay is a stiff clay in which an underground laboratory devoted to carry out research in radioactive waste disposal has been excavated near the city of Mol (Belgium). The retention properties of Boom clay have been investigated for two reasons: i) in good quality samples, a high suction develops in the saturated sample during extraction and its value is correlated with the sampling depth; ii) possible desaturation due to gallery venting during the operational phase may occur in the clay. Various suction control and measurement techniques have been used: osmotic, vapour equilibrium, filter paper, high-range tensiometer and chilled-mirror dew-point psychrometer readings. Some volume changes have also been measured along the equalisation or measuring stages. The values obtained are discussed according to the techniques used. They are compared with previous data on compacted Boom clay samples. The air entry value is estimated close to 4–5 MPa and the shrinkage-swelling properties are also examined. The sample suction at saturation is compared to the in-situ stress state.
1
INTRODUCTION
Various investigations have been and are being carried out on the coupled thermo-hydro-mechanical behaviour of Boom clay in relation with the research conducted on radioactive waste disposal at the Mol Underground Research Laboratory (URL). This URL has been excavated in a layer of Boom clay at a depth of 223 m by SCK-CEN, the Belgian organisation for nuclear studies, near the city of Mol. Various researches on Boom clay are presently being carried out by the EURIDICE group in Mol. Special attention has been devoted to the water retention properties of Boom clay, a lightly overconsolidated saturated stiff clay. On the one hand, the examination of suction effects in samples is a relevant indicator of the quality of the sampling (Skempton & Sowa 1963, Doran et al. 2000). On the other hand, water retention properties have to be investigated to better assess possible desaturation effects due to the venting of the galleries in the operational phase of the disposal facility during which the wastes will be disposed (one to three hundreds of years).
In this paper, various suction control techniques used on intact Boom clay samples at both ENPCCERMES (Paris) and UPC (Barcelona) are described and the results obtained are compared. The following control and measurement techniques have been used to cover a wide suction range: the vapour equilibrium method, the filter paper method, high-range tensiometer and chilled-mirror dew-point psychrometer readings. The paper also includes and discusses water retention properties of compacted Boom clay obtained with vapour equilibrium technique at an equivalent void ratio to that of the in situ state.
2 2.1
MATERIALS AND EXPERIMENTAL METHODS Boom clay
The Boom clay formation belongs to the Rupelian geological period in the Tertiary sub-era, which dated from 36 to 30 million years before present. This moderately swelling clay presents 20%–30%
229
kaolinite, 20%–30% illite and 10%–20% smectite. The geotechnical properties of Boom clay are presented in Table 1. In-situ water content measurements were made on excavated blocks during the excavation in the URL (Connecting Gallery, excavated between 23 January and 23 April 2002). Figure 1 presents the water content of soil samples excavated at different distances from the wall of the gallery, measured just when the excavation was made. It is observed that at distances smaller than 1 metre from the wall, the water content values vary between 24.3% and 25.9%. The value stabilises around 24.8% at a distance larger than of 1.5 m from the wall, showing a possible perturbation of the water content due to gallery excavation.
Table 1.
Geotechnical properties of Boom clay. Belanteur Dehandschutter et al. et al. (1997) (2005) UPC
Unit mass of solid (Mg/m3 ) 2.67 Unit mass (Mg/m3 ) Liquid limit wL 59–76
1.9 70
22–26 37–50
25 45
Plastic limit wP Plastic index IP Water content (%) Natural porosity (%) Poisson’s ratio Internal friction angle (◦ ) Permeability (m/s)
2.67 1.99 to 2.05 56 using SBCW (∗ )
25–30
23–25
35 0.4
38–39
18 10−12
Excavated blocks (2002) were immediately vacuum packaged in reinforced aluminium foil and thermowelded. They were stored in Mol in a room with temperature ranging between 15 and 20◦ C under an average relative humidity of 45% before being sent (2005) to the two laboratories. 2.2 Suction control and measurement techniques The experimental study carried out at ENPCCERMES was based on the use of the vapour equilibrium method, the filter paper method and high range tensiometers. The initial water contents of the sample used at CERMES are described in Table 2. Samples were trimmed from block 3 and 4 with respective water contents equal to 23 and 23.4 respectively. When considering i) the in-situ water content and ii) the age of the samples (excavated in 2002), the light decrease in water content from the average values given in Table 2 shows a reasonably good conservation of the sample with around 1 point of decrease in water content during 3 years. Note however that some drying occurred in the laboratory during sample preparation and trimming, resulting in water contents finally equal to 21.6% and 21.8% for blocks 3 and 4 respectively. The initial suction of the sample was measured by using the filter paper method and a value of 2 MPa was obtained. Along the drying path, starting from initial water contents close to 21%, rectangular clay samples were manually trimmed (30 × 30 × 10 mm approximately) and submitted to different values of suction by using the vapour equilibrium method (see for instance Delage et al., 1998). 5 saturated saline solutions were used, as shown in Table 3. Triplicate specimens were used at each suction level to determine the water content at equilibrium.
3 × 10−12 Table 2. Initial water contents. Changes in water content during the soil sample preparation.
(∗ ) SBCW: synthetic Boom clay water.
CERMES
UPC
26.0
w (%)
25.6
After package opening During sample preparation End of sample preparation
25.2 24.8
w (%) Block 3
w (%) Block 4
w (%) Block 2
23.0 22.6 21.6
23.4 – 21.8
23.9 – –
24.4
Table 3. Saturated saline solutions used in the vapour equilibrium method.
24.0 0
0.5
1
1.5
2
2.5
3
Distance from the gallery (m)
Salt
Figure 1. Water contents measured at different distances from the gallery’s wall (Li, 2007).
CuSO4
Suction (MPa) 2.8
230
K2 SO4
KNO3
NaCl MgCl2
4.2
8.5
37.8
152.8
The volume changes of the rectangular specimens were determined by hydrostatic weighing after having immersed the samples in a non aromatic hydrocarbon liquid called Kerdane. Along the wetting path, the three oedometer specimens (cylindrical oedometer samples: d = 70 mm, h = 20 mm) were smoothly wetted (from initial water content of 21%) by putting them in contact with humid filter papers and the resulting suction was afterwards measured by using a high range tensiometer. This tensiometer is based on the principle proposed by Ridley and Burland (1993) with some special adaptations carried out at CERMES (Mantho 2005). The volume changes of these samples were determined with a precision calliper. At UPC, laboratory tests were carried out on natural and compacted samples. The natural sample was trimmed from block 2 (Table 2) with dimensions of 15 mm in diameter and 12 mm high. Water retention properties of the natural sample under unstressed conditions were determined using a chilled-mirror dewpoint psychrometer (WP4 dewpointmeter, Decagon Devices, Inc, USA) and the vapour equilibrium technique. The volume changes were not registered. On the other hand, when preparing the compacted sample, Boom clay powder was left in equilibrium at a relative humidity of 40% to achieve a water content of around 2.5%. A soil sample (15 mm in diameter and 12 mm high) was one-dimensionally compacted at this water content to a dry density of 1.7 Mg/m3 (similar to the natural dry density). Details on the working principle of the dew-point psychrometer, as well as the different calibrations carried out, have been extensively described in Cardoso et al. (2007). A multi-stage drying path was first performed by allowing the natural sample to progressively dry for one hour in each step under controlled relative humidity (around 40%). After this period, the dried sample was equilibrated for one day under hermetic conditions before taking the reading with the psychrometer. The total suction measuring time was around 5 minutes. During this period some small drying occurred inside the measuring chamber, as shown in Cardoso et al. (2007). Water contents were determined using the initial and final weights (average values). After reaching a maximum total suction of around 130 MPa, a multi-stage wetting path was carried out. The path was performed by wetting the sample with small drops of distilled water. An equalisation period of one day under hermetic conditions was afterwards performed, before the determination of the total suction. The sample was trimmed from block 2, starting from an initial water content of 21.8%. An equivalent multi-stage drying path was carried out by letting the natural material to further dry for one hour in each step under a low relative humidity using LiCl. H2 O powder (around 11%). Progressive readings on
drying were taken with the psychrometer up to a maximum total suction of 330 MPa. Afterwards, the dried sample was progressively wetted by keeping it for one hour in each step under a controlled relative humidity of around 40%. Again, progressive readings on wetting were taken with the psychrometer (Pineda et al. 2008). The vapour equilibrium technique was also used to complement the information of the wetting and drying branches of natural and compacted samples. Partially saturated aqueous solutions of NaCl were used to apply different relative humidity values (Romero 1999) below a total suction of 38 MPa. In the upper total suction range, a saturated solution of NaBr.2H2 O was also used to apply a total suction of 75 MPa (Delage et al. 1998, Romero 2001). Multistage drying and subsequent wetting paths at the following steps 5, 10, 20, 38 and 75 MPa were carried out on the natural sample placed in a hermetic jar. At specific intervals of the equalisation process the mass of the sample was registered. An equivalent procedure was followed on a compacted sample. In this case, a multi-stage wetting path followed by a drying path was performed. Samples were allowed to equilibrate for a constant period of two weeks at different relative humidity values, corresponding to the following total suctions: 32, 10, 8, 6 and 3 MPa. 3
EXPERIMENTAL RESULTS
With regard to the CERMES results, Figure 2 presents the changes in water content observed under the various suctions values imposed by using the vapour equilibrium technique. As commented before and as seen in the Figure, three samples were used at each suction value. Stabilisation is observed after around two weeks with good repeatability at the two high values (37.8 and 152.8 MPa). Some fluctuations are observed at 8.5 MPa whereas the curves at 4.2 and 2.8 MPa are superimposed with a tendency of increasing water content along a wetting path. After drying in the oven (suction s estimated to 1 GPa), the dried samples (w = 0) were used to determine a wetting branch from the dry state by using the vapour equilibrium method. Figure 3 presents the water retention properties of Boom clay in terms of both water content (w) and degree of saturation (Sr ) as a function of the logarithm of suction (log s). Starting from initial water contents of 20.2–21.6%, three points were obtained along a wetting path (with measured suctions by tensiometer equal to 180, 280 and 600 kPa respectively). The data obtained along the drying path show a good compatibility between the various points obtained under the same suction, both in terms of water content and degree of saturation. Some hysteresis is observed
231
CuSO4 (2.8 MPa)
16
w (%)
KNO3 (8.5 MPa)
12 NaCl (37.8 MPa)
8
MgCl2 (152.8 MPa)
4
0
4
8
12
16
20
Time (days) Figure 2. Water content equilibration with the vapour control method. 35
Air entry value
w (from initial state) w (Romero et al., 1999)
30 25
100
w (from dry state) Degree of saturation
20 Initial water content w i = 20.2 - 21.6%
15
80 60 40
10
20
5 Drying
Wetting
0 0,1
Degree of saturation (%)
Filter paper
Water content (%)
120
w (Bernier et al., 1997)
1
10
100
0 1000
Suction (MPa)
Figure 3.
Water retention properties of intact Boom clay.
between the two branches of the water content versus suction (w − s) curve, one wetting from dry state, the other drying form initial state. The Sr -log s plot shows that the two points obtained along the drying path at suctions equal to 2.8 and 4.2 MPa indicate that the samples remained saturated. Desaturation starts above 4.2 MPa and the degree of saturation at a suction of 8.5 MPa is 90%. As shown in the figure, the air entry value of Boom clay can be estimated at approximately 5 MPa. At the highest suction (152.8 MPa), the degree of saturation is equal to 31%. Along the wetting path, the curve shows that, curiously, the degrees of saturation at suctions smaller than 1MPa are lying between 90 and 100% whereas samples under suctions of 2.8 and 4.2 MPa were saturated. This point is related to the volume measurement technique (precision calliper) used at lower suction. As compared to the hydrostatic weighing (used at
0.90
-20 -15
Wetting: de /dlogs = - 0.5
0.80
-10
0.70 -5 0.60
0 5
0.50 Drying: de /dlogs = -0.10
0.40
10
Volumetric deformation (%)
20
suction values of 2.8 and 4.2 MPa), precision calliper measurements are thought to be less precise, leading to under-estimated values of the degree of saturation. Under the hypothesis of saturated state, the increase in water content obtained along the wetting path corresponds to some swelling. Conversely, up to the air entry value pressure (5 MPa) drying occurs with some shrinkage under a saturated state. The curve follows the main drying path at suction higher than 5 MPa when the sample starts desaturating. At a suction as high as 152.8 MPa, Boom clay is able to retain 5% water content as a consequence of the smectite content. Water retention data obtained by Bernier et al. (1997) and Romero et al. (1999) on compacted Boom clay samples at a dry unit mass of 1.7 Mg/m3 are also represented for comparison. The data show that the curve of Romero et al. (1999) is parallel, with less water being retained by the compacted sample on a drying path at the same suction. The wetting curve of Bernier et al. (1997) is similar to that of Romero et al. (1999) at high suction. Figure 4 shows the volume changes with respect to suction that correspond to the drying and wetting paths of Figure 3. A significant swelling of 18% is observed when suction is reduced to 180 kPa. A shrinkage of 15% is observed at a suction of 152.8 MPa. The slope that characterises swelling (average slope e/ log s = −0.5) is larger than the shrinkage slope (average slope e/ log s = −0.1). Bernier et al. (1997) found a similar trend on compacted Boom clay specimens subjected to change in suction under a small vertical load in the oedometer. Regarding UPC data, Figure 5 presents the time evolution of the changes in soil mass (natural Boom clay) along the different wetting steps using vapour transfer with pure diffusion. The different wetting steps were 75 MPa to 38 MPa (corresponding to a relative humidity change from 58% to 76%), 38 MPa to 20 MPa (76% to 86%), 20 MPa to 10 MPa (86% to 93%) and 10 MPa to 5 MPa (93% to 96%). Vapour mass transfer rate for a given temperature, vapour
Void ratio
K2SO4 (4.2 MPa)
15 0.30 0.1
1.0
10.0
100.0
1000.0
Suction (MPa)
Figure 4. Variation in void ration and volume with respect to suction change during drying and wetting.
232
WP4 dewpointmeter Low-suction range drying wetting High-suction range (Pineda et al. 2008) drying wetting
1000
Wetting steps: ψ = 10 MPa to 5 MPa Total suction (MPa)
ψ = 20 MPa to 10 MPa ψ = 38 MPa to 20 MPa ψ = 75 MPa to 38 MPa
Soil mass change (g)
0.30
0.20
100 Vapour equilibrium drying wetting
10
1 0
5
10 15 Water content, w (%)
20
25
Figure 6. Retention curves of natural Boom clay using different techniques (WP4 psychrometer and vapour equilibrium technique).
0.10
0.00 0.1
1
10
Time (day)
Figure 5. Time evolution of changes in soil mass along different wetting steps.
diffusivity and sample size is assumed proportional to the relative humidity change applied in a wetting step. As observed in the figure, longer equalisation periods are required for the lower relative humidity changes at elevated total suctions. Equalisation time is observed after around three weeks for the total suction step 10 MPa to 5 MPa, whereas equalisation is completed in less than one week for the total suction step 75 MPa to 38 MPa. A good agreement with CERMES results is observed. Figure 6 summarises the water retention results obtained by UPC on natural Boom clay using psychrometer readings and vapour equilibrium results. As detected in the hysteresis loops in the figure, the shifting towards lower water contents of the wetting branches is more obvious at total suctions lower than 10–20 MPa. In addition to the hydraulic hysteresis, the irreversible shrinkage undergone by the sample on first drying is also affecting the water storage capacity of the sample at low suctions. This low-suction zone of the retention curve (below 10 to 20 MPa) is dependent on void ratio and is consequently sensitive to the stress paths followed (Romero & Vaunat 2000). As observed in the figure and with reference to psychrometer readings on drying, important changes in water content occur when total suction is increased over 5 MPa (air-entry value in terms of water content). Regrettably, degrees of saturation were not determined that could allow for a further reconsideration of this
value. Equivalent water retention results were obtained when comparing vapour equilibrium data and psychrometer readings at total suctions over 38 MPa. The lower water contents determined with vapour equilibrium technique compared to WP4 readings for suctions below 38 MPa, appear to be a matter of the equalisation process. As shown in Figure 5, the equalisation process is still ongoing after 30 days for total suctions below 20 MPa. In addition, the systematic higher total suctions measured with the psychrometer for specific water contents can be explained in terms of the hydraulic path undergone by the soil during the measurement process. As discussed by Cardoso et al. (2007), the sample placed inside the equalisation chamber of the WP4 psychrometer undergoes some drying along the main drying curve during equalisation, which can explain the systematic higher suction values. Figure 7 summarises the water retention results on drying obtained by CERMES and UPC on natural Boom clay, as well as the results measured by UPC on the compacted material at an equivalent void ratio to that of the in situ state. A quite good agreement is observed between both laboratories when comparing results on natural Boom clay using vapour equilibrium technique. Small discrepancies can be explained in terms of the testing protocols adopted by each laboratory (time to reach equilibrium, sample dimensions, and so on). Psychrometer results displayed slightly larger values compared to vapour equilibrium results, as previously discussed. When comparing natural and compacted states, systematically lower water retention capacity has been observed in the case of the compacted material. These differences are more important at total suctions below 10 MPa. Differences at this low-suction range can be explained as a consequence of the different pore size distributions of
233
REFERENCES
1000 Drying paths
Total suction (MPa)
WP4 psychrometer UPC Vapour equilibrium UPC
100
Romero (1999) Vapour equilibrium CERMES
10
1 0
5
10 15 Water content, w (%)
20
25
Figure 7. Retention curves on drying. Comparison between different states (natural and compacted) and different techniques (WP4 psychrometer and vapour equilibrium technique).
the material. The compacted material displays larger dominant macropore dimensions, which are associated with a lower air-entry value (around 0.7 MPa, according to Romero 1999).
4
CONCLUSIONS
The retention properties of Boom clay have been investigated by using various suction control and measurement techniques including the vapour equilibrium method, the filter paper, high-range tensiometer readings and the chilled-mirror dew-point psychrometer. The values obtained are discussed according to the techniques used. They are compared with previous data on compacted Boom clay samples. The swellingshrinkage behaviour under changes in suction was investigated. The water retention curves determined show that the air-entry value of the natural material is closed to 4–5 MPa, much higher than the corresponding one to the compacted state at equivalent void ratio. This feature explains the lower water retention capacity of the compacted material compared to the natural state for total suctions between 3 and 10 MPa.
ACKNOWLEDGEMENT EURIDICE (European Underground Research Infrastructure for Disposal of nuclear waste In Clay Environment, Mol, Belgium) is gratefully acknowledged for funding the work presented in this paper. This work has also been conducted within the MUSE European Research and Training Network (Marie Curie Action).
Belanteur, N., Tacherifet, S. and Pakzad., M. (1997). Étude des comportements mécanique, thermo-mécanique et hydro-mécanique des argiles gonflantes et non gonflantes fortement compactées. Revue Française de Géotechnique 78, 31–50. Bernier, F., Volckaert, G., Alonso, E. and Villar, M. (1997). Suction-controlled experiments on Boom clay. Engineering Geology 47, No. 4, 325–338. Cardoso, R., Romero, E., Lima, A. and Ferrari, A. (2007). A comparative study of soil suction measurement using two different high-range psychrometers. Proc. 2nd Int. Conf. Mechanics of Unsaturated Soils. Weimar, T. Schanz (ed.). Springer-Verlag, Berlin, 79–93. Dehandschutter, B., Vandycke, S., Sintubin, M., Vandenberghe, N. and Wouters, L. (2005). Britlle fractures and ductile shear bands in argillaceous sediments: inferences from Oligocen Boom Clay (Belgium). J. Structural Geology 27, 1095–1112. Delage, P., Howat, M.D. and Cui, Y.J. (1998). The relationship between suction and swelling properties in a heavily compacted saturated clay. Engineering Geology 50, 31–48. Doran, I.G, Sivakumar, V., Graham, J. and Johnson, A. (2000). Estimation of in-situ stresses using anisotropic elasticity and suction measurements. Géotechnique 50, No. 2, 189–196. Li (2007). Personal communication. Mantho, A., (2005). Echanges sol-atmosphère. Application à la sécheresse. PhD Thesis, Ecole des ponts, Paris. ONDRAF/NIRAS, (2001). Aperçu technique du rapport SAFIR 2. Safety Assessment and Feasibility Interim Report 2. Publication NIROND 20001–05 F, p. 280. Pineda, J., Lima, A. and Romero, E. (2008). Influence of hydraulic paths on the low-strain shear modulus of a stiff clay. Proc. 1 st Eur. Conf. Unsaturated Soils. Durham, United Kingdom. Ridley, A.M. and Burland, J.B. 1993. A new instrument for measurement of soil moisture suction. Géotechnique, 43, no. 2, 321–324. Romero, E. (1999). Characterisation and thermo-hydromechanical behaviour of unsaturated Boom clay: an experimental study. PhD Thesis. Universitat Politècnica de Catalunya, Spain. Romero, E. (2001). Controlled suction techniques. Proc. 4◦ Simposio Brasileiro de Solos Nao Saturados. Gehling and Schnaid (eds.). Porto Alegre, Brasil, 535–542. Romero, E., Gens, A. and Lloret, A. (1999). Water permeability, water retention and microstructure of unsaturated compacted Boom clay. Engineering Geology 54, 117–127. Romero, E. and Vaunat, J. (2000). Retention curves of deformable clays. Proc. Int. Workshop on Unsaturated Soils: Experimental Evidence and Theoretical Approaches, Trento, Tarantino & Mancuso (eds). Balkema, Rotterdam, 91–106. Skempton, A.W. and Sowa, V.A. (1963). The behaviour of saturated clays during sampling and testing. Géotechnique 13, No. 4, 269–290.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Determination of soil suction state surface in pure and composite clays by filter paper method M. Biglari, A. Shafiee & I. Ashayeri IIEES, International Institute of Earthquake Eng. & Seismology, Tehran, Iran
ABSTRACT: Filter paper method is used to measure total suction of compacted clay and clay-sand mixture. The samples are prepared by static compaction to the desired initial void ratio and degree of saturation to investigate effects of initial compaction on the drying soil water characteristic curves. Additionally, volume change of samples was measured during the drying process and its effect was considered in obtaining SWCC. The suction measurements were plotted in e-Sr space and equal suction lines obtained. These lines represent a surface in a 3D plot.
1
INTRODUCTION
The development of unsaturated soil mechanics based on the concept of using two independent stress state variables requires measurement of the soil suction. Several techniques have been developed to measure soil suction at laboratory and in-situ. The total soil suction is known to be summation of the osmotic suction and the matric suction. Osmotic suction is influenced by salt concentration in the pore water that is present in both saturated and unsaturated soils. Osmotic suction changes have an effect on the mechanical behaviour of a soil. Krahn & Fredlund (1972) studied variation of total, matric and osmotic suction of compacted Regina clay and glacial till respect to soil water content and showed the total and matric suction curves have almost similar variations, particularly in the higher water content range (Fig. 1). Matric suction is defined as the difference between the pore air pressure above the contractile skin and the water pressure below the contractile skin. The contractile skin is consisted of water molecules at the interface layer between the water and the air, where the surface tension of the water molecules presents. The maximum matric suction that can be maintained across contractile skin is called air entry value and can be determined using Kelvin equation (Eq. 1) ua − uw =
2Ts Rs
The use of filter paper for estimating the water potential was first reported by Gardner (1937) for agricultural applications. Currently, the filter paper method is a standard test method for measurement of soil suction in ASTM D 5298-94. The filter paper method is an inexpensive and relatively simple soil suction measurement technique. In addition, it can be applied for a wide range of suction values. With the filter paper method both total and matric suction can be measured. If the filter paper is allowed to absorb water through vapor flow (noncontact method) then only total suction is measured. Otherwise, if the filter paper is allowed to acquire
(1)
where; Ts is the surface tension of the contractile skin and Rs is radius of the maximum pore size distribution. Rahardjo & Leong (2006) have presented summary of several suction measurements techniques.
Figure 1. Variation of total, osmotic and matric suction of Regina clay by water content (after Krahn & Fredlund 1972).
235
2
MATERIALS AND TESTING PROGRAM
Two basic materials are used in this study; clay and sand. The suction measurements were performed on the samples of pure clay and artificial materials composed of 60 percent clay and 40 percent sand by weight. The pure clay is classified as medium plastic Kaolinite clay. The liquid limit of the clay soil is 42 percent, the
plasticity index is 18 percent, the specific gravity of particles is 2.69 and from hydrometer analysis the clay size fraction (finer than 2 μm) is about 60 percent and the remaining 40 percent is smaller than 75 μm (sieve No. 200). The sand is classified as medium to fine uniformly graded sand (SP in USCS) and its fine content is about 1 percent. The specific gravity of the material is 2.69. Figure 2 represents particle size distribution of sand. Different samples were prepared from pure clay (C100) and the composite material (C60). The soils were compacted statically to a disc shaped samples
100 90 80 70
Percent Passing
water through fluid flow (contact method), then only matric suction is measured. Meanwhile, the provision of contact between filter paper and the pore fluid is difficult in low water content samples, the contact filter paper method may measure either the total or the matric suction, depending on the degree of contact between the soil and the filter paper. The most commonly used filter papers for suction measurement are Whatman No. 42 and Schleicher & Schuell (S&S) No. 589-WH. The calibration curve for these two filter papers is given in ASTM D 5298-94 and is used in the measurements of the present investigation. The variation of matric suction in an identical soil specimen during drying and wetting versus soil specimen gravimetric water content, degree of saturation or volumetric water content is called soil-water characteristic curve (SWCC) or soil water retention curve. It has been found that at a given matric suction the soil water content during the wetting and drying process are different, that is known as the hysteretic behaviour of SWCCs. Furthermore, recent investigations revealed that there is no single, unique relationship between volume change and water content change for an unsaturated soil. The volume change and the water content change in an unsaturated soil are controlled by two independent mechanisms; the stress strain behaviour and the adsorption-drainage behaviour (Fredlund & Pham 2006). Conventionally, the SWCC is determined at zero net normal stress and the volume changes of soil specimen during the determination of SWCC are ignored. Ho et al. (2006), in a recent experimental studies, have used a volumetric pressure plate extractor and provided state dependent soil water characteristic curves (SDSWCC) where the degree of saturation is expressed by two stress state variables. In the present study, the total suction of pure and composite clay-sand mixture is measured by the filter paper method and the effects of initial degree of saturation and void ratio on the total suction are investigated. Furthermore, the soil samples were allowed to dry gradually and the variation of total suction is measured while considering volume changes of the specimen. The total suction measurements are presented by contour lines in e-Sr space for both materials and the possible state surfaces are shown in 3D plot.
60 50 40 30 20 10 0 0.001
Figure 2.
0.01
0.1 1 Particle Size (mm)
10
100
Particle size distribution of pure sand.
Table 1. Initial void ratio and degree of saturation for samples. Sample no.
e0
Sr 0 (%)
Sample no.
e0
Sr 0 (%)
C100-1 C100-2 C100-3 C100-4 C100-5 C100-6 C100-7 C100-8 C100-9 C100-10 C100-11 C100-12 C100-13 C100-14 C100-15 C100-16 C100-17 C100-18 C100-19 C100-20 Max Min
0.684 0.672 0.688 0.666 0.723 0.667 0.774 0.640 0.630 0.698 0.733 0.663 0.691 0.661 0.637 0.655 0.572 0.584 0.575 0.600 0.774 0.572
33.0 47.0 58.5 76.9 85.9 37.9 45.8 64.4 82.4 94.6 38.2 56.6 63.0 75.6 88.8 44.9 62.4 70.6 81.9 87.5 94.6 33.0
C60-1 C60-2 C60-3 C60-4 C60-5 C60-6 C60-7 C60-8 C60-9 C60-10 C60-11 C60-12 C60-13 C60-14 C60-15 C60-16 C60-17 C60-18 C60-19 C60-20 Max Min
0.677 0.705 0.762 0.835 0.767 0.673 0.660 0.724 0.772 0.729 0.624 0.688 0.648 0.643 0.659 0.534 0.557 0.572 0.589 0.603 0.835 0.534
30.6 36.4 44.1 49.4 65.3 29.9 40.2 42.7 50.2 61.2 35.1 40.7 49.2 54.4 63.4 38.8 44.7 47.4 54.6 59.6 65.3 29.9
236
with approximate diameter of 50 mm and height of 20 mm. In order to investigate effects of initial void ratio and degree of saturation on the suction, the samples were compacted to different e and Sr. Twenty samples were prepared for each soil group. Table 1 presents the initial conditions of the samples. The samples were weighted by a digital balance with 0.0001 gr accuracy and the average diameter and height of the sample for volume measurements were measured with 0.05 mm accuracy. Filter paper tests were performed according to ASTM D 5298-94 and total suction was measured in the samples. Whatman No. 42 filter paper was used for suction measurements and the corresponding standard calibration curve was applied. For the vapor equalization time the samples and two filter papers were placed into sealed jars and the jars were kept in an isolated container for 10 days. According to Marinho (1994) 7 to 15 days is suitable equalization time for total suction measurement in the range of 250 to 30000 kPa. The filter papers were placed above a piece of PVC pipe with height of 20 mm, itself placed above the soil sample in the jar. After 10 days the weight of filter papers was measured with the digital balance and then the filter papers were placed into oven with 110 ± 5◦ C for 10 hours. After 10 hours the dry weight of filter paper was measured. Detail of the procedure is presented by Bulut et al (2001).
Accordingly, the soil samples were placed into a desiccator for 3 days to reduce water content. In order to facilitate desiccation silica gel was used. After three days the soil samples weighted with the digital balance and their volume was measured. Afterward, they were placed into jars with new filter papers again. The procedure explained above was repeated four times for C100 samples and three times for C60 samples.
3
DISCUSSION OF TEST RESULTS
Figure 3 presents the drying SWCCs for both soils. It is clearly shown that the samples of the same material follow different drying curves according to their different initial conditions. The comparison between SWCC of C100 and C60 reveals that the SWCCs of C100 are more deviated than C60s’, although the deviation in e0 of C60s is more than C100s (Table 1). Furthermore, the average SWCC of C60 has smaller suction than the average C100 one. Figures 4 & 5 plot the variation of void ratio versus total suction along the drying path for C100 and C60 respectively. It is observed that again initial void ratio affects significantly the suction of the sample when the sample’s suction is less than a specific value. This specific value corresponds to the sample’s shrinkage limit. For instance, samples of C100 with suction more
100 90 80
Degree of saturation
70 60 50
C100-1
C100-2
C100-3
C100-4
C100-5
C100-6
C100-7
C100-8
C100-9
C100-10
C100-11
C100-12
C100-13
C100-14
C100-15
C100-16
C100-17
C100-18
C100-19
C100-20
C60-1
C60-2
C60-3
C60-4
C60-5
C60-6
C60-7
C60-8
C60-9
C60-10
C60-11
C60-12
C60-13
C60-14
C60-15
C60-16
C60-17
C60-18
C60-19
C60-20
40 30 20 10 0 100
1000
10000 Total Suction (kPa)
Figure 3.
Drying SWCC for C100 and C60.
237
100000
0.8
C100-1 C100-2 C100-3
0.75
C100-4 C100-5
0.7
C100-6 C100-7
Void Ratio (e)
0.65
C100-8 C100-9
0.6
0.55
0.5
0.45
0.4 100
1000
10000
100000
C10010 C10011 C10012 C10013 C10014 C10015 C10016 C10017 C10018 C10019 C10020
Total Suction (kPa)
Figure 4.
Void ratio variation in drying SWCC for C100.
50
C100-1 C100-3 C100-5 C100-7 C100-9 C100-11 C100-13 C100-15 C100-17 C100-19 C60-1 C60-3 C60-5 C60-7 C60-9 C60-11 C60-13 C60-15 C60-17 C60-19
45
Volumetric water content
40 35 30 25 20 15 10 5 0 100
Figure 5.
1000
10000 Total Suction (kPa)
Void ratio variation in drying SWCC for C60.
238
100000
C100-2 C100-4 C100-6 C100-8 C100-10 C100-12 C100-14 C100-16 C100-18 C100-20 C60-2 C60-4 C60-6 C60-8 C60-10 C60-12 C60-14 C60-16 C60-18 C60-20
0.9
C60-1 C60-2 C60-3 C60-4 C60-5 C60-6 C60-7 C60-8 C60-9 C60-10 C60-11 C60-12 C60-13 C60-14 C60-15 C60-16 C60-17 C60-18 C60-19 C60-20
0.85
0.8
Void Ratio (e)
0.75
0.7
0.65
0.6
0.55
0.5 100
1000
10000
100000
Total Suction (kPa)
Figure 6.
Volumetric water content versus suction for C100 and C60.
C100-1
0.9
C100-2 0.85
C100-3 C100-4
0.8
C100-5 C100-6
0.75
C100-7
Void Ratio (e)
C100-8 0.7
C100-9 C100-10
0.65
C100-11
1MPa
C100-12
0.6
C100-13 2MPa
0.55
C100-14 C100-15 C100-16
0.5
C100-17
5MPa
C100-18
0.45 20MPa
15MPa
C100-19
10MPa
C100-20
0.4 0
10
20
30
40
50
60
Degree of Saturation
Figure 7.
Contour lines of equal suction in e-Sr space for C100.
239
70
80
90
100
0.9
C60-1 C60-2 C60-3 C60-4 C60-5 C60-6 C60-7 C60-8 C60-9 C60-10 C60-11 C60-12 C60-13 C60-14 C60-15 C60-16 C60-17 C60-18 C60-19 C60-20
0.85
Void Ratio (e)
0.8 0.75 0.7 1MPa 0.65 0.6 3MPa
0.55 15MPa 10MPa 7MPa 5MPa 0.5 0
Figure 8.
10
20
30
40 50 60 Degree of saturation
70
80
90
100
Contour lines of equal suction in e-Sr space for C60.
than 5 MPa shows no correlation to void ratio and similarly, the samples with suction more than 3 MPa for C60s. Figure 6 presents drying SWCC of both materials by volumetric water content versus suction. Although different drying curves are observed for different samples, the volumetric water content versus suction looks less deviated than Figure 3. This can be interpreted as the incorporated presence of void ratio or porosity and degree of saturation in the volumetric water content definition. The variation of soil suction versus void ratio and degree of saturation (or volumetric water content) expresses that soil suction can be plotted versus these two parameters. Figures 7 & 8 present the positions of all samples in the e-Sr space. The dashed lines represent contour lines of equal suctions. These lines resemble a 3D surface in suction versus void ratio and degree of saturation space (Fig. 9). It is illustrated that total suction is more influenced by void ratio for an intermediate range of degree of saturation. The contour line of equal suction tends to vertical as the degree of saturation decreases and the variation of suction decreases as the degree of saturation tends to one. Comparison between Figures 7 and 8 reveals the shrinkage of this intermediate range by increasing sand content. Figures 10 & 11 replot variation of degree of saturation versus suction for some of the test results presented in Figures 7 & 8 respectively, where the void
Figure 9.
Suction state surface in 3D plot for C100.
ratio of samples are constant. These figures illustrate possible drying SWCCs for the samples that have similar void ratio. The lower the void ratio of the samples, the larger the air entry values and the larger the suction. Figure 11 represents increasing sand content of the material up to 40 percent has eliminated effect of void ratio to some extent. 4
CONCLUSION
Filter paper method is an inexpensive and relatively simple technique for measurement of both total and matric suction of soil. In addition, it can be applied for a wide range of suction values. In the present study, filter paper method was applied to investigate effect of initial void ratio on drying SWCCs. The material tested was composed of pure clay and clay-sand
240
100 90 Lower void ratio
80
Degree of Saturation
70 60 50 Higher void ratio 40 30 20 10 0 100
1000
10000
100000
Total Suction (kPa) Ave(e)=0.463, Stdev(e)=0.001 Ave(e)=0.635, Stdev(e)=0.006
Figure 10.
Ave(e)=0.499, Stdev(e)=0.005 Ave(e)=0.666, Stdev(e)=0.003
Ave(e)=0.561, Stdev(e)=0.007 Ave(e)=0.682, Stdev(e)=0.005
Drying SWCC at constant void ratio for C100.
100 90 80
Degree of Saturation
70 60 50 40 30 20 10 0 100
1000
Total Suction (kPa)
Ave(e)=0.685, Stdev(e)=0.005 Ave(e)=0.627, Stdev(e)=0.005
Figure 11.
10000 Ave(e)=0.658, Stdev(e)=0.003 Ave(e)=0.574, Stdev(e)=0.007
Drying SWCC at constant void ratio for C60.
241
100000
mixture. The tests results revealed that the initial condition of the samples significantly affects SWCCs but increasing sand content has reduced the extent of effects. Additionally, presenting SWCC by volumetric water content, instead of degree of saturation, results into less deviated SWCCs. Meanwhile, considering volume change of sample during measurement of total suction is found to be more important for an intermediate range of degree of saturation of samples and this range shrinks by increasing sand content. More accurate numerical modeling can be achieved by using 3D constitutive surfaces or constant void ratio SWCCs instead of single SWCC. REFERENCES Bulut, R., Lytton, R.L. & Wary, W.K. 2001. Suction Measurements by Filter Paper, Expansive Clay Soils and Vegetative Influence on Shallow Foundations, ASCE Geotechnical Special Publication No. 115 (eds. C. Vipulanandan, M.B. Addision, and M. Hasen), ASCE, Reston, Virginia, pp. 243–261.
Fredlund, D.G. & Pham, H.Q. 2006. A Volume-mass Constitutive model for Unsaturated Soils in Terms of Two Independent Stress State Variables, Unsaturated Soils, ASCE, Geotechnical special publication No. 147. pp. 105–134. Gardner, R. 1937. A Method of Measuring the Capillary Tension of Soil Moisture over a Wide Moisture Range, J. Soil Science. Vol. 43, No. 4, pp. 277–283. Ho, K.M.Y., Ng, C.W.W., Ho, K.K.S. & Tang, W.H. 2006. State-dependent Soil-water Characteristic Curve (SDSWCCs) of Weathered Soils, Unsaturated Soils, ASCE, Geotechnical special publication No. 147, pp. 1302–1313. Krahn, J. & Fredlund, D.G. 1972. On Total Matric and Osmotic Suction, J. Soil Science. Vol. 114, No. 5, pp. 339–348. Marinho, F.A.M. 1994. Medicao de succao com o metodo do papel fitro, In Proc. X Congresso Brasileiro de Mecanica do Solos e Engenharia de Fundacoes. Vol. 2, pp. 516–522. Rahardjo, H. & Leong, E.C. 2006. Suction Measurements, Unsaturated Soils, ASCE, Geotechnical special publication No. 147, pp. 81–104.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Soil water retention curves for remolded expansive soils K.C. Chao, J.D. Nelson, D.D. Overton & J.M. Cumbers Engineering Analytics, Inc., Fort Collins, Colorado, USA
ABSTRACT: Volume change in expansive soils occurs due to changes in the soil water system that change the stress equilibrium of the soil. Consequently, when determining the Soil Water Retention Curve (SWRC) of an expansive soil, it is important to consider the volume change that occurs as the suction, and hence water content, changes during the test. Experiments using the Fredlund SWCC device and the filter paper method were conducted to take into account the effect of the volume changes on the soil water retention relationship of expansive soils. Claystone samples of the Denver and Pierre Shale Formations obtained near Denver, Colorado, USA were used in the study. A moist tamping system was used to obtain ‘‘identical’’ soil specimens. The observed experimental data were used to evaluate the previously published mathematical equations of SWRC. It is shown that the Fredlund and Xing equation is in the best agreement with the experimental data among the equations. In addition, a bilinear form was used to express the SWRC for the expansive soils. It is concluded that the bilinear form of the SWRC gives the best fit to the measured experimental data.
1
INTRODUCTION
The soil water retention curve (SWRC) has played a dominant role in unsaturated soils in disciplines such as soil science, soil physics, agronomy, and agriculture. There is some discussion within the soil water research community regarding the use of the term soil water retention curve (SWRC) as opposed to the term soil water characteristic curve (SWCC). The term soil water retention curve (SWRC) has been adopted in this paper. However, when reference is made to the Fredlund SWCC device and test results therefrom, the term SWCC has been retained in connection with that device. The SWRC has been identified as the key soil information required for the analyses of seepage, shear strength, and volume change problems involving unsaturated soils. The SWRC is usually measured assuming no volume change of the soil specimen. This is not the case for an expansive soil. When determining the SWRC of an expansive soil, it is important to consider the volume change that occurs as the suction changes during the test. The SWRC of a soil is hysteretic. Therefore, depending on whether the process being simulated in the field is a wetting or drying process, an appropriate wetting or drying curve needs to be determined for the soil. Heaving of expansive soils/bedrock is related to the wetting process. Consequently, a wetting curve should be utilized in simulations of the migration of water in the subsoils/bedrock for modeling heave
phenomena. This paper focuses on an evaluation of the wetting curves of the expansive claystone of the Denver and Pierre Shale Formations. A moist tamping system was used to obtain identical soil specimens. The Fredlund SWCC device and the filter paper test were utilized in the experiments. The observed experimental data were used to evaluate previously published mathematical equations for the SWRC. This paper presents the results of the experimental data of the claystone and a proposed equation for the SWRC curve. 2 2.1
EXPERIMENTAL PROGRAM Soil description and index properties
Samples of claystone of the Denver and Pierre Shale Formations were obtained using drilling with a continuous core sample at sites near Denver, Colorado, USA. The boring log of the claystone of the Denver Formation indicates that the claystone bedrock was slightly moist and consisted of yellowish brown, hard claystone with some oxidation and occasional silty claystone lenses. The boring log of the claystone taken from the Pierre Shale Formation indicates that the claystone bedrock was slightly moist and consisted of light olive brown and gray claystone with oxidation along the bedding planes. The results of the laboratory tests are provided in Table 1. The samples of the claystone of both the Denver and Pierre Shale Formations were classified
243
Table 1.
Summary of geotechnical properties of Denver and Pierre Shale formations. Consolidation-Swell Test(2)
Formation of claystone bedrock
Natural water content (%)
Natural dry density (Mg/m3 )
LL/PL(1) (%)
Percent swell (%)
Swell pressure (kPa)
Denver Pierre shale
20.1–26.5 15.2–16.3
1.54 –1.67 1.81–1.92
56–68/32–43 60–61/41–42
6.5–7.4 3.1–5.7
1150–2550 710–1300
Notes: (1) LL = Liquid Limit, PL = Plastic Limit. (2) Inundation Pressure, σi = 48 kPa.
as high plasticity clay (CH). They exhibited moderate to very high swell potential. 2.2
Specimen preparation
A variety of methods have been developed for reconstituting soil specimens in the laboratory. The moist tamping method is one of the successful methods proposed for preparing nearly identical soil specimens (Mulilis, et al., 1975). The early implementation of the moist tamping method involved the soil specimen being prepared using a number of layers of equal dry weight and volume wherein each layer was being compacted to the same target density. Mulilis, et al. (1975) found that this could result in the lower portion of the specimen becoming denser than the desired specimen density because the compaction of each overlying layer also resulted in the densification of underlying layers. Noorany (2005) proposed to prepare a soil sample with a number of layers of equal soil weight and volume when compacting each layer into a compaction mold, as shown in Figure 1. Noorany (2005) found that this modified moist tamping method was successful in preparing uniform soil specimens for the oedometer test. The modified moist tamping method was utilized to prepare and compact soil specimens for the laboratory testing. The soil specimens were prepared for testing by compacting them to 100% of the maximum Standard Proctor dry density at a water content 3% less than the optimum water content. The sample rings used for the experiment have dimensions of 6.2 cm inside diameter and 3.1 cm thick. The thick steel plate shown in Figure 1 is 0.5 cm in height. The soil sample at the completion of compaction within each ring was 2.5 cm in height. In addition, four (4) layers with each layer being 0.6 cm in height were selected for the compaction process.
2.3
Experimental procedure
2.3.1 Filter paper test The filter paper method was used to obtain the soil water retention relationship of both soil types for a soil suction ranging from approximately 1 to 175,000 kPa.
Figure 1. Schematic of Moist Tamping System (modified from Noorany, 2005).
This range corresponds to a pF of 1.01 to 6.25. Whatman No. 42 filter paper was used in this study. The weight of the filter paper was measured to the nearest 0.0001 g during the test. The filter paper method was adopted to measure total and matric suctions of soil specimens in accordance with both non-contact and contact techniques described in ASTM D5298-94. ASTM D5294-94 recommends a minimum equilibration time of 7 days for running the filter paper contact and non-contact tests. However, in examining the required time for filter paper to reach equilibrium, it was found that the equilibration time is dependent on suction source, measured suction type (contact or non-contact method), material type, water content of soil specimen (suction level), number of pieces of filter paper used, relative humidity of the air, and soil mass and space in the container. The time required for equilibration of the filter paper when measuring the suction of the claystone from the Pierre Shale Formation was evaluated in Chao (2007). For determining the boundary wetting curve, the soil specimen was initially air-dried in the laboratory. The weight and volume of the air-dried sample were
244
measured. Calipers were used to measure the height and diameter of the sample in order to determine the volume. A filter paper test was performed on the airdried sample to obtain a soil suction corresponding to the lowest water content of the sample. At the completion of the first filter paper test, water was sprayed onto the soil specimen to obtain a desired water content of the sample for the next filter paper test. The values of water content of the sample were increased at intervals of approximately 5%. The wetting curve test continued until the last desired value of water content of the soil specimen was reached. Measurements of the weight and volume of the sample at equilibrium were taken throughout the experiment. In addition, five remolded samples of the Pierre Shale claystone were oven-dried to obtain the soil suction of the claystone at oven-dry water content conditions using the filter paper method. The sample was cut in two pieces and filter papers were placed between the pieces. A rubber band was placed around the sample to ensure contact between the filter papers and the soil. 2.3.2 Fredlund SWCC test The Fredlund SWCC device was utilized to determine the SWRC over a range of soil suction from 2 to 900 kPa for the claystone of the Denver formation. This soil suction range overlapped the range used in the filter paper tests to verify the measured laboratory data from each other. A schematic of the Fredlund SWCC device used in this study is shown in Figure 2. The sample rings used for the test are 6.4 cm in diameter and 2.5 cm in height. The Fredlund SWCC device was calibrated to account for compressibility of the device, filter paper, and porous stone (Chao, 2007). Similar to the filter paper test, the soil specimen was compacted to 100% of the maximum Standard Proctor dry density at a water content 3% less than the optimum water
content, and then air-dried until a minimum water content was reached in the laboratory. The weight and volume of the air-dried sample were measured. The air-dried soil specimen was transferred to a ceramic stone placed in the pressure cell of the Fredlund SWCC device. The water below the ceramic stone was maintained at atmospheric pressure. A specified air pressure was applied into the pressure cell. In response to the applied suction, the water was drawn into the soil specimen through volume indicator tubes and through the ceramic stone until equilibrium was established. It was possible for air to diffuse through the ceramic stone and collect on the bottom of the cell. Therefore, the diffused air was flushed out before reading the levels in the volume indicator tubes. The water content of the specimen was calculated using the volume indicator tube readings. The change in height of the soil specimen was measured from an attached dial gauge. This procedure was repeated for successive pressure decrements to obtain a series of data points on the wetting curve. The pressure values that were used were 900, 400, 100, 10, and 2 kPa. At the end of the wetting curve test, the soil specimen was removed from the cell and its water content and dry density were determined. 2.4 Experimental results Figures 3 and 4 present the SWRCs in terms of volumetric water content from the average values of the experimental data for the Denver and Pierre Shale Formation samples, respectively. The osmotic suction curves shown in Figures 3 and 4 were computed by subtracting the matric suction values from the total suction values. None of the SWRCs shown in Figures 3 and 4 exhibit a distinct point of bifurcation to define the displacement pressure head. This trend of not having a distinct displacement pressure head for expansive soil has also been reported by others (Chao, 1995;
Volumetric Water Content (%)
50 45
Total Suction
40
Matric Suction
35
Osmotic Suction
30 25 20 15 10 5 0 1
10
100
1000
10000
100000 1000000
Soil Suction (kPa)
Figure 2. Schematic of Fredlund SWCC device (from GCTS 2004).
Figure 3. Wetting SWRC—Total, matric and osmotic suctions from Filter Paper test—Remolded claystone of Denver formation.
245
60
45 40
Total Suction Matric Suction
35
Osmotic Suction
Volumetric Water Content (%)
Volumetric Water Content (%)
50
30 25 20 15 10 5
Measured Data Burdine (1953), r^2 = 0.8980
50
Gardner (1958), r^2 = 0.9559 Brooks & Corey (1964), r^2 = 0.8960
40 30 20 10 0
0 1
10
100
1000
10000
1
100000 1000000
Soil Suction (kPa)
Figure 4. Wetting SWRC—Total, matric, and osmotic suctions from Filter Paper test—Remolded claystone of Pierre Shale formation.
10
100 1000 Soil Suction (kPa)
10000 100000
1000000
Figure 6. Burdine, Gardner, and Brooks & Corey equations fitted to experimental data—Claystone of Denver formation.
60 Volumetric Water Content (%)
Volumetric Water Content (%)
60 Measured Data from Filter Paper Test 50
Measured Data from Fredlund SWCC Test
40 30 20 10
1
10
100
1000
10000
30 20 10
1
100000 1000000
10
100
1000
10000 100000 1000000
Soil Suction (kPa)
Soil Suction (kPa)
Figure 7. Mualem, van Genuchten, and Fredlund & Xing equations fitted to experimental data—Claystone of Denver formation.
Figure 5. Comparison of wetting SWRCs from Filter Paper test and Fredlund SWCC test—Remolded claystone of Denver formation.
Al-Mukhtar, 1995; Alonso, et al., 1995; Wan, et al., 1995; and Miller, 1996). The Fredlund SWCC test was conducted on the remolded claystone of the Denver Formation and the results were compared with those obtained using the filter paper method. Figure 5 shows that the filter paper test reproduced the results obtained from the Fredlund SWCC test.
3.1
40
0
0
3
Measured Data Mualem (1976), r^2 = 0.9136 van Genuchten (1980), r^2 = 0.9559 Fredlund & Xing (1994), r^2 = 0.9685
50
ANALYSIS OF EXPERIMENTAL DATA Curve fitting with previously published SWRC equations
The observed experimental data were fitted to the previously published mathematical equations for the SWRC. Selected mathematical equations include those proposed by Burdine (1953), Gardner (1958), Brookes and Corey (1964), Mualem (1976), van Genuchten (1980), and Fredlund & Xing (1994). Figures 6 and 7 show the curve fitting for the claystone of the Denver Formation. Figures 8 and 9
show the curve fitting for the claystone of the Pierre Shale Formation. The values of r 2 for regression analyses of the equations are also shown in the figures. Comparison of Figures 6 through 9 indicates that among all equations considered, the Brooks and Corey equation provides the least agreement with the experimental data. The reason for the poor fit of the Brooks and Corey equation is that this curve exhibits a sharp break at the air entry value. This is more representative of sandy soil having a relatively narrow grain size distribution. It should be noted that this equation was developed for a rigid porous medium (i.e. no volume change). It is seen in Figures 6 through 9 that the Fredlund and Xing equation exhibits the best agreement with the experimental data. An interesting observation is that the four-parameter equations (such as the van Genuchten and Fredlund & Xing equations) performed a better curve fitting than the three-parameter equations (such as the Burdine, Brooks and Corey, and Mualem equations). This observation was also made by Leong and Rahardjo (1997) for other soil types.
246
(%)
Measured Data Burdine (1953), r^2 = 0.9108
50
Volumetric Water Content,
Volumetric Water Content (%)
60
Gardner (1958), r^2 = 0.9574 Brooks & Corey (1964), r^2 = 0.8819
40 30 20 10 0 1
10
100
1000
10000
30 = -2.3404Ln( ) + 43.396 r2 = 0.9957
20 10
= -5.3991Ln( ) + 69.37 r2 = 0.9875
? 10
100 1000 Soil Suction,
10000 (kPa)
100000 1000000
Figure 11. Bilinear equation fitted to experimental data— Claystone of Pierre Shale formation.
and Miller, 1996). The results of the experimental data plotted in bilinear form are shown in Figures 10 and 11 for the claystone of the Denver and Pierre Shale Formations, respectively. It is shown in Figures 10 and 11 that the bilinear form of the SWRC gives the best fit to the measured experimental data compared to the published mathematical equations discussed previously. The question mark by the point at zero water content indicates that this point was not used in the curve fitting procedure.
60 Volumetric Water Content (%)
40
1
Figure 8. Burdine, Gardner, and Brooks & Corey equations fitted to experimental data—Claystone of Pierre Shale formation.
Measured Data Mualem (1976), r^2 = 0.9213 van Genuchten (1980), r^2 = 0.9570 Fredlund & Xing (1994), r^2 = 0.9727
40
Measured Data
50
0
100000 1000000
Soil Suction (kPa)
50
60
30 20 10 0 1
10
100
1000
10000
100000 1000000
4
Soil Suction (kPa)
Figure 9. Mualem, van Genuchten, and Fredlund & Xing Equations fitted to experimental data—Claystone of Pierre Shale formation.
Volumetric Water Content (%)
60 50
Measured Data
40 30 = -2.5853Ln( ) + 46.686 r2 = 0.982
20 10
= -6.2348Ln( ) + 80.671 r2 = 0.9865
?
0 1
10
100 1000 10000 Soil Suction (kPa)
100000 1000000
Figure 10. Bilinear equation fitted to experimental data— Claystone of Denver formation.
3.2
Curve fitting with bilinear equation
Chao, et al. (1998) indicated that a bilinear form gives a good agreement to the observed experimental data for expansive soils. The bilinear relationship of the SWRC for expansive soils has also been reported by others (McKeen and Neilsen, 1978; Marinho, 1994;
DISCUSSION AND CONCLUSIONS
Fredlund (2002) stated that matric suction dominates the lower suction portion of a SWRC, while osmotic suction dominates the high suction portion of the SWRC. Capillary effects dominate when there is a significant amount of liquid water in the soil, whereas the osmotic suction related to the adsorbed salts dominates the behavior of the soil at a high suction range. It was shown by van der Raadt, et al. (1987) that filter paper results used both in contact and noncontact modes were similar for values of suction above 1,000 kPa, but were different for values of suction less than 1,000 kPa. Leong et al. (2002) suggested that for ‘‘up to 1000 kPa suction, the contact filter paper method can be used to measure matric suction reliably, while the noncontact method can be used to measure total suction. Beyond 1,000 kPa suction, the filter paper method measures only total suction, regardless if the contact or the noncontact procedure is used.’’ Figures 3 and 4 indicates that this limit is much higher (closer to 10,000 kPa). The soil suction at zero water content is used as a boundary point in heave prediction using the soil suction method proposed by McKeen (1992). The soil suction at zero water content was stated by McKeen (1992) to be near 174,385 kPa (6.25 pF). Fredlund and Xing (1994) introduced a correction function, C(ψ),
247
in their SWRC fitting equation to force the SWRC to pass through a soil suction of 106 kPa (7.0 pF) at zero water content. The measured average total suction of the five oven-dried claystone samples shown in Figure 5 is approximately 245,000 kPa (6.40 pF) at oven-dry water content. This value of measured soil suction at oven-dry water content is closer to that expressed by McKeen (1992). The bilinear form used in this study is representative of the observed experimental data for expansive soils. At stress above 100 MPa, the curve tends to increase in slope to a limiting suction value of about 245,000 kPa (6.40 pF). Cumbers (2007) measured points that fell on a straight line between suction values of about 100,000 kPa and 245,000 kPa. Thus, the curves are in fact tri-linear, but for suction values below 100,000 kPa they will be referred to as being bi-linear. The change in slope of the SWRC for expansive soil has been attributed to the transition from macropore spaces, where water retention is governed by capillary mechanisms, to micropore spaces, where water retention is governed by thermodynamic forces (Miller, 1996). REFERENCES Al-Mukhtar, M. (1995). ‘‘Macroscopic Behavior and Microstructural Properties of a Kaolinite Clay Under Controlled Mechanical and Hydraulic State.’’ Proceedings, 1st International Conference Unsaturated Soils, Paris, I, 3–9. Alonso, E.E., Lloret, A., Gens, A., and Yang, D.Q. (1995). ‘‘Experimental Behavior of Highly Expansive Double-Structure Clay.’’ Proceedings, 1st International Conference Unsaturated Soils, Paris, I, 11–16. Brooks, R.H., and Corey, A.T. (1964). ‘‘Hydraulic Properties of Porous Media.’’ Hydrology Paper No. 3, Colorado State University, Fort Collins, Colorado. Burdine, N.T. (1953). ‘‘Relative Permeability Calculations from Pore Size Distribution Data.’’ Journal of Petroleum Technology, 5, 71–78. Chao, K.C. (1995). ‘‘Hydraulic Properties and Heave Prediction for Expansive Soil.’’ Maters Thesis, Colorado State University, Fort Collins, Colorado. Chao, K.C., Durkee, D.B., Miller, D.J., and Nelson, J.D. (1998). ‘‘Soil Water Characteristic Curve for Expansive Soil.’’ Thirteenth Southeast Asian Geotechnical Conference, Taipei, Taiwan. Chao, K.C. (2007). ‘‘Design Principles for Foundations on Expansive Soils.’’ Dissertation submitted in partial requirement for the Ph.D. Degree, Colorado State University, Fort Collins, Colorado. Cumbers, J.M. (2007). ‘‘Soil Suction for Clay Soils at Oven-Dry Water Contents and the End of Swelling Conditions.’’ Thesis submitted in partial requirement for the Mater Degree, Colorado State University, Fort Collins, Colorado. Fredlund, D.G. (2002). ‘‘Use of Soil-Water Characteristic Curves in the Implementation of Unsaturated Soil Mechanics.’’ Third International Conference on Unsaturated Soils. Recife, Brazil.
Fredlund, D.G. and Rahardjo, H. (1993). ‘‘Soil Mechanics for Unsaturated Soil.’’ John Wiley & Son, Inc., New York, NY. Fredlund, D.G. and Xing, A. (1994). ‘‘Equation for the Soil-Water Characteristic Curve.’’ Canadian Geotechnical Journal, 31(3), 521–532. Gardner, W.R. (1958). ‘‘Some Steady State Solutions of the Unsaturated Moisture Flow Equation with Application of Evaporation from a Water Table.’’ Soil Science, 85(4), 228–232. Geotechnical Consulting and Testing Systems, Inc. (GCTS). (2004). ‘‘Fredlund SWCC Device Operating Instructions.’’ Tempe, Arizona. Jefferson County GIS Department. (1997). ‘‘Designated Dipping Bedrock Area. 1: 62,500 scale.’’ Jefferson County, Colorado. Leong, E.C. and Rahardjo, H. (1997). ‘‘Review of Soil-Water Characteristic Curve Equations.’’ Journal of Geotechnical and Geoenvironmental Engineering, 123(12), 1106–1117. Leong, E.C., He, L., and Rahardjo, H. (2002). ‘‘Factors Affecting the Filter Paper Method for Total and Matric Suction Measurements.’’ Geotechnical Testing Journal, 25(3), 322–333. Marinho, F.A.M. (1994). ‘‘Shrinkage Behavior of Some Plastic Soils.’’ Ph.D. Dissertation, University of London, Imperial College of Science, Technology and Medicine. McKeen, R.G. (1992). ‘‘A Model for Predicting Expansive Soil Behavior.’’ Proceedings of 7th International Conference on Expansive Soils, Dallas, Texas. 1, 1–6. McKeen, R.G. and Nielson, J.P. (1978). ‘‘Characterization of Expansive Soils for Airport Pavement Design.’’ U.S. Dept. of Transportation, Federal Aviation Administration, Report No. FAA-120-78-59. Miller, D.J. (1996). ‘‘Osmotic Suction as a Valid Stress State Variable in Unsaturated Soils.’’ Ph.D. Dissertation, Colorado State University, Fort Collins, Colorado. Mualem, Y. (1976). ‘‘A New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous Medial.’’ Water Resources Research, 12, 513–522. Mulilis, J.P., Chan, C.K., and Seed, H.B. (1975). ‘‘The Effects of Method of Sample Preparation on the Cyclic Stress Strain Behavior of Sands.’’ EERC Report, 75–78. Noorany, I. (2005). E-Mail Letter to Kuo-Chieh Chao Regarding ‘‘Moist Tamping Equipment.’’ January 10th. SoilVision Systems Ltd. (2006). ‘‘SoilVision Software, Version 4.0.’’ Saskatoon, Saskatchewan, Canada. Tinjum, J.M., Benson, C.H. and Blotz, L.R. (1997). Soil-Water Characteristic Curves for Compacted Clays. Journal of Geotechnical and Geoenvironmental Engineering. November. 1060. van der Raadt, P., Fredlund, D.G., Clifton, A.W., Klassen, M.J., and Jubien (1987). ‘‘Soil Suction Measurement at Several Sites in Western Canada.’’ Transportation Res. Rec. 1137, Soil Mechanics Considerations in Arid and Semi-Arid Areas, Transportation Research Board, Washington, D.C., 24–35. van Genuchten, M.T. (1980). ‘‘A Closed-Form Equation for Prediction the Hydraulic Conductivity of Unsaturated Soils.’’ Soil Sci. Soc. Am. J. 44, 892–898. Wan, A.W.L., Gray, M.N. and Graham, J. (1995). ‘‘On the Relations of Suction Moisture Content and Soil Structure in Compacted Clays.’’ Proc. 1st Intern. Conf. Unsaturated Soils, Paris, I, 215–222.
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Hydromechanical couplings in confined MX80 bentonite during hydration D. Marcial Instituto de Materiales y Modelos Estructurales, Universidad Central de Venezuela, Caracas, Venezuela
P. Delage & Y.J. Cui CERMES, Ecole Nationale des Ponts et Chaussées, Paris, France
ABSTRACT: In order to characterize the hydromechanical (HM) properties of a MX80 bentonite, used as an Engineered Barrier (EB) material for nuclear waste disposal facilities, a 7 months infiltration column test with coupled measurement of swelling pressure and suction was carried out. The hydraulic conductivity was obtained using the Instantaneous Suction Profile (ISP) method (Daniel 1983) in an initial highly compacted unsaturated state (γd = 1.7 Mg/m3 ; w = 8.2 %), and the swelling pressure was monitored at different heights of the column. Also, some mercury intrusion porosimetry measurements were conducted at the end of the test to better understand the observed coupled behaviour. Important effects of suction gradients were observed; the transitory hydraulic conductivity values are higher when the bentonite is hydrated from very high suctions because of gradient effects. Then it drastically reduces as the hydration front advances and the microstructure is reorganized. Concerning the couplings of suction and swelling pressure, a softening threshold suction value was systematically observed at a value of 90 MPa. Also, low changes of stresses with suction δσ/δs were observed for a high range of suction values. These experimental evidences permit to better understand hydromechanical couplings during hydration of engineered barrier materials in confined conditions.
1
INTRODUCTION
Figure 1 presents a schema of an engineered barrier (EB) section of a disposal pit according to the concept of deep nuclear waste disposal. One can appreciate the EB surrounding the waste container (C) and filling up the void zone between the pit walls crossed in the host rock (HR) and the container. The EB is composed of specially shaped compacted bentonite bricks arranged in such a way that void zones (joints) are minimized. The joints are present in the EB-EB, EB-C and EB-RH contact surfaces and their presence within the barrier highlight the importance of the swelling potential of the EB material. The self sealing capacity of bentonites is particularly important to ensure an adequate isolation of the waste (Pusch 1982). Marcial et al. (2006) have shown with a reduced model test, that in bentonite based EB, such joint system could heal very soon with hydration if the joint sizes are small enough, even for a relatively low EB dry density. However, higher periods of time could be necessary as the joint size increases. Extensive experimental hydromechanical studies were done by the Soil and Rock Mechanics Research Centre, at the Navier Institute in France, on FoCa7 clay and a Kunigel VI bentonite—sand mixture in the recent past (See Yahia-Aissa 1999 and Loiseau 2001).
Figure 1. Cross section of a disposal pit with schematic representation of joints and an EB radial element.
Furthermore, advances in the characterization of compacted unsaturated MX80 bentonite has been achieved by incorporating the measurement of lateral stresses. This work concerns the suction—swelling pressure coupling observed in a 7 months infiltration column
249
test with measurement of swelling pressure and suction. The experimental set-up correspond to a reduced model that take into account the HM behaviour of an EB radial element, perpendicular to the disposal pit axis (axis symmetrical problem). Figure 1 also shows a radial EB element where the stress state, defined by σθ and σr , is dependent of the suction changes within the EB due to hydration. Since the test was conducted in isothermal conditions (T = 20◦ C) and temperature changes are present in a nuclear waste repository, it is not representative of the initial saturation cycle. However, the results obtained in this work permit an initial approach to the understanding of HM couplings in EB materials. 2
MATERIAL AND EXPERIMENTAL SET-UP
2.1
Index properties and initial conditions
The chosen material was a commercial MX80 bentonite whose index properties are summarized in Table 1. Concerning the initial conditions, a dry density γd = 1.7 Mg/cm3 and a water content w = 8.2 % (corresponding to a suction of 103 MPa) were fixed. The γd value was chosen to be high enough to obtain high swelling pressures, and low enough to have double porosity microstructure (Delage et al. 1996) permitting to observe interesting and complex phenomena concerning micro—macro fabric coupling as it will be shown later. 2.2
Experimental set-up
The experimental set up was essentially composed of an infiltration column (see Figure 2) with a 50 mm internal diameter, and a 250 mm height. Five resistive sensors were used to monitor relative humidity (RH) changes with water uptake, permitting to adequately estimate the hydraulic conductivity by the ISP method. Four of these sensors were placed in the column cylinderv at a distance of 4.5, 9.5, 14.5 Table 1.
MX80 bentonite index properties.
Property
Value
Mineralogy
(1)
C.E.C (meq/100 g) Liquid limit, % Plastic limit, % ρs (Mg/m3 ) Skempton’s activity Specific surface, m2 /g (1)
82% montmorillonite (Na/Ca=5.5) 69.6 (1) 520 42 2.65(1) 5.8 800(2)
Sauzeat et al. (2000) (2) Pusch (1982).
Figure 2. Infiltration column: (1) holes for RH sensors location (2) split head piston (3) piston cap (4) 2 mm thick zones for lateral stress monitoring (5) column base (6) porous stone (7) water intake circuit.
and 19.5 cm from the infiltration point. A fifth sensor is placed inside the piston at the top of the column, located at a distance of 25 cm from the infiltration point. The lateral stress changes were monitored by incorporating reduced thickness zones, where deflections were measured with highly sensitive strain gages. To do so, the column cylinder was mechanized in such a way that five thin wall zones (2 mm thick) were incorporated at the heights of 2, 7, 12, 17 and 22 cm. These zones, which work as semi rigid membranes, have 5 mm in height and were designed to experience a deflection of 5 μm under a 60 MPa pressure. Elsewhere, a global measure of the axial stress was done with an external 50 kN load cell. The soil was statically compacted in a rigid mould with an internal diameter slightly lower than 50 mm to avoid any unknown initial soil stress state due to friction (see Marcial et al. 2006). Compaction was done step by step adding 25 mm thick layers, and the target density was obtained after soil rebound, with a 39 MPa compaction stress. Three cylindrical bricks were placed to fill the column, with a height of 125, 75 and 50 mm. Figure 3 shows the progressive placement of the bricks in the column. After the insertion of each brick, the RH sensors corresponding to the filled height were carefully placed. Once the column was filled, special care was taken to guarantee the system sealing, which is particularly important in the ISP method (see Figure 4).
250
At this point, the infiltration test was ready to run. The compacted soil was hydrated from the base of the column with a volume—pressure controller, which was set at a 10 kPa water pressure. The hydration time was extended to 208 days.
3
Figure 3. View of a 75 mm height compacted brick (a) and the progressive placement of bricks to fill the column (b, c and d).
RESULTS AND DISCUSSION
To determine the hydraulic conductivity with the ISP method, it is necessary to register the changes of relative humidity with time, and to know the water retention curve (WRC) at constant volume conditions. Because of space limitations, the procedure for the determination of the WRC is not presented. However, for the interest of the readers, the curve is presented in Figure 5. The changes in RH with time are presented in Figure 6 for all measurement sections. A global typical trend is observed; the increase of RH is higher as the section of measurement is closer to the water source. Notice that all curves are superposed at time zero and they progressively separate for increasing times. The acceleration in the RH increase corresponds to
Suction (MPa)
1000 100 10 1 0.1 0
Figure 4. View of the experimental set-up. (1) Sealing detail at the head piston cap (2) sealing details at RH sensor caps (3) final view of the experimental set-up with thermal isolation.
The head piston was left free of movement during 13 days, until the stabilization of the relative humidity was reached along the whole length of the column. A relative humidity value of 46.7% was registered at a controlled room temperature of 20◦ C, corresponding to the initial condition of the test before hydration starts (103 MPa suction). Once the suction stabilized, the column was placed in a 50 kN digitally controlled press, and the head piston was blocked against the reaction frame. A 50 kN load cell was placed between the head piston and the reaction frame to obtain a global measure of the axial stress (swelling pressure). In order to avoid the test to be affected by temperature changes, the unit press—column was isolated with 50 mm polystyrene walls, and a 5 mm glass screen was left at its front face.
10
20 30 Water content (%)
40
Figure 5. Water retention curve obtained at constant volume conditions with a dry density of 1.7 Mg/m3 .
Figure 6.
251
Changes of relative humidity with time.
the arrival of liquid phase water, as the hydration front advances with time. Before liquid water arrives, RH curves stay superimposed because hydration is only done by vapour phase through macroporosity. The monotone and regular increase of RH with time shows that the system was adequately sealed. The suction profiles are shown in Figure 7; they were obtained with the RH—t curves and the WRC. To do so, polynomial functions were fitted at different time periods with the RH—t curves and the condition of zero suction at the bottom of the column, corresponding to the infiltration point. In order to get fitting curves less perturbed by measures taken away from a particular section of the column, only 3 points were considered. Thus, the corresponding profiles are also reported in sections, as shown in Figure 7. This aspect is very important because is from the slope of the suction profiles that hydraulic gradients are obtained. The profiles shown in Figure 7 correspond, from top to bottom to t = (0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50,
55, 60, 65, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200 and 208) days respectively. For the 0–9.5 cm section, the profiles are presented only to 120 days because at this time the RH sensor corresponding to 4.5 cm height was damaged due to an excess of humidity. As shown in Figure 6, at this height the RH sensor reads a value of 97.4% at the time of 126 days. The derivate of fitted polynomial functions of suction profiles, at each measurement point, and for each time, gives the changes of hydraulic gradient i with time. Figure 8 shows that i values are very high (about 116000 in the extreme case), specially when the distance to the hydration source is small. It is evident that i values do not correspond to the hydration pressure of 10 kPa. They are due to the strong hydrophilic character of the bentonite brick, initially equilibrated to a very high suction (103 MPa). Changes on i values are strongly influenced by the distance h and suction s. On the one hand, the higher is h, the lower is i. On the other hand, the increase rate of i slows down, and is even reversed as suction decrease. Both effects concern the hydrophilic character of the bentonite brick. As closer the considered section is to the hydration point, and higher is the thickness of non hydrated soil, higher is the hydraulic gradient. In addition, as suction reduces, the hydrophilic character of the soil reduces also, slowing down the increase of the gradient. The combination of both factors gives rise to the shape of the i − t curves shown in Figure 8. In the case of h = 4.5 cm, the thickness of the soil that participate in the adsorption process is important and the gradient is high. Otherwise, because the section is very close to the hydration point, the suction and the gradient reduce drastically (Figure 7) when hydration front approaches. These effects being less important when h is higher the changes observed in the gradient occur in a more progressive manner.
Figure 7. length.
Figure 8. hole test.
Suction profiles at different times for the whole
252
Changes of hydraulic gradient with time for
The hydraulic conductivity kw is obtained with the generalized Darcy’s law: kw = −
q 1 · A 1/2 · (it + it+dt )
(1)
where A is the infiltration section, i is the hydraulic gradient, t is the time and q is the flow rate, through the section A, established in the time interval dt . The q value in an unsaturated soil is obtained with the following expression: H q=A·
hi
θt+dt dh − dt
H hi
θt dh
(2)
The volumetric water content is obtained with the expression: θ=
w · ρd ρw
Figure 9. times.
Volumetric water content profiles at different
(3)
The volumetric water content profiles (Figure 9) were obtained for the same times of suction profiles. Notice that after 208 days, only the first 61 mm were saturated. Also, the degree of saturation reduces drastically as the distance to the saturation front increases to further stabilize at low values. This permits to better understand the gradient changes presented in Figure 8. For h = 4.5 cm, the lowest i values are obtained when hydration front approach this section. However, the gradient keeps high for h = 9.5 and 14.5 cm because in these sections suction changes are still important. For h = 19.5 cm hydration front is far enough, suction changes are less important and gradient changes are more progressive. With the volumetric water content profiles and Equation 1, the hydraulic conductivity at h = 4.5, 9.5, 14.5 and 19.5 cm was obtained. Figure 10 shows the changes of hydraulic conductivity with suction for different h values. First of all, notice that the highest kw values are obtained for the highest suctions. Then, kw values reduce drastically to stabilize later and even increase at lower suction values. These observations confirm the global trends obtained by Loiseau et al. (2002), with a Kunigel VI—sand mixture. Concerning global kw − h changes, a progressive reduction of kw values is observed as h increases. This trend is due to the effect of hydraulic gradient. For low h values, the thickness of unsaturated material is higher. Remember that it is not the 10 kPa hydration pressure of water source that impose hydraulic gradient, but the hydrophilic character of the unsaturated compacted bentonite brick. Thus, the influence of hydraulic gradient reduces as the h value increases, as shown by Loiseau et al. (2002). Also, notice the
Figure 10. Changes of hydraulic conductivity with suction at different sections.
increase of kw as suction decrease, at the lower suction range, like currently observed in unsaturated soils. Figure 11 presents the pore size distribution observed at the end of the test at different h values. This is a typical trend observed when bentonite based materials are hydrated at constant volume conditions. When hydration is important (lower h values), microstructure hydrate and accessible porosity reduces. Because of the constant volume condition, microstructure swelling reduces macroporosity. Notice a well defined inter—aggregate pore group for h = 25 cm at r = 3 μm that gradually disappears at more hydrated sections (h = 4.5 and 9.5 cm). These microstructure observations confirm the hypothesis that RH curves shown in Figure 6 stay superimposed while hydration occurs by vapour phase through macroporosity. Concerning the coupling of suction and swelling pressure, a typical trend with two maxima was
253
Figure 11. Pore size distribution at different sections of the column at the end of the test.
Figure 13. Changes of vertical stress with suction for different sections of the sample.
is observed until saturation approaches and the δσ/δs rate progressively increases to a value of about 0.1.
4
Figure 12. Changes of lateral stress and suction with time for different sections of the sample.
observed for lateral stress measurement at h = 2, 7, 12 and 17 cm. Particular attention was taken to the first maxima, corresponding to a softening point of clay aggregates due to hydration (Pusch 1981). Figure 12 presents the first maxima observed at different h values. Notice that all maxima occur systematically at a suction value of about 90 MPa. The repeated apparition of these maxima is important to confirm the existence of a softening threshold value. Figure 13 shows vertical stress changes with suction at sections located close to hydration point (h = 2, 3 and 4.5 cm). Notice that stress changes with suction δσ/δs are very high when hydration starts, but rapidly slow down as suction decrease. See that the maximum curvature occurs close to a suction value of approximately 90 MPa when the softening threshold is approached. Then, a low and quasi regular δσ/δs rate
CONCLUSIONS
The infiltration test permitted to confirm the results obtained by Loiseau et al. (2002), concerning the effects of suction gradients on hydraulic conductivity, but with a different EB material. The hydraulic conductivity is higher as the EB material is submitted to higher suction gradients. Then, hydraulic conductivity reduces drastically as the hydration front advances and microstructure is reorganized. When suction decreases enough, the hydraulic conductivity increases as typically observed in unsaturated soils. Obtained results suggest that, during the hydration phase, water transfers in the EB should be partially governed by the strong hydrophilic character of unsaturated zones, where suction values keep being high enough. Concerning the suction—swelling pressure coupling, a softening threshold was systematically observed at a suction of 90 MPa. This threshold value must be associated to the particular initial conditions of the studied material (γd = 1.7 Mg/cm3 and s = 103 MPa). The observed results show that above the threshold value the δσ/δs rate is very high, decreasing to a very low and quasi regular value when suction reduces below this point. When suction is low enough and saturation approaches, the δσ/δs rate progressively increases to a value of about 0.1. The study of some HM properties and microstructure of a compacted MX80 bentonite, in confined condition, permits to state a complex and highly coupled HM behaviour of EB materials. The results presented
254
herein give some elements to improve constitutive models that consider these aspects. REFERENCES Daniel. D.E. (1983). Permeability test for unsaturated soil. Geotechnical Testing Journal. 2, 81–86. Delage et al. (1996). Microstructure of compacted silt. Canadian Geotechnical J. 33, 150–158. Loiseau C. (2001). Transferts d’eau et couplages HM dans les barrières ouvragées. PhD. Thesis, ENPC, Paris, France. Loiseau et al. (2002). The gradient effect on the flux through a compacted swelling soil. 3rd Int. Conf. on Unsaturated Soils, Brazil. 1, 395–400. Marcial et al. (2006). Application of vertical strain control to measure swelling pressure of clayey soils. 4th Int. Conf. on Unsaturated Soils. Arizona, EE. UU.
Marcial et al. (2006). A laboratory study of the self sealing behaviour of a compacted sand-bentonite mixture. Geomechanics and Geoengineering An International Journal. 1, 73–85. Pusch R. (1981). Unsaturated and saturated flow in swelling clay. 10th IFSMFE, Session 6/14, Stockholm. pp. 369–373. Pusch R., (1982). Mineral-water interactions and their influence on the physical behavior of highly compacted Na bentonite. Canadian Geotechnical Journal. 19, 381–387. Sauzeat et al. (2000). Caractérisation minéralogique, cristallochimique et texturale de l’argile MX-80. LEM-CREGU. ANDRA Technical Report. France. Yahia-Aissa, M. (1999). Comportement HM d’une argile gonflante fortement compactée. PhD Thesis, ENPC, Paris, France.
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Effect of temperature on the water retention capacity of FEBEX and MX-80 bentonites M.V. Villar & R. Gómez-Espina CIEMAT, Madrid, Spain
ABSTRACT: The retention curves of the FEBEX and MX-80 bentonites compacted at dry densities from 1.3 to 1.8 g/cm3 have been determined using methods that allow the volume of the samples to remain constant during the determination. The methods have been upgraded to use them at high temperatures, and thus the range of temperatures between 20 and 120◦ C has been explored. For a given density and water content, suction decreases as temperature increases at a rate that is larger than that predicted on the basis of the water surface tension change with temperature. Hysteresis on heating/cooling cycles has been observed, especially in the MX-80 bentonite. For suctions higher than 10 MPa and for a given temperature and water content, the suction measured is slightly higher for higher dry density of the bentonite. However, for lower suctions this trend clearly inverts. The water retention capacity is lower for the MX-80 bentonite, although the difference is lessened for low suctions. The retention capacity of the FEBEX bentonite is more affected by temperature than that of the MX-80.
1
countries as reference materials for the sealing of HLW repositories.
INTRODUCTION
This research has been carried out in the context of projects concerning the engineered clay barrier of underground repositories for high-level radioactive waste (HLW). The barrier, made of compacted bentonite (a highly swelling material), will be placed between the waste canisters and the host rock, and will get saturated by the groundwater while it is subjected to high temperatures due to the radioactive decay of the wastes. These temperature changes affect the hydraulic and mechanical response of the bentonite, which has important implications on the design and performance of the repository. Particularly, the changes in the water retention capacity of the bentonite affect the hydration kinetics of the barrier and the time needed for its full saturation. The water retention capacity of a material is usually evaluated by determining its water retention curve, which relates suction and water content for a given temperature along a suction span as broad as possible. Previous investigations have shown that the retention curve, for the same initial conditions of the material, differs significantly depending on the volume restriction imposed to the sample during the determination (Yahia-Aissa, 1999; Villar, 2002). Thus the effect of temperature on the water retention curve of two natural compacted bentonites, the FEBEX and the MX-80, has been analysed by means of laboratory tests in which the volume of the samples has been kept constant. Both bentonites have been selected by different
2
MATERIAL
Two bentonites have been used in this investigation: the Spanish FEBEX bentonite and the American MX-80 bentonite. The FEBEX bentonite comes from the Cortijo de Archidona deposit (Almería, Spain) and its characterisation can be found in ENRESA (2006), Villar (2002) and Lloret et al. (2004). The smectite content of the FEBEX bentonite is higher than 90 percent (92 ± 3%) and it contains variable quantities of quartz (2 ± 1%), plagioclase (2 ± 1%), K-felspar, calcite and opal-CT. The CEC varies from 96 to 102 meq/100 g, and the major exchangeable cations are Ca (35–42 meq/100 g), Mg (31–32 meq/100 g), Na (24–27 meq/100 g) and K (2–3 meq/100 g). The liquid limit of the bentonite is 102 ± 4 percent, the plastic limit is 53 ± 3 percent, the total specific surface area is 725 ± 47 m2 /g and the specific gravity 2.70 ± 0.04. The hygroscopic water content in equilibrium with the laboratory atmosphere is 13.7 ± 1.3 percent. The MX-80 bentonite is extracted from Wyoming (USA). It is a worldwide known material supplied in the form of powder homoionised to sodium. The MX-80 bentonite consists mainly of montmorillonite (65–82%). It also contains quartz (4–12%), feldspars (5–8%), and smaller quantities of cristobalite, calcite
257
and pyrite. The CEC is 74 meq/100 g, and the major exchangeable cations are Na (61 meq/100 g), Ca (10 meq/100 g) and Mg (3 meq/100 g). The liquid limit of the bentonite as determined in CIEMAT laboratories is 526 percent, the plastic limit is 46 percent, the total specific surface area is about 512 m2 /g and the specific gravity is 2.82. The hygroscopic water content at laboratory conditions is 8–11 percent. The saturated permeability to deionised water of samples of these bentonites compacted at different dry densities is exponentially related to the dry density. The values of permeability to deionised water for dry densities of 1.6 g/cm3 are in the order of 10−14 m/s for the FEBEX bentonite and of 10−13 m/s for the MX-80 bentonite. The swelling pressure of bentonite samples compacted at their hygroscopic water content and flooded with deionised water up to saturation at room temperature can be related exponentially to dry density. For dry density 1.6 g/cm3 the swelling pressure of the FEBEX bentonite is about 6 MPa and of the MX-80 bentonite is about 8 MPa. 3
METHODS
To determine the water retention curve of the compacted bentonite at constant volume, two methodologies, the theoretical principle of which is different, have been followed. The cell method is carried out in special cells designed to avoid the swelling of the clay in wetting paths (Villar, 2002; Villar and Lloret, 2004). The cells consist of a corrosion-resistant stainless steel cylindrical body with two perforated covers joined by bolts. Granulated clay is compacted directly inside the cell ring at room temperature using static uniaxial compaction. The length of the specimen is 1.20 cm and its cross section, 11.34 cm2 . The cells are placed in desiccators with a sulphuric acid solution or with a NaCl solution. There are temperature-dependent experimental relations between the concentration of the solution and its water activity (aw ). The calculation of suction on the basis of relative humidity (RH = aw /100) is accomplished through Kelvin’s equation. In the cell method the suction is, therefore, imposed through the control of relative humidity. The perforated covers allow the exchange of water in the vapour phase between the clay and the atmosphere of the desiccators. Once the water content of the clay is stable (approximately 2 to 3 months, what is checked by periodic weighing), the solution in the desiccators is changed in order to apply a different suction. To determine the curve at different temperatures, the desiccators are placed inside ovens. At the end of the tests the final water content of the specimens is measured by oven drying.
The sensor/cell method consists on the compaction of a bentonite block with the clay previously mixed with the desired quantity of deionised water and the measurement of its relative humidity by means of a capacitive sensor while the bentonite is kept inside a hermetic cell made of stainless steel (Villar et al., 2005; 2006). To convert the values of RH to suction values, Kelvin’s law is used. The clay was used either with its hygroscopic water content, mixed with deionised water, or slightly dried at temperatures below 50◦ C, so as to obtain water contents between 4 and 22 percent. The block is introduced in the cell, the dimensions of the block being equal to the internal volume of the cell, 7 cm diameter and 10 cm height. A hole is drilled in the central upper part of the block to insert the sensor and the cell is closed. The external wall of the cell is covered with a silicone-rubber laminated heater that fixes the temperature all over the cell. After measuring the suction corresponding to the laboratory temperature, the temperature of the external heating mat was increased up to 120◦ C in intervals of 20◦ C. Each target temperature was kept for about two days, although the RH equilibrium is reached very quickly (in a few hours). Afterwards, the temperature was decreased according to the same pattern. This allows, in a single test, the determination of the change of suction with temperature for a given density and water content. At the end of the test, the block is extracted and its water content and dry density are measured. The drawback of the cell method is the duration of the tests, because the time to reach equilibrium for each suction is very long, this is why the sensor/cell method was fine-tuned. The results obtained with both methods are largely consistent, although the sensor/cell method is unsuitable for the very low and very high suctions (Villar & Gómez-Espina, 2007).
4
RESULTS
4.1 FEBEX bentonite The effect of dry density on the water retention capacity of the FEBEX bentonite has been checked using the cell method. It has been observed that there is a suction threshold value above which, for a given water content, the suction of the higher density samples is higher, and below which the trend inverts. For 20◦ C this threshold value is about 12 MPa (Figure 1). Tests with different densities have been also performed at different temperatures using both methods. Some of the results obtained are plotted in Figure 2. For the range of suctions considered, the retention capacity of the sample of dry density 1.7 g/cm3 is higher than of 1.5 g/cm3 . Also, the samples tested at 80◦ C have lower retention capacity than those tested at 20◦ C
258
140
1.4
1.6
1.7 Suction (MPa)
Suction (MPa)
Dry density (g/cm )
100 80 60 40
140 120 100 80 60 40 20 0
20
20
0 10
15 20 25 Water content (%)
30
100
1.5, 26 1.5, 80 1.7, 20 1.7, 80
1
15 20 25 Water content (%)
80
100
120
140
Figure 3. Evolution of suction with temperature (heatingcooling paths) for FEBEX samples compacted with different water content at dry density 1.6 g/cm3 (open symbols) and 1.5 g/cm3 (filled symbols).
4.2 MX-80 bentonite
0.1 10
60
the range of suctions considered, which could be a consequence of the closeness of the densities tested (1.5 and 1.6 g/cm3 ) and points also to the higher influence of temperature over density on the retention capacity. Anyway, the smaller slope of the curves for the dry density 1.5 g/cm3 would indicate a smaller effect of temperature on the retention capacity for the low density samples.
1000
10
40
Temperature (˚C)
35
Figure 1. Retention curves of FEBEX bentonite compacted at different dry densities obtained at 20◦ C following wetting paths with the cell method.
Suction (MPa)
11% 14% 16% 18% 19% 20% 21%
180 160
3
120
30
Figure 2. Retention curves obtained for the FEBEX bentonite compacted to different dry densities (indicated in g/cm3 ) and temperatures (indicated in ◦ C).
(Lloret et al. 2004, Lloret & Villar 2007). The effect of temperature on the retention capacity is greater for the higher dry density. Figure 3 shows the evolution of suction with temperature in samples compacted to different dry densities with various water contents tested with the sensor/cell method. The decrease of suction with temperature is significant, especially for temperatures above 60◦ C. There is also a small hysteresis between the initial heating and the subsequent cooling, the suctions measured during cooling being slightly higher. On the other hand, the influence of dry density is not very clear in
The influence of dry density on the retention capacity of the MX-80 is highlighted when the cell method is used. Figure 4 shows the results obtained at 60◦ C for a broad range of dry densities (Villar 2005). For suctions above approximately 20 MPa the behaviour of the different densities is similar, but below this value, the higher the dry density the lower the suction for a given water content. Although, for the sake of clarity, the drying paths are not included in the figure, it was observed that the hysteresis in wetting/drying paths is not very important. The dry densities 1.5, 1.6 and 1.75 g/cm3 have been tested with the sensor/cell method. The hysteresis on heating/cooling was found to be more important than for the FEBEX bentonite (Villar & Gómez-Espina, 2007). Some of the results obtained are plotted as retention curves in Figure 5, where the decrease of the retention capacity with temperature is noticeable, as well as the effect of dry density: since the suctions tested with the sensor/cell method are above the threshold mentioned before, the retention capacity is higher for the samples of higher dry density.
259
1000
Suction (MPa)
100
1.30
1.37
1.60
1.79
10
1
0.1 0
10
20
30
40
Water content (%) Figure 4. Retention curves of MX-80 bentonite compacted to different dry densities (indicated in g/cm3 ) obtained with the cell method in wetting paths at 60◦ C (Villar 2005).
Suction (MPa)
1000
100
1.75, 39 1.75, 99 1.50, 40 1.50, 100
10
basis of the change of surface tension of water with temperature. For the MX-80 bentonite it has been checked that the actual suction change measured is higher than the change computed by introducing in the Laplace equation the temperature dependence of the surface tension of water (Jacinto et al., in press a). The same has been checked for the FEBEX bentonite, as shown in Figure 6, in which the measured and computed evolution of suction with temperature have been plotted. This discrepancy (which is more significant for temperatures above 60◦ C) is probably due to the fact that capillarity is not the main mechanism of water retention in bentonite. Instead, physico-chemical interactions between the clay particles and the water tightly attached to them are responsible of the soil retention capacity, especially in the high suction range. In this low water content region, changes in the interaction mechanisms between the clay and water are considered the main temperature effects on water retention capacity (Romero et al., 2001; Villar & Lloret, 2004; Villar et al., 2005). Ma & Hueckel (1992, 1993) state that an increase in temperature produces a transfer of water from the interlayer region to the pores between the clay aggregates (macropores). Since the density of the interlayer, tightly-bound water in smectites is higher than one (Villar, 2002; Marcial, 2003; Jacinto et al., in press b), the volume occupied by the interlayer water transferred to the macropores will be higher and the degree of saturation of the sample will increase (provoking a suction decrease) when the temperature is increased (Villar & Lloret, 2004).
1
180
3
8 13 18 Water content (%)
23
160
14%
17%
21%
140
-0.33 -0.26
120 Suction (MPa)
Figure 5. Retention curves obtained with the sensor/cell method for the MX-80 bentonite compacted to different dry densities (in g/cm3 ) and temperatures (in ◦ C).
5
11%
-0.53 100 80
-0.16
-0.40
40
DISCUSSION
-0.57
60 -0.05
20
Although it is generally acknowledged that suction in clayey soils is not exclusively a capillary process, the Laplace equation, which relates the capillary pressure and the pore size distribution, is a first approximation to explain the water retention processes in soils. Thus, for the prediction of the effect of temperature on the retention capacity, the change of surface tension of water with temperature is usually included in this equation. However, the observed evolution of suction with temperature cannot be explained on the
-0.27
0 20
40
60
80
100
120
140
Temperature (ºC)
Figure 6. Change of suction with temperature for FEBEX bentonite compacted with different water contents to dry density 1.6 g/cm3 as measured with the sensor/cell method (continuous lines) and as computed by the change in water surface tension (dashed lines). The slope of the lines is indicated.
260
1.5 1.6 1.75
1.0 0.8
MX, 26˚C MX, 80˚C FBX, 27˚C FBX, 81˚C
160 Suction (MPa)
Relative suction change
200
1.2
0.6 0.4 0.2
120 80 40
0.0 3
8
13
18
23
0
Water content (%)
3
Figure 7. Relative suction change when temperature increases from 26 to 100◦ C in the FEBEX (filled symbols) and MX-80 (open symbols) bentonites compacted to different dry densities (indicated in g/cm3 ) and tested with the sensor/cell method.
8
13
18
23
Water content (%) Figure 8. Retention curves obtained with the sensor/cell method for the FEBEX (FBX) and MX-80 (MX) bentonites compacted at dry density 1.5 g/cm3 .
180 -0.53
160
FBX, 11%
140
Suction (MPa)
Figure 7 represents the relative change of suction experienced by samples of different dry density and water content tested with the sensor/cell method when the temperature was increased from 26 to 100◦ C. The suction decrease with temperature tends to be higher for the higher dry densities, both for the FEBEX and the MX-80 bentonites. It is known that the proportion of water in the interlayer of the smectite increases with the density of the bentonite (Pusch et al. 1990). This would explain the larger effect of temperature on high density samples. On the other hand, the retention capacity of the FEBEX bentonite is higher than that of the MX-80, as it can be observed in Figure 8 for the dry density of 1.5 g/cm3 . Numerous authors have pointed out that the retention capacity of predominantly divalent (Ca and Mg) smectites is higher than that of sodic ones, except for the lowest suctions (Hall & Astill, 1989; Saiyouri et al., 2004). This figure also shows how the difference between the two bentonites attenuates towards the low suctions, and this has been checked for several temperatures (Villar & Gómez-Espina, 2007; Villar, 2007). Also, Figure 9 shows that the effect of temperature on suction is higher for the FEBEX bentonite than for the MX-80 (note the higher slope of the lines that relate suction with temperature for the FEBEX bentonite). This would be a consequence of the predominance of interlaminar porosity (in which high-density water is placed) in the Ca-Mg bentonite, whereas in the Na bentonite the porosity among primary particles (in which ‘‘free’’ water is placed) prevails, since these particles are formed by fewer laminae (Pusch et al., 1990).
FBX, 14%
120
-0.32
100
FBX, 21%
-0.57
MX, 6%
80
MX, 11%
-0.37
60
-0.28
MX, 15%
40 -0.27
20
MX, 21%
-0.03
0 20
40
60 80 100 Temperature (˚C)
120
140
Figure 9. Evolution of suction during heating for FEBEX (FBX) and MX-80 (MX) bentonites compacted at dry density 1.6 g/cm3 and tested with the sensor/cell method. The slope of the lines is indicated.
6
SUMMARY AND CONCLUSIONS
The retention curves of two natural compacted bentonites have been determined trying to reproduce as well as possible the conditions of the engineered barrier of a HLW repository, for which reason the bentonites were used in their natural state (without previous drying or grinding), kept at constant volume during the determination and submitted to high temperatures. Results for dry densities from 1.3 to 1.8 g/cm3 and temperatures from 20 to 120◦ C have been reported. The suctions involved ranged from 0 to 200 MPa.
261
The effect of density on the retention capacity varies according to the suction range. For suctions below a threshold value (which is about 12–20 MPa) for a given water content and temperature the suction of the higher density samples is lower, and above this suction value the trend inverts. Anyway, the effect of dry density on the water retention capacity seems lower than that of temperature. The water retention capacity of the bentonite decreases clearly with temperature, especially when it is above 60◦ C and when the density of the bentonite is high. This decrease cannot be explained on the basis of the changes of water surface tension with temperature. Instead, mechanisms related to the physico-chemical interactions that take place at microscopic level (in particular the transfer of interlayer water to the macropores triggered by temperature) seem to explain qualitatively the experimental observations. There are also differences in the behaviour of the two materials tested. The FEBEX bentonite, which has mainly bivalent cations in the exchange complex, has a higher retention capacity than the MX-80 bentonite, which is predominantly sodic. Also, the effect of temperature on the water retention capacity is more noticeable for the FEBEX bentonite.
ACKNOWLEDGEMENTS Part of the work on the FEBEX bentonite has been co-funded by ENRESA (Spanish National Agency for Waste Management) and the European Commission (EC Contracts FI4 W-CT95-006 and FIKW-CT-200000016). The research agreements CIEMAT/ENRESA 00/271 and CIEMAT/CIMNE 04/113 have financed the research related to MX-80 bentonite. The laboratory work was performed by R. Campos and J. Aroz at CIEMAT (Madrid, Spain). The second author has a grant of the Spanish Ministry of Education.
REFERENCES ENRESA 2006. Full-scale Engineered Barriers Experiment. Updated Final Report 1994–2004. Publicación Técnica ENRESA 05-0/2006. 590 pp. Madrid. Hall, P.L. & Astill, D.M. 1989. Adsorption of water by homionic exchange forms of Wyoming montmorillonite (SWy-1). Clays and Clay Minerals 37(4): 355–363. Jacinto, A., Villar, M.V., Gómez-Espina, R. & Ledesma, A. in press a. Influence of temperature and density on the retention curve of compacted bentonite: modifications to the van Genuchten expression. Applied Clay Science. Jacinto, A., Villar, M.V. & Ledesma, A. in press b. Influence of water density on the water retention curve of expansive clays. Géotechnique.
Lloret, A. & Villar, M.V. 2007. Advances on the knowledge of the thermo-hydro-mechanical behaviour of heavily compacted FEBEX bentonite. Physics and Chemistry of the Earth, Parts A/B/C 32 (8–14): 701–715. Lloret, A., Romero, E. & Villar, M.V. 2004. FEBEX II Project. Final report on thermo-hydro-mechanical laboratory tests. Publicación Técnica ENRESA 10/04. 180 pp. Madrid. Ma, C. & Hueckel, T. 1992. Stress and pore pressure in saturated clay subjected to heat from radioactive waste: a numerical simulation. Can. Geotech. J. 29: 1087–1094. Ma, C. & Hueckel, T. 1993. Thermomechanical effects on adsorbed water in clays around a heat source. Int. J. Numer. Anal. Methods Geomech. 17: 175–196. Marcial, D. 2003. Comportement hydromécanique et microstructural des matériaux de barrière ouvragée. Ph. D. thesis. École Nationale des Ponts et Chausées, Paris, 316 pp. Push, R., Karnland, O. & Hökmark, H. 1990. GGM—A general microstructural model for qualitative and quantitative studies of smectite clays. SKB Technical Report 90-43. Romero, E., Gens, A. & Lloret, A. 2001. Temperature effects on the hydraulic behaviour of an unsaturated clay. Geotech. Geolog. Eng. 19: 311–332. Saiyouri, N., Tessier, D. & Hicher, P.Y. 2004. Experimental study of swelling in unsaturated compacted clays. Clay Minerals 39: 469–479. Villar, M.V. 2002. Thermo-hydro-mechanical characterisation of a bentonite from Cabo de Gata. A study applied to the use of bentonite as sealing material in high level radioactive waste repositories. Publicación Técnica ENRESA 01/2002. 258 pp. Madrid. Villar, M.V. 2005. MX-80 bentonite. Thermo-hydromechanical characterisation performed at CIEMAT in the context of the Prototype Project. Informes Técnicos CIEMAT 1053. 39 pp. Madrid. Villar, M.V. 2007. Water retention of two natural compacted bentonites. Clays and Clay Minerals 55(3): 311–322. Villar, M.V. & Lloret, A. 2004. Influence of temperature on the hydro-mechanical behaviour of a compacted bentonite. Applied Clay Science 26: 337–350. Villar, M.V. & Gómez-Espina, R. 2007. Retention curves of two bentonites at high temperature. In Experimental Unsaturated Soil Mechanics. Springer Proceedings in Physics, vol. 112: 267–274. Berlin: Springer. Villar, M.V., Martín, P.L. & Lloret, A. 2005. Determination of water retention curves of two bentonites at high temperature. In Tarantino, A., Romero, E. & Cui, Y.J. (eds.), Advanced experimental unsaturated soil mechanics. EXPERUS 2005. pp 77–82. London: A.A. Balkema Publishers. Villar, M.V., Gómez-Espina, R. & Martín, P.L. 2006. Behaviour of MX-80 bentonite at unsaturated conditions and under thermo-hydraulic gradient. Work performed by CIEMAT in the context of the TBT project. Informes Técnicos CIEMAT 1081. 45 pp. Madrid. Yahia-Aissa, M. 1999. Comportement hydromécanique d’une argile gonflante fortement compactée. Ph.D. thesis, École Nationale des Ponts et Chaussées, CERMES, Paris.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Soil-water characteristic curves and void ratio changes relative to suction for soils from Greece M.E. Bardanis & M.J. Kavvadas National Technical University, Athens, Greece
ABSTRACT: The paper presents the drying portions of the soil-water characteristic curves of five soils from Greece, along with the void ratio vs suction curves over the same drying portion, the one-dimensional compression curves of the same soils and their comparison. The curves were measured using the pressure plate extractor technique. The soils tested included one silt, two clays and two marls. Soil specimens used for soil-water characteristic curve determination were first reconstituted, reconsolidated under one-dimensional conditions to the in-situ vertical stress of each soil, and then unloaded. Undisturbed samples were available for one soil as well and the drying portion of the undisturbed material was measured for this soil too. The soil-water characteristic curve data presented are the first for soils from Greece and among the few presented for marls.
1
INTRODUCTION
Despite climatic conditions favouring the presence of unsaturated soils in Greece, the research in this subject has lagged behind research in fully saturated soils. This paper constitutes one of the first efforts to report unsaturated soil properties for soils from Greece. The property considered first and presented here is the drying portion of the soil-water characteristic curve (SWCC) of five soils. The SWCC constitutes a fundamental property for the study of unsaturated soils. It represents the relation between the distribution of solid, liquid and air phase in the volume of soil (as expressed by degree of saturation, Sr , gravimetric or volumetric water content, w or θ, and void ratio, e), as well as the total volume of the soil itself, and the negative pressure sitting on the liquid phase until desaturation occurs, or suction after desaturation has occurred. The soils tested included marls and other soils containing large amounts of calcite, for which it is hard to find SWCC data presented in the literature. Given that the compressibility properties of the soils have also been studied, and that the SWCC tests involved measurement of both void ratio and water content changes with suction, the comparison between void ratio changes with suction and vertical stress increase under one-dimensional conditions of loading is also presented. 2
THE SOILS TESTED
The soils studied were Ioannina Lake Silt, Corinth Marl, Chania Clay and Kifissia Clay and Marl.
The names used to describe the soils are empirical and the actual physical properties dictating the nature of each soil are presented in this section. Samples from all soils were disturbed samples from excavation materials or relatively low quality borehole cores, except for the samples of Corinth Marl which were carefully cut and preserved samples removed from the toe of the north slope of the Corinth Canal. For this reason, the soil-water characteristic curve of undisturbed samples was measured only for Corinth Marl, while for the others it was measured on specimens reconstituted, then reconsolidated to the estimated in-situ vertical stress and unloaded. This took place for Corinth Marl as well for comparison with the SWCC of the other soils and the SWCC measured on the undisturbed specimens of this material. Classification tests and mineralogical analyses were carried out on all five soils. The index properties of the soils tested are presented in Table 1 and the basic minerals found by x-ray diffraction and methylene blue methods are presented in Table 2. Ioannina Lake Silt is categorised as SM according to USCS, while all others are categorised as CL. Corinth and Kifissia Marls have the highest percentages of calcite. Kifissia Clay has a considerably high percentage of calcite as well, and Chania Clay has a very high percentage of quartz, despite the fact that both soils are commonly referred to as ‘‘clays’’. Highly active minerals such as illite and montmorillonite are present in all five soils, ranging from 3 to 10% and from 7 to 17% respectively. The absence of kaolinite is typical of most soils from Greece.
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Table 1.
Index properties of the soils tested.
Soil
wL (%)
Ip –
Gs –
Clay (%)
Silt (%)
Sand (%)
Ioannina Lake Silt Corinth Marl Chania Clay Kifissia Clay Kifissia Marl
24 34 24 41 31
1 12 9 21 16
2.55 2.67 2.68 2.67 2.66
8 11 18 33 25
27 86 50 64 68
65 3 32 3 7
Table 2. Basic minerals of the soils tested (measured on percentage passing through sieve No. 200).
