Laboratory Shear Strength of Soil-STP 740

LABORATORY SHEAR STRENGTH OF SOIL A symposium sponsored by ASTM Committee D-18 on Soil and Rock for Engineering Purposes...

Author: R. N. Yong | Frank C. Townsend

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LABORATORY SHEAR STRENGTH OF SOIL A symposium sponsored by ASTM Committee D-18 on Soil and Rock for Engineering Purposes AMERICAN SOCIETY FOR TESTING AND MATERIALS Chicago, III., 25 June 1980 ASTM SPECIAL TECHNICAL PUBLICATION 740 R. N. Yong, McGill University, and F. C. Townsend, University of Florida, editors ASTM Publication Code Number (PCN) 04-740000-38

m

AMERICAN SOCIETY FOR TESTING AND MATERIALS 1916 Race Street, Philadelphia, Pa. 19103

Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

Copyright© by AMERICAN SOCIETY FOR TESTING AND MATERIALS 1981 Library of Congress Catalog Card Number: 80-71002

NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication.

Printed in Baltimore, Md. September 1981


Foreword The symposium on Laboratory Shear Strength of Soil was held in Chicago, 111., on 25 June 1980. The symposium was sponsored by the American Society for Testing and Materials through its Committee D-18 on Soil and Rock for Engineering Purposes. R. N. Yong, McGill University, and F. C. Townsend, University of Florida, presided as symposium chairmen and served as editors of this publication.


Related ASTM Publications Behavior of Deep Foundations, STP 670 (1979), $49.50, 04-670000-38 Dynamic Geotechnical Testing, STP 654 (1978), $34.50, 04-654000-38 Dispersive Clays, Related Piping, and Erosion in Geotechnical Projects, STP 623 (1977), $40.75, 04-623000-38 Soil Specimen Preparation for Laboratory Testing, STP 599 (1976), $35.00, 04-599000-38 Field Testing and Instrumentation of Rock, STP 554 (1974), $18.75, 04-554000-38 Concrete Pipe and the Soil Structure System, STP 630 (1977), $14.00, 04-630000-07 Performance Monitoring for Geotechnical Construction, STP 584 (1975), $14.00, 04-584000-38 Laboratory Shear Testing of Soils, STP 361 (1964), $24.50, 04-361000-38 Evaluation of Relative Density and its Role in Geotechnical Projects Involving Cohesionless Soils, STP 523 (1973), $30.75, 04-523000-38


A Note of Appreciation to Reviewers This publication is made possible by the authors and, also, the unheralded efforts of the reviewers. This body of technical experts whose dedication, sacrifice of time and effort, and collective wisdom in reviewing the papers must be acknowledged. The quality level of ASTM publications is a direct function of their respected opinions. On behalf of ASTM we acknowledge with appreciation their contribution.

ASTM Committee on Publications


Editorial Staff Jane B. Wheeler, Managing Editor Helen M. Hoersch, Senior Associate Editor Helen P. Mahy, Senior Assistant Editor Allan S. Kleinberg, Assistant Editor


Contents Introduction

1 STRENGTH TESTING METHODS AND REQUIREMENTS

State of the Art: Laboratoiy Strength Testing of Soils—A. S. SAADA AND F. C. TOWNSEND

7

Comparison of Varions Methods for Determining Aô— MOSAID AL-HUSSAINI

78

Apparatus and Techniques for Static Triaxial Testing of Ballast— J. E. ALVA-HURTADO, D. R. MCMAHON, AND H. E. STEWART

94

Mechanical Behavior and Testing Methods of Unsaturated Soils— T. B. EDIL, S. E. MOTAN, AND F. X. TOHA

114

Determination of Tensile Strength of Soils by Unconfined-Penetration Test—H. Y. FANG AND JOSEPH FERNANDEZ

130

Torsion Shear Apparatus for Soil Testing—P. V. LADE

145

A Servo System for ControUed Stress Path Tests—K. T. LAW

164

A New Control System for Soils Testuig—R. J. MITCHELL

180

Lateral Stress Measurements in Direct Simple Shear Device— R. DYVIK, T. F. Z I M M I E , AND C. H. L. FLOESS

191

Tensile Properties of Compacted Soils—MOSAID AL-HUSSAINI

207

Effect of Organic Material on Soil Shear Strength— O. B. ANDERSLAND, A. S. KHATTAK, AND A. W. N. AL-KHAFAJI

226

Effect of Shearing Strain-Rate on the Undrained Strength of Clay— R. Y. K. CHENG

243

Undrained Shear Behavior of a Marine Clay—D. C. KOUTSOFTAS

254

Shearing Behavior of Compacted Clay after Saturation—c. w. LOVELL A N D J. M. JOHNSON Copyright Downloaded/printed University

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Plane-Strain Testing of Sand—N.

DEAN MARACHI, J. M. DUNCAN,

C. K. CHAN, AND H. B. SEED

294

Effect of End Membrane Tliiclcness on the Strength of "Frictionless" Cap and Base Tests—G. M. NORRIS

303

Field Density, Gradation, and Triaxial Testing of Large-Size Roclcfill for Little Blue Run Dam—G. R. TRIERS AND T. D. DONOVAN 315 DATA REDUCTION AND APPLICATION OF MEASUREMENTS FOR ANALYTICAL MODELING

State of the Art; Data Reduction and Application for Analytical Modeling—HON-YiM KO AND STEIN STURE

Normalized Stress-Strain for Undrained Shear Tests—v.

329 P. DRNEVICH

The Critical-State Pore Pressure Parameter from ConsolidatedUndrained Shear Tests—p. w. MAYNE AND P. G. SWANSON Nonlinear Anisotropic Stress-Strain-Strength Behavior of Soils— J. H. PREVOST

387

410 431

A General Time-Related Soil Friction Increase Phenomenon— J. H. SCHMERTMANN

456

On the Random Aspect of Shear Strength—R. N. YONG AND M. M. TABBA

485

Preconsolidation Pressure Predicted Using s„/p Ratio— T. C. ANDERSON AND R. G. LUKAS

502

Stress Path Tests with Controlled Rotation of Principal Stress Dhections—i. R. F. ARTHUR, S. BEKENSTEIN, J. T. GERMAINE, AND C. C. LADD

516

Shear Strength of Cohesionless Soils from Incremental Creep Test Data—GILBERT Y. BALADI, R. W. LENTZ, T. GOITOM, AND T. D. BOKER

541

Comparison of Shear Strength Values Derived from Laboratory Triaxial, Borehole Shear, and Cone Penetration Tests— J. R. LAMBRECHTS AND J. J. RIXNER

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Borehole Shear Test in Geotechnical Investigations— A. J. LUTENEGGER AND G. R. HALLBERG

566

Concepts for a Shear-Normal Gage to Estimate In Situ SoO Strength and Strength Angle—R. L. MCNEILL AND S.

L. GREEN

579

Residual Shear Strength Determination of Overconsolidated Nespelem Clay—DAVID MIEDEMA, JACK BYERS, AND RICHARD MCNEARNY

594

The Need for Pore Pressure Information from Shear Tests— D. H. SHIELDS AND N. A. SKERMER

610

Behavior of an Overconsolidated Sensitive Clay in Drained KgTriaxial Tests—VINCENZO SILVESTRI

619

DISCUSSIONS

Discussion of "State of the Art: Laboratory Strength Testuig of Soils" —SUZANNE LACASSE AND MLADEN VUCETIC

633

Discussion of "State of the Art; Laboratory Strength Testhig of Soils" —J. T. CHRISTIAN

638

PANELISTS' REPORTS

Discussion on Laboratory Shear Devices—c. c. LADD

643

Limitations of Duect Simple Shear Test Devices— PIERRE LA ROCHELLE

Discussion of Soil Testing Practices—s.

653

659

T. POULOS

Some Aspects of Clay Behavior and Thefa- Consequences on Modeling Techniques—FRAN(?OIS TAVENAS

667

Development, Testing Requhements, and Fitting Procedure of ElasticPlastic Models—GEORGE Y. B A L A D I

678

A Qualitative Stress-Strafai (Time) Model for Soft Clays— J. H. A. C R O O K S


685

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SUMMARY

Swmnaiy

703

Index

715


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STP740-EB/Sep.1981

Introduction

The increasing demand for better means and reliability for prediction of the yield or failure in soils, coupled with the ever present need to provide more realistic generalized stress-strain relationships of soils in design calculations and general analyses, make it very important that the geotechnical engineering profession be provided with an up-to-date appreciation of test techniques for measurement of shear strength and procedures for evaluation and reduction of measurements obtained from relevant test techniques. It has been at least 17 years since the last full documentation and evaluation of laboratory shear strength of soil has occurred {Laboratory Shear Testing of Soils. ASTM STP 361. American Society for Testing and Materials, 1964). There is a need for the profession to re-examine its position on the problems of yield and failure and to document the advances that have been made in the long intervening period in the development of new test techniques and methods for evaluation of the laboratory shear strength of soil. In the organization of this ASTM Symposium on Laboratory Shear Strength of Soil, advantage has been taken of the fact that two other companion exercises have been developed to complement this present study on laboratory test techniques for evaluation of shear strength. The many finer details of plasticity theory and generalized stress-strain relationships have been covered in the NSF/NSERC sponsored Workshop on Plasticity and Generalized Stress-Strain held at McGill University in May 1980, whilst the application of the theories to generalized practice was presented at an ASCE Symposium in October 1980. This ASTM symposium covers the very much needed study of laboratory techniques for evaluation of shear strength of soil. The object was (a) to meet the requirements for determination and assessment of the shearing resistance of soils, (b) to determine the kinds of strength parameters that can be derived from the various test techniques, (c) to assess the relevance of the various techniques presently available, (d) to establish the rationality of the test techniques, and (e) to examine the viability of the various models used for data reduction and the methods of application of data and measurements for assessment of shear strength of soils. There have been great advances made not only in equipment and instrumentation, but also in methods of tests and degree of sophistication of test techniques. In addition, advances have been made in methods of analysis, particularly with reference to the application of the measurements. The symposium was developed as a two-session presentation, each session Copyright by Downloaded/printed Copyright 1981 University of

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LABORATORY SHEAR STRENGTH OF SOIL

consisting of a state-of-the-art report and panel presentation. The program format and participants are given as follows: Session I—Strength Testing Methods and Requirements Chairman State-of-the-Art Speaker State-of-the-Art Report Panel Discussion Moderator Panelists

E. T. Selig, University of Massachusetts at Amherst A. S. Saada, Case Western Reserve University, Cleveland A. S. Saada, Case Western Reserve University, Cleveland, and F. C. Townsend, University of Florida, Gainesville

F. C. Townsend, University of Florida, Gainesville C. C. Ladd, Massachusetts Institute of Technology, Cambridge P. LaRochelle, Laval University, Quebec City S. Wright, Texas University at Austin S. Poulos, Geotechnical Engineers, Inc., Winchester, Mass.

Session II—Data Reduction and Application of Measurements for Analytical Modeling Chairman State-of-the-Art Speaker State-of-the-Art Report Panel Discussion Moderator Panelists

E. T. Selig, University of Massachusetts at Amherst H. Y. Ko, University of Colorado at Boulder H. Y. Ko and S. Store, University of Colorado at Boulder

R. N. Yong, McGill University, Montreal F. Tavenas, Quebec City J. H. A. Crooks, Golder Associates, Mississauga, Ontario George Y. Baladi, Waterways Experiment Station, Corps of Engineers, Dept. of the Army, Vicksburg, Miss. R. J. Krizek, Northwestern University, Evanston, III.

The contributions made by these participants and by the audience are gratefully acknowledged. The papers submitted to the symposium were divided into the two sessions, and were examined, evaluated, and discussed as part of the session presentation. These papers are organized in this STP as they appeared in each session. They provide the extension of the various test techniques and methods of analyses to specific examples of tests for various problem soil materials, new test techniques and applications, and particular methods of application of data reduction and evaluation. They serve as a means for demonstrating the wide range of applicability of test measurements and techniques. The editors also acknowledge the input and assistance


INTRODUCTION

provided by Professors H. Y. Ko, K. Y. Lo, H. W. Olsen, A. S. Saada, and E. T. Selig, who functioned as an ad hoc Task Committee.

R. N. Yong Geotechnical Research Center, McGill University, Montreal, Canada H3A 2K6; symposium co-chairman and co-editor

F. C. Townsend Department of Civil Engineering, University of Florida, Gainesville, Fla. 32611; symposium co-chairman and co-editor


Strength Testing Methods and Requu^ments


A. S. Saada^ andF. C. Townsend^

State of the Art: Laboratory Strength Testing of Soils

REFERENCE: Saada, A. S. and Townsend, F. C , "State of the Art: Laboratoiy Strength Testing of Soils," Laboratory Shear Strength of Soil. ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 7-77. ABSTRACT: A review and evaluation of the advantages and limitations of laboratory equipment for measuring the shear strength of soils are presented. Equipment evaluated include direct shear, torsional shear, simple shear, triaxial, multiaxial (true triaxial), plane strain, hollow cylinder triaxial, and directional shear devices. The evaluation indicates that the impetus to obtain parameters for constitutive equations and modeling has resulted in the development of improved equipment and testing techniques; specifically, the development of multiaxial (true triaxial) and hollow cylinder triaxial test equipment. Although these devices are more versatile, the conventional solid cylinder triaxial test is still the most popular. The evaluation suggests that direct shear and simple shear devices are best utilized by designers who have gained experience applying the results from such tests to structures that have behaved satisfactorily. Proper consideration must be given to the effects of membrane penetration, end restraint saturation and consolidation procedures, and rates of loading in any testing program. KEY WORDS: soils, shear strength, laboratory testing equipment, triaxial tests, direct shear, simple shear, torsional shear, hollow cylinder, true triaxial, anisotropy

The object of laboratory testing is to study the behavior of a given soil under conditions similar to those encountered in the field and to obtain those parameters which describe this behavior in a set of constitutive equations. In a laboratory test the specimen is intended and generally assumed to represent a single point in a soil medium. The validity of this assumption depends on the uniformity of stress and strain distributions within the soil samples. The uniformity will depend on the configuration of the specimen and the control and measurement of stress and strain on its surface. Separate measurements are often made for the soil phase, the water phase, and sometimes the air ' Professor and Chairman, Department of Civil Engineering, Case Institute of Technology, Case Western Reserve University, Cleveland, Ohio 44106. ^Professor of Civil Engineering, University of Florida, Gainesville, Fla. 32611.

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phase of the specimen in order to relate its contribution to the strength of the mass. While the data needed in design may be less extensive than those required for the development of constitutive equations, the present trend is to obtain as complete a record as possible. Constitutive equations are an indispensable ingredient in the application of the finite-element method to geotechnical problems; and the increased availability of computers has resulted in increased pressure for the development of testing equipment capable of covering the whole stress and strain spectra. Consequently, the last ten years have seen an explosion in the number of tools aimed at better measurements, better recording, and better processing of data obtained during laboratory testing. Testing units conceived many years ago but whose implementation was quite difficult are being used nearly on a routine basis. Automation, both electronic and fluidic, has taken most of the drudgery out of the stressing or straining systems. In this paper the various apparatuses in operation in soil laboratories for research or routine purposes are reviewed and their advantages and disadvantages are discussed. While it is advisable to have a uniform notation and sign convention in a given paper, such a uniformity is difficult to achieve when reference is made to so many publications, each with its own set of conventions. Therefore, when not specifically indicated, the sign convention used in this paper is shown in Fig. 1, where compression is positive and the arrows point in a direction opposite to that used in classical elasticity [1.2].^ For future reference the following definitions are in order [3]: The term "deviator" is used in conjunction with a state of stress or a state of strain (otherwise known as stress and strain tensors). It is a state in which the trace of the matrix representing stress or strain is equal to zero. In this paper the "difference between principal stresses" (aj — 02, for example) will be called the "principal stress difference". The term "pure shear", when used with a state of stresses at a point, is a special deviator in which two principal stresses are equal in magnitude and opposite in sign and the third one is equal to zero. Thus (Fig. 2a) a

0

0

0

-ff

0

0

0

0

represents a state of pure shear. The components here are given in the principal system of axes at Point 0. If we now rotate the system of axes by 45 deg to X-Y and use this new system as our reference (Fig. 2b), the previous matrix becomes •'The italic numbers in brackets refer to the list of references appended to this paper.


SAADA AND TOWNSEND ON STATE OF THE ART

0

-T

-T 0

0'

0

0

0

0

Notice that the small square element represents a point through which any plane can pass; on this plane any of the two previous matrices will give the same "stress vector". A state of plane strain is a state in which the three orthogonal displacements (M, V, and w) are such and u = uix.y), v = vix,y), and w = 0. Such displacements lead to a strain matrix of the form

y.y

0

0

0

yxy

0

The z-direction is a principal direction. The term "pure shear", when used with relation to a state of strain at a point, is a state of plane strain which consists of a uniform extension in the jc-direction, say, and a uniform contraction in the j^-direction of such an

FIG. 1—Sign convention for stresses.


10


o-cr 0

o -r o -V o o

O O 0

0 0 0

(TOO

FIG. 2—(a) Pure shear stresses at a point; coincident axes: (b) Pure shear stresses at a point; axes rotated by 45 deg.

amount that the volume remains unchanged. In this case (Fig. 3), a rhombus ABCD is distorted under a strain into a congruent rhombus A 'B 'C 'D' in which the acute and the obtuse angles have been interchanged. The three components of the displacement in this case are u = ex.

V —

= 0

1+c

where c is the strain e^. For small deformations in which c is small compared with unity, it can be neglected in the denominator of the value of v. The term "simple shear" refers strictly to a state of strain and not to a state of stress. It is a state of plane strain in which the points are displaced only in one direction (parallel to the x-axis, say) such that M =

cy.

0,

= 0

where c is the shear strain jj^y shown in Fig. 4. In this case all planes parallel to the jcz-plane slide in the direction of the x-axis without changing their distance from each other, and the displacements are proportional to their distance from the xz-plane. Like the case of pure shear it is a constant



m

11

^X

D

F//ÂL

/A/IT/AL

l/ = CX

l/^—£- y FIG. 3—Pure shear strain conditions.

T /

^1 / / /

'/ill

i 1 1 1 1 -X /Nt '7-/>iL.

f=/A/Al. U= CV yv= 0

FIG. 4—Simple shear strain conditions.

volume deformation. Simple shear is equal to pure shear plus a rotation. Finally, it is to be noticed that a uniform state of strain does not necessarily mean that the state of stress is uniform. A Brief Histoiy of SoU Strength Testing [4a] It appears that the first real soil shear test was described by Collin in 1846 [4b]. In this test a long specimen of clay 4 cm square in cross section was loaded transversely at its center until it failed in double direct shear (Fig. 5). Leygue in 1885 [5] tilted a shear box full of cohesionless soil until the top slid across the bottom. It is not known when the direct shear apparatus was invented and if Coulomb, whose formula it uses, had anything to do with it. In its present form, credited to Krey, Terzaghi, and Casagrande, the direct Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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i

A

FIG. 5—Double direct shear test of Collin [4a].

shear test employs a circular or a rectangular specimen encased in a split box (Fig. 6). A normal force, W, is applied to the top of the box after which a shearing force, 5, forces the top across the bottom, causing the soil to shear along the plane defined by the split between the two parts of the box. The double direct shear test, which seems to be the earliest true shear test for soils [4b], is still in use in its original form [6] or with normal forces applied at its ends (Fig. 7). The states of stress and strain in the aforementioned direct shear devices are not uniform, and the cross section of soil common to the two parts of the box changes continuously. Torsional direct shear machines with solid and hollow specimens were designed [7] to overcome part of the problem (Fig. 8). The Swedish Geotechnical Institute [8] developed an apparatus where the soil is confined laterally by a rubber membrane and a series of evenly spaced rings (Fig. 9). Roscoe [9] used rigid but hinged plates for the ends of his shear box (Fig. 10); these tilt so as to maintain a constant specimen length parallel to the direction of shear. Peltier [10] introduced a shear box (Fig. 11) with movable sides through which forces can be applied on the intermediate principal plane. The Norwegian Geotechnical Institute (NGI) modified the Swedish device by replacing the rings by a wire embedded in the rubber membrane [11]. Triaxial testing of soils seems to have evolved simultaneously in Germany [12], the Netherlands [13], and the United States [14,15] (Fig. 12). In Germany a machine was built at the Prussian Waterways Experimental Station for the purpose of studying the consolidation of clays under conditions of negligible side friction; the surrounding liquid was entirely confined and temperature and leakage had to be closely controlled. Several investigators recognized that the apparatus could be used to measure the ratio of the axial ^

-£E3L FIG. d—Direct shear test 14a].



13

FIG. 7—Double direct shear test |4a|.

FIG. 8—Torsional direct shear test |4a].

-C0MF/Ay/A/v 0\

in

< V t^

^- '*=

t^


26


I

.^

.a

I I

I Si



27

T h e average shear stress, T, is given by M n

2>M 27r(r2^-r,3)

(4)

iTtr'-dr

ri and r^ are the inner and outer radii of the hollow cylinder. There is no doubt that it is more difficult to install a specimen of undisturbed soil in a ring shear device than it is in a direct shear device for solid cylinders. However, instrumentation developed by Hvorslev and Kaufman \2S\ and by Bishop et al \2T\ appears to have been quite successful. It certainly is not more complicated than what is routinely used today in simple shear tests or triaxial tests, both static and dynamic. General Remarks on Direct Shear Tests As stated in the introduction, ideally a test specimen is assumed to be a point at which a state of stress (or stress tensor) is acting. This assumption is only valid if the state of stress in the specimen and on its boundaries is uniform. Considering the size of the samples in direct shear tests and the boundary conditions it is impossible to make this assumption. There is no room for St. Venant's principle to take hold, and load-deformation (or torque-rotation) curves cannot be used to establish accurate constitutive equations for the behavior of soils. At every point inside the specimen and along the plane of relative motion there is a different state of stress with different principal stresses and different principal planes. As the shearing force is applied, the principal stresses rotate, and at every point they vary both in magnitude and direction. An average stress-strain curve obtained from measurements of the shearing force and the shearing displacement cannot be depended upon to provide a true stress-strain picture for the assumed stress conditions; it could only possibly be used in comparative studies of various soils tested under the same conditions. This indeed has been done for years by practitioners whose structures have performed satisfactorily. Two quantities are frequently obtained from direct shear tests: the peak angle of friction, p', and the residual angle of friction, /. Both are computed from the value of the "stress vector" acting on the plane of relative motion. At the peak, the soil is assumed to have reached a condition of plasticity governed by Coulomb's Law at all points of this plane at the same time. This is obviously impossible because of the nonuniformity of the state of stress in the specimen and the fact that the principal stresses do not have the same direction. The residual strength and its corresponding <j)/ is perhaps the only reasonably reliable quantity that can be obtained from a direct shear test. It


28


does, however, require a very large displacement which often cannot be obtained in the translational device. Skemptom [29] described a technique of using multiple reversals to accumulate large displacements. This technique is based upon the concept that at residual strength the shear zone is entirely remolded and the previous fabric obliterated. Townsend and Gilbert [30] have shown in comparative tests on heavily overconsolidated clay shales that the residual strength measured by reversal direct shear and ring shear tests on intact and remolded specimens for practical purposes is the same. Multiple reversal tests have been conducted to simulate large displacements for softer materials, but they have been shown to give results which vary substantially from those obtained in the ring shear test. As noticed by La Gatta [31] and Bishop et al [27], the fundamental difference between the two tests lies in the failure of the multiple reversal direct shear box test to simulate the field condition of a large relative displacement uninterrupted by changes in direction. Such changes in direction cause rotation of the stresses and reorientation of the soil particles so as to result in different values of the measured parameters. Recent studies on the cyclic behavior of soils, and the observed changes in the fabric, the pore water pressures, and the dilatancy characteristics that occur upon reversal of the stresses, support Bishop's remark that the multiple reversal direct shear box test and the ring shear test cannot claim to be an acceptable way of measuring the same parameter. Finally, it is the opinion of the authors that direct shear tests are valuable tools to obtain the residual strength. The work of Hvorslev and Bishop show without doubt that when this quantity is needed, a ring shear test without reversal is quite appropriate. The details they give make it relatively easy for any laboratory to build similar devices. Translatory shear boxes will obviously remain in use. The hope is that if they are, only the square type will be used, and, with the exception of heavily overconsolidated clay shales, only for materials that do not require reversal to attain their residual strength.

Simple Shear Tests Because of the shortcomings of the direct shear devices mentioned in the last sections various attempts were made to modify them in the hope of imposing a uniform condition of simple shear to the soil specimens. One of the earliest attempts was made by Kjellman [8]. This apparatus, which is shown in Fig. 9, uses a cylindrical specimen laterally confined by a rubber membrane and a series of thin and evenly spaced rings. Roscoe in 1953 [9] used a square specimen in a box with hinged ends (Fig. 10), and while such a box may present improvements on Kjellman's apparatus, it still has many of its drawbacks. In 1966 the Norwegian Geotechnical Institute (NGI) refined Kjellman's device by replacing the rings with thin wires embedded in the rubber membrane [//].



29

It is interesting to note that Roscoe attempted to improve on Kjeliman's sample configuration using a square rather than a circular cross section. He also recognized that it was not likely that any apparatus could be made which would impose uniform pure shear stress to a specimen, because of what he called the "complementary shearing stresses" that have to be imposed on the lateral faces so that one can indeed have a condition of pure shear (Fig. 2b). He therefore imposed on the specimen a condition of simple shear strain leaving to the rigid faces of his apparatus the task of providing the necessary boundary stresses. In a series of photographs Roscoe [9] showed that a condition of uniform strain could be obtained under large normal loads, and, as pointed out in the introduction, this uniform state of strain certainly did not result in a uniform state of stress. Later [32] his device was instrumented to measure those boundary stresses. The NGI apparatus offers practical operational improvements over Kjeliman's. The Roscoe and NGI devices have been used very extensively in studying the static behavior of soils. More recently they have been modified for cyclic loading. Their critical appraisal is therefore quite warranted. Commenting on the Kjellman device Hvorslev said [28]: "The resultant of the vertical forces on the upper and lower end surfaces of the test specimen must form a couple in order to balance the moment produced by the shearing or tangential forces. Neither the vertical normal stresses nor the shearing stresses are uniformly distributed. This non-uniformity of stress distribution increases with increasing deformations, and the shearing resistance characteristics after initial failure can be investigated only to a limited extent". Such comments did not prevent this apparatus from being mechanically modified and used in I%6 [//]. It became quite popular because designers and some researchers needed "ease of use and convenience" or "a ball park value". The enormous proliferation of data generated by both static and dynamic tests made it very difficult to question its value. Both the Roscoe and the NGI devices claim a condition of plane strain; the second also claims reasonably uniform stress distributions. Whether the material can be in a state of plane strain in either can be "investigated" with the solution of the St. Venant problem of the fixed end beam of square or circular cross section subjected to an end load P. The solution is based on the theory of elasticity, and the boundary conditions are not exactly the same as in simple shear devices. Whenever the theory of elasticity is used in soil mechanics, the opinion is often voiced that, soils not being elastic, analyses based on such a theory are invalid. It would be unjustified to expect the magnitudes of the stresses given by elasticity to be the correct ones. However, a clear picture can be obtained regarding the components of the state of stress that come into play, their relative magnitude, and the validity of the plane strain assumption. Known elastic solutions, theoretical or experimental such as obtained from photoelasticity, are of vital importance in finding answers and making logical assumptions in soil mechanics. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

30


Analyses of Tests on Solid Square Specimens For a square cross section, the St. Venant solution [33] is shown in Fig. 21; Tyj. is the shearing stress in the direction of the applied shearing force and T^. is the perpendicular to it. To make the analysis more concrete, numerical values were chosen corresponding to actual cross sections of specimens used in practice, v has been chosen equal to 0.49, the cross section equal to 50 cm^ (7.79 in.2), a = 35.7 mm (1.40 in.), and the average shear stress P/A — 0.13P (psi). Fig. 21c shows the distribution of the shearing stress Ty^ along the line jc = 0; it is seen that there is a 38 percent difference between the center and the edge. Fig lib shows the parabolic distribution for z = 0 and z = a. Fig. 2ld shows the distribution of T^^ along z = ±0.6a as well as along the edges. Comparing the magnitudes of the shearing stresses (which are given in terms of P) in Fig. 21, we notice that T^, is very small compared with T„ except close to the edges. Neglecting Ty, seems to be quite acceptable and reduces the plane normal to the z-axis to a principal plane; smooth lateral restraint can then justify the assumption of plane strain. In the analytical solution of Roscoe [9] and later of Prevost [34] a plane strain condition is assumed and, as just demonstrated, legitimately so. The stress function type of solution brings in the normal stress components a^ that the St. Venant analysis does not. In addition, the normal stress components Oy are not linearly distributed. This is to be expected since in the St. Venant problem the lateral faces of the beam are free from restraint and the end effects are neglected. Roscoe's solution shows that, at best, only the middle third of the specimen can be considered in a state of uniform stress. In addition, in an actual test, high compressive stresses are required to overcome the tensile stresses that develop at the end platens (Fig. 22). The solution also involves the existence of tensile and compressive stresses on the sides, and it is hard to visualize how those tensile stresses can be developed by the rigid flaps of the Roscoe device. The analysis of Prevost [34] goes further and shows that if there is a small amount of slippage at the ends even this middle third area of uniformity completely disappears; the side effects, both tensile and compressive, that the device has to develop to satisfy the theory become quite preponderant (Fig. 22). In summary, we see that while the assumption of plane strain is reasonably justified, the solutions of both Roscoe and Prevost require boundary conditions that the device physically cannot achieve. Even if the required boundary conditions were satisfied, the stress distribution inside the specimen would still be totally nonuniform. The properties measured would not be those of the soil alone, but rather a combination of the properties of both soil and test apparatus; different sizes would give different results [35] and hard-to-interpret average pore pressure values if such measurements were made. Finite-element analyses have been made to study the distribution of stresses in the Roscoe device using nonlinear constitutive equations [36].