Mineral
Kifissia Ioannina Chania Corinth Lake Silt Clay Marl Clay Marl
Quartz Albite Calcite Dolomite Illite Montmorillonite Halloysite Chlorite Serpentine Muscovite
75 5 2.5 – 3 7 – 3 2 –
3
60 3 3 – 3 9 10 3 – 5
16 3 60 2 7 7 – 1.5 1.5 1
16 – 37 1 10 12 8 4 4 7
18 2 52 – 5 17 – 2 – 3
EXPERIMENTAL METHOD
Soil water characteristic curves were measured using the axis translation technique by means of a conventional Soil-Moisture Inc. pressure extractor with 15 Bar air-entry pressure ceramic porous stones. Air pressure was provided from an air compressor with the necessary filters connected to the air supply for air dehumidification. Different specimens were used for each suction value applied in the pressure extractor, rather than measuring the amount of water being extracted from the same specimen. This was considered important for the measurement of total volume changes (which in combination with water content measurement allow the calculation of void ratio changes with suction), as with the water movement measurements, both system complexities and assumptions involved may limit accuracy. With different samples, accuracy is determined only by soil homogeneity for undisturbed samples and careful preparation of identical reconstituted soil samples. Air pressure is supplied to the pressure extractor during the time needed for the suction to reach equilibrium in the specimens. Afterwards the air pressure is removed and the soil specimens are taken out immediately, cut in half, with one half used for water content measurement and the other half being immersed in melted
paraffin wax for total volume measurement. Assuming that the water content measured on one half is the same throughout the specimen, then the mass of the water in the half used for total volume measurement can be calculated from the total mass of this half. Once the mass of the water is known, the mass of the solid particles is also known, and then their volumes are calculated from the known density of water and specific gravity respectively. Having calculated the volumes of the water phase (Vw ) and the solid phase (Vs ) in the half of the specimen where total volume has been measured (Vtot ), the volume of the voids (Vv ) is calculated (Vv = Vtot − Vs ) and the degree of saturation (Sr ) of the sample is calculated by its definition as a property (Sr = Vw /Vv ). Once the degree of saturation has been calculated and the water content w and specific gravity Gs are already known then void ratio e can be calculated (e = w · Gs /Sr ). These calculations are based on the reasonable assumptions that the water content measured on one half of the specimen and the degree of saturation calculated for the other are the same throughout the specimen. An important detail is that when cutting the specimen, utmost care must be exhibited that the surface of the section in the half used for total volume measurement must be as flat as possible without cavities where air may be trapped. As far as one-dimensional consolidation is concerned, conventional deadweight, front-loading oedometers were used with a 10:1 beam-lever ratio and fixed-ring cells with lightly lubricated, smooth and polished inner surface rings, with a 70 mm internal diameter and 19 mm height. Reconstitution involved breaking of particle aggregations and thorough mixing with de-aired, de-ionised water until a slurry of 1.5wL water content was prepared. All slurries were left to hydrate under vacuum for sufficient time with occasional measurement of their water content and drying or addition of water to ensure homogeneity of the slurries prepared for each soil and consistent initial conditions for all reconstituted soils. As a general rule, a water content of ±10% from the target value of initial slurry water content was set, which has been found to ensure homogeneity of later consolidated specimens of reconstituted soils, provided the maximum vertical stress exceeds 50–100 kPa (Bardanis, 1999) as was the case for all 5 soils. All soils were consolidated to a maximum vertical stress corresponding approximately to the depth they came from and then unloaded; Ioannina Lake Silt to 100 kPa, Chania Clay to 200 kPa, and Kifissia Clay and Marl to 600 kPa. Corinth Marl specimens were consolidated to 800 kPa and then unloaded, mostly on the basis that this stress history created the same initial void ratio that was measured on the undisturbed specimens removed from the toe of the Corinth Canal slopes (approximately 70–75 m high).
264
As far as the samples of the undisturbed Corinth Marl are concerned, these were carefully preserved in a controlled humidity chamber. Larger blocks were taken out of the chamber when specimens had to be trimmed from them in order to be put in the pressure extractor. Corinth Marl as a geological formation may by no means be considered a homogeneous material; still the largest possible block of visually homogeneous material was used. Homogeneity within this block was later verified by numerous index tests on specimens from various positions in the block. The blocks came from the toe of the canal slope just above sea level (ca. 0.50 m) and in-situ suction was measured with a Quickdraw Tensiometer and found to be approximately 10 kPa. 4
RESULTS AND DISCUSSION
In Figure 1(a) degree of saturation is plotted against suction for Ioannina Lake silt, while in Figure 1(b) void ratio is plotted against the corresponding value of water content during drying. The solid line in 100
Sr (%)
80 60 40 20 0 10
100
(a)
1000
10000
s (kPa)
Figure 1(b) is the full saturation line corresponding to the specific gravity, Gs , of the material (e = w · Gs , for Sr = 100%). As seen in Figure 1(a), desaturation occurred between 25 and 30 kPa, while the second inflection point occurred between 150 and 200 kPa corresponding to a degree of saturation between 45% and 50%. This value seems too high to be the residual value of the degree of saturation. Specimens of the soil left to dry completely in the air yielded a value of the degree of saturation on average 7%. This value seems more likely to reflect residual conditions, whereas the value of 45%–50% observed on the SWCC corresponds most probably to the point where water retention characteristics start to be dictated primarily by the finer fraction of the soil’s grains. The grain size distribution of this soil (Fig. 2) is gap-graded, although slightly and only for the small percentage passing through sieve No.200. Still, this type of grain size distribution would justify a ‘bimodal’ SWCC with one inflection point at Sr 45%–50% and a second one at approximately 7%, which was not observed however as the maximum applied suction was 1500 kPa. Also as seen in Figure 1(b), the scatter of void ratio values is very large, as this is probably the coarsest material for which immersion in melted paraffin wax for total volume measurement may be applied. In Figures 3(a) & 3(b) degree of saturation is plotted against suction and void ratio against the corresponding water content during drying respectively for both reconstituted/reconsolidated and undisturbed Corinth Marl. As seen in Figure 3(a), desaturation occurred for both types of Corinth Marl, although a second inflection point was not observed for either soil up to the maximum applied suction of 1500 kPa. Similarly, a clear departure from the full saturation line can be observed for both types of this soil in Figure 3(b). Two other observations can be made. First, the scatter of measured values is larger for the
0.80
.
0.70
Percentage passing (%)
0.60
e
0.50 0.40 0.30 0.20 0.10 0.00 0
(b)
5
10
15
20
25
100 90 80 70 60 50 40 30 20 10 0 0.001
30
0.010
0.100
1.000
10.000
Sieve diameter (mm)
w (%)
Figure 1. (a) Degree of saturation Sr vs suction s, and (b) void ratio e vs water content w for Ioannina Lake Silt.
Figure 2. Lake Silt.
265
Grain-size distribution curve of Ioannina
100
80
80
60
60
Sr (%)
Sr (%)
100
40 20
20 0
0 10
100
1000
10
10000
100
(a)
s (kPa)
0.80
0.70
0.70
0.60
0.60
0.50
0.50
0.40
0.40
0.30
1000
10000
s (kPa)
0.80
e
e
(a)
0.30
0.20
Rec/Rec
0.20
0.10
Undisturbed
0.10
0.00
0.00
0
(b)
40
5
10
15
20
25
30
0
(b)
w (%)
5
10
15
20
25
30
w (%)
Figure 3. (a) Degree of saturation Sr vs suction s, and (b) void ratio e vs water content w for Corinth Marl.
Figure 4. (a) Degree of saturation Sr vs suction s, and (b) void ratio e vs water content w for Chania Clay.
undisturbed Corinth Marl, almost at the point of rendering the results meaningless, especially in the e-w plot of Figure 3(b). Still it is clear in Figure 3(a) that, despite the large scatter, the undisturbed Corinth Marl desaturates at a higher suction than the reconstituted and reconsolidated one (between 200 and 300 kPa as opposed to 100 to 200 kPa) and retains a higher degree of saturation for the same suction after desaturation, although both materials have the same void ratio at the beginning of drying. Bardanis & Kavvadas (2004) have elaborated more on this observation and attributed the observed behaviour to cementation of the undisturbed Corinth Marl, which does not exist in reconstituted/reconsolidated specimens. This is worth further investigation, as experimental results for unsaturated properties of marls (especially focusing on the effect of their cementation in their drying behaviour) are scarce, if any, in the literature. More information on the engineering behaviour of Corinth Marl and the role played by its cementation may be found in Kavvadas et al. (2003).
In Figures 4(a) & 4(b) degree of saturation is plotted against suction and void ratio against water content during drying for Chania Clay. As seen in Figure 4(a), desaturation seems to start occurring at approximately 1000 kPa but this is not supported by a similarly clear departure from the full saturation line in Figure 4(b). The observed departure is not considered clear given the accuracy of measurements. Still the picture is that the air entry pressure of Chania Clay must be between 1000 and 1500 kPa, although a few measurements at slightly larger values would have ascertained whether desaturation did actually occur or not. In Figures 5(a) & 5(b) degree of saturation is plotted against suction and void ratio against water content during drying for both Kifissia Clay and Marl. Given the same stress history of both materials, the Clay retains a higher void ratio, in agreement with its higher liquid limit. Kifissia Clay seems to desaturate close to 1000 kPa (Fig. 5(a)), which is supported by signs of departure from the full saturation line (Fig. 5(b)). Both the departure from line Sr = 100% in Figure 5(a) and
266
0.80
100
0.70 0.60 0.50
60
e
Sr (%)
80
40
0.40 0.30 0.20
SWCC
0.10
1D Compression
20
0.00
0 10
100
1
10000
s (kPa)
(a) 0.80
0.70
0.70
0.60
0.60
0.50
0.50
0.40
0.40
1000
10000
0.20
Clay
0.20
SWCC
0.10
Marl
0.10
1D Compression
0.00
0.00 0
5
10
15
20
25
1
30
w (%)
(b)
Figure 5. (a) Degree of saturation Sr vs suction s, and (b) void ratio e vs water content w for Kifissia Clay and Marl.
the full saturation line in Figure 5(b) are rather obscure relative to the accuracy achieved. As far as Kifissia Marl is concerned, desaturation has not occurred, as no departure is observed from the line Sr = 100% or the full saturation line. The opposite would have been expected given that the Marl contains slightly less clay-size material than the Clay (25% vs 33%), slightly more sand (7% vs 3%) and less clayey minerals in the fraction passing sieve No. 200 (a total of 27% vs 45%). The observed lack of desaturation up to 1500 kPa may therefore be attributed either to the presence of more montmorillonite (17% vs 12%) or to experimental error with the results of Kifissia Clay. 5
100
0.30
0.30
(b)
10
Suction/Vertical stress (kPa)
0.80
e
e
(a)
1000
VOID RATIO CHANGES WITH SUCTION AND VERTICAL STRESS
Given that the one-dimensional curves of most of the soils had already been studied, a comparison was attempted between void ratio changes due to suction and due to one-dimensional compression.
10
100
1000
10000
Suction/Vertical stress (kPa)
Figure 6. Void ratio vs suction during drying and one-dimensional compression curves for (a) reconstituted and reconsolidated Corinth Marl, and (b) undisturbed Corinth Marl.
In Figures 6(a) & 6(b) the void ratio-suction curve and the one-dimensional compression curve for reconstituted/reconsolidated specimens and undisturbed specimens of Corinth Marl are plotted. For Corinth Marl, sufficient quantities of the material were available for a special test with a loading-unloading loop, similar to that applied to reconstituted specimens before drying, to be performed. The compression curve for this test is shown in Figure 6(a). The compression curve shown in Figure 6(b) is an average of the one-dimensional compression tests performed on undisturbed Corinth Marl. The larger scatter of void ratio values of undisturbed specimens during drying relative to that of the values of the reconstituted/reconsolidated specimens is apparent in these plots as well. For reconstituted/ reconsolidated specimens there seems to be fair agreement up to 100 kPa. After that value of suction/stress, the void ratio during drying becomes smaller than that for the compression
267
1.20 1.00
e
0.80 0.60 0.40 0.20 0.00 10
100
1000
10000
Suction/Vertical stress (kPa) Figure 7. Void ratio vs suction during drying and onedimensional compression curves for reconstituted and reconsolidated Kifissia Clay. 1.00 0.80
e
0.60 0.40 0.20 0.00 10
100
1000
10000
Suction/Vertical stress (kPa) Figure 8. Void ratio vs suction during drying and onedimensional compression curves for reconstituted and reconsolidated Kifissia Marl.
curve, up to the value of stress where the intrinsic compression curve is reached and the opposite seems to happen. In Figures 7 and 8 the same curves are compared for Kifissia Clay and Marl respectively. Limited quantities of the samples from each material did not allow for special one-dimensional compression tests to be carried out with a loading-unloading loop to the maximum stress applied to reconstituted specimens before drying. One point on the void ratio-suction curve of Kifissia Clay corresponding to 1100 kPa (Fig. 7) departs significantly from the curve the rest of the points seem to follow. This point corresponds to the point indicating desaturation in the curves on Figures 5(a) & 5(b). This seems to support that either
the particular specimen had different properties or there has been some experimental error. Therefore it will not be considered that Kifissia Clay achieved desaturation. Returning to the comparison between void ratio vs suction and one-dimensional compression curves for each of the two materials, two observations can be made. First, the void ratio vs suction curves are for all practical purposes (and at least up to the maximum stress applied to specimens used for SWCC measurement) parallel to the unloading branches of the one-dimensional curves. This point seems to support that void ratio decrease with increasing suction up to the air-entry pressure during drying and increasing vertical stress during one-dimensional loading may be described by the same indices. The second observation regards the void ratio vs suction curve of Kifissia Clay, which seems to exhibit a change in its slope at 600 kPa (if the point at 1100 kPa is omitted). Unfortunately this has not been observed on the same curve for Kifissia Marl. Still it would be logical to expect such a change of slope when such conditions occur, i.e. a maximum preconsolidation pressure smaller than the air-entry pressure and a zero total stress suction path extending to suctions higher than the preconsolidation pressure. These observations need certainly to be supported by further experimental research (especially with tests where high values of suction will be applied so that desaturation does actually occur) as they are of considerable value in constitutive modelling of unsaturated soils. Void ratio vs suction curves described by the same indices as with compression curves could mean that κs could be substituted by κ in the Barcelona Basic Model (Alonso et al. 1990) family of constitutive models for air-entry pressure smaller than the maximum preconsolidation pressure. This would itself change to λ for air-entry pressure larger than the maximum preconsolidation pressure, in the suction range between preconsolidation pressure and the air-entry pressure. 6
CONCLUSIONS
The drying portions of the soil-water characteristic curve presented constitute the first ones for soils from Greece. Except for this they are among the few such results presented for marls and generally clay-size soils containing large amounts of calcite. Although they may by no means be considered representative of the properties of soils found throughout Greece or soils with high calcite fractions, they draw attention to the properties of such materials. The most important aspect needing further research is the possibility that cementation of undisturbed marls leads to retaining higher degrees of saturation for the same suction in the same soils with the same loading history but without
268
cementation. Further investigation into the decrease of void ratio with increasing suction for soils with a maximum preconsolidation pressure smaller and higher than their air-entry pressure may also help redefine the parameters used in constitutive modelling to describe these changes. ACKNOWLEDGEMENTS Part of the research by M.E. Bardanis has been funded by the National Scholarship Foundation (IKY) of Greece. REFERENCES
Bardanis, M.E. 1999. An experimental study of the properties of intrinsic compressibility of one clay and one marl, Proc. 13th Young Geotechnical Engineers Conference, Santorini, Greece, 23–25 September 1999, 88–97, Athens: Minoas. Bardanis, M.E., Kavvadas, M.J. 2004. Laboratory investigation of the virgin drying of the Corinth Marls, in T. Schanz (ed.), Unsaturated Soils: Experimental Studies, Proc. of the Int. Conf. ‘‘From Experimental Evidence towards Numerical Modelling of Unsaturated Soils’’, Weimar, 17–18 September 2003, 421–432, Berlin: Springer. Kavvadas, M.J., Anagnostopoulos, A.G., Georgiannou, V.N., Bardanis, M.E. 2003. Characterisation and engineering properties of the Corinth Marl, in Tan et al (eds.), Proc. Int. Workshop ‘Characterisation and Engineering Properties of Natural Soils’, Singapore, 2002, 2, 1435–1459, Lisse: Swets & Zeitlinger.
Alonso, E.E., Gens, A., Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Prediction of soil-water retention properties of a lime stabilised compacted silt M. Cecconi University of Perugia, Perugia, Italy
G. Russo University of Cassino, Cassino, Italy
ABSTRACT: The applicability of semi-empirical prediction methods of the water retention properties of unsaturated soils has been examined in detail. Among these methods, those based on the particle size distribution of samples seem to be very effective in predicting the soil water retention curve, as well as being very advantageous for their simplicity. On the other hand, other methods allow predicting indirectly the soil water retention curve from the mercury intrusion porosimetry technique. In the paper experimental soil water retention curves (swrcs) of a natural and lime stabilised compacted silt, obtained from pressure plate tests and mercury intrusion porosimetry tests, are respectively compared with those predicted by pore size distribution model and mercury intrusion porosimetry models. The comparison allows a critical review of the prediction methods and highlights the consistency of the predicted and the observed water retention properties of both natural and lime stabilised samples.
1
INTRODUCTION
The relationship between suction, s, and volumetric water content, θ , or degree of saturation, i.e. the soil water retention curve SWRC, can be experimentally measured in the laboratory by means of pressure plate or volumetric pressure plate extractor. Several mathematical expressions, both empirical and theoretical in nature, have also been proposed in the literature to describe the SWRC (see Scott et al., 2001). Moreover, the soil water characteristic curve can also be computed from the particle size distribution (PSD); this approach is based mainly on the similarity between shapes of the cumulative grain size distribution and the s(θ ) curves. The methods originally proposed in the field of soil physics by Arya & Paris (1981) and Arya et al. (1999) seem to be very effective in predicting the SWRC, as well as being very advantageous for their simplicity. However, since most predictions models are based on PSD information, the accuracy of a PSD curve may affect the estimate of s(θ). At present, there are a few attempts to quantitatively investigate the effect of the choice of a PSD model on the prediction of the soil water retention curve as well as the conductivity function k(s). A review of such models is critically examined in Hwang et al. (2002) and Hwang & Powers (2003). The water retention properties can be also obtained indirectly from the mercury porosimetry technique
(Aung et al., 2001; Kong & Tan, 2000; Prapaharan et al., 1985; Purcell, 1949; Penumadu & Dean, 1999), since the SWRC is intrinsically linked with the pore size distribution of the material (the equivalent pore radius can be somehow related to matric suction through the capillarity equation). Porosimeter tests in fact allow evaluating the pore size, their amount and their distribution, and in a much shorter time compared to pressure plate tests. In the paper, experimental soil water retention curves (SWRCs) of a natural and lime stabilised compacted silt, obtained from pressure plate tests and mercury intrusion porosimetry tests, are respectively compared with those predicted by Arya & Paris (1981) and Prapaharan et al. (1985) models. The pressure plate test results are reported in detail in a companion paper (Tedesco & Russo, 2008). The comparison allows a critical review of the prediction methods, and highlights the consistency of the predicted and the observed water retention properties of both natural and lime stabilised samples. 2
EXPERIMENTAL PROCEDURES AND RESULTS
Laboratory tests were performed on remoulded samples of an alluvial silty soil. The physical characteristics (grain size distribution, specific weight,
271
Table 1. (MIP).
Pressure plate tests (PP) and porosimetry tests
Test type
Test #
Sample
Curing time
PP PP PP PP MIP MIP MIP MIP MIP MIP MIP MIP
STDN01 STD02 L43CCT07(∗) L43CCT28(∗) L4NOF01 L4NOF02 L4NOF04 L43OF00 L43OF07 L43OF14 L43OF28 L43OF77
nat 3% lime 3% lime 3% lime natural natural natural 3% lime 3% lime 3% lime 3% lime 3% lime
− variable 7 days 28 days − − − 0 days 7 days 14 days 28 days 77 days
(∗ ) CCT: constant curing time.
Table 2. samples.
Natural 3% Lime
Physical properties of natural and stabilised γs (kN/m3 )
wL (%)
PI
wopt (%)
γdmax (kN/m3 )
26.4 26.1
25.0 24.0
8 –
14.5 17.5
18.6 17.3
1.0
0.8
no rm
plastic limit, liquid limit) of the natural soil were determined and standard Proctor tests were performed. Lime treated samples were prepared by hand mixing the oven dried soil with 3% quicklime powder and distilled water, allowing the quicklime to hydrate for 24 hours. The selected percent by weight of quicklime allowed the development of pozzolanic reactions (Rogers et al., 1997). The samples were finally compacted at optimum (wopt ) initial water content. Pressure plate tests were performed on both natural and lime stabilised samples. With reference to the standard testing procedure, the duration of the test does not allow the control of the curing time of the stabilised samples. Therefore, a new testing procedure was developed in order to obtain constant curing time water retention curves. Details of the procedure can be found in a companion paper (Tedesco & Russo, 2008). Two types of water retention curves of the stabilised samples have been considered, namely the standard retention curve, characterised by a variable curing time, and the ‘‘constant curing time’’ curves, for which the experimental data are determined at the same curing time (CCT tests). In particular, 7 and 28 days curing times were set for stabilised samples, traditionally considered in order to evaluate the effectiveness of lime stabilisation. In order to perform mercury intrusion porosimetry, samples were dehydrated by freeze-drying technique (Delage & Pellerin, 1984), that is rapid freezing in liquid nitrogen (boiling point −196◦ C) followed by sublimation in a true vacuum. Freezing was accelerated using small pieces of soil (1–2 mg in weight), as stated by Delage & Lefebvre (1984). The dehydrated lime stabilised samples were then cured for fixed time intervals under controlled conditions before performing MIP tests. The curing intervals of time selected were t = 0, 7, 28 days. In Table 1 pressure plate tests (PP) and mercury intrusion porosimetry tests (MIP) are summarized. Table 2 reports the main physical properties of both natural and lime stabilized samples. In Figure 1 the water retention curves of natural (STDN 01) and lime stabilised samples, at variable (STDN 02) and constant curing time (L43CCT07, L43CCT28), are reported. It can be seen that the addition of lime generally increases the water retention of the soil, and this increase is strongly affected by the curing time (Tedesco, 2007). Figure 2 and Figure 3 show the results of MIP tests respectively on natural and lime stabilised samples, the latter performed at constant curing time. A relevant modification of porosity for lime stabilised samples takes place immediately after the addition of lime. A subsequent reduction of this effect occurs increasing the curing time of the stabilised samples, bringing back the pore size distribution towards the
S TD02 L43CCT07 L43CCT28
0.6
S TDN01 Va n Ge nuchte n (1980)
0.4 1
10
100
1000
10000
s (kP a ) Figure 1. SWRCs of natural and lime stabilised samples (from pressure plate tests).
distribution of the natural samples. After a curing time of 28 days the stabilised samples show a very similar porosity and pore size distribution comparable with those of natural samples. More details on the observed behaviours can be found in Russo et al. (2007).
272
sands yields to a computed parameter α not depending on particle size (constant α = 1.38). Later investigations by Arya et al. (1999) were aimed to investigate on the variation of α with particle size distribution parameters. However, in the following α is assumed to be constant. In order to produce a mathematical representation of the complete PSD, the single-parameter unimodal Jaky model was used in the present study (Jaky, 1944):
L4NOF0 1 L4NOF02 L4NOF04
0.12 0.08 0.04
10
100
2 1 d P(d) = exp − 2 ln k d0
1000
diameter ( m)
Figure 2.
Results of MIP tests on natural samples.
cumulative volume (cc/g)
0.25 L43OF00 L43OF07 L43OF14 L43OF28 L43OF77
0.20 0.15 0.10 0.05 0.00 0.001
Figure 3.
3
0.01
0.1
1 10 diameter ( m)
100
1000
Results of MIP tests on lime-stabilised samples.
PREDICTIONS
3.1
Particle size distribution method
Very briefly, in the model proposed by Arya & Paris (1981) it is assumed the solid grains spherical and the pore volume approximated to that of cylindrical capillary tubes. For each ith particle-size class, the pore radius (ri ) can be related to the mean grain radius (Ri ), according to: ri = Ri [2eni (1−α) /3]1/2
where d0 represents the diameter corresponding to the 100% of passing in weight (P), and k the fitting parameter. The value of k was found to vary from 5 to 3 when passing from natural to lime stabilised soil (Fig. 4). The calculated PSD was then divided into thirty size fractions and values of s(θ) were then calculated by means of the procedure outlined by Arya & Paris (1981). The predicted SWRCs are shown in Figures 5a and b) in comparison with those obtained from standard and constant curing time pressure plate tests and fitted through Van Genucthen (1980) equation. The results are plotted in terms of the ratio = θ/θ0 , where θ0 represents the initial volumetric water content of the sample. For the material in its natural state (Fig. 5a), it can be noted that the predicted SWRC (α = 2.5) is twisted and smoothed with respect to the measured SWRC and the air entry value is questionable. The predictions improve for the stabilised samples. In this case, a larger value of Arya and Paris parameter α is needed (α = 4). By comparing the dotted curves in Figure 5b with the model prediction, it is found that the slope of the predicted SWRC is very similar to that obtained from a standard pressure plate test (test STDN02, see Table 1), even if the predicted curve is shifted downward.
(1)
1.0
where ni , e and α are respectively the number of spherical grains, the voids ratio and a constant parameter larger than unity. Then, for a tube of radius ri , the capillarity equation holds:
gravel
sand
silt
0.8
passing in weigth
(ua − uw )i = si = 2Tw /ri
(2)
0.6 0.4
nat
0.2
with Tw the surface tension of water (Tw = 7.27 × 10 N/m at 20◦ C). For a given grain size distribution, Equations 1 and 2 allow to calculate the value of suction required to desaturate a given fraction of pores. The application of the model to different soils varying from silty clays to
(3)
=3
1
y, k
0.1
Jak
0.01
=5
0.0 0 0.00 1
y, k
0.16
Jak
cumulative volume (cc/g)
0.20
lime-stabilised
−2
0.0 0.00 1
0.01
0.1
1
10
10 0
d (mm)
Figure 4. Grain size distributions and Jaky model for natural and lime-stabilised samples.
273
with Tm the surface tension of mercury (Tm = 480 × 10−3 N/m at 20◦ C) and δm the contact angle between mercury and soil (δm = 139◦ ). The soil gravimetric water content that should correspond to each intruded pore radius can be calculated from Equation 5:
1.0 nat.
= 2.5
norm
0.8
0.6
w=
pressure plate-nat. samples - - - - - - Van Genuchten (1980) 0.4 1
10
10 0
100 0
with n the soil porosity and n˜ the ratio of the volume intruded by mercury to pore radii as small as r to the total volume of the sample. Equation 5 is well-founded by assuming implicitly that the pressure um − ua intruding the air pores (Va ) of a soil sample of volume V and porosity n corresponds—through Equations 4—to the matric suction s required to desaturate an initially saturated sample with the same total volume and porosity. Experimental data obtained from MIP tests have been inferred and then ‘‘converted’’ to swrcs according to Equations 4 and 5. Figures 6a and 6b show the model
a)
1.0 lime s
tab.
=4
norm
STDN02
L43CCT28
0.6
(5)
10000
s (kPa)
0.8
n − n˜ (1 − n)Gs
L43CCT07 - - - - - - Van Genuchten (1980) 0.4 1
10
10 0
100 0
10000
1.0
s (kPa)
b)
Figure 5. Model predictions for a) natural and b) lime stabilised samples (from grain size distribution data). norm
0.8 STDN01 - - - - - - Van Genuchten (1980)
0.6
However, for the material at hand, the Arya and Paris (1981) model predictions are not sufficiently accurate. Further investigations are also required to explore the nature of parameter α; in fact values of α larger than unity render Eqution 1 dimensionally incorrect (Cecconi & Pane, 2002). 3.2
from MIP tests L4NOF01 L4NOF02 L4NOF04
0.4 1
10
100
1000
MIP method 1.0
Van Genuchten STDN02 L43CCT07 L43CCT28
norm 0.6
0.4 1
10
100
1000 s (kPa)
[4.1]
[4.2]
(4)
a)
0.8
– the mercury entry value, mercury entry value and the air entry value of the SWRC are closely related; – the equivalent pores radius (r) from MIP tests and the pores radius from experimental swrcs can be calculated by using the following equations (4.1) and (4.2) derived from Kelvin equations: 2Tm cos δm =− (um − ua )
100000
L43OF00 L43OF07 L43OF14 L43OF28 L43OF77
The method proposed by Prapaharan et al. (1985) was used to derive the SWRC from the results of MIP tests. Such method is based on the following experimental evidence:
2Tw r= (ua − uw )
10000
s (kPa)
10000
100000 b)
Figure 6. Model predictions for a) natural and b) lime stabilised samples (from MIP tests).
274
predictions estimated for natural and lime stabilised samples. From a critical inspection of these figures, the following considerations can be drawn:
4
– the predicted swrcs for tests L43OF00, L43OF07 and L43OF14 are very similar in shape, thus indicating that the short term effects induced by lime persist at least for 14 days; – the subsequent microstructural changes induced by lime with increasing the curing time up to 28 and 77 days (tests L43OF28 and L43OF77 modify the location and the shape of the swrc; due to long term effects (pozzolanic reactions), the increase of the retention properties are probably connected with the reduction of interconnected pores between aggregates and the increase of occluded intra-aggregate pores. – the predicted and experimental soil water retention curves—in Figure 6, the experimental data are fitted through the Van Genuchten equation—are substantially in good agreement. It is noted that data from constant curing time tests are very close to those calculate from MIP tests carried out at low curing time. Also, data from test stdn02 are definitely comparable with those obtained from MIP tests on stabilised samples and cured for four and more weeks. Finally, when comparing the whole set of predictions obtained from MIP tests discussed above and shown in Figure 7, it is synthetically highlighted the relevant dependency of water retention properties of the stabilised samples on the curing time. There are no sensible differences—in terms of retention properties—among natural and stabilised samples, as long as the curing time does not exceed two weeks. After that, the soil water retention curves increase significantly as the pozzolanic reactions develop.
1.0
norm
0.8
0.6 natural 3% stab. 0, 7, 14 days 3% stab. 28, 77 days 0.4
1
10
100
1000
10000
100000
s (kPa)
Figure 7. Model predictions for lime stabilised samples (from MIP tests).
CONCLUDING REMARKS
Two different empirical methods available in the literature for the prediction of the SWRCS of unsaturated soils, namely the models proposed by Arya & Paris (1981) and Prapaharan et al. (1985) have been applied to the experimental results of pressure plate and mercury intrusion porosimeter tests on natural and lime stabilised samples of a compacted sandy silt. By following the approach proposed by Prapaharan et al. (1985), based on the similarity between the pore size distribution and the soil water retention properties, the agreement between experimental results and predictions is very encouraging. The model is capable to capture the very complex evolution with curing time of the microstructure of stabilised samples, due to the development of cation exchange and pozzolanic reactions induced by lime. Moreover, the mercury porosimetry technique requires much shorter test duration than pressure plate tests and this certainly represents a great advantage.
ACKNOWLEDGEMENTS The Authors are very grateful to Prof. Giuseppe Mascolo for the support during the experimental work. Mercury intrusion porosimetry tests were developed at the University of Cassino under the careful supervision of Sebastiana Dal Vecchio. With gratitude the Authors thank Dante Valerio Tedesco for the helpful contribution to the laboratory work.
REFERENCES Arya, L.M., Paris, J.F. 1981. A physicoempirical model to predict the soil moisture characteristic from particle size. Soil Sci. Soc. Am. J. 45: 1023–1030. Arya, L.M., Feike, J.L., van Genuchten, M.T., Shouse, P.J. 1999. Scaling parameter to predict the soil water characteristic from particle size distribution data. Soil Sci. Soc. Am. J. 63: 510–519. Aung, K.K., Rahardjo, H., Leong, E.C., Toll, D.G. 2001. Relationship between porosimetry measurement and soilwater characteristic curve for unsaturated residual soil. Geotechnical and Geological Engineering, 19: 401–416. Cecconi, M., Pane, V. 2002. Comparison of some experimental and theoretical approaches for the determination of the soil water characteristic curve. Proc. of International Workshop on Environmental Geomechanics, Monte Verità, Ascona, Switzerland, 341–346. Delage, P., Pellerin, F.M. 1984. Influence de la lyophilisation sur la structure d’une argile sensible du Québec. Clay Minerals, 19: 151–160. Delage, P., Lefebvre, G. 1984. Study of the structure of a sensitive Champlain clay of its evolution during consolidation. Canadian Geotechnical Journal 21: 21–35.
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Fredlund, M.D., Fredlund, D.G., Wilson, G.W. 1997. Prediction of the soil water characteristic curve from grain size distributions and volume mass properties. Proc. 3rd Brasilian Symp. on Unsat. Soils, Nonsat97, Rio de Janeiro, vol. 1, 13–23. Hwang, S.I., Lee, K.P., Lee, D.S., Powers, S.E. 2002. Models for estimating soil particle size distributions. Soil Sci. Soc. Am. J. 66: 1143–1150. Hwang, S.I. and Powers, S.E. 2003. Using soil particle size distribution models to estimate soil hydraulic properties. Soil Sci. Soc. Am. J. 67: 1103–1112. Jaky, J. 1944. Soil Mechanics. Egyetemi Nyomda, Budapest. Kong, L.W., Tan, L.R. 2000. A simple method of determining the soil-water characteristic curve indirectly. Proc. of the Asian Conference on Unsaturated Soils, Singapore, 341–345. Penumadu, D., Dean, J. 1999. Compressibility effect in evaluating the pore-size distribution of kaolin clay using mercury intrusion porosimetry. Canadian Geotechnical Journal 37: 393–405. Prapaharan, S., Altschaeffl, A.G., Dempsey, B.J. 1985. Moisture curve of compacted clay: mercury intrusion method. Journal of Geotechnical Engineering, ASCE, 111(9): 1139–1143. Purcell, W.R. 1949. Capillary pressures, their measurement using mercury and the calculation of permeability therefrom. Petroleum Transactions, IME 186: 39–48.
Rogers, C.D.F., Glendinning, S., Roff, T.E.J. 1997. Modification of clay soils for construction expediency. Geotechnical Engineering 125: 1–8. Russo, G., Dal Vecchio, S., Mascolo, G. 2007. Microstructure of a lime stabilised compacted silt. In Tom Schanz (ed.), Experimental Unsaturated Soil Mechanics, Proc. of the 2nd Int. Conf. On the Mechanics of Unsaturated Soils, USS2007, Weimar (D), 7–9 March 2007. Heidelberg: Springer, 49–56. Scott Sillers, W., Fredlund, D.G., Zakerzadeh, N. 2001. Mathematical attributes of some soil-water characteristic curve models. Geotechnical and Geological Engineering 19: 243–283. Tedesco, D.V. 2007. Hydro-mechanical behaviour of limestabilised soils. PhD Thesis, University of Cassino. Cassino, Italy. Tedesco, D.V., Russo, G. 2008. Time dependency of water retention properties of a lime stabilised compacted soil. Submitted for publication to First European Conference on Unsaturated Soils, 2–4-July, Durham. Van Genuchten, M. Th. (1980). A closed-form equation for predicting the hydraulic conductivity off unsaturated soils Soil Sci. soc. Am. J. 44: 892–898.
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Time dependency of the water retention properties of a lime stabilised compacted soil D.V. Tedesco & G. Russo University of Cassino, Cassino, Italy
ABSTRACT: Lime stabilisation induces the development of chemical reactions which modify the microstructure of treated soils. Cation exchange and pozzolanic reactions are the two main phenomena responsible for those microstructural changes. Among the hydro-mechanical properties of the stabilised soil, the water retention properties are significantly modified with respect to those of the natural ones and are strongly dependent on curing time. An experimental investigation was carried out on a natural and lime-stabilised compacted silty soil. It was found that the water retention capacity increases after the addition of lime independently from the initial water content. The increase is significantly higher for longer curing times. The results of mercury intrusion porosimetry tests highlighted the fundamental influence of lime on the modification of inter-aggregate porosity.
1
INTRODUCTION
Lime stabilisation is widely used in order to improve the engineering properties of natural soils not suitable as construction materials in earthworks. The reuse of those soils represents a great chance in the reduction of the environmental impact of earthworks (Croce & Russo, 2002). Two different chemo-physical reactions take place after the addition of lime, namely cationic exchange and pozzolanic reactions, which develop simultaneously but on different time scales. Cationic exchange between calcium cations, made available by lime addition, and the hydrogen, sodium and potassium cations of the clay minerals takes place in the short period. This reaction induces the flocculation of clay aggregates. On the long term, pozzolanic reactions take place with the development of stable compounds, such as hydrated calcium silicates and aluminates (Eades & Grim, 1960, Glenn & Handy, 1963), responsible of cementation bounds among the soil aggregates. These two mechanisms are respectively referred to as modification and stabilisation of treated soils (Rogers & Glendinning, 1996). On the macroscopic scale, the treated soil shows a different grain size distribution and plasticity, a decrease in compressibility and a corresponding increase of shear strength, the latter being strongly dependent on curing time (Croce & Russo, 2003). The water retention of lime stabilised compacted samples is generally higher in comparison with natural compacted samples at corresponding initial water content (Croce & Russo, 2003). It has been observed
(Russo, 2005) that, as stated for natural compacted samples (Vanapalli et al., 1999), the higher water retention pertains to stabilised samples compacted wet of optimum. Despite the strong dependency of lime stabilised soil properties on the time needed for the development of cation exchange and pozzolanic reactions, the role played by curing time in the increase of water retention of lime stabilised samples is still not clear. In the paper the results of an experimental investigation on the influence of curing time on the water retention of lime stabilised soils are presented. Pressure plate tests on both natural and lime stabilised compacted alluvial sandy silt have been performed at fixed lime content. A new testing procedure has been adopted in order to determine soil water retention curves at constant curing time. The results have been interpreted by means of the Van Genuchten (1980) model. A discussion on the experimental findings has been developed with reference to the results of mercury intrusion porosimetry tests performed on the same natural and lime stabilised soils (Russo et al., 2007). 2
EXPERIMENTAL PROCEDURES
The natural soil used in the investigations is an alluvial sandy silt of low plasticity. The minimum amount of quicklime necessary to the triggering of pozzolanic reactions was about 1.0% by weight, as observed by means of the Lime Fixation Point Method (Hilt & Davidson, 1960, Rogers & Glendinning,
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1996). A fixed amount of quicklime (3.0% by weight) was set in order to allow the complete development of both cationic exchange and pozzolanic reactions (Rogers & Glendinning, 1996). After the addition of quicklime and distilled water, the samples were cured for 24 hours in order to allow the hydration of quicklime. Grain size distributions, Atterberg limits and specific weights of both natural and lime stabilised soils were determined. The same tests were repeated for stabilised samples at different curing times, namely 0, 7, 28, 60 days. Both natural and lime stabilised samples were compacted following the Standard Proctor procedure (ASTM D698-91ε1 ) at different initial water content, namely dry of optimum, optimum and wet of optimum water contents. It has been supposed that the structure of soils compacted at corresponding initial water contents is comparable (Seed & Chan, 1959, Alonso et al., 1987). Natural and lime stabilised samples (20.0 mm in height and 60.5 mm in diameter) were saturated with distilled water through the application of a hydraulic head and submitted to desiccation tests using a pressure plate apparatus equipped with a high air entry value porous stone (1.5 MPa). For each suction step, four days were needed for the specimens in order to reach the equilibrium between the internal and the applied air pressure. At the end of the tests the specimens were oven dried and the soil water retention curves (SWRCs) determined by back calculation. During the long duration of each test lime treated samples experience continuous changes in microstructure, due to the relevant dependency on curing time (Russo et al., 2007). The variations in soil water
Table 1.
Pressure plate tests (PP).
Sample
Test
Water content
Curing time (days)
Natural Natural Natural 3% Lime 3% Lime 3% Lime 3% Lime 3% Lime 3% Lime 3% Lime 3% Lime 3% Lime
ND NO NW STD STO STW CCTD07(∗) CCTO07(∗) CCTW07(∗) CCTD28(∗) CCTO28(∗) CCTW28(∗)
Dry Opt Wet Dry Opt Wet Dry Opt Wet Dry Opt Wet
– – – Variable Variable Variable 7 7 7 28 28 28
(∗)
For constant curing time (CCT) tests the average values are reported.
retention capacity detected at the end of the test must be considered as determined at variable curing time. Generally, at the end of the test the sample was cured for more than 28 days. In order to carry out tests at constant curing time on stabilised samples, a new experimental procedure was set up (Tedesco, 2007). Each point of the SWRC, corresponding to a fixed value of matric suction, was determined by means of three stabilised samples cured for 7 or 28 days. At the end of each step, the average degree of saturation of the three samples constituted the point of the SWRC at constant curing time. The samples were then removed and substituted by new stabilised samples cured for the same time, in order to perform the subsequent step. The final results formed the water retention curve of stabilised samples at constant curing time. In Table 1 the pressure plate test on both natural and stabilised samples are summarised.
3
RESULTS
The main physical properties of natural samples were initially determined (PI = 9.0%, LL = 23.0%, γs = 26.9 kN/m3 ). The same tests were then repeated on lime stabilised samples, taking into account an eventual time dependency. In Table 2 the Atterberg limits and the specific weights of the stabilised samples at different curing times have been reported. It is noteworthy that for every value of curing time the plastic limit of lime stabilised samples was not determinable. In Figure 1 the grain size distributions of natural and stabilised specimens are reported. The latter were determined as a function of curing time. Stabilised samples are characterised by a sensible decrease in fine grains, which seems to remain constant with curing time (Tedesco, 2007). In Figure 2 the compaction curve of natural and stabilised (for curing time t = 0) samples are plotted. The addition of lime induces a shifting of the curve, with an increase in the optimum water content and a decrease in the maximum dry density. Figures 3–6 show the results of pressure plate tests on natural and lime stabilised samples at constant curing time and at variable curing time. The SWRCs were plotted in terms of ratio between the actual average degree of saturation and the initial average degree of saturation. The experimental points were interpreted by fitting the available data with the Van Genuchten (1980) equation:
S=
278
1 [1 + (aψ)b ]c
(1)
Table 2. Atterberg limits and specific weights of the stabilised samples. Liquid limit (%)
Specific weight (kN/m3 )
0 7 28 60
23 25 29 25
2.66 2.69 2.69 2.67
95 90 85
S/S 0 [%]
Curing time (days)
100
80 ND
75 70
NO
65
NW
60 55 50 1
10
100
1000
100
1000
u a-uw [kPa]
100
Figure 3.
90 80 70 P [%]
SWRCs of natural samples.
natural
60 50
100
3% lime -t=7
95
3% lime -t=28
90
3% lime -t=60
85
S/S 0 [%]
40
3% lime -t=0
30 20 10
80 CCTD07
75 70
CCTO07
65
0 0,0001
0,001
0,01
0,1
1
10
CCTW07
60 55
D [mm]
50
Figure 1. samples.
Grain size distributions of natural and stabilised
1
10 ua-uw [kPa]
Figure 4. SWRCs of lime-treated samples at constant curing time t = 7 days. 1,90 natural 3% lime
1,85
100 95 90
1,75
85
1,70
S/S 0 [%]
g d [g/cm3]
1,80
1,65 1,60
80 CCTD28
75
CCTO28
70 65
1,55
CCTW28
60
1,50 8
10
12
14
16 w [%]
18
20
55
22
50 1
10
100
1000
ua-uw [kPa]
Figure 2. Standard proctor compaction curves of natural and stabilised samples.
Figure 5. SWRCs of lime-treated samples at constant curing time t = 28 days.
where S is the actual degree of saturation, ψ the matric suction, and a, b and c best-fitting parameters, respectively linked to the air-entry value, to the slope of the curve at the inflexion point and to the residual degree of saturation. This equation was modified in order to plot the results in terms of ratio between the actual degree
of saturation and the initial degree of saturation S0 of the samples:
279
1 S = √
C B·C S0 S0 + (Aψ)B
(2)
100 95 90
S/S 0 [%]
85 80 STD
75
STO
70 65
STW
60 55 50 1
10
100
1000
ua-uw [kPa]
Figure 6. time.
SWRCs of lime-treated samples at variable curing
Table 3. Best-fitting parameters of the modified Van Genuchten (1980) equation. Test
A
B
C
aev (kPa)
nd no nw
0.041 0.012 0.009
0.855 1.000 1.373
0.184 0.181 0.158
15 52 91
CCTD07(∗) CCTO07(∗) CCTW07(∗)
0.077 0.016 0.008
0.676 0.727 0.586
0.180 0.200 0.198
4 26 35
CCTD28(∗) CCTO28(∗) CCTW28(∗) STD STO STW
0.056 0.009 0.007 0.040 0.006 0.006
0.453 0.800 0.918 0.551 0.464 0.470
0.200 0.193 0.200 0.109 0.155 0.142
4 14 16 2 9 8
capacity of stabilised samples on the initial water content is relevant for short curing times, while for long curing times this dependency tends to be negligible with respect to the effects of curing time. In order to highlight this point, in Figures 7–9 the water retention curves of stabilised samples are compared with the natural ones at fixed initial water content and as a function of curing time. It can be observed that, for each initial water content, in the short term (t = 7 days) a slight decrease of the retention takes place for suction values lower than 100 kPa, with a reduction in the air entry values, while no significant changes take place for suctions higher than 100 kPa. As the curing time increases (t ≥ 28 days), the retention is higher in the upper suction range (100–1000 kPa), as detected for all the stabilised samples at each initial water content. The highest retention pertains to samples cured for long time intervals. For those samples, the air entry values are considerably reduced.
100
S/S 0 [%]
90 80 ND CCTD07 CCTD28 STD
70 60 50 1
Air-entry values were calculated using the average S0 .
Figure 7.
with A, B and C best fitting parameters. The A parameter can be related to air-entry value (aev) of the samples through the expression: aev =
1 B·C · S0 A
10
100
1000
ua-uw [kPa]
The best fitting parameters are reported in Table 3. From the experimental results the relevant influence of the curing time on the water retention properties of lime stabilised soils can be observed. Increasing the curing time of stabilised samples, water retention increases. The larger increment of water retention pertains to dry of optimum stabilised samples, but optimum and wet of optimum stabilised samples show the final higher water retention, as reported in Figure 6 for SWRCs at variable curing time. It can be stated, as observed for natural compacted samples (Vanapalli et al., 1999), that the dependency of the water retention
SWRCs of dry of optimum samples.
100
(3)
90
S/S 0 [%]
(∗)
80 NO CCTO07 CCTO28 STO
70 60 50 1
10
100 ua-uw [kPa]
Figure 8.
280
SWRCs of optimum samples.
1000
100
0,025
90
0,020 dV/d(logD) [ml/g]
S/S 0 [%]
Nat
80 NW CCTW07 CCTW28 STW
70 60
3%_28
0,015
3%_77
0,010 0,005
50
0,000 1
10
100
1000
0,01
ua-u w [kPa]
Figure 9.
4
3%_7
SWRCs of wet of optimum samples.
0,1
1 D [ m]
10
Figure 10. MIP of optimum samples: incremental distribution of intruded mercury volume.
DISCUSSION 0,25 Nat 0,20 V [ml/g]
The observed hydraulic behaviour of stabilised samples can be explained with reference to the reactions induced by lime. As observed before, those reactions are strongly dependent on curing time and largely modify the microstructure of the natural soil. Russo et al. (2007) carried out mercury intrusion porosimetry tests on natural and lime stabilised samples of the same soil; the stabilised samples were cured for increasing time intervals. Figure 10 and Figure 11 show the results of MIP tests on optimum water content stabilised samples in terms of incremental and cumulative volume of mercury intruded. Immediately after the addition of lime (t = 7 days) a relevant modification of porosity for lime stabilised samples takes place, with the formation of pore of relatively large diameter (between 4 and 40 microns). A subsequent reduction of this effect occurs increasing the curing time of the stabilised samples (t = 28 days), probably due to pozzolanic reactions which induce the development of bonds between the aggregates. A reduction in the frequency of pores with diameters between 0.2 μm and 2 μm can be also detected in the long term. Finally, pores ranging from 0.01 μm to 0.2 μm systematically increase their frequency as the curing time increases. In terms of water retention properties, the increase in frequency of pores of relatively large radius (short time effects mainly induced by cation exchange), together with the increase in the presence of sand sized aggregates in the grain size distribution, reduces both the air entry value and the retention capacity of the stabilised samples for values of suction lower than 100 kPa. The reduction persists for long curing times. For suction values greater than 100 kPa the water retention increases as the curing time becomes higher. A possible interpretation of this result, consistent with the larger amount of small radii pores observed as curing time increases, is that the cementation bonds between aggregates enhance the frequency
3%_7 3%_28
0,15
3%_77 0,10 0,05 0,00 0,01
0,1
1 D [ m]
10
Figure 11. MIP of optimum samples: cumulative distribution of intruded mercury volume.
of ink-bottle pores. In pores of this type, characterised by an entrance radius smaller than the dimension of the inner part of the pore, intrusion cannot occur until sufficient pressure has been attained to force mercury into the narrow neck, whereupon the entire pore will be filled. As ink-bottle pores upon depressurization entrap mercury in the wide inner portion of the pore, upon drying ink-bottle pores contribute relevantly to retain water into the stabilised soil. The smaller the narrow openings of the ink bottle pores, the higher the suction values needed to desaturate the soil.
5
CONCLUDING REMARKS
In the paper some results of an experimental study on the time dependency of lime stabilisation on the soilwater retention capacity of a compacted silty soil are presented. The comparison between water retention curves of natural and lime stabilised samples points out the general increase of the water retention capacity of the
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soil induced by the addition of lime. The role of both initial water content and curing time has been highlighted. From the results it has been found that stabilised samples compacted at optimum and wet initial water content show higher water retention. The microstructure modifications taking place as a function of curing time, assessed by means of MIP tests, allow an insight into the reaction mechanisms induced by lime and an explanation of the observed increase of water retention. The relevance of the MIP technique in this experimental investigations has been underlined, both for the short test duration and for the analogy between the results in terms of mercury intrusion and water outflow. Further research is required in order to assess the role of microstructure and its evolution with curing time on the retention properties of stabilised samples. Intrusion-extrusion cycles, performed through both volumetric pressure plate extractor and mercury intrusion porosimeter, could highlight the role and amount of ink bottle pores on the water retention of stabilised soils. ACKNOWLEDGEMENTS The Authors are very grateful to Prof. Giuseppe Mascolo for the support during the experimental work. Mercury intrusion porosimetry tests were developed at the University of Cassino under the careful supervision of Sebastiana Dal Vecchio. REFERENCES ASTM 1991. Standard Test Method for Laboratory Compaction Characteristics of Soil Using Standard Effort (12, 400 ft-lbf /ft3 (600 kN-m/m3 )), ASTM D698-91ε1 . In Annual Book of ASTM Standards 04.08: 77–84. West Conshohocken: ASTM International. Alonso, E.E., Gens, A. & Hight, D.W. 1987. Special problem soils-General report. In E.T. Hanran, T.L.L. Orr & T.F. Widdis (eds.), Ground effects in geotechnical engineering (3): 1087–1146; Proc. IX ECSMFE, Dublin, 1987. Rotterdam: Balkema.
Croce, P. & Russo, G. 2002. Reimpiego dei terreni di scavo mediante stabilizzazione a calce. In Proc. XXI AGI— Convegno Nazionale di Geotecnica: 211–216. L’Aquila: Patron Editore. Croce, P. & Russo, G. 2003. Soil-water characteristic curves of lime-stabilised soils. In Pieter A. Vermeer, Helmut F. Schweiger, Minna Karstunen & Marcin Cudny (eds.), Geotechnics of Soft Soils—Theory and Practice: 575–580; Proc. Int. Workshop, Noordwijkerhout (NL), 17–19 September 2003. Essen: VGE. Eades, J.L. & Grim, R. 1960. Reactions of Hydrated Lime with Pure Clay Minerals in Soil Stabilization. Highway Research Board Bulletin 262: 51–63. Glenn, G.R. & Handy, R.L. 1963. Lime-clay mineral reaction products. Highway Research Record 29: 70–82. Hilt, G.H. & Davidson, D.T. 1960. Lime fixation in clayey soils. Highway Research Board Bulletin 262: 20–32. Rogers, C.D.F. & Glendinning, S. 1996. Modification of Clay Soils using Lime. In Rogers, C.D.F., Glendinning, S. & Dixon, N. (eds.) Lime Stabilisation: 99–126. London: Thomas Telford. Russo, G. 2005. Water retention curves of lime stabilised soils. In A. Tarantino, E. Romero & Y.J. Cui (eds.), Advanced Experimental Unsaturated Soil Mechanics: 391–396; Proc. of the Int. Workshop on Advanced Experimental Unsaturated Soil Mechanics, Experus 2005, Trento (I), 27–29 June 2005. Rotterdam: Balkema. Russo, G., Dal Vecchio, S. & Mascolo, G. 2007. Microstructure of a lime stabilised compacted silt. In Tom Schanz (ed.), Experimental Unsaturated Soil Mechanics: 49–56; Proc. of the 2nd Int. Conf. On the Mechanics of Unsaturated Soils, USS2007, Weimar (D), 7–9 March 2007. Heidelberg: Springer. Seed, H.B. & Chan, C.K. 1959. Structure and strength characteristics of compacted clays. JSMFD 85 (SM5): 87–128. Tedesco, D.V. 2007. Hydro-mechanical behaviour of limestabilised soils. PhD Thesis at the University of Cassino. Cassino, Italy. Van Genuchten, M. Th. 1980. A closed form equation predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44: 892–898. Vanapalli, S.K., Fredlund, D.G. & Pufhal, D.E. 1999. The influence of soil structure and stress history on the soilwater characteristics of a compacted till. Geotechnique 49 (2): 143–159.
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Retention and compressibility properties of a partially saturated mine chalk H.D. Nguyen Ecole des Ponts (Université Paris-Est, Navier Inst. – CERMES), Paris, France INERIS, Verneuil-en-Halatte, France
V. De Gennaro & P. Delage Ecole des Ponts (Université Paris-Est, Navier Inst. – CERMES), Paris, France
C. Sorgi INERIS, Verneuil-en-Halatte, France (now RATP, Paris, France)
ABSTRACT: In relation with the assessment of the stability of underground chalk mines, a preliminary investigation of the behaviour of chalk samples retrieved from the pillars of the abandoned Estreux shallow mine (Northern France) has been conducted. Due to changes in hygrometry and water table (ambient relative humidity comprised between 80% and 100%), pillars are submitted to cyclic variations in degree of saturation. The potential impact of the changes in water content on the mechanical behaviour of the chalk has been assessed based on the methods and concepts of the mechanics of unsaturated soils. Water retention properties and volume change behaviour of the unsaturated chalk were investigated. Suction hardening was clearly identified, resulting in increasing yield stresses with suction, in agreement with the Loading Collapse (LC) yield curve of the Barcelona Basic Model (Alonso et al. 1990). Collapse compression under wetting at constant applied vertical load was also observed. As already discussed in the case of oil-reservoir chalks (De Gennaro et al. 2004), it is confirmed that the methods and concepts of the mechanics of unsaturated soils are relevant to better analyse the water weakening effects in chalks.
1
INTRODUCTION
Research into the stability of abandoned subsurface cavities in chalk is being carried out by the French Institute INERIS (Institut National de l’Environnement Industriel et des Risques) with a special attention devoted to the abandoned underground chalk shallow mine of Estreux (Northern France). The detailed monitoring of the periodic changes in relative humidity (hr ) in the mine showed that values as low as 80% could be reached, giving rise to possible desaturation of the pillars. In this regard, a study of the behaviour of the Estreux chalk under unsaturated states was found necessary. The mechanical behaviour of chalk is known to be significantly sensitive to changes in water content, an effect described as the water weakening effect. Water weakening has been particularly considered in the study of the reservoir chalks of the North Sea (Newman 1983, Andersen 1995; Schroeder et al. 1998, Gutierrez et al. 2000, De Gennaro et al. 2003 and 2004). Pore collapse under water flooding is a particular illustration of water weakening. Various investigations have been carried out on the pore collapse phenomena (Bonvallet 1979, Raffoux & Ervel
1980, Bell et al. 1999, Talesnick et al. 2001, Sorgi 2004, Priol 2005). Reservoir chalks contain two immiscible pore fluids (oil and water). They are comparable to unsaturated soils that contain air and water. In this regard, Delage et al. (1996) showed that the mechanics of unsaturated soil could be fruitfully used to investigate the behaviour of fluids-filled chalks. In underground quarries, low relative humidity (hr = 80%) might possibly dry the chalk pillars at least near the pillar surface, with an introduction of air as the non wetting pore fluid. In this paper, the methods and concepts of the mechanics of unsaturated soils are applied to some specimen of Estreux Chalk. Firstly, the water retention properties are investigated. Secondly, volume changes properties are considered under suction controlled conditions in the oedometer. 2
MATERIAL AND EXPERIMENTAL METHODS
The study was carried out on chalk specimens extracted from the Estreux abandoned underground mine in Northern France, 10 km East of the city
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of Valenciennes in the vicinity of the Valenciennes—Bruxelles A14 highway. The Estreux chalk formation belongs to the late Cretaceous geological period, which dated from 89 to 94 M years ago. A square pillar (1.4 × 1.4 m with a height of 1.8 m) has been continuously monitored since 2003 in relation within the research programme conducted by INERIS about ‘‘Ageing phenomena in geomaterials’’ (Sorgi 2004), hr measurements showed that the relative humidity inside the mine varied between 80 and 100% with an almost constant temperature of 11◦ C. Cubic blocks of chalk (30 cm each side) were manually retrieved at a 20 meters depth. Table 1 presents the index properties of Estreux chalk. By using a helium picnometer, a specific gravity Gs of 2.74 was obtained. As compared to the specific gravity of pure calcite (Gs = 2.71), this higher value is related to the presence of a fraction of glauconite (with Gs = 2.99). Glauconite is often observed in Northern French chalks (Masson, 1973; Bonvallet, 1979; Hazebrouck & Duthoit, 1979). The glauconite fraction is also linked to the relatively high values of the specific surface (Ss = 13 m2 /g measured using methylene blue absorption, as compared to 9 m2 /g for a pure chalk like for instance Lixhe chalk, Belgium). The average porosity n close to 37% is in good agreement with literature values (Masson, 1973; Bonvallet, 1979). Typical Unconfined Compression Strength (UCS) values for Estreux chalk are UCSsat ∼ = 5MPa when saturated and UCSdry ∼ = 11MPa if dried (typically UCSdry /UCSsat ∼ = 2). The high value of degree of saturation measured in extracted specimens (Srw = 97%) indicates that chalk was probably saturated in the mine at the time extraction was carried out, with some possible further loss of water during testing. The water retention properties of Estreux chalk were determined by using cylindrical samples of 20 mm in diameter and from 20 mm to 25 mm in height. In relation with the relative humidity observed in the mine (hr between 80 to 100%), the suction values applied were taken between 0 and 24.9 MPa by using 3 methods of controlling suction: the osmotic method for low suctions (from 0 to 1.5 MPa) (Williams & Shaykewich 1969, Delage et al. 1998, Marcial 2003), the vapour equilibrium method at
Table 1.
higher suctions (from 2 to 24.9 MPa) (Delage et al. 1998, Marcial 2003) and the filter paper method with contact for sample in their initial state (Fawcett & Collis-George 1967, Chandler & Gutierrez 1986, Houston et al. 1994, Bulut et al. 2001). In the osmotic method, the sample is placed in a tube shaped cellulotic semi-permeable membrane (Spectrapor ® ) and then immersed in an aqueous solution of large sized molecules of Poly Ethylene Glycol (PEG 6000 or 20000) (Figure 1). The imposed suction was derived from the solution concentration by using the calibration data of Williams & Shaykewich (1969) and the correction proposed by Dineen and Burland (1995). Five suctions level (0 MPa using pure water instead of a PEG solution, 0.5, 1, 1.2 and 1.5 MPa) were imposed with the osmotic method. The vapour equilibrium method was carried out by using the device presented in Figure 2, in which desiccators are placed in a temperature controlled bath. As can be seen in the Figure, a circulation of air with a controlled relative humidity is ensured by circulating air in a bottle containing a saturated saline solution. The air is subsequently circulated in the desiccator that contains the sample. Experience showed that circulating air significantly reduced the period of time necessarily to reach equilibrium. Two saturated saline solutions: (NH4 )2 SO4 (hr = 83.5%, s = 24.9 MPa) and K2 SO4 (hr = 97%, s = 4.2 MPa) were used.
Cellulotic semipermeable PEG
Thermostat
Sample
Magnetic stirrer
Figure 1. Determination of the water retention curve by using the osmotic method.
Index data of Estreux chalk.
Properties Density of particles, ρs (Mg/m3 ) Degree of saturation, Srw (%) Dry density, ρd (Mg/m3 ) Porosity, n(%) Natural water content, w(%) Specific surface, Ss (m2 /g)
2.74 97 1.73 37 20.7 14
Pump
Saturated saline solution
Thermostat
Figure 2. Determination of the water retention curve by using the vapour equilibrium technique.
284
Two PEG solutions at controlled concentrations corresponding to 2.5 MPa (hr = 98.2%) and 2 MPa (hr = 98.4%) were also used in the same fashion to impose lower suctions. Two filter papers measurements were carried out to determine the initial suction of the intact sample. In order to avoid any contact with chalk, both papers were placed between two protection papers and then positioned between two halves of chalk samples. The whole system was then isolated from the ambient relative humidity and stored in a temperature controlled room (20◦ C ± 0.1◦ C) for at least 15 days before weighing the filter papers (accuracy 1 × 10−5 g). Finally, a high stress double lever arm oedometer equipped with a suction control system was used (e.g. Marcial et al. 2002) to investigate the compressibility of partially saturated Estreux chalk samples. The control of the suction was carried out either by using the osmotic method (suctions smaller than 1.5 MPa) (see Kassiff & Benshalom 1971, Delage et al. 1992, Dineen and Burland 1995, De Gennaro et al. 2003, Priol 2005). The same cell was also used at higher suctions with the vapour equilibrium method (Esteban 1990, Oteo-Mazo et al. 1995, Oldecop & Alonso 2001, Marcial 2003) for suctions higher than 4.2 MPa. In this case, air with controlled hr was circulated in the oedometer cell through the bottom of the sample (see Figure 3). Samples of 38 mm in diameter and 19 mm ±2 mm in height were reshaped on a lathe. A dry sample was obtained after a period of 48 hours in an oven at 60◦ C following the recommendations of the International Society of Rock Mechanics. Since the mechanical response of chalk is strain rate-dependent (e.g. De Gennaro et al. 2003, Priol et al. 2007), it was decided for multiple loading stages oedometer tests to
consider a period of sustained loading of 48 hours in the pseudo-elastic regime and 7 days in the plastic regime, resulting in total tests durations from 45 to 60 days. Deformation regimes (elastic and plastic) were defined based on results from constant rate of strain oedometer tests (Priol et al. 2007), that allowed to identify the expected yield stress. Isotach behaviour (i.e. only dependent on the strain rate) was adopted to define the compressibility curves obtained by means of oedometer tests. Following this methodology for each loading stage the corresponding vertical strain was measured when the axial strain rate was lower than 10−10 sec−1 . Based on the experimental results from the determination of the water retention properties, four oedometer compression tests were carried out as follows: two tests in dry conditions (T1 & T2), one test at controlled suction (T3: s = 4.2 MPa with the vapour equilibrium method and K2 SO4 salt) and one test at saturated conditions (T4).
3
RESULTS AND DISCUSSION
3.1 Water retention properties The water retention curve of Estreux chalk is shown in Figure 4 in terms of changes in degree of saturation (Srw ) with respect to the logarithm of suction (log s). Beside the points obtained at various controlled suctions along the drying and wetting paths, the initial suction obtained with the filter paper method is also represented. A suction value of 40 kPa with a degree of saturation of 97% indicated that the sample was probably saturated when excavated.
100 Hr = 83.5% ( s = 24.9 MPa)
10
Hr = 97% ( s = 4.2 MPa)
v
Hr = 98.2% ( s = 2.5 MPa)
Sample 1 SUCTION, s :MPa
Sieve
Hr = 99.8% ( s = 1.5 MPa)
0.1
Dry path
0.01
Wetting path Initial state
0.001
Pump
Figure 3.
Saturated saline solution
0
Thermostat
Scheme of the vapour equilibrium oedometer.
Figure 4.
285
0.2
0.4 0.6 DEGREE OF SATURATION, S rw
0.8
Water retention curve of Estreux chalk.
1
SUCTION, s
T2
T3
∼ – Test T1 (ei = 0.575): dry compression (s = 30 MPa) up to 39.7 MPa, unload down to 0.44 MPa, soaking under 0.44 MPa and subsequent loading up to 39.7 MPa. – Test T2 (ei = 0.61): dry compression (s ∼ = 30 MPa) up to 22.41 MPa, unload down to 10.19 MPa, reload to 29.28 MPa and soaking. – Test T3 (ei = 0.602): suction controlled compression (s = 4.2 MPa) up to 39.7 MPa, unload down to 8.82 MPa and reload to 39.7 MPa. – Test T4: (ei = 0.581): saturated compression up to 20.38 MPa, stress release at 0.26 MPa and reload at 40.76 MPa.
s = 4.2 MPa
saturated, s = 0 MPa T4
100
1000 10000 VERTICAL STRESS, v : kPa
Figure 5.
100000
Loading paths.
0.65
0.6
WATER INJECTION
0.55
3.2 Oedometer tests The two independent stress variables commonly used in the investigation of the mechanical behaviour of unsaturated soils are the suction, s = ua − uw (where ua and uw are the air and water pressure respectively) and the mean net stress pnet = p − ua (where p is the total mean stress). The loading paths followed in a vertical stress suction (σv : s) are presented in Figure 5. The compressibility curves in [log σv : e] diagrams are presented in Figure 6. The testing program comprises three compression tests carried out as follows:
Dry, s = 30 MPa
T1
VOID RATIO, e
The slight differences observed between the drying and wetting paths denote a moderate hysteresis effect, also observed in partially air-water saturated Lixhe chalk by Priol (2005). A possible effect of the glauconite fraction in reducing the hysteresis effect is suspected, although a clear explanation of the slight hysteresis is not straightforward. The drying curve shows that the air entry value of Estreux chalk can be estimated at approximately 1.5 MPa. Following desaturation, the degree of saturation exhibits a dramatic reduction with a value as low as 30% at 2.5 MPa. At the highest suction (s = 24.9 MPa, hr = 83.5%) the degree of saturation is as low as 2–5%, showing that chalk is nearly completely desaturated. Based on the water retention curve, the suction of a dry sample can be estimated at 30 MPa. The shape of the water retention curve of Estreux chalk and the sudden decrease in saturation above 1.5 MPa shows that the changing values of the ambient relative humidity in the mine (between 80% and 100%) can definitely lead to significantly unsaturated states, at least at the surface of the pillar directly in contact with the ambient relative humidity. It is then suspected that the mechanical properties of the chalk in unsaturated states have to be considered when addressing the long term stability of the pillars. As a first step, the compressibility properties of the chalk under various controlled suctions are now presented.
WATER INJECTION 0.5 SWELLING 0.45 COLLAPSE
T1 (dry) T2 (dry) T3 (s = 4.2 MPa) T4 (saturated)
0.4
0.35 100
Figure 6. ters.
1000 VERTICAL STRESS,
10000 v : kPa
100000
Compressibility curves obtained with oedome-
The compressibility curves of Figure 6 show some responses that are compatible with that of unsaturated soils:
286
– Increase in yield stress with increased suction. – Increase in compressibility with decreased suction. – Slight suction dependency of the pseudo-elastic compressibility module. – Slight swelling due to suction release in the elastic zone. – Significant collapse when soaking under high stress when the sample is located on the LC curve.
Table 2.
Compressibility data taken from oedometer tests.
State
Elastic
T1 T2
40
Stiffness Plastic
Yield stress (MPa)
LOADING
LC i
LC 1 LC 3
0.0022 0.0055
0.1082 0.094
16 13.5
0.0095 0.0039
0.1137 0.135
11.4 7.5
30 SUCTION, s :MPa
Dry (T1) Dry (T2) Suction controlled (T3) Saturated (T4)
Water injection 20 Collapse
Swelling
10
Interestingly, the position of the collapsed sample is close to the saturated compression sections of tests T2 and T4.
LC 2 LOADING
0
The corresponding numerical values are given in Table 2. These trends illustrate the sensitivity of the mechanical response of the Estreux chalk to change in suction. They are in good agreement with the water weakening effects described by Matthews and Clayton (1993) and with earlier observations on reservoir chalks (with water and oil as pore fluids) by De Gennaro et al. (2004) and Priol (2005). Water sensitivity is denoted by the swelling observed in test T1 (soaking under 441 kPa) and by the collapse observed in T2 when soaking under 29.28 MPa. The increase in compressibility and decrease in yield stress with increased degree of saturation (decreased suction) are two other manifestations of the water weakening effect. 3.3
BBM modelling
The results of Figure 6 are now qualitatively interpreted in the framework of the Barcelona Basic Model (Alonso et al., 1990). Figure 7 shows the Loading Collapse (LC) curve that can be derived from the experimental data of Figure 6. With suction at dry state equal to 30 MPa, the LC curves exhibit fairly regular and satisfactory shapes. A tentative identification of the initial LC curve can be obtained assuming the following constitutive parameters for the BBM: λ(0) = 0.12, pc = 0.002 MPa, p∗o = 8 MPa. Owing to the reduced effect of suction on the virgin compressibility of the material, λ(s) values were found assuming β = 0.5 and r = 0.94. The loading path of test T1 crosses the initial dry LCi curve at (σvo − ua ) = 16 MPa, displacing the LC curve up to LC1 at the maximum 39.7 MPa value (hardening process). After unloading down to 0.44 MPa, water soaking was performed under 0.44 MPa resulting in reducing suction from 30 MPa down to 0 MPa. The swelling under stress release observed (increase in void ratio from 0.466 to 0.476) is also in good agreement with
0
Figure 7.
10
20 VERTICAL STRESS,
30 v: MPa
40
Loading Collapse yield in the test T1 and T2.
the BBM model, the suction release occurring inside the elastic zone delimited by the LC curve. The subsequent compression at zero suction carried out during the T1 test evidenced a yield at 20 MPa that is finally moved towards the LC2 position at 39.7 MPa. Further validation of the BBM is provided by the results of test T2 that defines a yield stress at dry state (σvo − ua = 13.5 MPa). This slightly smaller value is related to the higher porosity of the sample (37.9% instead of 36.5%) as explained by Matthews & Clayton (1993). At s = 30 MPa, the yield curve is moved during dry compression up to the position LC3 (29.3 MPa). The soaking induces here significant collapse (decrease in void ratio from 0.500 to 0.389) that further moves the LC curve to the right, with an intersection with the x axis at 29.3 MPa.
287
4
CONCLUSIONS
The water retention properties and compression behaviour of unsaturated samples of chalk from an abandoned underground mine were investigated in relation with the long term stability of abandoned underground quarries. A slight hysteresis was observed on the water retention curves, together with a significant desaturation that occurred along the drying path just above the airentry value of the chalk (1.5 MPa). This confirmed that the desaturation of the pillars had to be considered when assessing the long term stability of the abandoned mine.
Four suction controlled oedometer tests showed that the volume change behaviour of the unsaturated chalk was fairly comparable to that of unsaturated soils. The Barcelona Basic Model could be successfully used to account to some extent for water weakening effect in partially saturated chalk, both in terms of swelling when releasing suction at low stress and collapse compression during soaking under high stress. It should be mentioned however that the behaviour of Estreux chalk during oedometric loading doesn’t reflect completely the in situ conditions. Further knowledge on the effect of changes in degree of saturation on the collapse behaviour of the material at low stress levels is needed in order to have an insight into the water weakening mechanisms in chalk.
ACKNOWLEDGEMENT The results on Estreux chalk have been obtained during the French National Project BCRD coordinated by INERIS. The collaboration of Dr G. Priol is also acknowledged.
REFERENCES Alonso, E.E., Gens, A. & Josa, A., 1990. A constitutive model for partially saturated soils. Géotechniques 40, No. 3, 405–430. Andersen, M.A., 1995. Petroleum research in North Sea chalk. Joint chalk research, phase IV, 47–153. Bell, F.G., Culshaw, M.G. & Cripps, J.C., 1999. A review of selected engineering geological characteristics of English chalk. Engineering Geology, 54, 237–269. Bonvallet, J., 1979. Une classification géotechnique des craies du nord utilisée pour l’étude de stabilité des carrières souterraines. Revue Française de Géotechnique, 8: 5–14. Bulut, R., Lytton, R.L. & Wray, W.K., 2001. Soil suction measurements by filter paper. Proc. Of Geo-Institute Shallow Foundation and Soil Properties Committee Sessions, ASCE Conference, Geotechnical Special Publication Number 115, 243–261. Chandler, R.J. & Gutierrez, C.I., 1986. The filter papar method of suction measurement. Géotechnique 36, 265–268. De Gennaro, V., Delage, P., Cui, Y.J., Schroeder, Ch. & Collin, F. 2003. Time-dependent behaviour of oil reservoir chalk: a multiphase approach. Soils and Foundations, 43 (4), 131–148. De Gennaro, V., Delage, P., Priol, G., Collin, F. & Cui, Y.J., 2004. On the collapse behaviour of oil reservoir chalk. Géotechnique, 54 (6), 415–420. Delage, P., Suraj De Silva, G.P.R. & Vicol, T. 1992. Suction controlled testing of non saturated soils with an osmotic consolidometer. 7th Int. Conf. Expansive Soils, Dallas, 206–211.
Delage, P., Schroeder, C., & Cui, Y.J. 1996. Subsidence and capillary effects in chalks. EUROCK ’96, Prediction and performance on rock mechanics and rock engineering 2, 1291–1298, Turin, Italy. Delage, P., Howat, M.D. & Cui, Y.J., 1998. The relationship between suction and swelling properties in a heavily compacted unsaturated clay. Engineering Geology, 50, 31–48. Dineen, K. & Burland, J.B., 1995. A new approach to osmotically controlled oedometer testing. Proc. 1 st Int. Conf. on Unsaturated Soils UNSAT’95, Paris, 459–465. Esteban Moratilla, F., 1990. Caracterizacion experimental de la expensividad de una roca evaporitica. Identificacion de los mecanismos de hinchamiento. PhD thesis, Universidad de Cantabria, Santader, 352 p. Fawcett, R.G. & Collis-George, N., 1967. A filter paper method of determining the moisture characteristics of soil. Austr. J. of Exp. Agr. and Animal Husb. 7, 162–167. Gutierrez, M., Øino, L.E. & Hoeg, K., 2000. The effect of fluid content on the mechanical behaviour of the fractures in chalk. Rock Mechanics and Rocks Engineering, 33 (2), 93–117. Hazebrouck, R. & Duthoit, B., 1979. Particularité du comportement mécanique des craies: rôle de l’eau—rupture sous contrainte hydrostatique. Revue Française de Géotechnique, 8, 45–50. Houston, S.L., Houston, W.N. & Wagner, A.M., 1994. Laboratory filter paper suction measurements. Geotechnical Testing Journal, 17 (2), 185–194. Kassiff, G. & Ben Shalom, A., 1971. Experimental relationship between swell pressure and suction. Géotechnique, 21, 245–255. Marcial, D., Delage, P. & Cui, Y.J., 2002. On the high stress compression of bentonites. Can. Geotech. J. 39, 812–820. Marcial, D., 2003. Comportement hydromécanique et microstructural des matériaux de barrières ouvragées. PhD Thesis, Ecole Nationale des Ponts et Chaussées, Paris: 316 p. Masson, M., 1973. Pétrophysique de la craie. In La craie, Bull. Labo. Ponts et Chaussées, Special V, 23–48. Matthews, M.C. & Clayton, C.R.I, 1993. Influence of intact porosity on the engineering properties of a weak rock. Proc. Geotechnical engineering of hard soils—soft rocks, vol. 1, Anagnostopoulos et al. (eds), Balkema, 693–702. Newman, G.H., 1983. The effect of water chemistry on the laboratory compression and permeability characteristics of some North Sea chalks. J. of Petroleum Eng., 976–980. Oldecop, L.A. & Alonso, E.E., 2001. A model for rockfill compressibility. Géotechnique 51, No. 2, 127–139. Oteo Mazo, C., Saez Aunon, J. & Esteban, F., 1995. Laboratory tests and equipment with suction control. Proc. 1st Int. Conf. on Unsaturated Soils UNSAT’95, 3, Paris, Balkema, Rotterdam, 1509–1515. Priol, G., De Gennaro, V., Delage, P. & Cui, Y.J. 2004. On the suction and the time dependent behaviour of reservoir chalks of North sea oilfields. Proc. 2nd Int. Workshop on Unsaturated Soils, Capri (Italy), 43–54. Priol, G., 2005. Comportement mécanique différé et mouillabilité d’une craie pétrolifère. PhD Thesis, Ecole Nationale des Ponts et Chaussées, Paris, 217 p. Priol, G., De Gennaro, V., Delage, P., & Servant T., 2007. Experimental investigation on the time dependent behaviour of a multiphase chalk. Springer Proceedings
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Physics 112, Experimental Unsaturated Soil Mechanics, T. Schanz (ed.), 161–167. Raffoux, J.F. & Ervel, C., 1980. Stabilité générale de la carrière souterraine d’Estreux. Rapport CEECHAR, 8 p. Schroeder, Ch., Bois, A.P., Maury, V. & Halle, G., 1998. Water/chalk (or collapsible soil) interaction: Part II. Results of tests performed in laboratory on Lixhe chalk to calibrate water/chalk models. SPE/ISRM (SPE 47587) Eurock’98, Trondheim. Sorgi, C., 2004. Contribution méthodologique et expérimentale à l’étude de la diminution de la résistance des massifs
rocheux par vieillissement. BCRD Final Report (conv. 2001–01111), INERIS-DRS (in French), 132 p. Talesnick, M.L., Hatzor, Y.H. & Tsesarsky, M., 2001. The elastic deformability and strength of a high porosity, anisotropic chalk. Int. J. of Rock Mech. & Min. Sci., 38, 543–555. Williams, J. & Shaykewich, C.F., 1969. An evaluation of polyethylene glycol PEG 6000 and PEG 20000 in the osmotic control of soil water matric potential. Can. Geotech. J., 102 (6), 394–398.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Effect of grain size distribution on water retention behaviour of well graded coarse material C. Hoffmann & A. Tarantino Dipartimento di Ingegneria Meccanica e Strutturale, Università degli Studi di Trento, Italy
ABSTRACT: The paper presents an experimental investigation on water retention behaviour of well graded coarse-grained soils. Two ‘reduced’ grain size distributions were tested to investigate how the removal of the larger grain size fraction needed to reduce field samples to appropriate grain size for laboratory testing affects water retention behaviour. As expected, the removal of larger particles significantly modified the water retention characteristics of the soil. An approach to ‘scale’ water retention curves obtained in the laboratory to the soil in the field is then presented. This approach was successfully tested against the soil investigated in this programme.
1
INTRODUCTION
Coarse well graded unsaturated soils often compose earthen constructions (earth dams, road and railway embankments, and flood defence embankments). These soils also compose shallow landslides that evolve into debris-flows. Their water retention behaviour is a key to understanding the effect of changing boundary hydraulic conditions (rainfall, water table, water reservoir level, river level) on shear strength and, hence, on stability. Water retention behaviour of coarse well graded soils is often inferred from index properties (grain size distribution and dry density) in preliminary design and large area projects. These indirect methods are also used when direct laboratory measurements are costly and/or time consuming. A number of methods have been proposed in the literature for the estimation of the water retention curve based on statistical and physico-empirical approaches. However, these methods have essentially been validated on agricultural soils (Vereecken et al. 1989, Arya and Paris 1981). A very limited database is available for coarse well graded materials. Another problem arising when investigating water retention behaviour of coarse-grained materials is the need of reducing field samples to appropriate grain size for laboratory testing. A question that might be asked is how to extrapolate the water retention curves obtained in the laboratory on reduced-size samples to the soil in the field. This paper presents an experimental investigation on the water retention behaviour of a well graded coarse material. Two different ‘reduced’ grain size distributions were considered to investigate how the
removal of the larger grain size fraction affects water retention behaviour. The soil was tested along wetting paths under different void ratios to investigate the main wetting surface in the space suction-void ratio-degree of saturation. The experimental data were then compared with the water retention curves estimated using indirect methods presented in the literature.
2
EXPERIMENTAL EQUIPMENT
The box illustrated in Figure 1, which is equipped with one Trento high-capacity tensiometers (Tarantino &
Tensiometer
O-rings Compacted specimen
Spacer
Figure 1.
291
Schematic layout of suction measurement box.
Tensiometer support
CLAY
Tensiometers Weight
SAND
GRAVEL
d10 (d < 10 mm) d25 (d < 25 mm)
0.8
Fraction finer
75-85 mm
Membrane
SILT
1
Compacted sample
0.6
0.4
0.2
Ø = 252 mm 0 0.0001
0.001
0.01
0.1
1
10
Particle size, d: mm
Figure 2. Schematic layout of the oedometer cell used to measure suction of statically compacted specimens.
Figure 3. ‘Reduced’ grain size distributions investigated in this programme.
Mongiovì 2002), was used to carry out matric suction measurement on dynamically compacted samples. Tensiometers were locked in place to ensure contact with the sample by using caps tightened to the cell upper base (not shown in the figure). O-rings ensured air tightness so that water vapour could reach equilibrium with the soil water. Matric suction measurements on statically compacted samples were carried out in the same oedometer cell used to compact the sample (Figure 2). Two tensiometers were installed through a metal support connected to a flexible membrane used to ensure air tightness. To ensure contact of the tensiometers with the sample, two weights obtained by filling plastic bags with steel spheres were placed over the metal support. 3
MATERIAL AND SPECIMEN PREPARATION
Two ‘reduced’ grain size distributions having maximum particle size of 10 and 25 mm respectively were tested in this experimental programme (Figure 3). These soils will be referred to as d10 and d25 respectively. Air-dried soil was laid in a large plastic basin and sprayed with demineralised water to reach the target water content. The moistened powder was handmixed and then wrapped inside two sealed plastic bags, placed in a plastic container and stored in a high-humidity room for 1 day. The soil d10 was dynamically compacted into a 101.6 mm diameter mould in three layers to 30%, 50%, or 100% of Proctor energy. The sample was trimmed to 117 mm height, extruded and stored for 2 days at least to allow moisture equalisation. A first series of samples were directly put into the suction
Figure 4. ‘As-compacted’ states of statically and dynamically compacted samples. Arrows show the path followed by the samples wetted after compaction.
measurement box for tensiometer measurement (specimens compacted to 100% and 50% Proctor energy in Figure 4). A second series of samples were wetted by spraying demineralised water to reach a target water content checked by weighing. The wetting stage was then followed by a period of 2 days for moisture equalisation. The samples were then put into the suction measurement box for tensiometer measurement (specimens compacted to 30 % Proctor energy in Figure 4). The soil d25 was statically compacted into the 252 mm diameter oedometer cell shown in Figure 2. The moistened powder was placed in the oedometer and compressed by increasing the air pressure in
292
the upper compartment of the cell. A rigid plate (not shown in the figure) was interposed between the flexible membrane and the top surface of the sample to ensure uniform vertical deformation. The sample was compacted in stages to four different vertical stresses: 75, 150, 300, and 600 kPa. The as-compacted states of the statically compacted samples are shown in Figure 4.
Degree of saturation, Sr
1 0.8 0.6 100% Proctor 50% Proctor 30% Proctor(wetted) 75 kPa 150 kPa 300 kPa 600 kPa 75 and 150 kPa
0.4 0.2
(a)
300 and 600 kPa
0
EXPERIMENTAL PROCEDURE
Tensiometers were calibrated in the positive range of water pressure and the calibration curve was then extrapolated to the negative range of water pressure according to Tarantino & Mongiovì (2003). Before testing, the saturation of the tensiometer porous ceramic was checked following the procedure illustrated by Tarantino (2004). After assembling the suction measurement box (Figure 1) or the oedometer cell (Figure 2), the tensiometers were installed and fixed by screws. To improve contact with the sample a paste made by the finer fraction of the soil was applied on the porous stone of the tensiometer. A single suction measurement was performed on each dynamically compacted specimen (d10) . In contrast, multiple suction measurements were performed on each statically compacted specimen (d25). After applying the 75 kPa vertical stress, the loading pad was removed and the tensiometers were installed as shown in Figure 2. Afterwards, the tensiometers were removed, the specimen was compacted to 150 kPa vertical stress, and suction measurement was carried out again. This procedure was repeated for the vertical stresses of 300 and 600 kPa. 5
EXPERIMENTAL RESULTS
The experimental results in terms of degree of saturation are shown Figure 5a. All these data may be assumed to be ‘main’ wetting data. Compaction produces an increase in the degree of saturation by reducing void ratio at constant water content. This mechanism can be referred to as ‘mechanical’ wetting. Since compaction induces the lowest void ratio, compacted samples also experience the highest degree of saturation. Data relative to ‘as-compacted’ states (statically compacted samples and samples dynamically compacted to 50 and 100% Proctor energy) can therefore be assumed to be ‘main wetting’ data. Samples compacted at 30% Proctor energy were further wetted by spraying water. This mechanism of degree of saturation increase can be referred to as ‘hydraulic’ wetting. Since hydraulic wetting followed a mechanical ‘main’ wetting, these data can
Effective water ratio, ew-ewh
4
(b) 0.1
1
10
100
Matric suction, s: kPa
Figure 5. Water retention data for statically and dynamically compacted samples.
still be assumed to be ‘main wetting’ data. Here, we are implicitly assuming that the two modes of degree of saturation increase, hydraulic and mechanical, are equivalent as demonstrated by Tarantino & Tombolato (2005) and Tarantino (2008). Figure 5a shows that the relationship between suction and degree of saturation for the d10 and d25 soils is not unique but depends on void ratio. The higher the compaction energy, the lower the void ratio, and the higher the air-occlusion suction. This is consistent with the capillary model which predicts an increase in the air-occlusion suction as the diameter of the capillary tube decreases. Data shown in Figure 5a therefore suggests that main wetting data should be modelled in the space suction, void ratio, and degree of saturation. Figure 5b shows the same data plotted in terms of effective water ratio, which is defined as the difference between water ratio ew and hygroscopic water ratio ewh , the water ratio being the volume of water to volume of solids ratio (ew = Vw /Vs ) . The effect of void ratio is now much less pronounced and data seems to converge in a log-log plot at high suctions. This was also observed by Tarantino (2008) for a number of different soils. This means that the effective water ratio ew − ewh at high suction is described by a power function of suction. The power interpolation is shown in Figure 5b for d10 and d25 soils.
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MODELLING VOID-RATIO DEPENDENT WATER RETENTION BEHAVIOUR
1 d10(d 5 MPa), it was observed that constant slope was kept in the case of controlled suction whereas the slope became smaller when the pressure was higher than 10 MPa in the case of constant water content. It was noted also that the effect of void ratio on the compressibility is more significant than the effect of suction. ACKNOWLEDGMENT The authors are grateful to Ecole Nationale des Ponts et Chaussées and French Electricity Company (EDF) for their financial support.
REFERENCES Alonso, E.E., Vaunat, J. & Gens, A. 1999. Modelling the mechanical behaviour of expansive clays. Engineering Geology 54(1–2), 173–183. Blatz, J.A. & Graham, J. 2003. Elastic-plastic modeling of unsaturated soil using results from a new triaxial test with controlled suction. Géotechnique 53(1), 113–122. Delage, P., Marcial, D., Cui, Y.J. & Ruiz, X. 2006. Ageing effects in a compacted bentonite: a microstructure approach. Géotechnique 56(5), 291–304. Delage, P., Le, T.T., Tang, A.M., Cui, Y.J. & Li, X.L. 2007. Suction effects in deep Boom Clay block samples. Géotechnique 57(1), 239–244. Kawai, K., Weichuan, W. & Ogawa, K. 2002. The behavior of unsaturated soil compressed isotropically under undrained condition. In Jucá, J.F.T., de Campos, T.M.P. & Marinho, F.A.M. (ed.), Unsaturated Soils. Proc. 3rd Int. Conf. on Unsaturated Soils (UNSAT 2002), Recife, Brazil, Vol. 2: 521–528. Lisse: Swets & Zeitlinger. Kröhn, K.P. 2003. New conceptual models for the resaturation of bentonite. Applied Clay Science 23, 25–33. Lloret, A., Villar, M.V., Sanchez, M., Gens, A., Pintado, X. & Alonso, E.E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique 53(1), 27–40. Perdok, U.D., Kroesbergen, B. & Hoogmoed, W.B. 2002. Possibilities for modeling the effect of compression on mechanical and physical properties of various Dutch soil types. Soil & Tillage Research 65, 61–75. Pusch, R. & Yong, R. 2003. Water saturation and retention of hydrophilic clay buffer—microstructural aspects. Applied Clay Science 23, 61–68. Rahardjo, H. & Fredlund, D.G. 2003. K0 -volume change characteristics of an unsaturated soil with respect to various loading paths. Geotechnical Testing Journal 26(1), 79–91. Romero, E. & Vaunat, J. 2000. Retention curves of deformable clays. In Tarantino & Mancuso (ed.), Experimental Evidence and Theorical Approaches in Unsaturated Soils: 91–106. Rotterdam: Balkema. Tang, A.M. & Cui, Y.J. 2005. Controlling suction by the vapour equilibrium technique at different temperatures and its application in determining the water retention properties of MX80 clay. Canadian Geotechnical Journal 42(1), 287–296. Tang, A.M., Cui, Y.J., Eslami, J. & Défossez, P. 2007a. Compressive behaviour of four agricultural soils from France under confined uniaxial test. In T. Schanz (ed.), Experimental Unsaturated Soil Mechanics; Springer Proceedings in Physics 112: 475–482. Tang, A.M., Cui, Y.J. & Barnel, N. 2007b. A new isotropic cell for studying the thermo-mechanical behavior of unsaturated expansive clays. Geotechnical Testing Journal 30(5), 341–348. Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Géotechnique 55(4), 307–317.
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Theoretical modelling of the compaction curve N. Kurucuk & J. Kodikara Department of Civil Engineering, Faculty of Engineering, Monash University, Clayton, VIC, Australia
D.G. Fredlund Golder Associates, Saskatoon, Saskatchewan, Canada
ABSTRACT: Soil compaction is one of the major activities in geotechnical engineering involving earthworks. The compaction curve is used to find the optimum water content that maximizes dry density. Since its introduction by Proctor in 1933, several researchers have provided qualitative explanations for the inverted parabolic shape of the compaction curve. However, fundamental research on the compaction process and the evolution of compaction characteristics are limited, particularly from a quantitative sense. In order to understand the driving mechanisms of soil compaction, this paper investigates the effect of soil suction, stiffness and pore air pressure on the shape of the compaction curve, from an unsaturated soil mechanics standpoint. This paper presents an approach to predict the soil compaction curve during undrained loading. Particular attention is focused on the derivation of the compressibility coefficient due to net stress. Model predictions of the compaction curve are compared with some experimental results from the literature.
1
INTRODUCTION
Soil compaction is widely used in geo-engineering and is important for the construction of roads, dams, landfills, airfields, foundations, hydraulic barriers, and ground improvements. Compaction is applied to the soil, with the purpose of finding optimum water content in order to maximize its dry density, and therefore, to decrease compressibility, increase shearing strength, and in some cases, to reduce permeability. Proper compaction of materials ensures the durability and stability of earthen constructions. A typical compaction curve presents different densification stages when the soil is compacted with the same apparent energy input but different water contents. The water content at the peak of the curve is called the optimum water content (OWC) and represents the water content at which dry density is at its maximum for a given compaction energy. Since Proctor’s pioneering work in 1933, many researchers have attempted to explain qualitatively the leading mechanisms in the densification stages, mainly on the dry side of optimum water content. The compaction curve was explained in terms of capillarity and lubrication (Proctor, 1933), viscous water (Hogentogler, 1936), pore pressure theory in unsaturated soils (Hilf, 1956), physico-chemical interactions (Lambe, 1960), and concepts of effective stress theory (Olson, 1963). More recently, Barden & Sides (1970) undertook experimental research on the relation between the
engineering performance of compacted unsaturated clay and microscopic observations of clay structure. In addition, Lee & Suedkamp (1972) conducted research on the shape of the compaction curve for different soils. Despite this research work, and the importance and high demand for the compaction process in engineering practice, the compaction of soil is quite complex and not well explained, particularly from a quantitative sense. Theoretical modelling of the soil compaction curve will provide a better understanding of the main parameters that affect the shape of the compaction curve, and understanding the behaviour of compacted materials. Therefore, there is need for research to be undertaken at a fundamental level to understand the compaction characteristics of soil and the inverted parabolic shape of the compaction curve. This paper presents a theoretical explanation of the compaction curve using unsaturated soil mechanics principles. Particular attention is focused on the prediction of the compressibility coefficient due to net stress. Likely predictions of the model are compared with the experimental results from literature. 2
THEORETICAL BACKGROUND FOR MODELLING
Theoretical concepts utilized for the development of soil compaction curves are presented in this section.
375
Initially, Hilf ’s (1948) approach for pore pressure development is presented. This is continued with Fredlund & Morgenstern’s (1976) volume change theory for a compacted soil and the derivation of the dry density of soil. 2.1
Pore pressure development during static compaction
One of the main simulations for the generation of the compaction curve is that of pore pressure development. Hilf (1948) developed a relationship between pore pressure and applied stress, which is based on one-dimensional K 0 soil compression, Boyle’s law, and Henry’s law, and is expressed as follows: ua =
1 1+
(1−S0 +hS0 )n0 (ua0 +ua )mv
σy
(1)
where; ua = change in absolute pore air pressure, S0 = initial degree of saturation, h = coefficient of solubility, n0 = initial porosity, ua0 = initial absolute air pressure, mv = coefficient of volume change in saturated soil, and σy = change in applied vertical stress. Hilf (1948) developed this equation assuming that air and water phases are undrained, and volume reduction is due to air dissolving in the water and compression of free air. Both liquid and solid parts were considered to be volumetrically incompressible. Hilf also assumed that the change in pore air pressure is equal to the change in pore water pressure, and therefore, matric suction change was insignificant. Experimental results on suction change during compaction can be found in literature (e.g. Li 1995, Montanez 2002). It is shown that matric suction only decreases marginally with a density increase and may be approximated to be constant. Therefore, Hilf’s analysis assuming constant suction during compaction appears to be close to the real situation. Further justification for assuming constant matric suction during the compaction test is presented in Kurucuk et al. (2007). 2.2
3
MODELLING ASSUMPTIONS
Kurucuk et al. (2007) showed that the assumption of constant coefficients of compressibility during compaction does not produce a proper shape of the compaction curve especially on the dry side of the optimum water content. Their analysis showed that it is m1s that controls the volume changes during compaction because the associated change in suction may be neglected. The parameter m1s was represented as a function of saturation and decreases with decreasing saturation. However, the experimental results presented by Loret et al. (2003) showed that m1s decreased with both suction and net stress. Therefore, following the functional form suggested by Sheng et al. (2007), the volumetric strain, ignoring suction change, may be presented as: εv =
d (σnet − ua ) dV = λvp V (σnet − ua ) + s0
Vv = ms1 σy − ua + ms2 (ua − uw ) V
(2)
where; εv = volumetric strain, Vv = overall volume change of soil element, V = initial total volume of soil
(3)
where; εv = volumetric strain, (σnet − ua ) = mean net stress, ua = pore air pressure, s0 = suction, λvp = slope of the normal compression line (NCL) of the saturated soil, and V = initial total volume of the soil element. This gives m1s as:
Computation of volume change and dry density
The volume change constitutive relationship as applicable to K0 loading, which is defined in terms of two independent stress variables as proposed by Fredlund & Morgenstern (1976) for unsaturated soils, is used for the calculation of compaction curves: εv =
element, m1s = compressibility of soil particles with respect to net stress (σy − ua ), m2s = compressibility of soil particles referenced to matric suction (ua −uw ), (σy − ua ) = change in net stress, and (ua − uw ) = change in soil suction. Since soil particles are incompressible, it is accepted that deformation is primarily due to compression of the pore fluid (i.e., the air and air/water mixture). The independent stress state variable concept is utilized in the derivation; namely, net stress (σy − ua ) (causes a reduction in volume with compression), and matric suction stress (ua − uw ) (generally results in volume increase with compression). Once the overall volume change is computed, the corresponding dry density can be easily computed.
λvp σy − ua + s0
ms1 =
(4)
This assumption will be used and discussed further in the modelling of the compaction curve. It is reasonable to replace mv in Equation 1 by m1s . A numerical example of the variation of m1s during compaction process is given in the following section. Equations (1), (3) and (4) were used in incremental forms to compute the incremental and total volume change and the corresponding dry density values during compaction.
376
4
NUMERICAL EXAMPLES
The performance of the proposed model is demonstrated by comparing the experimental results presented by Montanez (2002) and Kenai et al. (2006). Figures 1 and 2 show the compaction curves for sandbentonite mixture with bentonite content of 5% and 15% by weight. Montanez’s experimental data present values for the Standard Proctor Test (BS, external gross energy input = 637 kJ/m3 or kPa). In Figures 1 and 2, two model predictions are also shown. The curves shown by dashed lines represent the static compaction curve predicted by the model for undrained (air/water) loading up to external quasi-static pressure, σy , of 637 kPa. The curves shown by solid lines are for equal energy input, calculated by integrating the applied stress σy with respect to volumetric strain. The actual energy input into the soil was computed on the basis of the values applicable at the optimum water content, which were found to be 16 kJ/m3 and 18 kJ/m3 respectively.
Figure 3 shows an example of compaction curve for clay sandy soil (liquid limit = 39%, plasticity index = 15%) adopted from Kenai et al. (2006). Experimental results shown in figure are for static (σy = 2100 kPa) and dynamic (external gross energy input 3000 kJ/m3 ) compaction tests. Both predicted compaction curves are produced from quasi-static compaction up to external pressures, σy , of 2100 kPa and 4000 kPa respectively. Model parameters used for prediction of the above compaction curves are shown in Table 1, 2 and 3. Initial pore air pressure (ua0 ) is taken to be equal to atmospheric pressure (101.3 kPa). For a certain soil, a lower initial porosity was assumed and the computations were performed for a range of moisture contents which also define the values of initial degree of saturation (S0 ). The water solubility value is adopted from Fredlund & Rahardjo (1993). The values of λvp (slope of the NCL) are selected to best fit the experimental results and compared with the measured values from literature. These values are found to be generally in the range of experimentally measured values. Table 2 shows the initial equilibrium suctions measured for compacted specimens at different moisture contents given by Montanez (2002). They are presented as constant suction contours which are
Figure 1. Comparison of predicted and experimental compaction curves for well graded sand with 5% bentonite (after Montanez, 2002).
Figure 3. Comparison of predicted and experimental compaction curves for clay sandy soil (after Kenai et al., 2006). Table 1.
Figure 2. Comparison of predicted and experimental compaction curves for well graded sand with 15% bentonite (after Montanez, 2002).
Parameter values for the proposed model. Well graded sand with 5% bentonite
Well graded sand with 15% bentonite
Parameter
Value
Value
h∗ λvp n0 Gs
0.02 0.045 34 % 2.656
0.02 0.13 36 % 2.660
∗
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Water solubility
Table 2.
Initial matric suction (s0 ) values.
Well graded sand with 5% bentonite content
Well graded sand with 15% bentonite content
w (%)
s0 (kPa)
w (%)
s0 (kPa)
3.9 5.8 7.8 9.7 11.7 13.6 15.6 17.5
4630 1130 350 130 54 32 26 22
4.9 6.4 8.5 10.6 12.7 14.9 17.0 19.1
17800 11500 2550 1260 850 530 290 270
Table 3.
Figure 4. Variations of m1s with initial degree of saturation (S0 ) and during compaction for well graded sand with 5% bentonite.
Parameter values for the proposed model. Clay sandy soil
Parameter
Value
h∗
0.02 1.3 46 % 2.66
λvp n0 Gs
generally perpendicular to the water content axis giving approximately constant suction values for a given compaction water content. This ignores the curving of these contours close to saturation towards the left eventually becoming almost parallel to the full saturation line. Figures 1 and 2 show comparisons between experimental and predicted values of compaction curves for sand-bentonite mixtures. The experiments were performed under dynamic conditions (Proctor compaction), whereas model prediction assumed static undrained conditions for both air and water. Despite these differences, it is clear that reasonable predictions of the shape of the compaction curve can be obtained with the proposed approach. Figure 3 shows comparison between experimental and predicted values of the compaction curve for sandy clay soil. For this example, experiments were performed under both dynamic and static conditions. It should be noted that in this example, experimental results did not include the initial suction values. Therefore, initial suction values are assumed to be same as well graded sand with 15% bentonite (Table 2). Differences in the predicted and experimental behaviour can be traced to a number of sources. One possibility is the drainage of air, particularly on the dry side of the optimum, which can lead to higher dry densities. This analysis, however, shows that the
development of air pressure on the dry side is not very significant, but will depend on m1s . It can be seen that the predicted and experimental density difference on Figure 1 is higher than that of Figure 2. In addition to the likely influence of the other assumptions made in the analysis, this difference seems to indicate that the drainage of air may lead to higher densities in the dry side. It is likely that the pore sizes in well graded sand with 5% bentonite content is higher than the same sand with 15% bentonite. These issues will be further examined through future targeted experiments. Figure 4 shows the variation of m1s with initial degree of saturation (S0 ) and during compaction for the well graded sand with 5% bentonite content. It can be seen that coefficient of compressibility due to net stress (m1s ) decreases with decreasing initial degree of saturation (S0 ), as assumed previously by Kurucuk et al. (2007). However, during the compaction process, the degree of saturation increases from the initial value, but the coefficient of compressibility (m1s ) decreases. This decrease of compressibility happens owing to the increase of net stress as the compaction progresses. It is also apparent that much of the compaction takes place in the early part of the process where the soil compressibility decreases rapidly.
5
CONCLUSION
This paper presents theoretical concepts to predict the compaction curve for soil during undrained K0 or isotropic loading using unsaturated soil mechanics principles. It highlights the fact that the wellknown inverted parabolic shape of the compaction curve may be theoretically predicted using unsaturated soil mechanics principles, arguably for the first time in literature. This was demonstrated using published experimental results, but it was necessary to make some assumptions. The controlling parameter
378
governing the compaction process was identified as the coefficient of compressibility with respect to net stress or m1s . It was also identified that the variation in drainage conditions during compaction may influence the results. Future experiments will be targeted to develop a comprehensive set of data to examine the modelling assumptions and improve modelling capability. ACKNOWLEDGEMENTS Thanks are rendered to Monash University for providing a Monash Graduate Scholarship and financial assistance to the first author for her PhD candidature. REFERENCES Barden, L. & Sides, G.R. 1970. Engineering behaviour and structure of compacted clay. Journal Soil Mechanics and Foundations Division, ASCE, 96, No. SM4: 1171. Fredlund, D.G. & Rahardjo, H. 1993. Soil mechanics for unsaturated soils. John Wiley & Sons, Inc. Fredlund, D.G. & Morgenstern, N.R. 1976. Constitutive relations for volume change in unsaturated soils. Canadian Geotechnical Journal, 14, 3: 261–276. Hilf, J.W. 1948. Estimating construction pore pressures in rolled earth dams. Proceedings of 2nd International Conference in Soil Mechanics and Foundation Engineering, 3: 234–240. Rotterdam, The Netherlands. Hilf, J.W. 1956. An investigation of pore water pressures in compacted cohesive soils. Technical Memorandum 654, U.S. Department of the Interior, Bureau of Reclamation, Denver, Colorado.