31

>^

f O


32


FIG. 22—Stresses on the upper and lower faces of a simple shear sample [after Ref 34].

Such analyses confirm the nonuniformities of the stresses that the closedform elastic solutions exhibit. Analysis of Tests on Solid Circular Specimens The St. Venant solution for a circular cross section is shown in Fig. 23; along the boundary every T^^. needs a T^^ SO that the resultant of the two is tangent to the periphery, v was chosen equal to 0.49 and the area equal to 50 cm^ (7.7912 in.2). Thus the radius is 40 mm (1.5748 in.) and the average shear stress P/A = 0.128P (psi). Figure 23b shows the distribution of T^^ along the line x = 0; it is seen that there is practically no difference between the center and the edge. Figure 23a shows the distribution of T^^ for 2 = 0, /?/V2, and z = K. It is only along the x-axis that T^^ starts and ends with a zero value. Fig. 23c shows the distribution of r^^ along the line z = ± /?/V2 as well as along the periphery. For comparison purposes the value of T„



!

g


33

34


along the periphery is also shown. Notice that both T^^ and T^^ are equal on the edge for z = ± ^ / V 2 as it is necessary to make the resultant shear stress vector at this point tangent to the contour. Contrary to what was seen in the case of a square cross section, T^^^ *nd T^, are of the same order of magnitude, and neglecting Ty. to satisfy the condition of plane strain is quite unacceptable. Similar results would have been obtained using other known types of stress-strain relations. The assumption of Bjerrum and Landva [//] is thus inadmissible for a circular specimen with free lateral surfaces subjected to simple shear. If circular cross sections are to remain circular, their spirally reinforced membrane would have to apply a pattern of normal tensions and compressions varying with depth and with the angle of rotation 6 around the origin. Physically this is beyond the capability of any flexible membrane or rigid circular outside stack of rings. Lucks et al [37] studied the stress conditions in the NGI apparatus using finite elements. In a short technical note, the results of two linear elastic analyses, one referred to as the three-dimensional analysis and the other as the Fourier analysis, are presented. The boundary conditions are given in terms of displacements, and for the Fourier analysis it is clearly specified that only one mode of deformation is involved. Both analyses use a Poisson's ratio of 0.49, which is close enough to the limit where numerical difficulties may result. As expected from the St. Venant analysis, equilibrium is maintained with a pattern of high normal, axial, and radial stresses in the boundary elements, the first varying with the angle of rotation 6 and the second varying with both 9 and the depth of the specimen. Lucks et al present the values of the horizontal shear stresses, T ^ , obtained from the three-dimensional analysis, the values of the boundary stresses obtained from the Fourier analysis, and contours of maximum shear stresses from the Fourier analysis. It would have been quite beneficial to see the values of T^. since they should be of the same order of magnitude as T^. The fact that the shear stress vector must be tangent to the boundary results in a value of T^, for every given value of Tj^. In this light, the published values cannot be evaluated. Finally, Lucks et al conclude with the statement that 70 percent of the sample is found to have a remarkably uniform stress condition. This percentage seems to be based on their vertical sections showing the contours of maximum shear stress. This statement would have been true if {/) the reinforcing membrane and the end platens could apply variable combinations of high radial tensions and compressions, such that the edge elements are stressed to correspond to the assumed boundary conditions, (2) the finite element mesh was fine enough to show serious stress concentrations, and (3) the Poisson's ratio of 0.49 did not distort the results of both analyses. Hara and Kyota [38] reported a study similar to the one by Lucks et al [37]. In this study the edge elements must be subjected to normal tensile and compressive stress close to 15 kg/cm^ for the state of stress in the middle part to be uniform. This is physically impossible. In a recent paper, Shen et al Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


35

[39] also used finite elements and took into account the confining effects of the membrane which Lucks et al had not. They concluded that the "strains" were highly nonuniform and consequently the stresses were too, although one does not necessarily imply the other. Photoelastic Studies [40] In order to examine experimentally the elastic stress distribution in simple shear models of the NGI and Roscoe types, with boundary conditions closer to reality than those of the St. Venant solution, the three-dimensional photoelastic method was chosen. Three-dimensional stress analyses may be made by the frozen-stress method, in which a model made of an annealable material is subjected to a heating and cooling cycle while under load, thus locking in the load-induced strains and the accompanying optical birefringence. Careful slicing of the model will then permit observation of the interference pattern from which the stress states may be determined. A special loading fixture was designed for this study; details can be found in Ref 40. End restraints were simulated by massive blocks of the same epoxy material used for the models. In fact, the models were machined each from one piece to the shapes shown in Fig. 24. The results of this study are quite revealing. Figure 25 shows the shear stress distribution on the center plane of a square specimen simulating the Roscoe test. Figure 26 shows the same shear stress but on an NGI round specimen. Such stress distributions are far from being uniform. Indeed, they can change by as much as 47 percent whether one moves in the direction of the applied shear force (x-axis) or normal to it (z-axis). Figure 27 shows experimentally determined normal stresses, a^ and a^, close to the top of the specimen in its central slice. Figure 28 shows the ratio of the shear stress T^, in the direction normal to that in which the shearing force is applied to the shear stress T„ in the direction of the shear force, in

5HEAe

FIG. 24—Photoelastic models of circular and square simple shear specimens [40].


36


1

[

1

-.85 .4

\\

0.44

_

- L/ ,?|.

y4

0.B

- ki

w

M

1

v! - 2 a = 1.361

1

1

1

FIG. 25—Shear stress from photoelastic analysis of square simple shear for y = 0 [40).

,1=0,60

-N,

I I UlNITE ELEMENT N ^ « - v ^ « ° ° ' f . - » C ^ '

FIG. 26—Shear stresses from photoelastic analysis of the central slice of round simple shear model [40].

the central plane of the specimen, at a distance of 15.2 mm (0.6 in.) from the jc-axis. For comparison the results of St. Venant for the cantilever beam are also shown. As can be seen, Ty. is of the same order of magnitude as T„. Essentially the photoelastic study lends support to the theoretical analysis of St. Venant and indeed complements it in those areas where the boundary conditions are different.



37

oUH

FIG. 27—Normal stresses from photoelastic analysis of the central slice of round simple shear model [40].

General Remarks on Simple Shear Tests Simple shear devices have very serious deficiencies that cannot be brushed off as unimportant or ignored for the salce of simplicity and the "ball park value" argument. In addition to the nonuniformities mentioned previously and which appear when shearing forces are applied to the device, additional difficulties appear when normal forces act on the loading plates. Such plates must be perfectly rough, as indicated by Finn and his co-workers [41]. This roughness will automatically contribute to additional normal confining pressures of the radial and hoop types acting on vertical planes. There are no theoretical or experimental studies giving an order of magnitude for those pressures in the simple shear apparatus, but studies conducted on triaxial specimens and hollow cylinders show that in the vicinity of the end plates they are of the same order of magnitude as the applied vertical stresses. One usually moves away from the loading plates and counts on St. Venant's principle to dismiss their effects. However, St. Venant is of no help at all when the thickness of the specimen is one third of the size of the loading plate. In addition, as simple shear takes place, additional couples are applied by the normal vertical stresses because of the increasing eccentricity. The analyses previously discussed involve nothing but linear elastic


38


APPLIED SHEAR

P' •yz

1.4

1

1.2

-

i 1.0

--

0.8

-

Vi^-SAINT

—

VENANT

\\ \\-PHOTOELASTICITy

0.6

-

0.4

-

0.2

—

\

-1.0

\ \

\

X

\

^^--^v

1 -0.5

—

—>

FIG. 28—Variation of Tyz along the line y = 0, z = 0.6 from photoetastic analysis of the round simple shear model [40].

assumptions with no coupling between normal and shear stresses and strain. This is only true for infinitesimal strain of the type obtained in resonant columns. Even there, at 10~^ strain, coupling has been noticed on saturated clays by the senior author. In soil mechanics even small shearing stresses cause normal strains, which increase as the shearing strains increase. As has been pointed out in the section on Torsional Direct Shear Tests on Solid Specimens, the volumetric strains resulting from nonuniform shearing stress will also be nonuniform; and since the porous stone through which the vertical stress is applied is rigid, there will be a nonuniform and unknown distribution of vertical normal stresses in response to this tendency for



39

volume change. Those nonuniformities are, of course, to be added to those deduced through the use of linear elasticity. Tests are sometimes conducted with the vertical load being changed such that the volume remains constant. For saturated soils these changes in the vertical load divided by the area (in other words, the average change in the vertical stress) are assumed to be equal to the excess pore pressure buildup. In view of the aforementioned analyses the pore pressure cannot be uniform and equal to the average normal stress for soils of low permeability. For sands, while uniformity of the water pressure can be expected, the distribution of the effective normal stresses is far from being uniform. The wirereinforcementin the NGI membrane is also used as a strain gage to measure KQ during the consolidation phase of the test. As indicated by Dyvik et al [42] the calibration is quite tedious. Any attempt to measure the lateral stresses during the shear phase would lead to meaningless results, since it was shown that such stresses vary with the height as well as with the circumferential position as one moves around the perimeter of the sample. When one looks at Hvorslev's evaluation of Kjellman's device [28], Roscoe's experimental and theoretical work [9], the discussion of DeJosselin de Jong [43] of the paper by Roscoe et al [32], the re-analysis of Prevost and Hoeg [34], the photoelastic study of Wright et al [40], the fact that more than half of the components of the state of stress are ignored, and the miracles that results of finite-element analyses [37,38] demand that the edge elements perform, one is bound to be cautious when evaluating the data simple shear devices yield. Inclined specimens of anisotropic soils have also been tested with them [44], adding to an already untractable state of stress the complexities of stress and strain analyses of anisotropic materials. The whole simple shear device is now placed inside a cell and pressurized; and here again, because of the closeness of the loading plates and their roughness, the lateral and circumferential stresses, a^ and og, within the body of the sample cannot be assumed equal to the outside confining stress [45a]. Indeed, a simple axially symmetric finite element analysis conducted on a triaxial test specimen of the size used in the simple shear device has shown that, for rigid perfectly frictional platens, only a very thin layer on the outer lateral surface actually "sees" the lateral cell pressure. Depending on Poisson's ratio, a^ and ae vary with the radius and can become nearly equal to the vertical stress at the center [45b]. Simple shear devices have been introduced as an improvement over direct shear devices. Are they? Though direct shear tests have recognized weaknesses, today what is expected from them is to give residual strengths; this they doreasonablywell, especially in the Hvorslev-type ring shear device [23.27]. Simple shear devices, on the other hand, cannot claim to yield either reliable stress-strain relations or absolute failure values. At best they can be exploited in comparing descriptively similar soils. Perhaps their proper place today is in the hands of designers who have already conducted a large Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

40


number of such tests and built structures which behaved satisfactorily. There, experience and data from other types of tests go together and yield acceptable design parameters. Triaxial Tests on Solid Circular Cylinders In the triaxial test shown in Fig. 12, the specimen is under a state of spherical stress to which is added an axial force. The fluid pressure provides two of the principal stresses while the third one (the axial one) is provided by both the fluid pressure and the axial force imposed by the piston. This axial force can be either compressive or tensile, and the axial stress can be either the major or the minor principal stress. The force is transmitted to the specimen by rigid porous plates which permit fluid flow in and out of the soil during loading. The specimen is generally encased in a flexible membrane, although other types of encasements such as paraffin have been used. Draining strips of filter paper placed on the lateral surface help speed the radial flow of water during consolidation and decrease the pore pressure gradients. Threads of wool along the axis of the specimen have also been used for the same purpose. The axial deformation of the specimen is measured directly by monitoring the movement of the end plates or that of the piston which is in solid contact with them. The lateral deformation is irregular due to bulging and can be measured by placing extensometers or transducers inside the cell [18]. Micrometers with their stem passing through the Lucite chamber have been successfully used [46]; with proper calibration optical methods can also be used [47]. Pore pressures can be measured manually [7^], but transducers seem to have replaced manual devices nearly completely. A wide variety of tests can be conducted in the triaxial cell, and Bishop and Henkel [18] give the necessary details on how to conduct them. Compression of the specimen can be induced by increasing the axial stress, decreasing the lateral stress, or both; in extension, the opposite is done. Consolidation can proceed spherically or at any given ratio of axial-to-lateral stress. By measuring lateral displacement and by controlling the pressure in the cell to maintain zero lateral displacement, a /To-consolidation can be induced. Shearing tests can be conducted at any ratio of principal stresses as well as keeping the mean stress constant. Pneumatic [48,49] and electronic feedback systems are routinely used to obtain a wide variety of stress paths. In addition to the restriction that two out of the three principal stresses must be equal, the results obtained from tests conducted in the triaxial cell are affected by the loading end plates; their smoothness, size, and permeability; by the flexible membrane surrounding the specimen; by the filter paper used; and, of course, by the measuring system. Nonuniform stress distributions and the bulging of the specimen are the most noticeable aspects of those unwanted effects. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


41

Theoretical Stress Distribution in Triaxial Tests The nonuniformities of the stress distributions within the specimen are primarily due to the effects of the friction on the end plates. The problem of the influence of end restraint during uniaxial or unconfined compression of cylinders has been under consideration since the latter part of the nineteenth century. In 1902 Filon [50] published his classical elastic solution in which he made the assumption that the ends of the cylinder were kept plane and that no point on the ends could move in a radial direction, as if the ends were glued. He was unable to meet exactly these boundary conditions. Pickett [51] solved this problem using a multiple Fourier technique. His graphical solution appears to be correct, with possibly some numerical inaccuracies due to the slowly converging infinite series and the difficulty in hand computation. D'Appolonia and Newmark [52] used a framework analogy, and while their solution agrees reasonably well with Pickett's solution, it does not exactly meet all the boundary conditions. Assuming slightly different boundary conditions, Balla [53] solved a similar problem. He considered that the cylinder ends remained plane and that the radial displacement on the periphery at both ends varied inversely with a friction factor. The end shear stress distribution was found to be linear, and when the friction factor was at its maximum value the radial displacement at the periphery was zero. The aforementioned solutions, except Balla's, considered an elastic material with a Poisson ratio of 1/4; Balla used 1/3. Using finite differences, Moore [45a] solved the problem of unconfined cylinders for six Poisson ratios varying between 0.15 and 0.48 and height to diameter ratios of 1 and 2. He also obtained solutions for confined cylinders, three Poisson ratios, and a ratio of height to diameter of 2. A feature that is common to all elastic solutions is the drop in the normal contact-stress as one moves towards the center of the specimen, and a very high concentration on the edges (Fig. 29). The values of the normal radial and circumferential stresses, a^ and a^, as well as the shearing stress, r^j, vary from author to author depending on how well the boundary conditions have been satisfied. Since the sides are free from shearing stresses, T^^ must be equal to zero at the top and bottom edges of the specimens. Yet except for Filon's all the solutions involve a relatively high value for T^^ there. The same is true for a^. Iti addition, Moore found that this concentration of stresses on the edges was quite sensitive to the chosen value of Poisson's ratio. Using finite elements, Girijavallabhan [54] obtained results practically identical to Pickett's [51]. While all the previous solutions dealt with a linear elastic material, Perloff and Pombo [55] considered materials with nonlinear constitutive equations of both the strain-hardening and strain-softening types. Using finite elements, they reached the conclusion that the effects of the end restraint on the observed axial stress-strain curve depends on the constitutive law of the Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

42


^^î» D

O £1. •a

c

gtib3

=§

lb*-

ki JO X

Si

•b''

b^

i

« •



43

soil; the influence of those restraints being more important for brittle materials. It is proper to remark at this point that this conclusion most surely applies to the simple shear test where end restraints are more pronounced than in the triaxial test. Experimental Observations on the Effects of the End Plates Experimental studies of the effects of end restraints during compression tests can be found in the literature of every engineering material. In soils it was brought to the forefront with the emergence of the triaxial test. The experimental work by Taylor [26] in the 1940s, summarized by Rutledge [56] in 1947, led to the conclusion that reliable results could be obtained with soil specimens between usual platens, provided the length to diameter ratio was in the range of 1.5 to 3.0. On the basis of these early studies, triaxial specimens for soils have been more or less standardized using regular ends with a length to diameter ratio of 2.0 to 2.5. In 1960 Shockley and Ahlvin [57\ conducted an investigation on the nonuniform conditions in the triaxial test. They found that on tests on dry sands there was a volume increase in the middle third or failure zone of specimens over a density from dense to loose and that a volume decrease occurs at the ends of the test specimens. A similar change occurred in saturated sand specimens subjected to axial strain under constant confining conditions. For clays, based on moisture content changes, they found a volume decrease in the zone of shear and a volume increase at the ends of the specimens. Tests on large triaxial specimens of dry sand showed higher than average values of both vertical stress and vertical strain in the portion of the mass near the vertical axis just below midheight where the maximum bulge takes place with lesser values toward the edges and the ends. Rowe [58] was apparently the first to use a combination of rubber sheeting and silicone grease to develop frictionless ends for triaxial compression test specimens. The Rowe and Barden [59] grease rubber system is the popular method of minimizing end restraints (Fig. 30). Sometimes a short porous dowel is used at the center of the platens to avoid side-slipping of the sample. The paper by Rowe and Barden [59] produced interesting discussions [60-62] and started a wave of research to bring out the advantages and disadvantages of oversized lubricated end plates. Barden and McDermott [63] tested compacted clays as well as remolded normally consolidated and overconsolidated clays with lubricated and nonlubricated platens. They concluded that lubricated ends markedly reduced the vertical and radial pore pressure gradients together with the moisture migration. Barrelling was minimized but the effective strength parameters were not altered when the results were compared with specimens with a length to diameter ratio of 2 tested between ordinary platens. Bishop and Green [64] tested one type of sand and reached the same conclusion regarding the maximum angle of


44

0-ring


c seals

greased membrane

H' diam. porous disc

A. ,araldite

I.

joint

FIG. 30—Enlarged frictionless end platen with central drainage for triaxial tests [after Ref 59].

shearing. Short samples with lubricated ends show larger axial strains and a larger dilation at failure than long samples without lubrication. Harden and Khayatt [65] refer to the necking encountered during extension tests, and show that the use of lubricated ends goes a long way in increasing uniformity. Kirkpatrick and Belshaw [66] used X-ray techniques to study the radial and circumferential strains during drained triaxial compression tests on large diameter triaxial samples of medium dense sand in which the end plates were either rough or lubricated. They found that the assumption of equality between the radial and the tangential strains is valid for lubricated samples but largely inadmissible for samples tested with rough platens. Rough platens were found to cause nonuniform strain conditions throughout the sample which are produced by the formation of quasi-rigid zones at both ends of the specimen. Kirkpatrick and Belshaw draw attention to the fact that while homogeneous strain conditions may result in homogeneous stress conditions, this was not necessarily true. In a subsequent study, axial strains were examined by Kirkpatrick and Younger [67\ and found to follow the same pattern. Duncan and Dunlop [68] tested undisturbed clay, and reached the conclusion that unless it was necessary to measure volumetric strains in drained tests on sand, the advantages gained from the use of lubrication were not worth the additional bother. Roy and Lx) [69] ran comparative drained triaxial tests at high confining pressures on strong-grained and weak-grained granular material with ordinary and lubricated ends. They found that the stress-strain relations were significantly influenced by the end conditions. For high-pressure tests, lubrication resulted in a much more uniform strain, volume change, and crushing of particles throughout the samples. Raju et al [70] found that, while the well-known failure plane develops in specimens of dense sand tested in compression between ordinary plates, no such plane occurred if the plates were lubricated. They deduced that the oc-



45

currence of this plane was not a property of the sand but was due to the testing procedure. Kirkpatrick et al [71], using dense and loose sand, measured the stress at the platens by means of diaphragm gages and found that lubricated platens lead to a reasonably uniform stress distribution, while nonlubricated platens resulted in nonuniformities which became more severe as the strains increased. In this last case the distribution of the normal stress bears great resemblance to the ones obtained in the theoretical elastic analysis. Finally, Lee [72] reviewed most of the aforementioned research and extended it to undrained sand. He concluded that for medium-to-dense sand there was a significant increase in static undrained strength with lubricated ends as compared with tests using regular ends. The effect was found to be significantly greater than observed for other studies pertaining to drained tests on sands and undrained tests on clays. He relates the influence of the friction to the tendency of the material to change volume, thus explaining why Duncan and Dunlop did not find much difference in their results using regular and lubricated platens.

Testing Procedures Backpressure Saturation—Since Lowe and Johnson's investigations [73], saturation of specimens by applying backpressure has become a widely used technique. The methods and magnitudes of backpressure required to saturate specimens are provided by various authors [18,74]. Lee and Black [75] provide theoretical and experimental data for the time and magnitude of backpressure to dissolve air bubbles. The procedure that has generally been adopted for backpressure saturation is to incrementally increase the chamber pressure and pore pressure simultaneously, allowing equalization at each increment. After equalization, the value of B{B = Au/Aa3) is measured before applying an additional increment. However, several variables are involved in this general technique; namely (/) the magnitude and duration of the backpressure increment, (2) the magnitude of effective consolidation pressure during saturation which may or may not permit the specimen to swell, (3) the magnitude of chamber pressure increase when checking the 5-parameter, and (4) the magnitude of back pressure applied obviously must never pre-stress the specimen, that is, apply an effective confining pressure greater than that under which the specimen is to be sheared. In this context, Donaghe and Townsend [76] suggest that the magnitude of backpressure increment and effective consolidation pressure during saturation be kept below the effective confining stress throughout the saturation procedure. Likewise, when checking the 5-parameter, the magnitude of pore pressure should be observed as the chamber pressure is increased to avoid pre-stressing. They also report that


46


for tests on a CL and a CH soil the magnitude of backpressure applied did not affect the principal stress difference or the induced pore pressures. However, a practical problem concerning the magnitude of backpressure can arise in the case of dilative soils. If the magnitude of backpressure is significantly higher than the anticipated neutral stresses in the field, then the amount of induced negative pore pressure before cavitation will cause excessively high measured principal stress differences, which most likely will not occur in the field. To minimize the use of backpressure, techniques of differential vacuum saturation consisting of applying a full vacuum to the specimen with a highly soluble gas (for example, CO2) have also been used [77]. Anisotropic Consolidation—Although in situ stress conditions are usually anisotropic, that is, a^ > 03, isotropic stress conditions are generally used in routine triaxial tests. The reason usually given for this testing inconsistency is that anisotropic consolidation requires more time and complicated procedures and constant-stress equipment capabilities. In addition, it was thought formerly that the angle of shearing resistance in terms of effective stress was not significantly affected by method of consolidation; however, this is not the case for all soils. Early work by Rutledge [56] suggested that the water content after consolidation and the undrained strength were independent of consolidation ratio, kc, provided the vertical consolidation stress, 0,^, is the same. A comparison of literature-reported data by Donaghe and Townsend [78] observed that this suggestion is valid for compacted soils; however, for undisturbed or slurry prepared soils the assumption does not hold. For tests on slurry consolidated specimens, they observed that the water contents after consolidation were not a unique function of ffic but were related to values of aod and Toct during consolidation. Anisotropically consolidated specimens had higher water contents than isotropically consolidated specimens for the same cj^. For any given ffi^-value, the maximum (ffrffj) decreased for increasing values of anisotropic consolidation, thus causing a decrease in values of 4)'. There is general agreement in the literature [78-81] that induced pore pressures and axial strain values at failure are considerably reduced for anisotropically consolidated specimens. In this context, development of constitutive relationship parameters will be greatly influenced by consolidation conditions. The reduction in axial strain at failure due to anisotropic consolidation means that the time to failure is also reduced compared with isotropically consolidated specimens. This time reduction presents the testing detail if time to failure is significantly important to warrant altering the strain rate to compare anisotropically and isotropically consolidated specimens. More recently, Saada and his co-workers [82,83], within the context of their study of anisotropic clays, have shown that /ko^consolidated slurries of clays were extremely brittle in compression, but very ductile in extension; and Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


47

while for normally consolidated clay the strength in compression is higher than in extension, the reverse is true for overconsolidated clays. Rates of Loading—It is common knowledge that rates of loading significantly affect the magnitude of shear strength. Increased rates of loading produce increased strengths and in the case of extremely slow loading rates creep movements will cause lower measured strengths. If saturated specimens are tested, then the loading rate selected must be slow enough so that excess pore pressures do not develop in the case of drained tests, and the pore pressures are equalized throughout the specimen for undrained ones. The selection of loading rate is of considerable practical importance as the time to perform a test is directly related to cost. Bishop and Henkel [18] propose that in drained tests 95 percent pore pressure dissipation will occur if 20H2

^'~

«C

where r , = time to failure, H — '/2 the specimen height, Cy — coefficient of consolidation, and M = a drainage boundary condition. In the case of undrained tests, it has been found [84] that for contractive soils, in the extreme, creep leads to failure without an increase in strength and thus modulus values as well as strength are low. In the case of dilative soils, it has been found [78,84] that the strength is not greatly affected by loading rate; however, modulus values may be. For normally consolidated (contractive) soils, Donaghe [85] reports a 5 percent decrease in strength per tenfold increase in time to failure. Various Corrections in the Triaxial Test—The measured strength of soils in a triaxial test is influenced by the membrane surrounding the sample as well as by the filter paper used to facilitate drainage. Bishop and Henkel [18] and Olson and Kiefer [86a] give ways to measure and correct for these effects. Conforth [86b] noticed that side drainage ceases to be effective in assisting drainage when the soil permeability is approximately 10"*" cm/s. When the residual strength is measured by means of a triaxial test, corrections must be made for soils shearing along a plane. Webb [87\ and Pachakis [88] studied this problem and recommended corrective operations. Duncan and Seed [89] reviewed the various errors that occur during triaxial testing and recommended corrections. Such corrections must be made when comparing results of different tests or trying to determine strength parameters. Piston friction has also been extensively studied, and its effects have been reduced to a negligible amount or totally bypassed through the use of ingenious bearings [90] or transducers placed inside the cell. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

48


In addition to its small but obvious confining effects the membrane, because of its penetration of granular materials, affects the measurement of volume changes in drained tests and of pore water pressures in undrained ones; effective stress paths and strength parameters are therefore modified. Newland and Allely [91] were the first to draw attention to the problem of membrane penetration. Assuming the soil to be isotropic, they suggested it can be evaluated for loading under spherical pressure as the difference between observed volumetric strain and three times the measured axial strain. Roscoe et al [92] used two methods for evaluating the membrane effects in sand specimens. The first was similar to that of Newland and Allely, the second consisted of testing under ambient pressure condition a 38.1-mm (1.5-in.)-diameter triaxial specimen containing a central brass rod throughout the height of the sample. Rod diameters varying between 6.35 and 35mm ('/4 and P/s in.) were used. The membrane penetration was obtained for each value of ambient pressure by plotting volume change measured against rod diameter and extrapolating the resulting straight line to obtain a volume change value corresponding to a rod diameter of 38.1mm (1.5 in.). While Roscoe et al [92] considered the first method to be more reliable, El-Sobhy [93] suggested that the second method was the one to use. Raju and Sadaswan [94] showed that the relation between the volume changes of a hollow cylindrical specimen and the diameter of the inserted brass rod was not linear and therefore the linear extrapolation of Roscoe was incorrect. Furthermore, they pointed out that the vertical stress of the specimen around the brass rod will not be the same as the radial stress. So they modified the top platen to achieve a spherical loading. Frydman et al [95] used hollow cylinders of glass spheres. They conducted tests with hydrostatic loading and varied the internal diameter of the cylinders. For a given stress, the various internal diameters yielded points for the measured volumetric strain which lay on a straight line. This line cut the volumetric strain axis at the true volumetric strain of the sand specimen and had a slope equal to the membrane penetration. They give semi-logarithmic relations between the penetration and D50 (the diameter of the particle corresponding to 50 percent passing in a sieve analysis). Kiekbusch and Schuppener [96] confirmed the relation of Frydman et al and found that by spreading a thin layer of liquid rubber on the membrane they could reduce the penetration by up to 85 percent. Using this technique in undrained triaxial compression tests on sands, they recorded pore water pressures 100 percent higher than in tests with normal membranes. Triaxial Tests on Anisotropic Materials Recent interest in the behavior of anisotropic /if o-consolidated clays has led many investigators to cut inclined specimens and test them in compression in the triaxial cell. Figure 31 shows specimens at various inclinations to the



49

direction of consolidation; Fig. 32 shows tlie bending moments and shearing forces that are generated at the ends when an inclined specimen is tested between two rigid platens [97\. Such end effects invalidate whatever information is obtained from the test. In order to illustrate that this is indeed what happens Saada [98] conducted a series of unconfined compression tests on specimens at various inclinations to the direction of consolidation, once between frictional plates and once between lubricated plates. The results are shown in Fig. 33. Unless the samples are totally free to deform, those extraneous effects will occur. Presently, the only way to study the behavior of cross anisotropic clays is to incline the principal stresses rather than incline the specimen. This will be discussed at length in the sections on Triaxial Testing on Solid Prismatic Specimens and Triaxial Testing on Hollow Circular Specimens; these examine the thin, long, hollow cylinder subjected to combinations of axial and torsional stresses. Torsional tests have been conducted on solid soil specimens by Habib [99], but their use is not recommended since the shearing stresses vary from zero

consolidation pressure

f

'-iiiJ i

»•

'^

2' /O

2

•^0

VERTICAL

2

y

INCLINED

!il_ 0 2 HORIZONTAL

FIG. 31—Orientation of triaxial compression specimens to investigate anisotropy.

y—piston

\—bushing

IM / 1^2

O^'^'CRIT. C

/-—

y-deformedi •^specimen ' -b^so «CfliT.*»«90'

FIG. 32—Bending moments and shearing forces introduced by testing inclined anisotropic specimens [97].