Hogentogler, C.A. 1936. Essentials of soil compaction. Proceedings Highway Research Board, National Research Council, Washington, D.C., 309–316. Kenai, S., Bahar, R. & Benazzoug, M. 2006. Experimental analysis of the effect of some compaction methods on mechanical properties and durability of cement stabilized soil. Journal of Material Science, 41: 6956–6964. Kurucuk, N., Kodikara, J. & Fredlund, D.G. 2007. Prediction of compaction curves. 10th ANZ Conference on Geomechanics, 2: 115–119. Lambe, T.W. 1960. Structure of compacted clay. Transactions, ASCE, 125: 682–705. Lee, D.Y. & Suedkamp, R.J. 1972. Characteristics of irregularly shaped compaction curves of soil. Highway Research Board, 381: 1–9. Li, Z.M. 1995. Compressibility and collapsibility of compacted unsaturated loessial soils. Unsaturated Soils. Proc. 1st Int. Conf. on Unsaturated Soils (UNSAT 95), Paris, France (ed. Alonzo, E.E. and Delage, P.), Rotterdam: Balkema, Vol. 1: 139–144. Lloret, A., Villar, M.V., Sanchez, M., Gens, A., Pintado, X. & Alonso, E.E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique, 53(1): 27–40. Montanez, J.E.C. 2002. Suction and volume changes of compacted sand-bentonite mixtures. PhD thesis, University of London, Imperial College of Science, London, England. Olson, R.E. 1963. Effective stress theory of soil compaction. Journal Soil Mechanics and Foundations Division, ASCE, 89, No. SM2: 27–45. Proctor, R.R. 1933. Fundamental Principles of Soil Compaction, Engineering News-Record, 111: 286. Sheng, D., Fredlund, D.G. & Gens, A. 2007. A new modelling approach for unsaturated soils using independent stress state variables. Research Report No. 261.11.06, University of Newcastle, NSW 2308, Australia.
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Prediction of the residual void ratio of clayey soils after drying based on their initial state, physical properties and structure M.E. Bardanis & M.J. Kavvadas National Technical University, Athens, Greece
ABSTRACT: Bardanis & Kavvadas (2006) proposed an empirical relation between residual void ratio er of clayey soils after drying and simple properties: initial void ratio eo , liquid limit wL and specific gravity Gs . Additional results are presented in this paper which support a new relation based on plastic limit wP , along with new results from undisturbed soil specimens, which indicate the possible effect of structure due to natural processes. A generalised relation therefore would predict er from eo , wP , Gs and an empirical parameter related to the structure of natural soils. However, the findings of this study indicate great scatter in correlations of er with soil index properties. Additionally, studies on undisturbed soils indicate considerable influence of soil stress history on er , thus complicating the development of a generalized relation for predictive purposes.
1
INTRODUCTION
Prediction of volume changes occurring with changes in suction is fundamental for the study of the mechanical behaviour of unsaturated soils. Constitutive models proposed for unsaturated soils predict volume changes by the corresponding parameters for elastic and plastic strains, κs and λs respectively (Alonso et al. 1990). As shown in Figure 1 (curve (a)) for changes in suction under zero total stress, specific volume υ(υ = 1 + e), and therefore void ratio e, vary linearly with suction (in logarithmic scale), according to parameter κs for suction values up to suction so (an arbitrary value of suction corresponding to yielding during drying, physically representing the maximum suction applied to the soil) and according to parameter λs for suction values past so . This type of formulation is in agreement with the formulation for the prediction of volume changes due to total stress changes under constant suction, according to parameters κ and λ(s). Such models predict realistic volume changes for suctions lower than that corresponding to residual water content, down to which shrinking during drying occurs. For suctions close to residual water content, or higher, this type of formulation overestimates volume change as it underestimates final specific volume/void ratio values. Numerous published test results (e.g. Fredlund & Rahardjo, 1993) and common experience with shrinkage tests have shown that total volume and void ratio during drying under zero total stress are expected to reach a limiting lower value er , which corresponds to residual water content and will be referred to as the residual void ratio. The value of er (or its
corresponding value of specific volume υr = 1 + er ) should be the lowest value predicted by constitutive models for unsaturated soils. Models have been proposed recently which introduce parameters limiting volume changes with increasing suction under constant total stress (e.g. Toll, 1995, Kohgo, 2004). Toll (1995) presented a conceptual model for the drying and wetting of soil which predicts the limiting of void ratio changes and therefore the calculated volume change up to the void ratio corresponding to shrinkage limit (curve (b) in Fig. 1). For this to be possible only one additional parameter is necessary. This is either the value of suction sr at which er is
e or
sO
sr
ln s
s
s
(b)
er (a)
Figure 1. Void ratio/Specific volume changes with increasing suction under zero total stress: a) without accounting for residual void ratio, and b) taking residual void ratio into account.
381
first achieved (second inflection point of curve (b) in Fig. 1) or simply er itself. Residual void ratio er therefore emerges as a critical parameter for constitutive modeling of deformable unsaturated soils.
0.8
er/eO
2
1.0
PREDICTION OF RESIDUAL VOID RATIO
0.6 0.4
Anticipating the advantages of using er rather than sr for use in constitutive modeling, Bardanis & Kavvadas (2006) proposed an empirical relation predicting er on the basis of tests on low to high plasticity clays and marls (Eq. 1). Residual void ratio er is predicted from the initial state of the soil, as expressed by initial void ratio when drying starts, eo , the physical properties of the soils, as expressed by their liquid limit wL and specific gravity Gs , and an empirical parameter m, found equal to 0.43. m · eo (1) er = eo 1 − wL · Gs Equation 1 was obtained from ten experimental points obtained for four materials. Residual void ratio values were measured on specimens left to dry in atmospheric conditions from a slurry condition or after being consolidated one-dimensionally and then unloaded to zero overburden stress. Since then experimental results from other soils have been collected and they are presented in Section 3. Index properties of the soils tested by Bardanis & Kavvadas (2006) are presented in Table 1, along with initial and residual void ratio values. The experimental results with the plot of Equation 1 are presented in Figure 2. Equation 1 Table 1. Index properties of the soils tested by Bardanis & Kavvadas (2006) along with eo and er values. Soil Chania clay
wL (%)
Ip –
Gs –
Condition1
eo –
0.2 0.0
9
2.68
0.5
1.0
1.5
2.0
2.5
eO/eL Figure 2. Normalised residual void ratio er /eo vs normalised initial void ratio eo /eL at the beginning of drying with the empirical relation proposed by Bardanis & Kavvadas (2006) and expected extensions (dashed lines).
obtained from the experimental results in Table 1 has 90% degree of correlation and passes through point {er /eo = 1, eo /eL = 0}. Equation 1 was derived from a small number of experimental points. Still the degree of correlation was very high, the best-fit equation passes through point {er /eo = 1, eo /eL = 0}, which is expected given the normalisations used, and the scatter of the points around the best-fit line is relatively small. For eo /eL tending to 0, er /eo is logically expected to tend to unity. Using eo to normalise er expresses essentially how much the total volume of an initially saturated specimen decreases due to drying, while using eL to normalise eo as correlation parameter expresses that the state relative to the nature of the soil (expressed by the void ratio at liquid limit, eL = Gs · wL ) is the determining correlating factor.
er –
3 24
0.0
Slurry Slurry 100 kPa 200 kPa 400 kPa 1600 kPa
1.05 1.04 0.59 0.52 0.51 0.43
0.35 0.34 0.33 0.31 0.34 0.31
Speswhite Kaolin Corinth Marl
64
32
2.61
Slurry
2.81
0.72
34
12
2.67
Slurry 800 kPa
1.27 0.66
0.51 0.51
Kifissia Marl
31
16
2.66
600 kPa
0.57
0.34
1 The stress reported in column ‘‘Condition’’ is the maximum stress applied one-dimensionally to a slurry of the soil and then removed before drying started.
ADDITIONAL EXPERIMENTAL RESULTS FOR RECONSTITUTED SOILS
Although small, the number of experimental points used by Bardanis & Kavvadas (2006) was sufficient to support a conceptual relation between er and the initial state and physical properties of reconstituted soil slurries as well as of reconstituted soils consolidated one-dimensionally and then unloaded. Still it was considered important that further experimental results were gathered in order to study residual void ratio and its correlation with the physical properties and the initial state of soil. In Table 2 additional experimental results obtained for two more soils tested at NTUA are presented and in Table 3 additional experimental results from various sources. With the experimental results presented in Tables 2 & 3 the total number of
382
Table 2. Index properties of additional soils tested along with eo and er values.
Ioannina lake silt Kifissia clay
wL (%)
Ip –
Gs –
Condition1
eo –
Bardanis & Kavvadas, 2006
0.8
er –
New data
24
1
2.55
100 kPa
0.69
0.58
41
21
2.67
600 kPa
0.70
0.34
eO/eL
Soil
1.0
0.6 0.4 0.2
1
The stress reported in column ‘‘Condition’’ is the maximum stress applied one-dimensionally to a slurry of the soil and then removed before drying started.
0.0 0.0
eo Condition1 –
er –
Soil
w L Ip (%) –
Fleureau et al. (1993) Sterrebeek loam
27
4
2.652 Slurry 200 31 9.5 2.652 Slurry 37 17.5 2.653 Slurry 61 30 2.673 Slurry 170 110 2.643 Slurry
0.78 0.61 1.23 1.26 2.00 7.40
64 74
32 45
2.61 2.64
200 200
1.15 0.76 1.12 0.42
95
48
2.652 200
1.27 0.80
35
16
2.71
Slurry
1.42 0.75
28
18
2.64
200
0.54 0.44
19
9
2.69
Slurry
0.77 0.35
75
50
2.65
6.2 kPa 400 kPa
3.00 0.45 1.40 0.45
130 97
2.65
Slurry
4.50 0.70
50
27
2.64
Slurry
1.98 0.51
32
15
2.71
Slurry
1.33 0.57
28.3 10.7 2.64
Slurry
0.53 0.44
Orly loam Jossigny loam White clay Montmorillonite Dineen (1997) Speswhite Kaolin London clay Melgarejo et al. (2002) Colluvium Fleureau et al. (2002) La Verne clay Cunningham et al. (2003) Silty clay Fleureau et al. (2004) Silty sand Fredlund (2004) Regina clay Agus & Schanz (2006) Bentonite/sand Abou-Bekr et al. (2006) Sikkak Peron et al. (2006) Bioley silt Pineda & Colmenares (2006) Clayey silt
1.0
1.5
2.0
2.5
eO/eL
Table 3. Index properties, initial void ratio and residual void ratio for soils from various sources. Gs –
0.5
0.61 0.52 0.39 0.46 0.88 0.95
Figure 3. Normalised residual void ratio er /eo vs normalised initial void ratio eo /eL with the empirical relation proposed by Bardanis & Kavvadas (2006), their experimental data and the new experimental data included.
Bardanis & Kavvadas (2006) and the empirical relation they proposed. As observed, the scatter of the sum of all data now is much larger, even though it seems evenly distributed on either side of the linear relation proposed. Regression analysis of the whole set of data shows that the equation describing the linear relation between er /eo and eo /eL does not change significantly but the degree of correlation drops from 90% to 44%. This picture of the whole set of data on the er /eo -eo /eL plot showed that an alternative relation should be investigated. Following the same line of thought regarding the parameters that should be used to express the relation of residual void ratio to physical properties and initial conditions, an alternative to eL was examined. In Figure 4 all the experimental data available are plotted but the void ratio at liquid limit has been substituted with the void ratio at plastic limit, eP (eP = Gs · wP ). As observed, the scatter of data decreases significantly and an exponential relation between er /eo and eo /eP appears as the best-fit curve. This is described by Equation 2. er eo = 1.108 · exp −0.42 · eo eP
1
The stress reported in column ‘‘Condition’’ is the maximum stress applied one-dimensionally to a slurry of the soil and then removed before drying started. 2 Assumed value. 3 Value derived from the slope of the full saturation line in the e-w plots presented by the authors.
experimental points rose to 30, obtained for 21 materials, ranging from pure high plasticity clays (even pure kaolinites and montmorillonites) to silty sands. In Figure 3, all the additional new data are plotted (empty circles) over the experimental points from
(2)
Equation 2 has 81% degree of correlation. The line described by Equation 2 does not pass through point {er /eo = 1, eo /eP = 0} as should theoretically be expected. If the best-fit line is forced to pass through point {er /eo = 1, eo /eP = 0} it is described by Equation 3 which has 80% degree of correlation. Equation 3 diverges only slightly from Equation 2 as shown by their comparison in Figure 4 (dashed and solid lines respectively).
383
1.0
1.4 +25%
0.8
Forced through 1
1.2
Best fit (exponential)
1.0
0.6
+50%
Predicted er
er/eO
Data
–25%
0.8
0.4
–40%
0.6 0.4
0.2
0.2 0.0 0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.0 0.0
eO/eL Figure 4. Normalised residual void ratio er /eo vs normalised initial void ratio eo /eP with best fit (exponential) and if forced through point {er /eo = 1, eo /eP = 0}. 1.0
0.8
Outliers
er/eO
0.6
0.4
+35%
0.2
0.0 0.0
–35%
1.0
2.0
3.0
4.0
5.0
6.0
eO/eP Figure 5. Normalised residual void ratio er /eo vs normalised initial void ratio eo /eP with best fit (exponential) curve forced through point {er /eo = 1, eo /eP = 0} and curves defining ±35%. Outliers are marked by dashed circles.
eo er = exp −0.38 · eo eP
Outliers in Fig. 5 0.2
0.4
0.6
0.8
1.0
1.2
1.4
Measured er Figure 6.
Predicted values of er against measured values.
shown in Fig. 5) although it may overestimate it even up to 50%. Still only 4 experimental points lie above the +25% line (and below the +50% line). Therefore for 24 out of 30 experimental points predicted values of er from Equation 3 lie within a range of ±25% of the measured values, and for the whole set of experimental points predicted values lie within a range of +50%/−40% of the measured values. This scatter is very large, especially for the empirical relation expressed by Equation 3 to be used for predictive purposes. Still it is the belief of the authors that this scatter is sufficiently low to support the theoretical relation between the parameters used. It is also sufficiently low to justify the need for further experimental research on various soils in pursuit of this type of empirical relation. Soils used in this research should be left to dry after they have been consolidated and unloaded to various eo values, ranging from those corresponding to slurries to those corresponding to high stresses (in the order of MPa).
4
EXPERIMENTAL EVIDENCE FOR NATURAL SOILS
(3)
As may be observed in Figure 5, all experimental data (with the exception of two outliers) lie within a range of ±35% from the line described by Equation 3. Predicted values of residual void ratio have been plotted against measured values in Figure 6. As it is observed, Equation 3 does not underestimate residual void ratio by more than 25% (except for the outliers
Apart from the additional data for reconstituted soils left to dry from a slurry condition and reconstituted soils consolidated one-dimensionally to a maximum stress and then unloaded, a limited number of additional experimental data have been collected for natural soils with structure that were left to dry. The experimental results are presented in Table 4. One of the soils was undisturbed Corinth Marl and the other a natural colluvium reported by Melgarejo et al. (2006).
384
Table 4. Index properties of natural soils tested or found in the literature along with eo and er values. Soil
wL (%)
Ip –
Gs –
Initial suction
eo –
er –
Corinth Marl Colluvium2
34 95
12 48
2.67 2.65
9 kPa1 1000 kPa3
0.64 1.10
0.62 0.80
1.0
0.8
1 Average
value of suction measured in-situ with a Soil Moisture Quickdraw tensiometer. 2 Melgarejo et al. (2002). 3 Measured with calibrated filter papers.
er/eO
0.6
0.4
Bardanis & Kavvadas (2004) have presented a laboratory investigation of the virgin drying of the Corinth Marls. These naturally occurring marls are found in the greater area around the city of Corinth in Greece and especially along the 6.3 km long and 80 m high Corinth Canal. The excellent long-term stability of the canal’s steep slopes (the canal is 115 years old and its slopes have an inclination of 4.5:1 without any benches or berms) has driven the research in the engineering behaviour of the Corinth Marls, as their structure and partial saturation contribute greatly to the stability of the slopes. Being cemented, this natural material exhibits higher values of air-entry pressure and residual void ratio than when reconstituted and reconsolidated to the same void ratio as the natural material. Bardanis & Kavvadas (2004) have attributed this behaviour to the cementation of the undisturbed Corinth Marl, which does not exist in the reconstituted/reconsolidated specimens. This point seems to be the one more worthy of further investigation, as experimental results for unsaturated properties of marls (especially focusing on the effect of their cementation in their drying behaviour) are scarce, if any, in the literature. More information on the engineering behaviour of Corinth Marl and the role played by its cementation may be found in Kavvadas et al. (2003). Melgarejo et al. (2002) presented preliminary results from their investigation into the unsaturated properties of a colluvium from Brazil. What their results show is that although the natural structured soil has lower initial void ratio than the same soil reconstituted to a slurry condition, consolidated to 200 kPa and then unloaded, they both dry to the same value of residual void ratio. In Figure 7 all the experimental data are plotted along with these additional data for undisturbed specimens of natural soils which are indicated by arrows starting from the experimental points corresponding to the same soils reconstituted, reconsolidated and then unloaded. These data are very few. They indicate however that natural soils exhibit a higher er /eo ratio than that exhibited by the same soils when reconstituted, reconsolidated and unloaded. A general form
+35%
0.2
0.0 0.0
-35%
1.0
2.0
3.0
4.0
5.0
6.0
eO/eP Figure 7. Experimental points for slurries and overconsolidated samples with best-fit curve (exponential) forced through point {er /eo = 1, eo /eP = 0}, the lines defining ±35% from the best-fit curve and two points for soils with natural structure (empty circles with shade). The arrows start from points corresponding to the same material reconstituted and reconsolidated.
of an empirical equation predicting residual void ratio therefore would have the characteristics of Equation 4; a parameter me controlling the curvature of the exponential equation and a parameter Ms introducing the structure of natural soils. In this study me was found equal to −0.38. er eo = Ms · exp me · eo eP
(4)
Parameter Ms cannot be measured yet with the very limited data available so far and should be considered conceptual for the time being. Still its presence is evident from the differences observed between reconstituted /reconsolidated soils and natural soils. Parameter Ms must take such values that er /eo never becomes higher than unity. From Equation 4 therefore it is easily obtained that although Ms is higher than unity, it also has an upper bound found to be equal to { exp[me · eo /eP ]}−1 . It is here emphasized that the increasing factor Ms reflects the structure of natural materials rather than that created by loading history.
385
The effect of this type of structure created in reconstituted soils is already taken into account in the empirical relation by using as a correlating parameter the ratio eo /eP rather than initial void ratio eo by itself.
one-dimensional conditions) will exhibit if this conceptual formulation is sound. If it is, such analysis will also yield a relation between the empirical factor Ms and structure.
5
ACKNOWLEDGEMENTS
CONCLUSIONS
The initial empirical relation proposed by Bardanis & Kavvadas (2006) that relates residual void ratio er with initial void ratio eo , liquid limit wL and specific gravity Gs has been found valid for additional experimental data from new tests and test results collected from various publications. Although the scatter of the additional experimental points seems evenly distributed on either side of the linear relation proposed by Bardanis & Kavvadas (2006), it is so large and the degree of correlation has dropped so much that an alternative relation where wL has been substituted with wP is proposed as this exhibits higher degree of correlation. All experimental points but two (out of a total of 30) lie within a range of ±35% from the best-fit exponential equation. As far as actual values of er are concerned, for 24 out of 30 experimental points the predicted values lie within a range of ±25% of the measured values, and for the whole set of experimental points predicted values lie within a range of +50%/−40% of the measured values. These ranges are very large for the proposed equation to be used for predictive purposes. Still this scatter is sufficiently low to support a soundly based theoretical relation between the parameters used. It is also sufficiently low to justify the need for further experimental research on various soils in pursuit of this type of empirical relation. Despite these limitations of the proposed empirical relation, comparison of the experimental data for reconstituted/reconsolidated soils with the very few experimental points from tests on undisturbed samples of soils indicates that natural soils exhibit a higher er /eo ratio than that exhibited by the same soils when reconstituted, reconsolidated and unloaded. Although this latter observation cannot yet be quantified (especially given the very small number of experimental data available for soils with natural structure), it may be conceptually expressed by the formulation of Equation 4, which introduces an empirical factor increasing the value of residual void ratio predicted from eo , wP and Gs . This increasing factor is expected to be a function of the structure of natural soils. Additional experimental data for more natural soils with the accompanying data for the same soils after reconstitution and consolidation to a void ratio similar to that of the natural soils, along with measurement of the structure of these soils (for example by measuring the yield stress of both the undisturbed samples and the reconstituted samples—after a loading unloading loop to the in-situ vertical stress—under
Part of the research by M.E. Bardanis has been funded by the National Scholarship Foundation (IKY) of Greece. REFERENCES Abou-Bekr, N., Bendi-Ouis, A., Taibi, S. 2006. Characterization of the clay of Sikkak earth dam core (west of Algeria). In Miller et al (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1607–1616, Reston, Virginia: ASCE Press. Agus, S.S., Schanz, T. 2006. Drying, wetting, and suction characteristic curves of a bentonite-sand mixture. In Miller et al. (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1405–1414, Reston, Virginia: ASCE Press. Alonso, E.E., Gens, A., Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430. Bardanis, M.E., Kavvadas, M.J. 2004. Laboratory investigation of the virgin drying of the Corinth Marls, in T. Schanz (ed.), Unsaturated Soils: Experimental Studies, Proc. of the Int. Conf. ‘‘From Experimental Evidence towards Numerical Modelling of Unsaturated Soils’’, Weimar, 17–18 September 2003, 421–432, Berlin: Springer. Bardanis, M., Kavvadas, M. 2006. Prediction of the limiting void ratio of clayey soils after drying. In Miller et al. (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1085–1096, Reston, Virginia: ASCE Press. Cunningham, M.R., Ridley, A.M., Dineen, K., Burland, J.B. 2003. The mechanical behaviour of a reconstituted unsaturated silty clay. Géotechnique 53(2): 183–194. Dineen, K. 1997. The influence of soil suction on compressibility and swelling, PhD Thesis, Imperial College of Science, Technology and Medicine, University of London. Fleureau, J.M., Kheirbek-Saoud, S., Soemitro, R., Taibi, S. 1993. Behavior of clayey soils on drying-wetting paths. Can. Geotech. J. 30: 287–296. Fleureau, J.M., Hadiwardoyo, S., Kheirbek-Saoud, S. 2004. Simplified approach to the behavior of compacted soils on drying and wetting paths. In Jucá et al. (eds), Proc. 3rd Int. Conf. Unsaturated Soils, UNSAT 2002, 10–13 March 2002, Recife, Brazil 3: 1147–1154, Lisse: Swets & Zeitlinger. Fleureau, J.M., Verbrugge, J.C., Huergo, P.J., Correia, A.G., Kheirbek-Saoud, S. 2002. Aspects of the behaviour of compacted clayey soils on drying and wetting paths. Can. Geotech. J. 39(6): 1341–1357. Fredlund, D.G. 2004. Use of soil-water characteristic curves in the implementation of unsaturated soil mechanics. In Jucá et al. (eds), Proc. 3rd Int. Conf. Unsaturated Soils,
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UNSAT 2002, 10–13 March 2002, Recife, Brazil 3: 887–902, Lisse: Swets & Zeitlinger. Fredlund, D.G., Rahardjo, H. 1993. Soil Mechanics for Unsaturated Soils, New York: John Wiley & Sons, Inc. Kavvadas, M.J., Anagnostopoulos, A.G., Georgiannou, V.N., Bardanis, M.E. 2003. Characterisation and engineering properties of the Corinth Marl, in Tan et al. (eds.), Proc. Int. Workshop ‘Characterisation and Engineering Properties of Natural Soils’, Singapore, 2002, 2, 1435–1459, Lisse: Swets & Zeitlinger. Kohgo, Y. 2004. Elastoplastic models for unsaturated soils with two suction effects and unsaturated soil behavior. In Jucá et al. (eds), Proc. 3rd Int. Conf. Unsaturated Soils, UNSAT 2002, 10–13 March 2002, Recife, Brazil 3: 905–915, Lisse: Swets & Zeitlinger. Melgarejo, M.L., Ridley, A.M., Dineen, K. 2002. A comparison of the soil water characteristic curves for reconstituted and undisturbed samples of a colluvium
from Rio de Janeiro. In Juca, et al. (eds), Proc. 3rd Int. Conf. Unsaturated Soils, UNSAT 2002, 10–13 March 2002, Recife, Brazil 1: 313–316, Lisse: Swets & Zeitlinger. Péron, H., Laloui, L., Hueckel, T., Hu, L. 2006. Experimental study of dessication of soil. In Miller et al. (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1073–1084, Reston, Virginia: ASCE Press. Pineda, J.A., Colmenares, J.E. 2006. Stress-strain-suction behaviour of two clayey materials under unconfined conditions. In Miller et al. (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1109–1120, Reston, Virginia: ASCE Press. Toll, D.G. 1995. A conceptual model for the drying and wetting of soil. In Alonso & Delage (eds), Proc. 1st Int. Conf. Unsaturated Soils, Paris, 2: 805–810, Rotterdam: Balkema.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
An evaluation of soil suction measurements using the filter paper method and their use in volume change prediction J.M. Cumbers & J.D. Nelson Colorado State University & Tetra Tech, Inc., Fort Collins, CO, USA
K.C. Chao & D.D. Overton Tetra Tech, Inc., Fort Collins, CO, USA
ABSTRACT: An evaluation of swell prediction utilizing the filter paper test for measurement of soil suction was conducted in this investigation. Filter paper tests were conducted on four types of clay soils including claystone of the Denver and Pierre Shale Formations, from Colorado, USA, Black Cotton clay from Texas, USA and a sandy clay from Nunn, Colorado, USA. This paper presents the results of the filter paper calibration and measurement of suction values at low water contents for unsaturated soils and their use in predicting volume change. Total oven-dry suction values for the four soil types tested ranged from 6.32 pF to 6.51 pF. The calculation of the suction compression index, Ch , based on an oven-dry suction value of 6.25 pF rather than an oven-dry suction value of 6.4 pF results in an increase in Ch of 19.4% for the Denver formation and 16.0% for the Pierre Shale tested.
1
INTRODUCTION
At water contents greater than the shrinkage limit for a given soil, decreasing water contents have been shown to be directly related to increasing soil suction values. This phenomenon also results in decreasing void ratios as the water content increases. The slope of this relationship was determined to be linear for a silty clay above the shrinkage limit (Hamberg, 1985; Nelson and Miller, 1996) and because of that, the slope of the linear relation between water content and void ratio along the SWCC can be used to predict volume changes or free field heave. When suction values are used as a means for estimating the amount of volume change a soil will undergo due to changes in water content, the end points of the curve relating suction and water content are important. McKeen (1992) suggested that the typical range of suction values over which volume change will occur is between 9.8 kPa (2 pF) and 31,010 kPa (5.5 pF). The higher end of this suction range corresponds fairly well with the air-dry condition for the soil. The oven-dry intercept for a typical soil was found to exhibit a suction value of about 980,000 kPa (6.25 pF) and McKeen’s method for calculation of predicted heave uses that value to determine the slope of the suction versus water content relationship, or the dh/dw parameter.
One aspect of this relationship for which limited experimental data exists, is the soil suction values for very dry to oven-dry water contents. The soil suction characteristics of four different clay soils were observed by measuring the total and matric suction of the specimens using the filter paper test method. Filter paper tests were performed on remolded specimens prepared at very dry water contents to measure the suction potential of the soils in dry conditions.
2
EXPERIMENTAL PROCEDURES
Laboratory experiments were conducted on four different clay soil types: (1) a claystone from the Denver formation, (2) a sandy clay identified as Nunn clay, (3) a claystone from the upper Pierre Shale formation, and (4) a Texas Black Cotton soil. The first and third soils were collected at residential sites in Denver, Colorado and the second at a site near Nunn, Colorado. The Texas soil was from a residential development east of Austin, TX. The overall testing protocol included a series of index tests to characterize the four soils, a series of filter paper tests to measure the soil suction over a prescribed range of water contents, and oedometer tests to evaluate the potential for one-dimensional swell.
389
2.1
Specimen preparation
The clay soil specimens were prepared for the filter paper and oedometer testing using a modified moist tamping system at the optimum water content and 100% of the maximum dry density. The soils were initially allowed to air dry and were processed to pass through the number 4 (4.75 mm) sieve. The soil specimens were remolded and compacted into rings suitable for the oedometer tests. The sample preparation procedure is presented in a companion paper (Chao et al. 2008). 2.2
Filter paper calibration
The filter paper calibration curve for the batch of Whatman No. 42 filter papers used in these experiments was developed by Chao (2007) using a NaCl solution and molalities ranging from 0.001 to 2.70. The range of filter paper water contents evaluated based on this range of molalities was approximately 13% to 35%. The resulting filter paper calibration curve is shown in Figure 1. Because the suction measurements were being attempted for filter paper water contents below the minimum water content for the calibration data (Chao, 2007) that was being used, an effort was made to determine the total suction for filter paper with a water content below 13%. To do this, a digital hygrometer was sealed inside the lid of one of the filter paper containers. Three oven-dried filter papers were placed in the container and the container was sealed. Three other containers were also prepared each containing three oven-dry filter papers. This allowed simultaneous measurement of the relative humidity and temperature within the environment. The equilibrated water contents of the filter paper could then be related to the relative humidity and temperature of the test environment. The total suction was calculated using
7.0 Data from 3-Week Equilibration Period
6.0 (kPa) Log Total Suction,
Data from 2-Week Equilibration Period 5.0 4.0
Whatman No. 42 Filter Paper
3.0 log = 5.4634 – 0.0933 wf r2 = 0.991
2.0 1.0
log = 23.012 – 0.6389 wf r2 = 0.712
0.0 0
10
20 30 40 Filter Paper Water Content, wf (%)
50
60
Figure 1. Filter paper calibration curve for total suction measurement (Chao, 2007).
Kelvin’s equation and the measured relative humidity and temperature within the container. The filter papers were removed from the containers at intervals of 2 days, 4 days, 7 days and 11 days and weighed to determine the water contents. The calculated suction value was then correlated to the measured water content of the filter papers. 2.3 Filter paper tests The specimens for the filter paper tests were prepared in pairs. Each pair of brass rings were measured and weighed. Based on the volume of the ring, the mass of soil at optimum water content needed to fill the ring at 100% of the maximum density was calculated. This total mass was divided in fourths and compacted into layers in the brass rings. Once the specimen pairs had been compacted, they were placed in an oven at 110◦ C to reduce the water content. The objective volumetric water contents were 10%, 7.5%, 5%, 3%, 2%, 1% and 0% or fully oven-dried. To achieve this, the specimens were removed periodically from the oven, allowed to cool briefly, and weighed. Based on the initial optimum water content and the change in mass, the water content after drying was determined. Once the calculated water content had been reduced to near the target water content, the drying process was discontinued. The specimens were then allowed to cool for approximately one half-hour, and new measurements of diameter and height were taken to calculate the dried volume of the specimen. The specimens were also weighed individually prior to being placed in the sealed container for the filter paper test. The filter paper tests were performed according to ASTM D5298-03. Two sizes of Whatman No. 42 filter paper were used for the tests. The slightly larger diameters of papers were as placed on either side of the smaller diameter filter paper to provide protection from soil contamination. The filter papers were placed in the oven overnight to remove any existing moisture. They were then removed, handled only with tweezers and placed in a dessicator to cool for several minutes prior to being placed with the soil. Because of shrinkage during drying the soil specimens typically slid easily out of the brass rings in which they were compacted. Two pieces of measurement filter paper were sandwiched between the larger protective filter paper, and were placed on top of the bottom specimen. The upper specimen was then placed on top of the protective piece of filter paper. Electrical tape was wrapped gently around the pair to seal the filter papers in-place and maintain good contact between the top and bottom specimens. The combined pair of specimens was then lowered into a plastic container with a resealable lid. A piece of metal window screen, slightly larger than the diameter of the
390
specimens was placed on top of the upper soil specimen and three additional filter papers were rested on the screen. The lid was sealed and a piece of electrical tape was placed around the lid to provide an additional seal for the jar. The container was then placed within a climate-controlled box for 7 days at a temperature of approximately 23.0◦ C(73.4◦ F). After a seven-day equilibration period, the container was opened and the mass of water within the filter papers was determined. Five water content tins with lids were weighed empty and cool using an enclosed scale, capable of precision to 0.0001 grams. Once the mass of the containers was obtained, the plastic jar containing the soil specimens and filter papers was unsealed and opened. The upper filter papers being used for measuring total suction were quickly placed into individual tins with lids and weighed. The pair of specimens were then separated carefully to prevent any soil contamination of the inner measuring papers. The two matric suction papers were then individually weighed in covered moisture tins as well. The moisture tins were then propped open slightly, to allow moisture loss during drying, and then placed in the drying oven so that the water content of the filter papers could be determined. The soil specimens themselves were then weighed individually and placed in the drying oven in order to determine the soil water content for the suction values. The moisture content tins were handled with latex gloves to prevent oils from the skin from affecting the weights of the tins. The filter papers were left in the oven overnight to dry. The soil samples were oven dried for 48 hours. Each was weighed after that period to determine the oven-dry mass and the water contents.
Table 1.
3
Figures 3 and 4 show second and third-order polynomial equations that were fitted to the data. The matric suction calibration curve shown by the dashed line in the figures is the curve outlined in ASTM D5298-03. Compared to the linear curve fit, the correlation coefficients did not increase significantly for the second and third-order polynomial equations. Also as indicated by the very small magnitudes of the coefficients for the second and third-order terms, even the polynomial equations represent a near linear relationship.
3.1
RESULTS AND ANALYSES Filter paper calibration
Four sets of three filter papers were prepared in separate containers and the papers were weighed at 2, 4, 7 and 11 days. The water content of the filter papers did not vary between days 2 and 4 days but increased by about 0.5% between days 4 and 7 and then by 0.9% between days 7 and 11. Table 1 presents a summary of the measured temperatures, relative humidities and calculated suctions within the filter paper container over the 11-day period. The soil suction results were then calculated using the calibration curves shown in Figure 2 which depicts a bilinear interpolation of the calibration shown in Figure 1 with the additional points included. The additional points shown on the curve depict the measured water contents of the filter paper which ranged from 2.75% to 4.29% and the decreasing total suctions for the monitoring period from 204,488 kPa (6.32 pF) initially to 170,950 kPa (6.24pF) on day 11.
Test conditions for filter paper calibration.
Time
Temp. ◦C
Relative humidity %
avg. filter paper water content(1) %
Initial 2 Days 4 Days 7 Days 11 Days
23.4 23.4 23.3 22.9 23.2
22.3 23.8 23.3 26.7 28.5
– 2.75 2.73 3.39 4.29
(1) Average
of three filter papers.
Total suction kPa, (pF) 204,488 (6.32) 195,617 (6.30) 186,156 (6.28) 179,665 (6.26) 170,950 (6.24)
7.0 Measured Total Suction 6.0
Chao (2007) ASTM Matric Curve
5.0 4.0 3.0
R2 = 0.997
2.0 1.0 R2 = 0.713
0.0 0
10
20 30 40 Filter Paper Water Content, wf (%)
50
60
Figure 2. Bilinear filter paper calibration curve for whatman no. 42 filter paper (Modified from Chao, 2007 and ASTM).
3.2 Filter paper test results The results for the four soils tested using the filter paper method are summarized in Table 2. Each total suction point represents the average total suction calculated from the water content of three filter papers and each matric suction value represents the average matric suction calculated from the water content of
391
Table 2.
7.0
Summary of filter paper test results.
Measured Total Suction 6.0
Chao (2007) ASTM Matric Curve
5.0
Soil type
4.0 3.0 R2 = 0.997
2.0 1.0 R2 = 0.713
0.0 0
10
20 30 40 Filter Paper Water Content, wf (%)
50
60
Figure 3. 2nd-order polynomial filter paper calibration curve for Whatman no. 42 filter paper (Modified from Chao, 2007 and ASTM).
Matric
Osmotic
Denver 8.22 Formation 3.68 3.18 1.18 1.05 1.08 Oven-dry Oven-dry
158,928 216,294 232,198 264,867 263,371 274,736 238,293 254,014
118,903 142,713 153,475 171,405 160,226 160,635 168,242 163,126
40,025 73,580 78,723 93,462 103,145 114,101 70,051 90,888
Nunn Clay
10.59 7.18 4.84 3.58 2.73 Oven-dry Oven-dry Oven-dry
29,083 62,446 111,325 168,635 183,428 301,573 271,151 238,543
22,009 49,870 77,372 103,418 119,722 177,495 161,833 152,406
7,074 12,576 33,953 65,217 63,706 124,078 109,318 86,137
Pierre Shale
8.07 5.54 5.52 2.90 2.11 1.22 Oven-dry Oven-dry
121,940 135,810 164,372 213,318 234,039 261,906 253,711 263,967
93,096 120,125 120,125 135,604 146,608 165,895 161,041 167,516
28,845 15,685 44,247 77,714 87,431 96,011 92,670 96,451
Texas Black Cotton Clay
12.92 6.05 2.17 1.48 0.99 0.78 Oven-dry Oven-dry
90,001 187,292 236,817 241,297 238,598 277,190 271,039 288,347
64,800 121,900 152,737 161,113 164,686 175,333 167,577 162,567
25,201 65,392 84,079 80,185 73,912 101,857 103,463 125,780
Measured Total Suction Chao (2007) ASTM Matric Curve 5.0 4.0 3.0 2.0
2
R = 0.998
1.0 R2 = 0.713
0.0
0
10
20 30 40 Filter Paper Water Content, wf (%)
50
60
Figure 4. 3rd-order polynomial filter paper calibration curve for Whatman no. 42 filter paper (Modified from Chao, 2007 and ASTM).
two filter papers. The osmotic suction was calculated as the difference between the measured value of average total suction and the average measured value of matric suction. The Texas Black Cotton soil (which was less expansive) had higher values of suction at oven-dry conditions. However, the differences in values of total suction are most likely statistically insignificant. Two tests were run on oven-dried samples of each soil type. The average total suctions resulting for the four soils tested at oven-dry conditions are shown in Table 3. Table 3 presents the range of oven-dry total suction values measured along with the inundation pressures and the corresponding percent swell results for the consolidation-swell tests. The more expansive soils, Pierre Shale and Denver Formations have lower total suction values at oven-dry water contents than the Nunn Clay and the Texas Black Cotton clay.
Suction, kPa Total
7.0 6.0
Volumetric Water Content, %
4
DISCUSSION
Initially the filter paper test results were calculated using the calibration function developed by Chao (2007) which extended only to a filter paper water content of approximately 13%. However, after additional points were obtained for the curve, the test results were adjusted by using a new curve fitted to the combined set of data covering the broader range of filter paper water contents including the dry end of the curve. With this adjustment to the calibration curve, the importance of utilizing data points over the full range of soil suction measurements became evident. By adjusting the calibration curve for total suction to include three additional points over the range from oven-dry conditions to a water content of 13%, gravimetric water content for the
392
Table 3. Summary of oven-dry suction values and percent swell results.
7.10 7.00 Calculated Points Using Kelvin's Equation
6.90
Denver formation Nunn clay
Pierre Shale Texas Black Cotton
Percent swell, %
9.58 19.15 47.88 9.58 19.15 47.88 9.58 − 47.88 9.58 19.15 47.88
5.23 0.60 2.66 0.40 0.37 −0.14 5.30 − 4.18 2.59 2.35 −0.89
kPa 246,153
Total Suction, pF
Soil type
Inundation pressure, kPa
Overall average total suction(1) pF
270,422
6.44
P Po
6.50
258,839
6.42
279,693
6.46
6.20 0%
5%
10% 15% 20% Relative Humidity, %
25%
30%
Figure 5. Plot of Kelvin’s equation and calculated filter paper calibration points.
filter paper—the total suction values calculated using the curve from Chao (2007) without the extended range—increased in amounts up to 40%. The calibration curves for Whatman No. 42 filter paper are shown in Figures 2 through 4 along with the fitted trendline equations and the R2 values for each. Based on curve fitting of linear, second, and third-order polynomials, each provided a quality fit with R2 values that are essentially identical. However, because of the dramatic change in the test results by adding just three points to the initial data set, additional points along this calibration curve would likely result in one of the curve fitting techniques being identified as superior to the others. The overall shape of the calibration curve tends to favor the third-order polynomial (Leong and Rahardjo, 1997 and Fredlund and Xing, 1994). Figure 5 shows the total suction calculated from Kelvin’s equation. Kelvin’s equation is a function of relative humidity.
6.60
6.30
values based on a minimum of two tests per soil with three filter papers each.
RT ∗ ln ν
6.70
6.40
6.40
(1) Average
ht =
Calculated Points Used in Calibration Curve
6.80
(1)
From Figure 5, the total suction at a water content of zero is shown to be approximately 1,000,000 kPa (7.01 pF). A straight line drawn through the four points used in the calibration curve intersects the vertical axis at a suction value of approximately 6.60 pF while extrapolation of points plotted more within the range of relative humidities encountered in geotechnical engineering applications would intersect the vertical axis
at lower values. This would account for the value of 6.25 pF used by McKeen (1992) or the value of 6.40 pF calculated by Chao (2007). Two important issues are related to this topic. The first is that the lowest values of filter paper gravimetric water content measured for the oven-dry soil specimens were approximately 1% with an average total suction of 6.43 pF which means the filter paper method may not be capable of measuring suctions higher than that unless the relative humidity of the test environment is controlled at a more humid state to perform the test. Second, as the relative humidities decrease, the calibration curve should be based on a logarithmic function (as Kelvin’s equation is) rather than a linear interpolation extending to zero. This will also increase the value of the estimated oven-dry suction.
4.1 The oven dry water content intercept and Ch One of the primary objectives of this research was to evaluate the total soil suction values for the test soils at oven-dry water contents. Previous research has indicated that this point is located in the range of 6.0 pF to 7.0 pF. McKeen (1992) stated that at zero water content the total suction is equal to 6.25 pF while data from Chao (2007) for the Denver Formation and the Pierre Shale indicated an oven-dry intercept of approximately 6.4 pF. However, the calibration curve used for that data set likely caused a slight underestimation of those oven-dry results. Values measured for the Pierre Shale were 6.41 pF and 6.43 pF while values measured for the Denver Formation were 6.39 pF and 6.41 pF. The importance of this intercept is related to the prediction of volume change using the slope of the soil water characteristic curve (SWCC). The suction compression index, Ch (McKeen, 1992), which is used to calculate volume change for a soil, can be calculated
393
directly from the slope of the SWCC between the existing water content of a soil and the assumed oven-dry intercept. Because of this, as this value of the soil suction at an oven-dry condition decreases, the value of Ch is going to increase, thereby resulting in higher values of predicted volume change. Table 4 presents a summary of calculations of Ch assuming different values of total suction, pFo , at an oven-dry state. The value of Ch was calculated using water contents close to the average in-situ water contents for the Denver Formation and the Pierre Shale tested in this research. For the Denver Formation, a water content of 18.6% with a total suction of 4.63 pF was used and for the Pierre Shale a water content of 17.0% and a total suction of 4.31 pF was used. The calculated values are plotted in Figure 6. Calculating Ch based on an oven-dry suction value of 6.25 pF rather than an oven-dry suction value of 6.4 pF will result in an increase in Ch of 19.4% for the Denver formation and 16.0% for the Pierre Shale tested. Often the value of this oven-dry intercept is assumed to be a constant value for all soils when predicting volume change for a particular soil. For the soils tested, which generally cover an assorted range
of swell potentials, the oven-dry suction values varied over a range of 63,280 kPa (0.06 pF). This means that assuming the same suction value for the oven-dry water content of a non-expansive soil and an expansive soil may result in miscalculation of the swell potential for both soil types. However, the range in values of oven-dry suctions is quite small and the differences measured may be due to the difficulties in calibrating the filter papers at very low water contents. A statistical analysis was performed to evaluate the results obtained from the individual filter papers for the soil specimens prepared at oven-dry water contents. Tests for equal variances were carried out to determine if the total suction values at oven-dry water contents, for each soil, displayed normal distributions. Additionally, student T-tests were performed using varying sets of oven-dry data, both among soil types and combining soil types into groups to determine if the total suctions were statistically different for the four soil types. The statistical results indicate that there is no significant difference between the results obtained for the Denver Formation and those obtained for the Pierre Shale. The values obtained for the Nunn Clay and the Texas clay were found to be significantly statistically different from the claystones yet not significantly different from each other.
Table 4. Comparison of Ch values calculated using different oven-dry suctions.
5 Denver formation
CONCLUSIONS
Pierre Shale
Oven-dry suction pFo
Calculated values of Ch using equation by Perko (2000)
6.25 6.40 6.42 6.44 6.46 7.0
−0.279 −0.233 −0.228 −0.223 −0.218 −0.130
Total suction values at oven-dry water contents for the four soil types tested ranged from 206,060 kPa (6.32 pF) to 315,021 kPa (6.51 pF). The soil with the largest percentage of clay size particles, Texas Black Cotton clay, did exhibit the highest average suction value at oven-dry conditions and the Nunn Clay which has the largest range of particle sizes, and had the least plasticity, exhibited the largest range of oven-dry suction values. Using values of the oven-dry total suction within the range of values measured appears to have a significant effect on the calculated value of the suction compression index Ch .
−0.179 −0.154 −0.151 −0.149 −0.146 −0.093
0.00
Suction Compression Index, Ch
–0.05
REFERENCES
–0.10 –0.15 –0.20 –0.25 Denver –0.30
Pierre Shale
–0.35 –0.40 –0.45 6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
Total Suction at Oven-Dry Conditions, pFo
Figure 6. Effect of oven-dry total suction on computed values of suction compression index, Ch .
ASTM D 5298–03. 1994. Standard Test Method for Measurement of Soil Potential (Suction) Using Filter Paper. 1996 Annual Book of ASTM Standards, Vol. 04.09, Soil and Rock, American Society for Testing and Materials, West Conshohocken, PA. Chao, K.C. 2007. Design Principles for Foundations on Expansive Soils. Dissertation, Colorado State University, Fort Collins, Colorado. Chao, K.C., Nelson, J.D., Overton, D.D. and Cumbers, J.M. 2008. Soil Water Characteristic Curves for Remolded Expansive Soils. First European Conference on Unsaturated Soils. Durham, United Kingdom.
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Cumbers, J.M. 2007. Soil Suction for Clay Soils at OvenDry Water Contents and the End of Swelling Conditions. Thesis. Colorado State University, Fort Collins, Colorado. Fredlund, D.G. and Xing, A. 1994. Equations for the soil-water characteristic curve. Canadian Geotechnical Journal, Vol. 31. pp. 521–532. Hamberg, D.J. 1985. A simplified method for predicting heave in expansive soils. M.S. thesis, Colorado State University, Fort Collins, CO. Leong, E.C. and Rahardjo, H. 1997. Review of Soil-Water Characteristic Curve Equations. Journal of Geotechnical and Geoenvironmental Engineering. pp. 1106–1117.
Nelson, J.D. and Miller, D.J. 1992. Expansive Soils: Problems and Practice in Foundation and Pavement Engineering, Wiley, New York. McKeen, R.G. 1992. A Model for Predicting Expansive Soil Behavior. 7th International Conference on Expansive Soils. Dallas, Texas, USA. pp. 1–6. Perko, H.A., Thompson, R.W., and Nelson, J.D. 2000. Suction Compression Index Based on CLOD Test Results. Geo-Denver 2000. pp. 393–408.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Validation of a swelling potential index for expansive soils J.L. Zheng, R. Zhang & H.P. Yang School of Highway Engineering, Changsha University of Science and Technology, Hunan, China
ABSTRACT: A new swelling potential index for expansive soils, the Standard Absorption Moisture Content (SAMC), was recommended in Chinese Specifications for Design of Highway Subgrades JTG D302004. In order to validate the index, sixteen soils were obtained from six typical areas where expansive soils exist in China. Extensive tests on soil properties indicative of swelling potential, such as Atterberg limits, free swelling ratio, clay content, SAMC, cation exchange capacity, specific surface area and montmorillonite content, were conducted. Correlations between the various indices were obtained and analyzed. The study shows that SAMC is more strongly correlated with the mineralogical and chemical properties, which determine swelling potential in nature, than other physical indices. Therefore, the new swelling potential index was validated to be reliable to identify and classify swelling potential of expansive soils.
1
INTRODUCTION
Soil property indices are the basis for identifying expansive soils and grading their swelling potential (Tan, 2007). Numerous studies have been carried out to obtain a suitable soil property index that can reflect and grade swelling potential of expansive soils. Karathanasis & Hajek (1985) found montmorillonite content (MC) as the only consistent soil property that significantly correlated with laboratory-measured shrink-swell potential. Ross (1978) concluded that swell potential of montmorillonitic soils were correlated with clay content (CC) and specific surface area (SSA). Gill & Reaves (1957) described cation exchange capacity (CEC), saturation moisture (SM) and plastic index (PI) as some of the most representative properties in the estimation of swelling potential having established them as highly correlated to the SSA. Snethen et al. (1977) evaluated 17 swelling indices and concluded that liquid limit (LL) and PI are the best indicators of potential swell and Parker et al. (1977) concluded swell index (SI) (Lambe 1960) and PI were superior to other indices. The free swelling ratio (FSR), defined as the volume increment of oven-dried soil passing 0.5 mm sieve and fully swelling in a graduated flask with distilled water expressed as a ratio of the initial volume of the soil (10 ml), is used as the sole swelling potential index in the Chinese Technical Code for Building in Expansive Soil Area (China Ministry of Construction
2003). The maximum linear shrinkage ratio, plastic limit (PL), the shrinkage limit, potential volume change index were also suggested and recommended by some researchers (Parker et al. 1977, Williams 1958). The indices used to characterize swelling potential of expansive soils can be classified into two types. The first type mainly involves mineralogical and chemical properties, such as MC, SSA, CEC, which determine the expansion of soils in nature (Mitchell 1976, Shi et al. 2002) and are reasonable to be used as swelling potential indices (Tan 2007). The second type involves physical properties, such as FSR, SI, Atterberg limit, swelling pressure, shear strength, and others, and are easily influenced by external environment and testing factors resulting in a wide range of values and misleading swelling potential grade. Thomas et al. (2000) suggested that shrinkswell behavior can best be predicted by examining a combination of physical and mineralogical properties. However, because the mineralogical and chemical properties are not easy to be measured, it is hard to apply them to grade swelling potential in engineering practice. In order to find a new swelling potential index, which would be easily measured and strongly correlated with the mineralogical and chemical properties of expansive soils, Yao et al. (2004) conducted many tests and put forward the standard absorption moisture content (SAMC). The index has been temporarily adopted as an index of the swelling potential rating
397
Table 1.
Swell potential rating system.
seal
Swell potential class
SAMC (%)
PI (%)
FSR (%)
Low Medium High
2.5–4.8 4.8–6.8 >6.8
15–28 28–40 >40
40–60 60–90 >90
glass container box soil sample porous plate saturated salt solution
system for expansive soils (Tab. 1) in the Chinese Specifications for Design of Highway Subgrades (China Ministry of Communications 2003). However, the index has been tested only for a small range of expansive soils, so the applicability to identify and classify expansive soils still needs further study. The objectives of this study was to validate and evaluate SAMC as a swelling potential index through (1) quantifying physical and mineralogical properties of 16 expansive soil samples in 6 areas in China, (2) examining and analyzing the correlation between SAMC and the mineralogical indexes, and (3) comparing the results of classifying swelling potential. It should be noted that the method has not yet been compared with direct measurements of swelling potential on undisturbed samples.
2 2.1
THE STANDARD ABSORPTION MOISTURE CONTENT Definition and physical meaning of SAMC
The standard absorption moisture content (SAMC) is the equilibrium water content when the soil is dried from its natural water content at (25 ± 2)◦ C and (60 ± 3)% relative humidity. The moisture absorbed on the surface (and in the interlayers) of montmorillonite mostly contributes to the amount of moisture absorption of the soil in this condition (Yao et al. 2005). The more montmorillonite the soil sample contains, the bigger SAMC is. Therefore, SAMC indirectly reflects the montmorillonite content of the soil.
Figure 1.
A glass container (Constant Humidity).
3. Desiccator, a glass container similar to the one shown in Figure 1, but with calcium chloride powder in the bottom instead of saturated salt solution. 4. Aluminum Box which is 1.5 cm in height and 6 cm in diameter and used to hold samples in the oven, desiccator or constant humidity container. 5. Electronic Balance with measurement precision of 0.001 g. The test procedure is as follows: 1. Weigh the oven dried aluminum box with the electronic balance, record the weight as W0 . 2. Cut undisturbed soil into slices, put 4 g of them into the box, weigh the aluminum box and soil sample together and record the weight as W1 . 3. Place the aluminum box holding the soil sample on the porous plate in the constant humidity container. Then seal the container and place it in a room with constant temperature of 25◦ C. 4. Take out and weigh the box holding the soil sample every day, then put it back into the container. Observe the change of weight till it changes little. Record the final weight as W2 . 5. Put the box holding soil sample into the oven and keep for 5 hours at 105–110◦ C. 6. Take the box out of the oven and put it into the desiccator. Keep for 1 hour to make its temperature reach the room temperature. Then, weigh the box holding soil sample as W3 . The SAMC can be calculated according to the following formula,
2.2 Test methods of SAMC The devices used to measure SAMC of expansive soils are as follows: 1. Constant Humidity Container, a glass container with 1000 ml saturated or oversaturated sodium bromide (NaBr) solution in the bottom, and it should be placed in a room at 25◦ C (Figure 1). 2. Oven where the temperature can be controlled at 105–110◦ C to dry samples.
wa =
W2 − W 3 W3 − W0
(1)
Where wa = SAMC (%); W2 −W3 = the maximum weight of absorbed moisture (0.001 g); and W3 −W0 = the weight of dry sample (0.001 g).
398
To ensure accuracy, parallel tests should be conducted. The permissible error is 0.2%, with regard the average. The average value is taken as the final result.
3 3.1
MATERIALS AND METHODS Sampling site selection
Sampling sites were carefully selected based on six physiographic zones described by Liao (1984). Undisturbed soil samples were obtained from Ningming basin and Nanning basin in the autonomous region of Guangxi Zhuangzu, Nanyang basin in Henan province, Hanzhong of Shanxi Province, and Zhaotong and Chuxiong of Yunnan province. These places are typical of areas in China that have widespread distributions of expansive soils. Sampling locations and description are summarized in Table 2. 3.2
Laboratory tests
Laboratory tests include measuring SAMC as well as Atterberg limits, free swelling ratio (FSR), particlesize distribution, CEC, SSA and mineralogical composition; these are usually used as swelling potential indices. The samples were sieved to remove coarse fragments >2 mm prior to analysis for the various indices. The Atterberg limits (PL, LL, PI), were measured according to JTJ-051-93: T0118-93 (China Ministry of Communications 1996). FSR was measured according to JTJ-051-93: T0124-93. The grain size analysis was conducted with the addition of (NaPO3 )6 as a dispersant to better determine the dispersive capability of the soil in its natural state. Then, the clay content (the percentage 27
100–190 190–360 >360
40–60 60–90 >90
Table 6.
Classification results.
Sample no.
Method 1
Method 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
moderate moderate moderate low moderate moderate low low low low low high moderate high high low
moderate moderate moderate low moderate moderate low low low low low moderate moderate high high low
5
CONCLUSIONS
Based on the above research results, the following conclusions can be drawn: 1. The swelling potential indices can be classified as physical properties indices and mineralogical properties indices. Mineralogical properties indices involve montmorillonite content, specific surface area and cation exchange capacity. These reflect and influence shrink-swell behavior of expansive soils in nature, and therefore they are reliable swelling potential indices. 2. The standard absorption moisture content is linearly correlated with mineralogical properties of expansive soils, it possesses clear physical meaning and reflects the characteristic of expansive soils, and therefore it can be used as a swelling index. 3. The classification results of the recommended swelling potential rating system involving of the new swell index SAMC are consistent with the rating system mainly involving of the mineralogical properties indices. It shows that swelling potential of expansive soils can be correctly identified and classified according to the recommended rating system. This suggests that SAMC can be used practically as a swelling index. However, it should be noted that the method has not yet been compared with direct measurements of swelling potential on undisturbed samples. REFERENCES Al-Homoud, A.S., Khoury, H. & Al-Omari, Y.A. 1996. Mineralogical and engineering properties of problematic expansive clayey beds causing landslides. Bulletin of the International Association of Engineering Geology, 54: 13–31. Paris.
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China Ministry of Communications. 2003. Specifications for Design of Highway Subgrades JTJ013-2002. Beijing: China communications Press, China. China Ministry of Communications. 1996. Test Methods of Soils for Highway Engineering JTJ051-93. Beijing: China Communications Press. China Ministry of Construction. 2003. Technical Code for Building in Expansive Soil Area GBJ112-87. Beijing: Chinese planning press. China Ministry of Railways. 2002. Code for Rock and Soil Classification of Railway Engineering TB 10077-2001. Beijing: China Railway Publishing House. Gill, W.R. & Reaves, C.A. 1957. Relationships of Atterberg limits and cation-exchange capacity to some physical properties of soil. Soil Sci. Soc. Am. Proc. 21: 491–494. Karathanasis, A.D. & Hajek, B.F. 1985. Shrink-swell potential of montmorillonitic soils in udic moisture regimes. Soil Sci. Soc. Am. J. 49:159–166. Lambe, T.W. 1960. The character and identification of expansive soils. Fed. Housing Admin. Rep. 701. U.S. Gov. Print. Office, Washington, DC. Liao, S.W. 1984. Expansive Soil and Railway Engineering. Beijing: Chinese Railway Publishing Press. Mitchell, J.K. 1976. Fundamentals of Soil Behavior. New York: John Wiley & Sons Inc. Parker, J.C., Amos, D.F. & Kaster, D.L. 1977. An evaluation of several methods of estimating soil volume change. Soil Soc. Am. J. 41: 1059–1064. Peck, R., Hanson, W. & Thornburg, T. 1974. Foundation Engineering. New York: John Wiley & Sons Inc. Ross, G.J. 1978. Relationships of specific surface area and clay content to shrink–swell potential of soils having
different clay mineralogical compositions. Can. J. Soil Sci. 58: 159–166. Shi, B., Jiang, H.T. & Liu, Z.B. 2002. Engineering geological characteristics of expansive soils in China. Engineering Geology 67: 63–71. Snethen, D.R., Johnson, L.D. & Patrick, D.M. 1977. An evaluation of expedient methodology for identification of potentially expansive soils. Soil and Pavements Laboratory, U.S. Army Eng. Waterway Exp. Sta., Vicksburg, MS, Rep. No. FHWA-RE-77-94, NTIS PB-289-164. Tan, L.R. 2007. Identification and Classification of Swellshrinking Soil. Soil Engineering and Foundation. 21(4): 85–88. Thomas, P.J., Baker, J.C. & Zelazny, L.W. 2000. An expansive soil index for predicting shrink-swell potential. Soil Sci. Soc. Am. J. 64: 268–274. Williams, A.B. 1958. Discussion of the prediction of total heave from double oedometer test. South African Institution of Civil Engineers, 5(6): 49–51. Xu, X.C., Chen, S.X. & Yu, F. 2006. Effect of different sampling methods on standard absorption water content. Chinese Journal of Rock Mechanics and Engineering. 25(10): 2135–2139. Yao, H.L., Yang, Y. & Cheng, P. 2004. Standard moisture absorption water content of soil and its testing standard. Rock and Soil Mechanics. 25(6): 856–859. Yao, H.L., Cheng, P., Yang Y., & Wu, W.P. 2005. Theory and practice concerning classification for expansive soils using standard moisture absorption water content. Science in China Ser. E. Engineering & Materials Science. 48(1): 31–40.
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Shear behaviour
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Effect of moisture content on tensile strength and fracture toughness of a silty soil M.R. Lakshmikantha, P.C. Prat, J. Tapia & A. Ledesma Technical University of Catalonia, Barcelona, Spain
ABSTRACT: Determination of fracture parameters (tensile strength, fracture toughness) is essential in determining the cracking behaviour of soils. In drying soils, a crack initiates when the tensile stresses exceed the soil strength. Crack propagation is considered to be governed by the stress state in the crack front and subsequent dissipation of fracture energy, for which Fracture Mechanics Theory can be used. In this context characterizing the soil for these two parameters require two different testing equipments. The tensile strength was determined using existing equipment (direct method) at the Soil Mechanics Laboratory of UPC whereas new equipment was designed for the fracture toughness determination. The results of tensile strength tests are consistent with published literature. Fracture toughness decreases as the moisture content increases; an attempt is made to explain this using the concept of Rate Process Theory and Activation Energy of soils.
1
soil densities, with average moisture content ranging from 12% to 30%.
INTRODUCTION
In a drying soil, a crack initiates when the tensile stresses exceed the soil strength. Crack propagation is considered to be governed by the stress state in the crack front and subsequent dissipation of fracture energy, for which Fracture Mechanics Theory can be used. In this context determination of fracture parameters (tensile strength, fracture toughness) is essential in determining the cracking behaviour. Characterizing the soil for these two parameters require two different testing equipments. The tensile strength was determined using existing equipment (direct method) at the Soil Mechanics Laboratory of UPC whereas new equipment was designed for the fracture toughness determination. To determine fracture toughness, two sizes (medium and big) of compact tension (CT) tests specimens were used. Originally there was another size (small) of CT test specimen, but due to the problems with sample preparation and handling the tests were not conducted with this size. Apart from the determination of fracture toughness, the effect of moisture content was also studied. Tensile strength of soils is an important indicator, as it depends on various other properties of soil. Until recently, determination of the soil’s tensile strength has not received the attention it deserves, mainly because of the difficulty of the experimental set-up. It is known that the tensile strength of soils varies with the degree of saturation (moisture content) as well as with the density, so, the tensile strength was determined for two
2 2.1
MATERIALS AND METHODS The soil
The soil used in the experiments is a Barcelona silty clay collected from a construction site near the laboratory at a depth of approximately 4 m below ground surface. This type of soil is commonly found in the area and has been extensively studied in the past in the laboratory, its geotechnical and hydro-mechanical properties being well known (Barrera 2002). Figure 1 shows typical grain size distribution and water retention curves for the soil used in the experiments. It is a fine grained soil, with 60.6% passing the No.200 sieve. Its main characteristics are: unit weight of soil particles γs = 27.1 kN/m3 ; liquid limit wL = 32%; plastic limit wP = 16%. According to the unified soil classification system, the soil can be classified as low plasticity clay (CL). 2.2
Compact tension tests
The equipment for the determination of fracture toughness (KIC ) was developed at the Soil Mechanics Laboratory of UPC, using the equipment design of Ávila (Ávila 2004). Test specimens of two different sizes were tested (Table 1) at different moisture content, with a constant density γ = 1.95 ± 0.05 kN/m3 . Figure 2 show the schematics of the equipment.
405
The dry soil was sieved through a mechanical sieve of 1.18 mm (sieve no. 16); the material passing was used for the test. Distilled water was added in required quantity to achieve the intended moisture content. Once a visibly homogeneous paste was obtained, its moisture content was determined before pouring it into the CT-moulds. Moisture content was determined again when the experiment was completed. The CTmould was filled with the prepared material in three layers in order to have a homogeneous density. Loading pins were inserted to the specimens after removing from the moulds and a Methacrylate plate was inserted between the specimen and the nuts of the loading pin in order to ensure the correct load transmission to the right fracture zone just below the initial crack. The load was applied manually, with a constant frequency. The fracture load was determined counting all the weights in the loading pan after the specimen failed. The procedure was repeated for all the specimens. The moisture contents of the test specimens were 16%, 18%, 19%, and 21%, with an initial crack length of 10, 15, and 20 mm for the medium and 20, 30, and 40 mm for the big specimen. For each size, moisture content and initial crack length, tests were repeated with a minimum of two specimens and in some cases with three. A total of 55 specimens were tested. Table 1 gives the details of the geometry of the test specimens, with length (L), width (B), and thickness (W). A circular hole of diameter (φ) was made form a distance (d) to the edge of the specimen for loading pins. Figure 1. a) Grain size distribution; b) typical water retention curves for different dry unit weights (Barrera 2002). Table 1.
KI =
P ˆ √ k(α) B D
(1)
KI2 (2) E Fracture toughness (K) was calculated by eq.1, where D is the characteristic dimension of the specimen (in the present case W = D); P is the fracture ˆ load; and B is the width of the specimen. k(α) is a function depending on the geometry of the specimen ˆ (α = a/W). k(α) was calculated using two different empirical formulas, given by Eq. 3 (ASTM-E399-83 1983) and Eq. 4 (Srawley 1976). The fracture energy (G) was calculated using Eq. 2, with υ = 0.3 and E = 4.2 MPa (Barrera 2002).
GIC = (1 − ν 2 )
Details of CT-test specimens.
Mould
L (mm)
B (mm)
W (mm)
d (mm)
φ (mm)
Medium Big
60 120
25 50
45 90
15 30
12 24
k(α) = (30.96α − 195.8α 2 + 730.6α 3 − 1186.3α 4 + 754.6α 5 )
(3)
k(α) = (2 + α) 0.886 + 4.64α − 13.32α 2 + 14.72α 3 − 5.6α 4 × (1 − α)3/2 Figure 2.
(4)
Schematic diagram of CT-test equipment.
406
Figure 3. Schematic diagram of direct tensile strength equipment.
2.3
Direct tensile strength test
Tensile strength was determined using an equipment designed by Rodríguez (Rodríguez 2002), the equipment is similar to the one explained by Mikulish and Gudeus (Mikulish and Gudeus 1995). The equipment is made up of 3 main parts, (see fig. 3): two pieces of trapezoidal shape, one fixed and another one freely movable on application of external force, and a central part that is removed just before the application of the load; this is the only part of the specimen which will be subjected to tension during the test. A total of 42 tests were conducted for two different densities (18 tests with γ = 16 kN/m3 , and 24 tests with γ = 19 kN/m3 ) with average moisture content ranging from 12% to 30%. For each density and moisture content the tests were repeated with a minimum of two specimens and in some cases three. The soil used and the preparation of the material was the same as explained earlier for the fracture toughness tests. The depth of the soil placed in the equipment was fixed and the weight of the soil was varied to obtain different densities. The tensile strength (σT ) was calculated directly by dividing the area of soil under tension by the total load applied.
3
variation of the tensile strength with moisture content for all tests carried out. The maximum tensile strength is obtained with a moisture content of about 16% to 17%. The OMC (Optimum Moisture Content) of the soil is around 13.5% with a degree of saturation of approximately 80%. According to Towner (Towner 1987), the tensile strength is a material property that depends in general on both suction and water content. Moreover the relationship also depends on the degree of inherent or induced anisotropy that may exist in the material. Several methods are available to determine the tensile strength of soils. Accuracy of the values depends on the test methods used and the equipment. The direct method is considered to be the most straightforward and reliable. In the present study, because of the trapezoidal shape of the equipment, the tension was applied only to the central zone. Figure 4 shows the variation of tensile strength with moisture content for two dry densities. A clear difference in the tensile strength for different densities on the dry-side is observed, whereas on the wet-side the difference is smaller. Similar behaviour has been observed by other authors (Favaretti 1996; Tamarakar, Toyosawa et al. 2005; Rodríguez 2006). 3.2
Fracture toughness
Figure 5a shows the variation of fracture load for the two specimen sizes (medium and big) at various moisture contents. As a common and well known trend, here also the fracture load increases with decrease in initial crack length (Lee, Lo et al. 1988; Nichols and Grismer
RESULTS AND DISCUSSIONS
3.1 Tensile strength The tensile strength was determined for two densities and at different moisture contents. Figure 4 shows the
Figure 4. content.
407
Variation of tensile strength with moisture
bond ruptures that constitute the mechanism of fracture are provoked by the energies of thermal vibrations (Cottrell 1964). This is valid for many materials: metals, glass, ceramics, rocks, concrete, etc. which can be considered as single phase and/or continuous medium. Soils, however are particulate media, and usually two-phase (solid particles and pore fluid when fully saturated) or three-phase systems (solidpore fluid-air when un-saturated). The most important characteristic of such materials is the behaviour of stress-strain relationship depending on the degree of saturation keeping aside the temperature effects. At a given temperature the variation in degree of saturation will affect the stress-strain behaviour. Therefore the fracture behaviour of soils depends largely on the variation of degree of saturation (suction and tensile strength) which affects the fracture toughness. Figure 6 shows the fracture toughness vs moisture content. The data points follow an exponential behaviour, with decreasing K values for increasing moisture content. Bazant and Prat (Bazant and Prat 1988) observed a similar behaviour on the fracture energy of concrete with temperature. Fracture energy decreased exponentially with increase in temperature. They used Rate Process Theory and Activation Energy to explain the behaviour, which generally follows a formula of the type a˙ = f (K) exp(−U /RT ) (Cherepanov 1979), where U = activation energy of bond rupture; R = universal gas constant; T = absolute temperature; K = stress intensity factor; and f (K) = empirical monotonically increasing function. Further studies are necessary to establish the applicability of the rate process theory and activation energy
Figure 5.
(a) Fracture load (b) Fracture energy.
1997) irrespective of specimen size and moisture content. Other observed important behaviour, particular to soils, is the effect of moisture content on the fracture load: fracture load decreases as the moisture content of the test specimens increases for both sizes’s tested. Figure 5b shows the variation of the fracture energy, G, with the initial crack length. The regression lines calculated with the ASTM and Srawley methods show that G is approximately constant (Lee, Lo et al. 1988) for a given moisture content, proving that G is a material constant (depending on moisture content for soils). 3.3
Activation energy
It is generally accepted that fracture is a thermally activated rate process. This means that the atomic
Figure 6. content.
408
Variation of fracture toughness with moisture
to explain the variation of fracture toughness with soil moisture change. 4
CONCLUSIONS
At lower moisture contents (drier moisture content to OMC), the effect of density is more pronounced on the tensile strength, whereas at moisture content wetter to OMC, there seems to be little effect of density and is almost negligible at saturation. Fracture toughness (Mode I) of Barcelona Silty soil significantly depends on the moisture content. It decreases monotonically with the increase in moisture content. The data points of fracture toughness vs moisture content follow an exponential curve. Similar behavior was observed for concrete with temperature. This prompts to check the applicability of Rate Process Theory and Activation Energy to explain such a behavior. ACKNOWLEDGEMENTS The research reported in this paper has been carried out within the framework of two research projects financed by the Spanish Ministry of Education and Science (BIA2003-03417 and CGL2006-09847). Their support is gratefully acknowledged. REFERENCES ASTM-E399-83. 1983. Standard test method for planestrain fracture toughness of metallic materials. American Society for Testing and Materials. Ávila, G. 2004. Estudio de la retracción y el agrietamiento de arcillas. Aplicación a la arcilla de Bogotá (In Spanish). Technical University of Catalonia.
Barrera, M.B. 2002. Estudio experimental del comportamiento hidro-mecánico de suelos colapsables (In Spanish). Technical University of Catalonia. Bazant, Z.P. and Prat, P.C. 1988. ‘‘Effect of temperature and humidity on fracture energy of concrete.’’ ACI Materials Journal (July–August): 262–271. Cottrell, A.H. 1964. The Mechanical Properties of Matter. New York, John Wiley & Sons. Cherepanov, G.P. 1979. Mechanics of brittle fracture. New York, McGraw-Hill Book Co. Favaretti, M. 1996. Tensile strength of compacted clays. State of the art in Unsaturated Soils, E.E. Alonso and P. Delage, eds, Rotterdam, Balkema. Lee, F.H., Lo, K.W. et al. 1988. Tension crack development in soils. ASCE J. Geotech. Engrg. 114(8): 915–929. Mikulish, W.A. and Gudeus, G. 1995. Uniaxial tension, biaxial loading and wetting tests on loess. First Int. Conf. on Unsaturated Soils, Paris, Balkema/Presses des Ponts et Chaussées. Nichols, J.R. and Grismer, M.E. 1997. Measurement of fracture mechanics parameters in silty-clay soils. Soil Science 162(5): 309–322. Rodríguez, R. 2006. Hydrogeotechnical characterization of a metallurgical waste. Canadian Geotechnical Journal 43: 1042–1060. Rodríguez, R.L. 2002. Estudio experimental de flujo y transporte de cromo, níquel y manganeso en residuos de la zona minera de Moa (Cuba): Influencia del comportamiento hidromecánico (In Spanish). Technical University of Catalonia. Srawley, J.E. 1976. Wide range stress intensity factor expressions for ASTM E-399 standard fracture toughness specimens. Int. J. Fracture 95: 475–476. Tamarakar, S.B., Toyosawa, Y. et al. 2005. Tensile strength of compacted and natural soils using newly developed tensile strength measuring apparatus. Soils and Foundations 45(6): 103–110. Towner, G.D. 1987. The mechanics of cracking of drying clay. J. Agric. Engrg. Res 36: 115–124.
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Tensile strength of some compacted fine-grained soils A.J. Lutenegger & A. Rubin University of Massachusetts, Amherst, MA, USA
ABSTRACT: Compacted soils are generally unsaturated soils, at least initially after compaction, although they may become saturated over time as a result of rising water tables, surface water infiltration, etc. The tensile strength of compacted soils can be an important design parameter for earth dams and embankments and should be considered in the design and development of earthwork specifications. A laboratory study was performed to determine the tensile strength of four compacted soils representing a wide range of geologic materials including an alluvial clay from Mississippi, a Piedmont residual soil from Georgia, a loess soil from Nebraska and a lacustrine clay from Massachusetts. Proctor curves for each soil were developed using Reduced, Standard, and Modified compaction energy. Following compaction the tensile strength of each specimen was determined using the Double Punch Test. The results showed that the Double Punch Test is most reliable near the Optimum Water Content. The measured tensile strength for each water content in the range of OWC ±6% was normalized by the tensile strength at the Optimum Water Content for each level of compaction effort. The results showed a linear trend between Normalized Tensile Strength and the deviation from the Optimum Water Content.
1 1.1
INTRODUCTION AND BACKGROUND Tensile strength of compacted soils
The tensile strength of soils has received relatively minor attention in the past 40 years, perhaps because it is assumed that the tensile strength is a small quantity in comparison to compressive strength or perhaps because engineers have a poor understanding of tensile strength. Tensile failure of soils can occur in natural soils, such as in slope failures, landslides, or cuts or in compacted soils in slopes, embankments, dams, or clay liners. The development of tension cracks in soils is an indication that tensile strength may be important in various design situations. Compacted soils are by default unsaturated and they may remain unsaturated throughout their life or they may take on water as a result of water infiltration or water flow, as through an earth dam. The engineering properties of compacted soils are therefore dependent on a range of water content that the soil may have after compaction, but in some cases may be critical immediately after compaction has been completed. Previous studies on the tensile strength of compacted clays have used both Direct Tensile Tests (e.g., Tschebotarioff et al. 1953; Dash and Lovell 1972; Ramiah et al. 1977) and Indirect Tensile Tests (e.g., Narain and Rawai 1970; Fang and Chen 1971, 1972;
Satyanarayana and Satyanarayana Rao 1972; Fang and Fernandez 1981; Favaretti 1991, 1995) to evaluate tensile strength. By far, the majority of previous studies have used Indirect Tensile Tests, including: 1) the Split Tensile Test; 2) Bending Tests; and 3) the Double Punch Test. 1.2
The Double Punch Test
The Double Punch Test (DPT) was developed by Fang and Chen (1971, 1972) as an indirect method for determining the tensile strength of compacted soils. A schematic of the Double Punch Test is shown in Figure 1. The Double Punch Test is essentially an unconfined splitting test which is performed by first centering a standard cylindrical compaction specimen between two steel discs centered on the top and bottom of the specimen. A vertical load is then applied slowly on the discs until the specimen reaches failure. The tensile strength of the soil is then calculated from the maximum load using the theory of plasticity. Fang and Chen (1972) plotted the results of tensile strength as calculated by the Double Punch Test versus the Split Tensile Test and found an excellent comparison. The Double Punch Test is an attractive approach to determining tensile strength of compacted soils for a number of reasons; 1) the test is easy to perform and
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clay from Mississippi; 2) Geo-Hydro (GH)—a Piedmont residual clay from Atlanta Georgia; 3) Nebraska Loess (NBL)—a Late Wisconsinan loess deposit from east-central Nebraska; 4) Connecticut Valley Varved Clay (CVVC)—a lacustrine clay and silt deposit from Amherst, Massachusetts. The soils represent a wide range of geologic materials. Standard engineering properties of the four soils are given in Table 1. 2.2
Figure 1.
Schematic of the Double Punch Test.
requires no particular special equipment aside from a loading frame and a set of steel punches; 2) the test may be performed in conjunction with a Proctor compaction test; 3) it appears that the tensile strength is not sensitive to the rate of strain within the range of 0.03 to 2.0 in per min.; 4) the test results appear to be very closely correlated to results from the Split Tension Test. However, the test is not without limitations: 1) the test procedure is not standardized; 2) Fang and Chen (1972) found that the punch size affects the tensile strength and recommend punch diameters between 12.5 mm and 37.5 mm to be used on Proctor compaction specimens; 3) homogeneity of the soil is assumed, but this is an unavoidable deviation from the ideal found in nearly all soil tests; 4) when very soft high water content clays (i.e., very wet of the Optimum Water Content) are placed on the bottom punch, they may slump or barrel out or the punches may simply penetrate into the ends of the specimen without creating a true tensile failure; 5) when soils compacted very dry of the Optimum Water Content are tested, the failure may not follow the idealized assumed tensile failure plane. Overall, for soils compacted slightly below and slightly above the Optimum Water Content, the test appears to provide very useful results. It is in this range of water content where the engineer is most interested for compacted works.
2 2.1
Test procedures
Test specimens were compacted using Standard Proctor (SP), Modified Proctor (MP) and Reduced compaction energies. Reduced compaction (RP) is identical to Standard Proctor except that each layer only receives 15 drops of the Standard hammer instead of 25 drops. After compaction, specimens were extruded from the compaction mold and Double Punch Tests were performed. Test specimens were carefully centered between the top and bottom loading stainless steel punches which had a diameter of 25 mm. Alignment of top and bottom punches was rechecked and zero readings were taken on an LVDT and electronic load cell connected to an automated data acquisition system. Specimens were loaded at a constant rate of vertical displacement of 0.5 mm per minute until peak load was reached. The tensile strength was calculated using the approach presented by Fang and Chen 1971; 1972) as: σt = P/(π(kbH − a2 )) where: σt = tensile strength P = maximum observed load k = tan(2α + ϕ) ≈ 1 a = radius of the punch b = radius of specimen H = height of specimen α = angle of the cone to the surface ϕ = friction angle of the soil The value of k in Equation 1 takes into account the friction angle of the soil, ϕ, the sample punch dimension Table 1.
Soil
INVESTIGATION Soils tested
Four fine-grained soils were selected for testing; 1) Buckshot Clay (BSC)—a high plasticity alluvial
(1)
BSC GH NBL CVVC
412
Summary of soil properties of soils tested. Liquid limit (%)
Plastic limit (%)
Shrinkage limit (%)
clay (%)
52.6 38.0 34.6 47.1
21.4 18.0 20.9 26.1
7.5 18.0 17.5 20.4
35.8 30.1 22.3 37.9
ratio bH/a2 , and the soil compression-tensile strength ratio qu /σt (Fang and Chen 1972). According to Fang and Chen (1972) the value of k for soils compacted in a Proctor mold is approximately 1. Favaretti (1995) suggested that using a k value of 0.9 would provide a better correlation between results from the Double Punch Test and the Brazilian Test.
3
RESULTS
Table 2 gives a summary of the Optimum Water Content (OWC) and the Maximum Dry Density (MDD) obtained for each level of compaction energy for each of the four soils. Results of all compaction and tensile strength tests are given in Table 3. Figures 2 and 3 show the variation in tensile strength with compaction water content and compacted dry density for all tests. The results are highly scattered and clearly show no apparent trend. This is generally to be expected as the soil specimens exhibit degrees of saturation from 60% to 90% along the compaction curves for each of the compaction energies. It should be expected however that for a given soil dry density the soil with the lower degree of saturation, will exhibit higher tensile strength. Some of the variation in Figures 2 and 3 may be related to problems in the testing procedure discussed in paragraph 1.2. This is particularly noticeable at very low and very high water content. At these extreme water contents, the soil dry densities are low and difficulties in performing the Double Punch Test are encountered. In particular, at very low water content, failure of the specimens is very abrupt and the specimen often does not fail along vertical failure planes as assumed; at very high water content, the end punches simply penetrate into the ends of the specimen without producing a tensile failure. Based on these observations, it appears that the DPT is likely to be most applicable within a relatively narrow range of water content near the Optimum Water Content where the soil behaves more plastic. Figure 4 shows the variation in tensile strength for the Buckshot Clay as a function of the compaction Table 2. Interpreted optimum water content and maximum dry density. Reduced
Standard
Modified
Soil
OWC MDD OWC MDD OWC MDD (%) (Mg/m3 ) (%) (Mg/m3 ) (%) (Mg/m3 )
BSC GH NBL CVVC
22.5 20.0 17.8 25.0
1.61 1.71 1.62 1.43
21.0 18.5 17.0 22.5
1.63 1.78 1.71 1.59
20.0 15.6 15.0 19.7
1.73 1.90 1.81 1.71
Table 3.
Summary of compaction and tensile strength tests.
Specimen
Water content (%)
Dry density (Mg/m3 )
Tensile strength (kPa)
Buckshot Clay 1R 2R 3R 4R 5R 1S 2S 3S 4S 5S 1M 2M 3M 4M 5M
10.7 16.8 19.1 21.9 24.1 10.3 15.4 18.1 21.6 24.5 10.7 15.4 18.0 20.7 23.8
1.42 1.40 1.43 1.55 1.45 1.54 1.48 1.60 1.61 1.60 1.64 1.68 1.64 1.70 1.64
3.8 10.8 10.4 10.0 5.4 11.3 16.5 18.1 15.6 8.3 21.6 38.2 33.1 17.6 11.0
Geo-Hydro 1R 2R 3R 4R 5R 1S 2S 3S 4S 5S 6S 1M 2M 3M 4M 5M
9.8 12.8 15.1 17.7 19.2 9.4 12.2 16.2 19.3 20.0 24.0 8.6 11.4 15.6 20.1 21.4
1.51 1.52 1.71 1.72 1.70 1.62 1.63 1.75 1.77 1.78 1.72 1.70 1.79 1.90 1.70 1.73
4.5 10.1 8.8 5.7 3.7 7.9 16.6 15.5 4.2 3.4 1.3 15.7 36.6 16.4 3.7 2.1
Nebraska Loess 1R 2R 3R 4R 5R 1S 2S 3S 4S 5S 1M 2M 3M 4M 5M
11.5 14.8 17.8 19.3 22.6 10.6 13.3 17.2 19.5 24.0 9.0 14.1 17.8 20.4 23.9
1.53 1.57 1.62 1.60 1.59 1.65 1.68 1.71 1.70 1.56 1.67 1.80 1.79 1.72 1.61
9.3 8.5 7.6 5.0 2.0 14.5 14.3 8.4 5.9 1.3 26.7 26.6 8.4 5.5 1.8
CVVC 1R 2R 3R 4R
8.1 12.3 15.9 19.8
1.41 1.41 1.38 1.41
1.9 2.9 3.8 6.0 (continued)
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Table 3.
(continued)
50 Buckshot Reduced
Specimen 5R 1S 2S 3S 4S 5S 1M 2M 3M 4M 5M
Dry density (Mg/m3 )
25.0 7.8 10.4 15.2 21.2 24.9 7.8 11.9 15.1 19.7 23.4
Tensile strength (kPa)
1.43 1.48 1.50 1.52 1.53 1.59 1.58 1.58 1.66 1.71 1.65
Buckshot Standard
40
Tensile Strength (kPa)
Water content (%)
6.5 4.6 5.7 10.6 11.9 7.5 18.3 19.5 24.3 19.3 3.7
Buckshot Modified 30
20
10
0 -6
-4
-2
0
2
4
6
Water Content Deviation from OWC (%)
Figure 4. Relationship between tensile strength and deviation from OWC. 50
Tensile Strength (kPa)
Table 4. content.
Buckshot GeoHydro Nebraska CVVC
40
Interpreted tensile strength at optimum water Tensile strength (kPa)
30
20
10
Soil
Reduced
Standard
Modified
BS GH NBL CVVC
8.0 3.0 7.2 6.0
15.0 7.5 9.0 10.5
22.5 20.0 17.5 15.5
0 6
8
10
12
14
16
18
20
22
24
26
Water Content (%)
Figure 2.
Variation in tensile strength with water content.
50 Buckshot GeoHydro Nebraska CVVC
Tensile Strength (kPa)
40
30
20
10
0 1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
Dry Density (Mg/m3 )
Figure 3.
Variation in tensile strength with dry density.
water content deviation (both + and −) away from the Optimum Water Content. The data indicate a variation that is approximately linear over the range OWC ±6%. Since it is unlikely that a specimen will be compacted exactly at the OWC, the tensile strength at the OWC
may be estimated from the linear trends shown in Figure 4. The other three soils showed similar results. The interpreted tensile strength at the OWC for each level of compaction energy for all four soils is given in Table 4. The interpreted tensile strength at the OWC may be then used to calculate the ‘‘Normalized Tensile Strength’’, i.e. tensile strength at any water content divide by the tensile strength at OWC. As an example, the variation in Normalized Tensile Strength as a function of the deviation from the OWC for the Buckshot Clay is Figure 5. These results also show an approximate linear trend. The combined Normalized Tensile Strength results for all four soils are shown in Figure 6. Even though the soils represent a wide range in geologic and geographic origin and have different properties, there appears to be a unifying linear trend between the Normalized Tensile Strength and the deviation of water content from the OWC for all levels of compaction energy within the window of water contents just below and just above OWC. Some of the variability shown in Figure 6 may simply be related to the interpretation of the Optimum Water Content from the compaction curve for each soil. The water content deviation from the OWC shown in Figure 6 is actually quite large (±6%) and most
414
a project. The results appear to be insensitive to soil type, at least within the range of characteristics for the four soils tested.
Normalized Tensile Strength
3 Buckshot Reduced Buckshot Standard Buckshot Modified Regression Line
2
4 1
0 -6
-4
-2
0
2
4
6
Deviation from Optimum Water Content (%)
Figure 5. Variation in Normalized Tensile Strength with deviation from OWC for Buckshot Clay.
Normalized Tensile Strength
4 Buckshot GeoHydro Nebraska CVVC Trend Line
3
2
0 -4
-2
0
2
4
The tensile strength of four fine-grained soils was evaluated using the Double Punch Test for three different levels of compaction energy. The results suggest that the Double Punch Test can be used to reliably estimate the tensile strength of compacted soils and is most applicable at water contents near the OWC. At extreme water content both dry and wet of OWC there are difficulties with the test in determining the tensile strength of the soil. The results also show a general global linear trend between the Normalized Tensile Strength and the water content deviation away from the OWC, particularly in the range of OWC ±4%, which is a typical working range for many field compaction specifications.
REFERENCES
1
-6
CONCLUSIONS
6
Deviation from Optimum Water Content (%) Figure 6. Variation in Normalized Tensile Strength with deviation from OWC for all four soils.
likely somewhat unrealistic for an actual field application for compacted soil, considering typical compaction specifications. The data shown in Figure 6 still indicate considerable scatter at low water content. A more realistic range in water content for field compaction specifications would likely be on the order of OWC ±3 to 4% depending on other design criteria. The results shown in Figure 6 suggest that tensile strength of compacted fine-grained soils may be described using Normalized Tensile Strength relative to the deviation of compacted water content away from the OWC within the window of typical field compaction procedures. This is convenient since it is only necessary to determine the tensile strength at the OWC in order to predict the range in tensile strength of other conditions of water content and compacted density on
Dash, U. and Lovell, C.W., Jr. 1972. Tensile Strength of Clays. Proc. 3rd Southeast Asian Conference on Soil Engineering: 205–210. Fang, H.Y. and Chen, W.F. 1971. New Method for Determination of Tensile Strength of Soils. Highway Research Record (345): 62–68. Fang, H.Y. and Chen, W.F. 1972. Further Study of DoublePunch Test for Tensile Strength of Soils. Proc. 3rd Southeast Asian Conference on Soil Engineering. 211–215. Fang, H.Y. and Fernandez, J. 1981. Determination of Tensile Strength of Soils by Unconfined Penetration Test. ASTM STP 740: 130–144. Favaretti, M. 1991. Tensile Strength Tests on Cohesive Compacted Soils. Proc. 9th Asian Regional Conference on Soil Mechanics and Foundation Engineering, 1, 37–40. Favaretti, M. 1995. Tensile Strength of Compacted Clays. Proc. 1st International Conference on Unsaturated Soils, 1: 51–56. Narain, J. and Rawai, P.C. 1970. Tensile Strength of Compacted Soils. Journal of the Soil Mechanics and Foundations Division, ASCE, 96 (SM6): 2185–2190. Ramiah, B.K., Purusothsama Raj, P., Chickanagappa, L.S. and Raghunatth, S.P. 1977. Some Studies on the Tensile Strength of Soils. Proc. 5th S.E. Asian Conference on Soil Engineering: 327–337. Satyanarayana, B. and Satyanarayana Rao, K. 1972. Measurement of Tensile Strength of Compacted Soil. Geotechnical Engineering, 3: 61–66. Tschebotarioff, G.P., Ward, E.R. and DePhilippe, A.A. 1953. The Tensile Strength of Disturbed and Recompacted Soils. Proc. 3rd International Conference on Soil Mechanics and Foundation Engineering, 1: 207–210.
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Unsaturated characteristics of rammed earth P.A. Jaquin, C.E. Augarde & L. Legrand Durham University, Durham, UK
ABSTRACT: Rammed earth is both an ancient construction technique and the name for the material produced by the technique. Rammed earth is gaining in popularity around the world due to its ecological and sustainable attributes. Walls of rammed earth are formed by taking a graded mixture of (usually) locally-won soil and compacting the mixture between formwork in a similar manner to concrete. The formwork is then removed leaving a solid earth wall. There is little scientific understanding of the source of strength in rammed earth and design to date has used empirical approaches. In this paper we consider rammed earth as an unsaturated soil thus explaining one source of strength to be from suction. Laboratory tests have been carried out on rammed earth samples including unconfined compression and Brazilian tests (to measure strength) and filter paper tests (to determine the water retention properties). The tests all indicate that a source of strength in rammed earth derives from suction and conclusions are drawn as to their levels in ancient rammed earth structures.
1
INTRODUCTION
Rammed earth is both a material (a compacted mixture of sand, gravel and clay) and the name for the construction procedure whereby walls are built using this material rammed in layers between formwork. The technique has been used by man for thousands of years and many historic structures containing rammed earth features remain standing to this day. Examples include the Potala Palace in Lhasa, Tibet and the Alhambra in Granada, Spain (Guillaud et al. 2004). Historic rammed earth structures have been studied by engineers and archaeologists at Durham for a number of years (e.g. Jaquin et al. 2006). The use of rammed earth for building has to date relied on empirical rules developed from experience, and often linked to a particular location in the world. A large number of heritage rammed earth structures exist, some of considerable antiquity. They are most commonly located in a belt around the equator reaching as far north as the UK (Jaquin et al. 2007). The nature of the material is such that arid conditions are favourable for long term durability and there are now concerns for the future of some of these structures under the effects of climate change. Increased interest in rammed earth for new buildings is being seen in countries away from this traditional zone of past use. The reason for this is the inherent sustainability of the material (it can be re-used), the often local sourcing and the avoidance of the use of cement. An exception to the last of these is the material termed ‘‘stabilised’’ rammed earth, where
cement or another stabiliser is added to improve durability. In the tests described later in this paper we will be concerned only with unstabilised rammed earth. Rammed earth mix design is somewhat of a black art with advice varying according to location, soil type and occasionally cultural constraints. A typical mix is well-graded, containing particles in each of the four soil fractions: gravel, sand, silt and clay. Walker et al. (2005) indicate that the majority of modern rammed earth mixes lie in the following ranges of percentages by mass: sand and gravel, 45–80%; silt 10–30% and clay, 5–20%. The large size of these ranges provides further evidence of the empirical nature of rammed earth design. It is clear that a material which can be formed into vertical walls which stand for hundreds of years has some cohesive strength. The source for this could be cementation between particles; however, walls can also be built from plain unstabilised rammed earth where no cementation is present. The source of strength must then lie elsewhere and suction appears to be a prime candidate, although to our knowledge this has not been highlighted before. Few studies exist where rammed earth is characterized as an engineering material using rigorous testing procedures. One example is Lilley and Robinson (1995) who describe tests on rammed earth walls built at near full-size studying the effects of making (or forming) various openings. In this work the authors undertook rudimentary materials testing including cube tests (as for concrete) finding compressive strengths of 1.8–2.3 MPa. Another example
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can be found in a series of papers by Hall (e.g. Hall and Djerbib, 2004) where the hydraulic behaviour is linked to particle size distribution through experimental and analytical work. However neither of these or the few other published studies make the link between suction and strength in rammed earth. Our contention is that rammed earth can be regarded as a compacted unsaturated soil. Modern rammed earth is usually prepared and compacted into place at optimum moisture content. With further drying, made easy by the large surface area of the walls, the material must reach a very low degree of saturation. This is likely to be even lower than the degree of saturation found in compacted soils with which geotechnical engineers are familiar. Therefore high suctions must be generated within the walls, hence providing some apparent cohesion. The purpose of the research described below is to begin to verify this theory. If rammed earth can be regarded as a manufactured unsaturated soil it is then possible to bring a greater degree of scientific rigour to the study of the material and to the development of economic design codes. Clearly this suction-induced increase of apparent cohesion with drying cannot be unlimited. A completely dry rammed earth mix would have no apparent cohesion due to suction as no water would be present. However this is both unrealistic (as rammed earth in a structure will never completely dry) and in the laboratory as, even at oven dry conditions (i.e. zero water content), adsorbed water will still be present on clay particles and will be available to generate suctions. Other studies (e.g. Toll and Ong, 2003) have shown that in soils similar to rammed earth the contribution to strength from suction reduces as the degree of saturation reduces, so although suction increases as the soil dries out, the contribution to strength reaches a peak and then drops away (Toll, 1990). The apparent cohesion in rammed earth is therefore expected to peak between the two limits of zero water content and saturation.
s=−
Suction and relative humidity
Rammed earth includes particles with a much greater range of sizes than in the unsaturated soils that are commonly studied. However, there is no reason why the presence of water in liquid bridges should not provide strength through established mechanisms. A liquid bridge exists in a soil pore where both air and water are present in the pore space. The surface tension acting at the interface of the water and air, combined with tension in the water, act to provide an attractive force across the pore, which provides an unsaturated soil with an apparent cohesion. This liquid bridge force between the soil particles was first idealised by considering the soil particles to be
ρw RT ln(RH ) wv
(1)
where R = the universal gas constant, T = absolute temperature, ρw = density of water and wv = the molecular mass of water vapour (Likos and Lu 2004). Equation 1 is plotted in Figure 1 for T = 20◦ C. The figure shows that small variations in RH between 100% and 95% lead to large changes in total suction up to around 1MPa. Small variations in RH below 95% then lead to relatively small changes in suction (although the actual values of suction are large). Such low values of RH are likely to be present in the arid parts of the world where heritage structures containing rammed earth can be found and thus supports the hypothesis that suction is the significant provider of strength in rammed earth. Structures existing in
Relative Humidity
1.1
spherical (Fisher 1926) assuming a wetting angle of zero. Developments of this theory towards realistic soils has progressed via the works of Gillespie and Settineri (1967) who extended to a finite liquid-solid contact angle, and Pietsch (1968) who took account of surface roughness of the particles by assuming a separation distance between idealised smooth spheres. Lian et al. (1993) provided a mathematical basis for the interactions between a liquid bridge and rough rigid spheres which were applied more recently by Molenkamp and Nazemi (2003). It is clear that further developments could begin to approach the pore structures likely to be present in rammed earth, with large particle size ranges, angularity and surface roughness. In addition, at the continuum level double-structure models for unsaturated soils (as reviewed recently in Gens et al. (2006)) could provide suitable frameworks for constitutive modelling of rammed earth materials. The effect of relative humidity (RH) is particularly important for rammed earth due to the large exposed surface areas. Total suction s (the sum of matric and osmotic suctions) is linked to the relative humidity of the pore air through Kelvin’s equation, which can be expressed as
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Suction (kPa)
Figure 1. suction.
418
Relation between relative humidity and total
regions in which RH is in the descending part of the curve of Figure 1 will experience relatively small changes in suction, thus leading to stability over time. Evaporation of pore water is affected by the relative humidity (RH ) of the pore air compared to that of the adjacent air outside the wall. In practice drying of the walls will continue until the pore air humidity equals the humidity of the surrounding air.
2
LABORATORY TESTING
The aim of the laboratory testing described below was to confirm a link between suction and strength in rammed earth and also to study the changes in water retention behaviour as changes are made to the mix constituents. Laboratory testing consisted of unconfined compression tests, Brazilian tests and filter paper tests. The basic rammed earth mixture used in this study was taken from a development site at Aykley Heads, Durham, which included a large rammed earth wall completed in 2006. The mixture used on site was blended from material dug from the site (alluvial sand), coarse aggregate and a powdered clay/silt mixed in proportions (0.25:0.60:0.15; aggregate:sand:clay) using a horizontal axis mixer. In the laboratory tests described here, this mixture was first sieved to remove material retained on a 14 mm sieve. This was necessary to enable testing on standard sized samples. The sieved basic mix constituents are given in Table 1. The basic mix was altered for the Brazilian and filter paper tests to include a 10% increase in sand (mix A) and a 10% increase in clay (mix B). The dry density/water content relationship for the basic mix was obtained using the vibrating hammer compaction test (BS1377:2, 1990) and showed an optimum water content of approximately 8–10%. The vibratinghammer was used as it was thought closer to the field compaction that would be used during wall construction and the method of sample preparation for the compression tests (in comparison to the standard Proctor test).
air-drying of the samples. A tensiometer was used in each test to measure suction during shearing. These instruments have been developed at Durham University for the measurement of high suctions up to the air entry value of the ceramic incorporated into these devices, in this case 1500 kPa (Lourenço et al. 2006). Cylindrical samples (200 × 100 mm dia.) were prepared using a Proctor split compaction mould, as outlined in Walker et al. (2005), with modifications following Horncastle (2006). Samples were compacted in 5 layers following which a screed of particles passing a 425 μm sieve was placed on the top surface of the cylinder. This screed served a dual purpose of producing both a flat loading surface and a fine particle paste on which to place the tensiometer. Immediately following application of this screed, the Proctor split mould was removed and the mass and height of the sample recorded. Dry densities of between 2017 and 2061 kg/m3 were achieved using the same compactive effort each time. Once samples had air dried to the required water content for testing they were wrapped in an impermeable sheath secured with rubber O-rings placed against steel loading plates at the top and bottom of the sample. The samples were then left for at least 7 days to allow suctions to equilibrate throughout the sample. When it was considered that the samples were ready for testing, the top plate was replaced with a loading plate drilled to accommodate a tensiometer. The samples were sheared under constant water content conditions in a triaxial testing rig. Displacement was controlled at a constant 0.1 mm/min and measurements of suction, load and axial displacement taken every 10 seconds using the logging software Triax (Toll 1999). Figure 2 shows plots of deviator stress against suction measured for the seven tests. The figure provides strong evidence of a link between starting water content and strength as indicated by the dotted envelope to the results. However, this can also be stated as a link between suction present in the sample at the start of testing and strength. 700
Unconfined compression tests
Deviator stress (kPa)
2.1
Seven unconfined compression tests at constant water content were carried out on the basic rammed earth mix at variable water contents achieved through Table 1.
% by mass
Passing
Size
Sand Silt Clay
21.5 52.3 26.2
D10 D30 D60
2.1 μm 85.9 μm 345.0 μm
500 400 300 200
100 10.2 0
Constituents for basic rammed earth mix.
Constituent
600
9.4
0
8.6
8.4
200
7.1
400 Suction (kPa)
5.5
600
800
Figure 2. Plots of deviator stress against suction for unconfined compression tests. Test water contents indicated against each test.
419
Another feature evident from this figure is the difference in the change in suction during shearing. In samples with initially high water contents, suction rises during the test. For the low water content samples the opposite is seen to happen. This is consistent with the concept of a unique water content to suction relationship at the Critical State as proposed by Toll (1990). It also complies with the framework including a Continuously Disturbed Line (CDL) for unsaturated soils proposed by Croney and Coleman (1954) and revisited recently by Tarantino (2007). Figure 3 shows plots of axial total stress against axial strain for the seven tests. Here it is notable that there is brittle behaviour for the low starting water content samples and ductile for high water content samples. Linking Figures 2 and 3 it is possible also to conclude that stiffness of a rammed earth sample is linked to suction. Further aspects of these tests are explored in more detail in Jaquin et al. (2007a). 2.2
Brazilian and filter paper tests
Following the unconfined compression tests described above the basic rammed earth mix was remixed to increase the coarse (sand) fraction (termed mix A) or to increase the fine (clay) fraction (termed mix B). What limited advice there is at present for the design of rammed earth mixes is based on mix proportions of the fractions. In this part of the study the aim therefore was to investigate the effects of changing the particle size distribution in a controlled way on the strength (and additionally) on the water retention properties. The filter paper test is an indirect method of measuring both matric and osmotic suction where filter papers are arranged adjacent to or sandwiched between, soil samples which are then left to equilibrate. The final water content of the filter paper provides the suction present in the soil sample via a calibration curve. In these tests the procedure described by Leong et al. (2002) was used. The advantage of 700 Deviator Stress (kPa)
600
5.5 500 400
7.1
300
8.4 8.6
200
10.2 9.4
100 0 0
1
2 3 Axial strain (%)
4
5
Figure 3. Plots of axial total stress against axial strain for the unconfined compression tests. Test water contents indicated against each test.
the filter paper method over the tensiometers used in the unconfined compression tests is that much higher suctions can be measured with the former. The filter paper specimens were prepared at 55 mm diameter with a height of 22 ± 2 mm from each of mixes A and B at a starting water content of 10%. Dynamic compaction of these specimens in an adapted Proctor apparatus proved difficult to control so these specimens were instead statically compacted in a triaxial rig to the required thickness maintaining the same target dry density of 2.05 Mg/m3 . Then a sandwich of three filter papers was inserted between two compacted samples and the joint wrapped with electrical tape. An additional filter paper was suspended above the soil sample and the whole system placed inside a closed sealed jar and left to equilibrate for two weeks inside a constant temperature container at 25 ± 1◦ C. By preparing a batch of samples and leaving them to dry to different moisture contents before filter paper testing it was possible to determine portions of the drying part of the soil water retention curve. Following the filter paper tests the same samples were then quickly tested using a modified Brazilian test. This test is widely employed to determine tensile strengths in rocks and involves compressive loading of a circular disc sample across a diameter to failure. An analytical solution exists (assuming elasticity) linking the tensile strength of the sample σt with the applied load P as follows: σt =
2P πdt
(2)
Where d = sample diameter and t = sample thickness. Clearly most soils are unsuitable for this type of test having little or no tensile strength and also often being too friable to withstand these conditions. For the rammed earth samples at low water contents no problems of this nature were experienced. The reuse of samples from the filter paper test for the subsequent Brazilian test proved successful although it was important to minimize the time between completing the filter paper test and starting the Brazilian test. Figure 4 shows the change in water content over time as samples air-dried. Note the scatter in the initial water contents. Although the mixes were prepared as a whole to uniform water content, the actual water content of each individual disc varied about this value. It is noticeable that mix B (clay added) dries to approximately the same water content in the first day as mix A (sand added) despite starting from a generally higher initial water content although the mechanism for this difference is not clear. The process of drying in rammed earth is complex. Knowledge of the particle size distribution does not provide sufficient information on the soil microstructure in the
420
6
12
5
Water content (%)
Water content (%)
14
10 8 6 4 2
Mix A Mix B
4 3 2 1
0 0
1
2
3 4 Time (days)
5
6
0
7
90
140
14
190 240 Tensile strength (kPa)
290
Water content (%)
12
Figure 6.
10
6 4 2 0 0
1
2
3 4 Time (days)
5
6
7
Figure 4. Drying of samples with time. Mix A (upper); Mix B (lower).