50


FIG. 33—Deformation of inclined specimens of an anisotropic clay [981.



51

at the center to their maximum value on the outer boundary. At best they can be used to study the behavior of iineariiy elastic materials prior to failure. General Remarks on the Standard Triaxial Test The more one studies the triaxial test, the more one seems to realize its shortcomings. Yet of all the soil tests today it is the one which is the most popular. It is quite versatile and offers one the opportunity to study a wide range of parameters with relative ease. The corrections mentioned in the previous subsections are themselves often of doubtful value. Nonetheless, it is an improvement over both direct shear and simple shear tests. With or without corrections it is an excellent test for comparative studies of various soils, and there exist correlations between the results obtained by it and by field measurements that make it an excellent design tool. It is obvious from the previous discussions that any study involving materials with high volume change tendencies should use lubricated end platens. Also, if one is to test coarse sands in an undrained way, membrane penetration should be taken into account. One has also to consider the accuracies of the measuring equipment, the effects of backpressures, and the relative flexibilities of the soil and the pore pressure devices used [18]. Whether one runs a constant rate of deformation or a constant rate of stress depends more often than not on convenience. It is obvious, however, that constant rates of deformation tests are mandatory if information beyond the peak is required. Triaxial Testing on Solid Prismatic Specimens Devices Primarily Designed for Plane Strain Testing The fact that many practical problems in soil mechanics can be approximated by plane strain conditions led to the development of plane strain testing devices where the specimen is a cube or a rectangular parallelepiped. Two faces of the prism are prevented from moving while pressures are applied on the two other pairs of faces. The stationary faces are the intermediate principal planes; this means that no shearing stresses are acting on them. The intermediate principal directions of stress and strain must coincide (Fig. 34). The obvious next step was to introduce means of changing the intermediate principal stress at will, rather than just preventing the faces from moving, and measuring the resulting stresses. In any of the new apparatuses which can apply three different principal stresses or strains on a prismatic element, a way can always be found to fix two faces and operate in plane strain [100]. However, the difficulties involved in devices in which the three stresses or strains can be freely changed are much larger than those encountered when just two faces are to be kept in place. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

52


f^

\v^

F/X£0

F/X£D 0-3

^ ^ FIG. 34—Stresses in plane strain conditions.

Al-Husseini [101] has reviewed the various apparatuses as of 1971. In many the minor principal stress is the triaxial chamber pressure when such a chamber is used. Table 3 lists most of the plane strain devices that have been built by various institutions. To this list one must add the hollow cylinder with fixed length used by Whitman and Luscher [102]. Figure 35 shows a section through the WES apparatus whose configuration is similar to that of many in Table 3. The application of the pressure is made through a mixture of rigid and flexible boundaries. Figure 36 shows the principle on which Hambly's [103] device works. There the displacements are applied by rigid plates and the pressure, as measured by a set of transducers, is found to be quite uniform with a minimum of shearing restraint [104]. Some of the machines in Table 3 have been or could easily be modified to accommodate /ô-consolidation conditions [105]. The aforementioned devices apply normal pressures on the faces of the soil specimen. The soil must be isotropic; or the stresses must be applied along axes of symmetry by unrestricting surfaces to avoid the undesirable end effects illustrated in the section on Triaxial Tests on Solid Circular Cylinders. Recognizing the need for a device capable of rotating continuously the principal stresses, Arthur et al [106a] designed the directional shear cell (DSC) in which a cube is subjected to normal and shearing stresses on four of its faces while two others are not allowed to deform (Fig. 37). By varying a^,CT^,and T„ the major principal stress can be rotated without the sudden jump of 11/2 that takes place in the cyclic triaxial and simple shear tests. The behavior of anisotropic soils can be studied in this device. Some of its limitations, notably that the boundary shear stresses are limited to approximately 48.3 kPa (7 psi), are pointed out in a recent study conducted on sand materials [106b]. Multiaxial or True Triaxial Testing Devices There are three ways of applying normal stresses to a prismatic specimen of cubic or parallelepiped shape: either via rigid flat platens or flexible membranes, or a combination of both. Early attempts to test sands by Kjellman Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


53

TABLE 3—Summary of plane strain shear devices as of 1971. Designer

Location

Reference

Lorenz et al Bjerrum and Kummencji Christensen Leussink and Wittke Marsal et al Duncan and Seed Wood Dickey et al Al-Husseini and Wade Al-Husseini Hambly Campanella and Vaid Ichihara and Matsuzawa

Technische Universitat, Berlin NGI DGl Technical University of Karlsruhe Comision Federal de Electricedad, Mexico University of California Imperial College MIT Georgia Institute of Technology WES Cambridge University University of British Columbia Nagoya University

138 139 140 141 142 143 144 145 101 146 103 147 148

[79] and Jakobson [107] are of limited applicability due to basic mechanical difficulties. By using principles developed by Hambly [103], Pearce built a true triaxial apparatus [108] where the loads are applied by means of rigid plates. Using the proper grease between the rubber membranes and the plates apparently resulted in uniform normal stresses and negligible shear stresses on the plates (Fig. 38) [104]. The second method of using flexible membranes on each of the three pairs of faces was used for tests on sand by Ko and Scott [109]. Because of comer problems [110-112] this apparatus was modified by Arthur and Menzies [110] using specially reinforced multiple rubber bags to load the sand sample. Ramamurthy [113] used rubber balloons inside metallic guides to apply principal stresses to a cubical specimen; he prevented penetration of the balloons' edges into neighboring chambers and distortion of the edges by inserting prismatic pieces of sponge inside the balloons along the edges. Ko and Scott's device has been improved by Sture [114] and by Berends and Ko [115] who used Teflon tapes and sheets as well as aluminum foil to minimize intrusion of one pressure bag into another (Fig. 39). Various combinations of flexible and rigid or rigid-lubricated boundaries on two pairs of faces have been tried. Generally the third stress was applied by the cell pressure acting on the membrane surrounding the sample. Axial rigid platens and a lateral pair of rubber bags were used by Lenoe [116], Shibata and Karube [117], Bell [118], Yong and McKyes [119], Bennett [120], Mesdary [121], and Sutherland and Mesdary [122]. This method is satisfactory, provided the problems associated with the rubber bags can be overcome. Axial rigid platens and another pair of lateral rigid platens were used by Green [123a], Mitchell [100], and Lade and Duncan [123b]. Green used what he termed the ISC belt and managed to keep a small gap between the axial and lateral rigid plates; Mitchell used compressible side plates Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

54


9.

^ y

I I d



55

FIG. 36—Principle of Hambly's pUme strain device (1031.

T Reinforced rubber pulling sheets.

Rigid backing plate, /, Pressure bag Pressure bog retaining vones

rubber strips

%V///////////////^

(^

50mm

0

I T ^ X area

SCALE FIG. 37—Diagram of method used to apply normal and shear stresses in the DSC 1106).


56


FIG. 38—True triaxial apparatus using rigid platens.

MtT*UWlll*llM

FIG. 39—Cross-sectional view of assembled multiaxial cubical apparatus [114]. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


57

made of solid blocks connected by springs and covered with brass sliders; Lade and Duncan used side plates made of steel and balsa wood laminae proportioned so that the plates could be compressed about 20 percent in the vertical direction without excessive axial force (Fig. 40). It is obvious that no simple type of apparatus is most suitable for testing all types of soils over a wide range of stress levels and stress paths. Sture and Desai [124] in Table 4 summarize the advantages and disadvantages of the various types of devices. Most of them are mechanically complex and require special care in the preparation and placing of the specimen. Most will remain, at least for the near future, research tools to be used in the development of constitutive equations and the determination of soil properties. Table 4 is self-explanatory.

Triaxial Testing on Hollow Circular Specimens As early as 1936 Cooling and Smith [20] used a hollow cylinder laterally unconfined and subjected to torque to obtain the resistance of soils in pure shear. In 1952 Geuze and Tan [21] studied the rheology of clays on thin, long, hollow cylinders subjected to torque. Later, hollow cylinders were placed in a cell and pressurized in an effort to generate a wide variety of stress paths. Two approaches were used. In the first, the inner and outer pressures are different and in addition the specimen is subjected to axial loading. In the second, the inner and outer pressures are identical and in addition the specimen is subjected to axial and torsional loading.

State of Stress in the Hollow Cylinder If the internal and external pressures are different, the stress distribution across the thickness is necessarily nonuniform. Kirkpatrick [125] assumed the validity of the Mohr-Coulomb criterion and averaged the values of the radial stress, a^, and the circumferential stress, a^, across the thickness. Wu et al [126a] made a more complete analysis based on plasticity theory and also averaged the values across the thickness. If the internal and external pressures are equal, the stress distribution across the thickness due to these pressures is uniform, provided there are no end effects. In the hollow cylinder, geometry affects the uniformity of the stress distribution. Radial frictional forces are developed at the ends of the specimen if it has a tendency to expand or contract. This tendency is always present when there is volume change or a change in length at constant volume. The radial frictional forces are self-equilibrating and their influence vanishes as one moves away from the end platens. St. Venant's principle, which is often invoked to dismiss the effects of end platens, demands a certain minimum distance to become operative. In the triaxial test on solid circular cylinders, it is customary to consider that a length-to-diameter ratio of Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

58


0 FRAME FOR COMPRESSING HORIZONTAL LOADING PLATES

- HORIZONTAL LOADING SYSTEM

FIG. 40~Cubical triaxial apparatus [after Ref 123b].

2.5 to 1 is adequate for routine testing. For hollow cylinders, in addition to the thickness, the mean radius plays an extremely important part in the determination of the proper dimensions. The radial factional forces that are imposed upon the specimen by the platens cause circumferential normal forces (hoop forces), shearing forces, and bending moments whose magnitude decreases rapidly as one moves away from the ends. Using the equations of the theory of thin elastic cylindrical shells, it is possible to gain insight concerning the relative magnitude of the stresses and their relation to the generating frictional force [33]. Consider a thin hollow cylinder of length I, mean radius a, and thickness h subjected to a tangential force F per unit length at both its ends (Fig. 41). Equations for the radial displacement w^, the bending moment per unit length M,, the shearing force per unit length Q^, and the normal hoop force per unit length Ng can be found in Refs / and 33. All the equations are expressed in terms of a constant, i3 = [3(1 — v^)/a'^h'^Y'*, where v is Poisson's ratio. With these expressions, the state of stress can be computed at any point of the cylinder. Thus one can compute the proper ratios among length, mean diameter, and thickness so that the end effects are reduced to a minimum. The distance beyond which the various stresses caused by F become negligible can be estimated from the equations derived for a very long cylinder.



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106

UBORATORY SHEAR STRENGTH OF SOIL

FIG. 10—Removable rods being reinstalled.

suming that the value of cohesion (c) was equal to zero. When the confining pressure was increased, these values decreased for both compacted and uncompacted samples. The value was always higher for compacted samples than for uncompacted samples at the corresponding confining pressures. This difference in 4> increased with an increase in the confining pressure. Performance of replicate tests proved that this strength parameter was reproducible. The p-q stress paths are shown for the uncompacted specimens in Fig. 12 and for the compacted specimens in Fig. 13. These stress paths enable the Kf-Wne (failure line in p-q coordinates) to be determined. Using the relationCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

ALVA-HURTADO ET AL ON STATIC TRIAXIAL TESTING

107

FIG. II—Acrylic chamber being positioned.

ship sin $ = tan a, the average ^-value was determined for both types of specimens. The average / value for the compacted samples was 44.4 deg and for the uncompacted samples was 37.8 deg. From the construction of the A^-line, it can be seen that for both sample types the q'-intercept (a) was not equal to zero. The apparent cohesion value for the uncompacted samples (c = o/cos0) was 33.1 kPa (4.8 psi), and the value for the compacted samples was 19.3 kPa (2.8 psi). It is believed that this apparent cohesion was due to particle interlocking. This hypothesis has also been presented by Raymond and Davies [8]. The stress-strain and volume change relationships for the uncompacted Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

108


CID GRANITE BALLAST UNCOMPACTED SAMPLE

FIG. 12—Strength envelope for uncornpacted ballast samples (I psi = 6.89 kPa).

P

(PSI)

FIG. 13—Strength envelope for compacted ballast samples (I psi — 6.89 kPa).

and compacted samples are shown in Figs. 14 and 15, respectively. These stress-strain figures show that the static test results followed the expected trends. As confining pressure was increased, the deviator stress at failure increased. Also, the deviator stress at failure was greater for the compacted samples than for the uncornpacted samples. This difference in deviator stress at failure between compacted and uncornpacted samples increased with increasing confining pressure. This fact was also pointed out by Raymond and Davies [8].



109

?3 = 20 02 psi

X^

^^'

^

^ ^ 3

.

„

faj-

= 15 05 PS.

= 10,16 P5

501 psi

FIG. 14—Stress-straiii-volume change behavior for uitcompucted ballast samples (I psi — 6.89 kPal.

As the confining pressure was increased, the vertical strain at which the sample failed also increased. The compacted samples reached greater vertical strains at failure than did uncompacted samples at confining pressures lower than 103.4 kPa (15 psi). It is important to point out that, near failure, particle slippage was noticed, which made an accurate determination of the axial strain at failure difficult. The volumetric strain plots show that the ballast followed the well-established behavior trends for granular material. Volumetric strain was defined as positive when the total specimen volume decreased and negative when the volume increased. As the confining pressure was increased, the tendency for sample dilation decreased. The compacted samples tended to dilate at smaller vertical strains than did uncompacted samples at corresponding confining pressures. These observations indicate that the behavior of granular materials under low confining pressures, as in the case of railroad ballast, is different from that under high confining pressures.


110


6" =l4 79psi

STRAIN (%)

e" 3= 5,01

psi

§" =10 01 psi ^ 5 5 - e j = 14,79 PS

< ttr K

5

^''^r::!;^!^-^ ' STRAIN (%)

IJ

15

S O

FIG. 15—Stress-strain-votume change behavior for compacted ballast samples II psi ~ 6.89 kPa>.

Hyperbolic Parameters The hyperbolic transformations [9] were applied to the stress-strain and volume change-strain data obtained from the ballast static triaxial tests. A typical plot of the stress-strain data in linearized hyperbolic form indicated that this behavior was approximately hyperbolic. However, the volume change relationship was not. Dilation plays a major role in this type of behavior. Replicate tests showed good reproducibility for the initial tangent modulus, Ej, and the ultimate deviator stress, {<j\-a3\\f The values of Rf [{oi-ai)f/ (ai-a3)uit)] from 0.74 to 0.98. These values are in agreement with the values given by Raymond and Davies {8\. The results of the hyperbolic fitting techniques are shown in Table 1. The logarithm of the initial tangent modulus (£,) as computed from the hyperbolic model is plotted in Fig. 16 as a function of the logarithm of the effective confining pressure (aj) for both compacted and uncompacted samples.



111

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Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorize

112


50,000

E, = 3000 o;

g o

6,000 _ 0.46

E.= 1500 o ;

O COMPACTED SAMPLES A UNCOMPACTED

1,00 0

•

SAMPLES

•

5 CONFINING

•

I — I — I

I

10 P R E S S U R E : , O",

(PS!)

FIG. 16—Variation of initial Young's modulus with confining pressure (I psi = 6.S9 kPu).

Naturally, the compacted samples has a greater initial tangent modulus than did the uncompacted samples. Generally, the relationship between these two can be represented asi', = K{ai)". A regression analysis using this functional relationship gave the following parameter values: Ei and a^ in psi units^

Compacted samples k n Uncompacted samples k It

3000 0.46 1500 0.46

Poisson's ratio is defined as the ratio of horizontal to vertical strain. The initial Poisson's ratio, (v,) and the final Poisson's ratio {v/) for both uncompacted and compacted samples are presented in Table 1. Although there was scatter in the data, the general trends were that both initial and final Poisson's ratios decreased with increasing confining pressures, and the initial Poisson's ratio was not affected by the ballast density. ^1 psi = 6.89 kPa.



113

Summary This paper presented the apparatus and techniques developed for static triaxial testing of railroad ballast. A large triaxial cell was designed and built. Laboratory sample preparation and setup techniques were also developed. Results using this equipment were presented for a typical railroad ballast. The results indicate that the ballast possesses many characteristics common to granular materials. Strength and hyperbolic parameters for the stressstrain-volume change behavior of the granite railroad ballast were determined based on test results obtained using the apparatus and techniques developed. Acknowledgments The study described in this paper is part of a research program dealing with track maintenance life prediction currently underway at the University of Massachusetts at Amherst under the direction of Prof. E. T. Selig. The research was supported by funds from the Office of University Research of the U.S. Department of Transportation. Phillip Mattson was the technical monitor. References |/1 Alva-Hurtado, J. E., "A Methodology to Predict the Elastic and Inelastic Behavior of Railroad Ballast," Ph.D. dissertation, Department of Civil Engineering, University of Massachusetts at Amherst, 1980. (2) Alva-Hurtado, J. E. and Selig, E. T., "Static and Dynamic Properties of Railroad Ballast," Proceedings. Sixth Pan-American Conference of Soil Mechanics and Foundation Engineering, Lima, Peru, 1979. |J| Silva-Tulla. F., "Predicting Settlement of Clay Foundations Subjected to Cyclic Loading," D.Sc. thesis. Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 1977. [4] Chan, C. K.. Journal of the Geotechnical Engineering Division. Vol. 101, GT 9, September 1975, pp. 991-995. [5] Chan, C. K. and Duncan, J. M., Materials Research and Standards. Vol. 7, No. 7, Julv 1967, pp. 312-314. [6] Yoo, T. S., Chen, H. M., and Selig, E. T., Geotechnical Testing Journal. Vol. 1, No. 1, March 1978, pp. 41-54. [7] Thompson, M. R., "FAST Ballast and Subgrade Materials Evaluation," Ballast and Foundation Materials Research Program, University of Illinois at Urbana-Champaign. for U.S. Federal Railroad Administration, Report No. FRA/ORD-77/32, December 1977. |(^] Raymond G. P. and Davies, J. R., Journal of the Geotechnical Engineering Division. Vol. 104, GT 6, June 1978, pp. 737-751. [9] Duncan, J. M. and Chang, C. Y., Journal of the Soil Mechanics and Foundation Division. Vol, 96, SM 5, September 1970, pp. 1629-1653.


T. B. Edil,' S. E. Motan,' and F. X. Toha'

Mechanical Behavior and Testing IVIethods of Unsaturated Soils

REFERENCE: Edil, T. B., Motan, S. E., and Toha, F. X., "Mechanical Behavior and Testing Methods of Unsaturated Soils," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 114-129. ABSTRACT: The mechanical behavior of unsaturated cohesive soils under different common stress conditions, that is, static compression, dynamic shear, and repetitive compression, is considered as a function of induced initial matrix suction by desorption from the initially saturated state. The hysteresis of moisture retention is considered outside the scope of this work. The test results suggest that the moisture regime can be expressed most suitably in terms of matrix suction. The data suggest that a rather definite change in stress-strain response takes place at a critical value of the matrix suction with modulus values, in general, dropping beyond the critical suction. The direct measurement of the total soil suctio;n in the laboratory in connection with the triaxial compression test is sought by use of thermocouple psychrometers. The total suction of the soil decreases as the applied stresses increase; the quantitative relationship is complicated by a number of factors. The matrix suction appears to be the fundamental suction component controlling the mechanical behavior during a desorption schedule. This implies certain limitations for the use of psychrometers alone in indexing the mechanical behavior of soils, especially if they have a significant osmotic suction component. KEY WORDS: unsaturated soils, soil suction, modulus, strength, repetitive loading, unconfined compression, laboratory tests, psychrometer, ceramic plate extractor, Poisson's ratio, residual strain, resonant column test

As the water table is drawn below the ground surface, decreasing porewater pressure and evapo-transpiration result in desaturation of the soil above the water table. Such a desiccated natural soil is subject to changing environmental conditions which produce a wide variety of pore-water pressure distributions in the soil above the groundwater table. In addition to desiccated natural soils, compacted soils are also unsaturated due to insufficient water on the dry side and trapped air bubbles on the wet side of the optimum moisture content. The mechanics of the unsaturated soils, unlike the 'Professor of Civil and Environmental Engineering and Engineering Mechanics, graduate student, and graduate student, respectively, University of Wisconsin-Madison, 53706.

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19

Agreement.

EDIL ET AL ON BEHAVIOR AND TESTING OF UNSATURATED SOILS

115

saturated soils, has not been fully developed because of the difficulties in defining the stress conditions and in relating them to the observed behavior [1].^ Unsaturated soils exhibit basic differences from saturated soils in mechanical behavior and have been receiving more attention in recent years. The results of an experimental study of the mechanical behavior of unsaturated soils under different stress conditions and the methods of testing unsaturated soils are presented herein. Soil Suction Unsaturated soil is a multiphase material consisting of a particulate solid phase and pores which are filled with liquid and gas. There occurs specific interaction of these phases which, in turn, defines the overall mechanical integrity of the soil in terms of the interparticle forces. Numerous "effective stress" equations have been proposed for unsaturated soils [2-8] in order to relate the observed mechanical behavior to the stress conditions. The stress variables, in general, include total stress (a), pore-water pressure (M„,), and pore-air pressure (M„). The proposed relationship of these stresses to an "effective stress", a conceptual normal stress that can be shown to control the mechanical behavior, as in the case of saturated soils, is at best tentative at this time. Effective stress in unsaturated soils is controlled, among other factors [2], by the difference between pore-air and pore-water pressures, («„ — u„), which is called the matrix suction. Matrix suction is therefore the negative gage pressure at a point in the soil-water relative to the external gas pressure. It may be considered as equivalent to the work required to transfer a unit volume of soil-solution from a reference pool at the same elevation and temperature as the soil to the point in the soil. It results from the capillary and adsorptive surface forces arising from the soil matrix. When expressed as energy per unit volume, it reduces to a pressure unit. From thermodynamic or total energy considerations of the pore water, its total suction (^,) can be subdivided into a matrix suction component i\l/,„) and an osmotic (or solute) component (î-J [5] such that ^, = ^m + \^s = (W« - W«.) + Î's Osmotic suction arises from the differences in the ion concentration of soilwater at different points in a soil. The main postulate of this paper is that soil suction can be considered to include implicitly the net effect of all the individual interparticle forces (with the exception of cementation bonds) that influence the stress-strain and strength characteristics of the unsaturated soil. In other words, soil suction may be considered an important stress variable which controls the "effective stress" and therefore the mechanical behavior. ^The italic numbers in brackets refer to the list of references appended to this paper.


116


Measurement of Soil Suction It is difficult to measure matrix suction in the field due to cavitation of the measuring system at pore-water pressures approaching 100 kPa negative. In the laboratory, matrix suctions in excess of this value (up to 1500 kPa) can be induced in soil specimens by placing them in a ceramic plate soil-moisture extractor [9]. The soil-moisture extractor consists of a pressure chamber containing a porous ceramic plate with a sheet-rubber backing, as shown schematically in Fig. 1. A metal screen provides space under the plate for bulk water, which is kept at atmospheric pressure by the tubular connection to the atmosphere. The bubbling pressure (that is, the pressure at which the menisci in the pores of the ceramic plate break and let air pass through) can be as high as 1500 kPa. Various matrix suction values can be induced in a specimen placed on the ceramic plate by applying an equivalent air pressure in the chamber under isothermal conditions and, thus, driving that portion of the soil-water at an energy state less than this value out of the specimens. This axis-translation technique induces matrix suction since the ceramic plate is permeable to solutes in the soil, and the soil-water is in equilibrium with a solution of the same concentration (that is, itself) in the burette. Recently psychrometers, which measure total suction, have received increased usage in measuring the suction of a soil in the laboratory and the field (Fig. 2). The low cost of psychrometers and the measuring equipment makes them attractive for engineering usage. Their use is restricted to soil suctions greater than 100 kPa. The psychrometer makes use of the Peltier effect to condense water from the air in the psychrometer chamber onto the measuring junction of a thermocouple formed commonly by fine copper and constantan wires welded together [10]. As the condensed water on the junction begins to evaporate, a potential difference is created between this junction and a reference junction resulting in an electrical current. This small potential difference can be measured by a microvoltmeter. The magnitude of this current depends, among some other factors, on the rate of evaporation, which in turn depends on the relative humidity of the air in the psychrometer chamber. If this air is in equilibrium with soil pore-air, then total soil-water potential, that is, total suction (i/-,), can be inferred from the measured relative humidity at any given temperature T from the relationship RT rP, = - ^

log P/P,

where R = V = Pg = P =

universal gas constant, specific volume of water, vapor pressure of pure water in the reference state, and vapor pressure of soil-water.



\rubbcr bJckinq

117

^cerdmic plate

FIG. 1—Ceramic-plate extractor.

Mechanical Behavior—Soil Suction Relations Proceeding from the premise that soil suction is a fundamental state variable controlling overall mechanical integrity of soils, a series of tests corresponding to different loading conditions was undertaken at different initial suctions. Deformability and Strength Response in Uniaxial Compression Uniaxial compression (unconfined compression) tests were performed on specimens from laboratory consolidated samples of a kaolinitic clay [//]. Test specimens with varying fabrics (microstructures) were brought to equilibrium at various matrix suctions in a ceramic-plate extractor. Only variations from the initially saturated state were studied by means of a desorption schedule. After a particular specimen was brought to equilibrium in the extractor, it was taken out and tested in unconfined compression. The lateral deformations at the midheight were also measured during the test at three points spaced 120 deg apart by use of micrometers. The stress-strain response is essentially strain-softening for matrix suctions less than a critical value, termed î'^., which appears to be in the range of 500 to 700 kPa. For ^,„ > iZ-^., the stress-strain response is essentially linear with a constant modulus E, after which a strain-softening phenomenon prevails. For \l/,„ < xp^, the stress-strain response is described by a hyperbolic equation [12] and a parameter which represents the inverse of the initial tangent modulus is empirically determined. Figure 3 shows the range of values for the initial tangent modulus E, (which becomes equal to the constant modulus E for !/-„, > \t^) as a function of the initial matrix suction; it is seen that Ej generally increases with increasing 4/,,, up to a critical value, beyond which it


118


.ceramic bulb

airline

thermocouple

(A)

(B)

FIG. 2—(a) Thermocouple psychrometer: (b) Psychrometers placed in the cap and base for use with compression test.

exhibits a decrease. As shown in Fig. 4, the unconfined strength increases rapidly with increasing values of \j/„ without any noticeable change in behavior at or above the critical suction as noted in Fig. 3. The radial deformations (average of three readings 120 deg apart) at the midheight of each specimen were used in conjunction with the axial deformations and the specimen dimensions to determine values of Poisson's ratio. Typical values of Poisson's ratio corresponding to axial strain levels of 0.01 and 0.05 are given in Fig. 5 for a range of initial matrix suctions. Poisson's ratios, in general, increased with increasing values of axial strain approaching a value of 0.5 at large axial strains. In general, as the initial matrix suction increases, the value of Poisson's ratio at a given axial strain becomes smaller, dropping to less than 0.1 at an initial matrix suction of 1500 kPa.



119

S highly oriented fabric (H highly random fabric

_l

102

initial

I . I I I I II io3 matrix suction, t|J^(kP8)

FIG. 3—Modulus as a function of initial matrix suction.

14 0

highly oriented fabric

Q highly random fdbric

' 'I

V'

lo-' initial m a t r i x •uctlor\\^) (kPa)

FIG. 4—Unconfined compressive strength as a function of initial matrix suction.


120


0 V at axial strain = 5% B W at axial strain. 1 %

I

I

I

' ' I I

initial matrix suction, 1(1 (kPa)

FIG. 5—Poisson's ratio as a function of initial matrix suction.

Dynamic Response The dynamic properties (shear modulus and damping capacity) of this kaolinitic clay were also determined using resonant column test after equilibrating specimens to various matrix suctions [13]. In Fig. 6, reference shear modulus G„ (defined as the modulus at a shear strain amplitude of 2.5 X 10~^ radians) is given as a function of initial matrix suction for two samples with distinctly different fabrics. G„ increases sharply with increasing suction up to a critical suction, \l/c = 400 kPa; thereafter it drops as the matrix suction increases, in a manner similar to the one observed in the case of the static modulus (Fig. 4). This response was typical of other specimens tested. Such a drop beyond this critical suction value was not observed with respect to the damping capacity. Response Under Repetitive Loading The important input parameters to a design program for asphaltic concrete pavements include subgrade resilient modulus (E^) and residual strain (e,,). Resilient modulus is defined as the ratio of the repeated axial stress (or the repeated principal stress difference) to that portion of the total strain that is recovered after the repeated axial load is removed. Residual or plastic strain is that portion of the total strain that is not recovered after the repeated axial load is removed. Fatigue prediction is highly sensitive to changes in subgrade resilient modulus which, in turn, varies with the

Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorize


O

highly orientad fabric

•

highly random fabric

121

-^^ a°,

\ is 6-

\

„

•

initial matrix suction, LjJ^ (kPa)

FIG. 6—Reference ilynamic shear modulus as a function of initial matrix suction.

moisture regime of the subgrade throughout the year. Moisture regime has special significance in highway pavement systems because such structures are generally associated with the surficial boundaries of the terrain where large moisture content variations are likely to occur throughout the year in response to changes in environmental conditions. Soil suction is a fundamental soil parameter that can reflect the influence of climate on the moisture regime, since it can be correlated with a climatic moisture index such as Thornthwaite moisture index [14], Because of these considerations, soil suction is conceived as the most appropriate parameter for characterizing the subgrade moisture regime [75], and tests were carried out to study the relationship of Er and e,, with soil suction using compacted specimens of a silt loam soil (Fig. 7). Er does not change appreciably up to i/-,,, = 100 kPa. Thereafter there is generally a sharp increase in E^ with increasing suction except at \l/,„ = 1500 kPa. The critical suction value at which the change in behavior occurs cannot be precisely determined; however, it probably has a value slightly in excess of 800 kPa. This change in mechanical behavior at a certain critical suction is similar to the one observed in static compression and dynamic shear. Major changes in e^ take place for the suction range less than 100 kPa, beyond which irrecoverable strain stabilizes at a nearly constant value. The dependency of resilient behavior for dry, wet, and optimum samples appears similar without any distinguishable trends with respect to the compaction moisture content and the resultant fabric. The same resilient


122


I

D d r y of optimum O optimum

lniti«l Soil Suction,!!!

A w t of optitnum

|

MVnf-]

FIG. 7—Resilient modulus and residual strain as a function

of initial matrix suction.



123

parameters, when plotted as a function of water content or degree of saturation (as indices characterizing the soil moisture regime) resulted in considerable scatter of the data [15]. These indices alone are found inadequate in reflecting moisture effects accurately. Direct Measurement of Suction During Mechanical Tests In the aforementioned experiments, values of matrix suction were induced by desorption in the specimens, and the response was studied as a function of the initial suction of a specimen free of external stresses prior to loading. This is appropriate when the significance and nature of initial soil suction effects are being investigated. In order to investigate the changes in soil suction due to externally applied stresses and to study the mechanical response as a function of the resulting suction, it is desirable to measure soil suction directly during a test. Furthermore, direct measurement provides a way of relating the laboratory results to the field behavior. Therefore the adoption of thermocouple psychrometry to the compression testing of unsaturated soils was considered to be promising, as it was also used by other investigators [16.17]. In this study, psychrometers were installed and sealed in the cap and base of the triaxial specimens (Fig. 2b). Experimental Problems An important aspect of testing unsaturated soils in triaxial compression is the prevention of vapor migration from specimens caused by leakage around the end caps and by diffusion through the rubber membrane. This requirement is more critical in the case of testing the unsaturated soils than the saturated ones. Use of three very tight 0-rings for sealing three membranes against the caps and filling the triaxial chamber with a sodium chloride (NaCl) solution with an appropriate osmotic pressure (about 50 percent of the total soil suction measured 24 h after placing the specimen) were found to be effective in preventing vapor migration [18]. Pore-air pressure was measured using a pressure transducer connected by a fine line in the top cap (Fig. 2b). Thermocouple psychrometers (Wescor Model PT51-05) were placed in the middle of the caps (symmetry is important in minimizing errors resulting from temperature gradients) and sealed by injecting epoxy resin. In some cases, the ceramic tip was left on the psychrometer and placed in holes drilled at the top and the bottom of the specimen. However, better results were obtained when the ceramic tips were removed and the psychrometer junction was placed in a recess of proper volume in the cap. The time to reach equilibrium may be considerably long. For the soils used in this study, (a silt loam and Grundite clay), it was two days. If a change in stress state was effected, it took more than three days to establish a suction equilibrium inside the specimen so that an equilibrium value could be measured at the


124


boundary (top or bottom). Lack of isothermal conditions, psychrometer junction size and shape, and presence of temperature and vapor pressure gradients contribute to the increase in time to reach equilibrium or to the inaccuracies or to both. Suction Response Under Applied Stresses In order to study changes in suction as a result of applied stresses, specimens from a low-plasticity silty clay were compacted using a Harvard miniature compactor with great care to make them as uniform in moisture distribution as possible. The specimens were subsequently placed in a modified triaxial cell as described previously. The total suction response, as measured by the top and bottom psychrometers under initially isotropic and subsequently under anisotropic applied stresses, is given in Fig. 8 as a function of time. The equilibrium suction subsequent to stress increment application was reached within 3 to 4 days. The initial suction at the top of the specimen was higher than at the bottom, and the change in suction as a result of isotropic stress changes was higher at the top than at the bottom of the specimen. Suction changes due to anisotropic stress applications were relatively small initially; as axial strains approached failure large changes in suction were observed. Equilibrium total suction is given as a function of applied mean stress a„ [a„ = (CTJ + 2CT3)/(3)] in Fig. 9. There appears to be a stress path dependency for the suction response. Furthermore, the slope of the suction-applied stress plot is not constant; it varies, in general, with stress level, stress path, and initial suction. The relationship does not appear to be a simple function of the applied stress. It should be noted, however, that the slope of the suction-applied stress curve is equal or less than unity for the most part. For the soil used, the measured total suctions approximate the matrix suctions closely, since the osmotic component is believed to be insignificant. Relationship of Suction Components One of the questions which needs clarification is to what extent the matrix component of the total suction controls the mechanical behavior of soils. Four specimens of Grundite clay were prepared by mixing the clay powder with NaCl solutions of 0, 0.1, 0.5, and 0.8 m concentrations at a moisture (solution) content of about 40 percent. These mixtures were subsequently compacted to the same density. The compacted specimens (35.6 mm in diameter and height) were placed in the ceramic-plate extractor and were equilibrated to a matrix suction of 200 kPa. Their total suction was then measured by psychrometers at the top and the bottom. Fig. 10 gives total suction as a function of NaCl concentration. The dashed line gives the


EDIL ET A L O N BEHAVIOR A N D TESTING OF UNSATURATED SOILS

(r^* fl-J-iiJ

ff-/ "•rffj

t op bottom

•o

0 8 0 140 0 9 10 280 0 420 0 n 420 160 12 13 420 250 14 4 20 340 7 * p r t s s u r e B in k Pa

S60 420 140 !40 140 140 140

1 2 3 4 5 6

X

s

125

320 70 0 180 350 510 660

••MM**-*

i.? 10

20

30

40

50

60

70

80

t i m e , (days)

FIG. 8—Measured total suction response under applied stresses.

O

isotropic s t r e s s

D dnisotrop A dnisotropic

2

4 dDplicd mcdn stress

loading (Otidinq

ff

=420kPd .140l tan ' (2a///). The upper-bound solution of Eq 2 can be reduced to P^p"

= TciKbH - a^)

(4)

Rearrange Eq 4 and it becomes Eq 1, where K = tan (2a + 0)

(5)

The value /f in Eq 5 depends not only on the angle of friction, but also on the compression-tensile strength ratio and specimen-punch ratio, as indicated in Eq 3. A comparative study of /C-value has been carried out


134


i

y////A-

PUNCH (DISC)

RIGID AR

(a)

CROSS-SECTION

AR -SPECIMEN

(b)

VELOCITY REUTIONS

FIG. 2—Failure mechanism of unconfined-penetration test.

previously by using concrete [12] and soil {4\. Table 1 summarizes the proposed /^-values for the various types of soil and specimen-punch size. An examination of the horizontal and vertical strain distribution in the UP test at failure was also evaluated by use of concrete specimens and measured with strain gages [7]. This experiment showed that vertical strain distribution on the middle horizontal section of the cylindrical specimen was almost uniform. Good agreement between experimental and theoretical results was found. Other theoretical comparisons between UP tests and conventional splittension tests have been made by use of elastic solution, limit analysis, slipline, and finite-element solutions [7,12.13] Experimental Study The experimental study includes two phases. The first phase is to evaluate the test procedures and methods for preparation of test specimens. The second phase covers the correlations of tensile strength with other soil constants


FANG AND FERNANDEZ ON TENSILE STRENGTH OF SOILS

135

and strength parameters. The effects of some of the variables, such as sample-punch size, rate of loading, and soil types, have been previously examined [3,4]. The correlation between unconfined compressive strength and split-tensile strength has been reported [4]. The present experiments include a further examination of soil types and correlation with unconfined compressive strength. The additional variables considered include punch alignment, molding water content, and moisture conditions during the tensile tests. Correlations with additional parameters, including Atterberg limits, activity, toughness index, cohesion, and friction angles, are also presented.

Soil Types The soil mixtures illustrated throughout this study are composed of silty clay (liquid limit = 30, plasticity index = 10) with various percentages of sand, bentonite, and biotite added. All samples passed No. 10 sieve and were air-dried. The standard Proctor mold was used for preparation of test specimens. For each type of mixture, the Atterberg limits, gradations, optimum moisture content, and maximum dry unit weight were determined in accordance with ASTM standard procedures.

Specimen-Punch Sizes and Punch Alignment For preparation of a tension test specimen, a standard Proctor mold is commonly used. However, for stabilized soil, such as cement-treated base material, the CBR mold may be used or, for saving soil material, the Harvard miniature compaction mold may also be used. As long as the ranges of the specimen-punch ratio stay within 0.2 to 0.3 and the height-specimen diameter ratio stays within 0.46 to 1.0, any size of specimen and punches can be used. Proposed values of K for various sizes of specimens are presented in Table 1. The UP test requires two steel punches (disks) centered at both top and bottom surfaces to penetrate into an unconfined soil specimen. The alignment of these two punches—that is, whether or not in the same plane—is important. Two cases were examined where the punches were eccentrically loaded. The first case had both punches in the same plane, but off-center of the specimen. The second case had one punch on the center of the specimen and the other off-center. From the experiments for each case, it was found that the maximum error that could be expected was 10 percent. To resolve this problem of alignment, two plastic tampers have been made. The diameter of the tamper is the same size as the soil specimen. At the center of each tamper is a hole with a diameter equal to the punch diameter. The use of these tampers should ensure proper alignment of the punches. The hardness of the punch material should also be investigated, especially


136


for testing hard rocks or stabilized soils. The commonly used reamer blank tool steel is suitable for punch material. Correlation Study When the soil is saturated or very wet, it has very little tensile strength existing with no engineering significance. When the soil gradually reduces in moisture content, its tensile strength gradually develops. Therefore the moisture content during the tension test is extremely important. For comparison purposes, all specimens were tested at two moisture conditions, one at the optimum moisture content (OMC) and the other at air-dried condition. The test results are summarized in Tables 2 and 3. Experiments were performed to obtain Atterberg limits, activity, toughness index, unconfined compressive strength, cohesion, and friction angles. These are discussed in the following sections. Atterberg Limits, Activity, and Toughness Index As previously reported [3,4], the tensile strength increases as the plasticity index and liquid limit increase. Similar conclusions were reported by other investigators by using conventional split-tension tests [14], All previous study on test specimens for tension tests was based on the OMC. In this experiment further evaluations include correlation of the tension test results with activity and toughness index. The activity is defined as the plasticity index divided by the percent of clay [15]. In general, the activity value increases as the plasticity index and liquid limit increase. The tension tests were performed at both OMC and air-dried conditions. Six types of soil were'tested. The first group of soil specimens was molded at OMC and the tension test was performed at OMC condition. The second group of specimens was also molded at OMC, but was dried in air at room temperature for 40 h, then the tension tests were performed. Tension test results and activity values for both cases are plotted in Fig. 3. It is clearly indicated that the tensile strength increased significantly for all types of soil when they are air-dried. However, the amount and rate of increase in strength depends on the soil types. For a low-plasticity soil, the differences between two moisture conditions are more pronounced than for a high plasticity soil. The toughness index is defined as the ratio of plasticity index to the flow index [75]. The flow index is determined from the standard liquid limit test. This toughness index frequently is used as an indicator for the evaluation of soil stabilizing materials. Figure 4 shows the tensile strength test results versus toughness index for both moisture conditions. Similar trends are indicated in Figs. 3 and 4. From these results, it can be projected that there will be greater differences in strength between the two moisture conditions for a low-plasticity soil than for a high-plasticity soil.



137

o -- -^ -^ r- ô •
tu aa

E.i'

ll^lt-s

< ^

^ i

t/5 Z

—I •«!r O r n 00 r ^ TT — r - ' OO i/)' (N - ^ (->! ^ .— (N r*^

< W (J O W ti.

H a E

1 1•oo s its s

0

1)

c JM iai oc

i-siU^î =~k^--


138


TABLE 3—Summary of tensile and undrained direct shear tests at various molding moisture contents. NOTES: (1) An asterisk indicates samples molded on wet-side of optimum moisture content (CMC). (2) CMC values for each soil type are presented in Table 2. (3) The data shown in the table are the average values of two or more tests. (4) 1 psi = 6.9 kPa.

Direct Shear Test Molding Moisture Content, %

Tensile Strength (a,), psi

Cohesion (C), psi

Friction Angle (). deg

C/ff,

A

10.8 12.9 12.9 13.0* 14.4* 15.3*

6.69 1.59 1.78 2.57 0.67 0.32

19.9 15.2 22.7 19.0 13.0 10.0

40.0 30.6 25.5 31.5 22.5 20.2

2.97 9.56 12.75 7.39 19.40 31.25

D

11.9 12.5 13.1 13.2 13.2 13.9 14.2* 15.8* 16.8*

8.18 9.48 6.78 7.94 7.93 4.79 5.25 1.54 0.68

21.5 22.5 23.4 24.3 22.5 21.0 30.0 16.8 14.0

42.5 37.6 36.2 34.2 36.7 34.5 28.1 24.6 19.2

2.62 2.37 3.45 3.06 2.84 4.38 5.71 10.91 20.59

F

13.2 16.4 18.8* 20.4* 22.4*

10.86 7.02 4.03 4.26 2.03

33.0 27.5 23.0 27.6 13.5

28.2 25.5 16.0 10.5 4.5

3.04 3.92 5.71 6.48 6.65

Soil No.

Unconfined Compressive Strength The ratio of unconfined compressive strength to tensile strength of materials is of interest to all design engineers because of its practical uses. For soils, most tests for this ratio are performed at OMC condition. A curvilinear relationship has been reported for various soil types [3,4,14,16,17]. In this experiment an investigation of how the moisture condition affects this ratio was carried out. Six soil types were investigated. One group was tested at OMC in both tension and compression tests, while the other group was molded at OMC but allowed to air-dry in room temperature for 40 h, then tested for both tension and compression. The test results are shown in Fig. 5. It is evident that for air-dried specimens, the compressive-tensile ratios for the six types of soils were relatively constant. However, for higher moisture



ô-

139

v s . A CURVE (AIR-DRIED)

FIG. 3—Tensile strength versus activity of two moisture contents during tension tests.

contents, the ratios increased significantly for all types of soil, especially for the low-plasticity soils. Figure 5 mainly points out that effects of moisture content and soil type on the compressive-tensile strength ratio are equally important when the plasticity index is less than 20 (see Region I). However, the effect of moisture content is predominant in Region II, where the compressive-tensile strength ratio is insensitive to variation in percent of clay and soil types, as reflected in plasticity index. Cohesion and Friction Angles in Undrained Condition The relationship between cohesion and tensile strength is also useful to the practitioner, as pointed out previously [16]. When soil is dry, the ratio of cohesion and tensile strength influences only the soil types. Further investigation Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

140


S 35

/O- VS. I^ CURVE (AIR-DRIED)

0.4

0.8

1.0 1.2 TOUGHNESS INDEX, I^

1.4

FIG. 4—Tensile strength versus toughness index of two moisture contents during tension tests.

of the moisture content effect on cohesion-tensile strength relationships is needed. The direct shear apparatus with undrained condition was used for determination of cohesion (c) and friction angle (). Various molding moisture contents were evaluated. For each molding moisture content, three samples were prepared and various normal loads applied. The values of cohesion and friction angle were obtained from Mohr circle diagrams. Six soil types were tested in the same manner. Typical plots of cohesion-tensile ratio versus molding moisture content for three different soil types are shown in Fig. 6. Curve A, with a plasticity index equaling 4.9, shows that a slight increase of the molding moisture content sharply affects the cohesion-tensile ratio, while Curve F, with a plasticity index equaling 78.2, indicates that molding moisture content has lesser effect on the cohesion-tensile ratio. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


141

O 32.2

40

60

PIASTICITY INDEX, 1

Region I Region II

Percent of clay and moisture content, both significant. Moisture content more significant than percent of clay.

FIG. 5—Compressive-tensUe ratios versus plasticity index of two moisture contents during compression and tension tests. (Numbers beside points indicate percent passing 200 sieve. I

The curvilinear relationship between friction angle and tensile strength was observed for all six types of soils. Typical curves for three different soil types are shown in Fig. 7. It indicates that soils with higher plasticity indexes have lower friction angles. It can also be seen that at lower tensile strengths the rate of increase of the friction angle is much higher than at higher tensile strength. Sununaiy and Conclusions 1. The unconfined-penetration (UP) test is simple, easy to perform, and can be used conveniently in conjunction with routine compaction and CBR tests. 2. Good agreement between UP and conventional split-tensile tests exists. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

142


30

25

20

OMC •=

12.9%

F dp = 78.2)

OMC -

J 5

\ 10

i

\ 15

i

I 20

17.2T

L 25

30

MOLDING MOISTURE CONTENT, PERCENT

FIG. 6—Cohesive-tensile ratio versus molding moisture content with various soil types.

The UP test always causes failure on the weakest plane, which results in the measurement of the true tensile strength. 3. The constant AT-value depends on the specimen-punch ratio, heightspecimen diameter ratio, friction angle of the materials, and the compression-tensile strength ratio. This value ranges from 0.8 to 1.2. The specimenpunch ratio ranges from 0.2 to 0.3, and the height-diameter ratio of the specimen is 0.46 to 1.0. These values are summarized in Table 1. 4. The punch alignment is important. Both top and bottom punches should be at the center of the specimen and should be on the same plane. To avoid a problem, a plastic alignment tamper should be used. Hard tool steel should be used as punch material for testing hard rock or stabilized soil. 5. Six soil types and two moisture conditions were investigated. One series was conducted at optimum moisture content (OMC), while the second series, was completed on specimens air-dried in room temperature for 40 h. The



143

7.2)

32

o 24

z 16

2.0

4.0

6.0 8.0 TENSII£ STRENGTH, o^ PSI

12.0

FIG 7. —Friction angle versus tensile strength for various types of soil. (Solid points indicate samples at molding moisture contents on dry-side of optimum moisture condition. 1 psi = 6.9 kPa.)

significant differences of tensile strength at tliese two moisture conditions were observed. The amount and the rate of increase between the two moisture conditions depend on the soil types. For low-plasticity soil, the differences between the two moisture conditions is more pronounced than the higher plasticity soils for the activity and toughness index. 6. The compression-tensile strength ratios versus soil types with various molding moisture contents were also observed. They indicated that the influence of the molding moisture content is more significant than soil types for high-plasticity soils. For low-plasticity soils, both percent of clay and moisture are equally important (see Fig. 5). 7. Cohesion-tensile strength ratio has similar effects on the molding moisture content and soil types as does the compression-tensile strength ratio. For low-plasticity soil, it is shown that a slight increase of the molding moisture content sharply affects the cohesion-tensile strength ratio. On the other hand, the molding moisture content has less effect on higher plasticity soil. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

144


8. A curvilinear relationship between friction angle and tensile strength was observed (see Fig. 7). It indicates that as the plasticity index increases, the friction angle decreases. For lower tensile strength, the rate of increase of the friction angle is higher than at higher tensile strength. Acknowledgments The research reported herein was supported by the National Science Foundation under Grant GY-7459 awarded to Lehigh University. The authors express their thanks to N. S. Pandit for reviewing the manuscript. References [/) Tschebotarioff, G. P. and DePhilippe, A. A. in Proceedings, Third International Conference on Soil Mechanics and Foundation Engineering, Vol. 3, 1953, pp. 207-210. [2] Leonards, G. A. and Narain, J., Journal of the Soil Mechanics and Foundations Division. Proceedings of the American Society of Civil Engineers. Vol. 89. No. SM2, March 1963, pp. 47-98. [3] Fang, H. Y. and Chen. W. P., Highway Research Record. No. 354. 1971. pp. 62-68. [4] Fang. H. Y. and Chen, W. F., in Proceedings. Third Southeast Asia Conference on Soil Engineering, Hong Kong, 1972, pp. 211-215. [5] Dismuke, T. D.. Chen. W. F., and Fang, H. Y.. Rock Mechanics. Vol. 4, No. 2, Oct. 1972, pp. 70-87. [61 Cumberledge, G., Hoffman, G. L., and Bhajandas, A. C , Transportation Research Record. No. 560, 1976, pp. 21-29. 17] Chen, W. f.. Journal of the Engineering Mechanics Division. Proceedings of the American Society of Civil Engineers. Vol. 96, No. EM3, June, 1970, pp. 341-352. [H] Fang, H. Y. in Proceedings. 15th Annual Meeting of Society of Engineering Science. University of Florida, Dec. 1978, pp. 527-532. [9] Fang, H. Y., Geotechnical Engineering. Vol. 4, No. 1, June, 1973, pp. 59-60. I/O] Fang, H. Y., Soils and Foundations. Vol. 14, No. 3. Sept. 1974. pp. 81-82. (//] Chen, W. F. and Drucker, D. C , Journal of the Engineering Mechanics Division. Proceedings of the American Society of Civil Engineers. 95. No. EM4. Aug. 1969, pp. 955-978. [12] Chen. W. F.. Limit Analysis and Soil Plasticity. Elsevier Scientific, Amsterdam, 1975. \I3\ Chen, W. F. and Chang, T. Y. P., Journal of the Engineering Mechanics Division. Proceedings of the American Society of Civil Engineers. Vol. 104, No. EM3. June 1978, pp. 691-704. [14] Narain, J. and Rawat, P. C, Journal of the Soil Mechanics and Foundations Division. Proceedings of the American Society of Civil Engineers. Vol. 96, No. SM6, 1970. pp. 2185-2190. [15] Winterkorn, F. H. and Fang, H. Y., Foundation Engineering Handbook. Van Nostrand Reinhold, New York, 1975, Ch. 2, pp. 80-120. |/6) Fang, H. Y. and Hirst, T. J., Highway Research Record. No. 463, 1973, pp. 45-50. [17] Krishnayya. A. V. G., Eisenstein, Z., and Morgenstern, N. R.. Journal of the Geotechnical Engineering Division. Proceedings of the American Society of Civil Engineers. Vol. 100, No. GT9, Sept. 1974, pp. 1051-1061.


p. y. Lade'

Torsion Shear Apparatus for Soil Testing

REFERENCE: Lade, P. V., "Toision Shear Apparatus for Soil Testing," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 145-163. ABSTRACT; Laboratory studies of soil behavior during rotation of principal stress directions may be performed using a torsion shear apparatus. The requirements, construction, and operation principles for this apparatus are presented. The same confining pressure is applied to the inside and outside surfaces of a hollow cylindrical specimen. Both clockwise and counterclockwise shear stresses and vertical deviator stresses can be applied to the ends of the hollow cylinder. The entire setup is contained in a pressure cell, and the integrated loading system is located below the table which holds the cell. A variety of initial stress conditions may be used, and the behavior of soils during large stress reversals, as well as reorientation of principal stresses and combinations of these conditions, may be investigated in this apparatus. The loading system and the deformation measurement principles are described, and procedures for preparation of sand specimens are presented. The advantages and limitations of the torsion shear apparatus are discussed. KEY WORDS: geotechnical engineering, laboratory tests, mechanical properties, sands, shear strength, soil mechanics, strains, stresses, torsion

In order to perform laboratory tests for investigation of the behavior of soils during rotation of principal stress directions, it is necessary to apply shear stresses as well as normal stresses to the surfaces of the specimen. A brief review of several types of test equipment capable of transmitting normal and shear stresses for soil specimens has been presented by Lade [1]? Each of these equipment types presents difficulties in interpretation of test results caused by nonuniform stress distributions or the lack of ability to measure all stresses applied to the specimen, or both. A torsion shear apparatus, in which a hollow cylinder specimen is confined 'Associate professor, Mechanics and Structures Department, School of Engineering and Applied Science, University of California, Los Angeles, Calif. 90024. The italic numbers in brackets refer to the list of references appended to this paper. 145 Copyright by Downloaded/printed Copyright 1981 University of

ASTM by by ASTM British

Int'l International

Columbia

(all

rights

www.astm.org

Library

reserved); pursuant

Sun to

Dec License

19 Agreement.

02:25

146


between inside and outside membranes and between cap and base rings, offers the advantage of individual control of vertical normal stress, cell pressure, and applied shear stress. The same confining pressure is applied to the inside and outside surfaces of the specimen. The vertical normal stress and the shear stress are transferred to the specimen through cap and base rings. The entire setup is contained in a pressure cell, and the integrated loading system is located below the table which holds the cell. An earlier version of the torsion shear apparatus employed a hollow cylinder specimen with height of 5 cm, average diameter of 20 cm, and wall thickness of 2 cm. Some of the stresses and strains observed in this apparatus were shown to be nonuniform [2]. They were caused by restraint at the ends where shear and normal stresses are transferred to the specimen through full friction surfaces. While this restraint may not be completely eliminated, its effect can be substantially reduced by employing taller specimens. The hollow cylinder specimen used in the torsion shear apparatus presented here has a height of 40 cm and the same average diameter and wall thickness as described previously. Based on theory of elasticity, Wright et al [3] presented an analysis from which the ratios among height, average diameter, and wall thickness of a hollow cylinder specimen may be obtained to achieve a minimum of effects of end restraint. Data from tests with different specimen heights presented at the end of the present paper indicate that the specimen dimensions employed in the torsion shear apparatus result in negligible effects of end restraint.

Requirements for Apparatus A torsion shear apparatus for measurement of stress-strain and strength characteristics of soils during rotation of principal stress directions should satisfy the following conditions: 1. The apparatus must be capable of accommodating normal and shear strains which are large enough so that failure can be obtained with a minimum of induced nonuniformity in the stress and strain distributions in the specimen. 2. The shear stresses must be transferred to the specimen with no slippage between the specimen and the stress application mechanisms. 3. The horizontal normal stresses on the inside and outside surfaces of the hollow cylinder specimen should be identical in order to simplify the analyses of the results and in order that unjustified assumptions about the soil behavior be avoided. 4. The dimensions of the specimen should be such that it behaves as a thinwalled tube, in which case the stress condition imposed on the specimen can be regarded as a plane stress condition.