Water content (%)
Brazilian test results.
8
9 8 7 6 5 4 3 2 1 0
Mix A - total Mix A - matric Mix B - total Mix B - matric
0
10000
20000
30000
40000
Suction (kPa)
Figure 5. Soil-water retention curves for rammed earth mixes A and B.
two mixes, which has the greatest influence on drying. Rather it is the pore size distribution which must be critical, dependent on the former but also on compaction. From Equation 1 there is a direct link between suction and RH so it is natural that all samples dry to the same suction approximately. Figure 5 shows the drying portion of the soil-water retention curves for the two mixes A and B taken from the filter paper results. Both matric and total suctions are plotted showing that osmotic suction is of secondary importance in these samples, as might be expected from the nature of the pore water. The suctions rise to a high level at the very low water contents reached by the samples indicating again the need for the filter paper test in the determination of suctions. The coarser mix (A) appears to have a SWRC lying below that of the finer mix (B) thus having a lower water content for a given suction value. This
might be explained by consideration of the likely pore structures in these samples. The finer mix will have a more widespread network of smaller sized pores than the coarse mix. Therefore it is likely this mix will carry more of its pore water as bulk (funicular) water than the coarse sample. So for a given suction it will need more water as much will be trapped in the bulk masses, providing less potential than water in the pendular regime. This feature can also be linked to the theoretical analysis of Likos and Lu (2004) where theoretical soil-water retention curves for coarser materials lie below those for finer materials. Figure 6 shows the results of the Brazilian tests. The water content at the time of the test is plotted against tensile strength calculated from Equation 2. As water content reduces so tensile strength increases as expected if suction is a source of tensile strength. For a given tensile strength there is more water in mix B than in Mix A. Again this links to the idea that in mix B more water is held in the funicular regime, contributing less to strength than ‘‘equivalent’’ pendular water. The plot also shows that tensile strength increases rapidly at very low water contents as might be expected to occur in the surface of a rammed earth wall under prolonged dry conditions.
3
DISCUSSION
It seems obvious from these results that suction must provide a significant component of the strength of unstabilised rammed earth and therefore understanding of its evolution from compaction, through drying to long-term changes in relative humidity is important for the stability of a rammed earth structure. Considering that most walls are of considerable thickness (usually >300 mm and much greater in heritage structures) it can be surmised that a gradient of water content exists through the wall thickness. At the surface water content is low and suction is high. Permeability will also reduce as water content decreases in these locations. Thus the centre of a rammed earth wall
421
will be protected to some degree from water ingress, and will maintain a relatively constant level of suction and hence strength. This behaviour has been recorded in the laboratory by Hall and Djerbib (2004), referred to as the ‘‘Overcoat Effect’’. The high suctions present at the surface of a rammed earth wall will suck in impinging water. Surviving heritage structures often have design details that reduce impinging water, e.g. large overhanging eaves, features usually thought to aid longevity due to reduction in impact. The results above indicate that these features also serve to maintain surfaces at high suction and hence high strength. While knowledge of unstabilised rammed earth is vital to the conservation of existing structures it is accepted that it is unlikely to become widely used in temperate parts of the world for new-build due to its surface friability which, despite the discussion above, is inferior to concrete. It is stabilised rammed earth, however, that is likely to be the choice in these areas. For this material, in addition to suction there will be cementation between agglomerations of particles to add to the tensile strength. The interaction between the free water available in the material at time of compaction and the stabiliser (e.g. cement) is clearly important and much more difficult to study. The relative contributions to strength from cementation and from suction will depend on many variables, such as pore size distribution, proportions of stabiliser, curing conditions amongst others. This is an important area of future research.
4
CONCLUSIONS
This study is the first (to the authors’ knowledge) that has treated rammed earth as an unsaturated soil. The tests described above are intended to support this theory qualitatively and pave the way for further laboratory testing, which will be necessary if rammed earth materials are to be modelled in a modern geotechnical framework.
ACKNOWLEDGEMENTS The first author has been supported by an EPSRC DTA grant. The use of the rammed earth material from the Aykley Heads Site, Durham by Rivergreen Developments Ltd is gratefully acknowledged. The third author contributed through an ERASMUS placement at Durham University in 2007.
REFERENCES Croney, D. and Coleman, J.D. 1954. Soil Structure in Relation to Soil Suction (pF), J. Soil Science, 5(1), 75–84. Fisher, R.A. 1926. On the capillary forces in an ideal soil. Journal of Agricultural Science 16, 492–505.
Gens, A., Sanchez, M. & Sheng, D. 2006. On constitutive modelling of unsaturated soils. Acta Geotechnica, 1(3), 137–147. Gillespie, T. and Settineri, W.J. 1967. The effect of capillary liquid force on the force of adhesion between spherical solid particles. Journal of Colloid Interface Science 24, 199–202. Guillaud, H., Houben, H., Alva, A., Rodrigues, R., Pinto, F., Sastre, J.M., Shimotsuma, K. and Castellanos, C. 2004. Earthen Architectural Heritage on UNESCO’s ‘World Cultural Heritage List’. UNESCO, Paris, France. Hall, M. and Djerbib, Y. 2004. Moisture ingress in rammed earth: Part 1—The effect of soils particle size distribution on the rate of capillary suction. Constr. Bldg. Mats, 18(4), 269–281. Horncastle, T. 2006. Rammed earth construction. School of Engineering Durham University, MEng Dissertation. Jaquin, P.A., Augarde, C.E. and Gerrard, C.M. 2006. Analysis of historic rammed earth construction. Proc. 5th Int. Conf. Structural Analysis of Historical Constructions, Nov 6–8, New Delhi, India. Vol. 2, 1091–1098. Jaquin, P.A., Augarde, C.E. and Gerrard, C.M. 2007. Historic rammed earth distribution, International Journal of Architectural Heritage: Conservation, Analysis, and Restoration (submitted). Jaquin, P.A., Augarde, C.E., Gallipoli, D. and Toll, D.G. 2007a. The strength of rammed earth materials. Géotechnique (submitted). Leong, E.C., He, L. and Rahardjo, H. 2002. Factors affecting the filter paper method for total and matric suction measurements. Geotech. Test. J. 25(3): 322–333. Lian, G., Thornton, C. and Adams, M.J. 1993. A theoretical study of the liquid bridge forces between two rigid spherical bodies. Journal of Colloid Interface Science 161, 138–147. Lilley, D.M. and Robinson, J. 1995. Ultimate strength of rammed earth walls with openings, Proceedings—ICE: Structures & Buildings 110(3), 278–287. Likos, W.J. and Lu, N. 2004. Hysteresis of Capillary Stress in Unsaturated Granular Soil. Journal Engineering Mechanics ASCE 130(6): 646–655. Lourenço, S.D.N., Gallipoli, D., Toll, D.G. and Evans, F.D. 2006. Development of a Commercial Tensiometer for Triaxial Testing of Unsaturated Soils. 4th International Conference on Unsaturated Soils, April 2006 Phoenix, USA. Molenkamp, F. and Nazemi, A.H. 2003. Interactions between two rough spheres, water bridge and water vapour. Géotechnique 53(2): 255–264. Pietsch, W.B. 1968. Tensile strength of granular materials. Nature 217, 736–737. Tarantino, A. 2007. A possible critical state framework for unsaturated soils, Géotechnique 57, 385–389. Toll, D.G. 1990. A framework for unsaturated soil behaviour. Géotechnique 40(1): 31–44. Toll, D.G. 1999. A data acquisition and control system for geotechnical testing. Computing developments in civil and structural engineering, Edinburgh, Scotland. Toll, D.G. and Ong, B.H. 2003. Critical-state parameters for an unsaturated residual sandy clay, Géotechnique 53, 93–103. Walker, P., Keable, R., Martin, J. and Maniatidis, V. 2005. Rammed Earth, Design and Construction Guidelines. BRE Bookshop: Watford.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Experimental study of the influence of suction on the residual friction angle of clays V. Merchán, J. Vaunat, E. Romero & T. Meca Technical University of Catalonia, Barcelona, Spain
ABSTRACT: This paper presents a study on the effect of high suctions on the value of the residual strength of a high plasticity clay. Tests were carried out in a Bromhead ring shear apparatus adapted to allow for control of the relative humidity around the shear box during shearing. Data were obtained by testing samples of remolded FEBEX bentonite (wL = 102, IP = 53) prepared close to its plastic limit and further loaded and sheared under suctions ranging from 0 to 120 MPa. Experimental data shows evidence of a huge increase of the residual shear strength when the sample is sheared in unsaturated conditions. As a matter of fact, the shear strength envelope at a suction of 75 MPa is characterized by a null cohesion and a residual friction angle φrdry equal to 28◦ , that is 21◦ higher than the value in saturated conditions (7◦ ). Such a result extends to high plasticity clays the conclusions already obtained in previous studies on a low plastic silty clay (wL = 30, IP = 16, increment of φr between saturated and dry conditions equal to 5◦ ) and a medium plastic clay (wL = 55, IP = 28, increment of φr equal to 15◦ ). An explanation to such high changes in values of residual shear strength is finally discussed in the light of the process of clay aggregation during drying, whose existence is supported by visual observations (micrographs obtained in an Environmental Scanning Electron Microscope) and evidences of changes in the pore size distribution (measured by Microstructure Intrusion Porosimetry).
1
INTRODUCTION
It is well-known that clay materials present a decrease in shear strength when submitted to large relative displacements as a result of particle reorientation (Skempton, 1964). Factors affecting such a decrease have been the object of numerous experimental studies, which used different equipment such as direct or the annular shear devices (Bishop, 1971; Skempton, 1985; Bromhead, 1979). They indicated that the shear strength reaches a lower bound for very large displacements, characterized by a null cohesion and a residual friction angle. Value of the residual friction angle appears to be controlled by the level of normal stress (Skempton, 1985; Stark & Eid, 1994), soil grading (Skempton, 1964; Kenney, 1967; Lupini et al., 1981; Skempton, 1985), particle mineralogy (Mitchell, 1993), rate of shearing (Tika et al., 1996), pore water chemistry (Di Maio, 1996a, 1996b, Chighini et al., 2005). More recently, the effect of suction on the residual strength had been studied at low suctions by Sedano et al. (2007) and at high suctions with by Vaunat et al. (2006) and Vaunat et al. (2007). The latter results indicate that high values of suction (typically higher than 10 MPa) increase significantly the residual strength and that this effect becomes more important when the material is more plastic. As a matter of fact,
the increase in friction angle has been observed to be around 5◦ in Barcelona silt, a low plastic silty clay and 15◦ in Boom clay, a medium plastic clay. The main explanation for such an increase is similar to that put forward by Toll (1990) for the strength at critical state. It is due to a process of enhancement of material aggregation during drying that makes it behave in a more granular way. The present work deals with a continuation of the study and address the effect of high suctions on the residual strength of Febex bentonite, a high plasticity clay. The experimental programme is based on tests carried out in a Bromhead apparatus adapted to control the relative humidity in the shear box. In order to verify the hypothesis of clay aggregation, it is completed by observations carried out in a Environmental Scanning Electron Microscope and by determination of pore size distribution by Mercury Intrusion Porosimetry before and after the tests in the ring shear box.
2
MATERIALS AND TEST PROCEDURE
Table 1 presents the main properties of the FEBEX bentonite. The properties of the low and medium plasticity clay tested in previous studies (Vaunat et al.
423
Table 1.
Properties of the tested materials.
Property
BCN silty clay
Boom clay
FEBEX bentonite
30 16 2.66
55 28 2.7
102 53 2.7
15
40
68
Liquid limit (%) Plastic limit (%) Particle density, ρs (Mg/m3 ) Clay fraction < 2 μm (%)
2006; Vaunat et al., 2007) are reported in the same table. As in the previous studies, the material has been tested in a Bromhead ring shear apparatus adapted to control the relative humidity inside the shear box (Vaunat et al., 2007). A general scheme of the apparatus is presented in Figure 1. A glass cap placed around the shear box allows the sample to be isolated from the laboratory environment. The value of suction is imposed in the isolated chamber by means of a closed circuit of forced vapor convection connected to a vessel with controlled relative humidity (the relative humidity in the vessel is in equilibrium with a solution saturated in salts placed at its bottom). A hole perforated in the glass cap and further sealed with silicon allows for installing a hygrometer (Model HMT 100, ±%RH at [0–90%RH] and ±1.7%RH at [90–100%RH]) that measures the temperature and relative humidity actually applied inside the chamber during the test. Data is stored in real time on a computer through a USB device (NI9001). The general procedure involves: a. Preparation of a remolded sample close to its plastic limit. b. Consolidation of the sample under a given normal stress. c. Suction application through the vapor transfer technique. From that time, the evolution of relative humidity and temperature inside the chamber started to be registered. Also, the vertical displacement experienced by the sample (uv ) was measured by the LVDT. This stage is considered equilibrated when the relative change in vertical displacement δuv /uv reaches values lower than 1%. Because of the low permeability of the clay, the time to reach equilibrium has proved to be very long: 22 days have been necessary for a sample of 5 mm height to reach a suction of 75 MPa (in equilibrium with a relative humidity equal to 58% in the chamber). d. Shearing at a controlled displacement rate equal to 0.32 mm/min. Pilot tests performed on Boom clay have shown that this velocity is low enough for keeping ‘drained’ conditions during the shear.
Figure 1. General scheme of the Bromhead ring shear apparatus adapted to suction control.
Due to the high plasticity of the clay, displacements required to attain the full residual state are of the order of 80 mm. As a result of the long times involved during suction equilibration and shearing stages, only three tests, labeled Test I, II and III, have been performed. TEST I aimed at determining the residual strength envelope of the saturated material. It consists of a twostage shearing test performed under normal stresses equal to 300 and 450 kPa. The results indicate that the residual strength of saturated Febex bentonite is characterized by a null cohesion and a friction angle equal to 7.5◦ (see Fig. 3). Test II is a five-stage test that aimed at defining the residual shear strength envelope of the material at a suction of 75 MPa and after resaturation. The sample was first equilibrated under a relative humidity equal to 58% (suction equal to 75 MPa) and sheared consecutively under a normal stress equal to 100, 200 and 300 kPa. Afterwards, the system to control relative humidity was removed and the sample brought to saturated conditions by flooding. Material was then sheared in two steps under normal stresses equal to 100 and 200 kPa, respectively. The accumulated displacement applied during all the test is 2535 mm. Test III is a seven-stage test that aims at studying the residual strength envelope under suctions equal to 18 and 45 MPa and after resaturation. The sample was initially sheared at a suction equal to 18 MPa and three levels of stress: 100, 200 and 300 kPa. The sample was then brought to a suction of 45 MPa by changing the saline solution controlling the relative humidity inside the vessel and further sheared under normal stresses equal to 300, 200 and 100 kPa, respectively. Finally, the glass cap was removed and the sample flooded before applying two shearing stages under normal stresses equal to 100 and 200 kPa. The total displacement applied during this test is equal to 3873 mm.
424
SHEAR STRENGTH VS DISPLACEMENT CURVES
B5
120 B3 B6
80 (kPa)
Figure 2 shows the shear strength vs displacement curve obtained during Test III at a suction equal to 18 MPa for both the initial stage (prepared sample dried to a suction equal to 18 MPa and sheared) and after application of a suction of 45 MPa (prepared sample brought to a suction equal to 18 MPa, sheared, then brought to a suction equal to 45 MPa, sheared and then wetted down to a suction equal to 18 MPa and sheared). The stress-displacement curves obtained in both cases show very similar values after a displacement equal to 50 mm. This result gives, on the one hand, good feedback concerning the reliability of the test procedure and, on the other hand, provides clues to the fact that the residual shear strength is, in that case, independent of suction history. Before 50 mm of displacement, the curve corresponding to the first shearing (Stages B1, B2 and B3) presents an initial peak which disappears when shearing is applied on an already pre-sheared sample (stages B5, B6 and B7). Such a kind of response is reported in the literature for the case of saturated materials and is generally attributed to the effort required initially to reorient the particles in the direction of shearing. Points relating the shear strength at large displacements to the normal stress are reported in Figure 3. They evidence a linear relationship between both variables for the range of loads considered. Parameters controlling the shear strength envelope at a suction equal to 18 MPa are cr = 0 and φr = 20◦ . The same linear trend can be observed in Figure 3 for the test performed under a suction equal to 75 MPa. Values of cohesion and friction angles obtained in this case are cr = 0 and φr = 28.2◦ . The shear strength envelope in saturated conditions is moreover depicted in Figure 3. The data show the huge effect exerted by the suction on the value of the friction angle that increases by a value of 21◦ when the soil passes from saturated conditions to a suction equal to 75 MPa. Such an outcome extends, in an amplified manner, to the case of active clays results already observed on low and medium plastic clays (Vaunat et al. 2006; Vaunat et al. 2007). Figure 4 summarizes the variation of residual friction angles with suction as measured on samples of Barcelona silty clay (wL = 30, IP = 16), Boom clay (wL = 55, IP = 28) and Febex bentonite (wL = 102, IP = 53). The increase in residual friction angle increases generally with the plasticity of clay. As a matter of fact, the increase in friction angle between saturated conditions and a suction equal to 75 MPa is around to 2.5◦ for the low plastic silty clay, 15◦ for the medium plastic clay and 21◦ for the high plastic clay. Another observation coming out from the figure is the non linear variation of residual friction angle
100kPa 100kPa after suction change 200kPa 200kPa after suction change 300kPa 300kPa after suction change
B2 B7 40 B1
0 0
50
100 150 Displacement (mm)
200
250
Figure 2. Residual strength measured in the ring shear apparatus at a suction equal to 18 MPa. 180
s = 75 MPa r = 28.2º
160
Shear stress (kPa)
3
140
s = 18 MPa, unloading r = 22.5º
120
s = 18 MPa, loading r = 22.1º
100 80 60
s=0 r = 7.5º
40 20 0 0
100
200 300 Normal stress (kPa)
400
500
Figure 3. Shear strength envelope of FEBEX bentonite at different suctions.
with suction. Most of the increase in friction angle occurs between 0 and 100 MPa. Afterwards, the effect of suction on φr becomes significantly smaller and tends to an asymptotic value for a suction close to 300 MPa. Such an increase is interpreted as being due to the process of aggregation during drying, that makes the material essentially more granular at high suctions. In the case of the low and medium plasticity clay, this interpretation has been reinforced by observations about the dilatancy of the material during first shearing. The latter appeared indeed to increase
425
40 35
tan–1( r / )
30 25 20 15
BCN silty clay data Boom clay data Febex Bentonite data Boom clay (Hyperbolic aproximation) BCN silty clay (Hyperbolic aproximation) Febex Bentonite (Hyperbolic aproximation)
10 5 0 0
50
100 150 200 Total Suction, S (MPa)
250
300
Figure 4. Variation of the friction angle with suction for the low, medium and high plastic clays.
Figure 5. Sample of remolded FEBEX bentonite prepared at the liquid limit (magnification 200x).
drastically when the material is sheared under high suction. In the present work, more direct evidence of the aggregation process have been looked for through two techniques: 1. The direct observation of microstructural changes during drying by Environmental Scanning Electron Microscopy (ESEM); 2. The determination of the pore size distributions for the saturated and dry material by the Mercury Intrusion Porosimetry technique (MIP).
4
MICROSTRUCTURAL OBSERVATIONS
ESEM is a technique that consists of performing the Scanning Electron Microscopy under gas pressure, which allows for observing materials with liquid constituents. It is in particular possible to observe changes in soil structure during drying by controlling the temperature and the partial vapour pressure inside the observation chamber of the microscope. Figures 5, 6, 7 and 8 show four ESEM micrographs taken on samples of remolded FEBEX bentonite prepared respectively at the liquid (Figures 5 and 6) and plastic limits (Figures 7 and 8). The as-prepared structure of the material can be observed in Figures 5 and 7. Figures 6 and 8 show the structure of the material after applying a relative humidity equal to 7%. At the liquid limit, the material presents a relatively homogeneous structure characterized by stacks of clay particles of typically 10 μm size and few macro-voids (two of them can be observed in the upper part of the micrograph). After drying at 7% of relative humidity,
Figure 6. Sample of remolded FEBEX bentonite prepared at the liquid limit and dried under a relative humidity of 7% (magnification 215x).
an important increase can be observed in the existing macro-voids accompanied by a general enhancement of the inter-particle porosity that degenerates in many points in the creation of new macro-voids. Further connection between macro-voids leads to the build-up of isolated aggregates in the clay. An incipient formation of aggregated structure due to drying can be observed in Figure 6. The picture is slightly different for the sample prepared at the plastic limit. Material presents initially a more complex structure where stacks of clay particles, micro-voids (with some local enlargements) and macro-voids can be observed. After application of drying under a relative humidity equal to 28%
426
Initial state (remoulded at plastic limit) Final state (after consolidation, drying and shearing)
Pore size density function ( e/ log )
2.5
2
1.5
1
0.5
0 1
Figure 7. Sample of FEBEX bentonite prepared at the plastic limit (magnification 200x).
10
100 1000 10000 Entrance por size, d (nm)
100000 1000000
a) pore size density function Initial state (remoulded at plastic limit) Final state (after consolidation, drying and shearing) 1.2
Intruded void ratio
1 0.8 0.6 0.4 0.2 0 1
10
100 1000 10000 Entrance por size, d (nm)
100000 1000000
b) accumulated pore size distribution Figure 8. Sample of remolded FEBEX bentonite prepared at the plastic limit and dried under a relative humidity of 7% (magnification 200x).
(suction approximately equal to 170 MPa), the size of the macro-voids gently decreases at the expense of an enhancement in the inter-particle porosity but without significant changes in the general pattern of material structure. It seems thus that preparation of the material close to the plastic limit create a pre-aggregated structure that remains stable during suction application. Effect of drying will in this case essentially stiffen the pre-existing structure. More quantitative insights can be realized by analyzing the pore size distribution of Febex bentonite before and after being tested in the ring shear apparatus. Two pore size distributions have been determined by the MIP technique: one corresponding
Figure 9. Pore size distributions in a remolded sample of FEBEX bentonite before and after being sheared under a vertical stress equal to 100 kPa and a suction equal to 120 MPa (sample was initially prepared close to the plastic limit).
to a remolded sample prepared close to the plastic limit and the other to the same sample once loaded under a vertical stress equal to 100 kPa, subsequently dried at a suction equal to 120 MPa and finally sheared in the Bromhead shear apparatus. A comparison between both curves can be observed in Figure 9. The sample prepared close to the plastic limit presents a mono-modal pore size distribution with pore sizes concentrated between 0.3 and 3 μm, that is at the inter-particle level (the size of a particle is typically of the order of 1 μm (1000 nm)—see Figure 5).
427
This peak disappears completely after the combination of loading, drying and shearing and the curve splits into two parts. One part is associated with pore sizes between 10 and 20 nm and existing thus at the intraparticle level. The other part contains pores of size higher that 10 μm, indicating the existence of an interaggregate porosity. It is expected that a peak in the pore size distribution would have existed around the value of 10 μm at the end of drying and would have further been erased and distributed over a wider range of pore sizes during shearing. 5
CONCLUDING REMARKS
The paper reports on a study on the effect of high suction on the residual strength of FEBEX bentonite. Experimental results allow for completing conclusions already drawn for materials of lower plasticity (Barcelona silty clay and Boom clay). They are: • Strong drying increases strongly the residual strength at relatively low normal stress (below 300 kPa) I. • The increase is due only to an increase in friction angle and not in cohesion. • Most of the increase in friction angle takes place for suction below 100 MPa. For higher suctions, the friction angle reaches an asymptotic value. • The increase in friction angle is higher when the plasticity of the clay is higher. For a low plastic silty clay (wL = 30, IP = 16), the increase in friction angle for a suction between saturated conditions and a suction equal to 75 MPa is equal to 2.5◦ , for a medium plastic (wL = 55, IP = 28) clay to 15◦ and for a high plastic clay (wL = 102, IP = 53) to 21◦ . • Such an increase is explained by a process of clay aggregation or aggregation stiffening during strong drying that makes the material behave in a more granular way. Pictures taken in the Environmental Scanning Electron Microscopy evidence indeed the incipient formation of aggregates during drying when the clay is prepared at the liquid limit. When the clay is prepared at the plastic limit, micrographs evidence a pre-aggregated structure that remains essentially unchanged during drying. In that case, suction stiffens the aggregates of the material. ACKNOWLEDGMENTS Mr. Merchán wishes to thank Alβan Program, the EU program of high level scholarships for Latin America, scholarship N◦ E05D052296CO. The support of the European Commission through the Research and
Training Network MUSE (Mechanics of Unsaturated Soils for Engineering) is gratefully acknowledged. REFERENCES Bishop, A.W. 1971. Shear strength parameters for undisturbed and remolded soil specimens. In Proceedings of the Roscoe Memorial Symposium, Cambridge, Foulis. Bromhead, E.N. 1979. A simple ring shear apparatus. Ground Eng., vol. 12, pp. 40–44. Chighini, S., Lancellotta, R., Musso, G. and Romero, E. 2005. Mechanical behavior of Monastero Bormida clay: chemical and destructuration effects. In Bilsel and Nalbantoˇglu (eds), Proc. Int. Conf. on Problematic Soils, Vol. 1, 381–388. Famagusta: Eastern Mediterranean University. Di Maio, C. 1996a. The influence of pore fluid composition on the residual shear strength of some natural clayey soils. In K. Senneset (ed.), Proc. 7th Int. Conf. on Landslides, 2, 1189–1194. Rotterdam: Balkema. Di Maio, C. 1996b. Exposure of bentonite to salt solution: osmotic and mechanical effect. Géotechnique, 46 (4), 695–707. Kenney, T.C. 1967. The influence of mineral composition on the residual strength of natural soils. Proc. Geotech. Conf. on the Shear strength properties of natural soils and Rocks, 1, 123–129. Lupini, J.F., Skinner, A.E. and Vaughan, P.R. 1981. The drained residual strength of cohesive soils. Géotechnique, 31 (2), 181–213. Mitchell, J.K. 1993. Fundamentals of soil behaviour. 2nd edition, John Wiley & Sons, New York. Skempton, A.W. 1964. Long-term stability of clay slopes. Géotechnique, vol. 14, no. 2, pp. 77–102. Skempton, A.W. 1985. Residual strength of clays in landslides, folded strata ad the laboratory. Géotechnique, vol. 35, no. 1, pp. 3–18. Sedano, J.A.I., Vanapalli, S.K. and Garga, V.K. 2007. Modified ring shear apparatus for unsaturated soils testing. Geotechnical Testing Journal, vol. 30, no. 1, pp. 39–47. Stark, T.D. and Eid, H.T. 1994. Drained residual strength of cohesive soils. J. of Geotech. Engng., ASCE, 120 (5), 856–871. Tika, T.E., Vaughan, P. and Lemos, L.J.L.J. 1996. Fast shearing of pre-existing shear zones in soil. Géotechnique, 46 (2), 197–233. Toll, D.G. 1990. A framework for unsaturated soil behaviour. Géotechnique, 40 (1), 31–44. Vaunat, J., Amador, C., Romero, E. and Djeran-Maigre, I. 2006. Residual strength of low plasticity clay at high suctions. In Proceedings of the 4th International Conference on Unsaturated Soils, Phoenix, Arizona, USA, vol. 1, pp. 1279–1289. Vaunat J., Merchán, V., Romero, E. and Pineda, J. 2007. Residual strength of clays at high suctions. In Proceedings of the 2nd International Conference on Mechanics of Unsaturated Soils, Weimar, Germany, vol. 2, pp. 151–162.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Ultimate shear strength of unsaturated soils T.B. Hamid GeoConcepts Engineering Inc., Virginia, USA
ABSTRACT: This paper presents triaxial and direct shear tests results from literature conducted on soils under unsaturated conditions with measurement of matric suction (ua − uw ). The results of these tests indicate that matric suction has less influence on ultimate shear strength than on the peak shear strength. It is inferred from the test results that neglecting suction is appropriate for analyzing slopes that contain pre-existing surfaces or that have history of previous sliding. However, suction has a significant effect on the depth of tension cracks in unsaturated soils and this should be considered as it reduces the factor of safety.
1
INTRODUCTION
The ultimate and residual shear strength of overconsolidated clay is an important parameter in evaluating the stability of new and existing slopes that contain a pre-existing surface or that have history of previous sliding. Ultimate shear strength is achieved when soil exhibits no appreciable changes in stress or volume during shearing. This ultimate state is followed by residual state that is reached after a large shear deformation. In residual state, soil particles increase in parallel orientation in the direction of shear deformation. Many researchers have studied the effect of matric suction on the peak shear strength of unsaturated soils (e.g. Escario & Saez 1986). However, lacking in the available literature is treatment of ultimate and residual shear strength in unsaturated soils. The results of triaxial and direct shear tests results with measurement of matric suction from literature are presented in this paper. The test results indicate that the effect of matric suction on ultimate shear strength is less significant as compared to the effect of matric suction on peak shear strength. Slope stability analysis is generally required as part of site development in Washington, D.C., Maryland and Virginia. Both natural and construction related landslides have occurred in these areas, which are underlain by overconsolidated clays, locally known as ‘‘Marine Clay’’. The marine clay deposits are considered problematic soils in these areas and several landslides and surficial slope failures have occurred in marine clay deposits. Geotechnical engineers are required to determine the engineering properties of marine clay for slope stability analysis. The local practice is to use residual shear strength of marine clay for slope stability analysis.
Marine clay deposits have many surface fractures and water can fill these fractures in wet seasons. Even in the dry season, free flowing water can enter in these fractures. The depth of these fractures increases as the negative pore water pressure (matric suction) of the soil increases. This paper indicates that a factor of safety computed using ultimate or residual shear strength parameters can decrease considerably in the wet season due to the horizontal water force developing in the tension crack.
2
ULTIMATE SHEAR STRENGTH OF UNSATURATED SOILS
Fredlund & Rahardjo (1998) indicated that in cases where groundwater table is deep, slope stability analyses should be performed using the shear strength contribution from the matric suction. However, the author of this paper understands that the use of shear strength contribution from the matric suction should be limited to the analyses where peak shear strength controls the stability of slopes. The peak shear strength of cohesive soils is generally used in the analysis of slopes in residual soils and normally consolidated clays, and in soils that have not undergone previous sliding. However, there are situations where ultimate or residual shear strength of unsaturated soils controls the stability of slopes, such as the stability of new and existing slopes that contain a pre-existing surface or that have history of previous sliding. Based on suction controlled and constant water content test results reported in the literature, the effect of matric suction on the ultimate shear strength of unsaturated soils is studied in this paper.
429
140 u a - u w = 100 kPa
Shear stress (kPa)
Deviator Stress, kPa
120 100 80
u a - u w = 20 kPa
60 40
(a)
20 0 0
2
4
6
8
10
Volumetric Strain, %
Horizontal displacement (mm) -0.015 -0.01 u a - u w = 100 kPa
v/H0
-0.005 0
Axial Strain, %
0.005
Figure 1. Stress-strain and volume change curves at cell pressure = 50 kPa and various suctions (after Cui & Delage 1996).
u a - u w = 20 kPa
0.01
(b)
0.015 0
Cui & Delage (1996) have presented suction controlled triaxial test results of an Aeolian Silt (Liquid Limit (LL) = 37% and Plasticity Index (PI) = 18%) and are reproduced in Figures 1a and 1b. Figure 1a indicates that for a cell pressure of 50 kPa, when suction value increased from 200 kPa to 1500 kPa, peak shear strength increased from about 320 kPa to 750 kPa. Volume change curves (Fig. 1b) indicate typical behavior of overconsolidated clay, i. e. initial compression followed by the dilation. The volume change curves indicate that dilatancy increased as suction value increased. The shear strength and volumetric strain curves indicate a tendency to level off at axial strains of about 8%, suggesting that the ultimate strength is being approached. However, at matric suction value of 800 and 1500 kPa volumetric strain is still changing towards the end of the tests. Although a true ultimate state is never reached in the tests presented in Figures 1a and 1b, the rate of change of shear strength and volumetric strain reduce considerably except for 1500 kPa suction. The degree of saturation after shearing was 79% for 200 kPa, 75% for 400 kPa, 67% for 800 kPa, and 56% for 1500 kPa matric suction. Figures 2a and 2b indicate the results of suction controlled direct shear tests conducted on Minco Silt
2
4
6
8
10
Horizontal displacement (mm)
Figure 2. Shear stress (a) and volume change (b) against horizontal displacement at net normal stress = 105 kPa for two values of suctions (Hamid, 2005).
(LL = 28% and PI = 8%). For a net normal stress (σn − ua ) of 105 kPa, increasing suction resulted in an increase of peak shear strength and stiffness. Strain softening behavior and a pronounced peak are obvious only for 100 kPa suction, illustrating an increasing brittleness of the sample with increasing suction. Figure 2 shows that both shear stress and volumetric strain, v/H0 (where v = vertical displacement and H0 = specimen thickness) generally reached a steady state at horizontal displacement of about 4–6 mm, indicating an ultimate state is achieved. In Figure 2a, the ultimate shear stress of 100 kPa suction sample is approximately similar to the ultimate shear strength of the sample tested at 20 kPa matric suction. The degree of saturation after shearing was about 90% and 75% for 20 kPa and 100 kPa matric suction, respectively. A similar picture is seen for σn − ua = 155 kPa in Figures 3a and 3b.
430
200 u a - u w = 100 kPa
180 Shear stress (kPa)
160 140 120 100
u a - u w = 20 kPa
80 60 40 20
(a)
0 0
2
4
6
8
10
Horizontal displacement (mm)
-0.015 u a - u w = 100 kPa -0.01
v/H0
-0.005 0
Figure 4. Deviator stress and volume change against axial strain at confining stress = 50 kPa and various suctions. (Toll & Ong 2003).
0.005 0.01
u a - u w = 20 kPa (b)
0.015 0
2
4
6
8
10
Horizontal displacement (mm) Figure 3. Shear stress (a) and volume change (b) against horizontal displacement at net normal stress = 155 kPa for two values of suctions (Hamid, 2005).
Figure 4 shows constant water content test results reported by Toll & Ong (2003). These tests were conducted on Jurong residual soil (LL = 36% and PI = 15%). It can be seen that ultimate state is being approached by the end of the tests cw50-230 (1), cw50230 (2), cw50-300, and cw50-400. Further, the rate of change of deviator stress (q) and volumetric strain generally reduce considerably toward the end of the tests and an ultimate state can be reasonably assumed (Toll & Ong, 2003). The degree of saturation after shearing was 66% for 230 kPa, 63% for 300 kPa, and 72% for 400 kPa matric suction. The results of Figures 1 through 4 are plotted in Figure 5 as peak and ultimate strength envelopes. In order to plot the strength envelopes the test results for net normal stress of 210 kPa presented in Hamid (2005) were utilized but the plot of horizontal displacement against shear strength and volume strain are not
presented in this paper. Similarly, constant water content test results for confining stress of 150 and 250 kPa presented in Toll & Ong (2003) are presented in Figure 5 but the plots of deviator stress against axial strain are not presented in this paper. The slope of the best fit lines of strength envelopes represents the friction angle for suction (φ b ). The values of φ b calculated from best fit lines of Figure 5 are given in Table 1. It is evident from laboratory test results presented in Figures 1 through 5 and in Table 1 that the effect of matric suction is generally less significant for the ultimate friction angle for suction than the peak friction angle for suction. Particularly for low confining and net normal stress (e.g. 50 kPa) the effect of sucb tion on φult is small (Figure 5). This conclusion is also supported by Tarantino & Tombolato (2005) who concluded that water menisci have a negligible effect on the ultimate shear strength. A possible explanation of the effect of matric suction on the peak shear strength and ultimate shear strength is presented in the following paragraphs. In unsaturated soil, the meniscus around soil grains contact points tends to draw the particles together. This attractive force, called capillary force (Nc ), acts perpendicular to the grain contact surface. It has been shown that under certain conditions Nc increases with an increase of suction (Kohgo et al. 1993). Increase in Nc induces an increase of shear resistance between the soil particles. This inhibits the relative sliding between
431
Shear stress (kPa)
860
Table 1. Peak Ultimate
660 460 260
(a)
60 100
600
1100
1600
u a - u w (kPa) 220 Shear stress (kPa)
n
b ) Peak (φpeak
b ) Ultimate (φult
50∗ 50• 150• 250• 105† 155† 210†
15 47 64 68 22 28 30
3 26 62 59 2 9 23
180 n
by adding water to the system the column of grains will collapse. Test results presented in Figures 1 through 4 indicate strain softening behavior that suggests beginning of destruction of bonding between soil particles due to interlocking and due to meniscus. In the ultimate state particles slide over each other, i.e. interlocking bond has been destroyed and bonding due to meniscus has also been destroyed. Therefore the soil shows a stable ultimate state, i.e. no further reduction in shear strength. In other words, as opposed to the peak shear strength, in the ultimate state meniscus bonds do not exist and an increase in matric suction does not cause an increase in ultimate shear strength.
- u a = 155 kPa
140 100 n
(b)
- u a = 105 kPa
60 0
50
100
150
u a - u w (kPa)
860 Shear stress (kPa)
Confining/Net normal stress (kPa)
Note: ∗ Cui & Delage (1996); • Toll & Ong (2003); † Hamid (2005).
Peak Ultimate
- u a = 210 kPa
Peak and ultimate friction angles for suction.
Peak Ultimate
3
- u a = 250 kPa
660 460 3
- u a = 150 kPa
3
260 (c)
3
- u a = 50 kPa
60 100
200
300
400
500
u a - u w (kPa)
Figure 5. Peak and ultimate shear strength envelopes for test results reported by (a) Cui and Delage (1996), (b) Hamid (2005), and (c) Toll and Ong (2003).
the particles and the magnitude of shear resistance of soil increases. Kohgo et al. (1993) suggested that the contribution of shear resistance caused by the capillary force may be regarded as nominal cohesion. Burland & Ridley (1996) used a grain column analogy to show that the meniscus around the soil particles results in increase in stability of soil structure. They suggested that the contact menisci can be thought of as ‘bonds’ holding the grains together. This bonded system can sustain some externally applied load without collapsing. However, if these bonds are then removed
SLOPE STABILITY APPROACH
In geotechnical practice, for small size projects, generally residual direct shear testing is not performed and conservatively, a low residual friction angle value generally 6◦ to 12◦ and zero cohesion are selected as residual shear strength parameters. The groundwater level used in the design is generally the highest recorded during the soil investigation program. However, the effect of rainfall and surface runoff water is not considered in the slope stability analysis and the upper crust is treated as unsaturated soil characterized using residual friction angle. A factor of safety ranging from 1.2 to 1.5 is generally considered satisfactory for slope stability analysis. As indicated previously, residual friction angle and zero cohesion are used as shear strength parameters in the slope stability analysis in marine clay. Neglecting the cohesion is considered a conservative approach. There are instances where ignoring the value of cohesion may result in a non-conservative value of factor of safety. If shear strength parameters are back-calculated assuming no cohesion, the estimated shear strength parameters may be overestimated. Cohesion also plays
432
an important role in the development of tension cracks in the slope. Ignoring cohesion implies that tension cracks can not develop in the soil. Tension cracks are generally developed above the groundwater table in unsaturated clay and the effect of the matric suction should be considered in the determination of depth of tension cracks. 4
EFFECT OF MATRIC SUCTION ON THE DEPTH OF TENSION CRACKS
As indicated previously residual shear strength is used for the slope stability analysis. However, the effect of tension cracks that may fill with water in wet seasons is not considered in the slope stability analysis. Tension cracks generally develop in a highly desiccated crust of soil and their depths may be calculated using Equation 1 (Fredlund & Rahardjo 1998): yt = (2c /γ ) tan(45 + φ/2) + [2(ua − uw ) tan φ b /γ ] × tan(45 + φ/2)
(1)
where yt = depth of tension crack; c = effective cohesion; γ = unit weight; φ = effective angle of internal friction; (ua − ub ) = matric suction; φ b = friction angle for suction. Equation 1 is used to calculate the depth of tension cracks for various values of matric suction and the results are plotted in Figure 6. Figure 6 indicates that the depth of tension cracks increase with increase in matric suction. For example, for matric suction 200 kPa and φ b = 10◦ , the depth of tension crack is almost double the depth of tension crack corresponding to the zero matric suction. It should be noted that, as the depth of tension crack is gradually increased, the factor of safety will
Depth of tension crack (m)
35 30
b
= 15 0
25 20
b
=10 0
15 b
10
decrease first (as tensile stresses are eliminated first), and then increase (as compressive stresses are eliminated). Factor of safety for slope stability should be calculated considering the depth of tension crack given by Equation 1. Alternatively one can calculate the factor safety for an assumed range of crack depths, and the appropriate depth is that producing the minimum factor of safety. For higher suction values crack depths calculated using Equation 1 may be more than the slope height. In this case a maximum depth equal to the height of slope should be utilized. Figure 7 presents chart developed by Janbu (1968) and can be used to calculate the tension crack adjustment factor (μt ). The tension crack adjustment factor indicates the effect of tension crack depth on the factor of safety. For example, for a slope angle of 60◦ and for Ht /H from 0 to 0.5, μt varies from 1 to about 0.75. A value of μt = 1 indicates no effect of tension cracks on factor of safety, on the other hand a value of μt = 0.75 indicate about 25 percent reduction in factor of safety calculated without considering the depth of tension crack.
=50
5
5
0 0
500
1000
1500
u a - u b (kPa) Figure 6. crack.
Figure 7. Tension crack adjustment factor (after Janbu 1968 via. EM 11102–2-1902, 2003).
Effect of matric suction on the depth of tension
CONCLUSIONS
As opposed to the peak shear strength, the effect of matric suction appears to be less significant on ultimate shear strength. Based on the laboratory test results of unsaturated soils presented in this paper, it may be concluded that suction can be neglected for analyzing slopes that contain pre-existing surfaces or
433
that have history of previous sliding. However, the effect of matric suction should be considered while incorporating the presence of a tension crack in slope stability analysis. ACKNOWLEDGEMENTS The author wishes to extend a special thank to O. Ayodeji, Fairfax County, Department of Public Works, Virginia, USA for reviewing this manuscript. Valuable comments and suggestions made by anonymous reviewers also helped to improve the quality of this paper. This paper reflects the personal opinion of the author and not necessarily those of GeoConcepts Engineering, Inc. REFERENCES Bishop. A.W. 1955. The use of the slip circle in the stability analysis of slopes. Geotechnique. 5: 7–17. Escario, I. & Saez, J. 1986. The shear strength of partly saturated soils. Geotechnique. 36: 453–456.
Fredlund, D.G. & Rahardjo, H. 1993. Soil Mechanics for Unsaturated Soils. New York: John Wiley and Sons, Inc. Janbu, N. 1968. Slope stability computations. Via US army Corps of Engineer, EM 1110-2-1901. 2003. Hamid, T.B. 2005. Testing and modeling of unsaturated interfaces. Ph.D. dissertation submitted to Civil and Environmental Engineering department. University of Oklahoma, USA. Kohgo, Y., Nakano, M. & Miyazaki, T. 1993, Theoretical aspects of constitutive modelling for unsaturated soils. Soils and Foundations. 33(4): 49–63. Morgenstern, N.R. & Price, V.E. 1965. The analysis of the stability of general slip surfaces. Geotechnique. 15: 70–93. Spencer, E. 1967. A method of analysis of the stability of embankments assuming parallel inter-slice forces Geotechnique. 17: 11–26. Toll, D.G. & Ong, B.H. 2003. Critical-state parameters for an unsaturated residual sandy clay. Geotechnique. 53(1): 93–103. Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Geotechnique. 55 (4): 307–317. US Army Corps of Engineer. Slope Stability. EM 1110-21901. 2003.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Critical State conditions for an unsaturated artificially bonded soil D.G. Toll School of Engineering, Durham University, Durham, UK
Z. Ali Rahman Faculty of Sciences and Technology, National University of Malaysia (UKM), Selangor, Malaysia
D. Gallipoli Department of Civil Engineering, University of Glasgow, Glasgow, UK
ABSTRACT: This paper reports on a set of triaxial test data on an artificially bonded sand tested in unsaturated conditions. Tests were performed using the axis translation technique to measure suctions while shearing under constant water content conditions. The results at the Critical State are interpreted to obtain the variation in the stress ratios: Ma representing the net stress component and Mb representing the suction component. These are also presented as Critical State angles of friction, (φ a )c and (φ b )c . It is found that Ma is higher than the saturated critical state stress ratio, Ms (i.e. (φ a )c > φc ). This supports the observation that we should not always make the assumption that φ a = φ . The changes in Ma and Mb can be related to the different phases of water retention behaviour. The regions of behaviour seem to be (i) before the air entry value Ma = Mb = Ms (ii) in the desaturation stage Ma rises above Ms but Mb = Ms (iii) in the residual stage Ma remains constant and Mb starts to reduce.
1
INTRODUCTION
This paper reports on a set of triaxial test data on an artificially bonded sand tested in unsaturated conditions. The results are relevant to the understanding of tropical residual soils, since these are typically bonded in nature and frequently exist in an unsaturated state. The use of artificial specimens allows reproducibility of bond strength, which is difficult to achieve with naturally bonded soils, such as residual soil. Tests on an artificially bonded sand in saturated conditions have been reported by Toll & Malandraki (1993); Malandraki & Toll (2000); Malandraki & Toll (2001) and Toll et al (2006). Further testing on saturated specimens has been carried out by Ali Rahman (2008). Tests on the unsaturated specimens were performed under constant water content conditions while using the axis translation technique to measure suctions. Shearing was carried out at three values of radial net stress (50, 100 and 300 kPa) and the suctions ranged from 0 to 560 kPa. The test results on the unsaturated bonded soil are interpreted by considering separately the contributions from net stress and suction. Critical State stress ratios are interpreted for each stress component: Ma for the
net stress component and Mb for the suction component. These are also presented as Critical State angles of friction, (φ a )c and (φ b )c . 2
MATERIAL & TEST PROCEDURES
The artificial soil was produced by mixing sand and kaolin (87% sand: 13% kaolin) and then firing the mixture at 500◦ C in a furnace. This was a technique first used by Maccarini (1987). At this temperature the kaolin changes in nature, forming a bond between the sand particles. The bond formed is not time dependent, so this technique has many advantages over using cement or other bonding agents that require a curing period and show a change in strength with time. The sand used for making the samples was Leighton Buzzard sand, a uniform medium sand (Figure 1). The tests described in this paper were all on specimens prepared at the same initial void ratio (e = 0.6). Specimens for testing in unsaturated conditions were initially prepared in a saturated state and then allowed to air-dry in the laboratory until each achieved a required value of water content. Figure 2 shows the water retention curve for the artificial soil. The drying curve was obtained from
435
The net stress was then increased to the desired value (50, 100 or 300 kPa) by reducing the pore air pressure at constant cell pressure under constant water content conditions (allowing volume change to occur due to air flow, but preventing any flow of water). The changes in pore-water pressure and volume were observed until consolidation was deemed to be complete. Specimens were then sheared under constant water content conditions with radial net stress held constant. Measurements of pore-water pressure and volume change were made during shearing.
3
Figure 1. Particle size distribution for the Leighton Buzzard sand used to make the bonded soil.
Degree of saturation, Sr: %
100
Fredlund et al (1978) gave the shear strength equation for unsaturated soils as:
Drying - Axis translation
80
SHEAR STRESS AT CRITICAL STATE IN UNSATURATED SOILS
τ = c + (σ − ua ) tan φ a + (ua − uw ) tan φ b
Wetting - Axis translation (Walker et al, 2005)
(1)
Wetting - Filter Paper (Walker et al, 2005)
60
where 40
τ σ ua uw c
20 0 0.1
Figure 2.
1
10 100 Matric suction (u a - uw): kPa
1000
φa
Water retention curve.
φb measurements of suction on different specimens following air drying from saturated conditions to a specific water content (or degree of saturation). It can be seen that the retention curve is very steep in the suction range 2–4 kPa, (with some scatter in the data, which is emphasised by the logarithmic scale) followed by an almost flat portion once the degree of saturation drops below 25%. This made the control of suction quite difficult. Nevertheless, it was possible to prepare specimens at a range of suction from se (4)
8
10
D Wetting
107
s
C
e
106 Yielding zone
105 B 104 Drying
1000 A E 100 100
(b) 4
6
10
108
10
Mean effective pressure p' (Pa) (c) A 0
B
(-)
Exp. ACMEG-s
v
(5)
pCR0
where are respectively the actual and initial critical state pressures ( pc = d · pCR , d is a material parameter), and β the coefficient of compressibility. 3.1
10
Stress path Initial LC Final LC
108
Volumetric strain
pCR ,
D 6
109
pc0 is the initial preconsolidation pressure at zero suction, γs is a material parameter, and se is the air entry suction (that is the suction beyond which the degree of saturation becomes smaller than 1). Eq. (4) accounts for the effect of capillarity on the size of the elastic domain. The reference stress-strain relationship in the saturated model is basically given by equation (1) for the elastic behaviour. Irreversible behaviour of the soil p gives birth to a volumetric plastic strain εv follow- p ing the normal compression line in plane εv − ln p which slope is defined by that of the critical state line: p log CR = βεvp pCR0
10
4
Matric suction (Pa)
Matric suction s (Pa)
⎩p˜ c (s)
C
E
0.8
i. The skeleton strain is directly linked only to σ (Eq. 1). Secondary effects of suction on mechanical compressibility are featured within the constitutive relations. ii. The distribution of pore fluids is described via the degree of saturation. In conformity with framework (3), Sr is related to s by the soil water retention curve anytime. An elementary non-linear reversible model is used here (Van Genuchten 1980) for the hydraulic behaviour. iii. The mechanical yield surface depends on the level of suction and, in particular, the preconsolidation pressure pc , is directly dependent on suction. Equation (4) below defines an improved ‘Loading Collapse’ curve: ⎧ ⎨p˜ c (s) = pc0
1
B
A
-0.12
Drying
-0.24 E C
-0.36
D
Wetting -0.48
Isotropic stress paths
100
Figures 2a and 2c plot the laboratory experimental result of a wetting drying cycle on clay under free mechanical boundary conditions. The fine grained material, initially slightly overconsolidated, is free to deform. Plastic straining is observed up to the air entry
104
106 se
108
Matric suction (Pa) Figure 2. Simulation of volumetric response to hydric cycle under constant null net stress. Experimental points from tests on white clay (Fleureau et al. 1993).
561
10
6
(a)
Matric suction s (Pa)
A
Wetting
10
5
B Yielding zone
s
e
10
C Wetting path Initial LC Final LC
D
4
5
10
Mean effective pressure p' (Pa) 0.03 (b) B
Wetting
Volumetric strain
v
(-)
0.015
A
0 -0.015 D C
-0.03 -0.045
Wetting path Mech. path -0.06
5
10
Mean effective pressure p' (Pa) 0.02 (c) B
v
(-)
0.01
Volumetric strain
value of suction se , while for suctions greater than se the material volume tends to stabilize. According to the present constitutive interpretation, the change in mean effective stress is caused by changes in both suction s and degree of saturation Sr . The soil water retention curve (Fig. 2a) is therefore an important input to the model. The mobilisation of the isotropic plastic mechanism is shown in the s − p stress plane, along with the followed stress path (Fig. 2b). The volumetric response εv is plotted as a function of matric suction in Fig. 2c. Even though the matric suction is the only control variable in this experiment, the model predictions are the result of the mechanical relationship linking εv to variations in p . Consequently, the elastic and plastic behaviour depends on the effective stress state (Fig. 2b) being inside the elastic domain or on the yield locus. The advanced shape of the loading collapse curve (Fig. 2b), combining a straight vertical part and an upper non-linear outline, contributes to achieving a proper fit. In the saturated domain s < se ; Sr = 1 any change in suction is directly equivalent to a change in p (Eq. 3) like during an isotropic purely mechanical loading. When Sr = 1, the volumetric response is thus identical in both εv − ln p and (εv − ln s) representations, with standard unloading-reloading paths (path AB and CE) and elasto-plastic part (path BC). Once se is reached the preconsolidation pressure is imposed to increase with suction (Eq. 4), faster than the mean effective stress increases (Fig. 2b), resulting in recovering an elastic response (CD). The elastic linear path in εv − ln p whose slope is indicated in dotted line in Fig. 2c for a matter of comparison permits to estimate (via Eq. 2) the response in (εv −ln s) plane. The obtained solid line CD in Fig. 2c is non linear. The swelling collapse behaviour upon soaking is a second inbuilt feature of the model. It is widely observable experimentally (Fig. 3c) when wetting a material under a high initial net stress. Again, this behaviour justifies the use of the Loading Collapse curve for the constitutive framework, even though the stress path is non-linear in s − p plane. Starting from the experimental initial state A (Fig. 3a), pc decreases faster than the mean effective stress upon wetting (Eq. 4). Two volumetric responses are predicted (Figure 3b and c); (i) a fully reversible swelling upon effective stress relief along paths AB and CD and (ii) a plastic compression due to yielding on LC curve along path BC. The superposition of numerical and experimental results for kaolin shows discrepancies between the predicted suction levels for the activation of the plastic response, mostly attributable to possible inaccuracy in the LC curve determination, carried out on the basis of other isotropic loading tests at various levels of suction. However, the volumetric variations are fairly
A
0 Wetting
-0.01 D -0.02
Exp. 1 Exp. 2 Exp. 3 ACMEG-s
C -0.03 -0.04 0
5
2 10
5
4 10
Matric suction s (Pa) Figure 3. Prediction of wetting collapse. Experimental points from tests on kaolin (Sivakumar 1993).
562
well predicted and the qualitative trends for alternative swelling and collapse are reliable. Oedometric conditions
Matric suction s (Pa)
3.2
9
10
Although oedometric paths are hardly ever used in conventional validation processes, they have major importance in experimental characterisation of unsaturated soil behaviour, provided that unsaturated oedometric cells are more widespread in geotechnical laboratories than unsaturated triaxial or isotropic compression apparatuses. Basically, experimental results from oedometric tests (e.g. Fig. 4) are similar to those of unsaturated isotropic compression, with an apparent preconsolidation pressure shifted with suction and modifications in compressibility. However, only an advanced numerical integration of the model catering for zero lateral total strain condition enables to reproduce such paths. The stress paths (Lloret et al. 2004) simulated here include a hydraulic equalization to a given level of suction and an oedometric compression at a constant level of suction (Figure 4a). Simulation of the wetting or drying processes from an initial suction of 138 MPa shows the model to predict satisfactorily the trend and magnitude of volumetric strains (Fig. 4b). Even though the global swelling trend is observed upon wetting for all tests, punctual decrease in εv is attributed to (i) the occurrence of mechanical compression prior to or during equalization and (ii) seamless plastic episodes with initiation of wetting collapse. Subsequent oedometric compression tests (Fig. 4c) at constant suctions from 0 (test5) to 500 MPa (test1) are also remarkably well-predicted with the proposed framework.
(a)
Test 2
Initial point
8
10
Test 3 7
10
Test 4 106 Final point
5
10
Test 5
4
6
10
8
10
10
Vertical stress
v
(Pa)
(b)
0.32
Volumetric strain
v
(-)
Exp. test 1 ACMEG-s test 1 Exp. test 3 ACMEG-s test 3 Exp. test 5 ACMEG-s test 5
0.24
0.16
0.08
Initial point
0
Wetting 5
7
10
9
10
10
Matric suction s (Pa) 0.4
Swelling pressure
Exp. 1 Mod. 1 Exp. 2 Mod. 2 Exp. 3 Mod. 3 Exp. 4 Mod. 4 Exp. 5 Mod. 5
(c)
(-)
0.3 v
The experimental behaviour of fully confined samples submitted to a wetting path is plotted in Fig. 5b and 5c. During swelling pressure tests, the total strain is imposed to remain null whereas effective and net stresses are generated within the cell. As soil wetting provokes swelling or collapse under free displacement conditions, confined soaking generates stresses to prevent such straining. According to the initial state (level of suction), the maximum generated pressures are variable. Also, the generated vertical stress σv does not hold a linear dependency on matric suction, and its evolution trend even tends to reverse twice (Fig. 5b). Again, with the help of the LC yield curve and effective stress concept together, ACMEG-s provides a straightforward interpretation of the swelling pressure with a distinctive stress path in the planes record, s − p and (s − pnet ) (Fig. 5a). The deduced stress
Volumetric strain
3.3
Test 1
0.2
0.1
0
-0.1 4 10
5
10
6
7
10
Vertical net stress
10 v
8
10
(Pa)
Figure 4. Back prediction of hydro-mechanical tests under oedometric conditions (Lloret et al. 2004).
563
Effective stress Net stress
100
Matric suction (MPa)
plane (s − σv ) (Fig. 5b) also reflects three zones of interest, the repartition of which is linked to the shape of the LC curve. At the initiation of wetting, i.e. domain A, the process is fully reversible as the stress state remains within the elastic domain; only constitutive equation (1) is needed. The elastic deformation is null so the variation in effective stress must be null too. This requires an increase in net stress to compensate the reduction of suction (Figure 5b). This phenomenon is in agreement with the unified framework according to which the increment of net stress is deduced from generalised effective stress definition: σnet ij = σij − Sr sδij = − Sr sδij (6)
(a)
A 10 Yielding zone B 1 C Wetting 0.1 Initial LC Final LC
0.01
1
100
Mean stress p', p (MPa) net
Equation (6) also indicates that the soil water retention curve model controls the non linearity of stress response in (s − σv ) plane anytime. Then, wetting in zone B implies yielding on the LC curve. The total deformations remain null but a plastic deformation is generated, balancing the elastic part of the deformation. The occurrence of elasto-plastic strains provokes a release of the effective stress according to the elastoplastic constitutive model, and obviously a different trend for the evolution of the net stress. Once suction drops down to the air entry value, the ultimate zone C is entered. Due to the shape of LC curve, all deformations are elastic in this zone so that Eq. (1) only is needed, with the simplification Sr = 1.
1000 SP1 EXP SP2 EXP SP3 EXP SP4 EXP
100
SP1 MOD SP2 MOD SP3 MOD SP4 MOD
10
Wetting
Matric suction s (MPa)
(b)
1
0.1
-2
0
2
4
6
8
10
12
Vertical net stress σ (MPa)
4
v
1.2
A unified constitutive framework for unsaturated soils is proposed. It takes advantage of the generalised effective stress along with advanced couplings including capillary effects. The experimental behaviour under free swelling as well as constrained conditions justify the need for an improved shape of the LC yield curve. Also, during the wetting-drying cycles the water retention curve has a strong influence on the mechanical stress-strain response. The unified framework thus provides a straightforward interpretation of swelling pressure tests without introducing further complex concepts linked to expansive materials.
(c) 1
r
Degree of saturation S (-)
CONCLUSIONS
0.8 0.6 0.4 0.2 Exp. Van Genuchten 0 0.1
10
1000
ACKNOWLEDGEMENTS
Matric suction (MPa) Figure 5. (a) (b) Stress responses to swelling pressure tests (c) Soil Water Retention Curve. Experimental points: bentonite (Lloret et al. 2004).
This work was partly supported by Swiss Competence Center Environment and Sustainability, project ‘Triggering of Rapid Mass Movements in Steep Terrain’.
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REFERENCES Alonso, E.E., Gens, A. & Josa, A. 1990. A Constitutive Model for Partially Saturated Soils. Geotechnique 40(3): 405–430. Bishop, A.W. 1959. The principle of effective stress. Tecnisk Ukeblad 39: 859–863. Fleureau, J.M., Kheirbeksaoud, S., Soemitro, R. & Taibi, S. 1993. Behavior of Clayey Soils on Drying Wetting Paths. Canadian Geotechnical Journal 30(2): 287–296. Geiser, F., Laloui, L. & Vulliet, L. 2006. Elasto-plasticity of unsaturated soils: laboratory test results on a remoulded silt. Soils and Foundations Journal 46(5): 545–566. Hujeux, J. 1985. Une loi de comportement pour le chargement cyclique des sols. In Génie Parasismique: 287–353. Paris, Les éditions de l’ENPC. Hutter, K., Laloui, L. & Vulliet, L. 1999. Thermodynamically based mixture models of saturated and unsaturated soils. Mechanics of cohesive-frictional materials 4: 295–338. Laloui, L., Nuth, M. 2005. An introduction to the constitutive modelling of unsaturated soils. European Journal of Civil Engineering, 9(5–6): 651–670.
Lloret, A., Romero, E. & Villar, M.V. 2004. FEBEX II Project: Final report on thermo-hydro-mechanical laboratory tests, ENRESA. Nuth, M. & Laloui, L. 2007. Effective stress concept in unsaturated soils: Clarification and validation of a unified framework. International journal for numerical and analytical methods in Geomechanics. DOI 10.1002/nag.645. Schrefler, B.A. 1984. The finite element method in soil consolidation (with applications to surface subsidence). PhD. Thesis. University College of Swansea. Sivakumar, V. 1993. A critical state framework for unsaturated soils. PhD. Thesis. Sheffield, University of Sheffield. Terzaghi, K. 1936. The shearing resistance of saturated soils and the angle between the planes of shear. International Conference on Soil Mechanics and Foundation Engineering: 54–56. Harvard University Press. Van Genuchten, M.T. 1980. A closed form of the equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal (44): 892–898.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Generalised elasto-plastic stress-strain relations of a fully coupled hydro-mechanical model M. Lloret, M. Sanchez & M. Karstunen University of Strathclyde, Glasgow, UK
S. Wheeler University of Glasgow, Glasgow, UK
ABSTRACT: Wheeler and co-workers have recently proposed an elasto-plastic framework involving the coupling of hydraulic and mechanical behaviour in unsaturated soils. A characteristic of the model is that it has been formulated in terms of Bishop’s stress and modified suction (i.e. suction multiplied by porosity). By using these new stress variables it is possible to predict the influence of the degree of saturation on the stress-strain behaviour. In particular, this new framework is able to represent the coupling between hydraulic and mechanical behaviour, allowing the prediction of influences of changes in the degree of saturation on the stress-strain behaviour and conversely, influences of volumetric strains on the water retention relationship. In this paper a 3D generalization of the stress-strain governing equations of this model is proposed based on concepts of multi-dissipative materials. This is a proper framework as in this model the coupled hydro-mechanical behaviour is described by three elasto-plastic mechanisms.
1 1.1
INTRODUCTION General
Recently, the interest for understanding the behaviour of unsaturated soils and for improving the knowledge of them has considerably increased. Reasons for that may be found by the fact that the unsaturated condition is observed in many engineering problems: construction of embankments, constructions near the ground surface and a wide range of geo-environmental problems. Moreover, the recently observed variability of climate, mainly in terms of dry-wet seasons (rainfalls, flooding, drought periods followed by wet season, etc.) may lead to the need of a better understanding of unsaturated soil behaviour. Constitutive models are very useful tools as they can be used as conceptual frameworks to improve our understanding by analysing the main mechanisms that underline the behaviour of unsaturated soils; and also, after the implementation of the models in computer codes, they can be used to solve actual problems involving unsaturated conditions. The Barcelona Basic Model, BBM (Alonso et al., 1990) is the most commonly used constitutive model for unsaturated soils. This is because the BBM is able to include, within the same framework, the main characteristics of unsaturated soil behaviour. However, some particular features of the unsaturated condition can not be fully described by this model. For
example, the model does not give complete information of the proportion of the void occupied by water; hence, mechanisms involving this variable, such as hydraulic hysteresis observed in wetting/drying paths, can not be completely described. In order to characterise these particular features, Wheeler et al. (2003) proposed a new framework of analysis involving the degree of saturation. In this work an extension to the 3D conditions of the isotropic model originally developed by Wheeler and co-workers is proposed.
2 2.1
MODEL FORMULATION Isotropic stress state
Due to space constraints only the main features of the coupled hydro-mechanical model are presented in this section. A more detailed description of it can be found in Wheeler et al. (2003). Considering the increment of work input per unit of unsaturated soil (Houlsby, 1997), the stress variables adopted in this work will be Bishop’s stress and modified suction (Wheeler et al., 2003). Particularly, for the isotropic stress state, the stress variables used can be expressed as: p∗ = p − Sr uw − (1 − Sr )ua
(1)
s∗ = ns = n(ua − uw )
(2)
567
Elastic volumetric strains can be expressed as: dεve =
κ dp∗ v p∗
(6)
where κ is the slope of an elastic swelling line in the (v, ln p ) plane for saturated conditions. When yielding only on the LC curve, plastic volumetric strains are given by: dεvp =
λ − κ dp∗0 v p∗0
(7)
where λ is the slope of the normal compression line for saturated conditions and p∗0 is the hardening parameter defining location of LC yield curve. The flow rule for the LC curve corresponds to:
Figure 1. LC, SD and SI yield curves for isotropic stress states (after Wheeler et al., 2003).
p
dSr p =0 dεv where p∗ is the mean Bishop’s stress, p is the mean stress, Sr is the degree of saturation, uw pore water pressure, ua is the pore air pressure, s is suction, n is the porosity and s∗ is the modified suction. Note that this choice implies that the Bishop’s stress tensor, σij∗ , is work-conjugate with dεij whereas modified suction, s∗ , is work conjugate with −dSr . Two elasto-plastic physical processes are considered within the model. One is the mechanical process of deformation of the soil skeleton under applied stresses and the second is the hydraulic process of water inflow and outflow to individual voids. The plastic mechanisms are described by three different yield surfaces (see Fig. 1). One is associated to the slippage at inter-particle or inter-packet contacts (Loading Collapse yield curve, LC) and the other two are associated to irrecoverable changes of Sr when drying (Suction Increase, SI ) or when wetting (Suction Decrease, SD). Yielding on LC curve causes plastic volumetric strain, which produces coupled upwards movements of SI and SD curves. Yielding on SI causes plastic decrease of Sr , which produce coupled upward movement of SD curve and outward movement of LC curve. Yielding on SD curve causes plastic increments of Sr , which produce coupled downward movement of the SI curve and inward of the LC curve. These curves can be expressed in the following form:
∗
p = s∗ = s∗ =
p∗0 sI∗ ∗ sD
Elastic increments of Sr can be expressed as dSre = −
(5)
κs ds∗ s∗
(9)
where κs is an additional elastic constant. When yielding only on the SI or SD yield curve, plastic changes of Sr are given by dSrp = −(λs − κs )
∗ dsI∗ dsD ∗ = −(λs − κs ) ∗ sI sD
(10)
Equations (9) and (10) predict the water retention behaviour showed in Fig. 2. As noted by Wheeler et al. (2003) the model of water retention behaviour shown in this figure is relatively crude, and refinement may be desirable. The flow rule for the SI and SD yield curves corresponds to: p
dεv p =0 dSr
(11)
When yielding only on SI or SD curves, coupled movements of the LC curve are given by: ∗ dsI∗ dsD dp∗0 = k = k 1 1 ∗ p∗0 sI∗ sD
(3) (4)
(8)
(12)
∗ where k1 is a coupling parameter and sD and sI∗ are the hardening parameters defining location of SD and SI curves respectively.
568
When yielding only on LC curve, coupled movements of the SI and SD curves are given by: ∗ dp∗0 dsI∗ dsD = = k 2 ∗ sI∗ sD p∗0
(13)
where k2 is the second coupling parameter. By considering these equations, the overall movement of the LC curve is given by: dp∗0 k1 dSr vdεv − = λ−κ λs − κs p∗0 p
p
(14)
And, similarly, the overall movement of the SI and SD curves is given by: ∗ dsD dsI∗ vdεv dSr + k2 ∗ = ∗ =− sI sD λs − κs λ−κ p
p
(15)
Figure 2. Model for water retention behaviour (After Wheeler et al., 2003).
Combining the last two equations a general expression for plastic volumetric strain increments and plastic changes of Sr can be obtained. ∗ ∗ dsD dp0 λ−κ − k (16) dεvp = 1 ∗ v(1 − k1 k2 ) p∗0 dsD ∗ dp∗0 dsD λs − κs − k (17) −dSrp = 2 ∗ ∗ (1 − k1 k2 ) dsD p0 2.2
3D generalisation
Based on the ideas collected from the 3D generalisation of the BBM (Alonso, 1993), a 3D extension of the model presented in Section 2.1 is proposed here. The model will be formulated in terms of the three stress invariants ( p∗ , J , θ ) and the modified suction (s∗ ). In addition, the concept of generalised stress and strain vectors proposed in Vaunat et al. (2000) is adopted here, being: ∗ ∗ ∗ T σ˜ ∗ = σxx , σyy , σzz , τxy , τyz , τxz , s∗ (18) T (19) ε˜ = εxx , εyy , εzz , γxy , γyz , γxz , −Sr The saturated model adopted as a limit condition is a version of the Modified Cam Clay model which is extended along the s∗ axis following the shape of the LC shown in Figure 1. Accordingly, it is proposed that the yield curve for a sample at constant s∗ will be described by an ellipse which exhibits an isotropic preconsolidation stress lying on the LC yield curve. The resulting shape of the yield surface in the ( p∗ , J , s∗ ) space is a half elliptic cylinder (see Fig. 2) extended ∗ from the plane s∗ = sD to the plane s∗ = sI∗ . In order to define the ellipse it is necessary to specify the failure states. A critical state line (CSL) for the unsaturated condition should be defined. In the BBM
Figure 3. Evolution of CSL with suction in ( p∗ , q) plane (data from Wheeler & Sivakumar (1995); after Khalili et al., 2004).
the increase of suction is represented by an increase in cohesion maintaining the slope M of the CSL for saturated conditions. In here, the same assumption about M is held and the increase of cohesion is implicitly considered by using p∗ and s∗ as stress variables. From the observed behaviour, the assumption of considering M constant in the plane ( p∗ , q) seems to be reasonable (see Fig. 3). In fact, as Khalili et al. (2004) showed using the triaxial experimental results of Wheeler & Sivakumar (1995), Cui & Delage (1996) and Maâtouk et al. (1995) re-plotted in the (p∗ , q) plane, that critical state is represented by a unique state line for different levels of suction (Laloui et al., 2005). From this assumption and considering the shape of the LC curve suggested by Wheeler et al. (2003), the yield surfaces can be represented as shown in Figure 4. A generalized version of the Modified Cam Clay in terms of (p∗ , J , θ, s∗ and p∗0 ) is proposed as follows: FLC =
569
1 J2 − ∗ p∗0 − p∗ = 0 g 2 (θ) p∗2 p
(20)
joint action of several mechanisms that can act simultaneously. Concepts of multi-dissipative materials introduced by Rizzi et al. (1996) have been considered to take into account that different mechanisms can induce plastic generalized deformations. To develop the governing equations, a procedure similar to the one presented in Sánchez et al. (2005) has been followed here. A first step is the assumption of an additive decomposition of the generalized strains into elastic and plastic components; so, the increment of total generalised strains can be expressed as: n=na
d ε˜ = d ε˜ e +
d ε˜ pn
(26)
n=1
Figure 4. Three dimensional view of the yield surface in ( p∗ , q, s∗ ) stress space.
where p∗ is the first invariant of the Bishop’s stress tensor: p∗ = 1/3(σ1∗ + σ2∗ + σ3∗ ); J2 is the second invariant of the deviatoric Bishop’s stress tensor (sij∗ = σij∗ − δij p∗ ), and g(θ) is a function of the Lode angle (equivalent to M in the (p∗ , q) space). Different expressions of g(θ) are given for different failure criteria (i.e. Alonso, 1993). The other two yield surfaces are the same of the isotropic conditions, equations (4) and (5), and are expressed in the following form: FSI = s∗ − sI∗ = 0 ∗
FSD = s −
∗ sD
(21)
=0
(22)
The generic expression introduced as follows will be used in this work: Fβ = s∗ − sβ∗ = 0
β = SI or SD
(23)
As a first approximation, associated plasticity is considered within this framework. Hence, the yield surfaces and plastic potentials are defined by the same equations. The hardening rules can be expressed as: dp∗0 = p∗0
p
p
k1 dSr vdεv − λ−κ λs − κs
p p dSr vdεv + k2 dsβ∗ = sβ∗ − λs − κs λ−κ
(24) β = SI or SD (25)
2.3
where na is the number of active plastic mechanisms that correspond to one subset of the total plastic possible mechanisms. The model has three inelastic mechanisms: LC, SD and SI. Two is the maximum number of simultaneous active plastic mechanisms i.e. LC plus SD or SI (see Section 2.1). In classical plasticity theory, it is assumed that the material behaves either in elastic or plastic fashion. The yield surface defines the transition from elasticity to plasticity, stress states inside the yield surface are considered as elastic (F < 0). When a loading process is inelastic, plastic strain rates are assumed to be governed by a flow rule. For the LC plastic mechanism, the generalized strain increment can be expressed as: d ε˜ p = χLC
∂FLC = χLC mLC ∂ σ˜ ∗
(27)
When the yielding is on the SI or SD surface, the generalized plastic strain increment can be obtained through:
d ε˜ p = χβ
∂Fβ = χβ mβ ∂ σ˜ ∗
(28)
In classical plasticity it is assumed that once yield occurs (that is F = 0), the stresses must remain on the yield surface during plastic deformation. This constraint is enforced by the consistency condition, which implies that dF = 0. The consistency conditions for the plastic mechanisms consider here are introduced as follows. Consistency condition: LC yield curve:
Governing equations
The behaviour of the soil described by the model introduced above can be regarded as the consequence of the
dFLC =
570
∂FLC ∗ ∂FLC ∗ d σ˜ + dp0 = 0 ∂ σ˜ ∗ ∂p∗0
(29)
Using equation (24), the consistency equation can be expressed as:
Introducing (39) and (40) in (37) and (38) the final expressions are obtained:
p ∂FLC ∗ ∂FLC ∗ v dSr ˜ + dεvp − k1 =0 ∗ dσ ∗ p0 λ−κ λs − κs ∂ σ˜ ∂p0
T mLC d σ˜ ∗ − HLC χLC − hβ χβ = 0
(43)
mβT d σ˜ ∗ − Hβ χβ − hLC χLC = 0
(44)
(30)
where HLC , Hβ , hLC , hβ are moduli related to the plastic mechanisms evaluated according to:
Consistency condition: SI/SD yield curves: dFβ =
∂Fβ ∗ ∂Fβ ∗ d σ˜ + ∗ dsβ = 0 ∂ σ˜ ∗ ∂sβ
(31)
Using the hardening rule for sβ (25), the following expression is obtained:
p −dSr
(32) The following expressions are adopted for the generalised moduli: ∂FLC ∗ v ∗ p0 ∂p0 λ−κ ∂FLC ∗ k1 H2 = p ∂p∗0 0 λs − κs ∂Fβ 1 H3 = ∗ sβ∗ λs − κs ∂sβ ∂Fβ v H4 = ∗ sβ∗ k2 ∂sβ λ−κ
(45)
hβ = H2 msT mβ
(46)
Hβ = H3 msT mβ
(47)
hLC =
∂Fβ ∗ ∂Fβ ∗ v d σ˜ + ∗ sβ + k2 dε p = 0 ∂ σ˜ ∗ ∂sβ λs − κs λ−κ v
H1 =
HLC = −H1 mεT mLC
(33)
(34)
(35)
(36)
(37)
mβT d σ˜ ∗ − H3 dSrp + H4 dεvp = 0
(38)
In this model the material behaviour is described by elasto-plastic mechanisms that can be activated during the loading process. The set of active plastic mechanisms is not known in advance. Therefore it is necessary to use an iterative procedure to find them (Simó & Hughes, 1998). A possibility is to assume that all the plastic mechanisms are initially active. Here it is assumed that both plastic mechanisms are initially active: LC and β (that is SD or SI ). The increment of generalised stress can be expressed in terms of the elastic operator and the elastic and total elastic generalised strain increment according to: d σ˜ ∗ = De d ε˜ − χLC mLC − χβ mβ ;
β = SI , SD (49)
where: ⎛ ⎜ ⎜ ⎜ ⎜ De = ⎜ ⎜ ⎜ ⎝
The plastic volumetric strain and the plastic change in degree of saturation are obtained as follows: dεvp = χLC mεT mLC
(48)
2.4 Elasto-plastic stress-strain relations
Using the notation introduced above the consistency equations (30) and (32) can be expressed as: T mLC d σ˜ ∗ + H1 dεvp − H2 dSrp = 0
−H4 mεT mLC
E11
E12 E22 sym
E13 E23 E33
0 0 0 E44
0 0 0 0 E55
0 0 0 0 0 E66
0 0 0 0 0 0 E77
⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠
(39) and:
dSrp
=
χβ msT mβ
(40)
E11 E44 E12 E77
where the auxiliary vectors are as follows: mε = (1, 1, 1, 0, 0, 0, 0)T
(41)
ms = (0, 0, 0, 0, 0, 0, −1)
T
(42)
= E22 = E33 = K + 4/3G = (v/k)p∗ + 4/3G; = E55 = E66 = G; = E23 = E13 = K−2/3G and = K¯ = (1/ks )s∗
Substituting this equation into the ones obtained from the consistency condition in the previous section,
571
the following expressions are obtained: T mLC De d ε˜ − χLC mLC − χβ mβ − HLC χLC − hβ χβ = 0 d ε˜ − χLC mLC − χβ mβ
(50)
− Hβ χβ − hLC χLC = 0
(51)
mβT De
−1
Rearranging,
χ =H e
c
c χLC HLC + HLC + χβ hβ + hβ = eLC χβ Hβ + Hβc + χLC hLC + hcLC = eβ
(52) (53)
c where HLC , Hβc , hcLC , hcβ , are moduli related to the plastic mechanisms and eLC and eβ are variables linked to the increment of generalised strains. The system formed by Equations (52) and (53) can be written as:
& χLC H¯ LC + χβ h¯ β = eLC χβ H¯ β + χLC h¯ LC = eβ
(62)
The choice of the plastic mechanisms initially assumed active should be verified by checking that they are actually active (Simó & Hughes, 1998). If one of them is not active, in this model, the case becomes a single dissipative model. Finally, the generalized stress increment (49) can be expressed as: d σ˜ ∗ = De d ε˜ −
(54)
n=na
d ε˜ p
(63)
n=1
After some algebra the following general equation can be obtained:
where: T c H¯ LC = HLC + HLC De mLC = HLC + mLC
(55)
T De mβ h¯ β = hβ + hcβ = hβ + mLC
(56)
T eLC = mLC De d ε˜
(57)
H¯ β = Hβ +
Hβc
= Hβ +
mβT De mβ
(58)
h¯ LC = hLC + hcLC = hLC + mβT De mLC
(59)
eβ = mβT De d ε˜
(60)
where H = H + H c
d σ˜ ∗ = Dep d ε˜
(61)
The hardening modulus matrix (H) is symmetric when there is reciprocity in the hardening rules of both mechanisms (reciprocal hardening implies that Hij = Hji for i = j). This model has non-reciprocal hardening (as for the general case H12 = H21 ). There is a unique increment of ε for any increment of σ if, and only if, H is a P-matrix (Rizzi et al., 1996). When this condition is satisfied, the flow rule of the multidissipative materials exhibits hardening, otherwise it exhibits softening. Finally, for H = 0 the behaviour is perfectly plastic. For the general case of non-associative plasticity, there is a unique increment of σ for any increment of ε if, and only if, the effective hardening matrix H is a P-matrix. Hc is the critical softening matrix.
(64)
The form of Dep (64) will depend on the plastic mechanism(s) active during loading (i.e. only the LC plastic mechanism is active, or only a β mechanism is active, or both plastic mechanisms are active). The specific elasto-plastic operators for each case, and more details of the generalized model, can be found in Lloret (2007). 3
Equivalently the system (54) can be written in a compact form as: Hχ = e;
The assumption that H is a P-matrix implies that each diagonal element of the H matrix plus the corresponding diagonal element of the Hc matrix is greater c than zero (i.e. (HLC + HLC ) > 0 and (Hβ + Hβc ) > 0). Therefore, the condition of H¯ > 0 is satisfied for each plastic mechanism. The solution of the system (62) requires the inversion of the H matrix which is assumed to be a P-matrix, obtaining:
CONCLUSIONS
A generalisation of the isotropic elasto-plastic framework presented by Wheeler et al. (2003) has been proposed in this work. A characteristic of the model is the proposal of a number of plastic mechanisms for describing the coupled hydro-mechanical behaviour observed in unsaturated soils. A formal framework for multi-dissipative materials has been used in this work to formulate the 3D generalised stress-strain relation of this model. REFERENCES Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Geotechnique (40)3: 405–430. Alonso, E. 1993. Unsaturated soils: recent developments and applications. Constitutive models of unsaturated soils.
572
Civil engineering European courses, UPC, Barcelona, Spain. Cui, Y.J. & Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Geotechnique (46): 291–311. Houlsby, G.T. 1997. The work input to an unsaturated granular material. Geotechnique (47) 1: 193–196. Khalili, N., Geiser, F. & Blight, G.E. 2004. Effective stress in unsaturated soils: Critical review with new evidence. International Journal of Geomechanics. ASCE; 4(2): 115–126. Laloui, L. & Nuth, M. 2005. An introduction to the constitutive modelling of unsaturated soils. Multiphysics Geomechanics 651–669. Lloret, M. 2007. Numerical Modelling of Coupled Behaviour in Unsaturated Soils. PhD Progress Report, University of Strathclyde and University of Glasgow, UK. Maâtouk, A., Leroueil, S. & La Rochelle, P. 1995. Yielding and critical state of a collapsible unsaturated silty soil. Geotechnique (45): 465–477.
Rizzi, E., Giulio, M. & William, K. 1996. On failure indicators in multi-dissipative materials. International Journal of Solids and Structures. 33 (20–22): 3187–3214. Sánchez, M., Gens, A., Guimarães, L. & Olivella, S. 2005. A double structure generalized plasticity model for expansive materials. International Journal for Numerical and Analytical Methods in Geomechanics (29): 751–787. Simó, J. & Hughes, T. 1998. Computational Plasticity. Springer: New York. Vaunat, J., Cante, J., Ledesma, A. & Gens, A. 2000. A stress point algorithm for an elastoplastic model in unsaturated soils. International journal of plasticity (16): 121–141. Wheeler, S.J. & Sivakumar, V. 1995. An elastoplastic critical state framework for unsaturated soil. Geotechnique (45) 1: 35–53. Wheeler, S., Sharma, R.S. & Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Geotechnique (53) 1: 41–54.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Effect of degree of saturation on mechanical behaviour of unsaturated soils A.R. Estabragh Faculty of Soil and Water Engineering, University of Tehran, Iran
A.A. Javadi School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter, UK
ABSTRACT: The effect of the unsaturated condition in soils is commonly expressed through suction. It is generally accepted that the suction and degree of saturation have a significant effect on the mechanical behaviour of unsaturated soils. However, the effect of degree of saturation is generally not included in the majority of existing elasto-plastic constitutive models. It is believed that inclusion of degree of saturation in constitutive models for unsaturated soils could lead to significant simplification for practical purposes. This paper presents the results of an investigation into the effect of degree of saturation on the behaviour of unsaturated silty soil in the light of a comprehensive set of experiments. The variation of degree of saturation during loading/unloading, wetting/drying and reloading is studied. The results show that the degree of saturation has a direct effect on the behaviour of unsaturated silty soil. The applicability of degree of saturation in an elasto-plastic constitutive model proposed in the literature is examined in the light of the experimental data and a suggestion is made for possible improvement in modelling of unsaturated soils.
1
INTRODUCTION
Unsaturated soil is a three phase material, containing solid particles, water and air. The presence of air along with water in the soil voids leads to two types of pore pressure: pore air pressure, ua and pore water pressure, uw . The pore air pressure is generally higher than the pore water pressure because of surface tension effects. It is generally accepted that suction, s (ua −uw ) and degree of saturation, Sr have a significant effect on the mechanical behaviour of unsaturated soils (Gallipoli et al., 2003). In fact suction influences the mechanical response of unsaturated soil through two basic mechanisms: the perturbing action of the average stress state and the stabilising effect of the water menisci at inter particle contacts. These two mechanisms that result from effects of suction are influenced by the state of saturation of the soil. The hysteresis phenomenon is usually observed in the soil-water characteristic relationship that is expressed in term of degree of saturation, Sr and suction, s. Many factors such as non-uniform pore size distribution and presence of entrapped air in the soil are considered to be the main causes for hysteresis in the soil-water characteristic curve. The occurrence of hydraulic hysteresis in the soil-water characteristic curve during drying and wetting means that two samples of the same soil
subjected to the same values of suction can have significantly different values of Sr if one is on the drying path and the other is on the wetting path. It shows that the inter-particle contact forces transmitted through the soil skeleton would be different in the two cases. Wheeler et al. (2003) indicated that two elastic-plastic processes can be considered for unsaturated soils: the first is the mechanical process of straining of the soil skeleton under changes of applied load which consists of elastic strain due to the elastic deformation of soil particles and plastic strain due to slippage of particles at contacts. The second is the hydraulic process of water inflow and outflow to individual voids that provides elastic deformation by changing the interface position (menisci separating air and water). 2
ELASTO-PLASTIC MODELS
Two well-known classes of elasto-plastic models for unsaturated soils have been published in the past years. The first class of models were presented in terms of the mean net stress, p (the difference between total stress and pore air pressure) and suction, s (the difference between pore air pressure and pore water pressure) (Alonso et al., 1990; Josa et al., 1992; Wheeler and Sivakumar, 1995 and Cui and Delage, 1996). In this
575
class of models the unsaturated condition is expressed through suction without any direct influence of degree of saturation, Sr . Therefore, these models are not able to provide correct predictions when the influence of hydraulic hysteresis on mechanical behaviour is prevalent (e.g., when studying behaviour of a soil under cycles of drying and wetting). The second class of elasto-plastic models for unsaturated soils are expressed in terms of a different set of constitutive variables that include the degree of saturation in their definition (Bolzon et al., 1996; Karube et al., 1998 and Karube and Kawai, 2001). The stress variable in this class of models has the form of Bishop (1959) relationship given as: σij = σij − δij [ua − χ (ua − uw )]
(1)
where σij is the total stress, σij has been referred to as Bishop’s stress (Bolzon et al. (1996) and Gallipoli et al. (2003)) or average skeleton stress (Jommi, 2000). χ is a soil parameter depending on the degree of saturation and ranges between one (at saturation) and zero (dry condition), δij is Kronker’s delta and ua and uw are pore air pressure and pore water pressure respectively. Although this class of models introduced Sr into the definition of a soil variable, they have some limitations when predicting certain important aspects of unsaturated soil behaviour such as irreversible compression during the drying stages of wetting-drying cycle and the influence of a wettingdrying cycle on subsequent behaviour during isotropic loading. Recently Wheeler et al. (2003) presented a new model which involves coupling of hydraulic hysteresis and mechanical behaviour and is suitable for prediction of hydraulic response and mechanical response of unsaturated soils. They concluded from Houlsby’s theoretical analysis (Houlsby, 1997) of work input for granular unsaturated soils that another alternative choice of stress state variables for isotropic condition would be as: p∗ = p − Sr .uw − (1 − Sr )ua ∗
s = n(ua − uw )
of the elasto-plastic model of Wheeler et al. (2003) for unsaturated silty soil is also examined in the light of experimental evidence and a suggestion is presented for elasto-plastic modelling of unsaturated soils.
3
EXPERIMENTAL PROCEDURE
A set of experimental tests were performed on samples of a compacted silty soil following the procedure explained by Estabragh et al. (2004). Several isotropic compression tests involving loading to a virgin state and unloading to a predefined stress, suction change (wetting or drying) and subsequent reloading were carried out in this research program. During each stage of the tests the variations of specific volume and degree of saturation were measured. From the results of these experiments the values of slope and intercept of normal compression lines in the v−ln p space were calculated for different values of suction. Typical experiments results are shown in Figs. 1 and 2. Data from these experiments were used to examine the prediction capabilities of the model proposed by Wheeler et al. (2003).
(2) (3)
where p∗ is mean Bishop’s stress, n is porosity and s∗ is modified suction. p∗ in the above equation represents the influence of applied total stress, pore air pressure and pore water pressure within bulk water whereas s∗ represents the influence within meniscus water. Wheeler et al. (2003) stated the elastic region in this model is surrounded by LC (loading and collapse), SD (suction decrease) and SI (suction increase) yield curves. In this paper, the variation of specific volume and degree of saturation during loading/unloading, wetting/drying and reloading are studied. The application
Figure 1. Effect of wetting on subsequent soil behaviour during loading, initial s = 300 kPa, final s = 50 kPa; variation of (a) specific volume; (b) degree of saturation with mean net stress.
576
Figure 2. Effect of wetting on subsequent soil behaviour during loading, initial s = 50 kPa, final s = 300 kPa; variation of (a) specific volume; (b) degree of saturation with mean net stress.
4
EXPERIMENTAL RESULTS
Figs. 1 (a) and 2 (a) show the results of two typical tests involving an isotropic loading and unloading cycle ab-c at constant suctions of 300 and 50 kPa respectively; followed by a wetting (or drying) cycle cd and subsequent isotropic reloading de. The results for each of these two tests are presented in a conventional format consisting of two plots; in the first plot the stress path followed in the test is shown (Figs. 1 (a) and 2 (a)) while in the second plot the variation of degree of saturation is plotted against mean net stress, p (on a logarithmic scale). In the test, the mean net stress was increased from 20 kPa to 550 kPa during loading path ab and then it was reduced from 550 kPa to 50 kPa in the unloading path bc. During the unloading path, suction was held constant throughout the test at 300 and 50 kPa in the first and second test respectively. Fig. 1 (a) shows the results from a typical test involving an isotropic loading and unloading cycle a-b-c at a constant suction of 300 kPa, followed by a wetting cycle cd and a subsequent isotropic reloading de. During the wetting stage, swelling occurred in the sample (path cd in Fig. 1 (a). As shown in Fig. 2 (a) loading and unloading were done at suction of 50 kPa; the drying stage continued until s = 300 kPa and was followed by the subsequent reloading stage.
Inspection of Figs. 1 (a) and 2 (a) shows that there was a change in the slope of compression curve during loading stage ab, corresponding to a yield point on the LC yield curve. During isotropic loading (path ab) when large plastic reduction in void ratio occurred, a significant increase in the degree of saturation was observed. In contrast, during subsequent unloading (path bc), when only a very small elastic swelling occurred, the changes of degree of saturation were very small and irreversible changes of degree of saturation were observed. As the specific volume decreases, the dimensions of voids and the connecting passageways between the voids tend to decrease, so that a higher value of suction is needed to produce a given degree of saturation. Figs. 1 (b) and 2 (b) show that the main variation in degree of saturation occurred after the yield point, as the great proportion of deformation occurred after yielding when large changes of specific volume were occurring. Inspection of Figs 1 and 2 shows that the degree of saturation increased in the wetting path cd (Fig. 1 (b)) and decreased in the drying path cd (Fig. 2 (b)). It shows that the value of Sr was higher in the drying path (Fig. 2 (b)) than in the wetting path (Fig. 1 (b)) at any given value of suction. The occurrence of hydraulic hysteresis is obvious by comparing the results of these two tests. In the subsequent reloading a yield point was observed, but the value of the yield stress does not correspond to the maximum value of mean net stress that was previously applied; this was because of the change in the initial value of suction in the sample during wetting or drying. 5
MODEL PREDICTION
In order to show the capabilities of the model in predicting different types of stress path in isotropic conditions the following values of soil constants were obtained for the soil from the experimental results: λ (parameter for volumetric strain on LC curve) = 0.075 k (parameter for elastic volumetric strains) = 0.013 λs (parameter for change of degree of saturation on SI or SD curve) = 0.12 and ks (parameter for elastic changes of degree of saturation) = 0.032. The initial state of the soil sample for test 1 is: p = 20 kPa, s = 300 kPa, v = 1.7519, Sr = 0.798 and pc = 190 kPa. The initial state of soil sample for test 2 is: p = 20 kPa, s = 50 kPa, v = 1.7519, Sr = 0.798 and pc = 150 kPa.
577
The increments of p∗ and s∗ can be expressed by the following equations (Wheeler et al., 2003): dp∗ = d(p − ua ) + Sr ds + sdSr
(4)
ds∗ = nds − sdε/v
(5)
The experimental and predicted results are shown in Figs. 3 and 4. The resulting stress paths in the s∗ : p∗ plane are shown in Figs. 3 (b) and 4 (c). The first case involves loading, unloading, wetting (suction decrease from 300 to 50 kPa) and reloading whereas the second case involved loading, unloading, drying and reloading. As shown in Figs. 3 (b) and 4 (c) during initial section AB of the loading path the value of s∗ reduces very slightly because of small decrease of porosity n, caused by elastic volumetric strain resulting from increase in p∗ . The LC yield curve is reached at B when substantial plastic volumetric strain commences. Large plastic increase of Sr therefore occurs as the loading proceeds beyond point B. During unloading the behaviour is purely elastic. During wetting (suction decrease from 300 kPa to 50 kPa) in test 1 (Figs. 1 (a) and 1 (b)) the volume of the sample increases and Sr increases significantly and overall there is a reduction in p∗ and a large reduction in s∗ . When reduction in suction takes place at p = 50 kPa the stress path remains inside the LC yield curve throughout the wetting process and
Figure 4. Model prediction of isotropic loading, unloading at constant s = 50 kPa, drying and reloading at s = 300 kPa; (a) specific volume; (b) path in modified stress space.
Figure 3. Model prediction of isotropic loading, unloading at constant s = 300 kPa, wetting and reloading at s = 50 kPa; (a) specific volume; (b) path in modified stress space.
volumetric response consists of elastic swelling caused by reduction of p∗ . In the second test (Fig. 2 (a)) drying (suction increase from 50 to 300 kPa) occurs at p = 50 kPa. In this case, reduction is observed in both Sr and volume of the sample. Overall increases are observed in p∗ and s∗ as shown in Fig. 4 (c) During drying suction increases and degree of saturation decreases and the net effect is a significant reduction in p∗ . Throughout the drying stage yielding occurs on the SI yield curve causing significant plastic increase in Sr . Figs. 3 (b) and 4 (c) show the path of the reloading stages for suctions of 300 and 50 kPa respectively. Fig. 4 (c) shows that the soil yields at point I on the LC yield curve so the value of p is less than 550 kPa that was previously applied. From I to F yielding takes place on the LC yield curve leading to plastic volumetric strain. Figs. 3(a), 4(a) and 4(b) show the comparison between the model predictions and
578
the measured results. It is shown that although the model is able to predict qualitatively various aspects of the soil behaviour, quantitatively, there are differences between the measured results and model predictions. 6
CONCLUSIONS
The results show that significant variations occurred in Sr during isotropic loading. This can be attributed to the influence of volumetric strains, as the main part of changes of Sr coincides with the post yield sections of loading stages where large changes of v are occurring. The experimental results indicate the occurrence of hydraulic hysteresis in the drying and wetting stages. The model that was proposed by Wheeler et al. (2003) for unsaturated soils is a new model that includes coupling of hydraulic hysteresis and mechanical behaviour. The performance of the model was examined in the light of results of experiments on an unsaturated silty soil in order to evaluate the capabilities of the model in predicting some aspects of unsaturated soil behaviour during loading, unloading, drying, wetting and reloading. It is concluded from the comparison of estimated and measured results that the model is able to predict qualitatively various aspects of the soil behaviour. However, the model predictions for some conditions do not coincide with the experimental results and in some cases there are considerable differences between them. It may be that some of the mathematical expressions of the model should be improved and the model needs to be fully validated by experimental data including extension to triaxial stress states. The effect of meniscus water on mechanical behaviour is likely to be dominantly a function of degree of saturation, Sr rather than s∗ . An increase of Sr suggests a decrease in the stabilising effect of meniscus. Therefore for modelling the hysteresis effects, a model which includes a link between Sr and s∗ might be appropriate.
REFERENCES Alonso, E.E., Gens, A. and Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique, Vol. 40, No.3, 405–430. Bolzon, G., Schrefler, B.A. and Zienkiewiez, O.C. 1996. Elasto-plastic soil constitutive laws generalised to partially saturated state. Géotechnique, Vol. 46, No. 2, 279–289. Cui, Y.J. and Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Géotechnique, Vol. 46, No. 2, 405–430. Bishop, A.W. 1959. The principle of effective stress. Teknisk Ukeblad 106, No. 39, 859–863. Estabragh, A.R., Javadi, A.A. and Boot, J.C. 2004. Effect of compaction pressure on consolidation behaviour of unsaturated silty soil. Canadian Geotechnical Journal No. 41: 540–550. Gallipoli, D., Gens, A., Sharma, R.S. and Vaunat, J. 2003. An elasto-plastic model for unsaturated soil incorporating the effect of suction and degree of saturation on mechanical behaviour. Géotechnique, Vol. 53, No. 1, 123–135. Houlsby, G.T. 1997. The work input to an unsaturated granular material. Géotechnique, Vol. 47, No. 1, 193–196. Jommi, C. 2000. Remarks on the constitutive modelling of unsaturated soils. In Proceedings of the International workshop on unsaturated soils. 139–153. Josa, A., Balmaceda, A. Gens, A. and Alonso, E.E. 1992. An elasto-plastic model for partially saturated soils exhibiting a maximum collapse. Proc. 3rd, Int. Conf. Computational plasticity, Barelona, 815–826. Karube, D., Kato, S., Honda, M. and Kawai, K. 1998. A constitutive model for unsaturated soil evaluating effects of soil moisture distribution. In Proceedings of 3rd Int. Conf. on Unsaturated soils, Beijing, 485–490. Karube, D. and Kawai, K. 2001. The role of pore water in the mechanical behaviour of unsaturated soils. Geotech. Geolog. Engineering, No.19, 211–241. Wheeler, S.J and Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Géotechnique, Vol. 45, No. 1, 35–53. Wheeler, S.J., Sharma, R.S. and Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Géotechnique, Vol. 53, No. 1, 41–54.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
An improved constitutive model for unsaturated and saturated soils K. Georgiadis Aristotle University of Thessaloniki, Thessaloniki, Greece
D.M. Potts & L. Zdravkovic Imperial College, London, UK
ABSTRACT: This paper presents a constitutive model for unsaturated and saturated soils based on the critical state framework. The model includes a versatile expression for yield and plastic potential surfaces, the option of linear or nonlinear increase of shear strength with suction and three options for the shape of the unsaturated isotropic compression lines. The latter feature is of particular importance as it controls the amount of potential collapse the soil can experience due to wetting. Depending on the type of boundary value problem analysed a linear, bi-linear or exponential relationship can be used. Two sets of finite element analyses are presented here which investigate the influence of the shape of the isotropic compression line on the behaviour of strip footings and axially loaded single piles.
1
INTRODUCTION
Most existing constitutive models for unsaturated soils are based on fully saturated models, and in particular on a critical state framework. The effects of partial saturation and suction within a three-dimensional constitutive model are taken into account by the introduction of suction or equivalent suction as an additional stress state variable. Many of these models assume a linear relationship for the variation of shear strength with suction (e.g. Alonso et al. 1990) and for the shape of the partially saturated isotropic compression lines (e.g. Alonso et al. 1990, Wheeler & Sivakumar 1995). Experimental evidence, however, suggests that these relationships are nonlinear. Of particular importance is the shape of the isotropic compression line for unsaturated conditions, as it is directly related to the amount of potential collapse that the soil will experience upon wetting. Experimental results indicate that the amount of potential collapse increases nonlinearly at low confining stresses, reaches a maximum at a certain value of the confining stress and decreases at high confining stresses (e.g. Booth 1975, Yudhbir 1982). This paper presents a number of refinements made to the existing critical state constitutive model for unsaturated soils presented by Georgiadis et al. (2003) and Georgiadis et al. (2005) that aid flexibility and applicability. These involve an exponential expression for unsaturated isotropic compression lines, a nonlinear expression for the variation of shear strength with suction, as well as a flexible function for the shapes
of the yield and plastic potential surfaces. The advantages of these improvements are demonstrated in the finite element analyses of a surface strip foundation and an axially loaded pile. 2 2.1
CONSTITUTIVE MODEL Stress invariants
Two independent stress variables are required to model unsaturated soil behaviour. A convenient choice of stress variables for partially saturated conditions is the pair of equivalent stress: σ˜ = σ¯ + sair
(1)
and equivalent suction: seq = s − sair
(2)
where σ¯ (= σ − ua ) is the net stress, s is the matrix suction and sair is the air entry value of suction. The constitutive model is formulated in four-dimensional stress space (J , p, θ, seq ), where J is the generalised three dimensional deviatoric stress, p˜ is the mean equivalent stress and θ is the Lode’s angle. 2.2 Yield function and plastic potential surface The following modified version of the Lagioia et al. (1996) expression is used for the yield function and plastic potential equations:
581
F G
'
1+
=
p˜ + k · seq − p˜ o + k · seq
1+
η K2 η K1
Kβ2
J
f
Kβ1 = 0 f
k = Sr
where p˜ o is the isotropic yield equivalent stress at the current value of suction, k controls the increase in apparent cohesion due to suction, K1 , K2 and βf are constants calculated from the model parameters αi and μi from the following expressions:
K1,2 =
μi (1 − αi ) 1± 2 (1 − μi )
( 1−
constant k
(3)
4αi (1 − μi ) μi (1 − αi )2
seq Figure 1. Linear and non-linear variation of apparent cohesion with equivalent suction.
(4) degree of saturation, Sr , to suction has been proposed by van Genuchten (1980):
βf = (1 − μi ) (K1 − K2 )
Sr =
(6)
where, ψ, m and n are fitting parameters, and Sro is the residual degree of saturation at very high values of suction.
where Mji is the ratio J/(˜p + f (seq )) at which either ∂F/∂ p˜ = 0 or ∂G/∂ p˜ = 0.Mji depends on the Lode’s angle θ and the model parameter Mi and is calculated from the Matsuoka—Nakai criterion (Matsuoka & Nakai 1974). The parameters αi , μi and Mi are equal to αf , μf and Mf when the yield surface is being calculated and equal to αg , μg and Mg when the plastic potential surface is being calculated. Mg is the gradient of the critical state line in the conventional q − p space, corresponding to triaxial compression (θ = −30◦ ). The parameters αf , μf and Mf and αg , μg and Mg control the shape of the yield and plastic potential surfaces, respectively. With appropriate choice of these parameters a wide range of surfaces can be achieved including most of the well-known yield and plastic potential surfaces. 2.3
Variation of apparent cohesion with suction
The parameter k in equation (3) controls the increase of apparent cohesion Jci with suction through the following expression: Jci = k · Mji · seq
m
(5)
and η is the normalised stress ratio: ! J p˜ + f seq η= Mji
1
(7)
A constant value of k is only realistic if the problem analysed involves small variations of suction. In other cases it must be a function of suction or the degree of saturation (Figure 1). An expression relating the
n 1 + seq · ψ
(1 − Sro ) + Sro
(8)
2.4 Isotropic compression line The isotropic yield equivalent stress, p˜ o , at the current value of suction depends on the shape of the isotropic compression line. Three different options are incorporated in the model. 2.4.1 Option 1—linear isotropic compression line This option is the same as that proposed by Alonso et al. (1990) in the Barcelona Basic model and has been adopted in many other models, such as the Bolzon et al. (1996), Cui & Delage (1995), Modaressi & Abou-Bekr (1994) models. The isotropic compression line for this option (Figure 2) is given by: v = v1 seq − λ seq ln p˜ o (9) where v1 (seq ) is the specific volume at unit pressure and the current value of equivalent suction and λ(seq ) is the partially saturated compressibility coefficient. λ(seq ) is given by the following empirical expression (Alonso et al. (1990)): (10) λ seq = λ(0) (1 − r) e−βseq + r where λ(0) is the fully saturated compressibility coefficient and β and r are model parameters which control the shape of the primary yield and plastic potential surfaces in the p˜ − seq plane. This assumption for the isotropic compression line leads, through the same calculations as those described
582
lnp
pm
p = 1kPa v1(0) v1(seq)
Option 1 1
(seq) ~
pc
1 1 Saturated
Figure 3. Variation of potential plastic reduction of specific volume due to wetting with isotropic yield stress.