LADE ON TORSION SHEAR APPARATUS

147

Before the torsion shear apparatus was constructed, three additional principles, mainly pertaining to simplification of the design and operation, emerged: 1. The procedure for preparing test specimens should be fairly simple. 2. The stress application mechanisms should be designed so that the applied normal and shear stresses can be measured independently of each other. 3. Moving parts that may result in friction of such magnitude that correction is necessary should be avoided if possible. While these latter principles may be less essential to the results, they do facilitate the performance of the tests. Stress Application in Torsion Shear Apparatus The torsion shear apparatus was designed and constructed to permit application of a confining pressure to a hollow cylinder specimen (the same confining pressure is applied to the inside and the outside surfaces of the specimen). Shear stresses and vertical deviator stresses can be applied to the top and bottom (the ends of the cylinder). The entire setup is contained in a pressure cell. A three-dimensional drawing of the torsion shear apparatus is shown in Fig. 1; a picture of the hollow cylinder specimen with cap plate and with clip gages mounted is shown in Fig. 2. The normal and shear stresses are applied to the specimen as follows: The confining pressure is applied through the cell water that surrounds the specimen. The vertical load is applied to the specimen through the cap. This vertical load is transferred to the specimen by a cap plate, which is connected to a shaft through the bottom of the cell. The resulting deviator stress, together with the cell pressure, provides for a vertical, normal stress larger than the confining pressure. The torque is transferred to the specimen through the center shaft and the cap plate. The shear stresses due to the torque cause reorientation of the principal stress directions and a stress state with three unequal principal stresses. If shear stresses are not applied to the specimen, the cell pressure is the minor principal stress. With torsional shear stresses applied, the cell pressure becomes the intermediate principal stress. The design and performance of the torsion shear apparatus and its integrated loading system are described in detail in the following sections. Specimen Setup Specimen, Cap, and Base Rings A vertical cross section of the specimen and apparatus is shown in Fig. 3. The hollow cylinder specimen is contained between a cap ring, a base ring.


148


LINEAR MOTION TRANSOUCEtU

CENTER SHAFT-

V

TORSION SHEAR LOADING CYLINDER

r^

X •«-

- - VERTICAL LOADING CYLINDER

FIG. 1—Torsion shear apparatus with 5-cm-tall specimen.



149

and a membrane along the inside and outside vertical surfaces. The apparatus can accommodate specimens with heights up to 40.0 cm. The inside and outside diameters are 18.0 cm and 22.0 cm, respectively, and the thickness of the specimen is consequently 2.0 cm. The cross section of the cap ring is designed to provide 0-ring seals between the inside and outside parts of the membrane (Fig. 3). The base ring, on which the specimens are prepared, is fastened to the bottom plate with three screws. The cap and base rings are made of stainless steel. Membrane The specimen is confined along the inside and outside vertical surfaces by one continuous membrane, in the bottom of which the base ring is placed. The cross section of the 0.028 to 0.030-cm-thick rubber membrane is U-shaped (Fig. 3). Holes are punched in the bottom of the membrane to provide for drainage lines and for the three screws with which the base ring is fastened to the bottom plate. Two grooves in the bottom plate below the base ring contain 0-rings which provide seals for the membrane along the base ring, when this is fastened to the bottom plate. The grooves are spaced to allow for the drainage lines and the screws (Fig. 3). Forming Jackets Circular forming jackets along the inside and outside surfaces of the hollow cylinder specimen support the membrane while the cohesionless soil is being placed. The inside forming jacket consists of a piece of thin aluminium tube, which fits inside the base ring and sits on the bottom plate. When the inside part of the membrane is pulled up, the Foisson effect makes it cling tightly around the forming jacket. The thin-walled tube is split parallel to the tube axis in order to facilitate its placement and removal. The outside forming jacket is designed as a regular vacuum jacket, which fits outside the base ring and sits on the bottom plate. Drainage Lines The cap and base rings are provided with three filter stones each. The filter stones, which are made of porous bronze, are countersunk in the rings 120 deg apart. Drainage lines, which allow measurement of the volume change of the specimen, are connected to the filter stones through fittings. The drainage lines consist of 0.32-cm (0.125-in.) Saran tubing, which pass through fittings in the bottom plate. The three lines from the filter stones in the cap ring are connected inside the cell to one line, which is led out through the bottom plate. The drainage lines from the base ring are connected outside the cell to one line.


150


FIG. 2—Hollow cylinder specimen with cap plate and clip gages mounted.

Full Friction

Surfaces

In order to transfer shear stresses from the cap and base rings to the specimen and to avoid slippage at their interfaces, full friction surfaces are provided on the rings. The surface of the base ring that faces the specimen is coated with a layer of epoxy and pressed down in sand of the type being tested. The sand grains in the lower layer of the specimen, which is deposited on top of the base ring, interlock with the sand grains, which are glued to the ring. After the hollow cylinder specimen has been deposited, the surface of the cap ring is coated with a layer of epoxy and pressed down on top of the specimen. The upper layer of sand grains is thereby rigidly glued to the cap ring.



151

Clip Gage

0 - R i n g Seals Cap Ring

Hollow Cylinder Specimen

H =40cm

;^^

-Membrane

fi)'22cin Dj = 18 cm

-Filter Stone Base Ring

- Drainage Line F I G . 3—Crass section

of hollow

cylinder

specimen

and

apparatus.

Torque and Vertical Load Transfer To facilitate assembly of the specimen and apparatus, the torsion shear unit is designed to be loaded from the bottom by an integrated loading system. The loading system is mounted on the reinforced frame of the cabinet on top of which the torsion shear apparatus is fastened. Both the torque and the vertical load are transferred to the stainless steel center shaft, which is maintained in its vertical position by a linear and rotary ball bearing encased in the bottom plate of the cell. A rolling diaphragm sealed against the bottom plate and the shaft (Fig. 3) provides a good seal around the shaft and ensures that the shaft is free to rotate and move vertically with negligible friction. The top part of the shaft has a square cross section, which fits in a square hole in the stainless steel cap plate (Fig. 1). This construction enables the transfer of the torque from the shaft to the cap plate. Figure 1 also shows a washer resting on the cap plate and fastened with a screw to the end of the shaft. The vertical load is transferred from the shaft through the screw and Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

152


washer to the cap plate, which fits on top of the cap ring to which it is fastened with three screws (Fig. 3). The cap plate is provided with three 1.9-cni (0.75-in.) holes, which ensures that the same horizontal normal pressure is applied to the inside and outside surfaces of the specimen. One leg of each of the pair of clip gages, which measure the thickness change of the specimen, sticks through each of two of these holes, (Fig. 3). Pressure Cell The top and bottom plates are constructed of 2.5-cm (1.0-in.) and 3.18-cm (1.25-in.)-thick aluminium, respectively. The cell water is led in through a female Foster fitting in the bottom plate. A female Foster fitting in the top plate provides an outlet for the air in the cell. The inside surface of the top plate is slightly tapered in order to minimize the trapping of air bubbles when water is introduced into the cell. The vertical cell wall is made of 1.27-cm (0.50-in.)-thick Lucite plastic tube. The inside diameter of the cell is 27.9 cm (11.0 in.) and the height is 53.3 cm (21.0 in.). The bottom plate, the Lucite cell wall, and the top plate are held together by six 1.27-cm (0.5-in.)-diameter tie-rods, which are put in place after the specimen is prepared and the cell wall and top plate are installed. A small cylindrical Lucite container, which clips on one of the tie-rods, is connected to the cell by a 0.64-cm (0.25-in.) plastic tube through the bottom plate. This cylinder is filled with water to such a level that the water surface is at midheight of the specimen. After the cell has been filled with water, the cell pressure is applied by air pressure on the water surface in the small Lucite cylinder. A pressure transducer mounted at the bottom of the small cylinder measures'the cell pressure. Loading System The torsion shear apparatus is designed so that the specimen is loaded from the bottom by an integrated loading system (Fig. 1). The loading mechanisms are mounted on the reinforced frame of the cabinet on top of which the torsion shear apparatus is fastened. Both the torque and the vertical load are transferred to the center shaft below the bottom plate of the apparatus, as seen in the upper part of Fig. 4. Vertical Load The vertical load is supplied by an oil-filled pressure cylinder, which is mounted directly below the center shaft. The oil enters the pressure cylinder through a 0.64-cm (0.25-in.) plastic tube on the side of the cylinder. A load cell, which measures the vertical load applied to the specimen, is fastened to the lower end of the center shaft. The vertical load is transferred from the pressure cylinder to the load cell through a 0.467-cm (0.188-in.)-thick



SIDE

153

VIEW Bottom Plate of Torsion Shear Apparatus •—Center Shaft

5

1 3^—r&^—^

)ue Load C e l l — 7

i k ^ r

||

IC

Linear and Rotary Beari Bearing

C a b l e s - l _ 3 F l ^ T o r q u e Arm h r ^ il" Inlet ^ ^ ^ : \ "Ôil Inl Vertical Load Cell Counter Balance Spring ; = - * - O i l Inlet

Vertical Loading Cylinder

Hollow Central Piston Rod

TOP VIEW Torque Loading

Cylinder—51

tt £

•4

#2

^

N A Square Hole for Center Shaft

m

n

"

-

"

-

^

Vertical Load Cell

^ y~—Vertical Loading ,,/ Cylinder J l ^ ^ C a Cable ble _ ^ j _ p p

#1

# 3

^—'

^

Torque Load Cell

'

==•

FIG. 4—Schematic diagram i>j loading system for torsion shear apparatus.

stainless steel cable. This cable extends through the hollow central piston rod in the pressure cylinder and is fastened to the lower end of the piston rod, as seen in the upper part of Fig. 4. Using a long, thin cable for the load transfer ensures that the vertical loading mechanism does not induce a moment. Torque The torque is applied to the center shaft, as seen in the lower part of Fig. 4. A torque arm with two branches is mounted on the center shaft just above the vertical load cell. This part of the center shaft has a square cross section that fits in a square hole in the torque arm. This construction enables the transfer of the moment from the torque arm to the center shaft. Four oil-filled Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

154


pressure cylinders supply the horizontal loads through cables to the torque arm, the ends of which have circular shapes, as seen in the lower part of Fig. 4. The distances from the center to the ends of the torque arm are consequently maintained constant at 14.0 cm when the center shaft with the torque arm is rotated. The arrangement of the four pressure cylinders makes it possible to apply torsional shear stresses in both the clockwise and the counterclockwise directions. Opposite pressure cylinders are interconnected (No. 1 with No. 2, and No. 3 with No. 4), so that the torque arm is symmetrically loaded. This ensures that no horizontal load is applied to the linear and rotary ball bearing, which guides the center shaft. Vertical deformations of the hollow cylinder specimen will cause the torque arm to move vertically and could result in changes in the vertical load applied to the specimen. However, long cables are used to connect the pressure cylinders to the torque arm, so that the angles between the cables and the horizontal loading plane are small, and the induced vertical load is thereby made negligibly small. The four pressure cylinders are mounted outside the cabinet to make the distances from the pressure cylinders to the torque arm as long as possible. The torsional load applied to the specimen is measured by four load cells attached to the piston rod of each cylinder. Their position is seen in the lower part of Fig. 4. Stress and Strain Control The pressures for confinement of the specimen, torque, and vertical load are obtained from air pressure. Both the vertical load and the torque can be either stress or strain controlled. A schematic diagram of the stress and strain control system is shown in Fig. 5. The principle of the strain control regulators, which are used on the oil lines to the vertical loading cylinder and to the torque loading cylinders, is shown in the lower part of Fig. 5. A differential flow controller maintains a pressure drop of 3 psi (0.2 kgf/cm^ = 20 kPa) across a needle valve. A feedback line from the top of the controller is connected to the upstream side of the needle valve. The pressure drop is determined by a spring-loaded diaphragm in the controller, and is independent of the pressures in the upstream and the downstream parts of the oil line. In order for the strain control regulator to work properly, it is required that the pressure difference between the two parts of the oil line be at least 3 psi (0.2 kgf/cm^ = 20 kPa). For strain-controlled tests, the needle valve is used to regulate the rate at which oil flows through the strain control regulator. A nondisplacement shut-off valve and a strain-control regulator are installed in parallel in each of the oil lines, as seen in the upper part of Fig. 5. The shut-off valve is closed when strain-controlled loading is desired, and the strain rate is regulated by the needle valve. When stress-controlled loading is



To Chamber

To Vertical Loading Cylinder

To Clockwise Torque Loading Cylinders

155

To Counter -Clockwise Torque Loading Cylinders

' — A i r Pressure Su pply

Strain Control Regulator

>

I T d^:=)-*^ => - 4 \

^—Flow Controller *— Needle Valve D i r e c t i o n of Flow

FIG. 5—Schematic diagram of stress and strain control system.

desired, the shut-off valve is opened, the needle valve is closed, and air pressure is used to control the load. All air pressure lines are connected through a selector valve to a manometer so that each air pressure can be measured as desired. The oil lines to the torque loading cylinders are connected to an oil pressure manometer. The difference between the pressures in the oil line upstream and downstream from the strain control regulator can therefore be monitored and kept above 3 psi (0.2 kgf/cm^ = 20 kPa).

Counterbalance System In order to counterbalance the weights of the parts that are attached to the force-transmitting shaft, such as the cap plate, top ring, torque arm, load cell, and the center shaft itself, a spring is placed between the top plate of the vertical cylinder and the vertical load cell (Fig. 4). The spring is chosen with a Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

156


suitable spring constant to balance the excess weights before the test is started.

Maximum Stresses In order to keep the equipment to a reasonable size and cost the tests were conducted at relatively low stresses. The maximum stresses which can be applied to the specimen are limited by the strength of the Lucite cell wall and the performance of the torque arm. The maximum cell pressure used in any test to date is 400 kPa (4.0 kgf/ cm^). The vertical load cell fastened to the lower end of the center shaft is designed for a maximum load of 1000 kgf corresponding to a deviator stress of 800 kPa (8.0 kgf/cm^). The torque load cells are designed for a maximum load of 5(X) kgf each, resulting in a maximum load of 10(X) kgf in one direction, corresponding to a shear stress of 8(X) kPa (8.0 kgf/cm^).

Maximum Strains The maximum vertical deformation of the hollow cylinder specimen is limited by the maximum stroke in the vertical pressure cylinder. This movement cannot exceed approximately 3.0 cm. The 40.0-cm-tall specimen can therefore be compressed vertically about 7.5 percent. The maximum shear deformation of the specimen is limited by the maximum stroke of the pistons in the horizontal pressure cylinders. Since this stroke is approximately 5.0 cm, the maximum shear strain that can be applied to the specimen is about 12 percent.

Defonnation Measurements Vertical and Shear Deformations Both the vertical and the shear deformations are measured with linear motion transducers outside the cell. A 0.64-cm (0.25-in.) stainless steel rod is installed centrally in a socket in a small beam on top of the cap plate (Fig. 1). The rod sticks out through ball bushings encased in the top plate and sealed with an 0-ring below the ball bushings. The coil of the vertical linear motion transducer is mounted solidly directly above the rod (Fig. 1). The rod is connected with the core in the transducer, which registers the vertical deformations. A horizontal arm is mounted on the rod outside the cell. The arm, which rotates with the cap ring, has a circular section with a groove (Fig. 1). The shear deformation transducer is mounted on one of the rods on top of the cell. The transducer is pointed tangentially to the grooved circular section of the arm. The core is connected with an unstretchable radio dial cord to the



157

arm, so that the cord will track in the groove as shear deformations are registered by the linear motion transducer. In order to ensure a steady movement of the core and to measure shear strains during unloading and reverse loading, a string is fastened to the opposite end of the core and provided with a small weight. The string is carried over a pulley behind the transducer, and the weight keeps the string stretched, thus avoiding jumps, and pulls the core back during unloading and reverse loading. The complete setup can be seen in Fig. 6. A grid consisting of appropriately spaced vertical and horizontal lines is drawn on the outside surface of the membrane (Fig. 2), in order that the uniformity of the shear strains can be observed during and after testing.

FIG. 6—Fully assembled upparuius.


158


Horizontal Deformations The horizontal deformations of the specimen are measured with clip gages. These consist of pieces of beryllium copper band on which strain gages are glued. Beryllium copper is chosen because it has a linear stress-strain relationship. A pair of clip gages measures the change in thickness of the specimen wall. The gages clip on the wall with one leg sticking inside the specimen through holes in the cap plate (Fig. 3). Each of the clip gages is made of aluminium and shaped as a narrow U with the leg sticking outside the specimen shorter than the inside leg. A beryllium copper strip is fixed to the short leg, which makes the total length of the two legs equal. Four strain gages are glued to the beryllium copper strip near the fixed end. The four gages are connected in a full bridge. The beryllium copper strip is much more flexible than the rigid aluminium frame, so that most of the bending of the clip gage due to change in wall thickness is concentrated at the strain gages on the strip. A single clip gage measures the change in the outside diameter of the specimen. This gage is made entirely of beryllium copper band, which is shaped as a half ring according to its position around the specimen. The tips of the gage clip onto the outside surface of the specimen at midheight points 180 deg apart. Four strain gages are mounted on the middle section, two on the inside and two on the outside surface. The strain gages are connected to form a full bridge. Since the tips of this horizontal clip gage barely hang on to the specimen, it is necessary to support the middle portion of the gage. A gallows, which stands on the bottom plate, is provided with a piece of copper wire in which the middle portion of the clip gage hangs. From each of the three full bridges a cable with four wires for measurement is led out of the cell through a watertight fitting in the bottom plate. The clip gages are consequently tied permanently to the bottom plate of the cell. The strain gages and the wires are thoroughly waterproofed. Each of the U-shaped clip gages measures the change in wall thickness, and the horizontal strains in the radial direction can be calculated directly from these measurements. The horizontal strains in the tangential direction can be calculated from the measurements of all the clip gages by At -

^D

A€h, -

(1)

where Af = change in thickness of the specimen wall, AD = change in outside diameter of the specimen, and D„ = average diameter of the specimen ( = 20.0 cm).



159

Volumetric Deformations The volume change of the specimen, which is saturated with water, is measured with the volume change device designed by Chan and Duncan [4]. Correlation between Linear and Volumetric Strains Since three perpendicular normal strains are measured, the volume change measurement provides a check on the performance of the clip gages through the following relation, which is valid for small strains. fv =

fvert +

fht +

fhr

(2)

Slight amounts of bulging of the outside surface of the specimen in the horizontal, radial direction were noticed after most tests. The value of At measured with the clip gages was therefore too high and Eq 2 was not satisfied in general. Since the bulging affects the measurements of At and AD equally, the calculated value of e^t is considered to be reasonably correct. To improve the accuracy of the measurements, average values of e^^ were calculated from Eq 2 knowing e,,, e^^^, and £|,t.

Corrections Corrections to Stresses The vertical load and the torque are corrected for the load carried by the membrane. The membrane load is calculated by using Hooke's law and the elastic modulus [approximately 1400 kPa (14.5 kgf/cm^)] and Poisson's ratio ( = 0.5) for the latex rubber. In addition to the corrections due to membrane load, the vertical load measured with the load cell is corrected for the effects of cell pressure on the center shaft and the stiffness of the counter balance spring. A calibration curve relating the spring load and the instantaneous height of the specimen is established. Thus the spring load can be calculated from the specimen height measured during the test. Because the specimen is relatively tall (40 cm), the vertical stress is calculated at midheight. Thus half of the specimen weight is included in the vertical force correction. Corrections to Strains Corrections to the measured deformations were found to be negligible.


160


Preparation of Test Setup The membrane is fitted around the base ring, and the holes for drainage lines and screws are marked and punched in the bottom of the membrane. The surface of the base ring, which faces the specimen, is coated with a layer of epoxy and pressed down in sand of the type being tested. The base ring is then placed in the bottom of the membrane and put in place on the bottom plate, so that the drainage lines fit in their respective holes. The base ring is fastened with three screws to the bottom plate, thereby sealing the membrane and the drainage lines. The total height of the top ring and the base ring with the full friction surface is measured. The forming jackets are placed, and the membrane is stretched up through and around the forming jackets. The outside part of the membrane is held in place with an 0-ring around the outside forming jacket, to which a vacuum is applied. A sieve, which fits inside the forming jackets, is put in place and a measured quantity of air-dry sand is poured inside the sieve. The sieve is lifted slowly out of the forming jackets, and the sand is deposited through the sieve in a loose state. The sand is deposited to overheight and, with the cap ring placed on top of the sand deposit, the forming jackets and the cap ring are vibrated until the desired density of the sand is obtained. The top surface is leveled, and the cap ring coated with a layer of epoxy is placed on top of the specimen. The rubber membranes are pulled up around the cap ring and sealed with 0-rings. The top drainage lines are then connected to the cap ring, and a vacuum [ ~ 30 kPa (0.3 kgf/cm^)j is applied to the specimen through a bubble chamber in order to be able to detect leaks. After removing the forming jackets, the dimensions of the specimen are measured and the void ratio of the specimen is calculated. If a leak is detected, the specimen is painted with layers of rubber latex until the leak is repaired. Each layer of rubber latex is allowed to dry before the next layer is applied. A grid consisting of appropriately spaced vertical and horizontal lines is drawn on the outside surface of the membrane. After the specimen is prepared, the cap plate and the washer are placed on the center shaft and fastened with a screw. The cap plate is then pushed down to contact with the cap ring and fastened with three screws. The large clip gage is installed, with its ends at points 180 deg apart on the outside surface of the specimen, and its middle portion suspended in a copper wire from a gallows. The gages, which measure the change in thickness of the specimen wall, are installed with one leg sticking through holes in the cap plate and clipping on the wall at midheight of the specimen. Gallows and copper wire are also used to support these clip gages. The small beam with the small center rod is fastened to the top of the cap plate, and the cell wall and the top plate are put in place and fastened with six tie-rods to the bottom plate. The linear motion transducers sitting on top of the cell are installed and connected to the small center rod sticking out through the top plate. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


161

The cell is filled with water and a confining pressure is applied simultaneously with the release of the vacuum in the specimen. The air-dry sand specimen is saturated with water employing the CO2method described in detail in Refs 5 and 6. Influence of Specimen Height The tangential, horizontal normal stress in the cylinder wall {aj is the only stress which is not measured in the torsion shear apparatus. The value of a,. may be assumed to be equal to the cell pressure during isotropic compression. However, due to end restraint, a^ is unknown when shear stresses are applied to the specimen. In previous studies of torsion shear tests on 5-cmhigh specimens, it was shown thatCTîs nonuniform along the height of the specimen [2] and that the values of (ff^r.average/ffceii) ^t failure were about 2.7 and 1.8 for dense and loose Monterey No. 0 Sand, respectively [/]. Using the apparatus described here, two series of tests were performed on specimens of loose Santa Monica Beach Sand with heights of 10 cm and 40 cm. No vertical deviator stress was used in these tests, and failure was produced by applying torsional shear stresses. If it is assumed that the end restraint has negligible effect on the average behavior of the 40-cm-tall specimens, so that a^ = tJceii' then the calculated friction angles compare very favorably with those obtained from corresponding cubical triaxial tests on the same sand. Using the friction angles from the 40-cm-tall specimens together with the stresses measured in the 10-cm-tall specimens, the unknown values of a^ at failure may be calculated for the latter specimens. Figure 7 shows values of (Â.average/ Values of Ocell ' "^ k g f / c m ^ ) aie Indicated at the Data Points

re

D

Average Dianietei = 20 cm Wall Thickness = 2cm I

I 10

1 20

S p e c i m e n Height

FIG. 7—Effects

1 3D

40

(cm)

of end restraint in torsion shear tests on hollow cylinder specimens.

below the table which holds the cell. A variety of initial stress conditions may be used, and because both clockwise and counterclockwise shear stresses can be applied to the specimen, the behavior of soils during large stress reversals, as well as reorientation of principal stresses, may be investigated. The apparatus fulfills all the stated requirements, and a study of the influence of end restraint indicates that the specimen dimensions are such that fairly uniform stress states are achieved. Acknowledgments The tests on Santa Monica Beach Sand were performed by Elisha Geiger of the School of Engineering and Applied Science at the University of California at Los Angeles. The torsion shear apparatus presented here was constructed with support from the National Science Foundation under Grant No. ENG 75-05325. References [1] Lade, P. V. in Proceedings, 5th Pan-American Conference on Soil Mechanics and Foundations Engineering, Buenos Aires, 1975, Vol. I, pp. 117-127. [2] Lade, P. V. in Proceedings. Second International Conference on Numerical Methods in Geomechanics, Blaksburg, Va., 1976, Vol. 1, pp. 381-389; errata m Journal of the Geotechnicul Engineering Division. Proceedings of the American Society of Civil Engineers. Vol. 104, No. GTl, Jan. 1978, pp. 173-174. [3] Wright, D. K., Gilbert, P. A., and Saada, A. S. in Proceedings. American Society of Civil Engineers Speciality Conference on Earthquake Engineering and Soil Dynamics, Pasadena, Calif., 1978, Vol. 2, pp. 1056-1075.



163

[4] Chan, C. K. and Duncan, J. M., Materials Research and Standards. Vol. 7, No. 7, July 1967, pp. 312-314. [5] Lade, P. V. and Duncan, J. M., Journal of the Soil Mechanics and Foundations Division, Proceedings of the American Society of Civil Engineers, Vol. 99, No. SMIO, Oct. 1973, pp. 793-812. 161 Lade, P. V., Geotechnical Testing Journal. Vol. I, No. 2, June 1978, pp. 93-101.


K. T. Law^

A Servo System for Controlled Stress Path Tests

REFERENCE: Law, K. T., "A Servo System for Controlled Stress Path Tests," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 164-179. ABSTRACT: This paper describes a servo system capable of imposing a prescribed stress path tor the study of soil behavior in the laboratory. Various conditions were examined: (/) stress paths resembling those in the field, (2) both axisymmetric and plane strain shearing, and (J) large strain or post failure (or yield) state. The servo system is composed of two main parts: A minicomputer and an electricpneumatic (E/P) transducer. The minicomputer collects and processes data while the experiment is in progress. The appropriate electrical signals are transmitted to the E/P transducer, which regulates the pressure connected to the back-pressure line of the triaxial or plane strain apparatus. With the axial load applied at a constant strain rate, it is possible to measure the complete stress-strain behavior, including that at large strains, along a prescribed stress path. A series of tests was carried out to illustrate the capability of the servo system. For the particular case of slope stability analysis, another series of tests was conducted from which peak and post-peak strength envelopes were obtained. KEY WORDS: servo system, computerized soil tests, controlled stress paths, triaxial tests, plane strain tests, strength envelopes, peak, post peak

Prediction of soil behavior under load is an essential requirement of engineering design. One way to improve such prediction is to examine the behavior of the soil by various test methods that yield results applicable under field conditions. The stress path involved in shearing soils is an important factor influencing soil behavior and is receiving growing attention. A stress path, a line drawn through points on a stress plot, denotes the sequence of stress changes experienced by a soil element during the shearing process. Under field situations it starts from the point representing the in situ stress condition and proceeds to other points, as dictated by the type of structure being considered and the geometry and characteristics of the entire subsoil. The effects of stress path 'Research Officer, National Research Council of Canada, Ottawa, Ontario, Canada. 164 Copyright by Downloaded/printed Copyright 1981 University of


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LAW ON SERVO SYSTEM FOR STRESS PATH TESTS

165

were recognized as early as 1948 when Taylor [1]^ pointed out the likelihood of being able to obtain the correct strength by reconsolidating soil specimens in the laboratory to the in situ pressures. Bozozuk and Leonards [2] and Bjerrum [3] provided evidence that such reconsolidated specimens do yield more consistent information than unconsolidated ones for estimating soil behavior under the loading condition. Following reconsolidation, shearing along different stress paths produces varying effects on different aspects of soil behavior. The general experience [4-6] has been that stress paths do not greatly influence cohesion (c') or the angle of internal friction (4>'); on the other hand [7-9], they strongly affect the deformational characteristics. Based on the second observation, Lambe [10,11] formulated the stress path method for solving deformation problems. A number of methods have been used for shearing soils under a controlled stress path condition. Some have used the triaxial cell with minor modifications [12-14]. Others [15-17] have employed a special apparatus designed and built to test certain soil types. The above test equipment, however, permits only one mode of shearing; that is, incremental loading or controlled stress loading. It is not possible to shear soil specimens under a controlled strain rate condition as is required for study of rate effect and the post-peak stress-strain relation for a brittle soil. The equipment described in Ref 16 can impose constant strain rate shearing, but the control of stress path is lost. With computer technology it is now possible to build a system that is capable of controlling the stress path under controlled strain rate conditions in the shearing of soil specimens. Such a system is described herein.

Description of Apparatus Figure 1 is a schematic diagram of the complete apparatus. Basically it consists of a servo system and a loading cell (triaxial or plane strain). The servo system is composed of two main parts: a minicomputer and an electricpneumatic (E/P) transducer. Figure 2 shows a plane strain test conducted using the servo system.

Operation Principle The principle of operation of the servo system can be illustrated by means of a constant strain rate test conducted along the stress path represented by a fourth-degree polynomial: 4

P'=

E a„q"

(1)

H=0

^The italic numbers in brackets refer to the list of references appended to this paper.


166


VOLTAGE ji

DIVIDER

E f TRANSDUCEK

P MINI MAGNETIC

<j

3

"ri

a>

s"«

%J

^ x)

& •^

CS

?. co

,>! 1 II w u ô Ul j o:

oa

-0.2

0.2

RC

-

Ko^v,

Z

o

-0.1

N

s o I-

u

/

1

O.I /

0.0 0.0

1

1

1

0.1

0.2

0.3

1

ai

1

1

OA

1

1

1

0.2

0.3

0.4

EFFECTIVE VERTICAL STRESS, 7 ,

0.5

1

'

0.5 (kg/cm>)

FIG. 6—Results of lateral stress measurements during 15 consolidation tests at 3 vertical stresses — Gulf of Mexico clay.


202


0.0

0.0

0.1

a2

0.3

0.4

as

? V

EFFECTIVE VERTICAL STRESS, 7^ (kg/cm^) FIG. 7—Results of lateral stress measurements during 5 consolidation tests at 3 vertical stresses — Gulf of Alaska clay.

for the Gulf of Mexico clay, and ff/,' = 0.536 CT„

0.034

(3)

for the Gulf of Alaska clay. Equations 2 and 3 are the result of 15 and 5 consolidation tests, respectively. Up to this point, the stress applied vertically to the soil specimen by the top cap and the porous stone has been ignored. This stress is 0.018 kg/cm^, and therefore the true vertical stress at each consolidation increment is 0.138, 0.258 and 0.518 kg/cm^. The true vertical stresses on the specimen and the slope of the /Co-line have been defined, and since KQ is assumed to be linear from zero stress conditions [8], the origin of the /Co-plot (a^ and a^ equal to zero) is defined as the intersection of these two knowns. This is seen as the unprimed axes in Figs. 6 and 7 for each clay.


DYVIK ET AL ON LATERAL STRESS MEASUREMENTS

203

Lateral stress readings have been attempted using a membrane reading of zero before it is mounted over the specimen. This procedure led to unsatisfactory results primarily due to (1) the subsequent expansion of the membrane necessary to install it over the specimen, (2) incomplete specimen seating against the membrane, (3) the change between dry air and a saturated sample in the membrane, (4) the need to maintain a slight hydrostatic head (necessary to keep the specimen saturated during a test), and (5) stress conditions such that the straight line portions of the membrane calibration curves cannot be used (as discussed previously). There was also some question as to whether /Co-conditions existed when the only vertical load was the top cap. To check this, the change in lateral stresses corresponding to a a^ of 0.24 and 0.5 kg/cm^ (the last two consolidation stresses) were calculated with the measured lateral stress at the end of the first consolidation stress, 0.12 kg/cm^, taken as zero. The slope of the resulting Kg-line was identical to the slope for all three stress levels (shown in Figs. 6 and 7), thus indicating /fo'Conditions. Indirect Measurements of Kg Several different semi-empirical equations for the determination of KQ have been proposed. Jaky has proposed the following equation based on the drained friction angle of the soil [9]: Ko = 0.95 - sin IN.

0.010

FIG. 6—Radial pressure—deformalwn relationship for CH soil II in. = 25.4 mm. I psi 6.9 kPa). TABLE 2—Summary o) hollow-cylinder tensile test results at failure.

Material Type

Water Content (W), %

Dry Density (7do). P'^f"

Inner Pressure (P,). psi''

Outer Pressure (P„). psi''

CL-1 CL-2 CL-3 CH-1 CH-2 CH-3 SC-1 SC-2 SC-3 CH-4 CH-5 CH-6

15.4 16.4 16.0 21.2 21.3 21.6 13.S 13.5 13.5 21.0 21.1 21.5

99.8 99.9 99.7 89.8 91.8 95.2 108.7 108.5 109.9 85.8 86.3 86.4

1.6 5.2 8.3 4.3 7.1 10.5 3.2 6.0 8.6 3.5 6.4 9.7

0 2 4 0 2 4 0 2 4 0 2 4

Tensile Stress, psi'' *f max

4.17 6.09 7.00 11.0 10.90 12.44 8.09 8.12 7.76 8.85 9.25 10.54

•^t max

2.52 2.89 2.65 6.65 5.80 5.94 4.89 4.12 3.11 5.35 4.80 4.79

îm

2.95 3.90 3.93 7.93 7.41 7.99 5.90 5.38 4.49 6.46 6.12 6.52

"1 pcf = 1 6 k g / m \ ''1 psi = 6.9 kPa. 'Calculated using r = r, in Eq 2. ''Calculated using r = r„ in Eq 2. ''Calculated using r = (2/3) [(r,,-" - r/)/(/-„2 - r,2)] in Eq 8.


AL-HUSSAINI ON TENSILE PROPERTIES OF COMPACTED SOILS

Po

4PS/~v^

^ P c

^

2 PS/

0

Po

0.001 0.002 0.003 0.004 DEFORMATION OF INNER RADIUS U;, IN

p3

217

0,005

4 PS/ ^

- Po

• Po

2 Pi

0

T O.OOI 0.002 0.003 0004 0.006 DEFORMATION OF OUTER RADIUS U Q , IN.

FIG. 7—Radial pressure—deformation relationship for SC soil II in. — 25.4 mm. I psi — 6.9 kPa).

shows that E decreased with increasing /*,, which reflects the nonUnear behavior of the soil tested. However, v varied within a very small range for each soil, and its average values were 0.20, 0.49, and 0.28 for the CL, CH, and SC materials, respectively. The interpretation of E and v for tests in which P„ equals 13.8 and 27.6 kPa (2.0 and 4.0 psi) is more difficult, since tangential stresses at the beginning of the tests were compressional and changed gradually to tensile stresses with an increase of P, over P„. Therefore values of E and v for these tests reflect both the compressive and tensile behavior of the soil tested. More complication with interpretation of the results is added by the fact that creep or viscoelastic behavior of the soil becomes more pronounced with an increasing stress level. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

218


FIG. %—Typical failure of hollow cylinder in tension test.

Unconfined Compression Tests Unconfined compression tests were conducted on 71.1-mm (2.8-in.) diameter specimens in addition to the tension tests in order to provide comparisons between soil parameters obtained from tension and compression testing. A standard triaxial compression cell with enlarged low-friction end platens was used for these tests. Direct measurement of radial deformation of the specimen was made during the tests using a lateral strain deformation sensor consisting of an LVDT attached to the specimen by a circumferential clamp at midheight of the specimen. Another LVDT attached to the loading



219

NNER PRESSURE P., PSI

FIG. 9—Variation of E with respect to P, for hollow cylinder test (I psi = 6.9 kPa).

piston was used to measure the axial deformation of the soil specimen. These two LVDTs enabled the measurement of the elastic parameters of the material tested (see Fig. 10). Unconfined compression stress-strain curves for the CL, CH, and SC materials (not shown for brevity) were used for determining the unconfined compressive strengths (SJ as well as the elastic constants under compression. The modulus of elasticity (E) was approximated by the initial slope of the stress-strain curve, while Poisson's ratio (v) was approximated by the ratio of the lateral strain (€3) to the axial strain (ei) for the linear portion of the stress-strain curve. A summary of the unconfined compression test data is presented in Table 3. Indirect Tension Test Apparatus The indirect tension test apparatus (Fig. 11) is used to test a cylindrical specimen 101.6 mm (4 in.) in diameter and 114.2 mm (4.5 in.) in height placed between the loading platen and the base. The base is made of a 457.2 mm (18 in.) long by 228.6 mm (9 in.) wide by 25.4 mm (1.0 in.) thick aluminum plate. Two stainless steel guide posts, 19 mm (0.75 in.) in diameter and 30.5 mm (12 in.) in height, are used to allow aligning the vertical movement of the top loading platen with respect to the base without allowing tilting. The top loading platen is made of a 457.2 mm (18 in.) long by 152 mm (6 in.) wide by 25.4 mm (1.0 in.) thick aluminum plate, and is provided with linear ball bushings to reduce friction along the guide posts. Axial


220


FIG. 10—Unconfined compression test assembly.

TABLE 3—Summary of unconfined compression test results at failure. NOTE—1 in. = 25.4 mm, 1 psi = 6.9 kPa, and 1 pcf = 16 kg/m^.

Average Material Type CL-1 CL-2 CH-1 CH-2 SC-1 SC-2

Water Dry Content Density (VK), % (7dry)- pcf 16.0 15.7 22.0 22.4 13.9 13.9

102.0 103.4 90.7 91.7 114.6 111.9

Height in.

Diameter,

6.32 6.31 6.32 6.31 6.32 6.32

2.83 2.82 2.83 2.83 2.84 2.82

in.

Unconfined Compressive Initial Poisson's Strength Modulus Ratio (5^.), psi (£;), psi M 22.22 22.04 22.44 23.78 20.40 21.20

3600 3400 3200 3200 3600 3000

0.24 0.24 0.30 0.20 0.32 0.28

diametric load is applied to the specimen through two curved aluminum loading strips, 12.7 mm (0.5 in.) wide and 152 mm (6 in.) long, attached to the top loading platen and the base. These strips are used to distribute the applied load on an area 12.7 mm (0.5 in.) wide along the loaded surface of the specimen.



221

FIG. 11—Indirect tensile test apparatus.

A load cell and LVDT that can be connected to the loading platen are used for measuring and recording the applied axial load and the change in the vertical diameter of the specimen, respectively. The change in the transverse diameter is measured by using a cantilever arm system. This system consists of two cantilever arms instrumented with strain gages that read to the nearest 0.025 mm (0.001 in.). The free end of each cantilever is placed in contact with the soil specimen along its transverse diameter while the fixed ends are attached to the cantilever block adjustable block (Fig. 11). All deformations and load measurements are recorded simultaneously on a strip-chart recorder (not shown) and can be observed on a digital readout system. Indirect Tension Test Procedure and Results The material was first compacted to 95 percent of Standard Proctor density, in accordance with ASTM Methods for Moisture-Density Relations of


222


Soils and Soil-Aggregate Mixtures Using 5.5-lb (2.49-kg) Rammer and 12-in. (305-mm) Drop (D 698-78) except that a sliding-weight rammer was used, and at a water content close to the optimum. Soil specimens were compacted, trimmed, extruded from the mold, and then measured accurately prior to testing. Each specimen was centered between the loading strips. The cantilever arms of the lateral sensors were brought in contact with the specimen, and the LVDT for measuring the vertical deformation was set in its proper position (Fig. 11). Vertical load was then applied to the specimen at a constant rate of strain. Simultaneous measurements of the axial load and diametric deformations in the axial and lateral directions were recorded on a strip-chart recorder. The tensile strength (j^) at failure may be expressed as IP irna where d ~ diameter of the specimen, P = load applied to the loading strip, and h = length of the specimen. Duplicate indirect tension tests were conducted on each soil to assure the validity of the test data; a summary of tensile strength for the material tested is shown in Table 4. Discussion of Test Results Tensile strength obtained from the hollow-cylinder and indirect tension tests are summarized in Tables 2 and 4, respectively; the compressive strength obtained from the unconfined compressive strength is presented in Table 3. Because of the difference in the initial density, water content, and TABLE 4—Summary of indirect tensile test results at failure. NOTE—1 in. = 25.4 mm, 1 psi = 6.9 kPa, and 1 pcf = 16 kg/m^.

Average Diameter W), in.

Tensile Strength

(Tdry)' P' for peat or muskeg (43.5 and 48 deg, respectively) reported by Hanrahan et al [8] and Adams [9] is high compared with inorganic soils. There is a lack of information on the use of these '-values ranging from 20 deg for kaolinite up to 80-f- deg for all fiber samples. 7. A failure criterion, based on the maximum ratio of shear stress to effective normal stress (maximum obliquity), gave '-values intermediate to the (CIU) and CID test values for high organic content soils. This criterion avoids the problem of the minor principal effective stress going to zero for the (CIU) test at axial strains of 15 percent or more. For all fiber samples this criterion gave 4>' equal to 39 deg compared with 80+ and 31 deg for the CIU and CID tests, respectively. Acknowledgments This study was supported by National Science Foundation Grant No. ENG75-13765 and by the Division of Engineering Research, Michigan State University. The kaolinite and pulp fiber were provided by the National Council of the Paper Industry For Air and Stream Improvement, Inc. Their support is gratefully acknowledged. References [/] Terzaghi, Karl and Peck, R. B., Soil Mechanics in Engineering Practice. 2nd ed., John Wiley & Sons, New York, 1967. [2] Arman, Ara, "Engineering Classification of Organic Soils," Highway Research Record, No. 310, National Academy of Sciences-National Academy of Engineering, Washington, D.C., 1970, pp. 75-89. 1.?] Franklin, A. G., Orozeo, L. F., and Semray, R., Journal of the Soil Mechanics and Foundations Division. American Society of Civil Engineers, Vol. 99, No. SM7, 1973, pp. 541-557. [4] MacFarlane, I. C. in Muskeg Engineering Handbook. Ch. 4, I. C. MacFarlane, Ed., University of Toronto Press, Canada, 1969. [5] Al-Khafaji, A. W. N., "Decomposition Effects on Engineering Properties of Fibrous Organic Soils," unpublished PhD. thesis, Michigan State University. E. Lansing, Mich., 1979. 16] Radforth, N. W. in Muskeg Engineering Handbook. Ch. 2, I. C. MacFarlane, Ed., University of Toronto Press, Canada, l%9. [7] Hanrahan, E. T., and Walsh, J. A. in Proceedings. 6th International Conference on Soil Mechanics and Foundation Engineering, University of Toronto Press, Canada, 1965. pp. 226-230. [8] Hanrahan, E. T., Dunne, J. M., and Sodha, V. G. in Proceedings. Geotechnical Conference, Norwegian Geotechnical Institute, Oslo, Norway, 1967, pp. 193-198. [9] Adams, J. I., in Proceedings. 6th International Conference on Soil Mechanics and Foundation Engineering, University of Toronto Press, Canada, 1965, pp. 3-7.


242


1/0] "Fiber Length of Pulp by Classification, Suggested Method T233 su-64," Technical Association of the Pulp and Paper Industry (TAPPI), Atlanta, Ga., 1964. 1//) "Instruction Manual of Perkin-Elmer Shell Model 212B Sorptometer," Instrument Divi sion, Perkin-Elmer Corporation, Norwalk, Conn., 1961. [12] Bishop, A. W. and Henkel, D. J., The Measurement of Soil Properties in the Triaxial Test 2nd ed., Edward Arnold, London, 1962. [13] Khattak, A. S., "Mechanical Behavior of Fibrous Organic Soils," unpublished PhD thesis, Michigan State University, E. Lansing, Mich., 1978. [14] Lambe, T. in Proceedings. Research Conference on Shear Strength of Cohesive Soils American Society of Civil Engineering, Boulder, Colo., 1960, pp. 555-580. [15] Lambe, T. W. and Whitman, R. V., Soil Mechanics, John Wiley & Sons, New York, 1969, [16] Charlie, W. A., "Two Cut Slopes in Fibrous Organic Soils, Behavior and Analyses," un published PhD. thesis, Michigan State University, E. Lansing, Mich., 1975. [17] Jankowski, W., "Peat Bogs as Building Sites," Polish Technical Abstracts. Vol. 1, No. 17, 1955.


R. Y. K. Cheng'

Effect of Shearing Strain-Rate on the Undrained Strength of Clay

REFERENCE: Cheng, R. Y. K., "Effect of Shearing Strain-Rate on the Undiataied Strength of Clay," Laboratory Shear Strength of Soil. ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 243-253. ABSTRACT; Dynamic testing method is required to determine the strength of soils for problems of dynamic loading. This paper presents an experimental technique for measuring the relationship of undrained shear strength and strain-rate of a clay. Torsion tests were performed on remolded hollow cylinder specimens. The test results show that the undrained shear strength increases initially with strain-rate from the static undrained strength, but subsequently the undrained strength reaches an ultimate value as the strain-rate increases. KEY WORDS: soil shearing strain rate, soil shear strength, dynamic soil testing

The shear stress and strain-rate relationship of soils is required to study problems involving loading. Some of these problems are those related to ground mobility, landing of aircraft on unpaved clay fields, tillage, rapid excavation of soils, and penetration of projectiles into soils. This paper presents a procedure for measuring the undrained strength of a clay specimen subjected to various straining rates. The results of the test give the relationship of the undrained strength and strain-rate of the clay. Torsion Test on Hollow Cylinder The experimental procedure herein [/]^ uses a hollow cylindrical specimen. A state of pure shear is induced in the specimen by rotating one end of the specimen at a constant rate. As this specimen will be deformed beyond its elastic limit, and as the wall of the specimen is relatively thin, the shearing stress across the wall is considered to be uniform. Geuze and Tan [2] and ' Professor of Civil Engineering, Old Dominion University, Norfolk, Va. 23508. ^The italic numbers in brackets refer to the list of references appended to this paper. 243 Copyright by Downloaded/printed Copyright"^ 1981 University of


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Saada and Ou [3] used hollow cylindrical specimens in their investigations of the stress-strain relations of soils. The state of stress of a hollow cylinder in torsion about the z-axis is shown in Fig. 1. The stress distribution in a hollow cylinder due to an applied torque is well established [4] for the case where the elastic limit of the material is not exceeded. Beyond the elastic limit and into the plastic range, the shear stress is considered to be constant radially across the wall of specimen (Fig. Ic). Considering the equilibrium condition that the external torque is equal to the internal twisting moment, as a result of the shear stress, yields T=\T„jdA

(1)

A

Imposing the boundary conditions with R\ and Rj as the inside and outside radius, respectively, the shear stress is related to the torque as

2x

(/?2^-/?,3)

(2)

where T„, is the ultimate undrained shear stress and T is the maximum torque. Referring to Fig. la, the shearing strain, y, is related to the angle of rotation, 0, at the top of the specimen by

Re tan where h is the specimen height and R is the mean of Rj and /?2. Taking the time derivative of y yields

h^ + RH^ J dt where 7 is the shearing strain-rate. For small values of 6, the second term in the denominator on the righthand side of Eq 3 may be neglected and the strain-rate expressed by

Torsion Apparatus Figures 2 and 3 show the torsion apparatus. The flywheel, weighing 356 N, is supported by a shaft which can rotate and move vertically. The flywheel is


CHENG ON EFFECT OF SHEARING STRAIN-RATE ON CLAY

245

(b) Stresses On Element

(c) Stress Distribution At Maximum Torque FIG. 1—Reference axes and stresses.

driven by an air jet, and the rate of rotation is measured by a magnetic counter. At the lower end of the flywheel shaft, a spring-loaded clutch can engage the flywheel to the torsional shaft, thereby applying an instantaneous rotation on the specimen in the triaxial chamber at the same rate of rotation as the flywheel. The rate of rotation of the specimen is also measured by a magnetic counter. A standard triaxial chamber was modified to contain the specimen. The specimen was held firmly at the base, and the top of the specimen was connected to the torsional shaft, which had to be fitted precisely to the chamber housing of the triaxial cell. This tight fit, which is required to contain the hydrostatic pressure in the chamber, develops substantial friction between the chamber housing and the shaft. To eliminate the effect of the friction, the torque transducer is mounted between the shaft and the top of the specimen plate.


246


A, B. C. D. E. F.

Turbine Flywheel Clutch Assembly Torsion Shaft Coupler Triaxial Cell

G, H. I. J. K. L.

Torque Transducer Test Specimen Loading Plate Clutch Handle Magnetic Counter Linear Ball Bearings

FIG. 2—Torsion apparatus.

Sample Preparation Unit and Procedure Mississippi Buckshot clay was used for all tests. The liquid and plastic limits are 61 and 28 percent, respectively [5]. A test specimen was prepared by consolidating a clay slurry at water content of 80 percent in a mold. The slurry was prepared by mixing dry clay powder with distilled water, and the mixture was allowed to soak for 24 h. The consolidation mold (Fig. 4) consisted of a split cylinder forming the outside mold and a solid core cylinder forming the inside mold. The base of the mold also served as the base plate for the specimen, and the top of the mold served as the top loading plate for the specimen. The inside face of the split cylinder and the surface of the solid core cylinder were lined with paper cloth which acted as a filter during consolidation by radial flow. The vertical compression of the sample was achieved by applying a vertical force on the top cap through a rigid piston driven by a pneumatic jack. By gradually varying the vertical consolidation pressure for approximately 48 h, a hollow cylindrical specimen, with the top and bottom loading plates in place, was 100 percent consolidated and was



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!®?-=in5e-"-' * FIG. 4—Specimen mold.

ready for testing. Figure 5a shows a sample mounted on the base of the triaxial chamber with the torque transducer placed on the top loading plate. The horizontal wrinkle lines on the specimen were formed by the vertical movement of the paper cloth, but these lines did not influence the shearing resistance of the specimen. Figures 5b and 5c show various deformed shapes of the specimen after the tests. The sample used in this study was 7.62 cm high with inside and outside radii of 7.62 cm and 10.16 cm, respectively. The wall thickness was 1.27 cm. The water content of all the specimens varied from 30 to 34 percent, corresponding to dry unit weights from 14.6 to 13.7 kN/m^. The average water content of a specimen was determined at the end of test from nine samples by taking three samples each from the top, middle, and bottom of the specimens. Variation of water content in each specimen was ±1.2 percent. Testing Procedure All tests were conducted with no confining pressure. By regulating the nozzle pressure, the air turned the flywheel (Fig. 2) until it reached a steady rate of rotation indicated by signals from a magnetic pickup. The clutch was



249

FIG. 5a—Specimen be/ore testing.

rapidly engaged and the specimen was subjected to an instantaneous rotation with the same rate as that of the flywheel, since the mass ratio between the flywheel and specimen was 30 to 1. A typical test result is shown in Fig. 6. Electrical outputs from the transducer and magnetic pickups were recorded on a direct-write oscillograph. The top trace indicates the rotation of the flywheel. With 80 peaks per revolution, the rate was determined from the time pulse which was set at 0.1-s intervals. The next lower trace indicated the rotation at the top of the specimen. The trace which recorded the signal of the torque transducer gives the variation of the torque, and it was determined from the calibration signals shown by the horizontal lines recorded just before and after each test. The calibration signal represented a torque of 4.86 N-m. The torque recorded for each test included the shearing resistance of the specimen and the effects of the inertia of the transducer and top loading plate. The torque measured in test without the specimen was due to the effects of the inertia of the transducer and top loading plate. The shearing stress in the specimen was determined from the difference of the maximum torques measured with and without the specimen at the same rate of rotation of the top loading plate.


250


FIG. Sb—Low water-content specimen after testing.

Results and Analysis Since the variation of water content in each specimen was ±1.2 percent, the specimens ranging in water content from 30 to 34 percent were divided into four groups consisting of 1 percent increment of water content for each group from 30 to 34 percent. The undrained strength was determined using Eq 2 from maximum torque; the strain-rate was determined using Eq 4 from the rate of rotation of the flywheel. All test results indicated that maximum torque developed within a rotation of 0.15 rad/s. The test results plotted in Fig. 7 indicated that for each group of specimens, the undrained strength is bounded by an upper limit henceforth known as the ultimate dynamic strength, S„, which can be written as Sm = So + a

(5)

where S^ is the static undrained strength and a is the dynamic component of the ultimate dynamic strength. For strain-rate less than 15 rad/s for all tests performed, the relation between undrained strength, S, and strain-rate, y, without any confining pressure can be written as S = So + a(l-e'^y) Copyright Downloaded/printed University

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CHENG ON EFFECT OF SHEARING STRAIN-RATE ON CUY

251

FIG. 5c—High water-content specimen after testing.

FIG. b—Typical recorded time history {specimen water content at 30percent: shearing strainrate at 4.8 rad/s).


252


Specimen Water Content, % 30 < w < 31 31 < w < 32 32 < w < 33 33< w OCR"

w o u

• •0.42 TO 0.41 (K»>»e'O.S TO 0.93 1

0

2

3

4

9

6

7

8 9 n

OVEKCONSOLIDATION RATIO, 9v max / 7ve

(a) FROM SPECIAL OEDOMETER TEST

lj-factors from isotropically consolidated specimens became negative at OCRs greater than 8, while Af factors from /Co-consolidated specimens remained positive for OCRs even greater than 10. This difference in pore pressure behavior is significant and would have an important influence on predictions of pore pressures. Another important characteristic related to pore pressure generation during shear is the fact that the specimens tested in C/iToU-compression showed a large increase in positive excess pore pressure after the peak deviator stress was reached. This observation could be very important in the prediction of pore pressures in a foundation when a limited yielded zone develops as can occur at high factors of safety as described by D'Appolonia et al [25].

Undrained Moduli Table 1 summarizes undrained Young's secant moduli at an incremental shear stress level of one half of the incremental shear stress required to reach failure. At corresponding overconsolidation ratios the secant moduli in compression are two to three times greater than the moduli in extension. This im-


KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE CLAY

o

I « 9\ 9

.T

> >»

B aj)^ It


336


The axial stress versus axial strain curves obtained under various values of confining pressure are related to a family of hyperbolas defined by five coefficients: modulus number, K\ modulus exponent, «; failure ratio [17], Rf\ and the two Mohr-Coulomb strength parameters: the cohesion intercept, c; and the friction angle, 4>- Thus, the tangent modulus, £ , , is given by Rf{\ — sin 4>){a\ — a^) E,

1 -

2c cos ''a)2 sin V3 (3 + sin )

(16c)

and _

6 c cos / v3 (3 + Sin 0)

Equations 15 and 16 clearly show that a proper definition of the coefficients a and it are required in order to perform realistic analyses. Normality is assumed so that, at yield, the incremental plastic stress-strain relationship can be written as 6,y'' = ^ | ^

(17)

where superscript p denotes the plastic component of the strain tensor e,, due to the increment in the stress tensor (T,,, and superdot denotes the increment (or rate). X is an arbitrary non-negative scalar parameter to be determined as a function of the strain rate tensor. The total strain rate e^, is the sum of the elastic and plastic components i/f and e,,''; that is. 'J iii = eif + ii/

(18)

The relation between the stress and elastic strain rate is given by Hooke's law as

where E is Young's modulus, v is Poisson's ratio, 6/, is the Kronecker delta. Combining Eqs 18 and 19, we obtain the relation between the stress rate and the total strain rate as a,-," = 1 + .;

..._xiÛ_J^r...-xJ/ ^tr. daj +Tî;A^^^-î^ 1 - 2v V ** da. h

(20)

Jkk

In order to determine X, we observe that during plastic loading the stresses must lie on the yield surface, / = 0, and furthermore, as the stress state changes, the yield surface must correspond to this change [6]: df


344


Since dJ doij

dan

I 2

ynÎm bay (21) -1/2 ,

Then, combining Eqs 20 and 21, we obtain

#=0=[ia6, + i / , , - . , ] ^ ('

£//

:

:

Si

+ 1 Ijv (^** ~ ^"/ ^''

(22)

X can be obtained from Eq 22 as X=

GJ2D ^'^Spqipg + B ikk G + ap

(23)

where 2(1 + ,)

(24)

and B =

2aG ( \ + V 1 - 2v

(25)

Thus, with X determined, the stress rate-strain rate relation can be obtained from Eqs 20 and 21 in terms of the current stress state. These incremental relations assume isotropic behavior and non-work-hardening perfect plasticity. Determination of Material Constants The elastic material constants appearing in the Drucker-Prager model (Eq 19) are Young's modulus E and Poisson's ratio v, which, of course, could be expressed in terms of the bulk modulus K and the shear modulus G. These moduli can be determined from the unloading curves from the isotropic consolidation and drained triaxial tests, respectively, conducted over the range of loading that is of interest. The constants, a and k, appearing in the yield function (Eq 14), can be determined from failure stress data, which usually are expressed in terms of c and 4> from which a and k can be calculated from Eqs 15 and 16.