Figure 2. Isotropic compression lines for options 1 (linear) and 2 (bi-linear).
for the yield surface in the isotropic yield equivalent stress—equivalent suction space becomes:
in Alonso et al. (1990), to the following expression relating the isotropic yield equivalent stress, p˜ o , to the equivalent fully saturated yield stress, p˜ ∗o : p˜ o = p˜ c ·
p˜ ∗o p˜ c
~
(0) (0) Option 2
p~m
1/b
(λ(0)−κ)!(λ(seq )−κ ) (11)
where p˜ c is the characteristic pressure defining the limiting lower value of the equivalent fully saturated yield stress, p˜ ∗o , for which the Loading-Collapse yield curve is a vertical line (initially introduced by Alonso et al. 1990) and κ is the compressibility coefficient along elastic paths and is assumed to be independent of suction. Equation (11) implies that the amount of potential collapse due to wetting (vertical distance between the fully and partially saturated lines in the v-ln˜p plane) increases linearly with the increase of the logarithm of the confining stress, p˜ . This is a realistic assumption for the low confining stresses at which many laboratory tests on partially saturated soils are performed, but may give unrealistically high values of the yield stress, p˜ o , and the wetting induced volumetric plastic strains, at high confining stresses. 2.4.2 Option 2—Bi-linear isotropic compression line The characteristic pressure p˜ c is an arbitrary parameter the value of which is selected such that the shape of the Loading-Collapse yield curve matches the experimental data, and is assumed to be constant and unique for a particular soil. However, to avoid inconsistencies at high stress levels it would appear that p˜ c must be stress level dependent. An alternative approach is to assume that the ratio p˜ ∗o /˜pc is constant for confining stress ranges higher than those at which the experiments where performed. Adopting this approach, the expression
!
(λ(0)−λ(seq )) (λ(seq )−κ ) p˜ o = p˜ ∗o · αc
(12)
where, αc = p˜ ∗o /˜pc is a model parameter. The partially saturated isotropic compression line for this option is bi-linear and is shown in Figure 2. At low confining stresses expression (11) is adopted giving a linear increase of the amount of collapse with stress, while at high confining stresses expression (12) is adopted giving a constant amount of collapse. The switch from expression (11) to expression (12) takes place when the two expressions are equal. It can be shown that the confining stress, p˜ m , at which this switch takes place, is given by: !
(λ(0)−κ)
p˜ m = p˜ c · αc
(λ(seq )−κ )
(13)
2.4.3 Option 3—Non-linear isotropic compression line The idealised relationship between the amount of potential plastic reduction of the specific volume, vp , due to wetting of a partially saturated soil lying on the isotropic compression line, and the isotropic yield stress, po , is given in Figure 3. A mathematical expression of this form is the following: vp = λm
p˜ o p˜ c
−b ln
p˜ o p˜ c
(14)
where λm and b are model parameters. The partially saturated isotropic compression line is shown in Figure 4 and is given by: v = v1 (0) − λ (0) ln p˜ + v
583
(15)
~
option is given by the following equation:
~
⎛
N(0) N(seq)
p˜ ∗o = p˜ c x
1
⎞
⎝1−
λm x−b ⎠ λ (0) − κ
,
where x =
1
Option 3
3
Saturated
p˜ o p˜ c
(21)
FINITE ELEMENT ANALYSES
3.1 General
Figure 4. Isotropic compression line for option 3 (non-linear).
Two boundary value problems analysed with the above constitutive model are presented in this paper. The analyses aim to highlight the influence of the shape of the isotropic compression line on the behaviour of shallow and deep foundations.
where 3.2 Surface strip footing
v = vp − ve −b seq + patm p˜ o p˜ o ln c − κs ln = λm p˜ c p˜ patm
The parameter λm is therefore a measure of the soil stiffness at low confining stresses and is dependent on equivalent suction. It can be assumed that the initial slope of the isotropic compression line, λin (seq ), is given by equation (10). λm is obtained from combination of Equations 10 and 18 as follows:
All analyses involved a 2 m wide rough rigid strip footing bearing on a uniform soil. The groundwater table was at −2 m with a hydrostatic pore pressure profile to the ground surface. An air entry suction value of zero was used and therefore the soil was treated as partially saturated from the water table to the ground surface. Two sets of analyses were performed. In the first set the footing was loaded to failure and in the second the footing was first loaded to a certain load with the water table at −2 m and subsequently the groundwater table was raised to the ground level at constant applied load. Three different loads were considered: 100 kN, 175 kN and 350 kN. Both sets of analyses outlined above were performed with options 1 (linear isotropic compression line) and 3 (non-linear isotropic compression line). The soil parameters used in the analyses are shown in Table 1. Three values of b were considered: 0.1, 0.226 and 0.472, which correspond to maximum potential collapse at a confining stresses, pm , of approximately 265 MPa, 1000 kPa and 100 kPa, respectively. A constant value with depth of 1.5 was assumed for the OCR throughout the soil. OCR in this case refers to the equivalent fully saturated state (seq = 0): OCR = p˜ ∗o /˜p.
λm = λ (0) (1 − r) 1 − e−βseq
Table 1.
(16)
The slope of the partially saturated compression line at any value of p˜ o is calculated as follows: λ seq = λ (0) − λm
p˜ o p˜ c
−b
1 − b ln
p˜ o p˜ c
(17)
The initial slope of the isotropic compression line, λin (seq ), is obtained by setting p˜ o = p˜ c in Equation 17: λin seq = λ (0) − λm
(18)
(19)
The value of p˜ o at which maximum collapse takes place is given by: p˜ m = p˜ c e1/b
(20)
The relationship between the partially saturated and the equivalent fully saturated isotropic yield stress which corresponds to the non-linear curves of this
αf μf Mf αg μg Mg pc λ(0) κ
584
Material properties for footing analyses. 0.4 0.9 1.2 0.4 0.9 1.2 12.0 kPa 0.066 0.0077
r β κs ν1 k μ sair Ko γ
0.35 0.0164 kPa−1 0.001 2.0 0.8 0.2 0.0 kPa 1.0 17.0 kN/m3
Load (kN)
500 450 400 350 300 250 200 150 100 50 0
For the lower load of 175 kN only small settlements take place, which initially increase linearly with the rise of the groundwater table but level off as the G.W.T. approaches the ground surface. For the higher load of 350 kN much larger settlements are predicted indicating failure. Unlike the predictions for the load-settlement curve, the shape of the isotropic compression line can be seen to greatly affect the behaviour of the footing due to wetting. The settlements reduce significantly with increasing b. For the lower load of 175 kN an increase of the parameter b from 0 (equivalent to the analysis with option 1) to 0.472 leads to a decrease of the final predicted settlement of approximately 73%. For the larger load of 350 kN the effect of the parameter b is even greater. At a rise of the G.W.T. from −2 m to −1 m the settlement predicted for b = 0 is 150% larger than that predicted for b = 0.472. For isotropic stress states it is only the relationship between the yield stress, p˜ ∗o , and the equivalent fully saturated yield stress, p˜ o , that controls the amount of wetting induced collapse. In any other case the change in apparent cohesion also affects the predicted amount of collapse, but generally to a much lesser extent.
Option model 11 b = 0.1 b = 0.226 b = 0.472 0
0.5
1
1.5
2
Rise of groundwater table (m) 0.5 1 1.5
2
Settlement (m)
Figure 5.
0
0
Load-settlement curves.
Settlement (m)
0.05 0.1 0.15 0.2 0.25
Option 1 (175kN) b = 0.1 (175kN) b = 0.226 (175kN) b = 0.472 (175kN) Option 1 (350kN) b = 0.1 (350kN) b = 0.226 (350kN) b = 0.472 (350kN)
Figure 6. Progression of vertical movement with rise of groundwater table—influence of the parameter b.
For simplicity and since the problem analysed does not involve high values of suction (s ≤ 39.24 kPa) a linear increase of the apparent cohesion with suction was assumed (k = const.). Finally, the same unit weight of 17 kN/m3 was assigned to the soil above and below the groundwater table for all analyses. The predicted load-settlement curves from the first set of analyses are plotted in Figure 5. It can be seen that the parameter b does not have any significant influence on the predicted curves. Consequently neither does the shape of the isotropic compression line nor the shape of the Loading-Collapse curve. It is evident from this that for the low suction levels of this particular problem it is the increase of apparent cohesion that controls the soil strength and not the value of the isotropic yield stress, po . At these low values of suction the value of the isotropic yield stress does not vary sufficiently enough to significantly affect the size of the primary yield surface. Figure 6 shows the progression of the settlement with the rise of the G.W.T. predicted by the second set of analyses (rise of the groundwater table at a constant load of 175 kN and 350 kN) The results are directly comparable as the initial stress-strain conditions at the beginning of wetting are very similar for the given loads. The settlements predicted with option 3 follow the same pattern as that observed in the option 1 analyses.
3.3
Single pile
The influence of the shape of the isotropic compression line on the behaviour of bored piles endbearing in partially saturated soil is investigated in this section. The analyses presented here are supplementary to the analyses of a pile in Canary Wharf, London presented by Georgiadis et al. (2003). The ground profile used in the finite element analyses comprised (from top to bottom) 10 m of fill, 3.8 m of Terrace Gravel, 3.9 m of Lambeth Group Clay, 6.5 m of Lambeth Group Sands, 12.8 m of Thanet Sands underlain by Chalk. The pile analysed was of 1.5 m diameter and 20.5 m length and was wished in place. Two sets of analyses are presented. The first set of analyses involves axial loading of the pile to failure with the ground water table at the initial level shown in Figure 7. The second set includes analyses in which the pile was loaded to a certain load and subsequently the groundwater table was raised to the final level, also shown on the same figure. The model parameters for the Lambeth sand and Thanet sand layers are given in Tables 2 and 3. Because of the large suctions involved in this problem the cohesion increase parameter, k, was set equal to the degree of saturation, Sr . The variation of the degree of saturation with suction was obtained from the particle size distribution curves of the materials using the Arya & Paris (1981) method. These were in turn fitted into the Van Genuchten (1980) expression for the soil water characteristic curve.
585
Table 4. Material properties for Terrace Gravel, Lambeth Clay and Chalk.
-5
-10 φ μ E
-15
Terrace Gravel
Lambeth Clay
Chalk
33◦ 0.2 30 MPa
29◦ 0.2 30 MPa
34◦ 0.2 1000 MPa
-20 Cessation of dewatering
-25
-30 Pile construction -35
-40 -20 -15 -10
Figure 7. profiles. Table 2.
-5 0 5 10 Piezometric Level
15
20
25
Canary Wharf pile analyses—Pore pressure
Material properties for Lambeth sand.
αf
0.08
β
0.02 kPa−1
μf Mf αg μg Mg αc λ(0) κ r
2.0 0.9 0.01 0.57 1.32 1.667 0.06 0.005 0.25
κs ν1 μ sair ψ m n Sro
0.001 1.826 0.2 15.0 kPa 0.03 kPa−1 0.35 4.5 0.15
Table 3. αf μf Mf αg μg Mg αc λ(0) κ r
Material properties for Thanet sand. 0.08 2.0 1.0 0.01 0.57 1.46 1.667 0.06 0.005 0.25
β κs ν1 μ sair ψ m n Sro
0.02 kPa−1 0.001 1.872 0.2 13.0 kPa 0.014 kPa−1 0.4 5.0 0.13
Three different values of the parameter b are investigated; b = 0.472 which corresponds to maximum potential collapse at pm = 100 kPa, b = 0.226 which corresponds to pm = 1000 kPa, and b = 0.1 for which
maximum potential collapse takes place at a very high confining stress pm ≈ 26000 kPa. The Terrace Gravel, Lambeth Clay and Chalk layers were modelled with the generalised Mohr-Coulomb model. The soil properties adopted for the analyses are shown in Table 4. A value of zero was set for the angle of dilation for these layers. The Lambeth Clay was assumed to behave undrained. The Ko values assigned to each soil layer were 0.5 for the Terrace Gravel, 1.15 for the Lambeth Clay, Lambeth Sands and Thanet Sands, and 1.0 for the Chalk. These values refer to the initial fully saturated conditions, prior to pile construction. The concrete pile behaviour was modelled as linear elastic. A Young’s modulus of 20 GPa and a Poisson’s ratio of 0.15 were used in the analyses. Figure 8 shows the load-displacement curves predicted with option 3 for the three different values of b. Unlike the footing case, where the parameter b did not affect the predicted ultimate load, the ultimate pile load increases with decreasing value of b, and consequently increasing isotropic yield stress p˜ o . In this case the suctions and stresses in the partially saturated zone are sufficiently high to produce p˜ o values much higher than the equivalent p˜ ∗o value, therefore affecting significantly the size of the primary yield surface. Plotted on the same figure is the load-displacement curve predicted with option 2. It can be seen that this curve is very close to and slightly lower than that predicted with option 3 for b = 0.226 (approximately 3% lower). This is due to the fact that the isotropic compression line for option 2 is very close to that corresponding to option 3 and b = 0.226 for the confining stress level relevant to this analysis (higher than 200 kPa). The progression of the vertical displacements of the pile with the rise of the groundwater table, at different constant loads, is shown in Figure 9, for option 2 and option 3 with b = 0.226. It can be seen that the results are in good agreement, with option 2 giving slightly lower displacements at the higher loads of 32 MN and 26 MN, and identical results at the low load of 19 MN. This is consistent with the results of the loading analyses discussed above, therefore confirming that the two models produce very similar results for the given αc and b values, and the stress and suction range under consideration.
586
Rise of water table (m) 0
50
0
40
10
Vertical Displacement (mm)
Load (MN)
60
30 Option 2 Option 3 - b=0.1 Option 3 - b=0.226 Option 3 - b=0.472
20 10 0 0
20
40
60
80
100
5
7.5
10
12.5
15
20 30 40 50 60 70
b=0.226 (d=14.2mm) b=0.472 (d=14.2mm) b=0.226 (d=20mm) b=0.472 (d=20mm) b=0.226 (d=30mm) b=0.472 (d=30mm)
80
Settlement (mm)
Figure 8.
2.5
Figure 10. Progression of vertical displacements for different values of b.
Load-settlement curves for different values of b.
Rise of water table (m) 0
2.5
5
7.5
10
12.5
they are not performed for the same load levels. However, close inspection of the load-displacement curves in Figure 8 shows that the b = 0.472 analysis starts closer to the ultimate pile load with the shaft friction fully mobilised and is therefore more likely to predict collapse. The difference between the analyses can therefore be attributed primarily to the value of the parameter b and the shape of the isotropic compression line.
15
Vertical Displacement (mm)
0 10 20 30 40 50 60
Op. 2 (L=19MN) Op. 3 - b=0.226 (L=19MN) Op. 2 (L=26MN) Op. 3 - b=0.226 (L=26MN) Op. 2 (L=32MN) Op. 3 - b=0.226 (L=32MN)
70 80
Figure 9. Progression of vertical displacements: comparison of option 2 and 3.
The influence of the parameter b on the pile response to wetting can be seen in Figure 10 which presents pile movements due to rise of the groundwater table for different values of b (0.226 and 0.472) and initial pile settlement (14.2 mm, 20 mm and 30 mm). It was chosen to make the comparison at the same values of initial settlement instead of the same load levels because the latter would have been meaningless, especially at high loads, where the settlements increase rapidly (see Figure 8). The pile loads which correspond to initial displacements of 14.2 mm, 20 mm and 30 mm are 19 MN, 26 MN and 32 MN for b = 0.226, and 19 MN, 25 MN and 28 MN for b = 0.472, respectively. For the lowest initial settlement of 14.2 mm the value of b has no influence on the pile response; both analyses give purely elastic heave. For 20 mm initial settlement the two analyses produce very close results, giving near-elastic heave. In contrast to them, for the large initial settlement of 30 mm the predictions are very different. The analysis with b = 0.226 predicts much larger settlements than the b = 0.472 analysis indicating failure of the pile. It is acknowledged that the two analyses are not directly comparable, as
4
CONCLUSIONS
A constitutive model is presented in this paper which provides three different options for the loading collapse yield surface. Option 1 gives a linear isotropic compression line leading to a constant increase of the amount of potential wetting induced collapse with the increase of the confining stress. Option 2 gives a bilinear compression line leading to a constant amount of potential collapse beyond a certain value of the confining stress. Finally, option 3 adopts an exponential expression, so that the amount of potential collapse increases with confining stress at low stresses, reaches a maximum value and then decreases to zero at very high confining stresses. The influence of the shape of the isotropic compression line was investigated for two common boundary value problems. The following conclusions can be drawn: • For the low suction and stress range involved in the strip footing analyses, the shape of the isotropic compression line does not affect the predicted loadsettlement curve (options 1 and 3 give similar results). This indicates that in this suction and stress range it is the variation of apparent cohesion with suction that controls the shear strength of the soil. The Canary Wharf pile analyses, however, showed that for higher stress levels, the shape of the isotropic
587
compression line has a significant effect on the predicted load-settlement curve. • For the suction and stress ranges involved in the problems analysed (both footing and Canary Wharf pile analyses), the response to rising groundwater table significantly depended on the shape of the isotropic compression line. • The Canary Wharf pile analyses showed that when the model parameters α c (for option 2) and b (for option 3) are selected such as to give similar isotropic compression lines over the stress and suction range relevant to the problem analysed, the finite element predictions are also very similar. REFERENCES Alonso E.E., Gens A. & Josa A. 1990. A constitutive model for partially saturated soils. Geotechnique 40, No. 3, pp. 405–430. Arya L.M. & Paris J.F. 1981. A physicoempirical model to predict the soil moisture characteristic from particle-size distribution and bulk density data. Soil Sci. Soc. Am. J., pp. 1023–1031. Bolzon G., Schrefler B.A. & Zienkiewicz O.C. 1996. Elastoplastic soil constitutive laws generalised to partially saturated states. Geotechnique 46, No. 2, pp. 279–289. Booth A.R. 1975. The factors influencing collapse settlement in compacted soils. Proc. 6th Reg. Conf. For Africa on Soils Mech. And Found. Eng. Durban, pp. 57–63.
Cui Y.J., Delage P. & Sultan N. 2003. An elastoplastic model for compacted soils. 1 st Int. Conf. On Unsaturated Soils, Paris, 2, pp.703–709. Georgiadis K., Potts D.M. & Zdravkovic L. 2003. The influence of partial soil saturation on pile behaviour. Geotechnique 53, No. 1, pp. 11–25. Georgiadis K., Potts D.M. & Zdravkovic L. 2005. ThreeDimensional Constitutive Model for Partially and Fully Saturated Soils. International Journal of Geomechanics, Volume 5, Issue 3, pp. 244–255. Lagioia R., Puzrin A.M. & Potts D.M. 1996. A new versatile expression for yield and plastic potential surfaces. Computers and Geotechnics 19, No. 3, pp. 171–191. Matsuoka H. & Nakai T. 1974. Stress-deformation and strength characteristics of soil under three different principal stresses. Proc. Jap. Soc. Civ. Eng. 232, pp. 59–70. Modaressi A. & Abou-Bekr N. 1994. Constitutive model for unsaturated soils: validation on silty material. 3rd Eur. Conf. Num. Methods Geotech. Eng. Manchester, pp. 91–96. Van Genuchten M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J., pp. 892–898. Wheeler S.J., & Sivakumar V. 1995. An elastoplastic critical state framework for unsaturated soil. Geotechnique 45, No. 1, pp. 35–53. Yudhbir 1982. Collapsing behaviour of residual soils. Proc. 7th Southeast Asia Geot. Conf. Hong Kong. Vol. 1, pp. 915–930.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Modifying the Barcelona Basic Model to account for residual void ratio and subsequent decrease of shear strength relative to suction M.E. Bardanis & M.J. Kavvadas National Technical University, Athens, Greece
ABSTRACT: The paper presents modifications to the Barcelona Basic Model to account for two aspects of unsaturated soil behaviour affecting the predictions for both fine-grained and granular soils: stabilisation of void ratio and different patterns of shear strength evolution with increasing suction. The first modification improves predictions of volume change at suctions close to the residual state. The second modification improves predictions of shear strength evolution with increasing suction for various types of soils. It is shown how the proper selection of values for the new parameters introduced allows the prediction of either continuously increasing shear strength, or stabilising shear strength, or even subsequently decreasing shear strength after an initial increase. The paper concludes with a presentation of the differences caused by these modifications in the shape of the yield surface in the p − q − s space and the possible shape of the boundary of plastic volumetric deformation in the p-s plane.
1
2
INTRODUCTION
The Barcelona Basic Model (BBM) introduced by Alonso et al. (1990) was the first complete constitutive model for non-expansive unsaturated soils to capture the fundamental aspects of unsaturated soil behaviour. Since then other models based on BBM have been proposed, which introduce more detail into the prediction of unsaturated soil behaviour. All these models are based on critical state theory extended to include suction as a separate stress parameter. While they succeed in predicting the general behaviour of unsaturated soils, such as the increase of shear strength with suction exhibited by clays and the volume changes with suction expected for the corresponding total stress magnitude, they cannot predict certain specific characteristics which have been experimentally established. The first is the prediction of the range of suction in which shrinkage actually takes place for relatively low total stress. The second is the possibility of subsequent stabilisation or decrease of shear strength after an initial increase up to the air-entry pressure, as alternatives to continuous increase of shear strength exhibited by BBM and other models. The modifications introduced predict volume decrease only up to the shrinkage limit and the possibility of any shear strength evolution scenario past the air-entry pressure of the soil, i.e. further increase of shear strength, stabilisation of shear strength or even decrease to a lower value or even zero.
BBM AND OTHER MODELS
BBM remains until today the reference constitutive model describing the mechanical behaviour of nonexpansive unsaturated soils. The model is formulated in the p-q-s space, where p = (σ1 + 2σ3 )/3 − ua , q = σ1 − σ3 and s = ua − uw (ua and uw are the pressures of the pore air phase and the pore water phase respectively, and σ1 , σ2 and σ3 are the principal total stresses). The yield locus in the p-q plane is described by Equation 1, where ps is the tensile strength developed by suction, as described by Equation 2, M is the slope of the critical state line, po the yield stress on the v-p plane (s = 0) and k the rate of the tensile strength increase with suction. f1 p, q, s, p∗0 = q2 − M2 (p + ps ) (p0 − p) = 0 (1) ps = ks
(2)
The yield stress po evolves with suction according to Equation 3 where p∗o is the yield stress on the v-p plane (s = 0), pc is a reference stress, κ and λ(0) the compression indices on the v-p plane (s = 0) and λ(s) the compression index for p > po (s = 0) as described by Equation 4, where r and β are empirical parameters. po = pc
p∗o pc
λ(0)−κ λ(s)−κ
λ(s) = λ(0) [(1 − r) exp(−βs) + r]
589
(3) (4)
The yield locus in the p-q-s space is supplemented by Equation 5, where so is the yield suction on the v-s plane. (5)
As can be seen from Equations 1 to 5 (and from Curve a in Fig. 1), BBM incorporates only 3 parameters describing volume change directly associated to a variation of suction: κs , λs & so . These parameters allow the prediction of an initial low volume decrease (determined by κs ) up to an essentially arbitrary value of suction so (which can be considered to describe physically the maximum suction applied to the soil) and then a further (and generally larger) value of volume decrease (determined by λs ). Although this formulation is adequate for the range of suction significantly below the shrinkage limit of the soil, with the additional advantage that it is analogous to the formulation for volume decrease under zero suction conditions, it does not include a boundary corresponding to the shrinkage limit (either in terms of suction or void ratio) up to which volume may decrease, as presented by Curve b in Figure 1. For suctions close to residual water content, or higher, this type of formulation overestimates volume change as it underestimates final specific volume/void ratio values. As far as shear strength is concerned, setting p = 0 into Equation 1, and replacing ps , po and λ(s) from Equations 2, 3 and 4 respectively yields Equation 6 which represents the intersection of the 3-dimensional yield surface with the q-s plane (for q > 0). Plotting Equation 6 in Figure 2 shows that BBM predicts continuous increase of shear strength with increasing suction. Although this is true for clays, it is not the case for sands, tuffs and sometimes silts, as shown by experimental results presented by Fredlund et al. (1995).
e or
300
q (kPa)
f2 (s, s0 ) = s − s0 = 0
400
so
sr
ln s
s
s
(b)
er (a)
Figure 1. Void ratio/Specific volume changes with increasing suction under zero total stress: Curve a does not account for residual void ratio, while Curve b takes residual void ratio into account.
200 100 0
0
200
400
600
800
1000
s (kPa) Figure 2. Shear strength evolution with increasing suction according to BBM (graphical representation of Eq. 6).
∗ 2·λ(0)[(1−r)·exp(−βs)+r]−2·κ √ √ ) po k · M · s · pc (6) pc λ(0)−κ
q=
The terms in Equation 6 have been placed in such a sequence, so as the different effect of each factor can be distinguished. k 1/2 expresses the effect of the evolution of tensile strength. M expresses the direct effect of the slope of the critical state line on unsaturated shear strength. s1/2 expresses the direct effect of suction increase on the increase of shear strength. The rest of the terms essentially express the effect of the loading history and the effect of drying-wetting cycles (indirect effect of suction on the evolution of shear strength). Despite the presence of numerous other factors however, none can alter the continuous increase of shear strength shown in Figure 2 (as was proven by extensive parameter analyses carried out). For comparison, the curve shown in Figure 2 has been obtained for the set of values used by Alonso et al. (1990) for the ‘reference soil’ they used for their predictions with BBM (λ(0) = 0.2, κ = 0.02, r = 0.75, β = 12.5 MPa−1 , pc = 0.1 MPa, p∗o = 0.6 MPa, M = 1, k = 0.6). Other constitutive models which do not incorporate a limiting value of void ratio change or alternative possibilities for shear strength evolution have been proposed (e.g. Wheeler & Sivakumar, 1995). Toll (1995) presented a conceptual model for the drying and wetting of soil which predicts the limiting of void ratio changes and therefore the calculated volume changes up to the void ratio corresponding to shrinkage limit. Kohgo et al. (1993a & b) and Kohgo (2004) have proposed models which have limiting parameters for volume change and the capability to model alternative patterns of shear strength evolution. Georgiadis et al. (2003) proposed among other modifications that parameter k can vary with suction by setting k equal to degree of saturation and therefore the evolution of
590
k with suction equal to the soil-water characteristic curve of the soil. This approach solves the problem for soils expected to exhibit an initial increase of shear strength with suction and then a subsequent decrease, like granular soils, but it does not provide a universally applicable equation for shear strength evolution, making it therefore necessary to switch between equations for k for each type of material. Other approaches in constitutive modelling of unsaturated soils have focused on combining LC and SI curves into one single surface. Delage & Graham (1996) proposed first that the two curves are probably one single locus in the p-s plane. Sivakumar & Doran (2000) presented first experimental evidence to support this, while Tang & Graham (2002) took the effort one step further by proposing a conceptual but complete constitutive model with one single continuous 3-dimensional yield surface in the p-q-s space. This constitutes a different approach towards incorporating the capability to model various scenarios of shear strength evolution. 3
THE MODIFICATIONS TO BBM
Common shrinkage limit tests and a large number of published drying curves indicate that clayey soils shrink to a minimum value of their void ratio during drying and then shrink no more, irrespective of how large the suction becomes. As shown by Curve a in Figure 1 therefore the specific volume-suction curve described by only 4 parameters (initial value N of specific volume at atmospheric pressure pat , κs , λs and so ) should be substituted by the idealised Curve b shown in Figure 1 with a flat final portion corresponding to the residual void ratio er (vr = 1 + er ). This curve needs only one additional parameter for its description, either the residual void ratio er , or the suction at which it is first achieved. Recently, Bardanis & Kavvadas (2006) proposed an empirical relation predicting the residual void ratio of low to medium plasticity clays and marls which have been consolidated to various stresses from a slurry condition and then unloaded and left to dry to residual water content in atmospheric conditions. The residual void ratio is predicted from the physical properties of the soil (wL , Gs ) and its initial state before drying, as expressed by initial void ratio before drying, eo , and an empirical parameter, m, found to be 0.43 for the soils tested by Bardanis & Kavvadas (2006). More recently Bardanis & Kavvadas (2008) proposed another empirical relation (derived from many more soils and test results) based on wp rather than wL and an empirical parameter, me , equal to −0.38, along with its conceptual generalisation for soils with structure by addition of another parameter, Ms . The proposed relations by Bardanis & Kavvadas (2006 & 2008) are represented by Equations 7 & 8 respectively for soils
without natural structure, and by Equation 9 for natural soils. m er = eo 1 − · eo (7) wL · Gs eo (8) er = eo · exp me · wP · Gs eo (9) er = Ms · eo · exp me · wP · Gs The set of Equations 7 to 9 allows the prediction of the residual void ratio and as a result the calculation of the residual specific volume for incorporation as a model parameter into BBM. The use of the residual void ratio in the formulation of the BBM allows more realistic predictions of volume changes due to suction increase under constant total mean stress during elastic or elasto-plastic loading. It allows for the derivation of a limiting line in the p-s plane up to which volume changes do actually occur due to suction changes for the same mean total stress magnitude. Past this line the only volume changes that may occur are due to mean stress p increase. This point is further discussed in Section 4. For the more accurate prediction of shear strength, the most suitable term from Equation 6 was selected. This was k and it was given such a form so as to predict either continuous increase of shear strength, or initial increase and then stabilisation, or finally initial increase and then decrease of the shear strength. In order for this to take place it is proposed that k may be described by a function of the degree of saturation which takes the form of Equation 10. k = ζk · Sηr k
(10)
In Equation 10, k is the factor giving tensile stress, Sr is the degree of saturation and ζk and ηk are empirical parameters. For ηk = 0 and arbitrary values of ζk , prediction of shear strength is essentially as in the BBM. For ηk = 1 and ζk = 1, k becomes equal to the degree of saturation as adopted by Georgiadis et al. (2003). For selected values of ηk and ζk the prediction of all scenarios of the evolution of shear strength with increasing suction is possible. In Figure 3 the effect of ηk for constant ζk is shown and in Figure 4 the effect of ζk for constant ηk is shown. In order to plot Figures 3 and 4 a soil-water characteristic curve was assumed for the material corresponding to the parameter values mentioned in Section 2. This soil-water characteristic curve was produced by use of the Fredlund & Xing (1994) equation assuming the following values for the empirical parameters of the equation: a = 600 kPa, n = 4, m = 2 and sr = 5000 kPa. For the set of values
591
the initial slope and subsequent position of the q-s curve.
800
600 q (kPa)
4 BBM, k=0.6
ηk=0.2
400 ηk=0.5 200
ηk=1 ηk=2
0
0
1000
2000
3000
s (kPa)
Figure 3. The effect of parameter ηk on the evolution of shear strength with suction. ζk is constant with a value of 0.6 and the rest of the parameter values are the same as those for the curve in Figure 2 (bold curve in this figure). 400 BBM, k=0.6
q (kPa)
300 ζk=1.0 200
ζk=0.6 ζk=0.3
100
0
0
200
400 600 s (kPa)
800
1000
Figure 4. The effect of parameter ζk on the evolution of shear strength with suction. ηk is constant with a value of 2 and the rest of the parameter values are the same as those for the curve in Figure 2 (bold curve in this figure).
selected to plot Figure 2 the same relation between q and s is predicted for ζk = k of BBM and ηk = 0. Continuous increase of shear strength is also exhibited for ηk = 0.2, but the increase is smaller, while for a value of ηk = 0.5 the strength practically stabilises after its initial increase, while for ηk = 1 and ηk = 2 rapid decrease occurs after the initial increase in strength. The parameter ηk can be used therefore for determining the evolution of the shear strength of unsaturated soils past the initial increase, whether that may be further increase, stabilisation, or decrease. As far as the parameter ζk is concerned, it determines
EFFECT ON THE SHAPE OF THE YIELD LOCUS
Apart from the direct effect on the predictions of volume change and shear strength evolution with increasing suction, the modifications introduced into BBM have a major effect on the shape of the yield surface in the p-q-s space. In Figure 5a the intersection of the 3-dimensional yield surface of the BBM with the p-s plane is presented. The increase in the size of the yield locus in the p-q plane (or its trace on the p-s plane) is continuous according to the tensile strength increase law on one side and the evolution of the LC curve with suction on the other. For a material exhibiting continuous increase of tensile/shear strength with suction, the shape of the intersection of the yield surface with the p-s plane for the modified BBM is expected to be the same as for BBM (Fig. 5a). For materials exhibiting shear strength stabilization or decrease after an initial increase of shear strength however, the shape of the intersection of the yield surface with the p-s plane is expected to change as shown in Figures 5b & 5c respectively. For a soil with continuously increasing shear strength with suction, the left point of the ellipse defining the yield locus will continuously move towards more negative values of total mean stress (Fig. 5a). For a soil with stabilizing shear strength after a certain value of suction, this point will stabilise in the p-q plane and the expansion of the yield locus will be only due to a mean total stress increase (Fig. 5b). Finally for a soil with initially increasing and subsequently decreasing shear strength with suction, this point of the ellipse on the p-q plane will tend to approach the origin of the plot of this plane and once again the expansion of the yield locus will be only due to a mean total stress increase (Fig. 5c). As already mentioned in Section 3, the use of the residual void ratio in the formulation of the BBM allows for the derivation of a limiting line in the p-s plane up to which volume changes do actually occur due to suction changes for the same mean total stress magnitude. Past this line the only volume changes that may occur are due to mean stress p increase. Using one of the Equations 7 to 9 residual void ratio may be predicted. The initial void ratio eo before drying needs to be specified first. Once the residual void ratio has been predicted, then using so and λs (already used parameters of BBM) the value of the suction at which the residual void ratio is achieved may be calculated. Introducing now the change in initial void ratio caused by κ for zero suction in the elastic region, then the evolution of the suction at which the residual void ratio is achieved for constant total
592
3.5
A 3.0
s (MPa)
2.5
B
2.0
1.5
1.0
0.5
0.0 0.00
po*=0.2MPa, so=0.3MPa
0.20
0.40
0.60
p (MPa)
Figure 6. p-s plane with SI and LC loci and the predicted curve limiting the region of possible states for volume change to occur due to shrinkage for p < po ∗ .
Figure 5. Intersection of the 3-dimensional yield surface with the p-s plane for a soil: a) with continuous increase of shear strength, b) with initial increase and then stabilisation of its shear strength, and c) with initial increase and subsequent decrease of its shear strength with suction.
stress suction paths (for p < p∗o ) is obtained. This is as shown by curve A-B in Figure 6 for the parameter values mentioned in Section 2 (assuming eo = 0.9 for p = 10 kPa, which yields er = 0.629 according to Eq. 8 for this value of net mean stress and e = 0.840 for κ = 0.02 at p = 200 kPa, which itself yields er = 0.601 according to Eq. 8). The space in the p-s plane between the SI locus and curve A-B constitutes the space where plastic volumetric strains (in the form of irrecoverable shrinking) due to suction increase will take place for p values in the elastic region of the fully saturated soil yield locus. For constant total stress suction paths corresponding to p values greater than p∗o (which means that plastic volumetric deformation has already occurred before drying commences) and more complex paths involving alternations between constant total stress paths and constant suction paths or simultaneous p and s change paths it is considered that Equations 7 to 9 are not appropriate for an estimation of the locus limiting volume changes due to constant total stress suction changes. This limiting line is strongly dependent on the value of κ as this parameter controls the values of initial void ratio in the elastic region of the fully saturated yield locus. Figure 7 shows the different lines defined for various values of κ ranging from 0 to 0.04. The limiting curves in Figure 7 do not start from the axis p = 0 because of the logarithmic nature of the elastic relation between void ratio and mean net stress. A value of
593
s (MPa)
4.0 3.5
κ=0
3.0
κ=0.01
2.5
κ=0.02
2.0
κ=0.04
1.5 1.0 0.5
so=0.3MPa
0.0 0.00
0.05
0.10
0.15
0.20
p (MPa) Figure 7. p-s plane with SI locus and the predicted curves limiting the region of possible states for volume change to occur due to shrinkage for various values of κ(p < p∗o ).
κ = 0 yields a limiting line parallel to the SI locus as no change to initial void ratio before drying can occur in the elastic region. As the value of κ becomes higher, then the value of the suction that residual void ratio is achieved becomes smaller with increasing p, greater than 1.5 MPa for the values selected for the rest of the parameters in Figure 7. For simplicity the p axis in Figure 7 has been limited to 0.2 MPa, which is the fully saturated yield total stress (shown also in Figure 6), so as not to show the different LC yield locus that is derived for each of the κ values used.
5
all types of materials, : maximum volume shrinkage limited by residual void ratio, and various scenarios of shear strength evolution with suction. Apart from achieving the goals for which these modifications were introduced, they also have a strong effect on the shape of the 3-dimensional yield locus in the p-q-s space as indicated by its intersections with the p-s plane in Figure 5. For a soil with continuously increasing shear strength with suction, the left point of the ellipse defining the yield locus will continuously move towards more negative values of total mean stress. For a soil with stabilizing shear strength after a certain value of suction, the distance of this point from the suction axis will stabilise and the expansion of the yield locus will be only due to a mean total stress increase. Finally for a soil with initially increasing and subsequently decreasing shear strength with suction, the distance of this point from the suction axis will tend to decrease to zero and once again the expansion of the yield locus will be only due to a mean total stress increase. As far as the effect of the residual void ratio is concerned, a line limiting the plastic strain due to constant total stress suction changes for total stress values lower than the yield stress of the fully saturated soil may be defined. The area between the SI curve of the BBM and this limiting line defines the area of possible plastic strains due to shrinkage in the p-s plane, for total stress values lower than the yield stress of the fully saturated soil.
ACKNOWLEDGEMENTS Part of the research by M.E. Bardanis has been funded by the National Scholarship Foundation (IKY) of Greece.
CONCLUSIONS
Most of the existing constitutive models cannot predict stabilization of void ratio as a result of attaining a minimum total volume during shrinkage. Also they do not incorporate the possibility to model various scenarios of shear strength evolution with suction increase (continuous increase, stabilization or decrease after an initial increase up to the air-entry pressure). Various approaches towards solving these two problems have been published but either they do not propose single equations predicting all types of response by controlling the values of parameters, or they have proceeded to totally different approaches in the treatment of the 3-dimensional yield surface; an approach that elevates constitutive modeling of unsaturated soils at another level of difficulty. The modifications proposed for BBM in this paper maintain the capability to work with a well-established and well-understood framework, while capturing important aspects of unsaturated soil behaviour by the use of one single equation, universally applicable for
REFERENCES Alonso, E.E., Gens, A., Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430. Bardanis, M., Kavvadas, M. 2006. Prediction of the limiting void ratio of clayey soils after drying. In Miller et al (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1085–1096, Reston, Virginia: ASCE Press. Bardanis, M., Kavvadas, M. 2008. Prediction of the residual void ratio of clayey soils after drying, from their initial state, physical properties and structure. Proc. 1st Eur. Conf. on Unsaturated Soils, Durham, UK, 2–4 July, 2008. Delage, P., Graham, J. 1996. Mechanical behaviour of unsaturated soils: Understanding the behaviour of unsaturated soils requires reliable conceptual models. In Alonso & Delage (eds), Proc. 1st Int. Conf. Unsaturated Soils, Paris, 3: 1223–1256, Rotterdam: Balkema.
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Fredlund, D.G., Xing, A., Fredlund, M.D., Barbour, S.L. 1995. The relationship of the unsaturated soil shear strength to the soil-water characteristic curve. Can. Geot. J. 32: 440–448. Fredlund, D.G., Xing, A. 1994. Equations for the soil-water characteristic curve. Can. Geot. J. 31: 521–532. Georgiadis, K., Potts, D.M., Zdravkovic, L. 2003. The influence of partial soil saturation on pile behaviour. Géotechnique 53(1): 11–25. Kohgo, Y. 2004. Elastoplastic models for unsaturated soils with two suction effects and unsaturated soil behavior. In Jucá et al. (eds), Proc. 3rd Int. Conf. Unsaturated Soils, 3: 905–915, Lisse: Swets & Zeitlinger. Kohgo, Y., Nakano, M., Miyazaki, T. 1993a. Theoretical aspects of constitutive modeling for unsaturated soils. Soils & Foundations 33(4): 49–63.
Kohgo, Y., Nakano, M., Miyazaki, T. 1993b. Verification of the generalized elastoplastic model unsaturated soils. Soils & Foundations 33(4): 64–73. Sivakumar, V., Doran, I.G. 2000. Yielding characteristics of unsaturated compacted soils. Mechanics of CohesiveFrictional Materials 5: 291–303. Tang, G.X., Graham, J. 2002. A possible elastic-plastic framework for unsaturated soils with high plasticity. Can. Geotech. J. 39 ( . . . ): 894–907. Toll, D.G. 1995. A conceptual model for the drying and wetting of soil. In Alonso & Delage (eds), Proc. 1st Int. Conf. Unsaturated Soils, Paris, 2: 805–810, Rotterdam: Balkema. Wheeler, S.J., Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Géotechnique 45(1): 35–53.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A cap model for partially saturated soils R. Kohler, M. Hofmann & G. Hofstetter University of Innsbruck, Austria
ABSTRACT: An elastic-plastic constitutive model for partially saturated soils is presented. It is formulated in terms of two stress state variables, consisting of the effective stress tensor for partially saturated soils and matric suction. The yield surface consists of a shear failure surface and a strain hardening cap. The plastic strain rate is computed by means of non-associated flow rules for both yield surfaces. The capability of the developed constitutive model is demonstrated by the numerical simulation of a series of suction controlled tests. In addition, an extension of the model in order to account for swelling soil behavior is presented.
1
2
INTRODUCTION
Partially saturated soils are three-phase media consisting of a deformable soil skeleton and the two fluid phases water and air. The difference between the pressures in the water and the air phase, called capillary pressure or matric suction, has a considerable impact on the mechanical behavior of partially saturated soils. Experimental evidence shows that an increase in matric suction in general results in an increase of the shear strength, the preconsolidation pressure and the elasto-plastic stiffness of the soil. Furthermore, a decrease in matric suction, i.e. an increase of the degree of water saturation, under high values of external stress can result in an irreversible decrease of the soil volume, denoted as collapse on wetting. Several elastic-plastic material models for unsaturated soils have been proposed in recent years, see e.g. (Alonso et al., 1990; Wheeler et al., 1995; Bolzon et al., 1996; Geiser et al., 2000; Gallipoli et al., 2003; Tamagnini, 2004; Santagiuliana et al., 2006). Most of these material models adopt some type of Cam clay formulation. In this contribution, a cap model for partially saturated soils is presented. It is formulated in terms of the effective stress tensor for partially saturated soils and matric suction, the latter playing the role of a stress-like plastic internal variable. The model is validated by an extensive series of suction controlled tests, described in (Macari et al., 2001) and (Macari et al., 2003). In addition, lab tests for swelling soil behavior are simulated numerically. To this end, the cap model is extended by adopting ideas for modelling of swelling presented in (Gens et al., 1992) and further developed in (Sanchez et al., 2005).
CONSTITUTIVE MODEL
A basic assumption of the elastic-plastic constitutive model is the additive decomposition of the total strain tensor ε into an elastic part ε e and a plastic part εp : ε = εe + εp
(1)
From thermodynamic considerations (Houlsby, 1997; Schrefler, 2002; Borja, 2004) it follows that a material model for the soil skeleton of a partially saturated soil can be formulated in terms of the effective stress tensor for partially saturated soils (i.e., the Bishop stress with the Bishop parameter equal to the degree of water saturation) σ = σ − p a I + S w ( pa − p w ) I
(2)
and matric suction pc = pa − pw
(3)
σ denotes the total stress tensor, S w represents the degree of water saturation and pa and pw are the pressures of the fluid phases air and water; I denotes the second order unit tensor. In the present model pc plays the role of a stress-like plastic internal variable. Hence, the elastic strain tensor solely depends on the effective stress tensor and for the special case of linear elasticity the constitutive relations are given as σ = C : εe = C : ε − εp with C denoting the elasticity tensor.
597
(4)
The degree of water saturation S w is expressed as a function of matric suction by the approximation proposed in (Van Genuchten et al., 1985) c n −m p S w = Srw + (Ssw − Srw ) 1 + pcb
(5)
In (5) Ssw and Srw denote the maximum and residual degree of water saturation, respectively, and pcb is the air entry value; m and n are parameters to fit the empirical equation to experimental data. For many soils, use of n = 1/(1 − m) can be made. The functional form of the shear failure surface is defined as f1 σ , pc = L(ϑ) s − Fe I1 − Fs ( pc ) (6) with Fe I1 = α + θ I1
and Fs ( pc ) = k pc ,
(7)
where I1 and s denote the first invariant and the norm of the deviatoric part of σ , L(ϑ) accounts for the dependence of the yield surface on the Lode angle ϑ according to (de Borst et al.,) and α, θ and k are material parameters. The functional form of the strain hardening cap is given as f2 σ , κ( pc ), pc = Fc s , I1 , ϑ, κ( pc ) (8) − Fe κ( pc ) − Fs ( pc ) with κ( pc ) ≤ I1 ≤ X (κ( pc )) and
(
Fc s , I1 , ϑ, κ( pc ) = L2 (ϑ) s 2 +
I1 −κ( pc ) 2 , R (9)
where R is a material parameter, defining the ratio of the major to the minor axis of the elliptic cap, and κ( pc ) is a hardening parameter. X κ( pc ) = κ( pc ) + R Fe κ( pc ) + Fs ( pc ) (10)
Figure 1.
The hardening law for the cap surface is given as ε˙ vp = λ( pc )
κ( pc ) = κ(0) +
X (κ( pc )) − X (κ(0)) − RFs ( pc ) 1 + Rθ (11)
X˙ (κ( pc )) − 3 (S˙ w pc + S w p˙ c ) X (κ( pc )) − 3 S w pc
(12)
It is obtained from a logarithmic hardening law, formulated in terms of net stress, relating the plastic p volumetric strain rate ε˙ v to the hardening parameter c κ( p ), which is transformed to effective stress. Since X is related to the first invariant of the stress, it follows from (2) that the difference between effective stress and net stress is given as 3S w pc , which results in the terms related to S w in (12). In (12) λ pc = λ(0) (1 − r) exp(−βpc ) + r
(13)
is a scaling factor for the plastic volumetric strain rate. It is assumed to decrease from λ(0) at zero matric suction to λ(pc ) → r · λ(0) for pc → ∞ with β and r (with r < 1) as material parameters accounting for the increasing plastic stiffness under hydrostatic loading with matric suction (Alonso et al., 1990). The plastic potentials g1 and g2 for the nonassociated Koiter’s flow rule are obtained from the yield functions (6) and (8) by setting L(ϑ) = 1 and by replacing θ by ψ, which determines the amount of plastic dilation. For more information on the constitutive model refer to (Kohler, 2006; Kohler et al., 2007).
3 denotes the apex of the elliptical cap. The yield surface of the cap model is shown in Fig. 1. The hardening parameter κ( pc ) is obtained by calculating the intersection of the elliptical cap and the failure envelope (Fig. 1) by inserting (71 ) with I1 = κ( pc ) into (10) and making use of the so obtained relation also for the special case of pc = 0 as
Yield surface of the cap model.
NUMERICAL SIMULATION OF SUCTION CONTROLLED TESTS
The extended cap model was validated by the numerical simulation of a series of suction controlled tests (Macari et al., 2001; Macari et al., 2003), which were conducted on cubical specimens of a silty sand. The stress paths followed in the experiments included hydrostatic compression (HC) tests, consisting of loading and unloading at different values of matric suction, triaxial compression (TC) tests and conventional triaxial compression (CTC) tests as well as triaxial
598
extension (TE) tests and simple shear (SS) tests at different values of matric suction and different values of hydrostatic pressure, and a wetting path. The material parameters for the cap model, determined from the experimental data, are given in the second column of Table 1. In this table Xinit denotes the initial value for the apex of the cap at water saturated conditions. Since the relationship between the degree of water saturation and matric suction was not known from the tests, the hydraulic parameters of the
Table 1.
S w pc -relationship (5) were chosen according to values for silty sands given in the literature. Here, only comparisons of the predicted and measured constitutive response for the HC tests (Fig. 2) and the TC tests (Fig. 3 to Fig. 6) are shown. Results for the CTC tests, TE tests, the SS tests and the wetting test can be found in (Kohler, 2006; Kohler et al., 2007). Since the test data are given in terms of net stress, the numerical results are also shown in terms of net stress.
Material parameters.
Parameter
Silty sand
Swelling soil
Unit
K G α θ R λ(0) Xinit Xc r β k ω η
42440 8803 0 0.269 3.0 0.095 126.3 108.0 0.2 0.018 0.6 0.8 -0.1
41700 19200 0 1.0 2.0 0.03 100.0 10.0 0.78 0.005 1.0 0.8 -0.1
kPa kPa kPa – – – kPa kPa – kPa−1 – –
Srw Ssw pcb m
0.25 0.95 50.0 0.32
0.0 1.0 500.0 2.1
– – kPa –
Figure 3. Comparison of the measured (dotted lines) and the computed (continuous lines) q − εq response for TC tests at I1 = 150 kPa and 3 different values of matric suction.
Figure 2. Comparison of the measured (dotted lines) and the computed (continuous lines) response for HC stress paths at 3 different values of matric suction.
Figure 4. Comparison of the measured (dotted lines) and the computed (continuous lines) q − εq response for TC tests at I1 = 600 kPa and 3 different values of matric suction.
599
Figure 2 demonstrates the ability of the model to describe the stiffening effect due to matric suction under hydrostatic loading. Fig. 3 and Fig. 4 show the measured and computed relations between the deviatoric stress q and the shear strain εq for TC tests, conducted at two different values of I1" (i.e. the first invariant of net stress) and three different values of pc (i.e., pc = 50 kPa, pc = 100 kPa and pc = 200 kPa). For the same tests Fig. 5 and Fig. 6 show the measured
Figure 5. Comparison of the measured (dotted lines) and the computed (continuous lines) v − εq response for TC tests at I1 = 150 kPa and 3 different values of matric suction.
and computed relation between the specific volume v and the shear strain εq . It follows from the latter figures that both the increasing shear strength with increasing matric suction and the dependence of the volume change on matric suction can be well described by the cap model. 4
MODELLING OF SWELLING
The cap model, presented so far, predicts an increase of the specific volume upon wetting by the change of the effective stress (2) due to changes in matric suction. Hence, the increase of the volumetric strain due to wetting depends on the bulk modulus of the soil skeleton K and the employed S w pc -relationship (5). However, in argillaceous rocks considerably larger volume changes are observed due to stress relief and/or wetting. This swelling behavior of argillaceous soil and rock often poses severe problems to the design and construction of tunnels. Tunnel excavation causes a stress redistribution in the vicinity of the tunnel, resulting in stress relief above the crown and below the invert. Additionally, water plays an important role for swelling. Water may already be present or, at initially unsaturated conditions, seepage water from adjacent zones might reach expansive zones by flowing along or beneath the invert of the tunnel. In the context of the cap model swelling is modelled by adopting ideas sketched in (Gens et al., 1992) and further developed in (Sanchez et al., 2005). A basic idea is to consider a microstructural and a macrostructural level of an argillaceous soil or rock. The origin of swelling are physico-chemical reactions at the microstructural level resulting in volumetric strains at the microstructural level, which lead to deformations at the macrostructural level depending on interactions between both levels. According to (Sanchez et al., 2005) the volumetric strain at the microstructural level depends on an effective pressure pˆ , which is given as pˆ = p − pa + χ pc
(14)
with p = σii /3 and a constant χ > 0. For p˙ˆ < 0 the microstructural volume is increasing whereas for p˙ˆ > 0 the microstructural volume is decreasing. The respective microstructural volumetric strain is determined assuming an elastic constitutive response as ε˙ vm = Figure 6. Comparison of the measured (dotted lines) and the computed (continuous lines) v − εq response for TC tests at I1 = 600 kPa and 3 different values of matric suction.
p˙ˆ Km
(15)
with K m representing the microstructural bulk modulus. The swelling strains at the macrostructural level,
600
caused by the microstructural strains, are considered as irreversible strains. They are added to the plastic strains due to loading. According to (Gens et al., 1992) the volumetric swelling strain at the macrostructural level is obtained from the microstructural strain through an interaction function h(Xr , X ), yielding
of Xr /X close to 1. Consequently, different interaction functions are used for microstructural swelling and microstructural contraction (Sanchez et al., 2005). For the numerical simulation of the swelling tests, presented subsequently, the interaction functions for swelling and contraction, are chosen as
p ε˙ v,sw = h(Xr , X ) ε˙ vm
Xr 2 hs (Xr , X ) = 1 − X
(16)
The interaction function depends on the position of the cap for the current stress point, X , and on the position of a ‘‘reference cap’’, Xr , which contains the current stress point (Fig. 7). The ratio Xr /X ≤ 1 characterizes the preloading of the macrostructure. A small value of Xr /X indicates large previous preloading and, hence, a dense macrostructure of the soil. In this case a larger fraction of the microstructural swelling strain will be present as deformations at the macrostructural level. Conversely, a smaller fraction of the microstructural swelling strain will be present as swelling strains at the macrostructural level in the case of a looser macrostructure, which is characterized by values of Xr /X close to 1. On the other hand, microstructural contraction has a stronger impact on the deformations at the macrostructural level for values s
* and hc (Xr , X ) =
Xr X (17)
First, the swelling pressure test, described in (Romero, 1999) is simulated. In this test an initially unsaturated soil specimen was wetted at fully constraint deformations and subsequently dried. It can be
pc Fe (I1) + Fs(pc)
r
Figure 7.
Xr
I' 1 X
Definition of X and Xr .
Figure 8. Comparison of the computed soil response in a swelling pressure test (continuous line) with experimental results (crosses).
Figure 9. Comparison of the computed response in a free swelling test (dotted lines) and a Huder-Amberg test (continuous lines).
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seen in Fig. 8 that the model allows to represent the development of the first invariant of net stress, I1 , due to wetting and subsequent drying quite well. An interesting feature of this test is the fact that the largest value of I1" , i.e. the largest swelling pressure, occurs before the specimen is fully saturated. This behavior is a consequence of the so-called collapse upon wetting, which is reproduced by the employed model (the two dotted lines in Fig. 8 represent the load collapse yield curve). Fig. 9 contains a comparison of the computed soil response between a free swelling test and a HuderAmberg swelling test. In a free swelling test the initially unsaturated soil specimen is wetted, which results in the soil response, shown in Fig. 9 by the dotted lines. In a Huder-Amberg test the soil specimen in an oedometer is loaded first in axial direction (part 1 of the continuous lines), followed by wetting (part 2 of the continuous lines) and, subsequently, the axial loading is reduced in several steps, in each step keeping the axial stress constant until no further increase of the deformations is observed (parts 3 to 5 of the continuous lines).
5
CONCLUSIONS
The proposed cap model allows to represent basic features of the behavior of partially saturated soils, e.g. the increase of the shear strength and of the elasto-plastic stiffness with increasing matric suction and an irreversible decrease of the soil volume, denoted as collapse on wetting, due to an increase of the degree of water saturation, under high values of external stress. For the extensive suction controlled tests conducted on a silty sand, documented in (Macari et al., 2001; Macari et al., 2003), the proposed cap model yields good agreement with the measured soil behavior. In addition, the cap model was extended to take into account swelling behavior of soils and it was shown that the soil behavior, observed in typical swelling tests, can be reproduced.
REFERENCES Alonso, E.E., Gens, A., and Josa, A. (1990). A constitutive model for partially saturated soils. Géotechnique 40(3):405–430. Bolzon, G., and Schrefler, B.A. (1996). Elastoplastic soil constitutive laws generalized to partially saturated states. Géotechnique, 46(2):279–289. Borja, R.I. (2004). Cam-clay plasticity. part V: A mathematical framework for three-phase deformation and strain localization analyses of partially saturated porous media. Computer Methods in Applied Mechanics and Engineering, 193:5301–5338.
de Borst, R., and Groen, A.E. (2000). Computational strategies for standard soil plasticity models. In Zaman, M., Booker, J., and Gioda, G., editors, Modeling in Geomechanics, John Wiley & Sons, Ltd. Gallipoli, D., Gens, A., Sharma, R., and Vaunat, J. (2003). An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Géotechnique, 53(1):123–135. Geiser, F., Laloui, L., and Vulliet, L. (2000). Modelling the behaviour of unsaturated silt. In Tarantino, A., and Mancuso, C., editors, Experimental Evidence and Theoretical Approaches in Unsaturated Soils, 155–176. 27:1079–1098. Gens, A., and Alonso, E.E. (1992). A framework for the behavior of unsaturated expansive clays. Canadian Geotechnical Journal, 29:1013–1032. Houlsby, G.T. (1997). The work input to an unsaturated granular material. Géotechnique, 47(1):193–196. Kohler, R. (2006). Numerical modelling of partially saturated soils in the context of a three-phase-FE-formulation. Dissertation, University of Innsbruck, Austria. Kohler, R., and Hofstetter, G. (2007). A Cap Model for Partially Saturated Soils. International Journal for Numerical and Analytical Methods in Geomechanics, in press. Macari, E.J., and Hoyos, L.R. (2001). Mechanical behavior of an unsaturated soil under multi-axial stress states. Geotechnical Testing Journal, 24(1):14–22. Macari, E.J., Hoyos, L.R., and Arduino, P. (2003). Constitutive modeling of unsaturated soil behaviour under axisymmetric stress states using a stress/suction-controlled cubical test cell. International Journal of Plasticity, 19:1481–1515. Romero, E. (1999). Characterisation and thermal-hydromechanical behavior of unsaturated Boom clay: an experimental study. Ph.D. Thesis, Technical University of Catalonia, Spain. Sánchez, M., Gens, A., Guimarães, L.d.N., and Olivella, S. (2005). A double structure generalized plasticity model for expansive materials. International Journal for Numerical and Analytical Methods in Geomechanics, 29:751–787. Santagiuliana, R., and Schrefler, B.A. (2006). Enhancing the Bolzon-Schrefler-Zienkiewicz Constitutive Model for Partially Saturated Soil. Transport in Porous Media, 65: 1–30. Schrefler, B.A. (2002). Mechanics and thermodynamics of saturated/unsaturated porous materials and quantitative solutions. Applied Mechanics Reviews, 55(4):351–387. Tamagnini, R. (2004). An extended Cam-Clay model for unsaturated soils with hydraulic hysteresis. Géotechnique, 54(3):223–228. Van Genuchten, M. Th., and Nielsen, D. R. (1985). On describing and predicting the hydraulic properties of unsaturated soils. Annales Geophysicae, 3(5): 615–628. Wheeler, S.J., and Sivakumar, V. (1995). An elasto-plastic critical state framework for unsaturated soils. Géotechnique, 45(1):35–53.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Boundary surfaces and yield loci in unsaturated compacted clay A. Tarantino & S. Tombolato Dipartimento di Ingegneria Meccanica e Strutturale, Università degli Studi di Trento, Italy
ABSTRACT: Water-undrained one-dimensional compression tests with suction monitoring using Trento highcapacity tensiometers were carried out. During the loading-unloading cycles, suction, total vertical stress, degree of saturation, and specific volume were measured. It was observed that water retention behaviour is coupled to mechanical behaviour through the specific volume and, in turn, mechanical behaviour is coupled to water retention behaviour through the degree of saturation. The average skeleton stress and modified suction were adopted as generalised stress variables to model coupled behaviour and derived a ‘virgin loading’ mechanical boundary surface in the space: average skeleton stress, modified suction, and specific volume and a ‘main wetting’ hydraulic boundary surface in the space: modified suction, degree of saturation, and specific volume. This made it possible to investigate the yield loci in the generalised stress plane and it was observed that their shape differs from those suggested in the literature.
1
INTRODUCTION
The degree of saturation has an independent role on the mechanical behaviour of unsaturated soils. At the same suction, the higher the degree of saturation, the stiffer the soil is in the net stress-void ratio plane during virgin loading (Gallipoli et al., 2003a), the lower is the yield point in the net stress-void ratio plane (Wheeler et al., 2003), the higher is the ultimate shear strength under the same normal net stress (Tarantino & Tombolato, 2005, Boso, 2005). To account for the effect of the degree of saturation, and more in general the coupling between mechanical and water retention behaviour, constitutive models have recently been proposed that incorporate the degree of saturation into the stress variables (Jommi, 2000; Wheeler et al., 2003; Gallipo li et al., 2003a; Tamagnini, 2004). In particular, the model by Wheeler et al. (2003) is formulated in terms of two generalised stress variables, the average skeleton stress and the modified suction, which can be written under one-dimensional conditions as follows: σv = σv + sSr s∗ = ns
(1)
where σv is the average skeleton stress, s∗ is the modified suction, σv is the total vertical stress, s is the suction, Sr is the degree of saturation, and n is the porosity. These stress variables can be extracted as workconjugate stress variables from the rate of work input
per unit volume of unsaturated soil (Houlsby, 1997). The advantages in using the average skeleton stress and the modified suction are discussed by Wheeler et al. (2003). The basic framework proposed by Wheeler et al. (2003) included simple water retention and mechanical constitutive relationships. These allowed complex forms of mechanical behaviour to be simulated though at a qualitative level. However, it is likely that more realistic water retention and mechanical constitutive relationships would be required to quantitatively reproduce observed unsaturated coupled behaviour. This paper presents an experimental study of onedimensional compression behaviour of non-active clay. Tests were carried out under water-undrained conditions with matric suction monitoring using Trento high-capacity tensiometers. During the loading-unloading cycles, the suction s, the total vertical stress σv , the degree of saturation Sr and the porosity n were monitored. As such, hydraulic and mechanical paths in terms of average skeleton stress and modified suction could be investigated. In particular, we could derive a ‘virgin loading’ mechanical boundary surface in the space: average skeleton stress, modified suction, and specific volume and a ‘main wetting’ hydraulic boundary surface in the space: modified suction, degree of saturation, and specific volume. We could also derive the mechanical and hydraulic reversible responses in the planes σv −v and the plane s∗ − Sr respectively. This made it possible to investigate the form of the yield loci in the generalised stress plane σv − s∗ .
603
2 2.1
EXPERIMENTAL EQUIPMENT Trento high-capacity tensiometer
The Trento high-capacity tensiometer was used to measure matric suction (Tarantino & Mongiovì, 2002). The tensiometer was calibrated in the positive range 0–1500 kPa with a measured standard deviation of accuracy of ±1.5 kPa. It was assumed that calibration could be extrapolated into the negative range according to Tarantino & Mongiovì (2003). 2.2
Oedometer cell for one-dimensional compression tests
The soil was one-dimensionally compressed in the apparatus shown in Figure 1 (Tarantino & De Col, 2008). It consists of an oedometer cell, a loading pad and a pneumatic actuator. The oedometer cell was made impermeable at its base by inserting a stainless steel sheet between the base and ring. Two holes were machined into the loading pad to install two tensiometers. An O-ring was positioned in the tensiometer hole to avoid evaporation of soil water from the measurement area. Tensiometers were kept in place by small caps (not shown in the figure) which were tightened to the pad by means of three screws. A membrane obtained by cutting and pasting nitrile elastomer Bellofram rolling diaphragms was used to seal the annular gap between the loading pad and the oedometer ring. The membrane attachment was designed to minimise the volume of air enclosed by the membrane. A sphere was interposed between the loading pad and the ram to ensure that no moments were transferred to the loading pad. The apparatus was equipped with a load cell for measuring the vertical force (2000 N capacity with a measured standard deviation of accuracy of ±3 N)
Figure 1. Schematic layout of the oedometer cell for onedimensional compression (Tarantino & De Col 2008).
and one potentiometer displacement transducer for measuring the vertical displacements (34 mm travel with measured standard deviation of accuracy of ±0.01 mm). An electrovalve connected to the laboratory air supply system was used to control air pressure in the pneumatic actuator. The oedometer ring had diameter of 100 mm and height of 40 mm. 3
MATERIAL AND SPECIMEN PREPARATION
Speswhite Kaolin with plastic limit, wP = 0.32 and liquid limit, wL = 0.64 was chosen for tests presented in this paper. The grain size distribution showed it to have 0.20 silt fraction, and 0.80 clay fraction. Samples were prepared according to the procedure described by Tarantino & Tombolato (2005). Dry powdered Kaolin was laid in a large plastic basin in layers of about 10 mm and each layer sprayed with demineralised water to reach the target water content. The moistened powder was hand-mixed and saturated lumps were cut using four spatulas attached together. The material was sieved through a 1 mm aperture sieve to reduce the aggregate size. This size was considered acceptable when compared to the 20–25 mm specimen height. The moistened powder was wrapped inside two sealed plastic bags, placed in a plastic container and stored in a high-humidity room for at least 7 days. For the one-dimensional compression tests, the powder was placed in the oedoemeter and then compressed at loading rate of 5 kPa/min. 4
EXPERIMENTAL PROCEDURE
The kaolin powder was placed in the oedometer ring up to its height (40 mm). After placing the loading pad on the powder, a vertical stress of 150 kPa was applied and the membrane was set in place. Tensiometers were installed after applying a soil paste to the porous ceramic and were allowed to equilibrate for typically 1–2 hours. Prior to measurement, tensiometers were conditioned according to the procedure described by Tarantino (2004). The loading path involved loading-unloading cycles to 300, 600, 900, and 1200 kPa (Figure 2). The total vertical stress σv was increased or decreased at the constant rate of 5 kPa/min and each applied vertical stress was maintained constant for 30 min. The states of the specimen under quasi-zero vertical stress (14 kPa) were assumed to correspond to the states referred to as ‘as-compacted’ in the literature. The loading rate was selected on the basis of preliminary tests carried out at loading rates of 20, 10, and 5 kPa/min (Tarantino & De Col, 2008). After applying 150 kPa vertical stress, a calliper having 0.02 mm resolution was used to measure the distance between the loading cap and a reference point.
604
3
11
d v/dt=5 kPa/min
1050 8
900
2.8
10
w=0.259 w=0.275 w=0.254 w=0.236 w=0.299 w=0.215 w=0.311
750 5
600
7 Specific volume, v
Vertical stress, v : kPa
1200
450 Tensiometer insertion 300 2 4 150
1
0 0
3 400
12
9
6 800
1200
1600
2.6
2.4
2.2
Time: min 2
Figure 2. Loading path in one-dimensional tests. Numbers indicate first loading (1, 2, 5, 8, 11), unloading (3, 6, 9, 12) and reloading (4, 7, 10) vertical stresses (Tarantino & De Col 2008).
1.8 1000 Average skeleton stress,
This made it possible to determine the initial height of the specimen. As the vertical displacement was monitored during the one-dimensional compression process, the void ratio and hence the degree of saturation could be back calculated at any stage of the test. As no drainage was provided during the test, water content remained constant during one-dimensional compression and was measured at the end of the test.
v
Figure 3. Mechanical paths in terms of average skeleton stress and specific volume. 1
0.8
EXPERIMENTAL RESULTS
One-dimensional compression tests with continuous suction monitoring were carried out at 7 different water contents: 0.215, 0.236, 0.254, 0.259, 0.275, 0.299, and 0.311. The mechanical paths are represented in terms of specific volume, v, versus vertical average skeleton stress, σv , in Figure 3. Irreversible virgin compression paths and ‘reversible’ unloading-reloading paths can be clearly recognised. After every unloadingreloading cycle, the specific volume recovers the virgin compression curve. The hydraulic paths are represented in terms of degree of saturation, Sr , versus modified suction s∗ in Figure 4. When the soil is ‘virgin’ compressed under constant water content, the soil experiences the highest degrees of saturation and is therefore subjected to ‘main wetting’. The implicit assumption throughout the paper is that an increase in saturation due to compression at constant water content is equivalent to an increase in water content at constant void ratio according to Tarantino & Tombolato (2005). When the soil is unloaded and reloaded, the degree of saturation moves along scanning curves. 6
Degree of saturation, Sr
5
0.6
0.2 0
To model ‘main wetting’ behaviour, data from the seven one-dimensional compression tests lying on the
200
400
600
800
Modified matric suction, s *: kPa
Figure 4. Hydraulic paths in terms of modified suction and degree of saturation.
main wetting paths (virgin compression) and having void ratios of 1.0, 1.2, 1.4, 1.6, and 1.8 were selected. These data were interpolated using an equation of the form suggested by Gallipoli et al. (2003a) for the main wetting surface: Sr =
BOUNDARY SURFACES
w=0.311 w=0.299 w=0.275 w=0.259 w=0.254 w=0.236 w=0.215
0.4
1 1 + (φvψ s∗ )n
m (2)
where v is the specific volume and φ, ψ, m and n are parameters determined by best-fitting using the least
605
1.6 Specific volume over 'saturated' specific volume, v/vs
Degree of saturation, Sr
1
0.8
0.6
0.4
1.4
1.2
1
0.2 100
1000
10000
0
100000
Figure 5.
Hydraulic ‘main wetting’ boundary surface.
Figure 6.
squares method. With respect to the equation originally proposed by Gallipoli et al. (2003b), the specific volume and modified suction now replace the void ratio and suction respectively. The main wetting surface given by Eq. 2 acts as lower boundary surface in the space (s∗ , v, Sr ) (Vaunat et al., 2000; Gallipoli et al., 2003a; Tarantino & Tombolato, 2005) and is associated with the suction decrease (SD) yield locus discussed by Wheeler et al. (2003). The capability of Eq. 2 to capture the effect of specific volume on degree of saturation is shown in Figure 5 where the degree of saturation is plotted against the modified suction normalized with respect to specific volume, vψ s∗ . To model ‘virgin loading’ behaviour, data from the seven one-dimensional compression tests lying on virgin compression curves and having void ratios of 1.0, 1.2, 1.4, 1.6, and 1.8 were selected. These data were interpolated using the following equation: ∗ b s v = vs · 1 + a (3) σv
0.8
1.2
1.6
(4)
where N1−D and λ are the saturated virgin loading parameters. The virgin loading surface given by Equation (3) acts as boundary surface in the space (σv , s∗ , v) and is associated with the load-collapse (LC) yield locus discussed by Wheeler et al. (2003). The capability of Eq. 3 to capture the effect of average skeleton stress and modified suction on specific volume is shown in Figure 6.
Mechanical ‘virgin loading’ boundary surface.
Within the boundary surfaces, the behaviour is reversible as shown in Figure 3 and Figure 4. In particular, reversible degree of saturation paths (scanning paths) appear to be independent of specific volume Figure 4 and can be described by the following equation: Sr = Sr0 − κs s∗
(5)
where κs is the slope of the scanning paths in the plane s ∗ − Sr . Reversible specific volume paths (unloladingreloading paths) appear to be independent of modified suction (Figure 3) and can be described by the following equation: v = vk − κ ln σv
(6)
where κ is the slope of the unloading-reloading paths in the plane ln (σv ) − v and vk is the specific volume at σv = 1 kPa. 7
where a and b are best-fit parameters and vs is the specific volume in saturated conditions at the same average skeleton stress. The saturated specific volume vs was derived from tests on saturated specimens (Tarantino & De Col 2008): vs = N1−D − λ ln σv
0.4
Modified matric suction over average skeleton stress s*/ "v: kPa
Normalised modified matric suction v s*: kPa
HARDENING LAWS
Wheeler et al. (2003) presented a constitutive model for isotropic stress states. Yield curves in the plane (p − s∗ ), with p being the mean average skeleton stress, were assumed to be as shown in Figure 7. The locations of the LC and SD curves are defined by p∗0 ∗ and sD and these are related to the plastic volumetric p deformations dεv and the plastic degree of saturation p change dSr by the following hardening laws:
606
p
dεv = p dSr
λ−κ v (1 − k1 k2 )
λs − κs =− (1 − k1 k2 )
∗ dsD dp∗0 ∗ − k1 ∗ p0 sD
∗ dp∗0 dsD ∗ − k2 ∗ sD p0
(7)
where λ and κ are the parameters of the mechanical model, λs and ks are the parameters of the water retention model, and k1 and k2 are coupling parameters. Let us assume that this constitutive model also applies to one-dimensional stress states with p replaced by σv . During the one-dimensional virgin compression, the soil contemporarily moves along the mechanical boundary surface (Eq. 3) and the water retention boundary surface (Eq. 2). The stress state is then located on the bottom-right corner of the elastic domain shown in Figure 7. As such, during virgin ∗ loading, s∗ ≡ sD and σv = σ0∗ . p The hardening law associated with dSr can then be derived by differentiating Eq. 2 and Eq. 5 and assuming that the specific volume is given by Eq. 3. The p hardening law associated with dεv can be derived by differentiating Eq. 3 and Eq. 6. The following hardening laws were thus obtained:
∗ dsD dσ0∗ B = (A+B−C) ∗ − ∗ σ0 A + B − C sD ∗ dsD ψ (A + B) dσ0∗ p − dSr = −DE ∗ σ0∗ sD E
p dεv
(8)
where: λ κ vsat A= ;C = ; ;B = b 1 − vsat v v
D = mnSr 1 −
1m Sr /
;
s∗ E = ψB + 1 − κs . D
(9)
This suggests that the yield loci SD and LC may not have the form proposed in Figure 7. 8
YIELD LOCI
The yield locus SD can be derived by the intersection of the ‘main wetting’ lower boundary surface (Eq. 2) with the elastic wall defined by Eq. 5. The specific volume that appears in Eq. 2 is the volume associated with an elastic path reaching the SD yield locus and this is given by Eq. 6. The yield locus SD is obtained in implicit form as follows: ⎧ ⎫m ⎪ ⎪ ⎨ ⎬ 1 " # Sr0 − ks s∗ = (10) n ⎪ ⎩ 1 + φ vk − k ln σv ψ s∗ ⎪ ⎭ The yield locus LC can be derived by the intersection of the ‘virgin loading’ boundary surface (Eq. 3) with the elastic wall defined by Eq. 6. The following implicit equation was obtained: ∗ b s vk − k ln σv = vs · 1 + a (11) σv The LC and SD yield loci derived from the water retention and mechanical boundary surfaces and their evolution with loading are plotted in Figure 8 for the compression test at w = 0.311. As expected, the LC and SD yield curve have a more complex shape than assumed by Wheeler et al. (2003) in their basic model.
If Eq. 8 is compared with Eq. 7, it can be observed that the coupling terms k1 and k2 are not recovered.
400
Modified suction, s *: kPa
300
Start of test
200
100
LC
SD 0 0
400
800
1200
1600
2000
Average skeleton stres, v" : kPa
Figure 7. LC, SI and SD yield curves for isotropic stress states according to the model by Wheeler et al. (2003).
Figure 8. LC and SD yield loci derived from the water retention and mechanical boundary surfaces for the compression test at w = 0.311.
607
9
CONCLUSIONS
The paper has presented water-undrained onedimensional compression tests with suction monitoring using Trento high-capacity tensiometers. Loading and water retention paths were investigated using two generalised stress variables, the average skeleton stress and the modified suction. We derived a ‘virgin loading’ mechanical boundary surface in the space: average skeleton stress, modified suction, and specific volume and a ‘main wetting’ hydraulic boundary surface in the space: modified suction, degree of saturation, and specific volume. In turn, these boundary surfaces were used to derive the yield loci in the generalised stress plane. It was observed that their shape differs from those suggested in the literature. Equations for the LC and SD yield loci were obtained in implicit form. Future work will involve defining simpler explicit equations for the yield loci and deriving suitable hardening laws. REFERENCES Boso, M. 2005. Shear strength behaviour of a reconstituted partially saturated clayey silt. PhD dissertation, Università degli Studi di Trento, Italy. Gallipoli, D., Gens, A., Sharma, R. & Vaunat, J. 2003a. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Géotechnique 53 (1): 123–136. Gallipoli, D., Wheeler, S.J. & Karstunen, M. 2003b. Modelling the variation of degree of saturation in a deformable unsaturated soil. Géotechnique, 53 (1): 105–112.
Houlsby, G.T. 1997. The work input to an unsaturated granular material. Géotechnique 47 (1): 193–196. Jommi, C. 2000. Remarks on the constitutive modelling of unsaturated soils. In Experimental Evidence and Theoretical Approaches in Unsaturated Soils, Proceedings of an International Workshop (eds A. Tarantino and C. Mancuso), pp. 139–153. Rotterdam: A.A. Balkema. Tamagnini, R. 2004. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Géotechnique 54 (3): 223–228. Tarantino, A. 2004. Panel report: Direct measurement of soil water tension. In Proceedings 3rd International Conference on Unsaturated Soils (eds J.F.T. Jucá, T.M.P. de Campos and F.A.M. Marinho), Recife, 3, pp. 1005–1017. Rotterdam: A.A. Balkema. Tarantino, A. & Mongiovì, L. 2002. Design and construction of a tensiometer for direct measurement of matric suction. In Proceedings 3rd International Conference on Unsaturated Soils (eds J.F.T. Jucá, T.M.P. de Campos and F.A.M. Marinho), Recife, 1, pp.319–324. Tarantino, A. & Mongiovì, L. 2003. Calibration of tensiometer for direct measurement of matric suction. Géotechnique, 53 (1): 137–141. Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Géotechnique 55 (4): 307–317. Tarantino, A. & De Col, E. 2008. Compaction behaviour of clay. Géotechnique, in press. Vaunat, J., Romero, E. & Jommi, C. 2000. An elastoplastic hydro-mechanical model for unsaturated soils. In Experimental Evidence and Theoretical Approaches in Unsaturated Soils, Proceedings of an International Workshop (eds A. Tarantino and C. Mancuso), pp. 121–138. Rotterdam: A.A. Balkema. Wheeler, S.J., Sharma, R.S. & Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Géotechnique 53 (1): 41–54.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Application to a compacted soil of a Cam Clay model extended to unsaturated conditions F. Casini Università Roma ‘‘La Sapienza’’, Roma, Italy
R. Vassallo Università della Basilicata, Potenza, Italy
C. Mancuso Università ‘‘Federico II’’, Napoli, Italy
A. Desideri Università Roma ‘‘La Sapienza’’, Roma, Italy
ABSTRACT: This paper presents an interpretation of experimental results obtained at the Department of Geotechnical Engineering of the Università di Napoli Federico II. The results are part of an extensive program carried out to investigate the effects of partial saturation on the volumetric behaviour and on the initial shear stiffness of a compacted silt. Tests were performed using two suction-controlled devices, a triaxial cell and a Resonant Column Torsional Shear (RCTS) cell. The compatibility of experimental data with a Bishop Stress Model (BSM) is discussed in the paper. The BSM permits highlighting of the two main effects of suction on soil behaviour: the increase of the average stress acting on the soil skeleton and the hardening—cementing of the soil packing. Hydraulic hysteresis is included in the definition of the water retention curve so that its effects, such as the irreversible component of volume change recorded during drying paths, are automatically incorporated in the predictions of the model.
1
INTRODUCTION
An extensive experimental program was carried out at the Department of Geotechnical Engineering of the Università di Napoli Federico II to investigate the effects of partial saturation on the volumetric behaviour and on the initial shear stiffness, G0 , of a compacted clayey silt (Vassallo et al., 2007a). A first interpretation of the results was provided by Vassallo et al. (2007b), using an approach in terms of net stresses and suction in the framework of the Barcelona Basic Model. In this paper some of the experimental data are re-interpreted using a Modified Cam Clay Model extended to unsaturated conditions (Jommi, 2000; Tamagnini, 2004). A similar approach has already been used by Casini et al. (2007) in order to understand if the model could predict the general features of the experimental results on the clayey silt. The model predicts correctly the influence of Sr on compressibility. However, for the sake of simplicity, the hydraulic hysteresis of the water retention curve was neglected.
This work takes a step forward by accounting for hysteresis and its effects on soil behaviour. The focus is on tests which included a compression stage and, then, wetting-drying cycles. 1.1 Material properties, experimental program The tested soil is the Po silt: a clayey—slightly sandy silt representative of the materials used for the construction of embankments on the Po river (Italy). On average, the material has a liquid limit (wL ) of 50.4%, a plastic limit (wP ) of 32.5% and therefore a plasticity index (IP ) of 17.9%. According to the Casagrande chart, it is classified as inorganic silt of medium/high compressibility. The material was compacted at the optimum water content by using the Standard Proctor procedure (ASTM, 2005). Table 1 summarises the average properties of the silt after compaction. Fifteen suction controlled tests were performed using a triaxial cell (Vassallo et al., 2007a). Three of them consisted of isotropic compression with
609
where σij are total stresses, ua is the air pressure, uw is the water pressure, δij is the Kronecker delta, χ(Sr ) is a weighing parameter which can account for the effects of surface tension. In this work χ(Sr ) was assumed equal to Sr . It has been argued that expression (1), often called Bishop’s stress with χ(Sr ) = Sr , represents the average stress acting on the solid phase if one neglects the work of the air-water interface (Hassanizadeh & Gray, 1980; Lewis & Schrefler, 1987; Hutter et al., 1999). Starting from the modified Cam Clay model for saturated conditions (Roscoe & Burland, 1968) and using the conceptual framework proposed by Jommi (2000) and Tamagnini (2004), the model is formulated as follows. As in the original modified Cam-clay model, elastic behaviour is defined by:
Table 1. Average properties of the tested material after compaction. w (%)
γd (kN/m3 )
v
Sr (%)
23.1 ± 0.3
15.59 ± 0.08
1.731 ± 0.009
86.9 ± 1.9
Table 2.
Stress paths of tests mp05RC and mp07RC.
mp05RC
mp07RC
p − ua ;
ua − uw (kPa)
p − ua ;
ua − uw (kPa)
10 200 200 200 200 200 200
200 200 400 100 400 100 200
10 200 200 200 200 550 –
400 400 100 400 200 200 –
ε˙ ve =
unloading and reloading stages. In the other twelve tests, the samples were isotropically consolidated at constant suction and then sheared. Besides the fully saturated condition, suctions of 50, 100, 200 and 400 kPa were investigated. Twelve suction controlled tests were carried out using a Resonant Column Torsional Shear (RCTS) cell (Vassallo et al., 2007a). During seven of them, after a preliminary equalization stage, an isotropic consolidation stage was carried out (in three cases including both loading and unloading) measuring almost continuously the initial stiffness G0 . The remaining five tests included stages of compression and of drying and wetting at constant mean net stress (p−ua ), again with a continuous measure of the initial stiffness G0 . Overall, three levels of suction (100, 200, 400 kPa) and mean net stresses ranging from 25 to 700 kPa were investigated. This paper focuses on two out of the five tests which included stages of drying and wetting. Table 2 summarises the stress paths followed in these tests, in terms of (p − ua ) and matric suction (ua − uw ). The soil parameters used to model the volumetric behaviour observed during these two tests are obtained from the complete set of isotropic stage results (both equalization and compression). 2
ELASTO-PLASTIC MODEL
1 p˙ K
ε˙ de =
1 q˙ 3G
(2)
where p is the mean effective stress, q is the deviator stress, ε˙ ve and ε˙ de are the increments of elastic volumetric strain and elastic deviatoric strain, respectively, K is the bulk modulus and G is the shear modulus. The yield locus has the usual form: f = q2 + M 2 p · (p − p c )
(3)
where M is the slope of the critical state line in the p : q plane, and pc is the scalar internal variable (overconsolidation pressure) describing isotropic hardening. The evolution of pc is defined in terms of a double hardening mechanism: p˙ c = p˙ c sat + p˙ c unsat
(4)
where p˙ c sat =
vpc v ε˙ λ−κ p
(5)
describes the evolution of the yield function produced p by plastic volumetric strains ε˙ v as predicted in the original model for saturated soils. Parameter λ is the slope of the normal compression line, κ is the slope of unloading-reloading lines, and v is the specific volume. On the other hand, the expression: p˙ c unsat = −bpc S˙ r
(6)
2.1 Bishop stress model The classic Bishop equation for effective stress is adopted: σ ij = σij − ua + χ(S r )(ua − uw )δij
(1)
describes the evolution of the yield surface produced by changes in the degree of saturation, which may occur even if the current stress lies in the elastic domain. Parameter b is a constant soil property.
610
pc = pc sat · exp[b(1 − Sr )]
(7)
Thus, b controls the rate of change in pc caused by variations in Sr . Hardening has an irreversible component dependent on the development of plastic volumetric strains, related to the evolution of pc sat , and a reversible component related to changes in Sr . The model requires a hydraulic constitutive relationship describing the water storage mechanism, as shown in Figure 1. The retention curve θw = θw (s) obtained upon an imbibition process differs from that obtained upon drying (hysteresis). Equilibrium at a given suction may be obtained with different θw . The two main curves are linked by scanning curves that can be linear or not. The issue of the hydraulic component of constitutive models was first addressed by Wheeler (1996) and by Dangla et al. (1997). Probably, the first full attempt to couple hydraulic behaviour with a mechanical model for unsaturated soils was proposed by Vaunat et al. (2000). More recently, Wheeler et al. (2003) presented an elastoplastic constitutive model that also fully couples hydraulic hysteresis with mechanical behaviour of unsaturated soils. A comprehensive review of constitutive models for unsaturated soils, including those based on Bishop’s stress, was presented by Gens et al. (2006). In this study the equation proposed by Van Genuchten (1980): θw = θw sat
1 1 + (αs)n
m (8)
is used, where θw is the volumetric water content, θw sat is the volumetric water content under saturated conditions and s is matric suction.
The main drying and wetting curves are obtained assuming different values for the constitutive parameters α, n and m (Romero & Vaunat, 2000). Scanning curves are assumed linear in the θw : s plane: θ˙w = −ks s˙
(9)
in which the constitutive parameter ks is the slope of the scanning curves. Since different values of θw can correspond to the same value of s, as shown in Figure 1, the hardening parameter p c in Equation (7) results smaller along the main drying curve than along the main wetting curve for the same values of suction and porosity. The physical meaning of the assumptions above rests on the fact that lower degree of saturation implies a higher number of contact zones between the pore fluids (menisci) so that the bonding effect exerted by the menisci is higher along a wetting path than along a drying path (Tamagnini, 2004).
2.2 Modelling of experimental results Figure 2 reports, in the θw : s plane, the 26 experimental points relative to the end of the equalization stages for all triaxial and resonant column tests together with the adopted water retention relationship. The average suction of the tested soil after compaction is about 140 kPa (Vassallo et al., 2007a). Therefore, equalization at suction 200 and 400 kPa is a drying process while equalization at lower suction is a wetting process. Table 3 summarises the parameters chosen for the water retention curve. All the available experimental data from compression stages were analysed to obtain the parameters of Equations (5) and (6), reported in Table 4.
400
s
s (kPa)
300
main drying
drying
scanning curve
The integration of Equation (4) yields to:
wetting
200 main drying
100
scanning curve
0 30
main wetting
main wetting
35
40
45
w (%)
w
Figure 1. Constitutive relationships describing water storage mechanism.
Figure 2. Experimental results of equalization stages versus the adopted water retention relationship.
611
The performance of the model was verified for tests mp07RC and mp05RC, whose results are described in detail by Vassallo et al. (2007a). Figure 3a reports a comparison between model predictions and experimental results for test mp07RC. As reported in Table 2, this test consisted of a compression at constant suction s = 400 kPa, up to p ∼ = 510 kPa (path 0-1), followed by several wetting-drying stages to s = 100–400–200 kPa (path 1-2-3-4) and finally by compression to p ∼ = 710 kPa (path 4-5). Experimental data for drying and wetting stages show only two data points at the beginning and at the end of each stage. Since suction was applied immediately at the boundary of the specimen, then waiting for the achievement of equilibrium, only the initial and final specific volumes can be attributed to the imposed net stress and suction. Differently, a complete v : p curve was obtained for each stage by modelling. During the first wetting stage at s = 100 kPa (path 1-2) the material swells. During the following drying at s = 400 kPa (path 2-3) there is a small accumulation of irreversible deformations due to the increase in suction, as shown by the specific volume at point Table 3.
Drying Wetting
3 which is smaller than that at point 1. During the subsequent wetting at s = 200 kPa (path 3-4) the material swells. Then, in the final stage of compression, the material seems to reach a normally consolidated state at p ∼ = 490 kPa. Model predictions are also reported in Figures 3b and 3c in θw : s and p : (1 − Sr ) planes. An overconsolidated state is predicted at point 0 (beginning of compression). Points 0 and 1 lie on the main drying curve (Fig. 3b) as the imposed suction (400 kPa) is greater than the after compaction suction. Compression stage 0-1 does not affect the predicted value of θw (Fig. 3b). On the other hand, there is a change in Sr , and thus in variables (1 − Sr ) and p , due to the change in porosity (Fig. 3c). For this stage, the prediction in the p : v plane is satisfying. The model also predicts well soil behaviour for the wetting stage 1-2 from s = 400 kPa to s = 100 kPa, that lies completely in the elastic domain, and for the drying stage 2-3 from s = 100 kPa to s = 400 kPa, that represents an elasto-plastic path. In the first case the state path follows first a scanning curve and then reaches the main wetting curve; in the second case, the model predicts that the state path returns to the same value of θw of points 0-1. Furthermore, the model predicts some (slight) hardening in the p : (1 − Sr ) plane due to the different changes which both p and p c experience along paths 1-2 and 2-3 (Fig. 3c). The subsequent wetting 3-4 to s = 200 kPa only induces elastic strains, in good agreement with experimental data. The final compression stage is also well predicted by the model. Figure 4a compares experimental results to model predictions for test mp05RC. This test included a compression at constant suction s = 200 kPa, up to p − ua = 200 kPa (path 0-1), then several dryingwetting stages s = 400–100–400–100–200 kPa (path 1-2-3-4-5-6) (see Table 2).
Parameters describing soil water retention curve. α(kPa−1 )
n
m
θw sat (%)
ks (kPa−1 )
0.11 0.07
1.07 1.10
0.07 0.09
44 44
0.00256 0.00256
Table 4. Parameters describing soil compressibility and the evolution of the yield surface produced by changes in Sr . λ
κ
b
N (Sr = 1)
0.06
0.018
7
2.015
experimental data model predictions 300 4
1 3
4-5
w.
1.70 100
1000 p'=p–ua+Sr(ua–uw) (kPa)
Figure 3. plane (c).
in
100 5 30
5
0.1
3-4 1-2 Y.L. 0
40
w (%)
612
3
2
2
35
Test mp07RC. Experimental data versus predictions in p
1 4
5
s.c.
ma
1.72
0.2 1-S r
1.74
s.c.
.
2
0
d main
0
1.76
0.3
0-1-3
s (kPa)
1.78
v
(c)
(b)
(a)
10
100
1000
p' (kPa)
: v plane (a); predictions in θw : s plane (b) and p : (1−Sr )
(a)
(b)
(c)
experimental data model predictions
1.76
0.3
2-4
0
0-1
6 s.c.
100
w.
6mod
42 mod 24
3 5 0.1
1000
30
35 (%)
p'=p– ua+Sr(ua–uw) (kPa)
w
2-3
3-5 Y.L. 0
mod
1.68 100
1
1-S r
v
s (kPa)
6
5mod 3
s.c.
in ma
3mod 5
0
0.2
d.
1
1.72 1.70
main
300
1.74
40
10
2 4 6 4-5-6
1
100
1000
p' (kPa)
Figure 4. Test mp05RC. Experimental data versus predictions in p : v plane (a); predictions in θw : s plane (b) and p : (1−Sr ) plane (c).
The first drying at s = 400 kPa (path 1-2) induces irreversible deformations due to the increase in suction above its maximum past value (Vassallo et al. 2007ab). The irreversibility of previous volume changes is shown by the much smaller absolute value of the variation of v observed during the first wetting at s = 100 kPa (path 2-3). As expected, this wetting path induces swelling. The subsequent drying and wetting stages cause volume changes comparable to those of wetting 2-3 and smaller than those of drying 1-2. The material always swells along wetting paths and shrinks along drying paths. Substantially, all the experimental points, from 2 on, are very close to a single line in the p : v plane. Figures 4b and 4c show model predictions in the θw : s and p : (1 − Sr ) planes. The model predicts an overconsolidated state at the beginning of compression. Similarly to test mp07RC, the results of the first compression stage are well predicted. The model also predicts an irreversible reduction of v, quite close to the measured one, during the subsequent drying 1-2 to s = 400 kPa. For the model, the path 2-3 from s = 400 kPa to s = 100 kPa is elastic. The second drying 3-4 to s = 400 kPa is elasto-plastic like the first one, although predicted shrinkage is much smaller than for path 1-2. Irreversible strains along cycle 2-3-4 are due to the different changes which p and pc experience along path 2-3 and 3-4 (Fig. 4c), linked to the shape of the water retention relationship in the θw : s plane (Fig. 4b). The closed cycle in this plane does not correspond to a closed cycle in the Sr : s plane, which is relevant for model predictions. The second wetting 4-5 and the final drying 5-6 are elastic. It is worth noting that the measured value of v in point 2 is slightly smaller than that of point 4, i.e., the material accumulates a small swelling during a drying-wetting cycle. This cannot be easily explained from a physical point of view and could be due to incomplete equalization during some stages of
the test. More appropriately the model predicts a slight accumulation of shrinkage. However predictions are substantially in good agreement with measurements from point 2 to point 6. Points 0 and 1 in Figure 4b lie on a scanning curve because the imposed suction, s = 200 kPa, is just slightly higher than the after compaction suction. Similarly to test mp07RC, which was analyzed above, compression 0-1 does not influence the value of θw while it changes porosity and, thus, variables p and (1 − Sr ), as shown in Figure 4c. During the first drying 1-2, the main drying curve is reached and the yield locus is significantly shifted rightwards. This confirms that path 1-2 is elasto-plastic. During the wetting 2-3 a scanning curve is followed until the main wetting curve is reached; an elastic path is predicted in the plane p : (1 − Sr ). The same value of θw as at point 2 is reached after the second drying path 3-4. The model predicts a slight hardening, i.e., a slight further shift rightwards of the yield locus, linked to the different changes which both p and p c experience along paths 2-3 and 3-4 (Fig. 4c). The yield locus remains unvaried during the final wetting-drying stages 4-5-6. 2.3
Interpretation of stiffness measurements
Vassallo et al. (2007a-b) used the framework of the Barcelona Basic Model to interpret the measurements of initial shear stiffness G0 along both compression and wetting-drying paths. It was concluded that there is a significant influence of suction on stiffness, which generally increases as (ua − uw ) increases. Nevertheless, changes of suction may cause significant accumulation of irreversible changes of specific volume, accompanied by a further increase of G0 relative to a general stress state (p − ua ), (ua − uw ). In other words, there can be a significant effect of the stress history, expressed in terms of (p − ua ) and (ua − uw ), on the initial stiffness.
613
(a)
(c)
(b) mp05RC mp07RC
250
0.3
0.3
05-2
0
150 100
0
0.2 07-2
05-1
05-P
07-1
07-0
2 2
0.1 P
05-0
2 0.1
1
200
300
400
500
10
100
p' (kPa)
1-2
Y.L. 0
Y.L. 0 50
1
0.2
P1
1-Sr
G0 (MPa)
200
1000
p' (kPa)
10
100
1000
p' (kPa)
Figure 5. Measured initial stiffness G0 versus p for tests mp05RC and mp07RC (a); predictions in the p : (1 − Sr ) plane for tests mp05RC (b) and mp07RC (c).
As highlighted by Casini et al. (2007), an alternative approach is using Equation (1) and referring G0 measured values to corresponding p values. This way, the effects of partial saturation on the initial shear stiffness result similar to those ascribable to the structure of a natural soil compared to the same soil reconstituted (Rampello et al. 1994). In fact, as far as data collected during isotropic compression are concerned, moving from complete saturation to partial saturation induces a translation of experimental G0 : p curves. Figure 5a reports for tests mp05RC and mp07RC stiffness versus p , measured during the first compression stage and the subsequent first wetting or drying stage. Compression stage data belong to a narrow range centred on the dashed line plotted in the same figure. This proves that the stiffness of the unsaturated soil can be fundamentally interpreted by a single curve in the p : G0 plane. On the other hand, the stiffness measured after a drying or a wetting stage results significantly higher than the values on the dashed curve. Comparison can be made between points 05-2 and 07-1, characterized by the same (p−ua ) and (ua −uw ), and 05-P and 07-2, characterized by the same p . This suggests that there is also an effect of stress history in terms of Bishop’s stress. Figures 5b and 5c report model predictions in the plane p : (1 − Sr ) for the same tests. Point 2 of test mp05RC and point 1 of test mp07RC belong to different yield loci and have different (1 − Sr ) and p . The yield locus is more expanded for test mp05RC. As a consequence of different history, point P of test mp05RC is on the current yield locus while point 2 of test mp07RC is inside the yield locus. All this could justify the differences in measured stiffness. 3
CONCLUDING REMARKS
This paper verifies the possibility of interpreting some data from the comprehensive experimental study by
Vassallo et al. (2007a) within the framework of a Bishop Stress Model (BSM). Casini et al. (2007) had already confirmed that the BSM can interpret the progressive shift of normal consolidation lines as the degree of saturation decreases and, more in general, the influence that Sr has on compressibility. Herein, a step forward was taken in modelling, by accounting for the hysteresis of the water retention curve and for its effects on soil behaviour. This determines a hysteresis in the internal variable describing isotropic hardening (Tamagnini, 2004) and can justify the occurrence of irreversible deformations such as those induced by drying-wetting cycles. The predictions of the chosen model are in good qualitative and quantitative agreement with the experimental data in terms of specific volume changes plotted versus Bishop mean effective stress p . The representation of test paths and of yield loci in the plane p : (1 − Sr ) also seems quite useful to interpret the effects of stress state and stress history on the initial shear stiffness G0 . REFERENCES ASTM 2005. D0698-00 AE01 Test method for laboratory compaction characteristics of soil using standard effort (12, 400 ft · lbf /ft3 (600 kN · m/m3 )), ASTM Book of Standards, vol. 04.08, Philadelphia, USA. Casini F., Vassallo R., Mancuso C. & Desideri A. 2007. Interpretation of the behaviour of compacted soils using Cam-Clay extended to unsaturated conditions. Proceedings of the Second International Conference Mechanics of Unsaturated Soils, Weimar (Germany), 29–36. Dangla O.L., Malinsky L. & Coussy O. 1997. Plasticity and imbibition-drainage curves of unsaturated soils: a unified approach. 6th International Conference on numerical models in geomechanics, Montreal, 141–146. Gens A., Sanchez M. & Sheng D. 2006. On constitutive modelling of unsaturated soils. Acta Geotechnica, 1, 137–147.
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Hassanizadeh S.M. & Gray W.G. 1980. General conservation equations for multiphase systems: 3. Constitutive theory for porous media flow. Advanced Water Resource, 3, 25–40. Hutter K., Laloui L. & Vulliet L. 1999. Thermodynamically based mixture models for saturated and unsaturated soils. Mechanics of Cohesive-frictional Materials, 4, 295–338. Jommi C. 2000. Remarks on the constitutive modelling of unsaturated soils. Proceedings of the International Workshop Experimental Evidence and Theoretical Approaches in Unsaturated Soils, Trento (Italy), 139–153. Lewis R.W. & Schrefler B.A. 1987. The finite element method in the deformation and consolidation of porous media. Wiley, Chichester. Rampello S., Silvestri F. & Viggiani G. 1994. The dependence of small strain stiffness on stress state and history for fined grained soils: the example of Vallericca clay. Proceedings of the First International Symposium on Prefailure Deformation of Geomaterials, Sapporo (Japan), 273–278. Romero E. & Vaunat J. 2000. Retention curves of deformable clay. Proceedings of the International Workshop Experimental evidence and theoretical approaches in unsaturated soils, Trento (Italy), 91–106. Roscoe K.H. & Burland J.B. 1968. On the Generalized StressStrain Behavior of Wet Clay. Engineering Plasticity, Cambridge University Press, 535–609.
Tamagnini R. 2004. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Géotechnique, 54, 223–228. Van Genuchten M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44, 892–898. Vassallo R., Mancuso C. & Vinale F. 2007a. Effects of net stress and suction history on the small strain stiffness of a compacted clayey silt. Canadian Geotechnical Journal, 44, 447–462. Vassallo R., Mancuso C. & Vinale F. 2007b. Modelling the influence of stress-strain history on the initial shear stiffness of an unsaturated compacted silt. Canadian Geotechnical Journal, 44, 463–472. Vaunat J., Romero E. & Jommi C. 2000. An elastoplastic hydro-mechanical model for unsaturated soils Proceedings of the International Workshop Experimental evidence and theoretical approaches in unsaturated soils, Trento (Italy), 121–138. Wheeler S.J. 1996. Inclusion of specific water volume within an elastoplastic model for unsaturated soil. Canadian Geotechnical Journal, 33, 42–57. Wheeler S.J., Sharma R.S. & Buisson M.S.R. 2003. Coupling of hydraulic hysteresis and stress strain behaviour in unsaturated soils. Géotechnique, 53, 41–54.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Mixed isotropic-rotational hardening to model the deformational response of unsaturated compacted soils C. Jommi Department of Structural Engineering, Politecnico di Milano, Milano, Italy
E. Romero Department of Geoengineering and Geoscience, Universitat Politècnica de Catalunya, Barcelona, Spain
ABSTRACT: The pattern of volumetric strains of unsaturated compacted soils along drying and wetting cycles have received considerable attention in the last years due to its practical implications during the service life of earth structures and backfills. Much attention has been devoted to the amount of collapse upon wetting as a function of suction and stress level. Oedometer test data are presented here to quantify the amount of collapse and shrinkage strains in wetting-drying-wetting cycles. Besides, results of an isotropic wetting test show that collapse is in general accompanied by distortional strains as a result of the initial anisotropy created during compaction. An elastic plastic model, in which the evolution of the soil structure is described by means of a mixed isotropic-rotational hardening, is presented. Coupling between hydraulic and mechanical behaviour is provided by a hysteretic retention curve. Comparison between model simulations and experimental data show that the model is able to reproduce correctly the whole irreversible strain path upon both wetting and drying.
1
INTRODUCTION
The deformational response of compacted soils under environmental actions is of paramount importance in the analysis of the service life of earth constructions such as dams, embankments, waste disposal facilities. Hydraulic loads, i.e. cyclic drying and wetting, besides changes in external loads, may condition to a large extent the overall behaviour of this class of structures. The abrupt volume reduction, termed collapse, that a compacted soil may undergo upon wetting, is considered to be the most problematic aspect of the deformational response of a compacted soil (e.g. Pereira & Fredlund 2000, Lim & Miller 2004). That soils compacted dry of optimum at low dry density undergo collapse when wetted under constant total stress is well known (Jennings & Burland 1962, Barden et al. 1973). More recent experimental results have shown that even soils compacted at optimum conditions or wet of optimum may experience collapsible behaviour at high stresses, if they undergo drying before wetting (Gens et al. 1995, Suriol et al. 1998). These experimental data suggest that the whole suction history, besides void ratio and suction, rules the overall deformational response of compacted soils. Less attention was paid in the past to irreversible volumetric strain experienced by compacted soils upon first drying, which are of the same sign as collapse
strains and may even be of comparable magnitude (e.g. Dif & Bluemel 1991, Fleureau et al. 1993). Besides, the role played by the initial anisotropic fabric created by the compaction procedures on the deformational response of compacted soils has not been studied in detail, although different researchers have highlighted the significant initial anisotropy developed under one-dimensional oedometer compaction (Zakaria et al. 1995, Cui & Delage 1996, Estabragh & Javadi 2006). Moreover, Zakaria et al. (1995) and Barrera et al. (2000) observed that a clear evolution of the anisotropic fabric occurs along the subsequent loading paths. In particular, Romero (1999) showed that, due to the initial anisotropic fabric, distortional strains may be appreciable along wetting paths under an external isotropic stress state. Shrinkage strains upon drying and collapse or swelling strains developed upon wetting are considered to be the result of different irreversible deformational mechanisms. Consequently, in the framework of elastoplasticity they are usually modelled with separate, although coupled, yield funcitons (e.g. Alonso et al. 1990, Wheeler et al. 2003, Sheng et al. 2004, Sun et al. 2007). A possible alternative unified view of the overall volumetric strains experienced by compacted soils along generalised hydraulic paths is suggested here. A rather simple elastic plastic constitutive model
617
is proposed, which exploits the hysteretic retention characteristics of compacted soils to describe both irreversible collapse upon wetting and irreversible shrinkage upon drying in a unified framework. A unique mixed isotropic-rotational hardening law describes the evolution of the soil fabric along generalised stress paths, allowing for irreversible shrinkage, irreversible collapse and anisotropy evolution to be taken into account at the same time. Relevant experimental results, coming from a wide investigation performed on compacted Boom clay (Romero, 1999) are presented and simulated numerically by means of the proposed model. Oedometer tests are exploited to analyse volumetric strains as a function of the stress level. A wetting-drying-wetting test under constant isotropic external load is then presented to highlight changes in the direction of plastic strain increments occurring along the hydraulic path. The latter test clearly shows the distortional effects caused by the initial anisotropic fabric and the evolution of fabric anisotropy, and allows a complete description of the general deformational response of the compacted soil.