KO AND STURE ON STATE OF THE ART

345

Limitations of Model Because the failure envelope, expressed in linear form in Eq 14, is also used as the plastic potential, the plastic volumetric strains predicted are usually much greater than those observed in laboratory tests. This contradicts the concept of critical void ratio, which represents the state reached at relatively large, plastic shear strains. In addition, because the failure envelope represented by Eq 14 does not cross the hydrostatic 7]-axis when plotted in principal stress space, the model does not predict the irreversible volumetric strains observed under isotropic consolidation of normally consolidated clays. As mentioned before, these limitations led to the development of the cap models, which will be described next. Cam-Clay Model The Cam-Clay model is a work-hardening plasticity model based on the work of Drucker et al [8], with two important points of difference. The first is the introduction of the concept of critical states corresponding to critical void ratio versus stress locus, proposed by Roscoe et al [22], which suggests that all shear tests on a soil will produce end conditions which lie on a critical state line in the space of p, q. and e (Fig. 6), which for the conditions of triaxial compression are defined as p=i:(ax-\-

02 + Oi) = -z(a\+2ai)

(26)

q = a^-

(27)

Gi

and e = void ratio where a represents effective stresses. Thus the Mohr-Coulomb envelope, or any other surface that has been used to connect failure stress data, is just a collection of such end points, and therefore is not a complete yield locus. It is the yield surface at ultimate strength. The second point of difference lies in the formulation of a basic energy dissipation expression in order to develop an equation for the yield surface. Roscoe et al [23] assumed that there is no recoverable component in the shear distortion of wet clay and derived the Cam-Clay model, which was described in detail by Schofield and Wroth [24]. The original Cam-Clay constitutive equations overpredicted the observed values of the strain increments at small shear stress levels. This was presumably due to the original assumption regarding zero recoverable shear strain. The original "bullet" shaped cap, moreover, predicted shear strains in isotropic compression. Burland [25] and Roscoe and Burland [9] have suggested a modified ver-


346


q=<j|-a3

Critical State Line 'In q-p Plane Critical State Line In Space Elastic Wall

Yield Surfaces In q - p Plane

Swelling Line

IMormol Consolidation in pê Plane

Critical State Line In p ~ e Plane

FIG. 6—State boundary surface in p-q-e space.

sion of the Cam-Clay model, which we will describe in the next section. Many other versions of the original and modified Cam-Clay models have been forwarded over the years. For the sake of brevity and simplicity we shall direct our attention to the first modified version. Description The Cam-Clay model developed for axially symmetric stress conditions on the basis of experimental observations in the "triaxial" compression tests can best be described in relation to a three-dimensional p-q-e (state boundary) space from which sections can be shown for further delineation. Based on isotropy, two components of strains are defined as v = ei + 2 63, and e — (2/3)(6| — €3). The isotrppic consolidation line in the e ~ Inp plane has a slope of —X analogous to the compression index C^, while the elastic rebound and reloading curve has a slope of — K analogous to the swelling index Cj (Fig. 7). For a soil in the virgin compression state, the irreversible volumetric strain rate from .4 to fi is given by vP =

(X - K) p \ + eo p

(28)

where eo is the void ratio corresponding to the current hydrostatic stress p, and p is the increment or rate. This stress fraction is the source for the natural logarithm mentioned earlier. The elastic volumetric strain recovered during rebound from B to C is Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


347

(29)

I + Co p

The plastic volumetric strain expression given in Eq 28 governs the change of the compaction state of the soil and controls the strain-hardening. Thus the soil had passed through a succession of yield surfaces from A to B. When a shear stress q is applied, a point can be plotted in p-q-e space representing the state of the sample. Therefore the state boundary surface represents the convergence of all state paths, and it separates the admissible and inadmissible state points. On this surface we find the critical state line representing the end points of the state paths, where no further change in the stress state or the void ratio of the soil will take place under continual, large shear strain. The projection of the critical state line on the p-q plane is linear and has the equation q — Mp

(30)

where M is the frictional constant, equal to 6 sin 7(3 — sin ') in triaxial compression and 6 sin 7(3 + sin 0') in triaxial extension. Subscripts C and E are often added to the coefficient M to characterize these respective conditions. The projection of the critical state line onto the e ~ \x\p plane is also a straight line parallel to the virgin compression curve, with equation e — Br

Xlnp

(31)

where e^ is the void ratio when p = 1. A soil is "wet" when its state corresponds to a point between the critical state line and the virgin compression curve, and will strain-harden when loaded in shear until it reaches critical state. "Wet" soils are therefore those that are normally or lightly overcon-

g^

A

^Normol

Consolidation Line

Critical - A . State Line ^ -AK

* \ *

\

'dry' \ w e t ' \ es

C

"

~" X — ^ ^ e-ei- Kin p

P'l

mp FIG. 7—Isotropic consolidation

and swelling

behavior.

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348


solidated. A soil is "dry" when its state corresponds to a point on the dense side of the critical state line. For a wet soil, the strain-hardening effects can be described in terms of a succession of yield surfaces. For the modified Cam-Clay model, Roscoe and Burland derived the following expression for the yield surface: 9

(32)

where po is the strain-hardening parameter or isotropic consolidation stress representing the hydrostatic pressure at the point where the rebound curve containing the projection of the state would intersection the virgin compression curve in e ~ \np plane. This, of course, is the same as the preconsolidation pressure, if no shear stress has been involved. Eq 32 represents an elliptical yield curve in the p — q plane, as shown in Fig. 8, where the critical state line intersects the ellipse at its maximum point. As the soil strainhardens, the strain-hardening parameter po increases by an amount po given by Eq 28 as

1+eo Po =

(33)

PovP

Compression (3|>02=CT3)

Yield Surfaces: Original Com - Cloy Modified Cam-Clay

Po

p= 1/3(01+253)

Extension (o, < ^3 • 03)

FIG. 8—Yield surfaces in Cam-Clay models.



349

where VP remains to be calculated by using an assumed associated flow rule in conjunction with the yield function in Eq 32. Thus the critical state line in p — q plane is not a yield locus in itself, but is the termination of yield loci where they have horizontal slopes, and therefore, under the normality rule, predicts zero plastic volumetric strain increment at critical state (that is, shearing at constant volume). With the aforementioned description of the yield function/ and the strain hardening parameter po. the strain increments due to any stress increment (,p,q) under an existing stress state (p,q) can be calculated as 1 1 + e

(X-/C)

2l/7j

M^ + r{^

(X-/C)

2T;7J

1 + e

M2 + r,2

e = iP

+ X^

(35)

+

2v

X- K

(34)

1 + e \ M 2 -

IJV

\M^

l-qi] + ^p + n^

(36)

where rj = q/p. In this version of the model the elastic shear strain ^ is assumed zero. More recent formulations include elastic shear strain where ^ = q/3G. Determination of Material Constants The four material constants appearing in the modified Cam-Clay model are easily determined from conventional triaxial tests. The constants X and K are the compression and swelling indices based on isotropic consolidation tests. If an isotropic consolidation test is used, the compression and swelling indices from that test, C^j and Q , can be used to compute X and K as X = Cei/2.303

(37)

K = Csi/2.303

(38)

where In 10 = 2.303. The elastic constants A^(bulk modulus), £'(Young's modulus), and G(shear modulus) can be determined from

K =

pa+ eo)

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^ 3p{l + eo)(l E =

2P)

^ ^ 3(1 - 2v) p 2(1 + v) K The frictional constant M can be determined by carrying out triaxial compression (Mc) or extension (ME) tests to ultimate loading. The ratio of q/p at ultimate loading when critical void ratio is reached is then equal to M. Such a test also provides the information necessary to calculate e^ defining the critical state line. Limitations of Model The modified Cam-Clay model in the form just described was originally developed for representing soil behavior under axially symmetrical, triaxial compression loading. The extension of the model to triaxial extension and plane strain loadings was described by Roscoe and Burland [9] and good agreement was obtained. In order to further extend this theory to truly threedimensional loading, it is necessary to replace the shear stress q in the triaxial case by \ ( ^ , where J2D is the second invariant of the deviatoric stress tensor. The modified Cam-Clay model was originally developed for "wet" clays that are normally or lightly overconsolidated, and which strain-harden, that is, contract in volume, when sheared. The model has not been successfully applied to heavily overconsolidated clays which strain-soften, and a large part of the reason for this lack of correlation between theory and experimental data is due to the heterogeneity in deformation developed during shearing of overconsolidated clays. The model performs best for clays that have initially experienced isotropic consolidation. A /Co-consolidation history frequently results in yield loci which seem to be centered on the A'o-line rather than the/j-axis. Such behavior can only be modeled by anisotropic hardening models.

Weidlinger C ^ Model Description A series of constitutive models with a capped yield surface has been developed for use in large finite element analysis codes for ground shock computations, as described by DiMaggio and Sandler [10], Sandler et al [26], Sandler and Baron [27], and Baladi and Rohani [28]. These models have also been applied in analyses of static problems. This particular cap



351

model concept, which is frequently termed the Weidlinger model after the company affiliation of the original developers, is in many respects quite different from most conventional critical-state soil mechanics cap models. It resembles more closely the MIT model described by Christian [29] and Tang and H6eg [30]. The model is based on classical incremental elasto-plastic strainhardening theory. Besides a hardening rule, a flow rule, and the constitutive parameters characterizing the material's elastic component behavior, the model consists of a stationary ultimate strength or failure surface, which also serves as the bounding yield surface, and a strain-hardening moving cap that is situated between the ultimate strength surface and the hydrostatic stress axis (Fig. 9). Stress states on any one instantaneous surface are characterized by a common single value of a strain parameter such as volumetric plastic strain, which in turn appears as the state parameter in the hardening rule. This hardening parameter is therefore the characteristic that governs the movement of the cap surface according to a semi-empirically developed hardening rule. The yield surface is symmetric about the hydrostatic compression axis, and the moving hardening plastic cap intersects the hydrostatic axis at right angles at X. The comer region resulting from the intersection between the moving cap and the stationary ultimate strength surface is arranged in such a way that the tangent to the cap at this point is always parallel to the hydrostatic axis. This feature assists in securing that no volume change occurs when the stress state arrives at the ultimate strength surface by route of the moving cap. The flow rule continues to be expressed in terms of the equation of the cap at the comer point. The ultimate strength surface serves in those instances merely as the end point of the loading process. In these respects, this cap model is very similar to the Cam-Clay model described earlier. However, the ultimate strength surface is curved as opposed to the straight line surface used to characterize the Cambridge and MIT models. The curved surface in conjunction with the translating cap is used to control dilatant behavior at higher stress levels commensurate with observed behavior of real soils. It is composed of a combination of normal and extended Von Mises criteria in conjunction with a transition surface that links these. The extended Von Mises or Drucker-Prager conical surface bounds the yielding behavior at lower stress levels, and the Von Mises cylindrical surface bounds the yielding behavior at higher stress levels, as seen in Fig. 9. This ultimate strength criterion was devised in order to provide a better control on the amount of dilatancy predicted by conventional models at higher levels of mean stress. The transition surface in Fig. 9 is fitted in such a way that its end points approach asymptotically the Dmcker-Prager or extended Von Mises criterion at very low mean stress levels and the normal Von Mises criterion at the higher mean stress levels. The derivation of the comCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

352


J^Di.

Drucker - Prager ^^ Line X

I

^^ Mises Line

\ Retracted i ' L

i

^

\ \

Elliptical Cap f (Jl.JzD.K)

X

•*J,

FIG. 9—Ultimate strength and yield surfaces in cap model.

plete bounding or ultimate strength surface is based on conventional laboratory shear tests to be described later. The moving position of the yield surface or the cap has been given an elliptical shape with constant eccentricity. This concept is therefore similar to the Modified Cam-Clay yield criterion of Roscoe and Burland. The convex cap extending from the ultimate strength surface to the hydrostatic stress axis constitutes one quadrant of the ellipse; this is the only portion of the yield surface that is used to describe the material's behavior. Stress states on the ultimate strength surface situated behind the intersection of the moving and stationary surfaces normally produce strain-softening responses in conventional critical state soil mechanics models. However, the Weidlinger cap model is restricted to strain-hardening plasticity, since strain-softening behavior is neither envisioned in the materials for which the model was developed nor accounted for in the model theory. The cap expands monotonically as the volumetric plastic strain increases. Unloading under the ultimate strength surface in most instances leaves the cap fixed at its outermost position, and such stress paths therefore result only in elastic deformation. Interpretation of nonlinear stress-strain behavior in unloading and reloading under the current yield surface has frequently been devised by introducing nonlinear elastic moduli. A partial contraction of the cap has been incorporated in some versions of the model, especially those developed for rocks, in those instances where the ultimate strength surface is reached prior to attaining a preconsolidated position of the cap. The normality condition on the ultimate strength surface subsequently results in

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353

volume expansion which is often observed in fracturing rocks. In these cases the retracted cap has often served the purpose of controlling such volume expansions. In conventional critical state models, the lower intersection of the elliptical cap and the hydrostatic axis remains fixed. In fact, most models place the lower extreme stress state of the ellipse right at the origin, and in a few instances a small penetration of the ellipse into the tensile regime is used to characterize tensile behavior. On the other hand, the Weidlinger cap models do not possess this restriction, since the entire cap translates in such a way that neither the lower extreme of the ellipse nor any other point on the cap is tied down to any particular location on the hydrostatic stress axis. The instantaneous position and the translational behavior of the cap are controlled entirely by a hardening rule, which usually is characterized in terms of volumetric plastic strain, in addition to the geometric condition that the intersection point between cap and ultimate strength surface bisects the ellipse. As mentioned previously, the ratio between the major and minor ellipse axes is ordinarily assumed constant for all stress states and yield surfaces. Baladi and Rohani [28] have suggested means for changing this ratio depending on the stress path. Although the models do not explicitly account for path dependent effects and other features of anisotropic hardening plasticity, such phenomena can to a limited extent be simulated by the features described previously. A recently developed version of the model, described by Sandler and Baron [27], introduces kinematic hardening, which enables the prediction of hysteresis in repeated loading and unloading cycles. The Weidlinger model belongs essentially to the class of isotropic hardening, incremental elasto-plastic constitutive models. The cap models satisfy nearly all the original requirements for continuity and uniqueness put forward by Drucker in the definition of stable plastic materials. These conditions lead to associated plastic flow and, thus, normality conditions. In addition to the conditions which were originally devised for metal plasticity, many aspects of realistic soil behavior have also been incorporated into the cap models, such as dilatancy, hysteresis, and densification in isotropic compression. The strain-hardening and volume change characteristics are controlled by volumetric strain rather than void ratio terms, which frequently appear as state variables and moduli in many critical state models, although the relationship between volumetric strain and void ratio change is obvious. Analytical Description In describing the Weidlinger-type cap models emphasis is put on those versions which have seen widest application in the literature. We will begin with a description of the ultimate strength surface, the hardening capped yield surface, and the hardening rule. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

354


The composite ultimate strength surface consists, as earlier mentioned, of a Drucker-Prager and a Von Mises surface. The Drucker-Prager criterion is characterized as //(DC) — ^ / ^ — aJi — ki — 0

(39)

and the Von Mises criterion is described as

-kjÔ

//(VlM)

(40)

where /j is the first invariant of stress, and JID is the second invariant of stress deviator. The constants ki and A: 2 characterize strength contributions from cohesion. The analytical forms of these criteria have been discussed in previous sections. The term a is a coefficient which is directly related to the internal angle of friction for the soil, it also denotes the angle of the DruckerPrager cone. The ultimate strength or failure surface ff has also frequently been described in the literature as the/i-surface. The complete transition surface is described in terms of linear and exponential terms as ffiJuJio)

= ho"^ -A

(41)

+ C-BJ^ = 0

where A, B, and C are material constants. The evaluation of these will be discussed later. This ultimate strength surface degenerates to the DruckerPrager criterion for/j approaching zero where in turn k\— A — C. When/j becomes sufficiently large relative to B, the exponential term becomes insignificant and the regulating expression approaches asymptotically the Von Mises criterion. In this case, k2 = A. The elliptically shaped yield surface that constitutes the cap is often described by

fcUx,hD^'\li) =

Ji X{K)

UK)

- L{K)

1 2

12

+

A - Ce-^^*"'

1= 0 (42)

or as fciJuho^'^, x) = R^ho + Ui - UK)? - RV

=0

(43)

where the subscript c in /n(l + .P)7,2\——

(63)

/,(^)+27

by

ASTM

Int'l

British

Columbia

by of

(al

366


n Actual Data at Failure

"'

o

. ».

[m

C3»

^

1

Po/Ji'i

\ log(pg/J|) FIG. 12—Evaluation of coefficients in Lade's model.

As described earlier, experimental evidence suggests that conventional triaxial compression tests at certain stress levels will produce the necessary information. The expansive yield function ff appears as a variable in the expression for 7/2- A graph is produced by plotting the computed expression for »j2 as a function of^ for a given triaxial cell confining stress. A typical graph is shown in Fig. 13. The incremental "plastic" Poisson's ratio is determined from triaxial tests by subtracting the elastic and the collapse strain increments from the total strain increment. de/jP = deij - de,/ - de,/

(64)

It is usually observed that rj2 is almost a linear function otff in spite of the elaborate expression (Eq 63) relating the two terms. Furthermore, it appears as if the slopes of the straight lines pertaining to certain confining stress levels are identical, although the intercept of the lines with the 7/2 axis is dependent onff3.Lade has suggested that ri2 can be expressed by (65)

where S is the slope of the straight fitted lines, and the two last terms characterize the intercept. The coefficients R and S are obtained from the diagram shown in Fig. 14. Lade [32] has elaborated further on the characteristics of 1J2 and/^. The work-hardening law is characterized by a semi-empirical procedure. It is obtained by fitting curves to experimental data relating plastic work to the degree of hardening. It is described in part by the proportionality \p which after an appropriate analytical operation can be expressed as Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


X„ =

367

AW„ Pa

3gn + mi)2

(66)

where AWp is the increment in plastic work corresponding to an increase in the stress level characterized by A/j. In order to derive a semi-empirical expression for the parameter Xp, it is necessary to describe an increment in plastic work per unit volume, AWp, by means of known quantities. Experimental evidence suggests that the yield function fy can be expressed in terms of the plastic work as /W„\i/i

f'="-'^'{7:)

(67)

where ^ > 0.

Increasing 03

Intercepts at

ff • 0

FIG. 13—Evaluation of coefficients in Lade's model.

J'3/Pa FIG. 14—Evaluation of coefficients in Lade's model.


368


In this expression the coefficients a, b, and q are constant for a given triaxial confining pressure a^. The constant a is determined by

"~''Mw

]

^^^^

V'^p peak/

where e is the base for the Napier logarithms and Wp peak is the value of Wp at peak ultimate strength. The constant q is discussed subsequently. The constant b is determined by 1 q^p

(69) peak

The plastic work at peak strength varies with the confining stress, and the relationship can be investigated further by plotting the variables in a log-log diagram (Fig. 15). W'ppeak=^/'a(y-)

(70)

The constants P and t are determined as the value when (oz/pa) = 1 and the slope of the fitted straight line in the diagram, respectively. The constant q is formally defined as

" p peak

(71)

60/

where the functional combinations {Wp (^,fp «>) and (Wp ^î,, T/J) constitute two sets of corresponding values on a curve where {Wp/pJ is plotted versus fp. In principle, it can be stated that any two points on the given curve can be used for defining q, but Lade found that the optimum curve fit was achieved when the peak point value of the curve and the point value corresponding to 60 percent of r/j on the pre-peak work-hardening part of the curve were utilized. This particular scheme for evaluating q is performed for a certain confining stress level. The variation of q with confining stress can be plotted in a separate diagram (Fig. 16); the relationship often appears to be linear.

. = a + ^(g)


by

(72)

ASTM

Int'l

British

Columbia

by of


369

where a and 0 are the intercept between the straight line and the ^-axis where (aj/j?,,) = 0, and the slope of the straight line, respectively. Lade has discussed certain details pertaining to the distinction between workhardening and work-softening parts in the Wp versus/) relationship [32]. Anisotropic Elasto-PIastic Model of Prevost Description A set of elasto-plastic anisotropic hardening models for characterizing many categories of soil responses ranging from undrained behavior of

I /

'

p

FIG. 15—Evaluation of coefficients in Lade's model.

0

)

[^(m)]2 = 0

(73a)

The parameters a,,''"' characterize the material's memory of past loading or unloading events, and represent the center coordinates for the current yield surface, /„,, which appears as a circle when projected on the octahedral plane. The parameter k^"'^ constitutes the current size or radius of the yield surface, which appears as a right circular cylinder in stress space with its axis parallel to the hydrostatic line. Since the model is stated in terms of deviatoric stresses, it is realistic to introduce an outermost or bounding yield surface that also serves the part of an ultimate strength surface, outside which no stress state is admissible. In the new model version, which incorporates the effect of the mean normal stress, the piecewise evolving surface has the form /„_ = - | [s.. - a,y] + C\p-

/3-axis. The surfaces described in Eq. 13b are ellipsoids of revolution with the major principal axis initially coaxial with the isotropic stress axis for an initially isotropic material. A general description of these surfaces is shown in Fig. 17, which includes


372


Path of movement of nested surfaces

p= l/3(oy+2o,:

(a)

In p-q

Plane

(b) In Transformed

Plane

FIG. 17—Nesting yield surfaces in Prevost s model generalized to three-dimensional loading.

definitions in the triaxial compression as well as extension regimes. It is interesting to note that circular projections in the deviatoric subspace or octahedral plane are indicated in spite of the separate compression and extension descriptions. Drained soil behavior would probably exhibit hexagonal yield surface features on such planes. Ease of model representation is achieved by introducing a new parameter Cp for the mean effective stress axis, where C is termed the yield surface axis ratio, which in turn gives the yield surfaces a circular shape instead of the more cumbersome elliptical shape [38]. The new and old model theories have many common features; for the sake



373

of brevity emphasis will here be put on the old model. Readers are referred to the quoted references. During the course of loading or unloading, the constitutive relationships are governed by the expansion or contraction as well as translatory features of the yield surfaces and by the associated hardening rule. The initial position of the yield surfaces prior to a loading and unloading program is prescribed by the preconsolidation state. An isotropically consolidated specimen would be represented by a stress point on a surface of infinitesimal magnitude located at the center and coinciding with the hydrostatic axis, whereas an anisotropically consolidated specimen would produce a stress point on a surface displaced asymmetrically with respect to the hydrostatic axis (Fig. 18). The preconsolidation stress axis describes the initial position, and since the parameters a,y*"'' may be different from each other and not equal to zero, the yielding is anisotropic (Fig. 17). If the material is inherently anisotropic-orthotropic and consolidated in such a way that the principal material axes are oriented differently from the global system axes, it is to be expected that all a//"'* ^ 0. But if the principal material axes and the system axes coincide, then the mixed terms, a^/'"' = a.^S"''' = «,,*'"' = 0 prior to applied loading. The more ideal case of complete isotropy is encountered for axe'""' — a^'""' = a.^^"'^. A A^Q-consolidation, for example, would result in a displaced circular yield surface which would be located on the particular vertical stress axis. It is therefore important to maintain a physical reference axis system independent of material axis systems. Movement of the stress point from the initial position in loading is defined by the field of plastic moduli, which in turn are defined in stress space by a collection of yield surfaces/o,/i,/2, •••,/„,. • •• ./p. where/,, is the bounding surface, with respective circle sizes, A:*"* < fc'" < kS^^ . . . < A:'''' and center positions a;,", a//", a^/^', . . . , a^/P* (Figs. 17 and 18). The yield surfaces are said to be nesting because they do not intersect. The surfaces are translated by the stress point and under certain conditions may move to new positions, as if they were pushing each other on common tangent planes. The expression describing the geometric features under these conditions is

A:(0)

-

^(1)

-

• •• -

pj)

(74)

During loading and in those instances where the deviatoric stress increment vector is directed out from the current yield surface,/„,, the total deviatoric strain increment is given by dei^ = de^f + def


(75)

by

ASTM by

of

British

374


dsii

de,:

2G

+ HJ

m)12 [*' and the slope by sin (^'. Next, consider some increment b-c along the stress path. This increment is shown in larger scale in Fig. 2b. The vertical component of this increment b-d, corresponds to an increment of shear stress. If this increment of shear stress were associated with a drained simple shear test having a vertical stress path, then the value of T^^^ and Gmax would be known and constant. From these, the reference strain, 7^, would be calculated from

By Eq 1, reference strain would also be constant. In a manner analogous to the stress path diagram, it is possible to construct a strain path diagram (from the Mohr's circles for strain). The vertical component of the associated strain path increment would be one half the shear strain increment. If the shear strain increment is divided by the value of reference strain, 7^, a value of incremental normalized shear strain is obtained. This incremental normalized shear strain is assumed to be independent of the direction of the stress path increment or the direction of the strain path increment. The total normalized shear strain for the end of the stress path increment (Point c in this example) is obtained from


390


(7/7r), = (7/7r),-l + (A7/7r> (2) where J and j — 1 are the 7th and {j — l)th stress points, respectively, along the stress path. The corresponding normalized shear stress for each point along the stress path is obtained from the value of T associated with that stress point divided by the value of Tâx associated with the assumed vertical effective stress path for pure shear. The initial portions of incrementally normalized stress-strain curves, where little or no excess pore pressures are generated, will be consistent for both drained and undrained loadings. Furthermore, at failure, the value of T/Tjaax wiU be Unity for both drained and undrained loadings. Techniques for Special Loadings General Two types of tests are addressed in this section: simple shear and triaxial compression. The loading phase for each may be drained or undrained. Specimens may be isotropically or anisotropically consolidated. The former (a)

q ,

c cos 0

(b)

Actual Stress Path Increment

Associated Sttear Stress Increment

FIG. 2—(a) Typical stress path increment: (b) Enlarged view of stress path increment.


DRNEVICH ON NORMALIZED STRESS-STRAIN

391

is considered a special case of the latter. For anisotropically consolidated specimens, the normalized shear stress and the normalized shear strains do not include shear stresses or shear strains associated with the consolidation process but only those associated with the loadings applied after consolidation. Simple Shear Tests Anisotropic consolidation can be achieved in both direct simple shear tests and in torsional simple shear tests. In the former, the lateral effective consolidation stresses are related to the vertical effective stresses by the coefficient of lateral earth pressure at rest, KQ. In torsional simple shear tests, anisotropic consolidation stresses are achieved by applying axial stresses (positive or negative) in addition to the isotropic confining stresses. Nearly any principal stress ratio, less than that required for failure, may be achieved. In Fig. 3a, the stress point with coordinates (p,', q,) is associated with anisotropic consolidation. The corresponding Mohr's circle is the small dashed half circle passing through this point. The point in Fig. 3a marked (aj'), corresponds to the horizontal planes in the specimen which are major principal planes. The shearing stresses applied during the shear loading phase of the tests are applied to this plane. The vertical vector, labeled T, represents the applied shear stress. For a given value of shear stress applied during a drained test, the major and minor principal stresses change and may be established by means of a new Mohr's circle which is the solid half circle in Fig. 3a. The stress path associated with the value of T for drained loadings goes from the point with coordinates (p,', ^,) to the point (p,', q). Additional shear stress could be applied until the stress path intersects the Kf line. The value of the stress point ordinate at failure is defined as qf, and the head of this vector is shown in Fig. 3a. The Mohr's circle corresponding to failure is shown in Fig. 3a by the dashed partial circle passing through the point (p,', qj). Note that the applied shear stress associated with failure is given by 7^,3, with the head of this vector also shown in Fig. 3a. By geometry, it can be shown that ^max = K p ' s i n . / , ' + C' C0S', a distance equal to the excess pore pressure. Likewise, the effective vertical stress is reduced by the excess pore pressure and the vector T represents the applied shear stress. For the normalization process proposed herein, the value of Tâx for point b in Fig. 3Z) would be the value of applied shear stress required for a simple



393

shear loading through point b to the Ay-line. The large dashed portion of a circle intersecting the A^-line would be the corresponding Mohr's circle; the value of Tmax (with head of vector shown in Fig. 3b) associated with this circle is calculated from Eq 3. The value of p ' in Eq 3 for this case isp,' minus the excess pore pressure. It is plain to see that the value of râx varies with the excess pore pressure generated and that each undrained stress path increment will have a different value of r^^^. The next item needed for the normalization process is the initial tangent shear modulus, Gmax- It can be measured at the onset of applied shear loadings. Typically, these measurements should be made at shear strains of 0.001 percent or less. Ultra sensitive static tests or resonant column tests can be used. Both give essentially the same values [3,4]. For stress path increments after the first, the value of Gâx for the normalization process may change due to changes in a variety of parameters, most of which were discussed by Hardin and Black [5]. The most significant parameters are accounted for in the Hardin Equation. An improved version of this equation (Hardin [2]) is

""-=

625 (OCR)'^ , 0.3 + 0.7e^ ^^"-" ^ "

^'^

where e = void ratio of the soil, OCR — Over Consolidation Ratio, K — coefficient based on plasticity index from Table 1, Pa = atmospheric pressure in same units as a„' and Gmax- and = mean effective confining stress. The ideal way to obtain G„,ax-data for each stress path increment would be to use wave propagation techniques (resonant column or ultrasonics) in conjunction with the applied shear stress. However, this would be quite cumbersome and impractical for most situations. It is recommended that either precise static measurements or wave propagation techniques be used to get [GmaxJi for the first stress path increment. In lieu of this, values of [Gmaxl/ may be estimated from Eq 4. For subsequent stress path increments, values of [Gmax]. may be adjusted to account for changes in void ratio and mean effective confining stress according to the following equation which is based on Eq4.