2 2.1
CONSTITUTIVE FORMULATION Theoretical basis
Referring to axisymmetric test conditions, a full description of the soil state may be accomplished by adopting triaxial stress and strain variables. Total stress state will be described by total mean stress, p = (σa + 2σr )/3, deviator stress, q = (σa − σr ), and suction, s = (ua − uw ), where ua and uw are the air and the water pressures, respectively. As for the strain variables, volumetric strain, εv = εa + 2εr , and shear strain, εs = 2(εa − εr )/3, will be adopted. Subscripts a and r refer to axial and radial components, respectively. The amount of pore water will be described by both gravimetric water content, w, and degree of saturation, Sr . The average stress acting on the soil skeleton (‘‘skeleton stress’’ in the following) is adopted in the development of the constitutive formulation. With reference to axisymmetric conditions, mean skeleton stress, pˆ = [(p−ua )+Sr s] and deviator stress, q, describe the constitutive stress state. The modelling criteria suggested by Jommi & di Prisco (1994) are followed. Given an elastic plastic model conceived for soils in saturated conditions, its extension to unsaturated conditions may be simply conceived as follows. By substituting the skeleton stress for effective stress in the original constitutive equations, increase in the average stress acting on the soil skeleton due to suction may be taken into account. Besides, the ‘‘bonding’’ effect provided on the soil macrostructure by water menisci may be translated in
a generalisation of the hardening rules, by inserting a suitable dependence of the hardening parameters on suction or on degree of saturation. To keep the model as simple as possible, Modified Cam Clay with associated plastic potential is adopted herein as a reference for the saturated state. The formulation for unsaturated conditions is a rather simple extension of the works by Jommi (2000) and Tamagnini (2004). To complete the description of the soil behaviour a model for the retention curve is mandatory. Consistent advantages in modelling the deformational behaviour of unsaturated soils are provided if hysteresis in the soil water retention mechanism is taken into account, as previously discussed by Tamagnini (2004). To the latter aim, the hysteretic retention model proposed by Romero & Vaunat (2000) is introduced in the coupled hydro-mechanical model, and formulated as an additional constitutive law. 2.2
Mechanical model equations
Starting from Modified Cam Clay, a rotation of the axis of the yield surface and plastic potential can be introduced to allow for the description of an anisotropic response, following the proposal by Dafalias (1986): 2 f = q − Mα pˆ + M 2 − Mα2 pˆ pˆ − pˆ 0 = 0
(1)
where M describes critical state obliquity, which is assumed to be independent of suction. The internal variables pˆ 0 , describing the current preconsolidation pressure, and Mα , representing the inclination of the current rotated yield surface with respect to the pˆ axis, govern the isotropic and rotational hardening, respectively. The evolution of the two variables is ruled by both plastic strains and degree of saturation. The preconsolidation pressure in unsaturated conditions, pˆ 0 , is defined as the sum of the preconsolidation pressure in saturated conditions, p∗0 , depending on volumetric plastic strains, plus a term depending on degree of saturation, pˆ 0 = p∗0 {1 + b1 [exp [b2 (1 − Sr )] − 1]}
(2)
governed by parameters b1 and b2 . For p∗0 , the classical critical state evolution law is adopted: dp∗0 =
(1 + e) p∗0 p dεv λ−κ
(3)
where λ and κ are the elastic-plastic and elastic logarithmic volumetric compliances, e is the void ratio and p dεv the volumetric plastic strain increment.
618
Following Dafalias (1986), rotational hardening is assumed to be governed by the current angle between the obliquity, ηˆ = q/ˆp, and the inclination Mα of the yield surface:
Table 1. Parameters adopted in the simulation of compacted Boom clay.
. . dMα = c . dεvp . ηˆ − ξ Mα
κ G (MPa) λ M ξ b1 b2 c
0.014 40 0.125 0.87 1.484 0.11 8.2 136
Hydraulic parameter
Wetting
Drying
Scanning
a (MPa) α (MPa−1 ) n m l (MPa−1 )
300 19.3 1.12 0.20 –
400 1.4 0.95 0.41 –
– – – – 0.02
where c governs the rate of evolution of Mα , while ξ controls the target value of Mα for a given obliquity, hence dMα = 0 for ξ = η/M ˆ α. A constant shear modulus, G, completes the description of a classical hypoelastic behaviour. The model is defined in terms of eight material parameters. Four of them, M , λ, κ and G, describe the behaviour of the isotropic soil under saturated conditions, and may be calibrated on the basis of conventional laboratory tests performed on saturated samples. In principle, parameter c, ruling the velocity of rotational hardening, can be determined with reference to saturated samples too. Due to lack of information, in the present case, c was calibrated on the basis of the triaxial data on the unsaturated soil presented in the following. Parameter ξ can be calibrated from compaction data, assuming that at the end of compaction the direction of plastic strain increment were not changing any more. The initial values of the hardening parameters, pˆ 0in and Mαin can also be determined from the compaction data. Only the calibration of the two parameters b1 and b2 , governing the rate of evolution of the preconsolidation pressure with the degree of saturation, need experimental data from tests run on samples in unsaturated conditions. Here, they were calibrated in order to minimise the difference between experimental data and numerical simulation of volumetric plastic strain along the first wetting path of the isotropic test presented in Section 5. The complete set of parameters adopted is listed in Table 1. 2.3
1000
wetting: experimental data drying: experimental data drying: model wetting: model
100
Suction, s (MPa)
(4)
Mechanical parameter
10
1
0.1
0.01 0
Figure 1. model.
20
40 60 Degree of saturation, Sr (%)
80
100
Water retention curve: experimental data and
a function of suction, s (Romero & Vaunat 2000):
Hydraulic model equations
Literature data (e.g. Gallipoli et al. 2003, Tarantino & Tombolato 2005) show that irreversible strains undergone by a compacted soil along different hydromechanical stress paths affect its water retention properties. Nevertheless, a unique hysteretic retention curve in the suction-degree of saturation plane was chosen here, as a first approximation. Figure 1 shows the main wetting and drying branches of the water retention curve of Boom clay, based on experimental data obtained with both vapour equilibrium and axis translation techniques, for a constant void ratio of e0 = 0.93 characterising the as-compacted conditions (Romero 1999). The water retention data were fitted to a modified form of van Genuchten’s expression for degree of saturation, Sr , as
Sr = C(s)
1 1 + (α s)n
m ;
C(s) = 1 −
ln 1 + as . ln(2) (5)
Fitted parameters for the description of the retention curve are listed in Table 1. Parameters n, m and α are the same as used in van Genuchten’s expression. Parameter α is inversely associated with the air-entry value of the soil in the drying branch and with the air occlusion pressure in the wetting branch. The correction function C(s) is introduced to fit retention curve data for clayey soils at high suctions. The slope of the scanning curves, l, is given a constant value. It is worth noting that the hydraulic model
619
equation may be interpreted as a reversible-perfectly irreversible constitutive law, with no hardening.
-2
Volumetric strain, εv (%)
3
-4
MATERIAL AND EXPERIMENTAL TESTS
The experimental data refer to Boom clay from Mol (Belgium). The moderately swelling clay (20%–30% kaolinite, 20%–30% illite and 10%–20% smectite) has a liquid limit of wL = 56%, a plastic limit of wP = 29%, density of solid particles ρs = 2.70 Mg/m3 and a clay fraction CF = 50%. The samples were prepared by static oedometer compaction, on the dry side of optimum, at constant water content w = 15% to a dry density ρd = 1.40 Mg/m3 . Initial void ratio, e0 = 0.93, and degree of saturation, Sr0 = 0.44, are not far from the optimum standard Proctor value. The loading path to fabricate the soil and the following unloading path prior to testing were performed at an approximately constant suction, s = 1.9 MPa, which was determined from psychrometer readings. Maximum fabrication net vertical and horizontal stress were around 1.2 MPa and 0.44 MPa, respectively. After preparation, some samples were reloaded at constant water content in a controlled-suction oedometer up to four different net vertical stresses, namely 0.085, 0.30, 0.60 and 1.2 MPa. Wetting was then carried out using axis translation technique with four equalisation stages (s = 0.45, 0.20, 0.06 and 0.01 MPa). Afterwards, a multi-step drying, up to s = 0.45 MPa, and a subsequent wetting path were performed at the same net vertical stresses, following the same equalisation stages. Air pressure was maintained constant at 0.5 MPa throughout the wetting-drying-wetting process. The soil sample tested in the triaxial cell was removed from the oedometer ring after unloading and the lateral stress was released. Afterwards, the sample was mounted in the triaxial cell and subjected to an isotropic loading path at constant water content. At p = 0.6 MPa, the sample underwent a wettingdrying-wetting cycle, with the same four equalisation stages as before, by means of axis translation technique applied to both ends of the sample.
2 4 6
net vertical stress 0.085 MPa experimental numerical with rotational hardening numerical isotropic
8 10 12 0.01
0.02
0.05
0.2
0.1 Suction, s (MPa)
0.5
1
2
-4 net vertical stress 0.3 MPa experimental numerical with rotational hardening numerical isotropic
Volumetric strain, εv (%)
-2 0 2 4 6 8 10 12 0.01
0.02
0.05
0.2
0.1 Suction, s (MPa)
0.5
1
2
-4 net vertical stress 0.6 MPa experimental numerical with rotational hardening numerical isotropic
Volumetric strain, εv (%)
-2 0 2 4 6 8 10 12 0.01
0.02
0.05
0.2
0.1 Suction, s (MPa)
0.5
1
2
-4 net vertical stress 1.2 MPa experimental numerical with rotational hardening numerical isotropic
-2
Volumetric strain, εv (%)
4
0
OEDOMETER TESTS
0 2 4 6 8 10
In Figure 2 the experimental data of the oedometer tests performed at constant net vertical stress, ranging from 0.085 MPa and 1.2 MPa are presented together with the numerical results. Numerical simulations run with the mixed isotropic-rotational hardening model presented herein are compared with the prediction of a
12 0.01
0.02
0.05
0.2
0.1 Suction, s (MPa)
0.5
1
2
Figure 2. Oedometer tests: experimental data and numerical simulations.
620
rotational model) evolves differently in wetting and drying paths, hence allowing for irreversible strains to be correctly predicted in both cases. This model feature was highlighted by Tamagnini (2004). Here, its quantitative reliability is verified against data spanning over a wide stress range. 5
ISOTROPIC TRIAXIAL TEST
The advantages provided by the possibility of reproducing an anisotropic response by means of rotational hardening can be appreciated much better with reference to the experimental data presented in the following. Figures 3–4 show the whole strain path experienced by the initially anisotropic sample, reloaded to the isotropic pressure, p = 0.6 MPa, and then subjected to a hydraulic cycle. Figure 3 shows the axial and the radial strain data. In Figure 4, the evolution of volumetric and distortional strains with suction are shown, to highlight the influence of the initial anisotropic fabric and its evolution on the overall deformational response of the soil sample. Along the first wetting stage, distortional strain, due to anisotropy, accompanies the plastic volume collapse. Accumulated plastic strains eventually erase initial anisotropy. Starting from a suction value of 0.2 MPa, in the last wetting stages and in the following drying-wetting cycle the behaviour of the sample is isotropic. As in the previous oedometer tests, the following drying path induces a small, but irreversible, volume reduction. Distortional strains are negligible in the drying-wetting cycle, and the deformational response is fully isotropic. The numerical simulations of the triaxial test data, presented in Figure 3, show that the axial strain evolution is well predicted by both models. Rotational hardening does not seem to influence this strain component to a large extent. Differences are observed in numerical with rotational hardening numerical isotropic experimental
0.0
a
(%)
1.0 2.0 3.0 0.0
(%)
1.0 r
conventional isotropic hardening model (Jommi 2000, Tamagnini 2004). The influence of stress level on the volumetric strain experienced by the soil in the first wetting path, as well as in the following drying and wetting paths, may be clearly appreciated by comparison of the experimental data presented in the figures. During the first wetting stages, the competing deformational mechanisms, unloading of the aggregates (possibly accompanied by swelling of the aggregates themselves) and collapse of the macrostructure, may result in a net increase or a net decrease of volume, as a function of the applied vertical net stress. In any case, the volumetric strain experienced during the whole first wetting stage is almost irreversible, as the data for the following drying stage clearly show. In the first drying path, the soil experiences again a considerable irreversible volume reduction. At low stress levels shrinkage can be comparable to, or even higher than, the amount of collapse previously due to wetting. The ratio between the amount of collapse during first wetting and shrinkage during first drying increases with the stress level, as expected. The last wetting path induces a moderate elastic swelling, and further drying-wetting cycles, not shown here, are almost completely reversible (Romero 1999). Comparison between experimental data and numerical simulations show that the constitutive model with rotational hardening is able to capture all the relevant features of the experimental behaviour in the hydraulic cycle. The numerical simulations run with a simpler isotropic model are worse for low stress levels, while for the higher stress levels they are very similar to the previous ones. The differences at the lower stress levels are mostly due to a wider elastic domain predicted by the isotropic model with respect to the anisotropic one. If the isotropic model is adopted, for a net vertical stress of 0.0085 MPa the whole first wetting path lies inside the elastic domain, which overestimates the overall swelling. In any case, the volumetric strains predicted by the two models at the end of each whole hydraulic cycle do not differ much, which is consistent with the dependence of the hardening function on volumetric plastic strains only. In fact, some literature data seem to substantiate this choice (e.g. Lawton et al. 1992). It is worth noting that, in the elastic plastic models in which hardening is ruled by suction, two distinct yield functions, usually termed loading-collapse (LC) and suction increase (SI) yield functions, must be introduced in order to describe irreversible collapse upon first wetting and irreversible shrinkage upon first drying. On the contrary, if the hardening laws are ruled by degree of saturation (Eqs. 2,4), and hysteresis is explicitly taken into account, the preconsolidation pressure (and the direction of the yield surface axis for the
2.0 3.0 4.0 0.01
0.02
0.05
0.2
0.1 Suction, s (MPa)
0.5
1
2
Figure 3. Isotropic test (0.6 MPa): axial and radial strain evolution: experimental data and numerical simulations.
621
(%)
-0.6
s
Rotational hardening, describing the evolution of the anisotropic fabric of a compacted soil along its mechanical and hydraulic history, could be easily introduced thanks to advanced experimental data allowing for calibration of the evolution laws. Extension of the model to general stress and strain paths, accomplished following literature suggestions, may provide a useful tool for engineering purposes.
numerical with rotational hardening numerical isotropic experimental
-0.4 -0.2
v
(%)
0.0 0 5
w (%)
10 30 25
ACKNOWLEDGEMENTS
20 15 0.01
0.02
0.05
0.2
0.1 Suction, s (MPa)
0.5
1
2
Figure 4. Isotropic test (0.6 MPa): distortional strain, volumetric strain, and water content evolution: experimental data and numerical simulations.
The financial support of the Spanish Ministry of Science (CGL2005-03677/BTE: Advances in Unsaturated Soil Mechanics: Behaviour under Generalised Stress States) is gratefully acknowledged. REFERENCES
the prediction of the radial strain component. While the model with rotational hardening allows for different values to be predicted, axial and radial strain components are obviously equal if an isotropic model is adopted. Advantages coming from rotational hardening appear clearly if attention is focused on the distortional strain, which cannot be reproduced by the isotropic model (Fig. 4). As a result, the total volumetric collapse is a little underestimated by the isotropic model. Experimental data in Figure 4 show that water content changes in the drying-wetting cycle following collapse are almost reversible. This observation confirms that plastic strains affect the retention properties of the soil too. Although the numerical predictions are still good quantitatively, the latter feature is not reproduced by the present model, in which a fixed retention curve in the suction-degree of saturation plane is assumed. 6
CONCLUDING REMARKS
The results presented show that the evolution of a compacted soil fabric may be correctly reproduced with simple, but coupled, elastic plastic models, by adopting the average stress acting on the soil skeleton to reproduce the confining stress increment due to suction, taking into account the hysteretic and irreversible water retention properties of the soil, and ruling hardening via both plastic strains and degree of saturation. The latter choice appears crucial in the interpretation and in the description of the overall deformational response. Lack of information on the evolution of hydraulic properties complicates the interpretation of the behaviour of unsaturated soils, which may be greatly simplified if a complete description of the hydraulic state evolution, besides stresses and strains, is provided.
Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430. Barden, L., McGown, A. & Collins, K. 1973. The collapse mechanism in partly saturated soil. Engrg. Geol. 7: 49–60. Barrera, M., Romero, E., Lloret, A. & Gens, A. 2000. Collapse test on isotropic and anisotropic compacted soils. In A. Tarantino and C. Mancuso (eds.). Experimental Evidence and Theoretical Approaches in Unsaturated Soils: 33–45. Rotterdam: Balkema. Cui, Y.J. & Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Géotechnique 46: 291–311. Dafalias Y.F. 1986. An anisotropic critical state soil plasticity model. Mech. Res. Comm., 13(6): 341–347. Dif, A.E. & Bluemel, W.F. 1991. Expansive soils under cyclic drying and wetting. Geot. Testing J., 14(1): 96–102. Estabragh, A.R. & Javadi, A.A. 2006. Yielding of unsaturated compacted silty soil under anisotropic conditions. In G.A. Miller, C.E. Zapata, S.L. Houston and D.G. Fredlund (eds.). Unsaturated Soils 2006, 1: 1259–1266. Virginia: ASCE. Fleureau, J.-M., Kheirbek-Saoud, S., Soemitro, R. & Taibi, S. 1993. Behaviour of clayey soils on drying-wetting paths. Can. Geotech. J., 30: 287–296. Gallipoli, D., Wheeler, S.J. & Karstunen., M. 2003. Modelling the variation of degree of saturation in a deformable unsaturated soil. Géotechnique 53(1): 105–112. Gens, A., Alonso, E.E., Suriol, J. & Lloret, A. 1995. Effect of structure on the volumetric behaviour of a compacted soil. In E.E. Alonso and P. Delage (eds.), Unsaturated Soils, 1: 83–88, Rotterdam, Balkema. Jennings, J.E. & Burland, J.B. 1962. Limitations to the use of effective stresses in partly saturated soils. Géotechnique 12(2): 125–144. Jommi, C. 2000. Remarks on the constitutive modelling of unsaturated soils. In A. Tarantino and C. Mancuso (eds.). Experimental Evidence and Theoretical Approaches in Unsaturated Soils: 139–153. Rotterdam: Balkema. Jommi, C. & di Prisco, C. 1994. A simple theoretical approach to model the mechanical behaviour of partially
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saturated granular soils (in Italian). Proc. of Italian Conf. Role of fluids in Geotechnical engineering. Mondovì, 1(II): 167–188. Lawton, E.C., Fragaszy, R.J. & Herington, M.D. 1992. Review of wetting-induced collapse in compacted soil. J. Geotech. Engrg. ASCE, 118(9): 1376–1394. Lim, Y.Y. & Miller, G.A. 2004. Wetting-induced compression of compacted Oklahoma soils. J. Geotech. Geoenv. Engng. 130(10): 1014–1023. Pereira, J.H.F. & Fredlund, D.G. 2000. Volume change behaviour of collapsible compacted gneiss soil. J. Geotech. Geoenv. Engng. 126(10): 907–916. Romero, E. 1999. Characterisation and thermo-hydromechanical behaviour of unsaturated Boom clay: an experimental study. PhD Thesis, UPC, Barcelona. Romero, E. & Vaunat, J. 2000. Retention curves of deformable clays. In A. Tarantino and C. Mancuso (eds.). Experimental Evidence and Theoretical Approaches in Unsaturated Soils: 91–106. Rotterdam: Balkema. Sheng, D., Sloan, S.W. & Gens, A. 2004. A constitutive model for unsaturated soils: thermomechanical and computational aspects. Computational Mechanics, 33: 453–465.
Sun, D.A., Sheng, D.C., Cui, H.B. & Sloan, S.W. 2007. A density-dependent elastoplastic hydro-mechanical model for unsaturated compacted soils. Int. J. Numer. Anal. Meth. Geomech., 31: 1257–1279. Suriol, J., Gens, A. & Alonso, E.E. 1998. Behaviour of compacted soils in suction-controlled oedometer. In Proc. 2nd Int. Conf. on Unsaturated Soils. Beijing, China, 1: 438–443. Beijing: International Academic Publishers. Tamagnini, R. 2004. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Géotechnique, 54(3): 223–228. Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Géotechnique, 55 (4): 307–317. Wheeler, S.J., Sharma, R.S. & Buisoon, M.S.R. 2003. Coupling hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Géotechnique, 53(2): 41–54. Zakaria, I., Wheeler, S.J. & Anderson, W.F. 1995. Yielding of unsaturated compacted kaolin. In E.E. Alonso and P. Delage (eds.), Unsaturated Soils, 1: 223–228, Rotterdam: Balkema.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
An anisotropic elasto-plastic model for unsaturated soils K. Stropeit & S.J. Wheeler University of Glasgow, Glasgow, UK
Y.J. Cui Ecole Nationale des Ponts et Chaussées, Paris, France
ABSTRACT: A new anisotropic elasto-plastic constitutive model for unsaturated soils (ABBM) has been developed, by combining features of the conventional Barcelona Basic Model (BBM) for unsaturated soils and the anisotropic S-CLAY1 model for saturated soils. In addition, the possibility of a non-linear variation of cohesion intercept with suction is introduced for both the BBM and the ABBM. Simulations with the ABBM and the BBM have been compared with experimental data from tests on compacted Jossigny silt reported by Cui & Delage (1996). The ABBM is able to provide a much better match than the BBM to the observed shape and size of the yield surface produced by one-dimensional compaction. In addition, the ABBM is able to provide improved predictions of yield stresses and volumetric strains during constant suction shearing, particularly if a non-linear variation of cohesion intercept with suction is incorporated. The current version of the ABBM can, however, sometimes result in unrealistic predictions of immediate post-yield softening, and further work is required to refine and fully validate the model.
1
2
INTRODUCTION
Many soils display anisotropy of mechanical behaviour, as a consequence of anisotropy of the soil fabric (e.g. Graham et al. 1983, Cui & Delage 1996). This anisotropy of fabric may be initiated during formation of the soil (e.g. deposition of natural soils or placement and compaction of fills), but it can be altered subsequently by plastic straining, which can produce re-arrangement of the fabric. Many anisotropic elasto-plastic constitutive models for saturated soils have been published in the literature. One of these anisotropic saturated models is S-CLAY 1, presented by Wheeler et al. (2003), which has a rotational hardening law (describing the development of anisotropy during plastic straining) that has now been extensively validated by experimental programmes on several soft saturated clays. Little, however, has been published on development of anisotropic elasto-plastic constitutive models for unsaturated soils. This paper presents a new anisotropic unsaturated elasto-plastic constitutive model (ABBM), in which the modelling of anisotropy from SCLAY1 is used to enhance the conventional Barcelona Basic Model (BBM) of Alonso et al. (1990).
ABBM MODEL
The new anisotropic elasto-plastic model for unsaturated soils (ABBM) is presented here for the simplified stress space of the triaxial test, in terms of mean net stress p, deviator stress q and suction s. Generalization of the model to three-dimensional stress states, including the possibility of rotation of principal stress directions, can be achieved by following the same logic as presented by Wheeler et al. (2003) for the saturated model S-CLAY 1. Modelling of elastic anisotropy that can change with plastic straining would be extremely complex (see Wheeler et al. 2003). In the interest of simplicity, therefore, the ABBM (like S-CLAY 1) assumes isotropic elastic behaviour. The elastic increments of volumetric strain and deviatoric strain are given by the same expressions as in the BBM. 2.1
Yield surface
Constant suction cross-sections of the ABBM yield surface take the form of geometrically sheared ellipses in the q: pf plane: 3 (q − αp)2 = (M2 − α 2 ) p + f (s) ( pm (s) − p) 2 (1)
625
where M is the saturated critical state stress ratio. The parameters α and pm (s) define the inclination and size respectively of the yield curve (see Fig. 1), with the magnitude of α representing a measure of the current degree of plastic anisotropy. The value of α can change during plastic straining (as anisotropy changes), but it is assumed that cross-sections of the yield surface at different suctions all have the same inclination α (see Fig. 1). This assumption appears reasonably consistent with the experimental yield curves presented by Cui & Delage (1996). The yield curve for a given suction s has vertical tangents at two points, A and B, both falling on a line of gradient α through the origin, with point A having a coordinate p = −3f (s)/2 and point B having a coordinate p = pm (s) (see Fig. 1). f (s) is a function of suction (see later) which has a value of zero at s = 0. The yield curve for s = 0 corresponds to the S-CLAY1 anisotropic model for saturated soils. With α = 0 (isotropic behaviour) and a linear variation of f (s) with suction, Equation 1 gives the BBM yield curve expression. A single value of M can be used for the entire yield curve, or alternatively a lower triaxial extension value of M can be used for the section of yield curve below the vertical tangent points A and B (a possibility introduced in S-CLAY 1 by Wheeler et al. 2003). The size of the yield curve pm (s) is assumed to vary with suction according to the LC yield curve expression of the BBM: pm (s) = pc
pm (0) pc
2.2 Flow rule and hardening laws The ABBM employs an associated flow rule, which can be expressed as: p
2 (ηα − α) dεs p = M2 − ηα2 dεv
(3)
where ηα is the gradient of the line in the q: p plot from the vertical tangent point A (see Figure 1) to the current stress point: ηα =
! q + α · 3 2 f (s) ! p + 3 2 f (s)
(4)
Equation 3 reverts to the flow rule of the S-CLAY 1 model for the case s = 0. Wheeler et al. (2003) showed that, for saturated soils, an associated flow rule combined with the inclined S-CLAY 1 yield curve gives a reasonable match to observed patterns of behaviour, in contrast to the isotropic Modified Cam Clay model, where a non-associated flow rule generally gives improved predictions. Similarly, Alonso et al. (1990) suggested the use of a non-associated flow rule in the isotropic BBM. The ABBM incorporates two hardening laws. The first hardening law takes a similar form to the BBM hardening law and relates the change of size of the yield surface to the plastic volumetric strain:
λ(0)−κ λ(s)−κ
p
dpm (0) v · dεv = pm (0) λ(0) − κ
(2)
where pm (0) gives the size of the yield curve at s = 0 (see Fig. 1) and pc is a reference pressure (a soil constant). The variation of λ(s) with suction follows the same expression as in the BBM.
(5)
The second hardening law gives the change of yield surface inclination α produced by plastic straining: dα = μ
. η . / 0 3ηα α − α · dεvp + b − α · .dεsp . 4 3 (6)
where μ and b are two soil constants. For the case s = 0 (when ηα is replaced by the conventional stress ratio η), Equation 6 corresponds to the rotational hardening law of the S-CLAY 1 model. This saturated version of Equation 6 has now been extensively validated in experimental test programmes on several soft saturated clays, but there has been no validation for unsaturated conditions. An explanation of the rotational hardening law is given by Wheeler et al. (2003). 2.3 Critical states Figure 1.
Constant suction cross-sections of yield surface.
Equation 3 indicates that critical states are reached when ηα = M . Inspection of Equation 6 then shows
626
that the ABBM (like S-CLAY1) predicts a unique critical state value of yield curve inclination αcs : αcs =
M 3
(7)
For each value of suction there is a unique critical state line in the q:p plane, defined by: q = Mp + Mf (s)
(9)
where k is a soil constant. With this assumption, the critical state line defined by Equation 8 coincides with the BBM critical state line expression. In the second version of the model, a non-linear variation of cohesion intercept with suction is assumed: s f (s) = a 1 − exp − a
(10)
where a is a soil constant. Equation 10 gives a nonlinear increase of shear strength with suction, as reported by many authors (e.g. Gan et al. 1988), with f (s) reaching a limiting value, of magnitude a, as suction tends to infinity. The form of Equation 10 ensures that a plot of f (s) against s has an initial gradient of unity at s = 0, thus satisfying the saturated effective stress requirement as s tends to zero. The non-linear cohesion intercept expression of Equation 10 can be used in the BBM as well as in the ABBM. 3
G κ κs pc λ (0) N (0) r
19.0 MPa 0.0047 0.004 2.0 kPa 0.064 1.9 0.8
β M k a μ b
0.004 kPa−1 1.1 0.29 352.0 kPa 187.5 1.0
(8)
i.e. critical state lines for different values of suction all have the same gradient M , with an intercept on the p axis at—f (s) (see Fig. 1). When α reaches the critical state value given by Equation 7, the vertical tangent point A falls on the extension of the critical state line defined by Equation 8 (see Fig. 1). As a consequence, when α = αcs the horizontal tangent point on the yield curve coincides with the intersection of the yield curve with the critical state line. This is not true for other values of α, except for the case s = 0. Two different forms have been assumed for the variation of f (s) with suction. The first version involves a linear variation of cohesion intercept with suction: f (s) = ks
Table 1. BBM and ABBM parameter values for compacted Jossigny silt.
INVESTIGATION OF MODEL VALIDITY
Experimental data from controlled-suction triaxial tests on unsaturated compacted Jossigny silt reported by Cui & Delage (1996) have been used to evaluate the ability of the ABBM to reproduce observed behaviour. Tests were performed at four different values of constant suction: 200, 400, 800 and 1500 kPa, and the
programme involved isotropic loading tests, proportional (constant η) loading tests and conventional shear tests (with radial net stress held constant). Simulations were performed at a stress point level with both the new ABBM and with the conventional BBM. In both cases, two versions of the model were employed, with either a linear or a non-linear variation of cohesion intercept with suction (Eqs. 9 and 10 respectively). For the ABBM simulations the associated flow rule of Equation 3 was employed, whereas the non-associated flow rule suggested by Alonso et al. (1990) was used in the BBM simulations. Parameter values employed in the simulations were selected using all the experimental data from Cui & Delage (1996) and are presented in Table 1. For the ABBM, the value of the parameter μ was determined using the empirical method suggested by Wheeler et al. (2003). In the absence of direct evidence on the value of the parameter b, a value of unity was selected (rather than using the indirect procedure for selecting a value for b suggested by Wheeler et al. 2003). The simulations presented here focus on two issues: the ability of the models to match the shape and size of the yield surface produced by one-dimensional compaction and the prediction of stress-strain behaviour during constant suction shearing. 3.1 Yield surface prediction from compaction procedure The samples of Jossigny silt were one-dimensionally compacted in a mould under an average vertical net stress of 840 kPa (the value varied slightly between samples). The suction after removal of the compaction load was measured at 200 kPa. Experience on other compacted soils suggests that the suction probably changed very little during removal of compaction load, and it was therefore assumed that the same suction of 200 kPa was present when the vertical compaction stress was applied. To calculate the values of mean net stress p and deviator stress q applied during compaction, it was necessary to estimate the value of horizontal net
627
stress induced during compaction. For the ABBM simulations, the value of horizontal net stress was estimated by assuming that the value of ηα during one-dimensional compaction (at a suction of 200 kPa) was the same as the saturated normally consolidated K0 value of stress ratio η (calculated by assuming K0 = 1 − sinφ = (6 − 2M )/(6 + M )). For the BBM simulations an equivalent assumption was made. This resulted in slightly different sets of estimated p and q values during compaction for the different simulations, depending on the model used and on the assumed value of α in the ABBM simulations (see below). Knowing the values of p and q applied during compaction, it was possible to fit the ABBM yield curve expression of Equation 1 through the compaction stress point and hence calculate a value of yield curve size pm (s) at a suction of 200 kPa. To do this, a value had to be assumed for the yield curve inclination α induced by the one-dimensional compaction process. Wheeler et al. (2003) presented a method for calculating the value of αK0 , produced by K0 consolidation of a saturated clay under normally consolidated conditions. This procedure has now been well validated for a range of soft saturated clays, but it is unlikely to be valid for one-dimensional compaction under unsaturated conditions, because the ABBM predicts that the resulting value of α would also be affected by any change of suction occurring during the application of compaction load. Different values of α were tried, in order to examine the fit with the experimental yield curve data. The value that was selected as giving the best match (α = 0.75) is much higher than the value of saturated αK0 = 0.42 calculated according to the method proposed by Wheeler et al. (2003). Having calculated the value of pm (s) at a suction of 200 kPa, it was then possible to use the LC yield curve expression of Equation 2 to calculate the sizes of yield curves at different values of suction and hence the complete form of the yield surface. An equivalent procedure was used with the BBM. Figure 2a shows the predicted BBM yield curves (assuming a conventional linear variation of cohesion intercept with suction) for the four experimental values of suction. Also shown are the corresponding experimental yield points, as reported by Cui & Delage (1996). The experimental yield points were taken from isotropic loading, constant η and conventional shear tests. Interpretation of yield points from experimental data generally involves significant subjectivity, and therefore all experimental yield data should be viewed with a degree of caution. It is, however, clear from Figure 2a that, as expected, the isotropic BBM is unable to provide a good match to the experimentally observed yield curves. Figure 2b shows the predicted ABBM yield curves (assuming a non-linear variation of cohesion intercept
Figure 2. Comparison of yield surface model predictions with experimental yield points: (a) BBM; (b) ABBM with α = 0.75.
with suction) for the case α = 0.75. This provides a significantly better match to the experimental yield points than the BBM model, although yield stresses still appear to be over-predicted by the ABBM. The experimental yield points measured during isotropic loading were probably the most reliable. Figure 3 therefore examines the ability of the two models to match these isotropic yield points. The BBM (curve (a)) grossly overpredicts the yield points observed during isotropic loading (see also Fig. 2a). The ABBM with α = 0.75 (curve (c)) predicts substantially lower isotropic yield stresses (the effect is less marked with α = αK0 = 0.42, see curve (b)). Even with α = 0.75, however, the ABBM still overpredicts the experimentally observed isotropic yield stresses (see also Fig. 2b). The final curve in Figure 3 (curve (d)) shows the ABBM prediction with α = 0.75 but with a lower value of critical state stress ratio Me = 0.9 assumed in triaxial extension. This lower value Me has been used in the yield curve expression for the part of the yield curves below the vertical tangent points A and B (see Fig. 1), as suggested by
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Figure 3. Comparison of model predictions with experimental yield points measured during isotropic loading; dashed lines linear cohesion intercept, solid lines non-linear intercept.
Figure 5. Variation of specific volume with mean net stress during constant suction shearing: (a) s = 200 kPa; (b) s = 800 kPa.
shows that the combination of a lower Me value and α = 0.75 allows the ABBM to provide an excellent match to the experimentally observed isotropic yield stresses.
3.2
Figure 4. Variation of deviator stress with shear strain during constant suction shearing: (a) s = 200 kPa; (b) s = 800 kPa.
Wheeler et al. (2003), whereas the triaxial compression value Mc = 1.1 has been retained for the upper part of the yield curves, above the vertical tangent points. Use of a lower value of M in triaxial extension than in triaxial compression is consistent with expected behaviour for all soils. Inspection of Figure 3
Predicted behaviour during shearing
All constant suction shear tests reported by Cui & Delage (1996) have been simulated with the ABBM and the BBM. Two tests are shown here as examples. Both tests were conducted at a constant net radial stress of 200 kPa, with the first test at a suction of 200 kPa and the second at a suction of 800 kPa. For the ABBM simulations an initial yield curve inclination of α = 0.75 was assumed, and a single value of M = 1.1 was used for the entire yield surface. The initial value of po (0) (for the BBM) or pm (0) (for the ABBM) was selected to provide a best fit to the measured isotropic yield stresses at the 4 values of suction. This would be a common practice in selecting an appropriate initial state for numerical simulations. Figure 4 shows the variation of deviator stress with shear strain for the two example tests. Inspection of Figures 4a and 4b shows that the use of a non-linear variation of cohesion intercept with suction provides a
629
simulations, in terms of both the yield stress and the final magnitude of the change of v during shearing. Again, however, the form of immediate post-yield behaviour predicted by the ABBM is unrealistic, as a consequence of the initial softening described in the previous paragraph. Figure 6 shows plots of volumetric strain against shear strain for the two example shear tests. The best match to the experimental results is produced by the ABBM with a non-linear variation of cohesion intercept with suction.
4
Figure 6. Variation of volumetric strain with shear strain during constant suction shearing: (a) s = 200 kPa; (b) s = 800 kPa.
significant improvement in the prediction of the final critical state values of deviator stress. In Figures 4a and 4b the yield stresses predicted by the ABBM are significantly higher than those predicted by the BBM, and this provides a better match to the observed behaviour, which is relatively stiff up to high values of q. The ABBM predictions of immediate post-yield behaviour are however a poor match to observed behaviour. In particular, the ABBM simulations at a suction of 800 kPa (Fig. 4b) show a small drop of deviator stress immediately post-yield, which is not seen in the experimental results. The unrealistic immediate post-yield softening in some of the ABBM simulations is mainly a consequence of the selection of an initial value of α much higher than the final critical state value αcs . The precise form of the yield curve expression of Equation 1 together with the flow rule of Equation 3 and the rotational hardening law of Equation 6 also contribute to the unrealistic prediction of immediate post-yield softening, and the validity of all three requires further investigation for unsaturated conditions. Figure 5 shows the variation of specific volume v with mean net stress p during the shearing stages of the two example tests. Inspection of Figures 5a and 5b shows that the ABBM simulations provide a better match to the experimental results than the BBM
CONCLUSIONS
Simulations with the new ABBM and the conventional BBM have been compared with experimental data from tests on compacted Jossigny silt reported by Cui and Delage (1996). The comparisons show that the ABBM is able to provide a much better match than the BBM to the observed shape and size of the yield surface produced by one-dimensional compaction. To provide a good match, the compaction-induced value of yield curve inclination α used in the ABBM must be much greater than would be predicted for K0 consolidated saturated samples of the same soil. Using a high value of α and different values of critical state stress ratio M in triaxial compression and triaxial extension, the ABBM is able to provide an excellent match to the values of yield stress observed during subsequent isotropic loading, whereas the isotropic yield stresses are grossly overpredicted by the BBM. Simulations of constant suction shear tests generally show better predictions from the ABBM than from the BBM. Final critical state values of deviator stress are best predicted by assuming a non-linear variation of cohesion intercept with suction (this feature can be incorporated in either the ABBM or the BBM). Yield stresses during shearing are better predicted by the ABBM than the BBM, and the magnitudes of volumetric strain during shearing are best predicted by the ABBM with a non-linear variation of cohesion intercept with suction. ABBM simulations of constant suction shearing sometimes show unrealistic softening in the immediate post-yield response. Final recommendations on the best forms for the ABBM yield curve expression, the flow rule and the rotational hardening law, which could address this problem, will require comparisons with experimental data from other unsaturated soils. Overall, the results presented here suggest that incorporation of anisotropy in elasto-plastic constitutive models for unsaturated soils may result in significantly improved predictions, but further work is required to finalise aspects of a fully realistic model.
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ACKNOWLEDGEMENTS The support of the European Commission via ‘MarieCurie’ Research Training Network contract number MRTN-CT-2004-506861 is gratefully acknowledged. REFERENCES Alonso, E.E., Gens, A., Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430.
Cui, Y.-J., Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Géotechnique 46(2): 291–311. Gan, J.K.M., Fredlund, D.G., Rahardjo, H. 1988. Determination of the shear strength parameters of an unsaturated soil using the direct shear test. Can. Geotech. J. 25(3): 500–510. Graham, J., Noonan, M.L. and Lew, K.V. 1983. Yield states and stress-strain relations in natural plastic clay. Can. Geotech. J. 20: 502–516. Wheeler, S.J., Näätänen, A., Karstunen, M., Lojander, M. 2003. An anisotropic elastoplastic model for soft clays. Can. Geotech. J. 40: 403–418.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
An elasto-viscoplastic model for chalk including suction effects F. Collin Université de Liège (FNRS, Department ARGENCO), Belgium
V. De Gennaro & P. Delage Ecole des Ponts, Paris (Université Paris-Est, Navier Institute – CERMES), France
G. Priol Arcadis, Paris, France
ABSTRACT: During the six years long Pasachalk project devoted to the mechanical behaviour of high porosity chalks from North Sea oilfields, the constitutive model Pasachalk (Collin et al., 2002) was proposed based on the Barcelona Basic Model (BBM) (Alonso et al., 1990). The approach was based on the similarities found between the oil-water interactions (oil and water being the non wetting and wetting fluid respectively) in oil reservoir chalk and the air-water interactions in unsaturated soils. This approach appeared to be relevant to interpret the subsidence of the seafloor during waterflooding operations for enhanced oil recovery that has been observed in North Sea oilfields (e.g. Ekofisk oilfield). Another important component of subsidence was then related to the creep behaviour of the multiphase chalk (De Gennaro et al., 2003). A modified Pasachalk model was proposed to account for time effects using the framework of Perzyna’s viscoplasticity (1964) but without considering suction effects. Based on available experimental results (Priol et al., 2007), a modified version of the viscoplastic Pasachalk model including suction effects is proposed in this paper.
1
INTRODUCTION
The mechanical behaviour of chalk has been extensively studied since the early eighties, in particular with regard to the behaviour of oil reservoir chalks in the North Sea (Ekofisk oilfield, see Hermansen et al., 2000, Nagel 2001). More recently, the risk assessment of the long-term stability of chalk pillars in mineworkings has been considered. In both situations, two poorly miscible pore fluids of different wettabilities are contained by chalk: water and oil in reservoir chalks and water and air in continental chalks from mines and quarries. In multiphase chalks, the partial saturation can change with time. The water saturation in oil reservoir chalks can increase due to reservoir enhanced exploitation by waterflooding (e.g. Ekofisk oilfield). Water saturation changes in mine chalks can be a consequence of the combined effects of changes in water table and in the hygrometry of the mine. Like in unsaturated soils, it has been showed that changes in partial saturation have an influence on the mechanical response of chalk, the higher the degree of water saturation, the higher the compressibility and the lower the strength (water weakening effect). In oil reservoirs, mines and quarries, the overburden formations apply long term hydro-mechanical loadings,
resulting in creep, a behaviour feature particularly pronounced in chalks. Some recent experimental and theoretical approaches carried out on partially saturated chalks have confirmed the relevance of some concepts of the mechanics of unsaturated soils to multiphase chalk behaviour, as suggested by Delage et al. (1996). Collin et al. (2002) proposed a modified version of the Barcelona Basic Model (BBM, Alonso et al., 1990) called Pasachalk model to model the behaviour of oil reservoir chalks. This model was extended to include viscoplastic behaviour of reservoir chalk but this latter model did not take implicitly the suction effect into account (De Gennaro et al., 2003). The effects of the oil-water suction on the time dependent behaviour of reservoir chalks has only been partially explored up to now. In this regard, recent findings (Priol, 2005; Priol et al., 2007) from oedometer tests carried out on chalk samples seem to suggest that the delayed strain of chalk is well correlated with the over-stress ratio (i.e. the ratio between the actual stress and the yield stress). Based on these findings and on other available results, a modified version of the viscoplastic Pasachalk model including oil-water suction effects is proposed in this paper.
633
2
EXPERIMENTAL EVIDENCE OF CREEP IN CHALK
Priol (2005) and Priol et al. (2007) reported results of oedometer compression tests carried out on Lixhe chalk (an outcrop chalk from Belgium) saturated with oil, with water, partially saturated and dry (Fig. 1). By analyzing the evolution of the creep curves obtained during multiple step loading tests, it was suggested to consider the following rheological law to fit the experimental data: e = βi t −αcr eoi
(1)
where e is the void ratio, eoi the initial void ratio, t the time, βi a coefficient accounting for the instantaneous
NORMALISED VOID RATIO e/eo
1
0.9
settlement and αcr for the time dependent settlement. The evolution of αcr is directly related to the creep behaviour of chalk (Fig. 2). One can observe that the amount of creep is both stress and suction dependent, the higher the wettability of chalk, the larger the amount of creep.
3
MODEL FORMULATION
Perzyna’s viscoplastic approach (Perzyna, 1964) has been adopted because it is based on a framework similar to that of elastoplasticity, facilitating further time-dependent developments of the elastoplastic Pasachalk model. Various viscoplastic models have been formulated adopting the Bjerrum’s notion of equivalent (or reference) time (e.g. Bjerrum, 1967; Borja & Kavazanjian, 1985; Hickman & Gutierrez, 2007). Other models have used the concept of the Non Stationary Flow Surface (NSFS) theory (e.g. Nova, 1982; Liingaard et al., 2004). A recent review of the literature is given by Liingaard et al., (2004). The Pasachalk model (Collin et al., 2002) is a cap model with a yield surface composed of three components: (i) Cam-Clay pore collapse model The Cam-Clay yield surface is adopted at low stress inclinations, with the following expression: 3c(s) f1 ≡ IIσˆ2 + m2 Iσ + (Iσ − 3p0 ) = 0 tan φC
0.8
DRY SAMPLE OIL SATURATED SAMPLE s = 200 kPa WATER SATURATED SAMPLE 0.7 100
1000
10000
100000
VERTICAL STRESS (kPa)
Figure 1. Oedometer compression tests on Lixhe chalk at various saturation states (Priol et al., 2007).
where Iσ and II σ are the first and second stress invariants, c is the cohesion, φC is the friction angle in compression path, p0 is the apparent pre-consolidation pressure that defines the size of the yield surface and m is a coefficient taking into account the effect of the Lode angle β. The coefficient m is defined by: m = a (1 + b sin 3β)n
0.02
B 0.016
WATER SATURATED
WATER SATURATED S S = 200 kPa OIL SATURATED SAM SAMPLE sDRY = 200 kPa
Water infiltration 0.008
0.004
(3)
where parameters a, b and n must verify some convexity conditions (Van Eekelen, 1980). Assuming associated plastic flow, the apparent preconsolidation pressure p0 is related to the volumetric plastic strain dεvp following the kinematic equation:
0.012
A
(2)
OIL SATURATED
dp0 =
1+e p0 dεvp λ−κ
(4)
DRY
0 0
10000
20000
30000
VERTICAL STRESS (kPa)
Figure 2. Influence of stress level and suction on the creep coefficient αcr (Priol et al., 2007).
where λ is the compression coefficient and κ is the elastic coefficient. Expression (4) allows both hardening or softening behaviour to be accounted for according to the sign of the volumetric plastic strain. However the softening zone will not be considered here. It can also be
634
noted that the irreversible volumetric strain includes the coupled effect of mechanical and suction changes. (ii) Internal friction model In order to formulate a friction model based on a MohrCoulomb type failure criterion with a smoothed plastic surface, Van Eekelen’s (1980) formulation has been adopted. It is based on a modification of DruckerPrager’s failure cone by introducing a dependence on Lode’s angle β, leading to the following expression of the failure criterion: 3c(s) f2 ≡ IIσˆ − m Iσ + =0 (5) tan φC An associated plasticity is considered also for the friction mechanism. (iii) Suction effect on yield surface (BBM model) Several phenomena are typical of unsaturated soils: – The yield stress p0 and the material stiffness increase with suction. In BBM this is described by the LC curve, the formulation of which has been adapted for chalk as follows: p0 (s) = p0 (0) + p0
s s + s∗
(6)
where p0 (0) is the yield stress for s = 0, p0 is the variation of p0 between water and oil saturated sample and s∗ is a parameter controlling the shape of the LC curve. – Cohesion increases with suction. This is modelled using Eq. (7). c(s) = c(0) + k s
(7)
where k is a material constant, c (0) is the cohesion at water saturated state. Note that in chalk, experiments showed that the friction angle is independent of the saturating fluid. Mechanical elastoviscoplastic model Viscous effects in chalk may be observed in triaxial tests performed at various stress rates and/or involving creep stages (Pasachalk2, 2004). The timedependent behaviour of chalk is introduced here based on the elastoviscoplastic approach proposed by Perzyna (1964). Hence, strains are divided into reversible and irreversible parts (related mechanical and suction loading): m,vp
ε˙ ij = ε˙ ijm,e + ε˙ ijs,e + ε˙ ij
s,p
+ ε˙ ij
time-dependent. The following relationship is taken [Alonso et al., 1990]: ε˙ ijs,e =
κs s˙ δij = heij s˙ (1 + e) (s + pat )
(9)
The stress increment can thus be expressed as follows: σ˙ = C e (s) (˙ε − ε˙ s,e − ε˙ m,vp )
(10)
Since only the irreversible behaviour is timedependent, the elastic moduli of the Pasachalk model can be kept. The values of the moduli defining Hooke’s law are recalled in Table 1. The elastic parameters are suction dependent. The following linear expressions (Pasachalk 2, 2004) have been chosen for the volumetric and shear moduli as a function of suction: K(s) = K(0) + ks · s
(11)
G(s) = G(0) + gs · s
(12)
where K(0) and G(0) are the elastic moduli for a nul suction (water saturated condition), ks and gs are equal to 38 and 66.7 respectively to model the increase of stiffness with the suction. The irreversible strain may be described as normal to some potential g: ε˙ m,vp = γ φ(f )
∂g ∂σ
(13)
This formulation is similar to the elastoplastic one, but it is not based on the consistency condition. The amount of strain rate is described with respect to a reference surface f , similar to the yield surface. Then, one may define two irreversible mechanisms, one dedicated to the pore collapse mechanism named fc , the second one to friction failure named fd . The reference surfacefc has the same equation as f1 in the Pasachalk model. The reference surface actually represents the elastoplastic yield surface defined based on a hypothetical experiment with an infinitely low strain rate. The function fc may help to define the overstress, as a measure of the amount of the stress state going outside the reference surface. Table 1.
Elastic parameters (Collin et al., 2002). Water
Oil
612 500 1180 0.18
726 700 1590 0.14
(8)
It has been observed that suction variations do not evolve permanent strains. Moreover, it is assumed that reversible strains related to suction are not
K [MPa] G [MPa] E [MPa] ν [−]
635
Concerning the pore collapse mechanism, the creep potential is based on the following equations: φc (fc ) =
Table 3.
αc
pd0 vp − 1 p0
(14)
and (Shao et al., 1993): γ =ω
Iσ pa
Pre-consolidation Parameter αc Parameter ω Parameter ι
vp p0
[MPa]
Water
Oil
2 5 5.1 10−9 0,0
5 5 5.1 10−9 0,0
ι (15)
where the viscous parameters are: γ , the fluidity parameter, ω, pa and ι, the parameters defining the influence of stress on the fluidity parameter and αc , the exponent of the visco-plastic strain relation (14). The parameters defining the yield surface of the elastoplastic model for a stress rate of 10−3 MPa/s are given in the Table 2. The viscous parameters concern mainly the pore collapse mechanism because the failure criterion is assumed to be time-independent. Hence, only the viscous parameters γ (fluidity parameter), the reference surface fc and the exponent αc of visco-plastic strain relation have to be determined. As shear failure is assumed to be time independent, the reference surface fc related to pore collapse only depends on the apparent viscoplastic prevp consolidation pressure p0 . Experiments have shown that the pre-consolidation pressure depended directly on the stress-rate. This relation is not defined directly in the model: the effect of rate dependence comes as a result of the chosen visco-plastic formulation. vp The p0 value and the other viscous parameters have been determined by trial and error process in order to fit isotropic compression tests on saturated chalk (oil and water), with loading rate ranging between 5 × 10−5 and 10−2 MPa/s (Pasachalk 2, 2004). Within the assumed loading rate range the final values of all parameters are given in Table 3. Note that, in agreement with the notion of overstress, it is not necessary to chose different values of viscous parameters (α, ω, ι) for oil or water saturated samples, as the influence of suction is taken into account through the apparent pre-consolidation pressure. For intermediate degrees of saturation, the LC curve adopted is similar to that used in the elastoplastic vp vp model, using Eq. (6) with p0 = 3 MPa, p0 (0) = 2 Table 2. model.
Viscous parameters of the model.
Yield surface parameters of the elastoplastic
Friction angle φ [◦ ] Cohesion c [MPa] Pre-consolidation p0 [MPa] Compressibility index λ
Water
Oil
22 1.5 10 0.195
22 2.0 21 0.195
MPa et s∗ = 0.2 MPa. It is important to notice that the same value of the compressibility index λ has been used for the definition of the hardening law of the viscoplastic model.
4
ASSESSMENT OF THE VISCOUS PARAMETERS
One of the major shortcomings associated with Perzyna’s approach is the definition of the viscous parameters and of the reference surfaces, which are usually found by a trial and error process and not directly experimentally determined. In order to link more directly the parameters to experimental measurement the results of CRS (Constant Rate of Strain) oedometer compression tests at different strain rates and suction (water or oil saturated, 200 kPa suction and dry samples) are first analysed (Priol, 2005; Priol et al., 2007). It was observed that for a given suction the yield limit (i.e. apparent pre-consolidation pressure) is a function of the imposed strain rate, as already shown in clays by Leroueil et al. (1985). The following relationship coupling the yield limit and the strain rate proposed by Leroueil appeared to fit reasonably data obtained on Lixhe chalk: log10 (σp ) = A +
1 log10 (˙ε1 ) m
(16)
where σp is the yield limit, ε˙ 1 is the strain rate and A and m two material parameters. Table 4 summarizes the values of A and m obtained for Lixhe chalk. Equation (16) describes a linear relationship between yield limit and strain rate in a log10 (σp ) : log10 (˙ε1 ) plot. It is worth noting that values of m depends now also on suction (Tab. 4). In other words the slope of the linear relationship (16) increases when suction decreases. This is a new further coupling which extends the original Leroueil’s relationship. Equation (16) gives the opportunity to define the size of the reference surface defined as the elastoplastic yield surface based on a hypothetical experiment with an infinitely low strain rate. Considering an extremely low strain rate (10–13 s−1 ), the yield stress of the reference surface
636
Table 4.
0.020
Material parameters of Leroueil’s law.
0.018
A
m
4,462 4,516 4,451 4,499
9,25 10,9 16,66 22,2
0.016 0.014 0.012 αcr [-]
Water s = 200 kPa Oil Dry
Water
0.010
Oil
0.008
Suction 0.006
Dry
0.004 0.002 3.5
0.000 0
3
2
4
6 8 Normalized stress [-]
10
12
14
Suction [MPa]
2.5
Figure 4. Influence of ‘‘normalized’’ stress level and suction on the creep coefficient αcr (Priol et al. 2007).
Experimental data
2
LC curve
1.5
Table 5. Viscous parameters of the model for unsaturated conditions.
1 0.5
Water
0 0
1
2
pvp 0
Figure 3.
3
4
5
[MPa]
vp
LC curve of the reference surface.
for the different suction conditions could be defined, together with the LC curve of the viscous reference surface (Fig. 3). Viscous parameters should now to be linked to the βi and αcr parameters of equation (1). Figure 2 shows a first discrepancy between the evolution of αcr and the viscous parameters of the model. Indeed Figure 2 does not show a unique relation between αcr and the stress state for the different saturation conditions. On the other hand, it is not necessary to chose different values of viscous parameters for oil or water saturated samples. The influence of suction is only taken into account through the LC curve. The apparent contradiction can be explained by inspecting Figure 2. One can observe that the creep parameter αcr remains very low up to a threshold that depends on the saturation conditions. Above the threshold, parameters follow a more or less linear relationship with slopes also depending on the saturation conditions. However, if the stress value is normalized with the apparent pre-consolidation pressure of each test as presented in Figure 4, the observed behaviour becomes reasonably independent of the saturation conditions. It would be interesting to find a direct relationship between the αcr and βi parameters of equation (1) and the ω and αc parameters of the viscous model (Equation 13). Unfortunately, it was not possible to find such a relationship analytically. The main reason is that equation (1) defines the total creep strain and the viscous strain rate is modelled through equation (13). Moreover, the analytical integration of the
Pre-consolidation p0 [MPa] at s = 0 MPa vp Parameter p0 [MPa] Parameter s∗ [MPa] Parameter αc Parameter ω
1,143 4 0.5 5 5,1 10−9
viscous model is not possible for any values of the material parameters. It was thus decided to keep the first estimation of the two viscous parameters for the modelling of the multi-stage loading tests.
5
NUMERICAL MODELLING
Some experimental results obtained by Priol (2005) by running creep oedometer tests under different suction conditions (water saturated, oil saturated and suction equal to 200 kPa) are reported in Figure 5 in terms of strain versus time curves. One can clearly see in the figure the various loading steps and the creep deformations under different applied stresses. With the single set of parameters and the proposed visco-plastic model, the three tests have been modelled. Figures 6–8 show satisfactory agreement between experimental data and numerical predictions. It should be emphasised that, besides creep tests, the collapse experiment can also be modelled by the proposed constitutive law. Indeed, during waterflooding, the suction is decreasing as well as the pre-consolidation pressure following the LC curve. This means that the overstress is growing during waterflooding, leading to an increase of the viscous creep deformation.
637
0.14
0.02 0.018
0.12
0.016 0.014
0.08
Strain [-]
Strain [-]
0.1
Water Oil Suction
0.06
0.012 0.01 0.008
Step 6 Modelling (6) Step 7 Modelling (7) Step 8 Modelling (8)
0.006
0.04
0.004 0.02
0.002 0 0
500
1000
1500
2000
2500
3000
3500
4000
0 0.0E+00
4500
2.0E+05
4.0E+05
6.0E+05
Time [hour]
Figure 5. Multiple stage loading tests for different saturation conditions (Priol, 2005).
0.05 0.045 0.04 0.035 Strain [-]
8.0E+05
1.0E+06
1.2E+06
1.4E+06
Time [s]
0.03 Step 13
0.025
Modelling (13) 0.02
Step 12
0.015
Modelling (12)
0.01 0.005 0
0.0E+00 1.0E+06 2.0E+06 3.0E+06 4.0E+06 5.0E+06 6.0E+06 7.0E+06 8.0E+06 9.0E+06 1.0E+07
Time [s]
Figure 6. Numerical modeling of creep phase for water saturated chalk samples.
0.04 0.035 0.03
Figure 8. Numerical modeling of creep phase for unsaturated chalk samples (s = 200 kPa).
significant creep deformations. The Pasachalk elastoplastic model (Collin et al., 2002) derived from the Barcelona Basic Model for multiphase reservoir chalk has been extended to account for time effects and creep behaviour as a function of suction. Some experimental results of multiple stage loading tests carried out on Lixhe chalk under different suction conditions showed that the results obtained under various suctions could be summarized into a single normalized curve. The relevant viscous parameters of the model were determined based on these experimental results, without using a trial and error method. This has only been possible for the definition of the viscous reference surface. We did not succeed to find an analytical relationship between the parameters of the viscous model and the constitutive law. By using one single set of parameters, different creep experiments under various suction conditions were simulated, with a satisfactory agreement between experimental data and numerical predictions.
Strain [-]
0.025 Step 7 0.02
Modelling (7)
ACKNOWLEDGMENTS
Step 8
0.015
Modelling (8) Step 10
0.01
The authors thank the FNRS for its financial support during the stay of the first author in CERMES.
Modelling (10)
0.005 0 0.0E+00
1.0E+06
2.0E+06
3.0E+06
4.0E+06
5.0E+06
6.0E+0
Time [s]
REFERENCES
Figure 7. Numerical modeling of creep phase for oil saturated chalk samples.
6
CONCLUSIONS
High porosity chalks have a complex mechanical behaviour that depends on chalk porosity, mineralogy, pore fluids, of temperature and of time with
Alonso, E.E., Gens A. and Josa A. 1990. A constitutive model for partially saturated soils. Géotechnique 40 (3): 405–430. Bjerrum, L. (1967): Engineering geology of Norwegian normally-consolidated marine clays as related to settlement of buildings. Géotechnique, 17: 81–118. Borja, R.I., Kavazanjian, E. 1985. A constitutive model for the stress—strain-time behaviour of wet clays. Géotechnique, 35 (3): 283–298.
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Collin F., Cui Y.J., Schroeder C. and Charlier R. 2002. Mechanical behaviour of Lixhe chalk partly saturated by oil and water: experiment and modelling. J. Num. Analytical Meth. In Geomechanics, 26, 897–924. De Gennaro V., Delage P., Cui Y.C., Schroeder Ch. & Collin F. 2003. Time-dependent behaviour of oil reservoir chalk: a multiphase approach. Soils and Foundations, 43 (4), 131–148. Delage P., Schroeder C. & Cui Y.J. 1996. Subsidence and capillary effects in chalks. Proc. EUROCK’96 Conf., vol. 2, 1291–1298, Torino, Italy. Hermansen H., Landa G.H., Sylte J.E. & Thomas L.K. 2000. Experiences after 10 years of waterflooding the Ekofisk field, Norway. J. of Petroleum Science and Eng., 26, 11–18. Hickman, R.J. & Gutierrez, M.S. 2007. Formulation of a three-dimensional rate-dependent constitutive model for chalk and porous rocks. Int. J. of Numerical and Anal. Meth. in Geomechanics, 31 (4): 583–605. Leroueil S., Kabbaj M., Tavenas, F. and Bouchard, R. 1985: Stress-strain-strain rate relation for compressibility of sensitive natural clays. Géotechnique 35 (2): 159–180. Liingaard M., Augustesen P. & Lade P.V. 2004. Characterization of Models for Time-Dependent Behavior of Soils. Int. J. of Geomechanics ASCE, 4 (3): 157–177. Nagel N. 2001. Ekofisk geomechanics monitoring, Int. Workshop on Geomechanics in Reservoir Simulation, IFP, Reuil-Malmaison, France.
Nova, R. 1982. A viscoplastic constitutive model for normally consolidated clays. Proc. IUTAM Conf. on Def. and failure of Granular Materials, Delft 1982: 287–295. Pasachalk2. 2004. Mechanical Behaviour of PArtially and Multiphase SAturated CHALKs Fluid-skeleton Interaction : Main Factor of Chalk Oil Reservoirs Compaction and Related Subsidence, Part 2, Publishable Final report, European contract N˚ ENK6-CT2000-0008, Brussels. Perzyna, P. 1964. The constitutive equations for rate sensitive plastic materials. Quart. Appl. Mech., 20, 321–332. Priol G. 2005. Comportement mécanique d’une craie pétrolifère—comportement différé et mouillabilité. PhD Thesis, Ecole des ponts, Paris. Priol G., De Gennaro V., Delage P. and Servant T. 2007. Experimental investigation on the time dependent behaviour of a multiphase chalk. Experimental Unsaturated Soil Mechanics, Proc. Physics 112, Springer, T. Schanz (ed.), 161–167. Shao J.F., Bederiat M. and Schroeder C. 1993. A viscoplastic theory for soft rock behaviour and application. Proc. Geotech. Eng. Hard Soils—Soft Rocks Conf., Balkema. Van Eekelen H.A.M. 1980. Isotropic yield surfaces in three dimensions for use in soil mechanics. Int. J. Num. and Anal. Meth. in Geomechanics, 4, 98–101.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
New basis for constitutive modelling of unsaturated aggregated soil with structure degradation A. Koliji, L. Vulliet & L. Laloui Soil Mechanics Laboratory, Ecole polytechnique fédérale de Lausanne (EPFL), Switzerland
ABSTRACT: The paper deals with the unsaturated aggregated state of soils, a commonly occurring state in natural and engineered materials. These soils are characterized by a double porosity fabric and exhibit a strong interaction between the fabric and inter-particle bonding in their structure. A new baseline for a hardening elasto-plastic constitutive model for these materials is proposed which incorporates the combined effects of soil structure (fabric and inter-particle bonding) and partial saturation. It uses a generalized effective stress and the critical state concept in unsaturated soils. Based on multi-scale experimental evidences, a state parameter is introduced to quantify the soil structure. An expression of apparent preconsolidation pressure is presented with respect to the combined effects of soil structure and partial saturation that describes the extension of the yield limit in unsaturated aggregated soil compared with the corresponding saturated reconstituted soil. 1 1.1
INTRODUCTION Background
Aggregation of particles is a commonly observed phenomenon in natural and agricultural soils (Horn 2003), compacted clays at dry side of optimum water (Sridharan et al. 1971, Collins & McGown 1974) and compacted expansive clays (Lloret et al. 2003). However, size of aggregates in expansive and compacted clays are some orders of magnitude smaller than aggregates in natural or agricultural soils. Aggregated soils, in general, are characterized by a fabric with two dominant pore sizes corresponding to micro (intra-aggregate) and macro (inter-aggregate) pores. The presence of the aggregated structure and double porosity fabric was found to have a major influence on the water retention properties and hydraulic behaviour of both agricultural (Coppola 2000) and compacted clays (Romero et al. 1999). Moreover, the mechanical behaviour of the soil is reported to be significantly influenced by the inter-particle bonding effects (e.g., Leroueil and Vaughan 1990). When dealing with unsaturated soils in a hydromechanical process, the coupling between the mechanical and hydraulic behaviour of unsaturated soils as well as the factors influencing this behaviour are of significant importance, specially, if the constitutive stress of the model depends on the degree of saturation. An appropriate constitutive model for unsaturated aggregated soil, therefore, should
incorporate the combined effects of soil structure (fabric and inter-particle bonding) and partial saturation on the hydro-mechanical behaviour of the material. Increasing interest in understanding and modelling of the influence of soil structure on the mechanical behaviour of unsaturated soils, in particular expansive soils, has led to development of new constitutive models. The proposed models are aimed to describe the material behaviour with respect to the microstructure and double porosity fabric (Alonso et al. 1999, Sanchez et al. 2005). In these models, however, soil structure effects are considered only through the fabric effects and the interparticle bonding and its degradation are not essentially considered. Alternatively and in line with the experimental observations revealing the importance of soil structure effects on the mechanical behaviour of natural structured soils, improvements to constitutive models for these materials have been proposed by making explicit consideration of soil structure and its degradation (Rouainia & Wood 2000, Gens & Nova 1993, among others). Although many natural structured soils are unsaturated, few studies have considered the combined effect of partial saturation and inter-particle bonding on soil behaviour (Alonso & Gens 1994, Leroueil & Barbosa 2000). It is reported in these works that suction in bonded soils has two effects corresponding to capillary effects on soil matrix and strengthening of inter-particle bonds.
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1.2
2
Modelling approach
In aggregated soils, there is a strong interaction between the soil structure components, namely, soil fabric and inter-particle bonding. The macropores are retained by an aggregated structure and the openness of fabric depends on the size and strength of aggregated particle assemblages which are formed as a result of inter-particle bonding. The aim of this paper is to propose a baseline for a constitutive model capable of describing the behaviour of aggregated soils over a wide range of saturation conditions with explicit consideration of soil structure evolution. Based on multi-scale experimental evidences, the model is expected to unify the effects of inter-particle bonding, fabric and partial saturation in a single framework. The model is based on the framework of strain hardening elasto-plasticity. For the constitutive stresses the model adopts the matric suction, s, and a generalized effective stress which is the Bishop’s effective stress (Bishop 1959) with the Bishop’s parameter being equal to the degree of saturation, Sr . Accordingly, the relation between the so-called general effective stress tensor, σ , and the total stress tensor, σ , reads: σ = (σ − pa I) + Sr sI
(1)
where pa is the air pressure and I is the second order identity tensor. Although the representation of stress paths in this stress framework is rather complex, the transition from the saturated to the unsaturated state is smooth and straightforward. The critical state concept for unsaturated soils has been evaluated by different authors (Alonso et al.1990, among others). Khalili et al. 2004 successfully investigated the uniqueness of the critical state line (CSL) in the q−p plane (deviatoric stress versus mean effective pressure) for unsaturated soils with different suctions. They used the Bishop’s effective stress with a particular expression for the Bishop’s parameter. Uniqueness of the CSL in terms of generalized effective stress has been further evaluated by Nuth & Laloui (2007b). These authors reported the unification of the CSL in the stress space of q−p for unsaturated soils regardless of the suction level. Adopting the generalized effective stress as the constitutive stress, the general incremental stress-strain constitutive relation reads: dσ = Dep : dε
FEATURES OF BEHAVIOUR
An extensive oedometric testing programme has been carried out by the authors to evaluate the mechanical behaviour of aggregated silts at different saturation conditions. The main features of this behaviour are outlined here. Figure 1 shows the oedometric compression of an aggregated silt sample (average aggregate size of about 2 mm) and a sample of the corresponding reconstituted soil of the same mineralogy, both tested under the constant matric suction of 1500 kPa. The aggregated sample was initially in a normal consolidation state. However, an initial stiff behaviour followed by yielding was observed in the oedometric compression of this sample. The yield limit is here referred to as apparent preconsolidation stress, which is a function not only of stress state and stress history but also of soil structure. At a given value of applied stress, a sample of aggregated soil has a higher void ratio than reconstituted soil and the compression curve of aggregated soil is located to the right side of the reconstituted compression curve at the same suction. The compression curves of aggregated and reconstituted soils at the same suction tend to converge at higher values of applied effective stress. The main effect of suction in reconstituted samples was found to be the increase of effective apparent preconsolidation stress with suction. In structured samples, however, a combined effect of suction and soil structure was observed. In these samples, similar to reconstituted samples, a higher matric suction results in higher values of effective apparent preconsolidation stress. This is linked to the capillary effects. In addition to this
(2)
where ε is the strain tensor and Dep is the elastoplastic constitutive matrix. In this equation, symbol ‘:’ denotes the inner product of tensors with double contraction and d(.) denotes the incremental value.
Figure 1. Oedometric response of unsaturated aggregated (average aggregate size 2 mm) and reconstituted silt.
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structure and its degradation requires an internal parameter capable of representing the state of the material in relation to its initial intact condition. Accordingly, a state parameter called degree of soil structure is here introduced as the ratio of the current macro void ratio, to its initial value at intact state. On the basis of the pore-scale experimental observations, the evolution of the degree of soil structure has been found to be reasonably reproduced by a decreasing exponential function of plastic strain (Koliji et al. 2007): R = exp(−ωεD ) Figure 2. 3D neutron tomography volume of an aggregated silt sample (sample size 35 mm in height & 80 mm in diameter).
effect, the horizontal separation between the compression curve of structured soils and normal consolidation line of reconstituted soil in the oedometric compression space was found to increase with suction. This evidence shows that suction has a hardening effect on the inter-particle bonding in the soil structure. In addition to the macro scale experiments, the behaviour of the material and the soil structure at the pore-scale has been evaluated using a combination of different methods. Results of mercury intrusion porosimetry showed that unsaturated aggregated samples initially exhibit a multi-modal PSD with at least two dominant pore radii corresponding to micro- and macropores. At the same condition, a corresponding reconstituted soil exhibits a uni-modal PSD with the dominant pore radius coinciding with the micropores in structured samples. During a wetting or mechanical loading, however, aggregated samples undergo structure degradation and they end up with a structure identical to that of reconstituted soil. On the other hand, the advanced method of neutron tomography was employed for a 3-dimensional evaluation of soil structure modifications during the oedometric testing (Fig. 2). Results of these tests showed that changes in macroporosity are associated mainly with plastic strain. This important experimental finding has a major impact on the modelling of this phenomenon. 3 3.1
CONSTITUTIVE FRAMEWORK Degree of soil structure
At a given state for an aggregated soil, the macro void ratio (ratio of macropore volume over the solid volume) could represent the actual state of the soil structure with respect to its initial state and a fully reconstituted state. However, quantification of soil
(3)
where R is the degree of soil structure, εD is a combination of volumetric and deviatoric plastic strains, and ω is the parameter controlling the rate of structure degradation. The expression of the degree of soil structure given by Equation 3 provides an experimentally based relation which establishes a link between the pore-scale structure of the soil and the macroscopic behaviour of the material. 3.2
ACMEG-2S constitutive framework
The constitutive model ACMEG-2S, (Advanced Constitutive Model for Environmental Geomechanics, extension for unsaturated structured soils) is an elastoplastic model based on the critical state concept. It uses non-linear elasticity and two plastic mechanisms: one isotropic and one deviatoric. The plastic mechanisms are coupled through the volumetric plastic strain. The model adopts an isotropic plastic strain hardening with the volumetric plastic strain being the hardening parameter. The flow rule is associated for isotropic mechanism and could be associated or non-associated for the deviatoric mechanism. The limit of elasticity and the onset of plastic deformations in each mechanism are determined by the yield criterion corresponding to that mechanism: fiso = p − pc riso = 0 p d fdev = q − Mp 1 − b ln rdev = 0 pc
(4) (5)
In these equations, riso and rdev are degrees of mobilization of the isotropic and deviatoric plastic mechanisms and are hyperbolic functions of the plastic volumetric strain provoked by the isotropic mechanism and of the plastic deviatoric strain respectively. M , b and d are material parameters directly inherited from the saturated reconstituted soil and pc is the apparent effective preconsolidation pressure. The elastic region
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apparent preconsolidation suction effects: ⎧ ⎨ 1; ψs = 1 + γs log(s/se1 ); ⎩ 1 + γs log (s/se );
pressure due to primary if 0 < s < s1e if s1e ≤ s < sref if s ≥ sref
(8)
in which s1e and se are the air entry value suction of micropores and reconstituted soil respectively; and, γs and γs are two dependent material parameters. The relation between the two parameters γs and γs is derived from the second and third expression in Equation 8: Figure 3. model.
Yield surfaces and elastic region in ACMEG-2S
γs =
given by Equations (4) and (5) in the q − p plane is depicted in Figure 3. Detailed description of the model formulation will be presented elsewhere. Here attention is given to the evaluation of the apparent preconsolidation pressure and its evolution. Combining the effects of suction and soil structure, a general expression for the apparent preconsolidation pressure in unsaturated structured soils is: ∗
pc = ψ st ψ s pc0
(6)
∗
where pc0 is the reference effective preconsolidation pressure in saturated reconstituted soil, and, ψ st and ψ s are two functions which incorporate the effects of soil structure and of suction respectively. The preconsolidation pressure of saturated recon∗ stituted soil, pc0 , evolves according to a plastic strain hardening rule similar to the Cam-clay model (Roscoe & Schofield 1963): ∗
dpc0 =
ν ∗ p dεp λ∗ − k c0 ν p
(7)
where εν is the plastic volumetric strain, ν is the specific volume, and, λ∗ and k are material parameters for reconstituted soil. The primary effects of suction on the increase of effective preconsolidation pressure are of the same nature in reconstituted and aggregated soils and are taken into account by ψ s . These effects are linked to the capillary effects and depend on the geometry of the pores and the air entry value of the system of the pores. Adopting an approach similar to that presented by Nuth and Laloui (2007b), a reversible function is proposed to quantify the evolution of
log (sref /se1 ) γ log (sref /se ) s
(9)
In the expression of apparent preconsolidation pressure (Eq. 6), ψ st is a function of degree of soil structure and it controls the extension of yield limit with respect to the reconstituted reference state. At constant suction, the following evolution rule has been derived for this variable (Koliji et al. 2007): ψ st = exp[R ln ψist ]
(10)
where the subscript i designates the initial value. In the presence of suction variation, however, secondary effects of suction on soil structure should be considered in ψ st . The following relation is proposed to account for the additional effects of suction: s + pat nst st , ψist = 1 (11) ψ st = ψref sref + pat st is the value at the reference suction in which ψref sref and the exponent nst is a material parameter. The atmospheric pressure pat in the denominator is added to avoid infinite values when the saturated state (zero suction) is the reference state. The condition ψist = 1 limits the validity of this equation to the structured soils, in which the initial yield limit is basically influenced by the inter-particle bonding effects. Figure 4 plots the prediction of the proposed equation (bold line) and the experimental values of ψist for three unsaturated aggregated silt and the corresponding reconstituted samples (dots). With a reference suction of 500 kPa and nst = 0.375, this relation appears to successfully reproduce the experimental data. Double effects of suction on the apparent preconsolidation pressure in structured soils are illustrated in Figure 5. In this figure, the abscissa is the ratio of apparent preconsolidation pressure over the saturated preconsolidation pressure in reconstituted sate ∗ (pc /pc0 ). The increase of apparent preconsolidation
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Figure 4. Influence of suction on the soil structure parameter.
combined effects of partial saturation and soil structure, have been reviewed on the basis of multi-scale experimental evidences. The constitutive framework, ACMEG-2S, based on the critical state concept was presented within the framework of strain hardening elasto-plasticity. The model adopts the generalized effective stress to describe the material behaviour in different conditions of saturation. A new state parameter called degree of soil structure is introduced to quantify the soil structure and its evolution. This parameter establishes the pore-scale information of the soil to the macroscopic response in terms of plastic strains. The apparent preconsolidation pressure, as the main parameter controlling the yield limit, was formulated with respect to the combined effects of partial saturation and soil structure. The proposed modelling approach provides a logical unification of the effects of inter-particle bonding, fabric and partial saturation in a single framework.
REFERENCES
Figure 5. Combined effects of suction and soil structure on the apparent isotropic preconsolidation pressure.
pressure due to intrinsic suction effect ( ψ1 ) is represented by curve a. Multiplication of this curve with a st reference soil structure function ψref gives the curve b which represents the increase in the apparent preconsolidation pressure due to intrinsic suction ( ψ1 ) and pure soil structure effects ( ψ2 ) without considering the suction-hardening of soil structure. Accounting for this latter effect by Equation 11, the final evolution of apparent preconsolidation pressure with suction in structured soils is represented by curve c. The gray area between curve b and c ( ψ3 ) corresponds to the effects of suction on the soil structure given by Equation 11. This effect is a hardening effect for suctions beyond sref and a softening effect for suction below this suction.
4
CONCLUSIONS
The main features of the mechanical behaviour of unsaturated aggregated soils, stemming from the
Alonso, E. and Gens, A. 1994. Keynote lecture: on the mechanical behaviour of arid soils. In Conference on Engineering Characteristics of Arid soils. London, pp. 173–205. Alonso, E.E., Gens, A. and Josa, A. 1990. A constitutive model for partially saturated soil. Géotechnique 40(3): 405–430. Alonso, E.E., Vaunat, J. and Gens, A. 1999. Modelling the mechanical behaviour of expansive clays. Engineering Geology 54: 173–183. Bishop, A.W. 1959. The principle of effective stress. Tecknish Ukeblad 106: 859–863. Collins, K. and McGown, A. 1974. The form and function of microfabric features in a variety of natural soils. Géotechnique 24(2): 223–254. Coppola, A. 2000. Unimodal and bimodal descriptions of hydraulic properties for aggregated soils. Soil Science Society of America Journal, 64(4): 1252–1262. Gens, A. and Nova, R. 1993. Conceptual bases for a constitutive model for bonded soils and weak rocks. In A. Anagnostopoulos, F. Schlosser, N. Kalteziotis & R. Frank (eds), Geotechnical Engineering of Hard Soils— Soft Rocks: 485–495. Rotterdam: Balkema. Horn, R. 1993. Mechanical properties of structured unsaturated soils. Soil Technology 6: 47–75. Khalili, N., Geiser, F. and Blight, G.E. 2004. Effective stress in unsaturated soils: Review with new evidence. International Journal of Geomechanics 4(2): 115–126. Koliji, A., Vulliet, L. and Laloui, L. 2007. Soil structure evolution: Experimental and constitutive consideration. In Edited by G.N. Pande & S. Pietruszczak (eds), Numerical models in geomechanics, NUMOG X: 133–138. Balkema. Leroueil, S. and Vaughan, P.R. 1990. The general and congruent effects of structure in natural soils and weak rocks. Géotechnique 40(3): 467–488.
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Leroueil, S. and Barbosa, A. 2000. Combined effect of fabric, bonding and partial saturation on yielding of soils. In Asian Conference on Unsaturated Soils: 527–532. Lloret, A., Villar, M.V., Sanchez, M., Gens, A., Pintado, X. and Alonso, E.E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique 53(1): 27–40. Nuth, M. and Laloui, L. 2007a. Implications of a generalized effective stress on the constitutive modelling of unsaturated soils. In T. Schanz (ed.), Theoretical and Numerical Unsaturated Soil Mechanics: 75–82. Springer. Nuth, M. and Laloui, L. 2007b. New insight into the unified hydro-mechanical constitutive modelling of unsaturated soils. In Z. Yin, J. Yuan & A.C.F. Chiu (eds), The 3rd Asian Conference on Unsaturated Soils: 109–126. China: Science Press. Romero, E., Gens, A. and Lloret, A. 1999. Water permeability, water retention and microstructure of unsaturated compacted Boom clay. Engineering Geology 54(1–2): 117–127.
Roscoe, K.H. and Schofield, A.N. 1963. Mechanical behaviour of an idealised wet clay. In European Conference on Soil Mechanics and Foundation Engineering Vol.1: 47–54. Rouainia, M. and Wood, D.M. 2000. A kinematic hardening constitutive model for natural clays with loss of structure. Géotechnique 50(2): 153–164. Sanchez, M., Gens, A., Guimarães, L.N. and Olivella, S. 2005. A double structure generalized plasticity model for expansive materials. International Journal for Numerical and Analytical Methods in Geomechanics 29: 751–787. Sridharan, A., Altaschaeffl, A.G. and Diamon, S. 1971. Poresize distribution studies. Journal of the Soil Mechanics and Foundation Division ASCE 97: 771–787.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A damage model for unsaturated natural loess submitted to cyclic loading J.M. Pereira, A.N. Ta, Y.J. Cui & J.P. Karam Université Paris-Est, UMR Navier, Ecole des Ponts – CERMES, Marne-la-Vallée, France
H.Y. Chai Chinese Academy of Sciences, Institute of Rock and Soil Mechanics, Wuhan, China
ABSTRACT: High speed railway from Northern France has encountered several stability problems in zones where loessic soils are present. Important sinkholes have been observed and were mainly due to the collapse susceptibility of the encountered loess when submitted to the cyclic loadings imposed by the passage of the high speed trains. This collapse susceptibility seems to be related to the degradation of the cemented bonds and to either the collapse under wetting at constant applied load or liquefaction depending on the natural water content of the soil. In this paper, a constitutive model is developed to gain insight into cyclic behaviour of theses soils. This model is an extension of a model previously proposed by the authors for modelling degradation of bonds and liquefaction potential of natural cemented soils under saturated states. The platform model, from which the extension is carried out, is based from one hand on the bounding surface plasticity theory for the description of the cyclic response of the soil and is inspired on the other hand from the work of Vaunat & Gens (2003) concerning bond degradation modelling. Influence of non-saturation effects is introduced following an approach similar to that of the Barcelona Basic Model (Alonso et al. 1990). The developed model is thus capable to describe the mechanical behaviour of unsaturated bonded soils under cyclic loading.
1
INTRODUCTION
High speed railway from Northern France crosses areas characterized by important loess deposits (aeolian sediments) which may reach some meters in thickness. In that region, sinkholes have been observed along the railway thus showing an important collapse risk for this kind of soils. Loessic soils are composed of a solid matrix made of sand grains which are cemented by various materials such as calcium carbonate, clay and silica. Figure 1 shows a schematic representation of loess in an unsaturated state. Due to the mode of deposition of these sediments, loessis soils present a high porosity which may lead in some cases to significant collapse deformations. Among the possible physical explanations at the origin of these phenomena, degradation of soil structure can be cited. As for other cemented geomaterials such as soft argillaceous rocks, stiff clays, aged sands, residual soils etc., the overall mechanical behaviour of loess is largely influenced by the presence of these bonds in terms of stiffness, yield locus and strength. Under mechanical loadings, the bonding between matrix grains may be affected by damage. Furthermore, since this degradation may lead to significant volumetric deformations and thus to large increases in pore water
Figure 1. Schematic representation of loess in an unsaturated state.
pressures, these soils present a risk of liquefaction when loaded from an initial saturated state or even near to it. A precise description of bond damage is thus of first importance in order to obtain a satisfactory constitutive model able to simulate the cyclic behaviour of loess and its liquefaction potential. For this purpose, a model has been proposed in Chai (2005) and Chai et al. (2007). Besides damage and liquefaction potential, environmental loadings imposed by rainfalls or flooding
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may induce collapse due to wetting if the soil is non-saturated, this phenomenon being well known in unsaturated soil mechanics. Of course, observed collapses along the high speed railway may originate from bond degradation, wetting and more probably from couplings between these two phenomena. For instance, bond degradation will facilitate collapse under wetting or wetting could reduce the strength of bonds. Furthermore, a collapse under wetting may be followed by a liquefaction of the soil if cyclic loadings are subsequently applied to wetting. Due to the complexity of possible phenomena and couplings between them, this paper aims at presenting a constitutive model in order to assess the collapsibility of loess under cyclic and environmental loadings, from the point of view of unsaturated soil mechanics. After a concise description of the platform model, its extension to unsaturated states is presented. The paper ends with simulations of laboratory tests in order to demonstrate the capabilities of the proposed model.
stresses in the triaxial stress space. The indices m and b respectively refer to the matrix and to the bond material. Strains of the bonds εvb and εqb are defined over the bond phase (volume Vb ) and their apparent expressions (i.e. defined over total volume Vt ) are the following, after having defined the bond concentration β = Vb /Vt : βεvb ;
βεqb
(2)
Similarly, apparent strains of the matrix which are defined over voids Vv and solid matrix Vm volumes write as follows: (1 − β)εvm ;
(1 − β)εqm
(3)
A relation between total strain and strains in the matrix and bond phases can then be derived: dεv = (1 − β)dεvm + βdεvb
2
dεq = (1 − β)dεqm + βdεqb
CONSTITUTIVE MODEL
The proposed model consists in the extension of a model developed for saturated loess under cyclic loading (Chai 2005, Chai et al. 2007). This platform model is based on the theory of bounding surface plasticity (Dafalias 1986) to simulate cyclic behaviour of loess. To account for the possibility of damage of the soil structure, modelling of bond degradation follows the work of Vaunat & Gens (2003). The extension to unsaturated states of the platform model is dealt with by following the framework introduced in the Barcelona Basic Model from Alonso et al. (1990). Net stress (excess of total stress over gas pressure, pg ) and matric suction (s = pg − pw where pw stand for water pressure) are used as independent stress state variables and yield limit is assumed to be dependent of suction in order to simulate collapse under wetting according to the loading-collapse (LC) equivalence principle. Before going deeper in the unsaturated damage model for loessic soils, the bases of the saturated version from which it is extended are recalled. Interested readers may find further details in (Chai 2005, Chai et al. 2007). 2.1
Cementation effects
A partition of the total effective stress between matrix and bond contributions is assumed as follows: pm = p − pb ;
qm = q − qb
(1)
where p and q are respectively the total (apparent and saturated) effective isotropic and deviatoric
(4)
Elastic relations with respect to the different strains previously introduced are assumed as follows: e dεvm =
dpm ; Km
e dεqm =
e = dεvb
dpb ; Kb
e dεqb =
dq 3Gm dqb 3Gb
(5) (6)
where Km , Gm are the elastic moduli of the matrix and Kb , Gb are those related to the bonding phase under current state of degradation. Using Equations (4), (5) and (6) together with (1) provides total elastic strain increments: dp Kb e + β − (1 − β) dεvb Km Km dq Gb e dεqe = (1 − β) + β − (1 − β) dεqb 3Gm Gm dεve = (1 − β)
(7)
Since pb and qb are unknown, elastic strain increments of bonds remain to be computed. Following Vaunat & Gens (2003), the ratios of elastic strains of e e bonds dεvb , dεqb to total elastic strains dεve , dεqe are assumed constant before damage and depending on this latter afterwards: e dεvb /dεve = χ0 ;
e dεqb /dεqe = χ1
(8)
where χ0 and χ1 are positive scalars lower than 1. For simplicity, it will be assumed that χ0 = χ1 .
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2.2
Description of damage of bonds
Following basic elastic damage theory, it is supposed that bonds are submitted to elastic strains only. Beyond a certain level of energy elastically stored, a degradation of their mechanical properties is assumed. A damage scalar variable D varying from 0 to 1 can classically be introduced (Lemaître & Chaboche, 1985). However, as previously done by Carol et al. (2001), a rescaled counterpart L (varying from 0 and infinity) of the damage variable D is preferred in what follows. It is defined by: L = ln
1 1−D
The yield function and plastic potential are inspirited from (Pastor et al. 1985). After modifications to account for interparticle bonding and its damage, they both read as follows: αf 1 p¯ F(σ , p0 ) = q¯ − Mf p¯ 1 + 1− αf p¯ 0 1 p¯ αg 1− G(σ , pg ) = q¯ − Mg p¯ 1 + αg p¯ 0g (15)
(9)
Expressions (8) can then be rewritten to account for the damage state of bonds: e /dεve = χ0 e ; dεvb
e dεqb /dεqe = χ1 e (10)
where L0 is associated to the energy level at which degradation effectively starts and <x> represents the positive part of x. The evolution of L is assumed to depend on both volumetric and shear strains as follows: 1 1 . . L(ε) = kv ξv + kq ξq ; ξv = |dεv |; ξq = .dεq . (11)
where σ = ( p , q)T and Mf , αf , Mg , αg are parameters to determine and p¯ 0g is related to the size of the plastic potential. As in (Pastor et al. 1985), the bounding and yield surfaces are assumed to coincide. On the bounding surface, the plastic strain increment is defined by the following flow rule: dε p = (dεvp , dεqp )T =
Constitutive model for the matrix
A model based on bounding surface plasticity theory (Dafalias, 1986) has been rimentally simulate observed accumulation of irreversible strains even if the loading cycles are small compared to the yield limit estimated from monotonous tests. Bonding effects are introduced in the plastic potential and the yield function by defining the following changes of variable: p¯ = p + χpbc ;
q¯ = q + χqbc
(12)
where pbc and qbc are material constants to be determined and: χ = χ0 e
∂F ∂σ
T · dσ +
∂F ∂p0
∂p0 ∂εp
T · dε p +
∂F dL = 0 ∂L (17)
Inside the domain delimited by the bounding surface, the following mapping rule, inspired by the works presented in (Zienkiewicz et al. 1985, Pastor et al. 1985), is used to link the hardening modulus of the current stress point HL/U to that of the conjugate stress point cs HL/U : HL/U = cs HL/U
δ0 δ
γ0 (18)
where γ0 is a material parameter. Following the theory of bounding surface plasticity, HL/U is then used to classically compute the plastic strain increment inside the elastic domain. Figure 2 presents schematic representation of this mapping rule.
(13) 2.4 Extension to unsaturated states
The hardening parameter pc is also modified in the following way: p¯ 0 = (1 + χ)p0
(16)
with ngL/U and n the normal tensors to respectively the plastic potential surface during loading or unloading cs and the bounding surface and HL/U , the plastic modulus during loading or unloading. This latter can be computed using the consistency condition:
where kv and kq are materials constants to be determined. 2.3
ngL/U (nT · dσ ) cs HL/U
(14)
The extension to unsaturated states is implemented following the framework of the Barcelona Basic model (BBM) from Alonso et al. (1990).
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The energy-linked threshold L0 can be assumed to be dependent on the suction value. Concerning the modification of the yield surface, it is directly inspired from the Barcelona Basic Model (Alonso et al. 1990) so that: F(σ, p0 , L, s) Figure 2. Schematic representation of the mapping rule used to link plastic moduli at actual and conjugate stress points.
The main part of the saturated model presented here before remains valid. The effective stress p only has to be replaced by the net stress. The other modifications that are required to define the unsaturated model are now presented. By analogy to the mechanical behaviour, total elastic strains associated to suction variations are given by: dεvse =
1−β β + s s Km Kb
αf 1 p¯ 1− (24) = q¯ − Mf (¯p + ps ) 1 + p¯ 0 αf
with p¯ = p + eL0 −L pbc ; p¯ s = k0 s;
Kbs = Kb
(20)
After some derivations, it can be shown that the variations of the stress in the bond are given by:
p0 = pc
(27)
p∗0 pc
λ(0)−κ λ(s)−κ
(28)
λ(s) = λ(0) ((1 − r) exp(−bs) + r)
(29)
where p∗0 corresponds to the saturated yield limit introduced in Equations (14) and (15). The plastic potential is chosen as: G(σ , p0 , L, s)
αg 1 p¯ 1− (30) = q¯ − Mg (¯p + ps ) 1 + αg p¯ 0
and the plastic strain increment formally given in the saturated case by (16) and (18) remains the same. The hardening law is given by: dp∗0 1+e ∂ξ dεvp + β0 β1 e−β0 ξ p dεqp (31) ∗ = p0 λ(0) − κ ∂εq
(21) L0 −L
dqb = Gb0 χ11 e " # × dεqe − εqe (−1)n kv dεv + (−1)m kq dεq
∂F ∂σ +
(22)
T
∂F · dσ + ∗ ∂p0
∂F ds = 0 ∂s
(23)
∂p∗0 ∂εp
T · dε p +
∂F dL ∂L (32)
The suction increase yield locus (SI) introduced in BBM that is: SI (s, s0 ) = s − s0
and, in the matrix, by: dqm = dq − dqb
(26)
The consistency condition now takes into account suction changes and writes as follows:
dpb = Kb0 χ00 eL0 −L " # × dεve − εpe (−1)n kv dεv + (−1)m kq dεq
dpm = dp − dpb ;
(25)
The so-called LC curve is defined by:
(19)
where Kms and Kbs are the bulk moduli associated to suction variations of, respectively, the matrix and the bonds. Interparticle bonding being constituted of clay and calcite, it will be assumed further on that the air entry value of the bond material is larger than usual values of suction to which the soil is submitted. Since in that case the bonding material remains saturated, Terzaghi’s effective stress remains valid. With this assumption, the following simplification can be added to the previous equation:
p¯ 0 = (1 + χ)p0
χ = χ00 exp(L0 _L)
ds
q¯ = q + eL0 −L qbc
(33)
is not considered in this study due to a lack of experimental data justifying its existence. In other words,
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the suction value s0 which corresponds to the highest value at which the soil as ever been submitted is assumed to be larger than usual values encountered in the applications here considered. Concerning the hydraulic behaviour, van Genuchten’s equation (van Genuchten 1980) is considered for the water retention curve modelling so that:
Sr (s) =
1 1 + (Bs)n
Shear stress (kPa)
700 600 500 400 300 200 s=25 kPa s=1 kPa
100
m
0 0
(34)
where B, m and n are material parameters. Another choice is also considered, following Brooks & Corey’s proposal (1964): Sr (s) =
800
2
4
6
8
Figure 4. Influence of suction on monotonous triaxial tests performed at constant suction.
700 600
s α e
(35)
s
where se and α are material parameters.
500 400 300 200 100
s=1 kPa s=25 kPa
0 0
3
10
Axial strain (%)
Shear stress (kPa)
900
2
4
6
8
10
Axial strain (%)
PRELIMINARY RESULTS
Preliminary results are now presented. They aim at presenting the possibilities of the model to simulate the behaviour of unsaturated cemented materials. All simulation use van Genuchten’s equation to model the water retention curve of loess. The initial void ratio e is 0.83 and the initial stress is isotropic and close to zero since isotropic consolidation stages are simulated before starting triaxial tests. Figure 3 presents the water retention curves of the loess studied in this work obtained experimentally by Karam (2006) and simulated using Equations (34) and (35).
Figure 5. Influence of suction of cyclic triaxial tests performed at constant suction.
3.1 Monotonous triaxial tests Monotonous triaxial tests are simulated at two imposed suctions. They were performed after an isotropic compression stage. Results are presented in Figure 4 and show as expected an increase of the stiffness and the yield limit of the material when suction is increased. 3.2 Cyclic triaxial tests
1200 Experimental data van Genuchten Brooks & Corey
Suction (kPa)
1000 800 600 400 200 0 0.30
0.39
0.45
0.48
0.55
0.68
0.73
Degree of saturation
Figure 3. Experimental and simulated water retention curves of loess from Northern France (experimental data from (Karam 2006); simulated data using van Genuchten’s and Brooks & Corey’s models).
Finally, in order to illustrate the effects of bond degradation on the performance of the unsaturated model proposed in this paper, a cyclic triaxial test is simulated at two imposed suctions. These tests consist in imposing a given number of shear stress cycles after an isotropic consolidation stage. The results are presented in Figure 5. The influence of a suction increase is characterised by the reduction of axial strain at the end of a given cycle. Concerning the modelling of damage, it appears that the first cycles (for both suction values) present higher stiffness, higher yield limits and larger irreversible strains than the last cycles. This observation can be explained easily by considering that the first cycles involve a lowly damaged material which tends to increasingly degrade during the loading process.
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Table 1.
REFERENCES
Material parameters of bonds.
χ00 = χ11
β
kα = kβ
Kb (kPa)
νb
pbc (kPa)
0.35
0.35
2.0
5000
0.25
10
β0
β1
Table 2. λ1
Material parameters of matrix.
κ
ν
Mg
Mf
αg
αf
γ
0.17 0.012 0.25 1.35 0.58 0.45 0.45 4.3 0.23 1.4
Table 3. Material parameters of unsaturated extension and water retention curve (van Genuchten’s model). r
b
pr (kPa)
k
κs
n
m
B
0.75
0.01
25
0.02
0.01
0.5
1
5 × 10−5
3.3
Material parameters
The materials parameters used in the simulations are summarized in the Tables 1–3. Mechanical parameters (of bonding material and matrix, see Tables 1–2) were determined by curve fitting from experimental data in (Chai 2005). Unsaturated parameters were estimated from experimental results on similar soils and van Genuchten’s parameters were determined by curve fitting (see Figure 3 and Table 3). 4
CONCLUSIONS
A model that aims at assessing the collapsibility of loessic soils encountered along the high speed railway in Northern France has been presented. Theses soils are submitted to cyclic mechanical loadings and to environmental loadings which may lead to important collapse deformations. This model is able to simulate the effects of degradation of bonds and non-saturation on the behaviour of natural cemented soils. Preliminary results have been presented and show the good capabilities of the model.
Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430. Brooks, R. & Corey, A. 1964. Hydraulic properties of porous media, Colorado State University Hydrology Paper 3: 27 pp. Carol, I., Rizzi, E. & Willam, K. 2001. On the formulation of anisotropic elastic degradation. I. Theory based on a pseudo-logarithmic damage tensor rate. International Journal of Solids and Structures 38(4): 491–518. Chai, H.Y. 2005. Modelling of the Mechanical Behaviour of Loessic soils under cyclic loadings. Research report. ENPC. Chai, H.Y., Pereira, J.M., Cui, Y.J. & Karam, J.P. 2007. Modelling loess behaviour under cyclic loadings using a damage model. International Journal for Numerical and Analytical Methods in Geomechanics (submitted). Dafalias, Y.H. 1986. Bounding surface plasticity: I. Mathematical foundation and hypoplasticity. Journal of Engineering Mechanics (ASCE) 112(9): 966–987. van Genuchten, M.T. 1980. Closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Science Society of America Journal 44(5): 892–898. Karam, J.P. 2006. Étude de la rhéologie des loess du Nord de la France. Application à l’évaluation de leur risque de liquéfaction. PhD Thesis, Ecole Nationale des Ponts et Chaussées, Paris, France. Pastor, M., Zienkiewicz, O. & Chan, A.H.C. 1990. Generalized plasticity and the modelling of soil behaviour. International Journal for Numerical and Analytical Methods in Geomechanics 14(3): 151–190. Pastor, M., Zienkiewicz, O.C. & Leung, K.H. 1985. Simple model for transient soil loading in earthquake analysis. II. Non-associative models for sands. International Journal for Numerical and Analytical Methods in Geomechanics 9: 477–498. Ta, A.N. 2006. Prise en compte de la non-saturation dans un modèle élastoplastique avec endommagement. MSc Thesis, Ecole Nationale des Ponts et Chaussées, Paris, France. Vaunat, J. & Gens, A. 2003. Bond degradation and irreversible strains in soft argillaceous rock. In Proc. of the 12th Panamerican Conference on Soil Mechanics and Geotechnical Engineering: 479–484. Zienkiewicz, O.C., Leung, K.H. & Pastor, M. 1985. Simple model for transient soil loading in earthquake analysis. I. Basic model and its application. International Journal for Numerical and Analytical Methods in Geomechanics 9: 453–476.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Desiccation shrinkage of unconstrained soil in the saturated phase L.B. Hu & T. Hueckel Duke University, Durham, North Carolina, USA
H. Peron & L. Laloui EPFL, Lausanne, Switzerland
ABSTRACT: Analysis of macroscopic desiccation shrinkage experiments indicates that most of the shrinkage occurs during drying while soil is still 100% wet. When air starts penetrating the soil, shrinkage practically ceases, while the water content is still above 20%. The remaining drying process occurs with a much-reduced shrinkage. In this context we look at the data of pore space evolution during saturated phase of drying as obtained via porosimetry. The observed behavior is modeled at a microscale using Poiseuille flow in capillary vessels with deformable walls driven by evaporation flux at the external boundary. A macroscopic model using Biot and Darcy theories for the continuum were recently presented by the authors.
1
INTRODUCTION
Desiccation phenomena in soils have been investigated for decades bringing progressively a better understanding of the mechanisms and physics involved (Abu-Hajleh & Znidarcic 1995, Kodikara et al. 1999, Konrad & Ayad 1997, Miller et al. 1998). Recent desiccation experiments (Peron et al. 2006) on initially saturated soils near liquid limit point out to the conclusion that most of the shrinkage occurs during saturated phase of the process. This is in agreement with a general perception that unsaturated soil has a much higher stiffness than saturated soil. This is quite a universal behavior independently of the type of soil and type of pore fluid, as shown by Hu et al. 2007 (Fig. 1). That includes shrinkage of soil permeated with ethanol solution, which has surface tension coefficient that is less than a half of that of water. When soil becomes unsaturated, shrinkage practically stops, while the water content is still above 20%. The remaining drying process occurs with a muchreduced deformation. Hu et al. 2007 have also shown that the amount of deformation during the saturated drying and the shrinkage limit in terms of void ratio depend on the compressibility of the solid, but seems to be independent of surface tension and/or fluid saturation vapor pressure which characterizes evaporation process, or finally, from fluid viscosity. However, the rate of fluid loss and rate of shrinking are controlled by the evaporative and hydraulic conductivity properties, thus, those of the fluid. As it is generally agreed that capillary effects are caused by the fluid surface
Figure 1. Void ratio evolution during drying versus the volumetric fluid content change in clayey silt [Bioley silt] (left) and a granite powder (right) filled with water, water/ethanol 50–50 mixture and water-ethylene glycol 65–35 mixture (see Peron et al. 2007 for details).
tension, it is postulated that the saturated phase of drying is largely independent from capillary effects, and shrinkage is due to the fluid removal from the pore space via Darcian flow, while fluid-gas interface is confined to the external soil mass boundary, where all the phase transition takes place. Furthermore, possible capillary effects at the boundary appear to play a minor role in deformation, and hence the so-called ‘‘skin effect’’ is a negligible factor in deformation analysis. A microscopic model of pore system deformation and transport is proposed to corroborate this hypothesis in relationship to the actual data on the evolution of the pore space. A macroscopic counterpart model has been recently developed using Biot and Darcy theories by Hu et al. 2007.
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2 2.1
PORE SPACE EVOLUTION Pore size distribution
Pore size distribution was obtained for Bioley clayey silt filled with water using Mercury Intrusion Porosimetry. The measurements were conducted at three stages of unconstrained desiccation: at the value of the water content of 33.1%, 24.8% and at 0.8%. These instants correspond to the initial state, near the shrinkage limit, and after the completion of the process. Figure 2 visualizes the volume fraction for each instant. The evolution of the pore space can be summarized as follows: (1) the initial pore size is visibly bi-modal, with Large Pores (LP), ranging between 0.6 μm and 3 μm occupying initially 17% of the volumes of the medium, and Small Pores (SP), ranging between 0.09 μm and 0.6 μm occupying initially 21% of the volume of the medium. There are also minor volumes of peripheral size pores outside of the range of MIP, including those of clayey fraction (see Peron 2008 for details). (2) At near shrinkage limit the LP take less than 5% of the volume of the medium, whereas the SP amount to 29%. Finally at near the completion of drying, the LP take less than 0.5% of the volume of the medium, whereas the SP still amount to 27%. 2.2
Assessment of the pore space evolution during drying
This result is very significant, as it indicates that during the entire process the Small Pores do not decrease significantly, neither in size nor in total volume they occupy. To the contrary, at near shrinkage limit, they probably include the volume of former LP. The LP themselves practically all close during the saturated phase of drying and disappear at completion of the process. Similar results were recently obtained by
Figure 2. Pore size distribution evolution during drying of Bioley silt.
Cuisinier & Laloui (2004) and Koliji et al. (2006) during suction induced desaturation process. Interestingly, it has been known for sometime that in bi-modal porosity soils, the SP remain virtually unchanged during consolidation process, whereas all volume changes are accommodated by LP (Delage & Lefebre 1984). In reference to the desiccation process such evolution of the pore space implies that only the water volume contained in the LP is subject to evacuation during the saturated phase, and only that water volume produces the observed shrinkage.
3
MICROSCOPIC MODEL OF PORE SPACE EVOLUTION
3.1 Formulation The above observations will be framed into a model of an evolving microscopic structure, based on the following specific postulates. It is recognized that the pore system of soil is made of sectors of straight tubes of two initial sizes: small (ST) and large (LT), with their internal diameters coinciding with the average values of the pore modes, identified in the preceding Section as 0.5 μm and 1 μm. The total initial volumes of the pores are set as equal to the initial value of the pore space of the corresponding modal volumes. The external radii of the tubes are not connected to any physical currently used characteristics of soils, except that the total volume of the solids of all the tubes must be representative of the total volume of the solids. Hence its value is determined as 2.5 μm. The grain size distribution data could provide some help, but not without a more extensive study. To begin with we consider a representative elementary volume (REV) in a form of a single cylindrical deformable tube around a single cylindrical Large Pore located centrally and a series of parallel cylindrical Small Pores, all filled with water, and connected at their extremities to the atmosphere with which they can exchange gas and fluid. The tube representation is shown in Figure 3(a). The solid of the tube represents a granular material, hence deforming irreversibly. The macroscopic
Figure 3. Schematics of a pore system in a cylindrical REV (a) and a BVP for a Small (b) eventually approximated via (d) and for a Large Pore (c).
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experiments (Peron et al. 2006) indicate that drying shrinkage strain is largely irreversible, while in the unsaturated phase the deformation is reversible to the state of the onset of desaturation, upon the removal of suction or re-wetting. The behavior of the solid material surrounding the pores will be considered as plastic, however it will be approximated via a linearly elastic law during loading and considered as perfectly rigid during an unloading. The adoption of a linear deformation law allows one to use a principle of superposition and hence represent the pore system of Figure 3(a) as a superposition of effects of a LP and multiple SPs. Eventually, for the reasons of simplicity, SPs will all be located centrally as well. Hence, the problem is reduced to that of a single tube with a single cylindrical pore. The tube is considered as symmetric along and around its axis, loaded with a negative pore fluid pressure at the ends. It is assumed that a tube is completely filled with water during the considered phase (saturated). Water undergoes a viscous (Poiseuille) flow, i.e. an incompressible Newtonian fluid through a cylindrical tube. For the external boundary conditions for the fluid one can envision either a known (negative) water pressure history, or an imposed flux, resulting from the evaporation flux. The removal of water from the tube implies that its volume is compensated by the deformation of the tube. The time evolution of the negative pressure applied is reconstructed from the experiment (Peron et al. 2005, 2006) and shown in Figure 4. At the axis of the symmetry at the tube half-length the no-flow condition is imposed. Water transport in the tube is a viscous nonfrictional (Poiseuille) flow with the externally applied negative pressure, which is evaporation-driven. ∂p 8μ 8μ = − 4Q = − 2 F ∂x πa a
(1)
Q is the volume-flow rate, F is the volume flux, p is water pressure, μ is viscosity and a is the inner radius of the tube. We assume that the flow is solely attributed to the loss of volume of the inner conduit, i.e. due to the change in a, thus the volume change of an infinitesimal tube element per unit volume is ∂v 2πa ∂a 2 ∂a = = ∂t πa2 ∂t a ∂t And the mass conservation requires (in 1D) ∂F ∂v =− ∂t ∂x
(3)
Thus substituting the flux into Equation 3, an approximate Poiseuille’s equation for the collapsing tube is obtained ∂ 2 p 2 ∂a ∂p 16μ ∂a = + a3 ∂t ∂x2 a ∂x ∂x
(4)
It should be pointed out that a similar equation can also be obtained from Equation 1 by replacing the volume flow rate with the total volume loss of tube. 1
x
Q=− 0
2πa ·
∂a (x, t) dx ∂t
(5)
In reality the tube radius a varies with x because of the elastic deformation in response to the variable (negative) pressure. A classical tube expansion/compression solution provides such a relationship. To further simplify the mathematical solution Fung (1984) expresses the change in radius as a function of the inner pressure by ignoring the radial strain a0 p(x) −1 a(x) = a0 1 − Eh
Figure 4. The negative pore pressure function imposed at the boundary x = L (from the experimental data).
(2)
(6)
E is the Young’s modulus, a0 is the initial value of the inner radius a, h is the thickness of the tube. Fung has shown that the latter approximation is very good, especially for low values of Poisson coefficient. As indicated in the subsequent context, the simulated deformation appears to be rather large, hence, a finite strain configuration may become a better approach. However, as our current priority in this paper is to examine the idea of using a deformable pore model to simulate the shrinkage, the mathematical merit of employing large deformation will be pursued in future work.
655
Substituting Equation 6 into the original Equation 4 produces a partial differential equation for pore pressure p. 2a0 ∂ 2p + ∂x2 Eh 1 −
pa0 Eh
∂p ∂x
2 =
pa 16μ 1 − Eh0 ∂p a0 Eh ∂t (7)
The initial condition is: at t = 0, p = p0 = 0. The boundary conditions are as follows: x = 0, ∂p/∂x = 0 and x = ±L, p = p (t), see Figure 4. Equation 7 is a parabolic PDE. Its solution has been obtained using Mathlab© .
3.2
Figure 5(a). Evolution of radii in LP at x = L, x = L/2, and x = L/4.
Results
The solutions are obtained numerically for large and small pores separately. The numerical value of the deformability modulus E = 50 KPa, and water viscosity chosen the same for the analyses of the LP and the SPs. The length of the tubes is 15 cm, taken as the length of the macroscopic experiments (see Peron et al. 2005). Both types of pores are subjected to the same external negative pressure evolution, as resulting from the same flux of water vapor (see Hu et al. 2007). The most significant difference between the two types of pores is in the amount of closure of the inner cavity: in 5 hours needed for reaching the shrinkage limit, the SP closes over 0.08 μm from the original 0.5 μm at the external boundary, whereas the LP closure amounts to 0.33 μm from 1 μm. This reflects correctly the porosimetry observation that the Large Pores convert into 0.6 μm (or nearly Small Pore types) in that period of time. The evolution of radii for selected cross sections of the tube proceeds similarly, but with a small but marked delay, as seen in Figures 5(a) and (b). The profiles of the opening along the axis for each pore type are shown in Figure 6. The results also indicate a different efficiency of SPs and LPs in transport of water toward the evaporating boundary. Figure 7 shows water flux evolution at the boundary for both types of pore relative to their cross section surface area. A single LP provides more than twice of water than a SP after 5 hours. Notably, as the areas of the individual tubes decrease in a significantly different manner, the volume flow rates per single tube yield a different picture (Fig. 8). Indeed, because of a large reduction of the cross section area of the large pore tube, it appears that the latter reaches a maximum of the water output at about two hours from the onset of the process of drying. It may be expected that the small tubes reach a similar maximum at a later moment.
Figure 5(b). Evolution of radii in SP at x = L, x = L/2, and x = L/4.
Figure 6. Radius profile for small and large pore after 5 hours of drying.
Hence, the outflow from the system stabilizes and then gradually decreases, driven by the tube constriction. Whether this remains within the range of validity of the presented model remains an open question. The cumulative volume loss via single LP and SP from
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Figure 7. Water flux evolution at the external boundary for individual LP and SP.
Figure 10. Small pore tube: evolution of the pressure profile along the tube axis.
Figure 8.
Volume flow rate evolution per single tube.
Figure 11. Large pore tube: evolution of the pressure profile along the tube axis.
Figure 9.
Cumulative volume output per single tube.
the onset of evaporation is shown in Figure 9. On the mechanics side of the problem it is interesting to note that because of the common value of the externally applied negative pressure, both types of tubes are exposed to very similar pressure throughout almost the entire history of the drying process in the saturated range. Figures 10 and 11 present the evolution of such pressure along respectively LP and SP, indicating indeed very limited differences. It has to be realized however, that the two types of tubes have drastically different stiffness because of the differences in their thickness. This indeed produces such a dramatically different response in terms of the deformation of the tubes. Finally, it is also seen that for selected
Figure 12. Evolution of pressure in LP at x = L/2 and x = L/4. For comparison also the boundary pressure is shown.
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cross sections of the tube the negative pressure evolves similarly, but with a marked delay, as visible in Figure 12. In fact the pressure evolution mimics that of the radius of the pore as may be expected from the form of Equation 6. 4
DISCUSSION AND CONCLUSIONS
The presented highly idealized microscopic model and numerical simulations of the drying process in its saturation phase indicate a series of characteristics that agree qualitatively with the experimental findings. The centerpiece of the model is transport of water toward the perimeter of the drying body producing the collapsing of the vessels. The model is largely based on the evolution of the pore system, idealized as bimodal. In particular, a significant reduction in diameter of large pores is seen, compared to that of smaller mode pores that is attributed to the difference in their deformability due to size difference. Transport of water is characterized by an initial phase (two hours) when the discharge increases via large pores to stabilize at start to gently decrease after about four hours. An open question remains whether the aforementioned decrease remains within the range of the model validity. Several simplifications and assumptions require further investigations, to start with the deformation modulus of the medium that comprises (only) smaller pores. An obvious limit of the validity of the model is the air entry moment. However, a microscopic criterion for this occurrence is still a point of discussion. ACKNOWLEDGEMENTS This work is funded by a cooperation between the Swiss National Science Foundation, grant 200020109661 and the US National Science Foundation, grant # 0324543.
Delage, P. & Lefebre, G., 1984, Study of the structure of the sensitive Champlain Clay and of its evolution during consolidation, Canadian Geotechnical J., 21 (1): 21–35. Fung, Y.C. 1984. Biodynamics: Circulation. New York: Springer. Hu, L.B., Peron, H., Hueckel, T. & Laloui, L. 2006. Numerical and phenomenological study of desiccation of soil. In N. Lu, L.R. Hoyos and L. Reddi (eds.), ASCE Geotechnical Special Publication: Advances in Unsaturated Soil, Seepage, and Environmental Geotechnics, 166–177. Hu, L.B., Peron, H., Hueckel, T. & Laloui, L. 2007. Drying shrinkage of deformable porous media: mechanisms induced by the fluid removal. In H.W. Olson (ed.), ASCE Geotechnical Special Publication 157: Geo-Denver 2007, New Peaks in Geotechnics. 10 pages, CD-ROM. Kodikara, J., Barbour, S.L. & Fredlund, D.G. 1999. ‘‘Changes in clay structure and behaviour due to wetting and drying.’’ Proceedings of the eighth Australia New Zealand Conference on Geomechanics, Hobart, 1: 179–185. Koliji, A., Laloui, L. Cuisinier, O. & Vulliet, L. 2006, Suction Induced Effects on the Fabric of a Structured Soil, Transport in Porous Media 64: 261–278. Konrad, J.M. & Ayad, R. 1997. An idealized framework for the analysis of cohesive soils undergoing desiccation. Canadian Geotechnical Journal 34: 477–488. Miller, C.J., Mi H. & Yesiller, N. 1998. Experimental analysis of desiccation crack propagation in clay liners. Journal of the American Water Resources Association 34 (3): 677–686. Peron, H. 2008. Ph. D. Thesis, Ecole Polytechnique Federal de Lausanne, ENAC, Lausanne, Switzerland, in preparation. Peron, H., Laloui, L. & Hueckel, T. 2005. An experimental Evidence in Desiccation Cracking in Sandy Silt, in Tarantino, Romero and Cui (eds.), Advanced Experimental Unsaturated Soil Mechanics, Proceeding of Conference, Trento, Italy, April 2005, Taylor and Francis Group, London, 475–480. Peron, H., Laloui, L., Hueckel, T. & Hu, L.B. 2006. Experimental study of desiccation of soil. In G.A. Miller, C.E. Zapata, S.L. Houston and D.G. Fredlund (eds.), ASCE Geotechnical Special Publication 147: Unsaturated Soils 2006, 1073–1084. Peron, H., Hu, L.B., Hueckel, T. & Laloui, L. 2007. The influence of the pore fluid on desiccation of a deformable porous material. In T. Schanz (ed.), Springer Proceedings in Physics, Experimental Unsaturated Soil Mechanics, 413–420.
REFERENCES Abu-Hajleh, A.N. & Znidarcic D. 1995, Desiccation theory for soft cohesive soils, J. Geotech. Eng. 121 (6): 492–502. Cuisinier, O. & Laloui, L. 2004, Fabric evolution during hydromechanical loading of a compacted silt, Int. J. for Numerical and Analytical Methods in Geomechanics 28: 483–499.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Modelling of the collapsible behaviour of unsaturated soils in hypoplasticity D. Mašín Charles University, Prague, Czech Republic
N. Khalili University of New South Wales, Sydney, Australia
ABSTRACT: The paper presents a recently developed constitutive model for unsaturated soils, based on the theory of hypoplasticity and the effective stress principle. The mathematical formulation of the model is outlined and the required state variables and parameters are described. The model is, among other features of unsaturated soil behaviour, capable of predicting collapse upon wetting, a phenomenon that could not be modelled with earlier hypoplastic models. Predictions of wetting-induced collapse agree well with experimental data on statically compacted Pearl clay.
1
INTRODUCTION
Hypoplasticity, a particular class of incrementally nonlinear constitutive models, has undergone a notable development during last two decades. Recently, hypoplastic models cover a wide range of geomaterials, such as granular materials, soils with a low friction angle and clays. Procedures to incorporate anisotropy, viscosity, structure and the elastic behaviour in the very small strain range and the effects of recent history are available. To date, however, most contributions on the constitutive modelling of soils using the theory of hypoplasticity have been in the domain of saturated soils. Extension of this class of constitutive models to unsaturated soils is presented in this contribution. Mašín and Khalili (2007) have recently developed a new hypoplastic model for unsaturated soils. The model is based on the hypoplastic model for clays by Mašín (2005). It is thus, as other advanced hypoplastic models, characterised by the following rate form: T˚ = fs (L : D + fd N D )
(1)
˚ is the objective rate of Cauchy stress tensor, where T D is Euler stretching tensor, L and N are two constitutive tensors and fs and fd are two scalar factors (named barotropy and pyknotropy factors respectively) that incorporate the influence of mean stress and void ratio. The model by Mašín (2005) is characterised by a low number of parameters and a simple calibration procedure. This advantageous property of the basic model is naturally shared also by its extension for unsaturated soils.
The aim of this contribution is to outline mathematical formulation and basic features of the hypoplastic model for unsaturated soils. The model is then evaluated with respect to experimental data on one characteristic feature of the unsaturated soil behaviour—collapse of the structure caused by wetting. More detailed description and evaluation of the model may be found in Mašín and Khalili (2007). Throughout this paper, sign conversion of continuum mechanics is considered, i.e. compression is taken as negative.
2
STRESS STATE VARIABLES
Central to the framework presented here is the concept of effective stress which can be defined in the following general form, subject to the solid grains incompressibility constraint (e.g., Bishop 1959) T = Tnet + 1χs
(2)
Stress variables without any superscript (T) denote the effective stress, Tnet is the net stress defined as Tnet = Ttot − 1ua and s = ua − uw is the matric suction. Ttot is the total stress, ua is the pore air pressure and uw is the pore water pressure. A simple formulation for the effective stress tensor T based on Eq. (2), which is sufficient for many practical applications, has been put forward by Khalili and Khabbaz (1998) and further evaluated by Khalili et al. (2004). On the basis of an extensive
659
is controlled by the isotropic virgin compression line with the formulation according to Butterfield (1979)
evaluation of experimental data they proposed the following empirical formulation for χ: χ=
& 1 s γ e
s
for s ≥ se for
s < se
(3)
where se is the suction value separating saturated from unsaturated states. It is equal to the air entry value for drying processes and the air expulsion value for wetting processes. γ is a material parameter, and it has been shown that for a broad range of different soils it is sufficient to assign γ = 0.55 (Khalili and Khabbaz 1998). For suctions lower than se the effective stress parameter χ is equal to 1, i.e. the soil is saturated and Eq. (2) reduces to the Terzaghi effective stress definition. Time differentiation of Eq. (2), with the use of (3) and taking into account rigid body rotations, imply the following formulation of the objective rate of the effective stress ˚ = T˚ net + 1(1 − γ )χ s˙ T
(4)
In addition to the effective stress tensor T, suction s is considered as a state variable that quantifies the stiffening effect of the water menisci. 3
HYPOPLASTIC MODEL FOR UNSATURATED SOILS
In this section, the hypoplastic model for unsaturated soils proposed recently by Mašín and Khalili (2007) will be presented. The basic aim of the derivations in this section is to demonstrate a conceptual way to incorporate the behaviour of unsaturated soils into hypoplasticity. The particular formulation adopted is very simple, but it may be readily modified by using the general rules outlined in this section. 3.1 Model for constant suction The overall mechanical response of a soil element is controlled by the effective stress tensor. Suction influences the effective stress and, in addition, it increases normal forces at interparticle contacts and thus acts as a quantity that increases the overall stability of the soil structure. In terms of the critical state soil mechanics, it increases the size of the state boundary surface (SBS), in a similar manner to bonding between soil particles in saturated cemented materials. State boundary surface is defined as a boundary of all possible states of a soil element in the stress vs. void ratio space. The incorporation of structure into hypoplastic model has been discussed in detail by Mašín (2007). In this context, the size of the SBS for unsaturated soils
ln(1 + e) = N (s) − λ∗ (s) ln
p pr
(5)
where e is the void ratio, which is considered as a state variable, and pr = 1 kPa is a reference stress. Quantities N (s) and λ∗ (s) define the position and the slope of the isotropic virgin compression line in the ln(p/pr ) vs. ln(1 + e) plane for given suction s. For the evaluation of model predictions through this paper, we assume for ln(s/se ) > 0 (unsaturated state) the following simple logarithmic dependency of N (s) and λ∗ (s) on s: s N (s) = N + n ln (6) se s (7) λ∗ (s) = λ∗ + l ln se where the quantities n and l represent two additional soil parameters. For ln(s/se ) < 0 (saturated state) N (s) = N and λ∗ (s) = λ∗ . It is, however, emphasized that the general formulation of the model can accommodate any other more complex relationships between N (s), λ∗ (s) and s. Mašín (2007) demonstrated that incorporation of variable virgin compressibility and the intercept N (s) into the hypoplastic model requires a modification of both barotropy and pyknotropy factors fs and fd in (1), which are now calculated in terms of N (s) and λ∗ (s). The respective expressions are given in Mašín and Khalili (2007). 3.2 Incorporation of wetting-induced collapse at normally consolidated states When an unsaturated soil with an initially open structure is subjected to a decreasing suction, the reduction in the normal forces acting at the inter-particle contacts may result in a situation in which the structure, for the given effective stress T and void ratio e, is no longer stable, and thus it collapses. This phenomenon, referred to as a wetting-induced collapse, cannot be modelled with the model for structured clays Mašín ˚ = 0 implies D = 0 (see Eq. (1)), i.e. no 2007), as T deformation of the soil skeleton can be predicted for variable suction with constant effective stress. In the context of the critical state soil mechanics, all admissible states of a soil element are bounded by the SBS. As the hypoplastic model from Sec. 3.1 predicts constant void ratio sections through the SBS of the same shape (see Mašín and Herle (2005)), it is advantageous to study collapse due to wetting in the stress space normalised by the size of the SBS
660
for current e. This size is quantified by the Hvorslev equivalent pressure pe , implied by Eq. (5). Mašín and Khalili (2007) have shown, that normalisation with respect to pe allows us to derive the following expression that ensures consistency of the model predictions with the SBS of suction-dependent size:
1
m=1 m=2 m=5 m=10 m=100
0.8
fu
0.6
˚ = fs (L : D + fd N D ) + H T
0.4
(8)
0.2
where H is a new term given by H=
T ∂pe s˙ pe ∂s
3.3
0.2
0.4
0.6
0.8
1
Figure 1. The influence of the parameter m on the value of suction hardening pyknotropy factor fu .
(10)
The following expression for the factor fu satisfying these requirements is proposed:
Model for any state of overconsolidation
The model from Sec. 3.2 may be used for constant value of suction (˙s = 0) and for wetting at normally consolidated states (states at the SBS). The following assumptions are utilised to extend Eq. (8) for arbitrary (physically admissible, i.e. inside the SBS) states and arbitrary loading conditions: 1. As suction controls stability of inter-particle contacts, increasing suction under constant effective stress imposes no deformation of soil skeleton. 2. The more open the soil structure, the larger the inter-particle contact shear forces and therefore the greater the number of inter-particle contact slips under wetting at constant effective stress. To reflect these two assumptions, the rate formulation of the model is written as ˚ = fs (L : D + fd N D ) + fu H T
0
p/pSBS
From the expression for the Hvorslev equivalent pressure pe follows T ∂N (s) ∂λ(s) pe − ln s˙ H= λ(s) ∂s ∂s pr
0
(9)
(11)
fu =
p
m (13)
pSBS
where pSBS is the effective mean stress at the SBS corresponding to the current stress state T/ tr T and current void ratio e and m is a model parameter controlling the influence of overconsolidation on the wetting-induced collapse. Eq. (13) is demonstrated graphically in Fig. 1. Clearly, value of the parameter m controlls dependency between collapse of structure and distance of the current state from the SBS. Note that basic elasto-plastic models based on suction hardening concept imply m → ∞ (collapse at the yield surface only). It may be shown from the definition of the pyknotropy factor fd of the basic hypoplastic model and using rules derived by Mašín and Herle (2005) that m/α fu = fd fs A−1 : N
(14)
with H=
T ∂N (s) ∂λ(s) pe − ln ˙s λ(s) ∂s ∂s pr
where the fourth-order tensor A is given by (12) A = fs L −
where the operator x denotes positive part of any scalar function x and fu is a new pyknotropy factor controlling tendency of the soil structure to collapse upon wetting. The factor fu must be equal to unity for states at the SBS (in that case the structure is as open as possible and collapse is controlled by H only) and fu → 0 for OCR → ∞ (no wetting-induced inter-particle slippage occurs in highly overconsolidated soil).
4
1 λ∗ (s)
T⊗1
(15)
WETTING-INDUCED STRAIN RATE
Wetting of normally consolidated soil at anisotropic stress state causes in addition to volumetric collapse development of shear strains (Sun et al. 2004, 2007). Eq. (8) allows us to derive an expression for the direction of stretching implied by wetting at constant
661
0.05
experiment m=1 m=2 m=5 m=10 m=100
0.6 0.04 0.4 0.03 εv [-]
q/p*e, dεs
0.2 0 – 0.2
0.02 0.01
– 0.4
0
– 0.6 0
0.2
0.4
0.6
0.8
–0.01
1
0
20
40
60
p/p*e, dεv
Figure 2. Direction of strain rate tensor induced by wetting at constant effective stress for Pearl clay parameters.
ϕc
λ∗
0.05
κ∗
0.005
100
120
140
Figure 3. s vs. v relationship for wetting of slightly overconsolidated soil at constant net stress.
Table 1. Parameters of the hypoplastic model for Pearl clay (calibrated using data from Sun et al. (2004)). 29◦
80 s [kPa]
N 1.003
0.86 0.84 0.82
r 0.5
0.8
l 0.024
m2
se [kPa] -15
ln (1+e)
n 0.164
0.78 0.76 0.74
effective stress for states at the SBS (see Mašín and Khalili (2007)). −1 =− A :N D A−1 : N
0.72 0.7 0.68
NCLs 3
(16)
3.5
4
4.5
5
5.5
6
6.5
5.5
6
6.5
ln (p/pref) 0.86
where the fourth-order tensor A is given by Eq. (15). Eq. (16) implies purely deviatoric strain rate at the critical state and purely volumetric strain rate at the isotropic stress state. Direction of the strain increment vector for different stress obliquities is graphically demonstrated in Fig. 2, together with the shape of the bounding surface for Pearl clay parameters (Tab. 1), evaluated by Mašín and Khalili (2007). It is clear that the strain increment vector is not perpendicular to the SBS (in terms of elasto-plasticity, neglecting the effects of elastic strains, this would be implied by a non-associated flow rule).
0.84 0.82
ln (1+e)
0.8 0.78 0.76 0.74 0.72 0.7 0.68
NCLs 3
3.5
4
4.5
5
ln (p/pref)
5
Figure 4. Isotropic compression tests at constant suction and wetting tests at constant net stress by Sun et al. (2007) replotted in the effective stress space (top) and predictions by the proposed model (bottom).
PREDICTING THE COLLAPSIBLE BEHAVIOUR OF UNSATURATED SOILS
Thorough evaluation of the hypoplastic model for unsaturated soils is presented in Mašín and Khalili (2007). It contains response to drying and wetting paths of soil specimens at isotropic and anisotropic stress states and response to constant suction shear tests and isotropic loading tests at different suction levels. Tests on five different soils performed in different
soil mechanics laboratories are used for evaluation. Due to the limited space, in this paper we restrict the model evaluation to tests at the isotropic and anisotropic stress state under constant and decreasing suction. The response to wetting paths is with respect
662
3
0.06
pnet=20 kPa pnet=49 kPa pnet=98 kPa net p =196 kPa net p =392 kPa pnet=588 kPa
0.05
2.5
0.03
R [-]
εv [-]
0.04
calib. m
2
0.02 1.5
0.01
R=1.5 R=2 R=2.5
0 1 – 0.01
0
20
40
60
80
100
120
0
140
0.02
0.04
0.06
0.1
0.12
0.14
0.16
0.18
0.16
0.18
εa [-]
– s [kPa] 3
0.06
pnet=20 kPa pnet=49 kPa pnet=98 kPa pnet=196 kPa pnet=392 kPa pnet=588 kPa
0.04
2.5
R [-]
0.05
εv [-]
0.08
0.03 calib. m
2
0.02 1.5
0.01
R=1.5 R=2 R=2.5
0 1 – 0.01
0
20
40
60
80
100
120
140
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
εa [-]
– s [kPa]
Figure 5. Wetting tests at constant isotropic net stress by Sun et al. (2007) plotted in s vs. v plane (top) and predictions by the proposed model (bottom).
to hypoplastic modelling the most important to study, as in this case the new terms H and fu are activated. The model is evaluated by means of experimental data on statically compacted Pearl clay by Sun et al. (2004, 2007). Pearl clay is a moderate plasticity soil with very little expansive clay minerals. The first set of experimental data consist of tests on soil specimens that have been isotropically compressed at constant suction −147 kPa to different mean net stress levels (49, 98, 196, 392 and 588 kPa). At this stage, the specimens were wetted at constant net stress and suction was decreased to zero. Some of the specimens were further compressed at zero suction to the mean net stress 588 kPa. Figure 3 shows response to wetting tests at the highest apparent overconsolidation ratio (the test where wetting took place at pnet = 49 kPa) and predictions by the model with different values of the parameter m from Eq. (14). The higher the value of m, the closer to the SBS the volumetric collapse takes place. The value of m = 2 has been considered as a suitable value to represent Pearl clay behaviour. Calibration of all other model parameters for Pearl clay (Tab. 1) is detailed in Mašín and Khalili (2007).
Figure 6. Constant net mean stress shear tests and constant R wetting tests by Sun et al. (2007) plotted in a vs. R = Ta /Tr plane (top) and predictions by the proposed model (bottom).
Figure 4 shows graphs of the constant suction isotropic compression tests and constant net stress wetting tests replotted in the effective stress space. Predictions are in a good agreement with the experimental results, the model predicts correctly both the constant suction and wetting parts of the experiments. In the wetting tests at the lower net mean stresses, the experiments show the initial decrease of the effective stress with very small change of void ratio. This aspect of the observed soil behaviour, which is progressively less pronounced with decreasing apparent OCR, can be modelled correctly by the proposed model thanks to the new pyknotropy factor fu . Results of the wetting parts of the experiments from Fig. 4 are plotted in the suction vs. volumetric strain plane in Fig. 5. The model predicts correctly the qualitative influence of the net mean stress on the volumetric behaviour. When the soil is wetted at low net mean stress (49 kPa), it first swells and only after the state gets closer to the state boundary surface the structure starts to collapse. On the other hand, specimens wetted at higher net mean stresses (i.e. at lower apparent OCRs) collapse since the beginning of the wetting test. This aspect of the soil behaviour is predicted correctly thanks to the proposed formulation for the
663
radial net stresses. At this stage, suction was decreased to zero under constant net stress, and finally the shear test continued under constant mean net stress and s = 0 kPa to failure. The specimens had approximately equal initial void ratios (initial apparent OCRs) and they were wetted at different values of the ratio R (1.5, 2 and 2.5). Figure 6 shows the results of the three constant net mean stress shear tests in the axial strain vs. principal net stress ratio plane. The corresponding radial strains are in Fig. 7. Correct predictions of the constant suction parts of the tests demonstrate the predictive capabilities of the basic hypoplastic model, which predicts the non-linear soil behaviour with gradual decrease of the shear stiffness. In the wetting parts of the tests, the model predicts significant increase of the collapse axial strains and of the negative radial strains at higher ratios R. The good quantitative agreement for both a and r demonstrates adequate modelling of the wetting-induced collapse strain rate direction. The analytical expression for this direction has been (for constant effective stress) derived in Sec. 4, see Fig. 2 for Pearl clay parameters.
3
R [-]
2.5
2
1.5 R=1.5 R=2 R=2.5
1 –0.07 –0.06 –0.05 –0.04 –0.03 –0.02 –0.01
0
0.01
0
0.01
εr [-] 3
R [-]
2.5
2
1.5 R=1.5 R=2 R=2.5 1 –0.07 –0.06 –0.05 –0.04 –0.03 –0.02 –0.01
6
εr [-]
Figure 7. Constant net mean stress shear tests and constant R wetting tests by Sun et al. (2007) plotted in a vs. r plane (top) and predictions by the proposed model (bottom).
factor fu . The experiments show the lowest collapsible strains for the wetting at the highest net mean stress (588 kPa). Correct predictions of the final value of the volumetric strains after collapse are achieved thanks to the converging normal compression lines of the saturated and unsaturated soils (Fig. 4), i.e. thanks to l > 0 (Eq. (6)). The predicted shape of the wetting path in the s vs. v plane is controlled by the factor fu (for the initially apparently overconsolidated specimens) and by the interpolation function for the quantities N (s) and λ∗ (s) (Eq. (6)). Good agreement between experimental data and model predictions also for wetting at higher net mean stresses (where the factor fu takes a constant value equal to 1) suggests that the logarithmic interpolation adopted is suitable to represent the actual soil behaviour. The second set of experimental data allows us to investigate the influence of the stress anisotropy on the wetting-induced collapse behaviour. The specimens were, after isotropic compression at constant suction s = −147 kPa to mean net stress pnet = 196 kPa, subjected to constant suction and constant net mean stress shear tests up to a target principal net stress ratio R = Tanet /Trnet , where Tanet and Trnet are the axial and
CONCLUDING REMARKS
A recently developed constitutive model for unsaturated soils is presented in the paper. The model is based on the theory of hypoplasticity, it is thus capable of predicting pre- and post-peak non-linear deformation behaviour of unsaturated soils, and the variation of the soil stiffness with loading direction—important aspects absent from many of the current constitutive models proposed for the behaviour of unsaturated soils. A specific feature of unsaturated soil behaviour— collapse of the structure induced by wetting—can be predicted thanks to the factors H and fu , novel to hypoplasticity. Predictions of the wetting-induced collapse, presented in this paper, agree well with experimentally observed behaviour.
ACKNOWLEDGEMENT The first author acknowledges the financial support by the research grants GAAV IAA200710605, GACR 103/07/0678 and MSM0021620855.
REFERENCES Bishop, A.W. (1959). The principle of effective stress. Teknisk Ukeblad 106(39), 859–863. Butterfield, R. (1979). A natural compression law for soils. Géotechnique 29(4), 469–480.
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Khalili, N., F. Geiser, and G.E. Blight (2004). Effective stress in unsaturated soils: Review with new evidence. International Journal of Geomechanics 4(2), 115– 126. Khalili, N. and M.H. Khabbaz (1998). A unique relationship for χ for the determination of the shear strength of unsaturated soils. Géotechnique 48(2), 1–7. Mašín, D. (2005). A hypoplastic constitutive model for clays. International Journal for Numerical and Analytical Methods in Geomechanics 29(4), 311–336. Mašín, D. (2007). A hypoplastic constitutive model for clays with meta-stable structure. Canadian Geotechnical Journal 44(3), 363–375.
Mašín, D. and I. Herle (2005). State boundary surface of a hypoplastic model for clays. Computers and Geotechnics 32(6), 400–410. Mašín, D. and N. Khalili (2007). A hypoplastic model for mechanical response of unsaturated soils. International Journal for Numerical and Analytical Methods in Geomechanics (submitted). Sun, D.A., H. Matsuoka, and Y.F. Xu (2004). Collapse behaviour of compacted clays in suction-controlled triaxial tests. Geotechnical Testing Journal 27(4), 362–370. Sun, D.A., D. Sheng, and Y.F. Xu (2007). Collapse behaviour of unsaturated compacted soil with different initial densities. Canadian Geotechnical Journal 44(6), 673–686.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Swelling pressure in compacted bentonite: Laboratory tests and modelling M. Sanchez University of Strathclyde, Glasgow, UK
M.V. Villar & R. Gómez-Espina CIEMAT, Madrid, Spain
A. Lloret & A. Gens UPC, Barcelona, Spain
ABSTRACT: The aim of this work is to extend an existent double structure model for expansive clays (Sanchez et al., 2005) to include the thermal effects in the analysis. Experimental results obtained in the context of the NF-PRO project have been used to extend the constitutive law. A fundamental characteristic of the double structure framework is the explicit distinction of two actual structural levels existent within the material: the macrostructural level, which accounts for the larger scale structure of the material and the microstructural level, associated with the active clay responsible for the swelling behaviour. In addition, the model considers the interaction between the two structural levels. In this paper the dependence of the swelling behaviour on temperature has been directly included in the constitutive law that describes the microstructural behaviour. This is the natural way to consider the thermal effects in expansive clays, as their swelling behaviour is controlled mainly by the clay minerals (microstructure).
1
INTRODUCTION
This research has been carried out in the context of projects concerning the engineered clay barrier of deep geological radioactive waste repositories. This barrier, made of compacted bentonite (a highly swelling material), will be placed between the waste canisters and the host rock, and will be saturated by the groundwater while it is subjected to high temperatures due to the radioactive decay of the wastes. These temperature changes affect the hydraulic and mechanical response of the bentonite, what has important implications on the design and performance of the repository. The behaviour of expansive soils is potentially very complex owing to the interaction between the volume change of aggregates made up of highly expansive clay minerals (microstructure) and the rearrangement of the granular-like skeleton formed by the aggregates (macrostructure). The BBM (Barcelona Basic Model), developed by Alonso et al. (1990) is able to deal with the main features of unsaturated soils but it is not able to describe the behaviour of expansive soils. The aim of this work is to extend an existent double structure model, specially developed for expansive clays (Sanchez et al., 2005), to include (in a consistent way) the influence of temperature on the expansive
clay behaviour. A basic feature of the model is the explicit distinction of two actual structural levels existent within the material: the macrostructure and the microstructure. The macrostructure accounts for the larger scale structure of the material and it is described using the BBM. The inclusion of the microstructural level (associated with the active clay particles) in the analysis allows the consideration of the physicochemical phenomena occurring at particle level. In addition, the model considers the interaction between the two structural levels. This is a key mechanism to describe the behaviour of swelling clays. The constitutive laws incorporate key aspects to model the complex behaviour of highly expansive material, such as, large swelling under wetting, yielding, stress path dependency, clay-fabric changes, among others. Even though the model is general, it has been mainly applied to explain and reproduce the behaviour of expansive clays used as engineered barrier to isolate high level radioactive waste (HLW). Figure 1 shows a typical scheme adopted in the design of clay barriers for HLW. In field conditions the clay barrier will be hydrated (due to the water coming from the host rock) under confined conditions and will also undergo heating (induced by the heatemitting waste) up to a maximum of 100◦ C (according
667
Rock Compacted bentonite Nuclear waste
Container
Figure 1. Scheme of an engineered barrier made up of compacted clay for a high level radioactive waste repository.
to the Spanish concept for the disposal of HLW). To understand and reproduce satisfactorily the behaviour of such kind of barriers it is crucial to validate a mechanical constitutive model able to reproduce the main trends of the expansive clays behaviour when are submitted to complex Thermo-Hydro-Mechanical (THM) paths. An extensive experimental campaign carried out on compacted FEBEX bentonite, which combined suction and load changes, has been used to validate the hydro-mechanical behaviour of the double structure model (Lloret et al., 2003). In the context of the ongoing NF-PRO project a research program is being carried out to advance the knowledge of the thermal behaviour of expansive clays. Results of saturation under load and swelling pressure tests at temperatures ranging from 30 to 80◦ C have been used in this work (Villar & Gómez-Espina 2006). For the material considered in this work, the FEBEX bentonite, a decrease of swelling capacity and swelling pressure with temperature has been observed. The upgrade of the model proposed in this work has been based on this experimental evidence. This work is organized as follows; firstly the main aspects of the experimental program are introduced. Then, the mechanical constitutive model for expansive soils is briefly presented. After that, the inclusion of the thermal effects in the analysis and the main results are discussed. Finally, the main conclusions of the work are presented.
2
EXPERIMENTAL WORK
The determination of the swelling pressure and permeability as a function of temperature was performed in high-pressure oedometer equipment. Granulated clay was compacted uniaxially and statically at room temperature in the oedometer ring, which had an inner diameter of 5.0 cm, the length of the resulting specimen being 1.2 cm. Nominal dry densities of 1.50 and 1.60 Mg/m3 were reached by applying vertical stresses of 11 and 16 ± 2 MPa, respectively.
Figure 2. Schematic representation of the oedometer cell for tests at high temperature.
The oedometer assemblage was placed inside a silicone oil thermostatic bath that kept target temperature. Once the temperature stabilised, the sample, confined between porous stainless steel sinters, was hydrated at constant volume through the bottom face with deionised water injected at a pressure of 0.01 MPa, while the upper outlet remained open to atmosphere. At the same time, a load cell installed in the loading frame measured the swelling pressure exerted by the clay. The small vertical deformation of the specimen, due mainly to load cell and frame deformability, was measured by two LVDTs. An automatic volume change apparatus measured the water exchange of the specimen. The values of load, strain and water exchange were automatically recorded. Figure 2 presents a schematic representation of the device used in the experimental program. Once the sample was completely saturated (which was assumed by the stabilisation of water intake and swelling pressure development), the injection of water was stopped, and the pressure registered was considered the swelling pressure value for the dry density attained. The actual density may differ slightly from the nominal one due to the small displacement allowed by the equipment (about 10 μm when a vertical stress of 2.2 MPa is applied). The main results of the swelling pressure tests are presented in Section 4.
3
DOUBLE STRUCTURE MODEL
Expansive clays generally present a clear double structure, made up from clay aggregates and large
668
Figure 3. Distributions of incremental pore volume obtained using MIP technique (Lloret et al., 2003) and schematic representation of the two structural levels considered.
macrostructural pores (e.g. Pusch, 1982). As an example, the mercury intrusion porosimetry tests preformed to examine the pore size distribution of the statically compacted samples of FEBEX bentonite are presented in Figure 3. This figure shows the measured incremental pore volume for two samples compacted to very different values of dry density (ρd ), 1.5 Mg/m3 and 1.8 Mg/m3 . It can be observed that the pore size distribution is clearly bimodal. The dominant values are 10 nm that would correspond to the pores inside clay aggregates and a larger pore size that depends on the compaction dry density and ranges from 10 μm (for ρd = 1.8 Mg/m3 ) to 40 μm (for ρd = 1.5 Mg/m3 ). These larger voids would correspond to the inter-aggregate pores. The boundary between the two pore size families can be seen to be around 0.13 μm, as pores smaller than this size do not appear to be affected by the magnitude of the compaction load. The pore space inside the aggregates is constituted by voids of a much smaller size. The two dominant pores size could be associated with two basic structural levels (Figure 3): • The macrostructural level, which accounts for the larger scale structure of the material. • The microstructural level, associated with the active clay responsible for the swelling behaviour. Only these two basic structural levels identified above are considered herein. The approach is open enough and it could be extended to include more structural levels in the analysis, if it deemed relevant. The soil fabric plays a crucial role to understand and to reproduce the behaviour of expansive clays. In this model, the inclusion of the clay fabric in the analysis is considered in the definition of laws for: 1) the macrostructural level, 2) the microstructural level, and 3) for the interaction between both structural levels.
Figure 4. a) BBM yield surface. b) Microstructural load directions on the p-s plane.
3.1 Macrostructural model The inclusion of this structural level in the analysis allows the consideration of phenomena that affect the skeleton of the material, for instance deformations due to loading and collapse. The BBM (Barcelona Basic Model) has been adopted to describe the macrostructural behavior (Alonso et al., 1990). The BBM considers two independent stress variables to model the unsaturated behaviour: the net stress (σ ) computed as the excess of the total stresses over the gas pressure, and the matric suction (s), computed as the difference between gas pressure and liquid pressure (pg − pl ). Figure 4a shows the BBM yield surface (FLC ), defined as: FLC = 3J 2 −
g(θ) g(−30◦ )
2 M 2 (p + ps )(p0 − p) = 0 (1)
where M is the slope of the critical state, po is the apparent unsaturated isotropic pre-consolidation pressure, g(θ) is a function of the Lode angle and ps considers the dependence of shear stress on suction
669
•
p∗0 = p∗0
(1 + e) • p ε (λ(0) − κ) v
(2) •
p
where e is the void index, εv is the volumetric plastic strain, κ is the elastic compression index for changes in p and λ(0) is the stiffness parameter for changes in p for virgin states of the soil in saturated conditions. In additions, the model is able to describe the reduction of the size of the yield surface and the strength of the material with the increase of temperature, according to the model suggested in Gens (1995). The Appendix contains the main model equations. 3.2
Microstructural model
The microstructure is the seat of the basic physicochemical phenomena occurring at clay particle level. The strains arising from microstructural phenomena are considered elastic and volumetric (Gens & Alonso, 1992). The microstructural effective stress is defined as: pˆ = p + χs
(3)
It is assumed that the total suction is equal to the matric suction (s), because the effect of the osmotic suction is not considered in this work. χ is a constant. It is also assumed hydraulic equilibrium between the water potentials of both structural levels. A more general formulation with non-equilibrium between water potentials is presented in Sanchez (2004). The increment of microstructural strains is expressed as: •
•
εv1 =
•
3.3 Interaction between macro and micro structure In expansive soils there are other mechanisms in addition to the ones included in the BBM which induce plastic strains. This irreversible behaviour is ascribed to the interaction between the macro and micro structures (Gens & Alonso 1992). It is assumed that the microstructural mechanical behaviour is not affected by the macrostructure but the opposite is not true. An assumption of the model is that the irreversible deformations of the macrostructure are proportional to the microstructural strains according to interaction functions f . The plastic macrostructural strains are evaluated by the following expression: (5)
p
4
EFFECT OF TEMPERATURE ON SWELLING
The swelling pressure results for the two dry densities tested are plotted in Figure 5. Deformations induced in the experimental device due to thermal effects have been calibrated and deducted from the informed results. The dispersion of data can be mostly attributed to the variations in dry density (whose average values were in fact 1.58 and 1.49 Mg/m3 ). This is caused by the small displacement allowed by the
(4)
where the subscript 1 refers to the microstructural level, the subscript v refers to the volumetric component of the strains and K1 is the microstructural bulk modulus. The Neutral Line (NL) corresponds to constant pˆ and no microstructural deformation occurs when the stress path moves on the NL (Figure 4b). The NL divides the p-s plane into two parts, defining two main generalized stress paths, which are identified as: MC (microstructural contraction) and MS (microstructural swelling).
•
where εvLC is the plastic strains induced by the yielding of the macrostructure (BBM). In fact the coupling is given by p∗o , hardening variable of the macrostructure (Figure 4a), which depends on the total plastic volumetric strain (Equation 2). In this way it is considered that the microstructural processes can affect the global arrangements of aggregates. More details can be found in Sánchez et al. (2005).
•
p s pˆ = +χ K1 K1 K1
• p
•
εvp = εvLC + f εv1
Swelling pressure (MPa)
and temperature. A basic point of the model is that the size of the yield surface increases with matric suction. The trace of the yield function on the isotropic p-s plane is called the LC (Loading-Collapse) yield curve, because it represents the locus of activation of irreversible deformations due to loading increments or collapse. The position of the LC curve is given by the pre-consolidation yield stress of the saturated state, p∗o (hardening variable), according to:
Error bars obtained from values of tests performed at laboratory
6
3
temperature (1.6Mg/m )
4
2
Dry density (Mg/m3) 1.5 1.6 Test Test Model Model
Error bars obtained from values of tests performed at laboratory temperature (1.5 Mg/m3)
0 20
30
40
50
60
70
80
Temperature (°C)
Figure 5. Swelling pressure as a function of temperature for saturated FEBEX clay compacted to different nominal dry densities. Experimental and modelling data.
670
K1 =
e−αm pˆ βm
(6)
where αm and βm are model parameters. The extension suggested here is to include a dependence of the parameter βm on temperature. The following expression is proposed: βm
βm = e
τ
T Tref
(7)
100.0
(p+s) (MPa)
equipment, as the swelling pressure value is very sensitive to small density changes. The error bars shown in the figure were obtained from values measured in tests performed at laboratory temperature (Lloret et al., 2003). A decrease of swelling pressure as a function of temperature is observed. This would be in accordance with the results obtained in soaking under load tests, which predict a decrease in swelling capacity with temperature (Villar & Gómez-Espina, 2006). The extrapolation towards higher temperatures would indicate that swelling pressures higher than 1 MPa would be developed even for temperatures of 100◦ C. Lingnau et al. (1996) also observed a reduction in swelling pressure with temperature for a sand/bentonite mixture, although it did not show any loss in the self-healing capability of the material, even for temperatures of up to 100◦ C. In order to represent more closely the behaviour of expansive clays it is important to consider the influence of temperature on swelling. With this aim the model presented in Section 3 has been extended to include thermal effects. In the constitutive law presented above, the large swelling of the material is modelled (mainly), through the microstructural law (Section 3.2). This has a strong physical sense because the expansive behaviour of soils is due to the wetting of the active clay minerals, which constitute the microstructure of expansive clays. So, the aim here is to include at this level the change in the swelling capacity of expansive clays due to thermal effects. The mechanical behaviour at microstructural level is represented by a non-lineal elastic model, because it is assumed that the expansion is controlled by physico-chemical effects occurring at clay particle level (microstructure) that are basically reversible. In this law (Equation 4) the expansion of the material depends on the microstructural effective stress (Equation 3) through a microstructural bulk modulus (K1 ). A first attempt to model the thermal effect is to include a dependence of K1 on temperature. The expression used to validate the expansive model with data of FEBEX bentonite (Lloret et al., 2003) is presented as follows:
ΔT (°C) τ : 0.12 0 20 40 60
10.0
1.0
0.1 1000
1500
2000
2500
3000
3500
K1 (MPa)
Figure 6. Changes in micro-structural stiffness with temperature.
where T is the temperature difference, that is the actual temperature minus Tref , a reference temperature (i.e. 20◦ C), and τ is a new parameter that may be obtained from experiments. In this analysis τ has been obtained by back-analysing the experiments. Figure 6 shows how the change of temperature affects the microstructural bulk modulus according to the suggested law. An increase in the microstructural stiffness with temperature is predicted with this law. This means lower expansion when tests are conducted at higher temperature. In order to check the capabilities of the extended constitutive law a series of analysis has been carried out in order to describe the dependence of swelling on temperature observed experimentally. Swelling pressure tests at constant temperature have been modelled (Figure 5). The initial suction has been determined from the retention curve. No major effects of temperature on retention behaviour of FEBEX bentonite have been observed, at least for the range of temperature analysed herein (FEBEX, 2006). The rest of initial and boundary conditions have been adopted to reproduce closely the conditions observed during the test (Villar & Gómez-Espina, 2006). As has been already mentioned, for the FEBEX bentonite, the main parameters of the constitutive law were previously obtained during the validation of the constitutive law (Lloret et al., 2003). In this work, the only parameters adjusted are the ones related to the new microstructural law. The main model parameters used in the analysis are presented in Table 1. In this model, the dependence of swelling on initial density is taken into account in a consistent way through the parameter p∗0 (Gens & Alonso, 1992). As can be observed from Figure 5, the model is able to reproduce quite well the dependence of swelling pressure on temperature for the two dry densities analysed.
671
Table 1.
Mechanical constitutive law parameters.
Parameters defining the BBM (macrostructure) κ
κs
λ(o)
r
ζ (MPa−1 )
p∗o (MPa)
α0 (◦ C−1 )
5−3
1−3
8−2
9−1
1.
(∗1 )
1.−5
Parameters defining microstructural behaviour (emicro = 0.46) αm (MPa−1 ) = 5.0 e−2
βm (MPa−1 ) = 7.8 e−4
τ = 0.12
χ=1
Interactions functions fC = 1 + 0.9 tan h (20 (pr /po ) − 0.25)
5
fS = 0.8 − 1.1 tan h (20 (pr /po ) − 0.25)
(∗1 ) dry density 1.6 (Mg/m3 ) p∗o = 7.0 (MPa)
e macro = 0.228
(∗1 ) dry density 1.5 (Mg/m3 ) p∗o = 4.5 (MPa)
e macro = 0.340
CONCLUSIONS
A double structure model, based on the general framework for expansive materials proposed by Gens & Alonso (1990) has been presented. In order to be closer to the typical fabric of expansive materials, the existence of two pore structures has been explicitly included in the formulation. The distinction between the macrostructure and microstructure provides the opportunity to take into account the dominant phenomena that affect the behaviour of each structure in a consistent way. The major advantage of this model is that it incorporates in a natural way the key aspects that control the behaviour of expansive clays, indicated as follows: the swelling features of clay minerals are explicitly considered through a microstructural law; the relevant effects of the granular-like skeleton are contemplated through the macrostructural law and the model also considers the interaction between both structural levels. In this paper the double structure model (Sanchez et al., 2005) has been extended to consider the effect of temperature on swelling. As the clay particles are mainly responsible for the expansive behaviour of clays a dependence of the microstructural law on temperature has been suggested in this work. It has been observed that the model is able to capture the main trends observed in the tests.
Gens, A. 1995. Constitutive Laws. In A. Gens P. Jouanna & B. Schrefler Modern issues in non-saturated soils: 129–158. Wien New York: Springer-Verlag. Gens, A. & Alonso, E.E. 1992. A framework for the behavior of unsaturated expansive clays. Can. Geotech. Jnl. 29:1013–1032. Lingnau, B.E., Graham, J., Yarechewski, D., Tanaka, N. & Gray, M.N. 1996. Effects of temperature on strength and compressibility of sand-bentonite buffer. Eng. Geol. 41 1–4: 103–115. Lloret, A., Villar, M.V., Sánchez, M., Gens, A., Pintado, X. & Alonso, E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique, 53(1): 27–40. Pusch, R. 1982. Mineral water-interaction and their influence on the physical behaviour of highly compacted Na bentonite. Can. Geotech. Jnl., 19: 381–387. Sánchez, M. 2004. Thermo-hydro-mechanical coupled analysis in low permeability media. Ph. D. Thesis, Technical University of Catalonia. Barcelona. Sánchez, M., Gens, A., Guimarães, L. & Olivella, S. 2005. A double structure generalized plasticity model for expansive materials. Int. Jnl. Num. Anal. Meth. in Geom. 29: 751–787. Villar, M.V. & Gómez-Espina, R. 2006. Deliverable 3.2.9: Progress report on laboratory tests performed by CIEMAT (WP3.2 NF-PRO Report). Madrid. EC.
APPENDIX The BBM plastic potential (G) is expressed as:
REFERENCES
Alonso, E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique, 40(3): 405–430. FEBEX Report. 2006. Full-scale Engineered Barriers Experiment. Updated Final Report 1994–2004. Publicación Técnica ENRESA 05-0/2006. 590 pp. Madrid.
G = α3J 2 −
g(θ) g(−30◦ )
2 M 2 (p + ps ) (p0 − p) = 0 (A1)
where α is determined according to Alonso et al. (1990). The dependence of the tensile strength on
672
suction and temperature is given by: ps = ks e−ρ T
(A2)
where k and ρ are model parameters. The dependence of p0 on suction is given by: p0 = pc
p∗0T pc
−κ λλ(0)−κ (s)
;
p∗0T = p∗0 + 2(α1 T + α3 T | T | )
(A3)
where pc is a reference stress, α1 and α3 are model parameters. λ(s) is the compressibility parameter for changes in net mean stress for virgin states of the soil; which depends on suction according to: λ(s) = λ(0) [r + (1 − r) exp (−ζ s)]
(A4)
where r is a parameter which defines the minimum soil compressibility. ζ is a parameter that controls the rate of decrease of soil compressibility with suction.
673
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Modelling water retention characteristic of unsaturated soils Y. Wang Institute for Materials Research, School of Computing, Science and Engineering, University of Salford, Manchester, UK
G. Wu Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai, P.R. China
S.M. Grove Advanced Composites Manufacture Centre, School of Engineering, University of Plymouth, Plymouth, UK
M.G. Anderson School of Geographical Sciences, University of Bristol, Bristol, UK
ABSTRACT: The water retention characteristic or Water Retention Curve (WRC) is an important constitutive feature of soils. Previous experiments have indicated that specific surface area has effects on the WRC. It has also been observed that a linear relationship generally exists between the air-water interface area and the pore saturation in unsaturated soils. However it seems that no study on their internal linkage with the WRC has been reported yet. This paper tries to explain the water retention curve according to the physical and chemical behaviours of the phases involved in unsaturated soils. Using the capillary, interfacial surface theories and averaging theorem, a deterministic formula which represents the water retention characteristic is derived. This formula demonstrates the internal linkage of the WRC to the specific surface area of porosities. It shows agreement with experimental observations. Based on this formula, a fitting model is proposed for the WRC of soils. Finally, this model is tested to fit the WRCs of a wide range of soils, and compared with other main models. 1
INTRODUCTION
The water retention characteristic or water retention curve (WRC) is an important constitutive feature of soils. It is an indispensable requirement in hydraulic transport modelling. Due to its great interest, a large number of research studies have been conducted and many models were proposed for the WRCs of soils. In general, these models could be classified into two groups, they are: the phenomenological or empirical models, and the conceptual or physical models. In the first group, van Genuchten’s model (van Genuchten 1980) could be the most popular one. But previous practice has shown it usually fails at low water content (Ippisch et al. 2006). Most conceptual models use a bundle of cylindrical capillaries (BCC) to represent the pore space geometry. They assume that the soil particle size distribution (PSD) due to the fragmentation processes decides the void/pore size distribution (VSD). It is the VSD that decides the WRC according to Laplace’s equation in capillary law. Different PSD models have been proposed, including power
functions (Assouline et al. 1998), which has been backed by the single fractal models (Xu & Dong 2004), and log-normal functions according to the probability of fragmentation theory (Tuli et al. 2001, Hwang & Choi 2006). A key issue of these models is that the relationship between VSD and PSD is not determinate, which could be linear or nonlinear (Assouline et al. 1998). Recently, a liquid configuration-based model was proposed to take account of the effect of the adsorption of solid surface (Tuller et al. 1999). But it has been pointed out that its representative unit cell cannot generally represent the irregular pore space in actual soils (Chertkov 2004). Precisely, all of these preceding models were proposed to model the WRC under static conditions, which do not take account of dynamic effects, such as the fluid in flowing processes, the viscous and/or gravity effects (Beliaev & Hassanizadeh 2001). The dynamic effects on WRC are very important. Some researchers ever studied the dynamic capillary pressure according to the thermodynamic behaviour of the fluids in multiphase flowing processes within porous media (Gray
675
and Hassanizadeh 1998). This paper, however, still only discusses the WRC under static conditions. Previous experiments have shown that unsaturated soils present a linear relationship between air-water interfacial area and the pore saturation. Petersen et al. (1996) found that water retention characteristic was significantly connected with the specific surface area of the soil (Bachmann & van der Ploeg 2002). This paper tries to investigate the internal relations between the WRCs and these observations. A traditional BCC model is employed to represent capillary pore geometry, meanwhile interfacial surface theory is used to describe the individual behaviour of the coexisting water and vapour phases in unsaturated porous media. Finally volume averaging analysis generates a determinate formula for water retention characteristic. Based on the formula, a simplified WRC model is proposed. The model is tested on different soils and compared with other models. 2
THEORY
In unsaturated soils, the curved meniscus is only a small part of the water-vapour interface. Because, at the start of a wetting or the end of a draining process, a thin uniform water film which coats the whole pore surface has been formed, the water-vapour interfacial area should decrease with water content once the meniscus is formed, and becomes zero at full saturation (Costanza-Robinson & Brusseau 2002). Modern interfacial science suggests that surface forces modify the properties and chemical potential of the interfacial region relative to their free bulk phase values (Tuller et al. 1999). Due to their surface interactions with the solid phase, the water and vapour phases in unsaturated soils have their individual pressures. Under equilibrium, the pressure difference of the two phases is balanced by the capillary pressure due to the meniscus, which follows the Young-Laplace equation (Dullien 1991): Pc = Pw − Pv =
2σvs 2σws − r r
meniscus. In another word, it could be said that, under equilibrium, the position of the meniscus just balances the pressure difference between the water and vapour phases. It is this mechanism that decides the WRCs of soils. It has been suggested that the chemical potential change caused by surface adsorption can be evaluated using Kelvin’s equation (Tuller et al. 1999): uf = RT ln
(2)
where uf is the molar chemical potential change of the adsorbed fluid on the substrate surface; R is the gas constant; T is temperature; and P/P0 is the relative pressure of the equilibrium vapour surrounding the adsorbed fluid. According to the mechanical equilibrium, the absolute pressure of the adsorbed fluid equals to its surrounding vapour pressure plus the chemical potential change due to adsorption, i.e.: Pfad
uf uf = + P0 exp Vf RT
(3)
where Vf is the molar volume of the fluid; Logically, Eq. (3) is applicable to both water and vapour phases in unsaturated soils. When the atmospheric pressure is set as reference, the individual absolute pressures of the two phases can be expressed as: Pw =
uw uw + P0 exp Vw RT
uv uv Pv = + P0 exp Vv RT
(4a)
(4b)
where the subscript w and v indicate the water and vapour phases, respectively. Substituting Eq. (4) into (1) yields:
(1) Pc =
where Pc is the capillary pressure; Pw and Pv are the absolute pressures of the water and vapour phases, respectively; σws is the interfacial tension between water and solid phases; σvs is the interfacial tension due to the molecular interaction between vapour and solid phases via a thin intervening water film (Iwamatsu & Horii 1996); r is the local pore size at the position of meniscus. Eq. (1) could be understood to mean that the pressures of the water and vapour phase in unsaturated soils are caused by their respective interactions with the solid phase, and related to the position of the
P P0
uv uw uw uv − + P0 exp − P0 exp Vw RT Vv RT (5)
Eq. (5) describes the phase equilibrium at microscopic pore scale. Using volume averaging theorem the macroscopic average of Pc is defined as: Pc =
676
=
1 Vpore 1 Vpore
1 Pc dV Vpore
1 Vpore
uw uw dV + P0 exp Vw RT
uv uv dV + P0 exp Vpore Vpore Vv RT 1 1 uw uw = + P0 exp dV Vpore Vwater Vw RT 1 uv uv 1 + P0 exp dV − Vpore Vvapour Vv RT 1
1
−
to the bulk volume of the porous material), the molar chemical potential changes of the water and vapour phases in unsaturated soils can be related to the specific surface areas of the two distinctive parts which are occupied by the water and vapour phases, respectively, i.e.: (6) 2 s 3 e uw = Am w Vw s¯ ws + Aw Vw s¯ ws + Aw Vw s¯ ws
where Vpore represents the total pore volume with an representative elementary volume (REV) of porous media; Vwater is water volume; Vvapour is vapour volume. Because the discussion is under the assumption of static/equilibrium states, when the local Pw and Pv are either constant (an intrinsic phase average) at any place where they occupy, respectively, or zero otherwise, Eq. (6) can be further developed as:
uw uw ds + P0 exp Vw RT 0 1 1−S uv uv d(1 − s) + P0 exp − RT Vv 0
1 Pc =
S
uv =
1 Vpore 1 Vpore
1 uw dV
(8a)
Vwater
1
uv dV
(8b)
Vvapour
According to Iwamatsu and Horii (1996) and Tuller et al. (1999), the molar chemical potential of an adsorbed fluid is related to the fluid thickness h on the substrate surface, and consists of several components, i.e.: uf (h) = Vf m (h) + e (h) + s (h) + a (h)
+ Asv Vv s¯vs
(10a) (10b)
s¯ws =
Sws Vbulk S
(11a)
s¯vs =
Svs Vbulk (1 − S)
(11b)
where Sws is the water-solid interfacial area; Svs is the vapour-solid interfacial area; Vbulk is the bulk volume of the porous material. Because a thin water film intervenes between all of the vapour-solid interfaces, it can be approximated that Svs ∼ = Svw by ignoring the extremely small cross section of the throats which connect pores, where Svw is the vapour-water interfacial area. Published experiments (Karkare & Fort 1996, Kim & Rao 1997, Costanza-Robinson & Brusseau 2002) and modelling works (Cary 1994, Bradford & 1997, Nordhaug et al. 2003) have generally demonstrated a linear relationship between vapour-water interfacial area and water saturation degree in unsaturated soils, i.e.: Svs ∼ Svw = s¯ (1 − S) = Vbulk Vbulk
(9)
where m (h) originates from van der Waals molecular interaction which is proportional to 1/h3 ; e (h) is the electrostatic component proportional to 1/h2 ; s (h) is the structural component proportional to 1/h; a (h) is a component due to non-uniform concentrations in the film which will be ignored in the following discussion. Using a BCC geometric model, the thickness h of the adsorbed fluid could be understood as the radius of the representing capillary. Under the rule of the same in pore surface area, the BCC model could be further equivalent to a single capillary with a ‘hydraulic radius’ which is defined as the ratio of the pore volume to the pore surface area (Dullien 1991). Because ‘hydraulic radius’ is inversely proportional to ‘specific surface area’ (the ratio of pore surface area
2 + Aev Vv s¯vs
where the subscript w and v indicate the water and vapour phases, respectively; A is constant; V is molar volume; s¯ws is the specific surface area of the waterfilled part of porosity, and s¯vs is the specific surface area of the vapour filled part of porosity, they are defined as:
(7)
where S is water saturation, uw and uv are the intrinsic average molar chemical potential changes of the water and vapour phases due to the adsorption effect of pore surfaces, which is defined as: uw =
uv =
3 Am v Vv s¯ vs
(12)
where s¯ is the specific surface area of the bulk porous material, which is defined as: s¯ =
Svs + Sws Vbulk
(13)
Substituting Eq. (12) into (13) yields: Sws = s¯ S Vbulk
(14)
Substituting Eqs. (12) and (13) into (11) yields that s¯ws = s¯vs = s¯ . So Eq. (10) represents two constants
which depend on the specific surface area of a porosity.
677
As a result, Eq. (8) can be rewritten as: uw = uw0 + uw S
(15a)
uv = uv0 + uv (1 − S)
(15b)
where uw0 and uv0 are initial chemical potential changes due to the formation of an initial water molecular film on pore surfaces before water and vapour phases start to accumulate within pore spaces. Substituting Eq. (15) into (7), then the integral produces: ⎡ 0 ⎢ uw
Pc = ⎣
Vw
S+
uw 2 S 2Vw
+
P0 exp
0 uw RT
exp
uw RT
uw S RT
⎤
⎥ −1 ⎦
3
0 uv ⎢ u − ⎣ v (1 − S) + (1 − S)2 Vv 2Vv
P0 exp
uv0 RT
uv RT
⎤ uv (1 − S) ⎥ −1 ⎦ exp RT (16)
If we set: 0 2 uw uw ; Pw0 = P0 exp RT RT 02 uv uv ; Pv0 = P0 exp RT RT φ0 = −
Pc = φ0 + P0 exp(αSe ) − exp(β(1 − Se ))
uv0 uv − + Pv0 − Pw0 ; Vv 2Vv
φ1 =
uw0 uv0 uv + + ; Vv Vv Vw
φ2 =
uw uv uw uv − ; αw = ; αv = , 2Vw 2Vv RT RT
Eq. (16) can be written as: Pc = φ0 + φ1 S + φ2 S 2 + Pw0 exp(αw S) − Pv0 exp(αv (1 − S))
(18)
where φ0 , P0 , α and β are four redefined fitting parameters. In the following, Eq. (18) will be compared with other models to fit the measurements of the WRCs of a wide range of soils.
⎡
+
Se = (S − Sr )/(Ss − Sr ) due to inaccessible pore spaces, where Sr is the remaining saturation and Ss is the saturated saturation. All of the constants, φ0 , φ1 , φ2 , Pw0 , Pv0 , αw and αv , are related to the specific surface area of the porous material. However, Eq. (17) is not convenient in practice. There are too many parameters and they are related to each other. To overcome this disadvantage, we propose to use the following model to fit WRCs (a detailed discussion on the reason to choose such form will be discussed elsewhere (Wang et al. 2008)):
(17)
Theoretically, Eq. (17) represents the water retention characteristic of porous media. The saturation S need to be replaced using the effective saturation
EXAMPLES
Figure 1 shows the fitting results for five soil samples and the comparison with van Genuchten model. The fitting parameters are listed in Table 1. As we can see, good fitting results have been obtained by both models, but a further improvement at the two ends can be observed in the case of Beit Netofa Clay when using the proposed model. An inflection point is seen in most cases, except for Beit Netofa Clay. If the measurements of Beit Netofa Clay are carefully studied, it can be noticed that its WRC is not continuous but presents an irregular concave shape in the middle of the curve. This is similar to an experimental result of dual-porosity soils (Kohne & Gerke 2002). That means two differently scaled pore systems could co-exist in the Beit Netofa Clay at the same time, for example, the clay sample could have fractures (a structured porosity) within it. According to the dual-porosity theory, the two different porosities have different ‘specific surface area’, and as a result the two different porosities have their individual WRCs which could be fitted using Eq. (16), respectively. A detailed study on the application on the multiporosity problems is underway. Figure 2 shows a comparison with a fractal model which is in a power-law form. It can be seen that the proposed model presents a much better result, particularly relating to the shape of the WRC. It demonstrates an inflection point which is in agreement with the experimental measurements. Figure 3 shows a comparison with two lognormal PSD models which assume a linear and nonlinear relation between PSD and VSD, respectively. It can be seen that the proposed model is even better than the original nonlinear model in the two cases, in particular on
678
Table 1.
Fitting Parameters for the Soil Sample in Fig. 1.
Hygiene Sandstone Touchet Silt Loam Silt Loam Beit Netofa Clay Guelph Loam (drying)
φ0 (cm)
P0 (cm) α
β
−127.8
0.2289 5.07
5.715 0.15
−209.8 −255.5
0.2342 6.227 6.745 0.18 0.47 2.048 4.728 7.223 0.131 0.396
Sr
Ss 0.25
−5.375e-5 1489
0.13
−98.69
3.166 5.726 0.218 0.52
3.673
5.342 0.0
0.446
(a) Fitting results use the proposed model
(b) Original data and modelling Figure 2. 2004).
Figure 1.
WRCs for soils (van Genuchten 1980).
Comparison with a fractal model (Xu & Dong P.
the side of low saturation where the accuracy improvement is more significant. Because the pressure head is presented in lognormal form, the fitting improvement at the low saturation (high pressure head) side will enhance the total accuracy significantly. Figure 4 shows a comparison with the configurationbased unit cell model. It can be seen that the proposed
679
volume averaging theorem, generates a deterministic formula for the water retention characteristic of unsaturated porous media. This formula demonstrates the internal linkage between the WRCs and the ‘specific surface area’. Based on this formula, a simplified fitting model has been proposed for the WRCs. Compared with other main models, it has been shown that this model is more accurate, particularly at the side of low saturation or high pressure head.
REFERENCES
Figure 3. Comparison with a lognormal PSD model (Hwang & Choi 2006).
(a) Fitting results using the proposed model
(b) Original data and modelling
Figure 4. 2002).
Comparison with a unit cell model (Tuller & Or
model works very well on both of the soil samples. The fitted WRCs present a very good shape and accuracy against the measurements.
4
CONCLUSIONS
This paper tried to explain the water retention characteristic according to the physical and chemical behaviours of the phases involved. The analysis, which follows the capillary, interfacial surface theories and
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Kohne, J.M. & Gerke, H.H. 2002. Estimating the hydraulic functions of dual-permeability models from bulk soil data. Water Resources Research 38: 26.1–26.11. Nordhaug, H.F. Celia, M. & Dahle, H.K. 2003. A pore network model for calculation of interfacial velocities. Advances in Water Resources 26: 1061–1074. Petersen, L.W. Moldrup, P. Jacobsen, O.H. & Rolston, D.E. 1996. Relations between specific surface area and soil physical and chemical properties. Soil Science 161: 9–12. Tuli, A. Kosugi, K. & Hopmans, J.W. 2001. Simultaneous scaling of soil water retention and unsaturated hydraulic conductivity functions assuming lognormal pore-size distribution. Advances in Water Resources 24: 677–688. Tuller, M. & Or, D. 2002. Unsaturated hydraulic conductivity of structured porous media: A review of liquid configuration-based models. Vadose Zone Journal 1: 14–37.
Tuller, M. Or, D. & Dudley L.M. 1999. Adsorption and capillary condensation in porous media: Liquid retention and interfacial configuration in angular pores. Water Resources Research 35(7): 1949–1964. van Genuchten, M.T. 1980. A close-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Soc. Am. J. 44: 892–898. Wang, Y. Grove, S.M. & Anderson, M.G. 2008. A physicalchemical model for the static water retention characteristic of unsaturated porous media, Advances in Water Resources (in press). Xu, Y.F. & Dong, P. 2004. Fractal approach to hydraulic properties in unsaturated porous media. Chaos Solutions & Fractals 19: 327–337.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Temperature effect on hydric behaviour for unsaturated deformable soils S. Salager, M.S. El Youssoufi & C. Saix Laboratoire de Mécanique et Génie Civil, Université Montpellier 2, France
ABSTRACT: Considering an unsaturated soil with pure water, the suction can be expressed with respect to three independent variables: water content, void ratio, and temperature. From the expression of the total differential of the suction, we propose a constitutive relation which links variations of suction, water content, void ratio, and temperature. This relation allows the analysis of several particular cases. At constant temperature, this relation could be represented by a characteristic surface in the parameter space (water content, suction, void ratio). This surface, which reflects the hydro-mechanical couplings in soils, can be considered as a generalization of the classical Soil Water Characteristic Curve (SWCC). At constant suction, the constitutive relation allows to predict the water content variations due to temperature changes. Thus, from a SWCC obtained at a given temperature, the model can predict this curve for other temperatures. This model has been successfully tested by the authors on experiments performed on two different materials.
1
INTRODUCTION
The relationship between suction and soil water content is generally presented through the Soil Water Characteristic Curve (SWCC); it is a fundamental relation used to describe the hydric behaviour of unsaturated soils. The SWCC was widely studied during the last decades: (i) fitting equation (Fredlund and Xing 1994), (ii) influence of soil compaction conditions (Sugii et al. 2002); (Verbrugge and Fleureau 2001); (Tarantino and Tombolato 2005); (iii) hysteresis modelling (Pham et al. 2005) (iv) temperature influence (Salager et al. 2006). Most of these authors present the SWCC using the saturation degree or the water content, but despite void ratio measurements in some cases, very few models taking into account volume changes have been proposed (Gallipoli et al. 2003); (Salager 2007). In the thermo-hydro-mechanical framework, a complete characterization of the hydric behaviour needs to use more complex tools than SWCC to take into account hydro-mechanical and hydro-thermal couplings. In this respect, this paper presents the development of constitutive relations which lead to provide a basis for analyzing the hydric behaviour of soil in a thermo-hydro-mechanical framework. At constant temperature, the constitutive relations define the characteristic surface which reflects the hydric behaviour of a soil taking into account hydromechanical couplings. The equation of this surface has been established in the case of a clayey silty sand from 250 experimental measurements. At constant suction, the constitutive relations lead to a thermo-hydric
model allowing to predict the effect of temperature on the SWCC. This model has been successfully tested by the authors on experiments performed on two different materials.
2
CONSTITUTIVE RELATIONS
To describe the evolution of the thermodynamic state of an unsaturated soil, the most frequently used variables are volume strain εv = tr(ε), water content w and temperature T . The volume strain, as usually in soil mechanics, will be linked to the void ratio variations e through the relation e = −(1 + e0 )tr(ε). The water content w could be substituted by the water volume fraction θ, or the degree of saturation Sr . The evolution of the thermodynamic state of a partially saturated soil could be, consequently, described by means of one of the three following sets of state variables: − water volume fraction θ, temperature T and void ratio e, − water content w, temperature T and void ratio e, − degree of saturation Sr , temperature T and void ratio e. The following theoretical developments are based on the different expressions of the suction differential with respect to the three variables of each set proposed above. In addition, only monotonic drying hydric paths are considered, permitting thus to avoid hysteresis phenomena.
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Suction differential with respect to θ , T , e
2.1
The suction differential with respect to the set of variables θ , T , e can be written: ∂s ∂s ∂s dθ + dT + de (1) ds = ∂θ T ,e ∂T θ ,e ∂e θ ,T In addition, the water volume fraction can be written as a function of the density of the solid phase ρs , the density of the liquid phase ρe , the water content w, and the void ratio: ρs w ρe (1 + e)
θ=
(2)
By introducing the volumetric thermal expansion coefe ficient of water βe = − ρ1e dρ dT and of the solid phase s − ρ1s dρ dT , the infinitesimal variation of θ
βs = written : dθ =
could be
ρs w ρs dw + (βe − βs )dT ρe (1 + e) ρe (1 + e) ρs w de − ρe (1 + e)2
(3)
Equation (2) also allows to write:
∂s ∂θ
ρe (1 + e) ρs
= T ,e
∂s ∂w
2σs cos φ r
∂s ∂T
θ ,e
=
(5)
∂φ ∂σs − s tan φ ∂T θ ,e ∂T θ ,e s ∂r − r ∂T θ ,e s σs
(6)
The surface tension of pure water depends mainly on the temperature. Thus, it comes:
∂σs ∂T
θ ,e
=
dσs dT
By introducing equations (3), (4) and (9) in equation (1), the final form of the suction differential is obtained: ∂s dw ds = ∂w T ,e s dσs dφ ∂s w(βe −βs )+ −s tan φ dT + ∂w T ,e σs dT dT ∂s w ∂s de (10) − + ∂e θ,T ∂w T ,e (1 + e) 2.2
Equation 5 allows to write :
The last term of equation (6) is the variation of the mean pore radius due to the temperature. The water volume fraction and the void ratio remaining constant, this term is equal to zero. Finally, equation (6) is reduced to: dφ s dσs ∂s − s tan φ (9) = ∂T θ,e σs dT dT
(4) T ,e
In pendular and funicular domains, water is in a capillary state, it is so justified to use Jurin’s law. This law expresses the suction s as a function of the surface tension of water σs , the mean pore radius r, and the contact angle φ. s=
the lack of information available in literature on this parameter, it is assumed that the contact angle is only a function of the temperature. This leads to: ∂φ dφ (8) = ∂T θ,e dT
(7)
The contact angle depends mainly on surface roughness of solid phase, temperature, and meaning evolution of the hydric state (wetting or drying). Given
Suction differential with respect to w, T , e and with respect to Sr , T , e
In the same way, the suction differential could be expressed with respect to the set of variables w, T , e: ∂s dw ds = ∂w T ,e dφ s ∂r s dσs − s tan φ − dT + σs dT dT r ∂T w,e ∂s de (11) + ∂e w,T and with respect to the set of variables Sr , T , e. The final form obtained is always written with the same set of variables than equations (10) and (11): ∂s dw ds = ∂w T ,e dφ s ∂r s dσs − s tan φ − dT + σs dT dT r ∂T w,e ∂s w ∂s de (12) − + ∂e Sr ,T ∂w T ,e e
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2.3
One can introduce in the three final equations obtained from each of the three previous developments the notations below: ∂s ∂s ; FT = ; Fw = ∂w T ,e ∂T w,e ∂s (13) Fe = ∂e T ,w
1. Fw =
∂s ∂w
(14) T ,e
Fw is a function associated with the suction variation due to the water content variation at constant temperature and void ratio. For an undeformable media, this term is the inverse of the SWCC slope. This function is negative because an increase of water content induces a decrease of suction. 2. FT = Fw w(βe − βs ) +
dφ s dσs − s tan φ σs dT dT
dφ s s dσs FT = − s tan φ − σs dT dT r
∂r ∂T
(15)
∂r ∂T
∂s ∂e
w Fe = − Fw (1 + e) θ,T w ∂s = − Fw e ∂e Sr ,T
=
∂s ∂e
T ,w
(18)
The sets of variables which involves the water content w is certainly the most appropriate for a comparison with experimental results. It is in connection with the easy determination of w which requires only mass measurements, in opposition to water volume fraction θ and degree of saturation Sr which require volume measurements. Nevertheless, ∂r one can note the ∂s difficulty to access the terms ∂T and ∂e . w,e θ,T Consequently to these two reasons, the following final form will be retained for the suction differential expression: ds = Fw dw dφ s dσs − s tan φ dT + Fw w(βe − βs ) + σs dT dT + Fe de
(16) w,e
= Fw w(βe − βs )
One can deduce from equations (15) and (16), a relation which links the volumetric thermal expansion coefficients of water and solid phase to meniscus radius as well as its variation with temperature. s r
3.
Fe is the function associated with the suction variation due to the void ratio variation at constant temperature and water content.
The identification between these three equations (equations (10),(11), and (12)) leads to make explicit the state functions Fw , FT , and Fe .
−
angle variation at constant water content and void ratio.
Parallel between the three developments
(17)
w,e
From the equation (15), one can also define three functions: − FT β = Fw w (βe − βs ) : which is the function associated with the suction variation due to the thermal expansion of liquid and solid phases at constant water content and void ratio, s − FT σ = σss dσ dT : which is the function associated with the suction variation due to surface tension variation at constant water content and void ratio, − FT φ = −s tan φ dφ dT : which is the function associated with the suction variation due to contact
(19)
Equation (19) defines an expression of the thermodynamic state evolution which links suction, water content, temperature, and void ratio variations in the general case. This expression will be used in the following in different particular cases. 2.4 Analysis of elementary cases Relation (19) can be used in the analysis of some elementary cases. This analysis, which allows the consistency of the proposed expression to be confirm, is based on the negative or positive sign of the three functions Fw , FT and Fe . Accounting for the SWCC shape, the function Fw is negative. The derivative of the surface tension with respect to temperature is negative, and therefore the function FT is negative. To determine the variation of the function Fe , in a first approximation, one can consider a physical model composed by two grains linked by a water meniscus. This function is determined at constant water content and temperature. The meniscus water volume is constant. If the grains are pulled aside to increase the void ratio, the meniscus hollow increases leading a decrease of the radius of curvature, and using the Jurin’s law, an increase of suction. Function Fe appears to be positive. Of course
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a variation of void ratio induces in the soil more complex phenomena but the characteristic surface that will be presented later confirms the results obtains with this simple physical model. Six cases where two of the four variables s, T , w, and e remain constant are presented here: – Case 1, e and T constant: in this case, equation (19) comes ds = Fw dw. Allowing that the function Fw is negative, a water content increase leads to a suction decrease. This is a classical result on the variations of water content and suction in the case of SWCC. – Case 2, w and T constant: in this case, it comes ds = Fe de. The function Fe is positive, and therefore void ratio increase leads to a suction increase. This result is also consistent because a void ratio increase at constant water content leads to a decrease of the degree of saturation Sr = Gs we and consequently a suction increase. – Case 3, e and w constant: in this case, it comes ds = FT dT . The function FT being negative, a temperature increase leads to a suction decrease. This means that the temperature and suction vary in opposite directions if the other variables are held constant. – Case 4, s and T constant: in this case, it comes Fw dw + Fe de = 0. The function Fw being negative and Fe positive, it is possible to infer that the void ratio and the water content vary in the same direction if the other variables remain constant. It means that a void ratio increase should be concomitant with a water content increase and vice versa. – Case 5, e and s constant: in this case, it comes Fw dw + FT dT = 0. The functions being negative, it is possible to infer that a temperature increase should be concomitant with a water content decrease if the other variables remain constant. – Case 6, w and s constant: in this case, it comes Fe de + FT dT = 0. The function Fe being positive and FT negative, it is possible to conclude that void ratio and temperature vary in the same direction; it means that a temperature increase should be concomitant with a void ratio increase if the other variables remain constant.
3
CONCEPT OF CHARACTERISTIC SURFACE
function could be represented by a surface in the space defined by the three variables. This surface which gives the retention capacity of the soil for any void ratio value could be named the Soil Water Characteristic Surface (SWCS). This surface has been established on a clayey silty sand in the case of monotonic drying hydric paths. This soil is classified as SC-CL according to the USCS. The liquid and plastic limits are respectively 25% and 14.5%. Sand, silt, and clay fraction are 72%, 18%, and 10% respectively. The clay fraction consists mainly of smectite, chlorite, and phyllite. Triplets (s, w, e) have been measured all along five drying paths corresponding to five initial void ratios. Each of these paths leads to 16 or 18 measurements (s, w, e). Each measurement itself is the average of the measurements done on three samples. Thus, the whole measurements are related to a total of 150 samples. These experimental results can be fitted to an analytical form of the characteristic surface which can be written (Salager et al. 2007): if w ≤ e/Gs ⇒ f = w − a · e − b · (1 − a · Gs ) = 0 e =0 (21) if w ≥ e/Gs ⇒ f = w − Gs where a and b are characteristic functions of the soil which depend on suction (a = a(s) and b = b(s)). These functions could be modeled by means of relations derived from the following expression (Fredlund and Xing 1994): ⎞ ln 1 + ssr x(0) ⎠ x(s) = ⎝1 − n m 106 ln 1 + sr ln exp(1) + ss ⎛
i
(22) where x(0) is the value of the function at saturation, sr , si , n and m are parameters adjusted from experimental results. The characteristic surface of the clayey silty sand is given in figure 1. The characteristic surface equation allows to proposed explicit expressions of the functions Fw and Fe : Fw =
At constant temperature, equation (19) leads to: ds = Fw dw + Fe de
(20)
This equation shows, that at a temperature T0 , there exists a function f which links the variations of suction, water content, and void ratio: f (s, w, e) = 0. This
Fe =
1 ∂a ∂s ∂a ∂s
(e − bGs ) + w a
−
b a
∂b ∂s
(1 − aGs )
−a +
∂b ∂s
(1 − aGs )
(23) (24)
Figure 2 represents the function Fw with respect to suction and void ratio; Figure 3 represents the function Fe with respect to suction and water content.
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To extract an equation of thermo-hydric evolution from the equation 19, one can consider, in the case of hydric loading path, a specified suction (s = cst, ds = 0). During a thermo-hydric process, the void ratio varies with suction and temperature. But it is already established that temperature has only a negligible effect on void ratio, compared to the suction effect (Francois et al 2007). In this case, specifying a suction implies specifying the void ratio too. In this condition, equation (19) could be reduced to a relation between water content and temperature variations. dw = − Figure 1.
Characteristic surface of the clayey silty sand.
FT dT Fw
(25)
In addition, there are few literature results concerning contact angle but it is known that, in natural soil, this angle and its variation versus temperature are very limited (Bachmann et al. 2000). Thus, it will not be taken into account. Futhermore, the volumetric thermal expansion coefficient of the solid phase is supposed to be negligible, compared with volumetric thermal expansion coefficient of water. It comes a simplified expression of the function FT and the explicit expression of the equation of thermo-hydric evolution could be written:
Figure 2. Fw evolution versus suction for different void ratios.
Figure 3. Fe evolution versus suction for different water contents.
4
PREDICTIVE EQUATION FOR TEMPERATURE EFFECT ON SWCC
Several mechanisms can be proposed to explain the influence of temperature on the unsaturated soil hydric behaviour: thermal expansion of liquid and solid phases, surface tension of water, and contact angle variations (Bachmann and van der Ploeg 2002). The equation of the thermodynamic state evolution (19) takes into account all these phenomena.
s dσs dw = − wβe + Fw σs dT
dT
(26)
βe and σs are water characteristics. Consequently, the equation of thermo-hydric evolution (26) needs only the knowledge of the function Fw . In the case of undeformable media, this function simply correspond to the inverse of the slope of the SWCC obtained at a reference temperature. In the general case, Fw depends on the suction and the void ratio. Consequently, its determination needs the knowledge of the derivative of the suction with respect to water content for each void ratio value. In this case, a reference SWCC is not sufficient. The approriate tool is the SWCS (Salager et al. 2007). The first media used to test the validity of the equation of thermo-hydric evolution is a ceramic. Its SWCC has been determinated experimentally for two temperature: 20 and 60◦ C. The SWCC obtained at 20◦ C is taken as reference. The function Fw is calculated from this curve. Using this function, equation (26) allows to predict the SWCC at 60◦ C. Figure 4 shows the SWCC obtained for the ceramic. The solid line represents the results corresponding to 20◦ C and the dashed line reprensents the ones corresponding to 60◦ C. These curves are modelled from experimental data using the fitting function of Fredlund and Xing (Fredlund and Xing 1994). The line with circle represents the SWCC corresponding to 60◦ C calculated
687
5
Figure 4. SWCC for the ceramic; experiments and modelling.
CONCLUSIONS
This paper proposed a constitutive relation which leads to a basis for the analyzis of the hydric behaviour of soil in a thermo-hydro-mechanical framework. In particular, this relation introduces the concept of soil water characteristic surface which appears to be relevant to model volume changes in deformable unsaturated soils. An example of soil water characteristic surface was presented in the case of monotonic drying paths for a clayey silty sand. This relation makes it possible to define a predictive equation on temperature effect on SWCC. This equation has been tested with success on two materials. REFERENCES
Figure 5. SWCC for the clayey silty sand; experiments and modelling.
from the predictive model. In spite of a little deviation around the slope changing of the curve, the results coming from the experiments and from the model are in good agreement for this material and validate the predictive function (26) for undeformable media. Like it has been done for the ceramic, two series of tests have been performed to determine the SWCC corresponding to 20 and 60◦ C of the clayey silty sand. This soil is deformable under hydric loading. Consequently, hydro-mecanical couplings have to be taken into account. The function Fw is calculated from its SWCS established beforehand and presented in Figure 1. Figure 5 shows the SWCC obtained for the clayey silty sand. The graphic guidelines is the same as for the ceramic. Concerning low suctions, the predictive model overestimates the temperature effect. However, for the rest of the suction range, the predictive model permits a good prediction of the SWCC at 60◦ C. This result validates the predictive function (26) for deformable media.
Bachmann, J., R. Horton, R. van der Ploeg, and S. Woche (2000). Modified sessile drop method for assessing initial soil-water contact angle of sandy soil. Soil Science Society of America Journal 64, 564–567. Bachmann, J. and R. van der Ploeg (2001). A review on recent developments in soil water retention theory: interfacial tension and temperature effects. Journal of Plant Nutrition Soil Science 165, 468–478. Francois, B., S. Salager, M. El Youssoufi, D. Ubals Picanyol, L. Laloui, and C. Saix (2007). Compression tests on a sandy silt at different suction and temperature level. In CDrom, 10 pages, Denver. GeoDenver. Fredlund, D. and A. Xing (1994). Equations for the soil-water characteristic curve. Canadian Geotechnical Journal 31(3), 521–532. Gallipoli, D., S. Wheeler, and M. Karstunen (2003). Modelling the variation of degree of saturation in a deformable unsaturated soil. Geotechnique 53(1), 105–112. Pham, H., Fredlund, D. and Barbour, S. (2005). A study of hysteresis models for soil-water characteristic curves. Canadian Geotechnical Journal 42, 1548–1568. Salager, S. (2007). Etude de la rétention déau et de la consolidation des sols dans un cadre thermo-hydro-mécanique. Ph. D. thesis, Université Montpellier 2. Salager, S., M. El Youssoufi, and C. Saix (2007). Experimental study of the water retention curve as a function of void ratio. In CDrom, Denver, pp. 10. GeoDenver. Salager, S., F. Jamin, M. El Youssoufi, and C. Saix (2006). Influence de la température sur la courbe de rétention d’eau. C.R. Mécanique 334, 393–398. Sugii, T., K. Yamada, and T. Kondou (2002). Relationship between soil-water characteristic curve and void ratio. Volume 1, pp. 209–214. 3rd International Conference on Unsaturated Soils: Swets and Zeitlinger. Tarantino, A. and S. Tombolato (2005). Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Geotechnique 55(4), 307–317. Verbrugge, J. and J. Fleureau (2002). Bases expérimentales du comportement des sols non satur´es. In O. Coussy and J. Fleureau (Eds.), Mécanique des sols non saturés, pp. 69–112. Hermes.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A study of applied pressure on the Soil Water Characteristic Curve J. Zhou Geotechnical Engineering Institute, Civil Engineering Department, Zhejiang University, China
ABSTRACT: In order to study the influence of applied pressure on the Soil Water Characteristic Curve (SWCC), samples with different initial void ratio/density were tested in a triaxial apparatus for unsaturated soil. This paper focuses on the influence of pressure on SWCC and hydraulic hysteresis by analyzing the data reported in the literature. Results show that the higher the pressure, the higher the saturation and the air-entry value. The size of hysteresis loop becomes smaller with the applied pressure, which indicates that the effect of hydraulic hysteresis on soil behavior gets smaller. Based on the study, the SWCC under different applied pressure can be easily modeled since the same mathematical expression can be used due to little change in the shape. The findings described in this paper can also be used as a proof of coupled effect of pressure and suction.
1
INTRODUCTION
The soil-water characteristic curve (SWCC) plays a very important role in the behaviour of partially saturated soils. A number of properties of a partially saturated soil can be obtained from the SWCC, such as the coefficient of permeability, shear strength and volume strain, pore size distribution, the amount of water contained in the pores at any suction. Due to the enormous potential in application, many researchers have proposed general mathematical expressions for SWCC, which suit various soil types and have only a few parameters with clear physical meaning. Models such as that of Gardner (1956), Brooks & Corey (1964), Brutsaert (1966), van Genuchten (1980), McKee & Bumb (1987), Burdine (1953), Mualem (1976), Kosugi (1994), Fredlund & Xing (1994) are widely used. However, studies on this subject are still carried out, because various factors influencing the SWCC have not received much attention. Of those the applied pressure is a crucial one. In the field, due to its depositional history, soil normally experiences a certain stress, which is recognized to have some influence on SWCC (Fredlund & Rahardjo, 1993). The suction probe and the filter paper technique are often used for determining a SWCC from unconfined soil samples. Models based on these techniques cannot consider the effect of applied pressure. However, preparing sample with different initial void ratio/density or using modified triaxial tests can be an alternative method. In fact it is neither possible nor necessary to conduct tests under every condition, since tests of SWCC are very time-consuming. Regarding this, it is meaningful and worthwhile to study
the effect of applied pressures on SWCC through the existing data. Hydraulic hysteresis is a significant characteristic for partially saturated soil. When a soil is saturated or de-saturated, the corresponding soil water characteristic curve is different. This means that there is two different degrees of saturation corresponding to the same predetermined suction; one is on the drying path and the other on the wetting path. How the pressure affects hydraulic hysteresis is considered, as well as its influence on a single drying/wetting curve. A modified mathematical expression is proposed to easily simulate SWCC under different pressures. 2
EFFECT ON A SINGLE DRYING/WETTING CURVE
As mentioned before, many current techniques for determining SWCC are incapable of applying vertical pressure on unsaturated soil. Some alternative methods can be used; among which preparing specimen with different initial void ratio is one of the indirect ways. 2.1
Effect of initial void ratio
Kawai et al. (2000) used a silty clay to study the effect of initial void ratio on the SWCC by oedometer apparatus, in which suction was applied by means of pressure plate method. How air-entry value (AEV) changes with void ratio is shown in Fig. 1. The AEV (denoted SA in Fig. 1) reflects the magnitude of the capillary saturation zone in a soil. The larger the bulk pore sizes, the smaller the AEV. It can be seen that the smaller the
689
Figure 3. Soil-water characteristics for specimens compacted at optimum water content (Vanapalli, Fredlund & Pufahl, 1999).
Figure 1. Relationship between void ratio and AEV (Kawai et al., 2000).
the results of two series of samples, namely 7–10 and 5–10. The properties of the samples and the test procedures can be referred to the original thesis. All the samples in each series have nearly the same moisture content, but different void ratio, as shown in the legend in Fig. 2. It is clear from the test results in Fig. 2 that, as the void ratio becomes smaller, the hysteresis loops tend to move to higher suctions on the Sr -suction plot. This indicates the hysteresis loops should be dependent on void ratio. 2.2 Effect of stress state
Figure 2. SWCC for series 7–10 and 5–10 during first drying and wetting (Jotisankasa, 2005).
initial void ratio (i.e. the denser the soil), the higher the air-entry value, and the higher the residual degree of saturation as well. The air-entry value and the residual degree of saturation Sr0 can be expressed in terms of void ratio e using empirical relationships. The AEV is an important parameter for partially saturated soils since the degree of saturation starts to drop rapidly when the suction exceeds the AEV. There is a large range of AEVs corresponding to different void ratio values, as shown in Fig. 1. The denser the soil the higher the AEV, which implies that for soils with low void ratio values, if only small changes in degree of saturation occurred at low suctions, the soil can be simplified as fully saturated. This is a helpful assumption when dealing with soils from different depths. Jotisankasa (2005) also investigated the influence of initial void ratio on SWCC. The soil was artificial silty clay compacted dry of optimum. Fig. 2 shows
Vanapalli et al. (1996; 1998 and 1999) studied the influence of total stress state on the SWCC of a compacted fine-grained soil indirectly by pressure plate apparatus. The concept of equivalent pressure was used to represent different stress state. The SWCCs for the specimens compacted at optimum water content and with equivalent pressures of 25, 35, 80 and 200 kPa are shown in Fig. 3. It clearly shows that the air-entry value of specimens increases with increasing equivalent pressure. Specimens subjected to higher equivalent pressure correspond to higher saturation. The same conclusion can be drawn from the results of different equivalent pressures dry of optimum water content and wet of optimum water contents. So as the pressure increases, SWCCs move towards the right hand side with an increased value of AEV (the air-entry value).
3
EFFECT ON HYDRAULIC HYSTERESIS
In the constitutive model considering hydraulic hysteresis proposed by Wheeler et al. (2003), the coupled effect of stress and hydraulic hysteresis was simplified, as shown in Fig. 4. The increased plastic volume strain,
690
Figure 6. Figure 4. Influence of plastic volumetric strain on primary drying and primary wetting curve (Wheeler et al., 2003).
0.44
0.42
Volumetric water content
0.40
0.38
0.36
CDV-N1 (0kPa) CDV-N2 (40kPa)
0.34
CDV-N3 (80kPa)
0.32
0.30 0.1
Figure 5.
1
10 Matric suction (kPa)
100
1000
Effect of stress state on SWCCs (Ng et al., 2000b).
which was induced by stress, caused the primary drying and wetting curves to shift from the position shown by the solid lines to that of chain-dotted lines. In other words, the soil subjected to higher stresses will have higher saturation. But no detail was presented about how the stress influences the hysteresis loop itself, i.e. will the loop change its size when subjected to different stress. To investigate this phenomenon, Ng and Pang (2000) studied the influence of stress state on the SWCC of an ‘‘undisturbed’’ or natural, completely decomposed volcanic soil. A conventional volumetric pressure plate extractor and a modified one were used together. The SWCCs under different net normal stress from their research are shown in Fig. 5. It can be seen that soil specimens loaded to higher net normal stress exhibit lower initial volumetric water contents. The result implies that as matric suction increases, the volumetric water content of the specimen decreases, but at a different rate. The higher the
Results of bentonite/kaolin (Sharma, 1998).
applied load, the lower the rate of reduction in volumetric water content. In the end all three wetting curves shift to the positions lower than the original. Fig. 5 also shows that the size of these loops becomes smaller with stresses. The point where the volumetric water content starts to decrease significantly indicates the air-entry value. A general tendency that soil specimens subjected to higher stress exhibits higher air-entry values, which is related to the presence of a smaller average pore sizes distribution in soil specimens under higher load, can be observed. Testing data reveal that stress history or applied stresses seem to have little effect on the shape of SWCC. This is good news for mathematical modeling. Sharma (1998) conducted suction tests on bentonite/kaolin samples with the same maximum suction 400 kPa under different compaction pressures of 400 kPa, 800 kPa and 3200 kPa. Results are shown in Fig. 6. Results demonstrate that with the increase of the compaction pressure, the size of hysteresis loop gets smaller. Since the sample is expansive soil, its behavior is expected to be a little different from nonexpansive soil. However the general tendency shows that the degree of saturation gets higher with pressure. This conclusion agrees with what Vanapalli et al. (1999) gained for a single drying/wetting path and Ng et al. (2000b) for drying-wetting cycle. 4
MATHEMATICAL EXPRESSION
From the above results, the shape of SWCC can be assumed not significantly affected by pressure. Hence the same mathematical expression for zero pressure can be chosen while using different parameters. For example if using the van Genuchten model, a different set of parameters can be used for the drying curve and the wetting curve to simulate hydraulic hysteresis. If considering the effect of pressure on SWCC, a simple modification can be made by either relating
691
Figure 7. SWCC changing with applied pressure (only m changing with pressure).
the m parameter, or m and a parameters to the pressure, while keeping the remnant unchanged, since m is related to the asymmetry of the curve and a shifts the curve towards the higher or lower suction regions of the plot, but does not affect the curve shape. If only considering the m parameter changing with pressure, the following modification can be used: m = m[(1 − r) exp(−βp) + r]
(1)
where m is the original parameter in van Genuchten’s model and m is the modified parameter. r and β are best-fitting parameters for a certain soil. p is the applied pressure. Assuming m = 1, n = 1.5, a = 0.00013, r = 0.26 and β = 0.0164 and only considering modified parameter m changing with pressure, results in Fig. 7 show that the influence of pressure is significant at lower values and becomes smaller at higher values. At lower pressure values the gradient of the change in degree of saturation is significant, while it reduces with the increase of pressure. The air-entry value is increased with pressure. This is consistent with what was observed for non-expansive soils. As for expansive soil, different modifications may be preferred since the soil behaves in a different way. In modeling hydraulic hysteresis, parameters in two sets (one for drying curve and another for wetting curve) both need to be modified. Following the same concept, other models can also be modified. 5
Figure 8. Illustration of SWCC changing with different applied pressure.
change, as illustrated in Fig. 8. With the increase of applied pressures, a) the size of the hysteresis loop becomes smaller; b) the slope of SWCC becomes flatter; c) the degree of saturation gets higher. Results here clearly demonstrate that the coupled movement of SWCC and the volumetric stain, shown in Fig. 4, need to be modified. The shape of SWCC is not strongly influenced by the applied pressure, so the same mathematical expression can be applied after modifying the parameters. This provides a convenient way for modeling. A simple expression of relating m parameter with applied pressure by using van Genuchten’s model is presented. More tests on different soils and with large stress range are necessary. Further numerical analyses to verify the conclusions are also needed. Conclusions obtained in this paper are not only useful for mathematical modeling of SWCC under different pressure, but also helpful for the validation of coupled effect of suction and applied pressure when dealing with hydraulic hysteresis in constitutive modeling.
ACKNOWLEDGEMENTS Financial support from China Scholarship Council through Grant No.22833012 and from Chinese Education Ministry for overseas scholars is gratefully acknowledged. The author also acknowledges the New Star Project of Zhejiang University for its support, as well as the support and help from the host Imperial College, London, and in particular Prof. David M. Potts & Dr. Lidija Zdravkovic.
CONCLUSIONS
The influence of applied pressure on SWCC was investigated from existing published data. Single drying/wetting curves and hysteresis loops were both studied. It can be seen that a higher pressure leads to a high air-entry value and a high degree of saturation. When applying different pressures p1 , p2 and p3 , the primary drying and wetting curves will shift and
REFERENCES Brooks, R. & Corey, A. 1964. Hydraulic Properties of Porous Media, Hydrology Paper No.3. Colorado State University, Fort Collins, CO. Brutsaert, W. 1966. Probability laws for pore size distribution. Soil Science, 101:85–92.
692
Fredlund, D.G. & Rahardjo, H. 1993. Soil Mechanics for Unsaturated Soils. New York: Wiley. Fredlund, D.G. & Xing, A. 1994. Equations for the soil-water characteristic curve. Canadian Geotechnical Journal 31: 521–532. Gardner, W. 1956. Mathematics of isothermal water condition in unsaturated Soils. Highway research board special report 40 international symposium on physico-chemical phenomenon in soils: 78–87. Washington D.C. Jotisankasa, A. 2005. Collapse behaviour of a compacted silty clay. PhD thesis, Imperial college, London. Kawai, K., Karube, D. & Kato, S. 2000. The model of water retention curve considering effects of void ratio. In: Rahardjo, H., Toll, D.G. & Leong, E.C. (Eds.), Unsaturated Soils for Asia: 329–334. Rotterdam: Balkema. McKee, C. & Bumb, A. 1987. Flow-testing coalbed methane production wells in the presence of water and gas. SPE Formation Evaluation 10: 599–608. Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research 12: 593–622. Ng, C.W.W. & Pang, Y.W. 2000. Influence of stress state on soil-water characteristics and slope stability. Journal of Geotechnical and Geoenvironmental Engineering 126 (2): 157–166.
Sillers, W.S., Fredlund, D.G. & Zakerzadeh, N. 2001, Mathematical attributes of some soil-water characteristic curve models. Geotechnical and Geological Engineering 19: 243–283. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E. & Clifton, A.W. 1996. Model for the prediction of shear strength with respect to soil suction. Canadian Geotechnical Journal 33: 379–392. Vanapalli, S.K., Pufahl, D.E. & Fredlund, D.G. 1998. The meaning and relevance of residual water content to unsaturated soils. Proceedings of 51st Canadian Geotechnical Conference: 101–108, Edmonton, AB. Vanapalli, S.K., Pufahl, D.E. & Fredlund, D.G. 1999. The influence of soil structure and stress history on the soilwater characteristic of a compacted till. Geotechnique 49 (2): 143–159. van Genuchten, M.T. 1980. A closed form equation predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44: 892–898. Wheeler, S.J., Sharama, R.J. & Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behavior in unsaturated soils. Geotechnique 53(1): 41–54.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Outline of the modelling of the excavated damaged zone in geological barriers C. Arson CERMES, Ecole Nationale des Ponts et Chaussées, France
B. Gatmiri University of Tehran, Tehran, Iran CERMES, Ecole Nationale des Ponts et Chaussées, France
ABSTRACT: This paper deals with the modelling of the massif neighbouring a nuclear waste repository before waste disposal. The main features of micromechanical and phenomenological damage modelling are reviewed. Flow computation tools provided by fracture network representations are also presented. A mixed damage model is developed for unsaturated porous media in isothermal conditions. It is formulated in independent state variables (net stress and suction), in order to be implemented in -Stock finite element software. 1
INTRODUCTION
Damage in unsaturated media is generally tackled either through purely mechanical theories or merely hydraulic flow representations. In the unsaturated Excavation Damaged Zone (EDZ) surrounding an empty nuclear waste repository, suction effects are combined with mechanical loading and fracturing. This induces complex coupled behaviour laws. It is thus necessary to combine Continuum Damage Mechanics concepts and fracture flow data in order to achieve a good representation of the EDZ. A relevant mechanical damage model has to be extended from dry to unsaturated materials, and damage has to be introduced in the formulas quantifying the flow in a porous medium. Firstly, the principles of micromechanical and phenomenological damage theories are reviewed. Secondly, the main highlights provided by hydraulic flow models are presented. Lastly, a damage model is proposed to extend the model of unsaturated soil programmed in -Stock software (Gatmiri 1997, Jenab-Vossoughi 2000) to fractured unsaturated porous materials.
2 2.1
is assumed that stresses are redistributed due to a decrease of the effective material area. Stress-strain relationships are thus written in terms of effective (or damaged) variables. The stress that develops in the fictive undamaged counterpart of the system is named the damaged stress σˆ , and is usually defined by means of a specific damaged stress operator M( ): σˆ = M( ) : σ
(1)
where is the damage variable, which may be a tensor. The damaged stress concept is often combined to the Principle of Equivalent Elastic Energy (PEEE) to compute the damaged rigidity tensor De ( ). As recalled in Hansen & Schreyer (1994), this approach consists in postulating that the elastic energy of the intact material submitted to the damaged stress σˆ is equal to the elastic energy of the damaged material submitted to the real stress σ : We (σˆ , = 0) = We (σ , )
(2)
which results in:
CONTINUUM-BASED DAMAGE THEORIES
De ( ) = M( )−1 : D0e : M( )−T
Micromechanical concepts
Micromechanical damage theories consist in modelling the influence of local damage on the macro-mechanical behaviour. Damage variables have a physical meaning related to the degradation of elastic properties or to the characteristics of the fracture network. It
(3)
D0e denotes the intact rigidity tensor. The definition of a damaged stress provides a framework to determine the damaged mechanical properties of the material.
695
However, damage remains an abstract notion, represented by its influence on behaviour laws. That is why in some models, damage is also given a physical meaning, generally related to fracturing. Cracks of close orientations are often gathered in ‘‘families’’ (Swoboda & Yang, 1999, Shao et al., 2005a). Supposing for example that the material is fractured in three principal directions, ni , the damage variable can be written as a diagonal tensor whose eigenvalues di represent crack densities: 3
=
di ni ⊗ ni
(4)
i=1
Adopting the definition 4 implies that damage can be quantified by three fictive homogenized fractures characterized by a normal vector ni and a relative volume di . 2.2 Phenomenological frames Energy considerations are particularly suited to model dissipative phenomena such as damage and plasticity. Thermodynamic potentials are given specific forms. The resolution of the problem of maximum dissipation makes it possible to deduce the behaviour, flowing and hardening/softening laws. The model is thus automatically thermodynamically consistent. Moreover, the manipulation of huge quantities of microscopic parameters is avoided, which accelerates numerical computations. In many models, the expression of the free energy is chosen depending on the expected behaviour law (Svedberg & Runesson, 1997; HomandEtienne et al., 1998; Menzel & Steinmann, 2001; Shao et al., 2005a,b). Formulations starting from the Principle of Virtual Power (Frémond & Nedjar, 1995; Pires-Domingues et al., 1998; Nedjar, 2001; Zhao et al., 2005) can encompass an enrichment of the material’s structure, implying the definition of higher-order stresses and specific boundary conditions. In phenomenological damage models, dissipation variables νi (x) are generally assumed to have the dimension of strains. In this case, it is possible to define stress-like variables conjugated to νi (x) through the free energy. The evolution laws of the dissipation variables νi (x) are then deduced from the derivation of a given dissipation potential, relatively to the stress-like conjugates of the νi (x). Alternatively, yield functions (fd ) have to be defined. If flow rules are non-associated, additional damage potentials have to be expressed. The damage multiplier increment (λ˙ d ) is computed by means of the consistency equation. The complementary conditions of Kuhn-Tucker have also to be met: λ˙ d ≥ 0,
fd ≤ 0,
λ˙ d fd = 0
(5)
Some conditions on the form of the internal power density may be set before assuming the expression of the free energy. By doing so, it is possible to change the global form of the Principle of Virtual Power, which influences the formulation of the balance equations. Moreover, the model of the material structure may be affected by the introduction of gradient variables in the expression of the internal power. For example, Frémond (Frémond & Nedjar, 1996) enriched the structure of the medium by introducing the gradient of damage in the expression of the internal power of the system. The gradient of damage plays the same role as the gradient of macrodeformations in the theory of Germain (Germain, 1973). Its introduction requires the definition of higher-order terms in the application of the Principle of Virtual Power. Other researchers followed the same reasoning, like Pires-Domingues (Pires-Domingues et al., 1998), who studied nonlinear elastic brittle materials, and Nedjar (Nedjar, 2001), who coupled the damage model of Frémond to an elastoplastic theory. Zhao and his co-workers (Zhao et al., 2005) based their model of coupled plasticity and damage on a second gradient theory, including the gradient of deformations in the internal power and the gradient of the hardening variable in the expression of the free energy.
3
HYDRAULIC PROPERTIES OF AN INTACT POROUS MEDIUM
Many flow theories are based on the van GenuchtenMualem model (van Genuchten, 1980). Originally, the purpose of this model was to give a framework to determine the hydraulic retention and conductivity properties of an unsaturated medium of heterogeneous porosity. Van Genuchten thus considered that a single porous network drove the flow. In multimodal or multi-continua models, each porous system is characterized by a set of hydraulic relations, which may be chosen similar to van Genuchten’s. But to represent the global hydraulic behaviour of the Representative Volume Element (RVE), an equivalent medium has to be defined. The equivalent hydraulic properties of the RVE are deduced from a homogenisation technique. Using the van Genuchten-Mualem model to study a fractured porous medium amounts to considering that cracks and matrix pores are all connected and form a unique network, of space-variable pore size. Moreover, a Bell-type relation is assumed between the adimensional water content (h) and pressure head h: −m (h) = 1 + (αh)n
696
(6)
in which the adimensional water content is defined as: (h) =
θw (h) − θwr θws − θwr
(7)
θwr and θws are the residual and saturated water contents respectively. α is the pore size for which pore density is maximal. The α parameter thus gives an idea of the more frequent pore size characterizing the material. m and n control the distribution extent towards a fine or coarse medium. Resorting to Mualem’s integral formula, the relative water permeability is defined as: ⎤2 ⎡3 (h) 1 dx 0 h(x) ⎦ kR ( (h)) = [ (h)]1/2 ⎣ 3 1 (8) 1 dx 0 h(x) The integration scheme imposes that: m =1−
1 , n
0<m 0.3, so the cells 4 & 5 remain wet. The evolution of cell suction is given by Table 3, where s(Sr ) denotes suction corresponding to the value of degree of saturation as given by the water retention curve (Figs 2 & 3). The soil state after drying is summarized in Table 4. The specific volume for each cell ν2i and preconsolidation pressure pi0 in Table 4 are calculated using: si + patm , patm
i = 1..5
Stress path, as calculated in the example. Initial condition of soil (Fig. 1, point A).
Cell (i)
1
2
3
4
5
Hard. par. p∗0 [kPa] Suction [kPa] Specific vol. N (0)*
10 0 2.6
10 0 2.6
10 0 2.6
10 0 2.6
10 0 2.6
*N (0) is the specific volume at the reference pressure pc . Table 2.
Soil state at p = 100 kPa (Fig. 1, point B).
Cell (i) p∗0 [kPa]
Hard. par. Suction [kPa] Specific volume ν1i
1
2
3
4
5
100 0 2.139
100 0 2.139
100 0 2.139
100 0 2.139
100 0 2.139
(3)
The average specific volume is
ν2i = ν1i − κs ln
Figure 1.
p∗,i 0 , pc
Figure 2.
729
Water retention curve.
(5)
Table 3.
1 " i ν21 + ν22 + ν23 + ν24 + ν25 = 2.097 (7) ν = n i=1 2 5 n
Evolution of suction during drying.
ν2 =
Suction Value [kPa] Cell (i)
1
2
3
4
5
Sr > 0.9 Sr = 0.9 0.9 > Sr > 0.7 Sr = 0.7 0.7 > Sr > 0.5 Sr = 0.5 0.5 > Sr > 0.3 Sr = 0.47
s(Sr ) 30 30 30 30 30 30 30
s(Sr ) 30 s(Sr ) 100 100 100 100 100
s(Sr ) 30 s(Sr ) 100 s(Sr ) 180 180 180
s(Sr ) 30 s(Sr ) 100 s(Sr ) 180 s(Sr ) 200
s(Sr ) 30 s(Sr ) 100 s(Sr ) 180 s(Sr ) 200
After drying, the soil is isotropically loaded to p = 500 kPa (Fig 1, C–D). This final value of mean net stress is higher than the value of the preconsolidation pressure p50 given in Table 4, so all the cells will be at stress states on the yield locus. The evolution of elastic and elasto-plastic loading is given in Table 5. The soil state after loading to 500 kPa is given in Table 6. Note that after loading the cell hardening parameters are different, ∗,3 ∗,4 ∗,5 ∗,2 p∗,1 0 > p0 > p0 > p0 = p0 ,
whereas the preconsolidation pressure p0 is the same for each cell. This is because the values of suction are different for cells 1, 2, 3 and 4. As the cells do not start yielding at the same mean net stress (compare Table 5) the transition between elastic and elasto-plastic regime appears smoother than in the original BBM. The greater the number of cells used in the model, the smoother the transition. The value of hardening parameters p∗,i 0 and specific volumesν3i in Table 6 are calculated using:
p∗,i 0
=p
Table 5. Figure 3. Illustration of suction distribution within cells after drying to s = 200 kPa (Fig. 1, point C). A cell is assumed to be dry when its Sr > 0.5.
c
pi0 pc
i )−κ λ(s λ(0)−κ
,
i = 1..5
(8)
Evolution of hardening during loading.
Loading Cell (i)
1
2
3
4
5
Table 4. Soil state after drying to s = 200 kPa (Fig. 1, point C).
p < p10
e
e
e
e
e
p10 < p < p20
ep
e
e
e
e
Cell (i)
1
2
3
4
5
p20 < p < p30
ep
ep
e
e
e
Hard. par. p∗0 [kPa] Suction [kPa] Specific volume ν2i Precons. pres. pi0 [kPa]
100 30 2.126 119.6
100 100 2.104 163.3
100 180 2.088 200.4
100 200 2.084 207.1
100 200 2.084 207.1
p30 < p < p40
ep
ep
ep
e
e
p > p40 = p50
ep
ep
ep
ep
ep
e–elastic; ep–elasto-plastic.
Table 6.
i c pi0 = p0 ( p∗,i 0 ,s ) = p
p∗,i 0 pc
λ(0)−κ i
λ(s )−κ
,
i = 1..5
(6)
where patm = 100 kPa is atmospheric pressure. The average specific volume is, similarly to equation (4), given by:
Soil state at p = 500 kPa (Fig. 1, point D).
Cell (i)
1
2
3
4
5
Hard. par. p∗,i 0 [kPa] Suction [kPa] Specific volume ν3i Precons. pres. p0 [kPa]
377.3 30 1.855 500
253.6 100 1.906 500
202.6 180 1.929 500
195.4 200 1.932 500
195.4 200 1.932 500
730
p0 si + patm − κs ln , c p patm
ν3i = N (0) − λ(si ) ln
i = 1..5
Table 9.
(9)
Loading Cell (i)
The average specific volume is:
p < p∗,1 0
n ν 1 + ν32 + ν33 + ν34 + ν35 1" i = 1.911 ν3 = 3 ν3 = n i=1 5
(10) In the next stage, the soil is unloaded until it reaches the mean stress of 100 kPa (Fig. 1, D-E). The specific volume for each cell is then: ν4i = ν3i − κ ln
p , p0
i = 1..5
(11)
The average specific volume is calculated similarly as before (see e.g. 4). At this stage the sample is wetted until fully saturated (Fig 1, E–F). The evolution of suction during wetting is given in Table 7 and the soil state after wetting is identified in Table 8. After saturation, the hardening parameters are unchanged and the value of preconsolidation pressure in each cell is equal to the value of hardening parameter in this cell. The specific volume in Table 8 is calculated as ν5i = ν4i + κs ln
Table 7.
p + patm , patm
Evolution of hardening during loading.
i = 1..5
p∗,1 0 p∗,2 0 p∗,3 0
−0.999αi κs (p, s) = κs0 κsp exp(αss s)
(6)
−20 ⎧ 10 ⎪ ⎪ 1 + α ln if p ≤ 10−20 ⎪ sp ⎪ ⎪ pref ⎪ ⎨ −1 κsp = 0 if p ≥ pref exp ⎪ αsp ⎪ ⎪ ⎪ p ⎪ ⎪ ⎩1 + αsp ln elsewhere pref The coefficient κi0 gives the slope of the rebound part of the void ratio versus effective pressure compression-rebound test graph at saturated condition. This parameter is supposed to be easy and confidently determined directly from the experimental data. Hence 5 parameters are chosen to be investigated
3.2 Hydraulic phenomena The liquid flow follows the generalized Darcy’s law and therefore we have two constitutive functions to be determined and calibrated. These functions are retention curve and relative permeability. The former is taken to obey the following analytical form: ⎡ Se =
Sl − Srl ⎢ = ⎣1 + Sls − Srl
p g − pl P0
1 ⎤−λ 1−λ⎥ ⎦
(7)
where Sl is the degree of saturation; Srl and Sls are model parameters related to the residual and maximum saturation. The relative permeability is supposed to be directly related to the retention curve equation and is given by: krl =
'λ 2 & Se 1 − 1 − Se1/λ
(8)
Intrinsic permeability is supposed to be isotropic, that is k11 = k22 = k33 The parameters k11 , λ, P0 , Srl are considered as prospective for optimization. The total number of the coupled HM model parameters is 23 with 8 for the elastic law, 10 for the plastic law and 5 for the constitutive functions characterizing soil-water interaction.
4
NUMERICAL IMPLEMENTATION
The material used for this example of model parameters identification is a mixture of calcium—type bentonite Calcigel and quartz sand. The material is heavily compacted based on dry mass 50% Calcigel and 50% sand mixture, (Agus ans Schanz 2005). Extensive experimental data for this material is reported in (Agus 2005). The liquid used in experiments and simulations presented in this section is distilled water. The gas pressure is taken equal to zero because the only gas considered here is air and it is freely drained from the sample. Results from swelling pressure tests were used for calibration of TEP model parameters. The swelling pressure test offers valuable information related to the behaviour of expansive soils. What makes this test exceptional is that both stress state variables, namely the net mean stress and the suction, are not constant during the test. The reason we chose elastic constitutive functions to be back analysed is that the swelling pressure target for optimization is less than the preconsolidation
799
pressure calibrated in (Agus 2005). Therefore we expect less influence of plastic law parameters. 4.1
Table 1.
Formulation of the forward problem
In this section simulations of the tests carried out by (Agus 2005) and (Arifin and Schanz 2007) on samples of Calcigel—sand mixture are presented. The swelling pressure cell used for obtaining the data and an exemplary FE model are given in Figure 1. The model predicted variables that serve as model ‘‘estimation’’ for the optimization procedure are obtained solving two types of problems, namely simulating multistep (MSP) and one-step swelling pressure (1SP) tests. The data from SP-HC-50B-4 test (axis translation test ATT) and SP-HC-50B-3 test (vapor equilibrium technique VET), (Agus 2005) are used as ‘‘observation’’ data for the MSP optimization. The ‘‘observation’’ data for the 1SP test is taken from (Arifin and Schanz 2007). Boundary conditions for displacements are imposed in the way to satisfy the constant volume condition. Boundary conditions for pore water pressure pl are: impervious top and lateral sides of the sample and at the bottom side imposed constant for 1SP and stepwise variable for MSP. The height of the sample is 0.02 m and the radius is 0.025 m. Initial suction of 22 MPa is imposed at each point of the domain. Initial porosity is taken according as reported in the corresponding experimental data. The problem is solved as axisymmetric even some problems with this type of FE has been observed during the simulations. The axial stress (σyy ) at a chosen point in the vicinity of the midpoint of the sample top side has been extracted from the solution and used to build the objective function for the consecutive optimization. It has to be mentioned that Code_Bright provides the output of the solution including stress values in prescribed domain points and not in the integration points. 4.2 Parameter constraints The two constitutive functions from the mechanical model that have to be fit in conformity with experimental data are given with Equations 5 and 6. Based on the observation that both κi and κs decrease
Figure 1.
Swelling pressure cell (UPC) and the FE model.
Constraints—retention curve, permeability.
Parameter
Unit
Min
Max
P0 λ k11 (log scale)
MPa
0.01 0.01 −21
10 0.8 −15
Table 2.
log m2
Constraints—TEP elasticity.
Parameter
Unit
Min
Max
αi κs0 αss αsp pref
MPa−1
−0.0066 0.0057 −0.4506 −0.9410 0.657
−0.0054 0.0171 −0.15019 −0.3137 0.803
MPa−1 MPa
with increasing their arguments an implicit constraint is that parameters αi , αsp and αss are not positive. Constraints intervals used in the optimization procedure are listed in Table 1 and Table 2. 4.3 Parameter sensitivity analysis For the sensitivity analysis, each of the parameters xj was varied over the constraint interval (Table 1 and Table 2) keeping at the same time all other parameters fixed allowing this way to evaluate γj from Equation 3. The vector y used to calculate CSS is obtained from the solutions of the 1SP and MSP problems. This procedure has been performed for 100 sets of parameters that are randomly chosen and belong to the entire admissible domain. The mean of the calculated γj , that is 2 i γ¯j = (1/100) 100 i=1 γj is used to compare the sensitivity of the model response to the corresponding parameter xj . Figure 2 shows the results for sensitivity analysis including both hydraulic and mechanical model parameters. The ‘‘observation’’ variables vector is the time evolution of the swelling pressure (σyy ) at a given point from the solution of the MSP problem. The analysis of the results in Figure 2 suggests special attention to intrinsic permeability and the parameters involved in the constitutive function κsp . Figure 3 depicts the results for the case where the solution of the 1SP problem has been used for collecting ‘‘observations’’. The pronounced significance of the retention curve parameters λ and P0 and the intrinsic permeability may be due to the poor ability of the model to simulate the first step of suction loading from the experiment. Still the importance of αsp is manifested and this is one of the parameters that are difficult to be assessed directly from experimental data.
800
1
pref alphasp alphai alphass kappas k11 lambda P0
Figure 2.
Sensitivity analysis—MSP numerical simulation.
pref alphasp alphai alphass kappas k11 lambda P0
Figure 3.
4.4
0.2
0.4 0.6 mean gamma
0.8
1
pref
alphasp
4 Loading Steps - PSO
Results of different optimization procedures.
Results—retention curve, permeability.
Parameter
Unit
Unitial
Final
P0 λ k11
MPa
1.2 0.386 6e-19
7.6 0.2685 2e-19
m2
Sensitivity analysis—1SP numerical simulation.
Table 4.
Results of the parameter optimization
Different optimization algorithms, part of VARO PT (VAROCON, Weimar) optimization program, have been used and we found the downhill simplex method (SNM) to provide fast, robust and reliable solution. The chart in Figure 4 compares the solutions obtained by two different optimization methods, namely SNM and PSO for MSP back analysis. It presents also the difference in optimization solution depending on whether we take 3 or 4 loading steps. The objective function reads: N "
3 Loading Steps - SNM
3 Loading Steps - PSO
Table 3.
2
F=
Initial
Figure 4.
0
1SP
alphai
1
alphass
0.8
kappas0
0.4 0.6 mean gamma
k11
0.2
P0
0
lambda
MSP
0
fn wn
(9)
n=1
2m i i where fn = i=1 ymeas − ycalc ri , wn and ri are weight factors, n = 1, . . . , N is the counter of loading steps used in optimization process. Therefore not only different optimization procedures give different results, but also different data sampling. The initial values for the parameter vector have been taken from (Agus 2005) where model calibration has been done by best fit to constant suction and constant net stress type of experimental data without doing back analysis. The solution obtained after SNM optimization procedure is given in Tables 3 and 4. The observed discrepancy between conventionally derived model parameters and the optimized after 1SP and MSP tests
Results—TEP elasticity.
Parameter
Unit
Initial
Final
αi κs0 αss αsp pref
MPa−1
−0.006 0.0047 −0.1128 −0.3 0.73
−0.0062 0.0123 −0.334 −0.6454 0.71
MPa−1 MPa
back analysis may be due to the much smaller number of data points specially for calibration of κs . It has to be pointed out that for the nonlinear function κs (p, s) even the variables are separated, it is difficult to prove the goodness of fit done as section fit with respect to each of the function variables (conventional model calibration practice). The reason is that constant suction type of tests can not be used for calibration of κs (p, s) because in this type of tests dε s−e = 0 and κs v plays no role. Uniqueness of the optimization problem solution has been verified by cross section graphs of the objective function along each of the back analysed parameters xj . An example of such matrix graph is given in Figure 5 and it shows well represented minima except for the intrinsic permeability . Figure 6 shows the results of MSP (ATT) simulations. These results are discussed here because of the discrepancy between calculated and measured
801
4.5
αi
κs0
αss
5
k11
Swelling Pressure
Cross sections of the objective function along xj .
Calculated
Figure 5.
To verify the parameters obtained after back analysis of the MSP and 1SP tests we performed a simulation of a compression-rebound test. The test procedure and the results of CR-3 test are reported in (Agus 2005). Results are given in Figure 7.
αsp
λ
MSP Measured
0
Figure 6.
.55 0
Time [h]
1500
Calculated vs measured swelling pressure.
axial displ. [mm]
0
0.5
experiment TEP model
1
1.5 10
axial stress [kPa]
Verification
CONCLUSIONS
The paper presents a procedure for identification of TEP model parameters based on swelling pressure tests data. The procedure consists in sensitivity analysis based on numerical simulations of swelling pressure tests, choice of optimization algorithm, solution of the optimization problem and verification of the calibrated model using compression—rebound tests data. The quality of the forward calculation is of significant importance and it has to be monitored during the run of the back analysis. The influence of the finite elements discretization and the loading path has to be taken into account when accepting the goodness of the fit. Large increments of suction in ATT tests lead to a solution with not constant porosity along the sample height. It is an object of future research to analyse this observation. The next outcome of the performed analysis is that within the experimental error the solution of the optimization procedure is not unique. The uniqueness of the solution particularly, is strongly dependent on the quality of the numerical model and on the error involved at different stages of the test. Different optimization procedures may also give different solutions. That is why the verification of the back analysis is important and integral part of the identification procedure. Finally one can state, that using swelling pressure test data and the proposed identification procedure a successful back analysis of the unknown TEP model parameters can be done.
100000
ACKNOWLEDGMENT Figure 7.
Compression—rebound test (verification).
swelling pressure at the first stage of the suction loading. Possible reason is the problem with the ceramic disk and the influence to the experimental data of its hydraulic conductivity of 1.12e-10 m/s. Another observation is the influence of the loading program to the porosity distribution at final equilibrium. The application of suction in ATT test is with large initial increment which leads to non constant porosity along the sample height at maximum swelling pressure. For this reason at this stage of our research we did not include the measured water intake in the definition of the objective function.
The financial assistance of German Federal Ministry of Education and Research (grant 02C0881) is gratefully acknowledged. Authors wish to express their gratitude to Mr Yulian Arifin for the valuable help with the experimental data. REFERENCES Agus, S. (2005). An experimental study on hydro— mechanical characteristics of compacted bentonite–sand mixtures. Ph.D. thesis, Bauhaus—Universitat Weimar. Agus, S.S. and T. Schanz (2005). Swelling pressure and total suction of compacted bentonite—sand mixtures. In Proc Int Conf on Problematic Soils, Cyprus, pp. 61–70.
802
Alonso, E.E., J. Vaunat, and A. Gens (1999). Modelling the mechanical behaviour of expansive clays. Engng Geol 54(12), 173–183. Anderman, E., M. Hill, and E. Poeter (1996). Twodimensional advective transport in ground-water flow parameter estimation. Ground Water 34(6), 1001–1009. Arifin, Y. and T. Schanz (2007). Modified isochoric cell for temperature controlled swelling pressure test. In T. Schanz (Ed.), Proc 2nd Int Conf Mech Unsat Soils, Weimar, Germany, pp. 229–242. Springer. Cividini, A., L. Jurina, and G. Gioda (1981). Some aspects of characterization problems in geomechanics. Int J Rock Mech Min Sci and Geomech Abstr 18(6), 487–503. Code_Bright (2002). USER’S GUIDE: A 3-D program for Thermo–Hydro–Mechanical analysis in geological media. UPC, Barcelona.
Davidon, W.C. and L. Nazareth (1977). OCOPTR—A Derivative Free FORTRAN Implementation of Davidon’s Optimally Conditioned Method. Argonne Nat Lab—Appl Math Div, Tech Memorandum No 303. Eberhardt, R. and J. Kennedy (1995). A new optimizer using particle swarm theory. In Proc 6th Int Symp on Micro Machine and Human Science, Nagoya, Japan, pp. 39–43. IEEE Service Center. Hill, M.C. (1998). Methods and Guidelines for Effective Model Calibration. Denver, Colorado: U.S. Geological Survey Water–Resources Investigation Report 98–4005. Nelder, J.A. and R. Mead (1965). A simplex method for function minimization. Computer Journal 7, 308–313. Zhang, Z.F., A.L. Ward, and G.W. Gee (2003). Estimating Soil Hydraulic Parameters of a Field Drainage Experiment Using Inverse Techniques. Vadose Zone Journal 2, 201–211.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Surface flux boundary simplifications for flow through clay under landscaped conditions H.B. Dye, S.L. Houston & W.N. Houston Arizona State University, Tempe, AZ, USA
ABSTRACT: The quality of the solution of moisture flow through expansive soils for the purpose of depth of moisture influence determination for residential foundation design depends on properly described flux boundary conditions including appropriate environmental factors and inclusion of the microclimate created by human activity. In this study, both climatic and human imposed conditions typical to Phoenix, Arizona, were considered in 1-D unsaturated flow modeling. Many years of recorded precipitation data were obtained, and common irrigation practice from surveys of municipalities, together with evapotranspiration data from the regions, were used to determine the surface flux conditions for modeling. Rigorously described surface flux boundary conditions were used in the analyses, and simplifications to these conditions were systematically made to determine the impact of simplified boundary conditions on the final solution. It was found that major simplifications, through averaging of flux conditions and increased time-steps for application, result in only negligible difference in computed matric suction compared to more detailed simulations of flux when the capacity of the soil to absorb applied surface water is not exceeded, such as for the desert landscape conditions of this study. Otherwise, as observed for the turf irrigation case of this study, averaging surface flux can result in significant over-estimate of the extent and degree of wetting in the profile.
1
INTRODUCTION
It is well established that damage to structures built on expansive soils is mainly caused by changes in soil suction (Chen 1988, Fredlund 1993). The suction change is generally attributed to environmental conditions, change in depth of water table, water uptake by vegetation, removal of vegetation or landscape irrigation. Foundations on expansive soils must resist short-term cyclic swell/shrinkage due to seasonal moisture variation and long-term swell/shrinkage. It was established by Fredlund (1993) that the prediction of expansive soil movement requires implementation of unsaturated soil mechanics where the moisture flow and deformation are analyzed in a coupled or uncoupled manner. There is a large body of literature on the measurement and prediction of swell/shrinkage of soils and analysis of actual soil behavior in the field. Some of these studies have resulted in numerical analyses for evaluation of unsaturated flow and heave in the soil profiles (e.g. Fredlund et al. 1984, 1993, and 2004). The implementation of these numerical methods involves a detailed description of the flux boundary condition that reflects the actual wetting and drying at the surface of the soil profile. The process of mathematically describing the surface flux condition
is tedious, and complex input generally requires long finite element code run-time. This paper focuses on the moisture flow portion of the problem, where the impact of input flux simplification on the solution is analyzed. Two different conditions were considered: desert landscape and turf landscape in an arid region. The analysis was performed for one Phoenix area expansive soil using SVFlux 5.80, a finite element computer program for unsaturated flow (Fredlund 2004). 2
PROBLEM SET-UP
The 1-D flow analyses were carried out on a 10-m deep profile using a finite element program, SVFlux 5.80. SVFlux utilizes adaptive unstructured mesh generation and adaptive time stepping using implicit 2nd order Backwards Difference (Gear’s method) to solve Richard’s equation adapted for both infiltration and evapotranspiration (SVS 2005a). The study was carried out to obtain soil response due to typical input flux discretized first on an hourly basis, and then monthly for both desert and turf landscapes. The profiles were assumed to be well-sloped at the surface so that run-off would occur. For all runs, mesh refinements and time-step refinements
805
Boundary and initial conditions
The profile has two boundary conditions (BCs). Total head of−153 m was applied to the bottom boundary. This value is based on laboratory testing of field samples, illustrating a 1000 to 2000 kPa matric suction range at depths of approximately 2 to 3 meters for undeveloped regions in the Phoenix area. A Neumann BC was applied at the soil surface. It consists of precipitation, typically applied irrigation, potential evaporation, relative humidity and temperature parameters representative of Arizona climatic conditions (see section 2.3 for details). The initial total head profile of was assumed to be constant with depth and equal to −153 m. 2.2
Soil properties
The expansive soil properties used in this study are given in Table 1 and Figure 1. The following required parameters were determined experimentally: specific gravity, saturated hydraulic conductivity, ksat , Soil Water Characteristic Curve (SWCC), and saturated volumetric water content. The SWCC experimental data were fitted using the Fredlund and Xing (1994) equation to yield the SWCC curve fitting parameters. The unsaturated hydraulic conductivity curve was estimated using the Leong and Rahardjo equation, where the slope of the curve was assumed to be similar to other clayey soils published in literature and available though SoilVision (Leong & Rahardjo 1997, SVS 2005b). Table 1.
Soil properties.
Parameter name LL PI γd Gs P-200 % clay θsat SWCC parameters (Fredlund and Xing, 1994) af bf cf hr kunsat parameters (Leong and Rahardjo, 1997) ksat p
Parameter value 85 53 13.4 kPa 2.80 86 33 51.2 140 0.6 0.9 2000 8.7e-6 m/h 12
1.0
1E-04
0.9
1E-05
0.8
1E-06
0.7
1E-07
0.6
1E-08
0.5
1E-09
0.4
1E-10
0.3
SWCC Lab Data
1E-11
0.2
SWCC, Fredlund Fit
1E-12
0.1
Kunsat, Leong Fit
1E-13
Hydraulic Conductivity [m/h]
2.1
Saturation [decimal]
were performed to assure convergence and stability of the matric suction response.
1E-14 0.0 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
Suction [kPa]
Figure 1.
Unsaturated soil property functions.
2.3 Input flux Expansive soils in the Phoenix metropolitan area can experience a wide range of flux conditions that include precipitation, evaporation and irrigation. Two extreme flux conditions typical for the Phoenix region were identified. They are turf landscape, where the lawn is irrigated every day, and desert or ‘‘xeriscape’’, where a negligible amount of water is introduced to the soil surface. These two fluxes were used in the one-year long analysis requiring four flux components to be described, flux onto the soil such as irrigation or precipitation, potential evaporation, relative humidity and temperature. 2.3.1 Desert landscape The potential evaporation data for the Phoenix region were obtained from three internet sources 1) US Weather Service, Arizona Department of Water Resources, 2) NOAA, Western Regional Climate Center, and 3) Arizona Meteorological Network (Internet source a, b & c 2006). Measured data for one year were available from source 1 and 2, while source 3 provided 6 years of estimated PE based on measured relative humidity, RH, and temperature data, T . The average from all three sources was used to develop PE flux used in the analysis, and is presented in Table 2. The SVFlux code utilizes the formulation developed by Wilson et al. (1994) for computation of actual evaporation, AE. The general relationship between AE and PE in terms of soil surface total suction is illustrated in Figure 2, where AE is equal to PE for soil suction smaller then 3000 kPa (Wilson et al. 1995). As the soil surface suction increases the AE decreases to a value of 0, corresponding to suction value at applied RH. The 6-year averages of RH and T from source 3 were further used to develop RH and T program input, Table 2. The amount of water typically applied to desert landscape or ‘‘xeriscape’’ is negligible. Therefore, the amount of water applied to the soil surface is assumed
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Table 2.
Desert flux input.
0.0020
#Rainy #Rainy PE hours days [m/h]
RH T Ave. Prec. [%] [C] [m/h]
1 2 3 4 5 6 7 8 9 10 11 12
7 8 8 5 1 1 5 2 3 4 6 6
53 49 45 34 26 25 32 42 39 50 50 52
7.1E-04 6.2E-04 7.2E-04 7.1E-04 1.7E-03 8.0E-04 1.1E-03 1.5E-03 1.5E-03 1.2E-03 8.8E-04 7.6E-04
6 6 7 4 3 2 8 9 5 4 4 5
1.2E-04 1.5E-04 2.3E-04 3.1E-04 4.0E-04 4.2E-04 4.3E-04 3.6E-04 3.1E-04 2.3E-04 1.5E-04 9.8E-05
12 13 17 21 27 31 34 32 30 22 15 10
3.3E-05 3.4E-05 3.8E-05 1.1E-05 5.1E-06 1.1E-06 3.5E-05 2.8E-05 2.5E-05 2.0E-05 2.4E-05 2.7E-05
Precipitation Evaporation Average Flux
0.0015 Flux [m/h]
Prec. Mo. [m/h]
0.0010 0.0005 0.0000
-0.0005 0
Figure 3.
Figure 2. Relationship between AE/PE to total suction for sand, silt and clay (after Wilson et al. 1995).
to be from precipitation only. For the purpose of developing a reasonable input flux, 24-year daily precipitation and 9-year hourly precipitation data obtained from National Climatic Data Center website was studied for the Phoenix area. The data revealed that the average rainfall in Phoenix is 20 cm/year with a standard deviation of 7.6 cm/year. Furthermore, the rainy days within a given month occurred close together and rainy hours within a day, for the most part, occurred one after another. The input used in this analysis consisted of a stepped function flux where a net precipitation of 20 cm is applied per year. The precipitation was applied on an hourly basis where the rainy days as well as the rainy hours within a day were grouped together because this grouping was consistent with typicallyobserved rain patterns. During each rainy day the precipitation was applied for the determined number of hours and then the rain was followed by a period of evaporation. Other than the rainy days, the flux BC consisted of evaporation only for the remaining portion of the month. Table 2 gives the applied desert landscape input data, which are plotted in Figure 3. The simplified average flux scheme consists of the same PE, RH and T input data and averaged precipitation over the period of each month. The last column of Table 2 gives the monthly averaged precipitation.
2000
4000 Time [h]
6000
8000
Desert landscape input.
2.3.2 Turf landscape The potential evapotranspiration data, ET0 , for tall, well watered, cool season grass were obtained from University of Arizona for a golf course in Cave Creek, Arizona (UA 2000). The evapotranspiration rates were modified by a 0.6 landscape coefficient to simulate the evapotraspirationexperiencedbywarmseasonBermuda grass, a plant commonly used in Phoenix landscapes. The plant evapotranspiration rate is, in part, a function of leaf length, since ET 0 was determined for long leaf vegetation, the correction was necessary to adequately describe the typical site conditions (UA 2000). Proper irrigation of turf landscape consists of a yearly flux equal to the yearly evapotranspiration rate. Therefore, the warm season Bermuda grass requires 117 cm/year (0.6 ∗ 196 cm/year) of water. The grass is semi-dormant in the wintertime (November through February) when a reduced watering regimen is required when compared to the summer months. The local recommendation on irrigation is to apply 1.9 cm of water during every irrigation event. In general, the warm season grass should be provided with about 2.5 cm of water once a month between November through February and 5 to 7.6 cm of water a week from May through September when the plants are irrigated once every few days. This kind of infrequent watering pattern encourages the plants to develop a deep root system and produces hardy plants (McCaleb 2005 and City of Mesa 2005). Based on information obtained from the landscape professionals and Phoenix area government agencies, it is estimated that the turf landscapes are often overwatered by 2 to 5 times the above recommended amount. The mismanagement of water use is mainly attributed to homeowners’ lack of knowledge about grass needs. Landscapes are typically irrigated every day where the water is applied once or twice a day. The common once a day option consists of 15–20 minute watering period equivalent to application of 0.1 to 1.6 cm of water per irrigation event. The twice a day watering pattern typically last 5 to 10 minutes and corresponds to 0.04 to 0.8 cm of water per application.
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Table 3.
3
3.1 Desert or low water use landscape The desert or low water use landscape consisted of 2.3-m of PE and 0.2-m of rainfall annually. The analysis with hourly discretized flux, HF, produced large matric suction variations at the soil surface ranging from 190 000 kPa at the end of dry period in Jun to 0 kPa after a precipitation event. These suction swings are not present in the average flux, AF, analysis as expected. The soil surface suctions approach the values calculated with HF analysis except for very shallow depth. Just below the surface, the soil response in terms of suction is similar for both types of analysis as illustrated in Figure 5. Figure 6 (suction variation with depth at the end of year) further shows that the discrepancy between these two approaches exists only in the initial 0.2-m of the profile. At larger depths the solutions are identical. 0
Turf flux input.
Mo.
Prec. m/h
PE m/h
Ave. Prec. m/h
1 2 3 4 5 6 7 8 9 10 11 12
4.61E-3 4.62E-3 4.64E-3 4.68E-3 1.06E-2 1.06E-2 1.06E-2 1.06E-2 1.06E-2 1.05E-2 4.65E-3 4.62E-3
4.45E-5 6.35E-5 9.59E-5 1.39E-4 1.81E-4 2.11E-4 2.16E-4 1.97E-4 1.72E-4 1.38E-4 9.75E-5 5.75E-5
1.32E-4 1.35E-4 1.42E-4 1.13E-4 4.41E-4 4.37E-4 4.82E-4 4.68E-4 4.63E-4 4.57E-4 1.25E-4 1.25E-4
MODELING RESULTS
Pore Water Pressure [kPa]
The typical flux input scheme for the numerical models of this study for turf landscape consists of one hour of irrigation every day followed by 23 hours of evapotranspiration. There are two magnitudes of applied irrigation. The first flux has magnitude of 0.19 cm/hour and is applied between November through April; it is referred to as the Winter irrigation. The second flux, also called the Summer irrigation is applied during the remaining portion of the year and has magnitude of 1.16 cm/hour. The evapotranspiration rate increases from winter months to the mid-summer and then it decreases towards December. The actual evapotranspiration rate varies parabolicly with time, but for the purpose of modeling, the rate was simplified to vary on a monthly basis. The applied flux consists of precipitation and irrigation where the precipitation data are given in Table 2, while the irrigation and PE data are provided in Table 3. The turf surface flux boundary condition is plotted in Figure 4. The simplified average flux scheme consists of the same PE, RH and T input data and averaged both precipitation and irrigation over the period of each month, as given in Table 3.
-50000
-100000 0m - HF 0m - AF 0.1m-HF 0.1m-AF 0.2m-HF 0.2m-AF
-150000
-200000
0
50
100
150
200
250
300
350
Time [d]
Figure 5. Desert landscape. Pore water pressure variation with time at selected depths for hourly flux (HF) and average flux (AF).
Distance from Surface [m]
-0.2 0.012 0.010
Flux [m/h]
0.008 0.006 0.004 0.002 0.000 -0.002 0
2000
Irrigation and Precipitation
Figure 4.
4000 Time [h]
6000
Evaporation
Turf landscape surface flux input.
8000 Average Flux
0 0.2 0.4 0.6 0.8
HF AF
1 -100000 -80000
-60000
-40000 -20000
0
Pore Water Pressure [kPa] Figure 6. Desert landscape. Pore water pressure variation with depth at the end of year for hourly flux (HF) and average flux (AF).
808
The net flux, as calculated by the computer program for 1 m2 surface area, is presented in Figure 7 for both HF and AF analyses. The cumulative flux is similar for HF and AF runs, and approaches −0.058 m3 at the end of one year. This helps explain why the results obtained with both approaches produce similar results. Although runoff of water that does not infiltrate is an option utilized for the desert landscape condition (i.e. well-graded/sloped soil surface), the surface flux conditions are such that essentially no runoff occurred for either hourly or monthly averaged flux steps.
3.2
Turf landscape
The turf landscape consists of 1.16-m of PE, 0.2-m of precipitation and 2.37-m of irrigation per year. The hourly discretized flux was applied daily per half an
0.01
HF
AF
0
Distance from Surface [m]
Cumulative Flux [m3]
0.02
hour during the winter regimen and per one hour during the summer irrigation schedule. The analysis with hourly discretized flux, HF, produced large matric suction variations at the soil surface ranging from 50 000 kPa at the end of April to about 0 kPa after precipitation or irrigation event as illustrated in Figure 8. The suction fluctuations due to individual irrigation or precipitation events were observed to a depth of 0.05-m from the surface. Figure 9 shows that although the suction variation at the soil surface might be quite large, the immediate influence of the wetting event does not exceed 0.05-m. Fluctuations due to monthly averaged input occur to a depth of about 0.5-m. The results obtained with monthly average flux are very different from the results obtained with hourly discretized conditions (Fig. 8). For the averaged monthly flux, the surface matric suction decreases from the initial condition to near 0 kPa, increases to about 200 kPa in April and goes back to 0 kPa after April, where it remains essentially constant. In contrast, the
-0.01 -0.02 -0.03 -0.04 -0.05 -0.06
0
50
100 150 200 250 300 350
Time [d] Figure 7. Desert landscape. Cumulative flux (for a 1 m2 surface area) for hourly flux (HF) and average flux (AF) analyses.
0.00 0.02 0.04 0.06 0.08
before rainfall after rainfall
0.10 -10000 -8000
-6000
-4000 -2000
0
Pore Water Pressure [kPa] Figure 9. Turf landscape. Pore water pressure variation with depth before and after a rainfall event (HF).
Distance from Surface [m]
Pore Water Pressure [kPa]
0 -10000 -20000 -30000 -40000
0m - HF 0m - AF
-50000 0
50
100 150
200
250
300
0 2 4 6
10 -2000
350
HF AF
8
-1500
-1000 -500
0
Pore Water Pressure [kPa]
Time [d]
Figure 8. Turf landscape. Pore water pressure variation with time at the soil surface for hourly flux (HF) and average flux (AF) analyses.
Figure 10. Turf landscape. Pore water pressure variation with depth at the end of year for hourly flux (HF) and average flux (AF).
809
deformations. Further studies evaluating the effect of shrinkage soil cracking on moisture flow, coupled and decoupled flow and soil deformation will be useful in refining recommendations of surface flux simplifications for modeling suction change-induced foundation movements for expansive soil profiles.
Cumulative Flux [m3]
0.35 HF
0.3
AF
0.25 0.2 0.15 0.1
ACKNOWLEDGMENTS
0.05 0
0
50
This work was supported by the Homebuilders Association of Central Arizona (HBACA) and Construction Inspection and Testing Co. (CIT). This support is gratefully acknowledged. The views presented are those of the authors, and not necessarily those of the supporting organizations.
100 150 200 250 300 350
Time [d] Figure 11. Turf landscape. Cumulative flux for hourly flux (HF) and average flux (AF) analyses.
surface suction varies widely for the HF input. The depth of influence obtained with AF is 2.5-m, compared to 1.9-m with HF, Figure 10, and the AF results in higher degree of saturation. The increased depth of wetting is associated with larger amount of water absorbed in the AF scheme, Figure 11. After one year, the cumulative flux, as calculated by the computer program, is 0.33-m3 for AF and 0.11-m3 for HF. The difference is attributed to runoff and reduced time for infiltration in the HF analyses. 4
CONCLUSIONS
The analysis of desert landscape revealed that simplification of precipitation data by averaging produces adequate approximation of soil behavior. This finding is applicable to flux conditions dominated by evaporation. However, the flux simplification scheme, wherein averaging of flux over each month is employed, is not appropriate for irrigation or precipitation dominated scenarios such as the turf landscape example of this study. The averaging overestimates both the degree of saturation and the depth of wetting for cases where there is surface run-off resulting from exceeding of the soil surface capacity to absorb water. It is recommended that the effect of simplification of surface flux conditions be carefully considered on a case-by-cases basis. While there is a high price to pay with regard to run-times for detailed modeling of actual surface flux conditions, it is clear that there are many important problems for which highly detailed flux input is required to achieve reasonable simulation of field conditions. Finally, the most important soil response with which to judge appropriate surface flux simplifications for the case of foundations on expansive soils is the surface
REFERENCES Chen, F.H. 1988. Foundations on Expansive Soils, Development in Geotechnical Engineering, 54, New York, Elsevier Science Publishers. Fredlund, D.G. and Rahardjo, H. 1993. Soil Mechanics for Unsaturated Soils, Wiley, New York. Fredlund, D.G., Vu, H., Fredlund, M.D. and Thode, R. 2004. Modeling soil-structure interaction of slabs on expansive soils. Soil Vision Systems Ltd. Saskatchewan, Canada. Fredlund, D.G. and Xing, A. 1994. Equations for the soil water characteristic curve. Canadian Geotechnical journal, 31(3): 521–532. Internet Source. 2006. http://ag.arizona.edu/azmet/15.htm Internet Source. 2006. http://www.peoriaaz.com/Utilities/ oldfiles/xeriscapef.htm Internet Source. 2006. http://www.wrcc.dri.edu/htmlfiles/ westevap.final.html#ARIZONA Leong, E.C. and Rahardjo, H. 1997. Permeability Functions for Unsaturated Soils. Journal of Geotechnical and Geoenvironmental Engineering, Dec., 1118–1126. Personal Communication. 2005. City of Mesa, Department of Water Use. Discussion about landscape schemes, irrigation systems and common issues. Personal Communication. 2005. McCaleb, Kevin, Orovalley owner, Discussion about landscape schemes, irrigation systems and common issues. Soil Vision Systems Ltd. 2005. SoilVision User’s and Theory Guide, Version 4. Saskatchewan, SK, Canada. Soil Vision Systems Ltd. 2005b. SVFlux User’s and Theory Guide, Version 5. Saskatchewan, SK, Canada. University of Arizona Cooperative Extension. 2000. Basics of Evaporation and Evapotranspiration. Turf Irrigation Management Series: I, paper #1194. Wilson, G.W., Fredlund, D.G. and Barbour, S.L. 1994. Coupled soil-atmosphere modeling for soil evaporation. Can. Geotech. J., 31: 151–161. Wilson, G.W., Barbour, S.L. and Fredlund, D.L. 1995. The prediction of Evaporative Fluxes from Unsaturated Soil Surfaces. Unsaturated Soils, Alonso, E.E, Delage, P. (eds.): 423–429.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Preliminary analysis of tree-induced suctions on slope stability N. Ali & S.W. Rees Cardiff School of Engineering, Cardiff, Wales
ABSTRACT: This paper explores the development and application of a numerical model of water uptake in the vicinity of established trees. A preliminary assessment of the significance of water content (and therefore suction) changes on the stability of soil slopes is provided. This is a problem that is exacerbated by climate change and increasingly intense rainfall events. Design, repair, maintenance and operation of railway and road earthworks are particular areas where this issue is important. For a typical slope geometry the research indicates that tree-induced suction variations can cause the factor of safety against failure to vary by between 5% and 7%. This result is independent of other associated contributions that may arise from root reinforcement, windthrow, weight of vegetation etc. Therefore, further work is needed to consider the overall effect of vegetation and to reduce parametric uncertainty.
1
INTRODUCTION
It is now recognized that variations in soil suction that may occur in the presence of vegetation, and indeed those that can occur on removal of vegetation, have an important role to play in the performance of engineered and natural soil slopes. This is a problem that is exacerbated by climate change and increasingly intense rainfall events. Repair, maintenance and operation of railway and road embankments are particular areas where this issue is important. Previous experience in Malaysia indicates that removal of vegetation can be the main cause for the failure of a slope (Technical Committee of Investigation 1994). In this tragedy, investigation of the substructure and the surroundings revealed that clearing of trees on the adjacent slope led to the water level in soil to rise, thus causing the instability of slope. Some researchers (Thorne, 1990, Simon et al. 2000, MacNeil 2001) claim that vegetation is widely believed to increase the stability of slope. Simon and Collison (2001) suggested that the impact of vegetation on slope or bank stability can be divided into mechanical and hydrologic effects. Mechanical effects are associated with the root tensile strength and hydrologic effects include increased slope stability by extraction of soil moisture for transpiration. In their work, it was found that hydrologic effects can be as important as mechanical effects and in certain cases. Ridley et al. (2004) discussed the relationship between climate, in the form of soil moisture deficit, the presence of trees and pore water pressures
in embankments. The study showed that most embankment failures in London were due to an increase in soil moisture content. Recently Greenwood (2006) considered the potential engineering influences of vegetation and how it can be characterized on site within a geotechnical framework for slope stability assessments. Greenwood’s software (SLIP4EX—based on equilibrium of forces) may be used for estimating the factor of safety (FOS) against slope failure and can be readily adapted to include vegetation effects. The program uses the method described by Greenwood et al. (2004) to include the influence of vegetation mass, effects on the groundwater regime, enhanced cohesion due to fine roots, wind forces and the anchoring effects of the larger roots. Changes in ground water table due to vegetation were included however the effect of negative water pressure was excluded from the equation. For the situations where the ground water table is deep and where tree root activity is involved, treeinduced suctions may be significant. In these cases, it may be appropriate to perform slope stability analyses which include the shear strength contribution from the negative pore pressure. A modified form of the MohrCoulomb equation can be used to link shear strength to soil suction. Therefore, this paper explores the application of the water uptake model described previously (Rees and Ali 2006) to provide a preliminary assessment of the significance of water content (and therefore suction) changes on the stability of unsaturated soil slopes. This research only considers hydrological effects (i.e. water uptake) at this stage.
811
Where (ua − uw ) is the matric suction and φ b is an angle indicating the rate of increase in shear strength relative to matric suction. (σn − ua ) is the net normal stress, c is the effective cohesion and φ is angle of friction. Combining equations (1) and (2), gives,
THEORETICAL AND NUMERICAL BACKGROUND
2.1
Limiting equilibrium forces for unsaturated slope stability
This study uses the theory of limit equilibrium of forces and moments to compute the FOS against failure. The limit equilibrium method of slices is widely used for its simplicity particularly when compared to the finite element method (Fredlund and Rahardjo 1993, Renaud et al. 2003). The FOS is defined as that factor by which the shear strength of the soil must be reduced in order to bring the mass of soil into a state of limiting equilibrium along a selected slip surface. Calculations for the stability of a slope are performed by dividing the soil mass above the circular slip surface into vertical slices. The limit equilibrium formulation assumes that the factor of safety is equal for all soils involved and for all slices. The current work aims to explore the importance of suction changes on shear strength. Therefore, in the example considered, the water table is assumed to be below the zone of interest. Tension cracks are, therefore, excluded from the current work. It is also assumed that there are no interslice shear forces involved in the equation for both horizontal and vertical forces. This assumption has been made for the following reasons; i. Vertical interslice forces can be assumed equal and opposite (Bishop, 1955). ii. The resultant of the interslice forces acting on a slice can be assumed to act parallel to the base of the slice. By resolving forces normal to the base of the slice, the interslice forces are eliminated. 2.2
FOS for an unsaturated slope
To calculate the FOS of an unsaturated soil slope and link this with the effect of tree-root-water uptake, a force equation which includes matric suction must be established first. The analysis is an extension of conventional limit equilibrium analysis where an equation is formed using the basic principle of static equilibrium of forces and moments. The mobilized shear force at the base of a slice can be written as (Lambe and Whitman, 1969) τl F
Sm =
l c + (σn − ua ) tan φ + (ua − uw ) tan φ b Sm = F
(3)
From Figure 1, (taking point O as centre of the moments) the summation of moments in the slope, yields: "
Wx −
"
Sm R = 0
(4)
Substituting equation (3) into (4) and substituting (ua − uw ) = S (matric suction) and assuming air pore pressure is atmospheric, ua = 0, equation (4) becomes 2 F=
c lR + NR tan φ + SRl tan φ b 2 Wx
(5)
Equation (5) has been used throughout this research for calculating the FOSs. Note that if the matric suction is zero (i.e. the soil is saturated) Equation (5) becomes the standard Fellenius’s method (Fellenius, 1936). 2.3 The water-uptake model The two-dimensional water-uptake model provided by Rees and Ali (2006) is used here. In Cartesian form, the sink term can be written as: 4T z x S(ψ, x, z) = α(ψ) 1 − 1− (6) zr xr zr xr Where S (ψ, x, z) is the sink term (cm3 /cm3 /s), T is the potential transpiration rate (cm/s), xr is the maximum rooting horizontal distance (cm), zr is the maximum rooting depth (cm), α(ψ) is a dimensionless water stress function (see Feddes et al. 1976), o
7
(1)
8 350cm
6 5
27˚cm
4
750cm
τ = c + (σn − ua ) tan φ + (ua − uw ) tan φ
b
(2)
2 2
Origin
Figure 1.
812
1
3
8 7
1
250cm
Where τ is shear strength of unsaturated soil. Fredlund et al. (1978) provided the following expression for shear strength:
!
3
1600cm
Test slope geometry.
4
5
6
500cm
2
z is the vertical coordinate (cm) and x is the horizontal coordinate (cm). Combining the Richards equation (Richards 1931) and the sink term in Equation (6), provides the following moisture transfer equation:
∂ψ ∂ ∂ψ = K(ψ) ∂t ∂x ∂x
∂ψ ∂K (ψ) ∂ K(ψ) + − S(ψ, x, z) + ∂z ∂z ∂z
The time dependent nature of Equation (9) is dealt with via a mid-interval backward difference technique, yielding: K n+1/2 ψ n+1 + C n+1/2
(7)
A solution of Equation (7) is obtained via a finite element spatial discretisation procedure and a finite difference time-stepping scheme. In particular, adopting a Galerkin weighted residual approach yields: − e
− e
∂Nr ∂Ns ψs ∂e − K ∂z ∂z
+
Nr λ∂ −
−
Nr Ns C e
e
∂K ∂e Nr ∂z
Nr S(x, z)∂e
∂ψs ∂e = 0 ∂t
(8)
For the purposes of this paper, a typical 1 in 2 slope has been considered. In this study, location of the critical slip surface has been determined using SLOPEW—employing 147 trial surfaces. For stability analysis, the slope has been divided into eight slices, numbered from 1 at the toe, to 8 at the crest of the slope. Figure 1 shows the geometry of the slope, the position of each slice and the location of the critical slip surface. 3.2 Soil properties
Using, Green’s formula and introducing boundary terms leads to the final discretised form: Kψs + C
∂ψs +J +S =0 ∂t
(9)
where
m " ∂Ns ∂Nr ∂Ns ∂Nr K= · +K · ∂e K ∂x ∂x ∂z ∂z e=1 e
(10) C=
CASE STUDY
3.1 Slope geometry and slip surface
e
(14)
This finite element spatial discretisation procedure and a finite difference time-stepping scheme has been coded in FORTRAN and used throughout the simulation in this study. Further detail of the water-uptake model can be found in Rees and Ali (2006). 3
∂Ns ∂Nr ψs ∂e K ∂x ∂x
+ J n+1/2 + S n+1/2 = 0
C(ψ)
ψ n+1 − ψ n t
m "
[Nr Ns C]∂e
The soil chosen for consideration here follows from the work of Rees and Ali (2006). In particular, the behaviour of Boulder clay is considered. The relevant shear strength properties of Boulder clay are given in Table 1. The water retention curve and the hydraulic conductivity relationship for this material are shown in Figures 2 and 3 respectively. The figures also show measured data for three other soils as references: typical sand, Kimmeridge clay and typical Loam (Rees 1990). A comparison of results would appear to suggest that the assumed relationship for Boulder clay is within the range of previously published data for this soil type.
(11)
e=1 e
J =
m "
Nx
e=1 e
S=
m " e=1 e
m " ∂K [Nx λ]∂ e ∂e − ∂x e=1
Table 1.
(12)
e
[Nx S (x, z)]∂e
(13)
Material properties (Bishop et al. 1960).
Soil type
γ (kN/m3 )
c (kPa)
φ (degrees)
φb (degrees)
Boulder clay
22
9.6
27.3
21.7
813
(Biddle, 1998). The mesh consists of seven hundred, eight-noded isoparametric elements with 2231 nodes in total. The mesh was configured to offer some refinement within the root zone area since this is the region where the most significant moisture content variations were expected to occur. The simulated period covered a spring/summer soildrying phase of 9 months (270 days). The simulation employed a time-step size of 21600 seconds, which was held constant for the entire period considered. A transpiration rate of 5 mm/day is used for this tree (Biddle, 1998). In this case, water extraction is assumed to take place at its potential rate. Throughout the simulation, capillary potential was dry from −20 cm to −130 cm. Therefore α(ψ) in Equation (6) has been taken as unity as this range of capillary potential is within the range of optimal water extraction (Feddes et al. 1976). A uniform initial value of capillary potential of −20 cm is assumed to apply throughout the domain. This indicates that this soil is close to field capacity (Biddle 1998). The drying phase was represented via the application of the above transpiration rate within the root-water uptake model. The surface boundary, the lower boundary and the far-field vertical boundary were unconstrained (natural) throughout the simulation. The results of the drying phase water-uptake simulation were first determined via the solution of Equation (7). The suction values this obtained were then fed into a slope stability analysis based on Equation (5).
Boulder Clay
1.0E+05 Capillary Potential (negative value,cm)
Sand Kimmeridge Clay 1.0E+04
Loam
1.0E+03
1.0E+02
1.0E+01
1.0E+00 0.05
Figure 2.
0.20
0.50
0.65
Water retention curve for Boulder clay.
0.05 1.0E-05
0.15
1.0E-06 Hydraulic Conductivity (cm/s)
0.35 Volumetric Water Content (%)
Volumetric Water Content (%) 0.25 0.35 0.45
0.55
0.65
Boulder Clay Kimmeridge Clay
1.0E-07
Silt
1.0E-08 1.0E-09 1.0E-10 1.0E-11
Figure 3.
Hydraulic conductivity for Boulder clay.
700 elements
Mature Tree
4
2231 nodes
2m
5m
5m
16m
Figure 4.
Finite element mesh.
The water-uptake problem considered here represents drying of the soil from a near-saturated initial state. Hysteresis is not considered.
RESULTS
Figure 5 summarizes the results of the water-uptake simulation. The figure shows simulated contours in terms of capillary potential after a 270 day drying period. The numerical solution yields raw output in terms of capillary potential. These values have been converted to matric suction for each node at the centre of the base of each slice. The resulting suctions have then been employed in Equation (5) to calculate the FOS of the slope.
7
8
6
Numerical representation
4 1
2
12.311.1 9.9
3 5m
In the first instance the case study presented here considers the effect of a mature lime tree located near the toe of the embankment. Figure 4 shows a diagrammatic representation of the tree, the extent of the root zone and the finite element mesh. The root zone is assumed to extend a depth of 2 m and a radial distance of 5 m both left and right direction
Origin line
3.3
5
8.8 6.5 4.2 2.0
6m 7.5 m 10 m 16 m
Figure 5.
814
Matric suction (kPa) contours at 270 days.
12.0
Slice 1 Slice 2
10.0
Matric Suction (kPa)
Slice 4 8.0
Slice 8
6.0
2.96 2.94
FOS
2.92 FOS
Although the active root zone of the tree lies below the start of the slope, Figure 5 reveals that suctions have been generated within on the lower section of the slope itself. The water-uptake model, only applies the sink (extraction) within the pre-defined geometry of the root zone. However, moisture is free to migrate towards this zone from the surrounding soil. Hence, a ‘drawdown’ of moisture from the slope can be expected. Figure 6 shows the changes of matric suction at nodes located at the centre of the base of some selected slices (see Figure 3). The most significant changes in matric suction occur near the centre of tree (i.e. slice no 1). This effect diminishes as the distance from the centre of tree increases (slice no 2 > slice no 4 > slice no 8). For ease of interpretation, Figure 7 also shows the results in terms of volumetric moisture content at these slices. Figure 8 shows the corresponding changes in the FOS computed at various times during the drying period. This figure shows that FOS varies with time and increases with matric suction.
2.90 2.88 2.86 2.84 0
50
Figure 8. Table 2.
100
150 Days
200
250
300
Variation of FOS with time. Comparison of FOS at various conditions.
Conditions Fully saturated Tree near toe
Description
Trial slope with no tree water up-take Position of tree; x = 6 m, y = 2.5 m Tree at Position of tree; mid-slope x = 10 m, Coordinate y = 4 m Tree near Position of tree; crest x = 12.5 m, y = 5.0 m
FOS
Percentage difference (%)
2.74
0
2.95
7.7
2.89
5.47
2.88
5.11
4.0
2.0
0.0 0
50
100
150
200
250
300
Days
Figure 6. Matric suction (kPa) at the base of selected slices (Refer to Figure 3).
Volumetric Moisture Content (%)
4.0E-01 3.8E-01 3.6E-01 3.4E-01 3.2E-01
Slice 1 Slice 2 Slice 4 Slice 8
3.0E-01 2.8E-01 2.6E-01 0
50
100
150
200
250
300
Days
Figure 7. Volumetric moisture content (%) at the base of selected slices (Refer to Figure 3).
Further work has also been undertaken to examine the effect of changing the position of the tree in relation to the slope. Presentation of the detailed results is not possible in this paper due to space limitations. However, a brief summary of the overall result is presented for two cases; 1) tree located at mid-slope, and 2) tree located at crest of slope. Based on these variations, two new water-uptake simulations have been performed. All other characteristics of these simulations remain as described above. Table 2 shows a comparison of the resulting FOS calculated at the end of each simulation. The table also indicates the percentage difference in the FOS as compared to the saturated base-line. The coordinates are based on the origin at lower left corner of the model (see Figure 1). This comparison indicates that changes in matric suction considered here can result in a variation in the FOS against slope failure of between 5 % and 7 %. This result is indicative of one particular possible benefit of root water uptake. It should be noted, however, that this variation in FOS arises as a result of only one specific aspect of the problem, i.e. suction induced variation in shear strength.
815
5
CONCLUSIONS
The application of a numerical model for the simulation of moisture migration patterns due to tree water uptake in relation to a soil slope has been presented. An approach has been illustrated that enables the resulting prediction of soil suction variations to be related to a subsequent calculation of slope stability. Stability calculations have been performed by application of the standard theory of limit equilibrium of forces and moments. The model proposed then extends the standard framework to include a shear strength equation that is suction dependent. Suction variations generated in relation to a mature lime tree located on (or near) a typical soil slope have been presented. A range of tree locations have been considered. The problem chosen for consideration covered a full spring/summer drying period. The results of this study indicate that matric suction generation caused by the presence of a mature tree can readily increase the factor of safety against slope failure by more than 5%. These results are independent of related vegetation effects e.g. weight of vegetation, windthrow, root strength etc. and must therefore be treated only as a one component of the overall problem. In addition, it is evident that vegetation may induce much higher suctions than those considered here. Further work is therefore needed to validate the approach presented and to set it in a more general context. REFERENCES Biddle, P.G. 1998. Tree Root Damage to Buildings. Willowmead Publishing Ltd, Wantage. Bishop, A.W. 1955. The use of the slip circle in the stability analysis of earth slopes. Géotechnique, 5(1): 7–17. Bishop, A.W., Alphan I., Blight, G.E. & Donald, I.B. 1960. Factors Controlling the Shear Strength of Partly Saturated Cohesive Soils. Proc. ASCE conf. cohesive soils, Colorado, 503–532. Fellenius, W. 1936. Calculation of the Stability of Earth Dams. Trans. 2nd Int. Cong. Large Dams, Washington, 445–459. Fredlund, D.G., Morgenstern, N.R. & Widger, R.A. 1978. The shear strength of unsaturated soils. Canadian Geotechnical Journal, 15: 313–321. Fredlund, D.G. & Rahardjo, H. 1993. Soil Mechanics of Unsaturated Soils. John Wiley & Sons: New York.
GEO—SLOPE ver 6.17 Software, GEO-SLOPE/W International Ltd, Calgary Alberta, Canada, 2004. Greenwood, J.R. 2006. SLIP4EX—A program for routine slope stability analysis to include the effects of vegetation, reinforcement and hydrological changes. Geotechnical and Geological Engineering, 24: 449–465. Greenwood, J.R., Norris, J.E. & Wint, J. 2004. Assessing the contribution of vegetation to slope stability. ICE Proc. Geotechnical Engineering, 157: 199–207. Janbu, N., Bjerrum, L. & Kjaernsli, B. 1956. Soil mechanics applied to some engineering problems. Norwegian Geotechnical Institute Publication, 16. Lambe, T.W. & Whitman, R.V. 1969. Soil Mechanics. Wiley, New York, 363–365. Morgenstern, N.R. & Price, V.E. 1965. The analysis of the Stability of General Slip Surfaces. Géotechnique, 15: 79–93. Rees, S.W. 1990. Seasonal Ground Movement Effects on Buried Services, PhD thesis, University of Wales, Cardiff. Rees, S.W. & Ali, N. 2006. Seasonal water uptake near trees: A numerical and experimental study. Geomechanics and Geoengineering, 1(2): 129–138. Renaud, J.P., Anderson, M.G., Wilkinson, P.L., Lloyd, D.M. & Wood, D.M. 2003. The importance of visualisation of results from slope stability. ICE Proc. Geotechnical Engineering, 156(1): 27–33. Richards, L.A. 1931. Capillary conduction of liquids in porous media. Physics, 1: 318–333. Ridley, A., Ginnity, M. & Vaughan, P. 2004. Role of pore water pressures in embankment stability. ICE Proc. Geotechnical Engineering, 157: 193–198. Simon, A. & Collison, A.J. 2002. Quantifying the mechanical and hydrologic effects of Riparian vegetation on streambank stability. Earth Surface Processes and Landforms, 27: 527–546. Simon, A., Curini, A., Darby, S.E. & Langendoen, E.J. 2000. Bank and near-bank processes in an incised channel. Geomorphology, 35: 193–217. Spencer, E. 1967. A Method of Analysis of the Stability of Embankments Assuming Parallel Interslice Forces. Géotechnique, 17: 11–26. Technical Committee of Investigation 1994. The Collapse of Block 1 and the Stability of Blocks 2 and 3 Highland Towers Condominium. Report of the Technical Committee, Hulu Klang, Malaysia. Terzaghi, K. 1936. The Shear Resistance of Saturated Soils. Proc. Conf. Soil Mech. Found. Eng., Cambridge, 54–56. Thorne, C.R. 1990. Effects of vegetation on riverbank erosion and stability. In Vegetation and Erosion: Processes and Environments, John Wiley and Sons, 125–144.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Numerical predictions of seasonal pore water pressure fluctuations using FLAC tp flow O.C. Davies, M. Rouainia & S. Glendinning School of Civil Engineering and Geosciences, University of Newcastle upon Tyne, UK
ABSTRACT: This paper details the development of a transfer method of the hydraulic boundary conditions from a hydrological finite difference code, SHETRAN, into a geotechnical finite difference code, FLAC two phase (tp) flow. This transfer allows the daily predicted surface pore water pressures from SHETRAN to be applied to the surface boundary of the FLAC tp flow model. Once the surface pore water pressures have been applied then any of the constitutive soil models within FLAC tp flow can be used to model the mechanical response. This process offers the advantage that actual or predicted climate data can be used together with soils and vegetation data to model the seasonal responses of an embankment. Ultimately this model will be used with predicted future climate data to predict the response of infrastructure embankments to climate change.
1
BACKGROUND
Observations have shown that embankments shrink and swell due to the cyclic changes in pore water pressures. These movements can lead to the progressive failure of an embankment. The rate of progressive failure depends upon the severity of the shrink/swell cycle together with the number of cycles (Kovacevic et al. 2001). SHETRAN is hydrological modelling software capable of modelling the complex surface boundary conditions of a catchment area together with saturated and partially saturated subsurface flow. It is for this reason that this model has been chosen to predict the pore water pressure changes within an embankment. FLAC tp flow is geotechnical modelling software capable of modelling saturated and partially saturated subsurface flow and coupling this with a mechanical simulation. However FLAC tp flow is not capable of modelling the surface boundary condition to the same accuracy as SHETRAN. It is for this reason that a method has been developed to allow the transfer of daily surface pore water pressures from SHETRAN to the FLAC tp flow boundary thus allowing a fully coupled simulation to be carried out. 1.1
face pore pressures to the FLAC tp flow model. The third test imitates the second but for an embankment model with bare slopes. The fourth test is as the third but with grass covered slopes. 1.2
SHETRAN
SHETRAN is a 3D coupled surface/subsurface physically based spatially distributed finite difference model for coupled water flow together with sediment and solute transport modelling capabilities (Ewen et al. 2000). For the purpose of this modelling only the water flow component is considered. The SHETRAN flow model for an embankment (Figure 1) can be thought to consist of 3 components: 1. Interception and evapotranspiration 2. Overland flow 3. Subsurface flow
Examples
For the purpose of this paper four tests have been conducted. The first test consists of a simple caisson where the SHETRAN—FLAC models have been run separately in order to validate the newer FLAC tp flow model against the more established SHETRAN model. The second test involves first running the SHETRAN model with actual climate data and transferring the sur-
Figure 1.
817
SHETRAN surface model.
Data requirements for the model are meteorological data, soils data, vegetation properties and overland flow data together with boundary and initial condition settings. SHETRAN will then automatically output pore pressures for each cell within the grid. At the surface boundary, interception of precipitation is modeled by a modified Rutter model (Rutter et al. 1971) allowing the calculation of net rainfall reaching the ground together with the amount of stored water on the vegetation canopy and evaporation from the canopy. Evapotranspiration, the movement of water from the soil and within plants, is modelled within SHETRAN using the Penman-Montieth equation for actual evapotranspiration (Monteith 1965). This is calculated as a loss term to describe the uptake of water through plant roots. Overland flow is also calculated within the program. The depth of runoff water is determined from the available water from the interception evapotranspiration component and the rate of infiltration into the subsurface. Flow resistance parameters are then used to model the overland flow using approximations of the St. Venant equations of continuity and momentum. The subsurface is assumed to consist of a porous medium with saturation a function of moisture content. Flow through the medium is calculated by solving the non-linear partial differential Richards equation. 1.3
FLAC tp flow
The FLAC finite difference code allows the numerical modelling of structures built of soil and rock. The twophase flow option within the FLAC program considers two immiscible fluids within a porous medium. This allows the modelling of an unsaturated soil assuming the fluids present within the soil are water and gas. FLAC tp flow is capable of solving a fluid only calculation and a fully coupled fluid mechanical calculation. For the purpose of this paper, only the fluid flow calculation is considered. FLAC tp flow requires soil properties, water properties and boundary and initial conditions to be specified. Water is able to enter the grid by specifying either a discharge or a pore water pressure at the boundary. The two phase calculation approximates the Richards equation if it is assumed that air within a partially saturated medium is at atmospheric pressure and has a density of zero, and that the porous medium has a constant volume and cannot deform. These assumptions are specified in the following examples in order to validate FLAC tp flow against the more established SHETRAN model. 2
with the more established SHETRAN model. This validation exercise involved the modelling of a partially saturated caisson. The caisson was 6 m deep and the pore pressure was hydrostatic with an initial head of −6 m at the surface and 0 m head at the base. Infiltration of the caisson took place at a rate of 0.2 m/day until full saturation was reached. The caisson was then permitted to drain. Each software model requires different input parameters for the soil. The soil parameters were set for the FLAC tp flow calculation and the SHETRAN parameters derived from these, as shown in Tables 1 and 2. Table 1.
FLAC tp flow soil properties.
Saturated mobility coefficient Porosity Residual saturation P0 a b c
2.92 × 10−10 m2 /(Pa-s) 0.33 0 0.699 × 104 Pa 0.336 0.5 0.5
where P0 , a, b and c are Van Genuchten parameters used in the FLAC tp flow program. Saturated hydraulic conductivity in SHETRAN is equal to the Saturated mobility coefficient in FLAC multiplied by ρω g. The parameters α and n used in SHETRAN are defined as follows: α=
ρω g P0
(1)
where ρω is the density of water = 103 Pa/m3 and g is the force due to gravity = 10 ms−2 . The Van Genuchten parameter n used in SHETRAN is defined as n=
1 1−a
Table 2.
(2)
SHETRAN soil properties.
Saturated hydraulic conductivity θs θr A N
2.92 × 10−6 m/s 0.33 0 1.43 (1/m) 1.506
CAISSON COMPARISON
Before a transfer of pore water pressures was attempted a simple validation exercise was conducted in order to compare the relatively new FLAC tp flow model
where θs is the saturated volumetric moisture content (porosity) and θr is the residual volumetric water content.
818
2.1
Saturation
2.2 Drainage
Figure 2 shows the variation of moisture content for both models during the saturation phase of the modelling. It can be seen that both models have identical initial conditions. Through the first 2.5 days the SHETRAN caisson was marginally more saturated than the FLAC tp flow caisson. This divergence of the models continued over time as can be seen from the plots at 4.25 days. Figure 3 shows the variation of head with depth for both SHETRAN and FLAC tp flow models for the caisson. Again both models have almost identical initial conditions. At 2.5 days negative pore pressures within both models were almost identical, however the FLAC tp flow model showed a slight positive pore pressure within the saturated zone. At 4.25 days the positive pore pressure continued within the saturated zone stabilising at just above 0.5 m within the top third of the caisson. Within the area of negative pore pressures both models again gave similar results.
Figure 4 displays the variation in pore pressure with depth under drainage from the base of the caisson (base boundary condition, head = 0 metres). The SHETRAN and FLAC codes correlate well with only some divergence at the base of the model. At this point over time the SHETRAN model loses some moisture content and is not fully saturated as within the FLAC model. Figure 5 displays variation of head over depth within the two modelled caissons. Due to the FLAC model having a much higher initial pore pressure throughout the grid the two models differ at day one but by no more than 0.2 m. The later measurements of head after day 4 correlate very well. These results provide confidence in the capabilities of the FLAC tp flow program to calculate the flow of water through a porous partially saturated medium. The next example attempts the transfer of the SHETRAN surface pore pressures to the surface of the FLAC tp flow grid.
Variation of moisture content with depth
Moisture content during drainage
6
6
5
2
4
elevation
elevation
3
initial SHETRAN day 1 SHETRAN day 4 SHETRAN day 20 SHETRAN day 100 FLAC day1 FLAC day 4 FLAC day 20 FLAC day 100
5
SHETRAN initial SHETRAN 2.5 days SHETRAN 4.25 days FLAC initial FLAC 2.5 days FLAC 4.25 days
4
3 2
1 1
0 0.1
0.2
0 0.15
0.3
moisture content
0.2
0.25
0.3
0.35
moisture content
Figure 2. Comparison of variation of moisture content within the caisson for SHETRAN and FLAC tp flow.
Figure 4. drainage.
Moisture content profiles of caisson during
Variation in pore pressure with depth Variation head with depth under drainage 6
6 5
SHETRAN initial 5
FLAC initial
3
4
SHETRAN initial SHETRAN 2.5 days SHETRAN 4.25 days
2
SHETRAN day 1 SHETRAN day 4
FLAC 2.5 days FLAC 4.25 days elevation
elevation
4
SHETRAN day 20 SHETRAN day 100
3
FLAC initial FLAC day 1
2
FLAC day 4
1
FLAC day 20
1
FLAC day 100
0 -6
-4
-2
0
0 -3
pore pressure (m)
-2
-1
0
1
head (m)
Figure 3. Comparison of variation of pore pressure within the caisson for SHETRAN and FLAC tp flow.
Figure 5.
819
Pore pressure profiles of caisson during drainage.
CAISSON WITH PORE PRESSURE TRANSFER
Saturation profile at 100 days
For this test the caisson model was run within the SHETRAN program but this time with climate data obtained for north Yorkshire, UK in 1994. A pore pressure boundary input file was then created from the SHETRAN results file. This file contained the daily pore pressures for the uppermost cell within the SHETRAN grid. Pore pressures within SHETRAN were calculated for the centre of each cell. These daily pore pressures were then transferred to the top of the FLAC tp flow grid at grid points. A pore pressure reading was transferred for day 1 and the FLAC tp flow model allowed to run for 1 day. The next day’s pore pressure was then applied and the model run again, and so on until the end of the simulation. Within the FLAC tp code, if a pore pressure is applied at the boundary then water is effectively exchanged with the outside world to maintain that pore pressure, i.e. for a negative pore pressure water is extracted from the grid and for a positive pore pressure water is pumped into the grid. This will effectively simulate the infiltration of water at positive pressures and the extraction of water due to evapotranspiration at negative pore pressures. The test was run for a period of 100 days. Figure 6 shows the variation in pore pressure within the caisson at depths of 0.9 m and 1.8 m below the surface of the caisson for both the SHETRAN simulation and the FLAC tp flow simulation. The figure again shows a slight delay within the FLAC tp flow calculation compared with the SHETRAN calculation. The differences are, however, negligible and the same steady states are achieved with reasonable correlation. Figure 7 shows the correlation between the models. At the surface there is an exact match due to the pore pressure calculated from SHETRAN being applied to the FLAC tp flow surface. Lower down in the grid FLAC tp flow shows marginally less saturation than
Variation of head over 100 days -1.00 -1.50 FLAC 0.9 m depth
-2.00
head (m)
-2.50 -3.00
SHETRAN 0.9 m depth
-3.50
FLAC 1.8 m depth
-4.00 SHETRAN 1.8 m depth
-4.50 -5.00
elevation (m)
3
6 5 4
FLAC saturation profile 100 days
3 2 1 0
SHETRAN saturation profile 100 days 0.4
0.6
0.8
1
saturation
Figure 7.
Saturation profiles after 100 days.
SHETRAN. Again it is apparent that the SHETRAN grid ‘wets up’ slightly faster than the FLAC tp flow grid. Below the 2 m mark both models show there has been no infiltration of water and initial conditions persist. The combined caisson modelling show that the FLAC tp flow model is capable of modelling the flow of water through the unsaturated zone and that the method of transfer of pore water pressure from the SHETRAN surface cells to the FLAC surface is effective. These tests were carried out under a onedimensional condition only, for the next test the same process was attempted for a two-dimensional problem.
4
EMBANKMENT TEST WITH BARE SLOPES
For this exercise an embankment was modelled in SHETRAN with initial very dry conditions and with the same climate data as used for the caisson with pore pressure transfer example (see above). The pore pressures within the centre of the top cell from the SHETRAN grid were then imported daily to the boundary grid points of the FLAC tp flow grid. Figure 8 shows how the FLAC tp flow grid and the SHETRAN grid overlap each other. The grey cells represent the cells for which daily pore pressures have been transferred. Several files were created from the SHETRAN simulations, one for each of the surfaces cells. Each file again contained the daily calculated pore pressures from the SHETRAN calculation. For day 1 the pore pressures were applied and the model run for a day, then day 2 pore pressures applied and so on as within the caisson examples. The soil properties for this simulation are given in Table 3.
-5.50 0
20
40
60
80
100
days
4.1 Comparison of results Figure 6. Pore pressure time series for SHETRAN and FLAC tp flow after transfer of surface pore pressures.
Figures 9, 10 and 11 show the variation in head over the SHETRAN grid and the FLAC tp flow grid for a
820
Head Variation 4yrs 0 -0.5 -1 -1.5 Head m
period of 4 years for 3 points within the grids (indicated by the dots on the grid on ech figure). It can be seen that the transfer method was efficient in applying the SHETRAN boundary condition to the FLAC boundary condition. Just below the embankment surface (Figures 9 and 10) the FLAC tp flow calculation shows an initial lag behind the SHETRAN simulation, this is due to the two phase model assumptions not exactly approximating to the Richards equation, but after a period of 100 days both models correlate well. Deeper within the embankment (Figure 11) the lag is more pronounced; good correlation is not achieved until 300 days. This initial lag deep within the embankment is caused by the excessively dry initial conditions. As it can be seen for the remaining 3 years the models correlate well. Such excessively dry initial conditions
-2 -2.5 -3
Flac tp flow 7.5m from cent 2m elevation
-3.5
Shetran 7.5m from cent 2m elevation
-4 0
200
400
600
800
1000
1200
1400
Days
Figure 10. Pore pressure variation for 4 years for embankment with bare lopes at height 2 m above foundation.
head variation 4yrs 0 -0.5 -1
head m
-1.5 -2 -2.5 -3
Flac tp flow 1.5m from cent 2m elevation -3.5
Shetran 1.5m from centre 2m elevation -4 0
200
400
600
800
1000
1200
1400
days
Figure 8. Table 3.
Overlap of SHETRAN and FLAC tp flow grids. Figure 11. Pore pressure variation for 4 years for embankment with bare slopes at height 2 m above foundation.
Embankment test FLAC tp flow soil properties. 2.04 × 10−10 m2 /(Pa-s) 0.5 0.15 9.810 × 104 Pa 0.16667 0.5 0.5
Saturated mobility coefficient Porosity Residual saturation P0 A B C
are unlikely to be encountered for a real embankment problem and were only used to create a robust test for the comparison.
5
EMBANKMENT TEST WITH GRASS COVERED SLOPES
Head over 4yrs 0.00 -1.00 -2.00
head (m)
-3.00 -4.00 -5.00
shetran 0.5m cent 5.5m elevation -6.00
Flac tp flow 0.5m cent 5.5m elevation
-7.00 -8.00 0
200
400
600
800
1000
1200
1400
days
Figure 9. Pore pressure variation for 4 years for embankment with bare slopes at height 5.5 m above foundation.
Figures 12, 13 and 14 show the variation of pore pressure over a period of 4 years for the embankment with a grass canopy. All other variables remained the same as for the previous simulation. It can be seen from these Figures when compared to Figures 9, 10 and 11, which represent the simulation for bare ground, there is a much greater range between the summer and winter pore pressures. This greater range is much more pronounced at the surface (Figures 8, 9, 11 and 12). The SHETRAN program results and the FLAC tp program results still compare well for the three areas investigated despite the greater variance in pore pressures.
821
6
Head variation over 4 years 1.00
From these simple tests it has been established that FLAC tp flow is capable of modelling unsaturated flow through a porous medium with a high degree of accuracy. It has also been shown that the method of transferring surface pore pressures from the SHETRAN grid to the surface grid points of the FLAC tp flow grid is an efficient way to apply the more complex surface condition model of SHETRAN to the FLAC tp flow calculation. It will now be possible to run a simulation within SHETRAN for a fully vegetated embankment with actual measured or predicted climatic data and transfer the pore pressures over to FLAC tp flow to run a fully coupled analysis and establish the mechanical response of the embankment.
-1.00
head (m)
-3.00 -5.00 -7.00 -9.00
Flac tp flow 0.5m from cent 5.5m elevation SHETRAN 0.5m from cent. 5.5m elevation
-11.00 -13.00 -15.00 0
200
400
600
800
1000
1200
CONCLUSIONS
1400
days
Figure 12. Pore pressure variation over 4 years for embankment with grass covered slopes at height 5.5 m above foundation.
Head variation over 4 years
REFERENCES
0.00 -1.00
head (m)
-2.00 -3.00 -4.00 -5.00
Flac tp flow 7.5m from cent 2m elevation
-6.00
SHETRAN 7.5m from cent. 2m elevation
-7.00 0
200
400
600
800
1000
1200
1400
days
Figure 13. Pore pressure variation over 4 years for embankment with grass covered slopes at height 2 m above foundation.
Head variation over 4 years
Ewen, J., Parkin, G. & O’Connell, P.E. 2000. SHETRAN: Distributed River Basin Flow and Transport Modelling System, Journal of Hydrologic Engineering, 5, (3), pp. 250–258. Kovacevic, K., Potts, D.M. & Vaughan, P.R. 2001. Progressive failure in clay embankments due to seasonal climate changes, 5th Int. Conf. Soil Mech. Geotech. Engng. Istanbul, 2127–2130. Monteith, J.L. 1965. Evaporation and environment. Proc. 18th Symposium Society for Experimental Biology. Swansea: Cambridge University Press, London, 205–234. Rutter, A.J., Kershaw, K.A., Robins, P.C. & Morton, A.J. 1971. A predictive model of rainfall interception in forests, 1. Derivation of the model from observations in a plantation of Corsican pine. Agricultural Meteorology, 9, pp. 367–384.
-1.00 -1.50
head (m)
-2.00 -2.50 -3.00 -3.50
Flac tp flow 1.5m from cent. 2m elevation
-4.00
SHETRAN 1.5m from cent. 2m elevation
-4.50 0
200
400
600
800
1000
1200
1400
days
Figure 14. Pore pressure variation over 4 years for embankment with grass covered slopes at height 2 m above foundation.
822
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Infiltration analysis in unsaturated soil slopes J.F. Xue & K. Gavin University College Dublin, Dublin, Ireland
ABSTRACT: This paper describes a simple model which can be used to estimate the time needed for a wetting front to develop in an unsaturated soil slope. The model is an extended form of the traditional Green-Ampt method. The first extension recognises that ponding of water cannot occur on a soil slope. It further allows the user to indirectly account for antecedent rainfall conditions by separating slopes into two categories depending on their initial suction profiles. In the first category, where the initial suctions are large, the rate of the development of the wetting front depth is controlled by the rainfall intensity. In the second, where the initial suction is low, the time taken for a wetting front to develop to a given depth depends on the infiltration capacity of the soil. In the final section of the paper results from the new model are compared to numerical predictions of wetting front depth in a fine sand slope.
1
INTRODUCTION
To analyse landslides triggered by rainfall, it is important to understand the infiltration process. In most current methods, such as the Green-Ampt model, the infiltration analyses are based on theories derived for saturated soils. However, the mechanisms controlling infiltration into unsaturated soil are different to the saturated condition. Key differences include the fact that the permeability of unsaturated soil changes continuously throughout infiltration, and that a major driving force for water flow in saturated soils is the head of water. In unsaturated soil flow problems such as slope failures, where there is no surface ponding, the main driving force is not gravity, but differential suction. In this paper a model which was developed to analyse the rainfall infiltration into unsaturated soils is presented and applied to a published case history of a numerical analysis of infiltration into a fine sand slope.
2
BACKGROUND
The stability of many man-made and natural slopes is enhanced by near surface negative pore water pressure (suctions). An understanding of how rainfall infiltrates into these slopes and reduces suction is critical to a full understanding of slope stability problems. Predicting the rate of infiltration of water into unsaturated soils is a complex process. This is due in part to the variable rainfall and irrigation patterns that occur, and the highly non-linear permeability of unsaturated soil. In addition the geometry, vegetation and the roughness of the ground surface will influence the infiltration
process (See Fredlund et al. 1994, Ng and Shi 1998, Zhan and Ng 2004, and others). Field measurements of the variation of suction in an instrumented slope by Rajhardjo et al. (2005) reveal some of the complexities involved in attempting to predict the infiltration response of soil slopes. The authors show that during the early stages of a low intensity rainfall event, when the infiltration capacity of the slope is highest, all of the rainfall infiltrates into the slope. As the rainfall continues, the in-situ suction and therefore the infiltration capacity of the slope reduce and run-off begins. The time at which run-off begins depends on the initial suction in the slope and the rainfall intensity, with the time to run-off, increasing when the initial suctions are highest and the rainfall intensity is low. By placing suction probes at various depths in the slope, and along the slope face, the effect of subslope drainage was observed, with the water content at a given depth in the slope being highest near the toe of the slope and lowest near the crest. There are several methods commonly used to analyze the infiltration process, ranging from simple methods such as the Green-Ampt model, to the more complex finite element method (FEM). Some of the simple methods are briefly reviewed as the new method is essentially an extended form of an existing model. 2.1
Green-Ampt model
The Green-Ampt (1911) model was first developed to analyze the infiltration process under ponded conditions (i.e. assuming standing water on a horizontal ground surface). The basic assumption underpinning the model is that infiltration causes the development
823
2.2 Horton equation H Infiltrating water Saturated soil
Wetting front; matric suction pulls water into dry soil
Figure 1. model.
Run-off from a slope will occur only when the rainfall intensity exceeds the infiltration capacity of the soil. Considering Equation 2 we see that the infiltration capacity of the slope reaches a limiting minimum value, equal to the saturated permeability of the soil (Ks ) when the near surface soils become saturated. Field measurements contradict this assumption. Rahardjo et al. (2005) revealed that run-off occurred on slopes when the rainfall intensity was lower than Ks . The Horton equation (Jury & Horton 2004) is used to describe the infiltration capacity of soil with time (t).
Zf
Wetting front moves down into dry soil
Two-layered soil profile defined in Green-Ampt
of well-defined wetting front (See Figure 1). The soil above the wetting front is fully saturated, whilst below the wetting front it remains at the initial (preinfiltration) water content. Gravity and matric suction effects control the movement of water in the saturated zone, and the hydraulic gradient (hi ) at the wetting front is: hi =
H + Zf + S Zf
(1)
where H is the depth of ponded water, Zf is the wetting front depth and S is the suction at the wetting front. Since the soil above the wetting front is assumed to be fully saturated, using the permeability coefficient of the saturated soil Ks , and applying Darcy’s Law, the infiltration rate of the soil can be calculated: H + Zf + S i = Ks Zf
(2)
The model was originally developed to analyse the infiltration of ponded water into homogenous soils. Variations of the Green-Ampt model to account for steady (Mein & Larson 1973) and unsteady (Chu 1978) rainfall events have been developed. However, the basic assumption of the two-layer model (with the wetting front forming a boundary between the saturated and unsaturated zones) remains. Research on infiltration in the field by Mishra et al. (2003) found the Green-Ampt model to be conservative, with the time predicted for a wetting front to develop being much lower the in-situ measurements reveal. This is at least partly due the use of the saturated soil permeability in Equation 2 (Bouwer 1966), and the assumption that the near surface soils are fully saturated. Field measurements show that near surface soils rarely become fully saturated Williams et al. (1998). Therefore the applicability of the Green-Ampt model for unsaturated soil infiltration analysis is questionable.
i = if + (i0 − if ) exp(−βt)
(3)
where: i0 is the initial infiltration capacity at t = 0; if is the steady state final infiltration capacity; β is a constant which describes the rate of decrease of the infiltration capacity; and t is time. From Equation 3, we see that the final infiltration capacity is not constrained to the limiting value Ks , rather a limiting value if , which is typically lower than Ks , can be used. Considering Equation 3, run-off will occur at any time when the rainfall intensity exceeds the infiltration capacity of the soil. Although Horton’s equation provides a simple mathematical description of the reduction of the infiltration capacity of a soil during rainfall, in practice it is difficult to implement because of difficulties associated with the choice a unique β value for a given slope, see Mishra et al. (2003) and Xue & Gavin (2007). 3
PROPOSED METHOD
Considering some of the drawbacks outlined above a modified model based on the Green-Ampt model, Darcy’s Law and the Law of mass conservation is developed in this section to analyse one-dimensional vertical infiltration into unsaturated soil slopes. 3.1 Infiltration capacity of unsaturated soil slopes Making the assumption that: 1. During rainfall on a slope where ponding cannot occur, the soil is continuously supplied with water, but not fully saturated within the wetted zone. 2. After rainfall the final suction profile in the wetted zone is linearly distributed within the wetting front (See Figure 2), where St and Sb are the initial suctions at the top and base of the wetting front, and Su is the limiting final suction. 3. The permeability of the soil above the wetting front is uniform with depth and time. In the class of simple infiltration models considered, the soil permeability is often assigned a constant value
824
and the hydraulic head in this zone is controlled exclusively by matric suction. Since the water supply at the ground surface is continuous during rainfall, suction values at the ground surface are zero. Setting the ground surface as the reference elevation and considering vertical flow only, the hydraulic gradient at depth y should be:
e
fac
p
slo
fall
ain er r
aft
r e su
tion
suc
fall
St Su
re efo
b
rain
ng
tti we
nt
fro
Hf Sb
hi =
Sy y
(4)
suction profile
where Sy is the suction value at depth y. The infiltration capacity of the soil at depth y is:
y Figure 2.
Suction profile assumed in the new model.
i=K
(5)
in which K is the permeability of the soil at the depth y. In Equation 4, the infiltration capacity is controlled by the permeability of the soil and the hydraulic gradient due to matric suction. The infiltration capacity will be greater than the permeability of the soil when Sy /y > 1. This situation occurs in dry soils with high initial matric suction. If during a rainfall event, the rainfall intensity (Ri ) is less than the infiltration capacity i, all the precipitation will infiltrate into the soil. In contrast if the rainfall intensity is larger than infiltration capacity, runoff will occur. As soils within the wetting front become more saturated and the matric suction at the wetting front reaches a limiting value, the infiltration capacity in Equation 5 converges to a constant value. This agrees with the trend of infiltration capacity decay described with the Horton equation. We therefore consider the infiltration process in two stages:
Figure 3. Hydraulic head due to water pressure from higher up the slope.
(usually the saturated permeability because of the assumption that the soil becomes fully saturated during infiltration). If the soil is partially saturated the permeability depends on the negative porewater pressure (or the degree of saturation), Ng & Shi (1998). Whilst it is strongly recommended that the permeability of the soil over the appropriate range of suction values is measured using the Soil Water Characteristic Curve (SWCC), in the absence of specific information the recommendation by Bouwer (1966) that K = 0.5 Ks can be adopted. 4. The model assumes one-dimensional vertical infiltration only. The water table is well below the ground surface and the slope is gentle. The head difference due to the sloping water table (See Figure 3) is small in comparison to matric suction effects. 5. Because of the assumption of 1-D flow, only flow perpendicular to the slope surface is considered; flow parallel to the ground surface is ignored. Since ponding cannot occur on a slope, the hydraulic gradient originating from the ponded water (H) in Equation 1 is neglected. As the water phase in the wetting front is not continuous, the water in this zone cannot impart a hydraulic gradient to the water beneath. Thus, the static hydraulic head (Zf ) in Equation 1 does not exist
Sy y
Stage 1: When the rainfall intensity is smaller than the infiltration capacity: Ri ≤ i. From Equation 5 we have: in stage 1, Sy ≥ (Ri /K)y. Stage 2: When Ri exceeds the infiltration capacity: Ri > i. In this stage we have: Sy < (Ri /K)y. Given the initial and final suction profile in the soil, the wetting front can be divided into two zones with the line Sy = (Ri /K) y as shown in Figure 4. The ratio Ri /K, which can be defined as the relative rainfall intensity (Rri ), describes the ratio between the actual rainfall intensity and the permeability of the soil. If the initial suction values in the soil are such that part of the profile falls into zone 1, the soil will initially have an infiltration capacity higher than the rainfall intensity. If the suction values in the soil fall into zone 2, and the rainfall intensity exceeds the infiltration capacity of the soil, run-off will occur (at the rate Ri − i).
825
4
zone 1
H2
H1 zone 2 Sy=(Ri/K)*y
H
Sb y Figure 4.
Suction profile divided into two zones.
According to the Law of mass conservation, in zone 1, we have: Ri dt = θ1 dy
(6)
Rewriting the equation and integrating with depth (y), we have the time required to form the wetting front to depth H1 in zone 1 (Figure 4): T1 =
θ1 H1 Ri
(7)
Tami et al. (2004) performed numerical simulations using SEEP/W (Geoslope Int.) to investigate the effect of the duration of a rainfall event on the infiltration response of a slope which was subjected to a fixed rainfall intensity of 86.4 mm/hr. Two rainfall durations were considered, 15 and 42 minutes. This rainfall intensity was chosen to correspond to a rate of 10% of the saturated permeability of the sand. The 30◦ slope considered was made up of a 400 mm deep fine sand layer overlying a 200 mm thick gravely sand. The fine sand had a saturated permeability (Ks ) of 2.4×10−4 m/s, and the variation of suction with water content is shown in Table 1. The initial and final suction profiles for the 15 minute infiltration event is shown in Figure 5. It is apparent that after 15 minutes rainfall there was a significant reduction in suction at the slope surface, a small reduction at a depth of 200 mm and no change at Table 1.
K
Sb y
Water content of the fine sand at different suctions.
Suction (kPa)
5.4
4
3.5
2.5
1
1.5
Water content
7%
8%
8.5%
10%
22%
15%
As infiltration continues, suction values in the soil decrease and eventually fall into zone 2. In this zone, the infiltration capacity is lower than the rainfall intensity. So in this zone we have:
APPLICATION OF THE MODEL
1.5 kPa
5.4 kPa Zone 1
Final
Initial
3.5 kPa
dt = θ2 dy
400 mm
St
200 mm
Su
(8) 2.5 kPa
T2 =
θ2 (H 2 − H22 ) 2KSb
Figure 5. Initial and final suction profile in the slope with the 15 min precipitation of 86.4 mm/h.
(9)
1.0 kPa Zone 1
So the total time is: T = T1 + T2
5.4 kPa
Final Initial
(10)
It should be noted that in stage 2 as the soil becomes nears full saturation, it may behave as a saturated soil. In such cases Equation 10 may be overestimate the actual time required for a wetting front to form in latter parts of stage 2.
400 mm
in which Sb is the suction value at wetting front and θ2 is the change of volumetric content in zone 2. So the time for zone 2 to develop can be calculated with:
Sy=0.2y
2.5 kPa Sy=0.2y Figure 6. Initial and final suction profile in the slope with the 42 min precipitation of 86.4 mm/h.
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Table 2. Comparison of result from FEM and proposed method in this paper. Time (min) This paper Case
FEM
Green-Ampt
T1
T2
Total
1 2
15 42
2.2 10.2
10.4 37.5
0 0
10.4 37.5
controlled by the infiltration capacity of the wetted soil. When compared to the results from FEM analyses and the Green-Ampt model, the new model provided estimates that were compatible with FEM results and a significant improvement on the Green-Ampt model, especially during the early stage of infiltration. This method has an obvious advantage in performing preliminary design prior to the decision to carry out a full FEM analysis. ACKNOWLEDGEMENT
400 mm, suggesting that the wetting front depth just exceeded 200 mm. When the duration was increased to 42 minutes the wetting front depth evidently penetrated through the entire 400 mm depth of fine sand (See Figure 6). Calculation of the time needed to form these wetting front depths was carried out using the Green-Ampt method and the new model and the results are shown in Table 2. Consideration of Figures 5 and 6 show that in both cases, because the rainfall intensity is low in comparison to the infiltration capacity, the soil falls completely in zone 1, and therefore only T1 needs to be calculated. Whilst the predictions made using the new model are compatible with the FEM analyses, the Green-Ampt model severely under-predicted the infiltration time. This is presumably due to the combined effect of the use of Ks and the role of the static water head (imparted by the wetting front) increasing the hydraulic gradient.
5
CONCLUSION
To determine the stability of unsaturated soil slopes, it is important to determine the depth of the wetting front. The Green-Ampt model and FEM analyses are widely used to predict the formation of the wetting front. Whilst FEM analyses can provide rigorous results, the input data required for the models is not readily available for all soils. Whist the Green-Ampt model is widely used and relative easy to apply, some of the fundamental assumptions used in its derivation are shown to be questionable when the soil surface is not subject to ponding. A simple extension of the Green-Ampt model is proposed in this paper. In the model the soil above the wetting front is assumed to remain unsaturated throughout infiltration. The time for a wetting front to develop is considered in a two-stage process. In the first stage infiltration is controlled by the rainfall intensity and in the second part infiltration is
This project is funded by Iarnród Éireann. The authors would like to thanks Mr. Brian Garvey, former Chief Civil Engineer with Iarnród Éireann for financial assistance received. The first author was the recipient of a Geotechnical Trust Fund award from the Geotechnical Society of Ireland. REFERENCES Bouwer, H. (1966). Rapid field measurement of air entry value and hydraulic conductivity of soil as significant parameters in flow system analysis. Water Resources Research 2(4): 729–738. Chu, S.T. (1978). Infiltration during an unsteady rain. Water Resources Research 14(3): 461–466. Green, W.H. & C.A. Ampt (1911). Studies on soil physics: Flow of air and water through soils. Journal of Agricultural Science 4: 1–24. Jury, W.A. & R. Horton (2004). Soil Physics. New Jersey, John Wiley & Sons, Inc. Mein, R.G. & C.L. Larson (1973). Modeling infiltration during a steady rain. Water Resources Research 9(2): 384–394. Mishra, S.K., J.V. Tyagi & V.P. Singh (2003). Comparison of infiltration models. Hydrological processes 7: 2629–2652. Ng, C.W.W. & Q. Shi (1998). A numerical investigation of the stability of unsaturated soil slopes subjected to transient seepage. Computer and Geotechnics 22(1): 1–28. Rahardjo, H., T.T. Lee, E.C. Leong & R.B. Rezaur (2005). Response of a residual soil slope to rainfall. Canadian Geotechnical Journal 42: 340–351. Tami, D., H. Rahardjo, E.C. Leong & D.G. Fredlund (2004). Design and laboratory verification of physical model of sloping capillary barrier. Canada Geotechnical Journal 41(9): 814–830. Williams, J.R., Y. Ouyang, J.S. Chen & V. Ravi (1998). Estimation of infiltration rate in the vadose zone: Compilation of simple mathematical models (2), United States Environmental Protection Agency. Xue, J. & K. Gavin (2007). Effect of rainfall intensity on infiltration into partly saturated slopes. Journal of Geotechnical and Geological Engineering. Published online October 2007, DOI 10.1007/s10706-007-9157-0.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Prediction of changes in pore-water pressure response due to rainfall events M. Karthikeyan, D.G. Toll & K.K. Phoon Department of Civil Engineering, National University of Singapore, Singapore
ABSTRACT: Global climate change is expected to result in worldwide increases in temperature and alteration of rainfall patterns. Such changes have the potential to activate rainfall triggered landslides and a study is underway in Singapore to investigate these possible effects. The main objective of this work is to calibrate a numerical model for future prediction by making use of cases where in-situ measurements of pore-water pressures/suctions have been made in Singapore. The results presented in this study show that the prediction of changes in the pore-water pressure profile is highly sensitive to the soil-hydraulic properties used in the analysis. It was found that a SEEP/W flow model is able to capture the general trend of field behaviour of the changes in the pore-water pressure profile response due to rainfall events. However, the results from the numerical models indicate that further research is warranted to improve the accuracy of the numerical analysis by better definition of critical input parameters.
1
INTRODUCTION
Rain-induced slope failures are a common geotechnical problem in tropical areas like Singapore (Pitts 1984, Chatterjea 1989, Toll et al. 1999). The tropical climate of Singapore causes slopes to remain unsaturated during long hot and dry periods. However, there are numerous cases of slope failures in Singapore during severe rainfall events. Recent predictions of climate change as a consequence of increased greenhouse-gas production suggest that the evapotranspiration—precipitation balance is likely to change. This will affect the hydrological environments governing slope instability through, for example, changes in antecedent pore-water pressures and alteration of triggering event magnitudes. This could increase the frequency of occurrence of high positive pore pressures, and thus the activity of rainfall-triggered landslides (Buma 2000, Dehan et al. 2000, Dixon and Brook 2007). Transient pore-water pressure in response to short intense rainfall plays an important role in shallow landslide occurrence. Highly negative pore-water pressures may exist in the slope because of moisture loss either through evaporation or evapo-transpiration. These negative pore-water pressures may be lost with the occurrence of rainfall. Landslides are generally caused by a gain in pore-water pressure (or loss of suction) as a result of rainfall infiltration from the slope surface. Field observations show that significant suctions (in excess of 80 kPa) can develop near the surface of a slope during dry periods in Singapore (Gasmo et al. 1999, Tsaparas et al. 2003). However, after
even relatively small amounts of rainfall the suctions can be lost, and small positive pore-water pressures (up to about 5 kPa) can develop to depths of 1–2 m (Tsaparas et al. 2003). The data show that, for a scenario where the water table is at significant depth, most pore-water pressure changes take place near the surface (