Gmax = [Gmax]/ Q J + ^QJ^^l


by

['ô'/(a„'),.]«-5

ASTM

Int'l

British

Columbia

(5)

(all

rights

by of

Library

pur

394


TABLE \—Coefficients

K/orEq4.

K

Plasticity Index

0 20 40 60 80

0 0.18 0.30 0.41 0.48 0.50

> = 100

For simple shear type loadings, it can be shown that [a„'/(a„'),] = [{p'-

qi/3)/(p,'

- q,/3)]

(6)

where each of the parameters are defined in Fig. 3b. Note that for drained simple shear loadings, p' = Pi' for all stress path increments and Eq 5 becomes only a function of void ratio. The initial void ratio can be calculated from measurements made at the specimen at the beginning of the test. These will have to be adjusted for volume changes associated with consolidation to get the void ratio at the time of shear loading. Volume changes associated with drained shear loading may be measured by monitoring the pore water entering or leaving the specimen. However, the initial tangent shear modulus is not too sensitive to changes in void ratio. This is demonstrated in Fig. 4 for different initial values of void ratio from 0.2 to greater than 1. Preliminary results have shown that volumetric strains due to applied simple shear are usually less than 2 percent. From Fig. 4 this would mean that volume changes due to applied simple shear loading would cause less than a 5 percent change in initial tangent shear modulus. Consequently, for drained simple shear tests, the initial tangent shear modulus may be constant. For undrained simple shear tests, only the portion of Eq 5 associated with mean effective confining stress needs to be applied and Eq 5 with Eq 6 becomes Gn,ax = [Gmax],- Kp ' '

9,/3)/(p,' -

9,/3)]0-5

(7)

where the parameters are defined in Fig. 3b. In summary, for simple shear tests, it can be said that the incremental normalization process is identical for both the direct simple shear and the torsional simple shear. If these tests are drained during the application of shear, the stress path is vertical, Tn,ax and Gâx are both constant for all stress path increments. Hence, for this case, the incremental process is not needed. For undrained simple shear loadings, the process for each stress path increment consists of determining a value of râx by use of Eq 3 and adjusting Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


Gmox

395

1.0

[^maxli

-5

0

5

Volumetric Strain (%) FIG. 4—Effects

of volumetric strain on G„„„..

tlie value of [G„ax\i by Eq 7. Henceforth the procedure is as outlined in the section on Basic Concepts on Incremental Normalization. Triaxial Compression Tests Consolidation PAaê—Specimens in the triaxial test may be consolidated isotropically or anisotropically. The state of stress and the stress path diagram for these tests are identical to those for simple shear. The stress point associated with the consolidated specimen has coordinates (p,', 9,). Axial Loading Phase—The total and effective stress paths associated with the axial loading phase of the triaxial compression test are shown in Fig. 5. For drained tests, the two stress paths will be identical and have a slope of unity. The horizontal differences between the total and effective stress paths is a measure of the excess pore pressure generated by the axial loading. The procedure for normalizing these data is similar to the procedure for normalizing the data from simple shear tests in that for each stress point on the effective stress path, values of T^^^, Gâx. and 7^ must be determined. In addition, values of axial stress and axial strain must be converted to values of shear stress, T, and shear strain, 7. In triaxial tests, the vertical and horizontal planes in the specimen always remain principal planes. Application of axial load increases the major principal stress which in turn causes the radius of the Mohr's circle to increase Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

396


q

1

^ ^^'l^^^-^^^ ^^^^'--^^^^-Excess Pore Pressure

^-'*C1 /

^ ' ' ^ ESP\

/ /TSP

''i 1

1

1

p. p FIG. 5—Total and effective stress paths for iiiidrained triaxial compression test on anisotropically consolidated specimen.

and hence causes the shear stress to increase. In Fig. 6a, the small dashed circle represents the condition at the end of the consolidation phase and the solid circle represents some point on the stress path for a drained axial loading. It can be shown by geometry that the value of r is related to agxiai by 9

= 0.5 a.axial

(8)

where a^^^^\ = axial stress applied in addition to consolidation stress. The value of q^^^^ associated with drained triaxial loadings is the shear stress associated with the large dashed Mohr's circle shown in Fig. 6a. The head of the vector representing q^^x is also shown in this figure. The magnitude of ^niax is given by c' cos 4>' + p' sin 4>'

(9)

The value of 7n,ax used for normalizing r is the portion of q^^^ due to the applied axial load and is the difference between q ^ and qj. Hence, the value of 'max is given by c ' cos 0 ' + /J' sin 0 ' — qr, (10) Note that values of q„^^ and r„^^ vary continuously with applied axial stress. At failure, the value of q^^,^ is equal to the shear strength and the value of r/Tmax equals unity. For undrained triaxial loadings, the procedure for obtaining T and Tma, is exactly the same as for drained loadings and Eqs 8 and 10 apply without modification. The corresponding Mohr's circles, stress path, and vectors are shown in Fig. 66. At failure, the value of ^âx will equal the undrained shear strength and the value of T/Tâx will again equal unity. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


397

(a)

(b)

FIG. 6—(a) Stress path diagram for anisotropic consolidation and drained triaxial compression loading: (b) Stress path diagram for anisotropic consolidation and undrained triaxial compression loading.

Values of Gmax for normalization may be obtained from torsional resonant column tests on the specimen after consolidation is complete. Use of the Hardin apparatus [6] is ideally suited for this because values of Gâx can be measured continuously during the axial loading phase. If this apparatus is not used, data from resonant column tests on similar specimens consolidated at the same mean effective confining stress may be used to obtain values of [CJ'max]/ for use in the data reduction process. If no test data are available, the value of [Gmax], may be estimated by use of Eq 4. Equation 5 is then used to adjust values of [G^^^]j for changes in volume and mean effective confining stress. For the situations where volume changes are small (less than 2 percent) and for undrained tests, Eq 5 reduces to Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

398


C?max -

[Gn,ax],- Hp' '

q/^ViPi

'

?,/3)]«-5

(H)

where the parameters are defined in Figs, ba and bb. Values of reference strain for each point on the triaxial compression test stress path are calculated by means of Eq 1 using the values of Tâ, and Gâx determined by use of Eqs 10 and 11. The last items needed for normalization of triaxial compression data are values of shear strain associated with a given stress point. For drained tests and for undrained tests on partially saturated soils, measurement of specimen volume changes or of lateral deformation is important if accurate normalized data are to be obtained from the triaxial test. If specimen volume changes are measured, the equivalent shear strain for the jth stress point is calculated from 7,- = 7,_, + 1.5 (e,- - e,-,) + 0.5 (V,. - V,_,)/V

(12)

where 7,-1 €,, 6,-1 V;- Vj-i V

= equivalent shear strain for {j — l)th stress point, = axial strain for thejth and {j — l)th stress points, — specimen volumes for thejth and (j — l)th stress points, and = initial specimen volume.

If lateral deformation measurements are made, the equivalent shear strain for the jth stress point is calculated from 7,- = 7/-, + (6/ - €,-i) - [(e,),- - (e,),-i]

(13)

where (e^);, (er),-i = radial strains for the./th and {j — l)th stress points, respectively. The development of Eqs 12 and 13 is based on the discussion of plastic dilation by Hardin [2] and on the use of the Mohr diagram for strain. The process is analogous to calculating a tangent Poisson's ratio and applying it to the axial strain increment to determine a shear strain increment. The total shear strain for that stress point is the shear strain for the previous stress point plus the increment in shear strain. Once the shear strain values are established, the procedure for obtaining normalized behavior is identical to that for the previous cases. Examples of Normalized Stress-Strain General Torsional simple shear tests and triaxial compression tests were conducted on a variety of undisturbed and on one laboratory remolded and compacted soil as part of a recently conducted research program [4]. Results of tests on Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


399

the laboratory compacted soil are presented herein to demonstrate the nature of the normalization process and to compare the results from one type of test to another. A description of the soil tested is given in Table 2. Torsional Simple Shear Tests A special torsional simple shear apparatus was used for conducting these tests. This apparatus, described in Ref 4, 7. and 9, had a shear strain resolution better than 0.001 percent and was capable of applying strains greater than 4 percent. Both torque-controlled and rotation-controlled tests could be performed. The tests reported herein were performed on isotropically consolidated and saturated specimens that were 5 cm (2 in.) in diameter by 7.5 cm (3 in.) long. The shear loading was done with the apparatus set for rotation control. Two tests were performed with drained conditions prevailing and two were performed with undrained conditions. The effective stress paths for these tests are given in Fig. 7 and the conventional shear stress-shear strain curves are given in Fig. 8. Incrementally normalized shear stress-shear strain curves are given in Fig. 9 for all four tests. From this figure, it is evident that a single curve can be used to represent this soil. Triaxial Compression Tests The triaxial apparatus that was used for these tests incorporated a Hardin resonant column oscillator [6] that made it possible to measure values of in-

TABLE 2—Summary of soil properties. Liquid limit Plastic limit Specific gravity

21 15 2.68

Particle Size Analysis % passing 100 79 57 Clay Fraction < 0.002 mm 20% Classification Unified CL-ML AASHTO A4(5) Textural Clay-sand Average compacted density 2085 kg/m3 Mean void ratio 0.521 18.4 % Mean water content Sieve No. 10 40 200


400


S.

40

60

80

100

120

140

p'(kPa) FIG. 7—Stress paths for torsional simple shear tests on remolded soil.

Shear Strain (%) FIG. 8—Shear stress versus shear strain for both drained and undrained torsional simple shear tests on remolded cohesive soil. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


401

1.25

0.00 ••

20

40

60

80

100

120

140

Norm. Shear Strain FIG. 9—Normalized shear stress-shear strain for both drained and undrained torsional simple shear tests on remolded cohesive soil.

itial tangent shear modulus during the entire testing operation from consolidation through axial loading to failure. Seven tests on the laboratory compacted soil were performed on specimens that were 5 cm (2 in.) in diameter by 10 cm (4 in.) in length. All specimens were isotropically consolidated and back pressure saturated. The effective stress paths for the three undrained tests are given in Fig. 10 and those for the four drained tests are given in Fig. 11. The Kj-lme (shear strength parameters) was the same for both types of tests. The conventional axial stress-axial strain curves for the undrained tests are given in Fig. 12 and those for the drained tests are given in Fig. 13. The incrementally normalized shear stress-shear strain curves for the undrained tests are given in Fig. 14 and those for the drained tests are given in Fig. 15. In both Figs. 14 and 15, the incremental normalization process appears to do a reasonable job of collapsing the data onto a single curve. It is of interest to compare the normalized curves of both the drained and undrained triaxial tests with each other and with the normalized curves from the torsional simple shear tests. This is done in Fig. 16 where the data points correspond to the mean values from Figs. 9, 14, and 15. Examination of Fig. 16 reveals that there is better agreement between the incrementally normalized torsional simple shear data and the undrained triaxial test data than there is between the drained and undrained triaxial data. Part of the disparity of the drained Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

402


200 I I I I I I I I I I I I I I I I I I I I I I I I I

150

100

150

200

250

p' (kPa) FIG. 10—Effective cohesive soil.

200

stress paths for undrained triuxial compression tests on remolded

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

I

100 FIG. 11—Effective soil.

I '

150 p' (kPa)

I I

I I I

200

I ' ' I

250

I I ' I

300

stress paths for drained triaxial compression tests on remolded cohesive



250 I

200

£ '

150

403

r

-

-

100

4

10

6

Axial Strain (%) FIG. 12—Stress-strain curves for undrained triaxial compression tests on remolded cohesive soil. 400

4

6

8

10

12

Axial Strain (%) FIG. 13—Axial stress-axial strain curves for drained triaxial compression tests on remolded cohesive soil.


404


100

200

Norm. Shear Strain FIG. 14—Normalized shear stress-shear strain curves for undrainecl triaxial compression tests on remolded cohesive soil.

and undrained triaxial data may be due to differences in the rate of testing. The rate for the drained tests was approximately one third of the undrained. Two additional undrained tests were performed at these slower rates. Results for these tests showed some rate effects, but were still very close to the faster undrained tests. Part of the difference may also be due to the differences in the distribution of axial strains within the triaxial test specimens. This topic is currently undergoing further study. One very interesting sidelight to these triaxial tests is the comparison of the values of G^^^ measured by the Hardin apparatus with those calculated by Eq 11. Data for these comparisons are presented in Fig. 17 for the undrained tests consolidated to 100 kPa (14.5 psi) and in Fig. 18 for the drained tests consolidated to 75 kPa (10.9 psi). In each figure, the data points denoted by circles are the measured values. Those denoted with the diamonds are those determined by use of Eq 11 where the value of [Gmax]/ was the value measured just prior to the initiation of axial loading and reflected the increase in shear modulus associated with about one log-cycie-of-time in secondary compression. The triangular data points utilize the value of initial tangent modulus measured at the end of primary consolidation for the value of [Gmax], and are closer to the actually measured values. The most probable reason for this is that the axial loading process destroys a large portion of the



100

405

200

Norm. Shear Strain FIG. 15—Normalized shear stress-shear strain curves from drained triaxial compression tests on remolded cohesive soil.

stiffness gained during secondary compression. It is recommended that the value of initial tangent shear modulus measured at the end of primary consolidation be used in the incremental normalization process. Use of Normalized Stress-Strain Curves A detailed presentation on the use of incrementally normalized stressstrain data is beyond the scope of this paper. This aspect is addressed to some extent in Refs 4 and 9 and is the subject of continued study. However, it is appropriate to give a brief overview of applications. In order to obtain stress-strain curves of shear behavior for in situ conditions from normalized stress-strain curves, the initial tangent shear modulus and the shear strength are needed along with some estimate of the loading stress path. With this information, the inverse of the normalization process is performed to get the desired stress-strain behavior. It was shown in Refs 4 and 9 that the normalized stress-strain curves were relatively independent of sample disturbance. Hence, curves generated from tests on "undisturbed" specimens should be quite applicable to in situ conditions even though some inevitable disturbance occurs due to stress release and other causes. It is suggested that the normalized curves define the sense


406


?—I—I—I—I—r

Slow Undrained Triaxial and Slow Drained and Undralned Torsional Simple Shear in

Very Slow Drained Triaxial Tests

J

I

I

I

I

_i

u

50

150

100

I

I

L.

200

Normalized Shear Strain

FIG. 16—Comparison of normalized data from triaxial compression tests and torsional simple shear tests, both on remolded cohesive soil.

150

Measured

o

o E

50

I 4

6

ID

Axial Strain (%) FIG. 17—Variation of initial tangent shear modulus versus axial strain for undrained triaxial compression tests on remolded cohesive soil.



200

'

\

407

^

Calculated Based on End of Primary & Secondary

-OOi

-AC Calculated Based on End of Primary Consolidation

50

Axial Strain (%) FIG. 18—Variation of initial tangent shear modulus versus axial strain for drained triaxial compression tests on remolded cohesive soil.

of soil behavior. Values of initial tangent shear modulus and shear strength measured in situ provide the scaling factors which are applied to the normalized stress-strain curves in the deconvolution process. It is also suggested that the incremental normalization process would be beneficial in the study of some of the lesser understood parameters affecting stress-strain behavior, such as creep, overconsolidation, and secondary compression effects. The normalization process accounts for the prime parameters and would permit their effects to be removed. Hence these effects could be studied much more efficiently. Summary and Conclusions An incremental normalization procedure is proposed and outlined. The procedure is applicable to simple shear and triaxial compression tests and may be used for drained as well as undrained tests. Typical test results on a given soil were presented, and it was shown that the incrementally normalized data from different types of tests are relatively independent of the test used. The process is based on the use of effective stress and requires that the initial tangent shear modulus be measured. For cases where this cannot be done, an equation is given which may be used to estimate this modulus. It was shown


408


that the initial tangent shear modulus varies with changes in void ratio and mean effective confining stress, but is relatively independent of the applied shear stress; this is a confirmation of the findings of Hardin and Black [5]. The normalized stress-strain concept should be helpful in the study of the effects of less dominant parameters on stress-strain because the process of normalization removes the effects of most major parameters. This concept should also be useful in analytical programs that require the stress-strain behavior for a wide variety of initial conditions and stress paths. The process used in the programs would be the inverse of the process used to obtain the normalized curves and would make use of initial tangent modulus, strength data, and effective stress paths which may be different from those used in generating the normalized curves. This feature, plus the fact that the normalized curves appear to be relatively insensitive to effects of sample disturbance, makes the method attractive for accurately describing in situ shear stress-shear strain behavior. Acknowledgments This work was sponsored by a cooperative effort among the University of Kentucky Research Foundation, the Department of Civil Engineering at the University of Kentucky, and the U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., Contract No. DACW39-78-C-0046. The author is grateful for this support. He also wishes to acknowledge the helpful suggestions of his colleague, B. O. Hardin, and the Army's technical monitor, W. F. Marcuson, III. Two graduate students, J. P. Koester and S. H. Bickel, were actively involved through most of the period. Each has written an M.S. degree thesis on his portion of the work. The hard work, long hours, and contributions of these gentlemen are most appreciated. Two additional graduate students, Johnson Toritsemotse and C. A. Rivette, assisted with the data reduction aspects of this work. Their patience and diligence is to be commended. Finally, the author wishes to acknowledge the ingenuity and resourcefulness of the Laboratory Technician, W. W. Thurman, who designed and constructed many of the accessories for the test apparatus. References [/) Hardin, B. O. and Dmevich, V. P., Journal of the Soil Mechanics and Foundations Division, American Society of Civil Engineers, Vol. 98, No. SM7, July 1972, pp. 667-692. [21 Hardin, B. O. in Proceedings, Specialty Conference on Earthquake Engineering and Soil Dynamics, Vol. 1, American Society of Civil Engineers, 1978, pp. 3-90. [3\ Tseng, Richard Jau Yu, "A Study of Liquefaction of Sand by Torsion Shear Test," a dissertation submitted in partial fulfillment of the requirements for the degree Doctor of Philosophy at the University of Kentucky, Lexington, Ky., 1974. [4] Dmevich, V. P., "Evaluation of Sample Disturbance on Soils Using the Concept of



[5] [6] [7]

[S]

|9]

409

'Reference Strain'," Final Report submitted to U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., on Contract No. DACW39-78-C-0046, May 1979. Hardin, B. O. and Black, W. L., Journal of the Soil Mechanics and Foundations Division. American Society of Civil Engineers, Vol. 94, No. SM2, March 1968, pp. 353-369. Hardin, B. O. in Special Procedures for Testing Soil and Rock for Engineering Purposes, ASTM STP 479, American Society for Testing and Materials, 1970, pp. 516-529. Koester, J. P., "Strain-Control Torsional Simple Shear Investigation of Sample Disturbance Using the Concept of Reference Strain," submitted to the Graduate School, University of Kentucky, Lexington, Ky., in partial fulfillment of the M.S. degree requirements, 1979. Biekel, S. H., "Examination of the Concept of Reference Strain Utilizing Triaxial/Resonant Column Tests on Remolded Cohesive Samples," submitted to the Graduate School, University of Kentucky, Lexington, Ky., in partial fulfillment of the M.S. degree requirements, 1980. Dmevich, V. P. and Massarsch, K. R., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, Vol. 105, No. GT9, Sept. 1979, pp. 1001-1016.


p. W. Mayne' and P. G. Swanson'

The Critical-State Pore Pressure Parameter from ConsolidatedUndrained Shear Tests

REFERENCE: Mayne, P. W. and Swanson, P. G., "The Critical-State Pore Pressure Parameter from Consolidated-Undrained Shear Tests," Laboratory Shear Strength of SoU. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 410-430. ABSTRACT: The results of isotropic and anisotropic consolidated-undrained shear tests (CIU, C/fo, U) are used to determine the critical-state pore pressure parameter (A„). The relative advantages of using the critical-state parameter (A„) over Skempton's pore pressure parameter (^4) and Henkel's parameter (a) are discussed. The effects of overconsolidation ratio (OCR) and initial stress state (Ka) on both Henkel's and Skempton's pore pressure parameters can significantly alter effective stress predictions of undrained strength. The critical-state parameter is independent of OCR, Ka, and level of shear to failure, thus requiring only two basic soil constants in order to predict undrained strength: (/) the effective stress friction angle ('), and (2) the critical-state pore pressure parameter (A„). An "extended" critical-state model is developed using the equivalent pressure concept for overconsolidated states. The method then provides a simple analytical representation of undrained stress-strain behavior and pore pressure response for clays with different values of OCR. One additional soil constant (C,.: the virgin compression index) is required in order to model stress-strain behavior. The validity of the critical-state theory is substantiated by data from over ninety different clay and silt soils reported in the geotechnical literature. Furthermore, the criticalstate concepts are shown to encompass both total stress and effective stress methods under one unified theory. KEY WORDS: clays, effective stresses, overconsolidation, strength, strain, total stresses, triaxial shear tests

pore pressure, shear

Effective stress methods have shown the importance of pore pressures on shear strength and stress-strain behavior of clay soils [l-95\.^ The pore pressures developed during undrained shear depend on several primary fac' Geotechnical engineer and senior geotechnical engineer, respectively. Law Engineering Testing Company, Washington, D.C. 22101. ^The italic numbers in brackets refer to the list of references appended to this paper.


Int'l InteiTiational

Columbia

(all

410 rights

www.astm.org

Library

reserved); pursuant

Sun to

Dec License

19

02:25:09

Agreement.

No

MAYNE AND SWANSON ON PORE PRESSURE PARAMETER

411

tors: (/) the initial effective vertical stress {aô'), (2) the degree of overconsolidation (OCR), (3) the initial stress state {KQ), and (4) the applied level of shear stress (or strain). Numerous empirical, experimental, and theoretical methods of representing the undrained response of clay and silt soils during loading have been proposed. The geotechnical community needs a reliable and theoretically sound predictive method which can accurately model the undrained behavior of clay soils from a variety of depositional environments and stress histories. Whether or not a method is applied in practice depends upon its versatility and simplicity. In addition, a good predictive method should require a minimal amount of field and/or laboratory testing and use basic soil constants which are currently recognized by practicing geotechnical engineers. This paper discusses the application of the critical-state pore pressure parameter in a simplified method of predicting undrained stress-strain behavior. The natural variations of the parameter are studied by reviewing data from over 90 different clay and silt soils reported throughout the geotechnical literature. The data are analyzed in terms of total stresses and effective stresses. Critical-state concepts presented by Schofield and Wroth [96] and Roscoe and Burland [97\ are used to incorporate total stresses and effective stresses into one rational theroy. Undrained shear behavior is described using only three soil constants: (i) the critical-state pore pressure parameter (Ao), (2) the effective stress friction angle ( 0.98), indicating an excellent fit. (Note: r = 0 indicates no correlation; r = I indicates a perfect fit). 3. The critical-state theory predicts by conservation of energy that a limiting condition exists (Ao(max) = 1), whereby the work dissipated in the soil must either be equal to or less than the energy input. The soils included in this study lie within the theoretically acceptable boundaries. In fact, the variation of A„ may be approximated as a normal distribution having a mean of 0.64 and standard deviation of 0.18. It should be noted that highly sensitive clays and cemented soils may prove exceptions to this upper limit. It is also observed that those soils in Fig. 1 which exhibit high values of A„ (greater than 0.9) are sensitive clays. 4. The relationships shown in Fig. 1 are from total stress strength data. No direct pore pressure measurements have been used in the analyses. Although most soils encountered in nature are overconsolidated to some degree, the OCR is not often known during testing unless supplementary consolidation testing is conducted or a SHANSEP [6] approach is employed. The parameter A^, may also be determined from the results of consolidatedundrained shear tests conducted at confining pressures less than the maximum preconsolidation pressure (a'^max) without knowledge of the OCR. The critical-state pore pressure parameter is then defined by the absolute value of the slope of a linear relationship between log [S^/a^'io.c.)] and log ( a ^ ' ) , as shown in Fig. 2. The parameter A„ has been defined in terms of initial vertical effective stresses ( a ^ ' ) . Therefore no distinction has been made between isotropic and anisotropic states of stress. A comparison A^ determined from both isotropic and anisotropic stress conditions is shown in Fig. 3. There appears to be little difference between A^ determined from these different test conditions. Mitachi and Kitago [60] have also supported these findings. In general, Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

418


i°g('%

.)

logl

y

/

/

/

/

/

^ A ,

C/

/

/

/

S 'a/u /

/

/

-A

/

6..

Note;

,("c.)

CTVO'

0"

1^0"!

" vo

\

"vmox.

log (OCR)

FIG. 2—Definitions of critical-state pore pressure parameter from undrained strength data.

however, the soils shown in Fig. 3 are laboratory-prepared materials; therefore these conclusions may not be relevant to natural anisotropic clays. In the preceding sections, it has been shown that the critical-state pore pressure parameter is a soil constant. The pore pressure parameter can be used to predict undrained shear strengths for various stress histories and initial stress conditions. The application of the pore pressure parameter is best presented in its relationship with the critical-state theory. The remainder of the paper describes the relatively simple analytical equations which use the pore pressure parameter to predict undrained behavior. Effective Sttess Theories

The normally consolidated undrained strength of a clay soil can be determined from the relationship between log [S„/a„,'] and log [OCR] as the intercept at OCR = 1, as shown in Fig. 2. Alternatively, an effective stress approach by Schofield and Wroth [96] proposes that the undrained stress path to failure for an isotropically normally consolidated soil is given by (?//") = ^ l o g e ( P „ ' / i " )

(8)

where A/ = (6 sin 0 ')/(3 — sin ') is the slope of the failure line m q — p space, and P„' and P' are the initial and current values of mean normal effective stress, respectively. Further derivation gives the Cam-Clay prediction of undrained shear strength for normally consolidated soils as Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


J„/(7^'(n.c.) = 0.5Mexp(— A„)

419

(9)

Measured and predicted values of S^/a^ '(n.c.) are compared in Fig. 4. The results of this study show that for all the soils considered with no adjustments made for test type, sample disturbance, testing rate, anisotropy, or inhomogeneity, a best fit straight line relationship with no intercept is S„/(j„'(n.c.) = 1.114[0.5Mexp(- A„)]

(10)

having a sample correlation coefficient r = 0.83. These findings suggest that the Cam-Clay theory of Schofield and Wroth [96], in general, underpredicts the undrained shear strength by approximately 11 to 12 percent. A similar linear regression study conducted solely on the anisotropic test data (CAU and C/C„U tests) indicated an underprediction of about 7 to 8 percent {r = 0.85). Equations 5 and 9 can be combined to represent the undrained strength for a clay soil over a range of OCR: S,/a^'{o.c.)

= 0.5M(e-' OCR)^"

0.5

(11)

1.0

AoO'sofropi'cJ FIG. 3—Comparison of Ao determined from CAU tests and CIU tests.


420


0.7

1

,

.

.^

...

.

J

1

,

.

,_

,_

•54

Legend 0.6

•

c m TESTS

•

CAU/CKoU TESTS

r

\r7 .63

Ai •89

0.5 •15

:s

0.4

./^

,74 .3/i J3V59 "77 y's *91. '84 / 10 ,,19*60 / •36 • ••^'^Ki.35^4 47i.58 64A^^ / ^ , 3 n • »16 f 4 0 / '•^ OR'

-

*68

X

53

.

-

!BR'B6 69iv«1

^26 " f p o s ^ e •64 f J '^tffe ^

0.3

*»^\, • 1 4 . ^ < 9 4 „ , 41 •90 760*^8 8^* . F"43 °^

0.2

Xf

/82

0.1

1

1

1

1

0.1

0.2

0.3

0.4

1

1

0.5

0.6

0.7

3 sin^' 3 -mf' FIG. 4—Measured and predicted values of Su/(Jvo'("c.) bv Cam-Clay theory of Schofield and Wroth (961.

Another version of the critical-state model, known as "modified CamClay", has been presented by Roscoe and Burland [97]. For normally consolidated behavior, their theory predicts that 5„/a,/(n.c.) = 0.5M(2-M

(12)

which is shown in Fig. 5 for the data included in this study. Linear regression analyses indicate the model slightly overpredicts the undrained strength by about 6 percent. A best fit line (b = 0) is found to be 5,,/a^'(n.c.) = 0.938 (0.5 Ml-"")

(13)

having a sample correlation coefficient r = 0.84.



421

0.7 Legend

0.6 ~

.

CIU

»

CAU/CKoU

c&K

TESTS

^ TESTS

^ ^ .63y

.87

"ts 0.5 -

I

74. ^^J^.m

\o.4 Q

JS. r .10 /

^

•'

„ *^

44

-

^"^ ^

/ ™ *'• &

-

*e

/ H 7

/

/

•«?

*«

01 -

1

0./

I

Oi'

1

1

1

0.3

0.4

0.5

1

0.6

07

FIG. 5—Measured and predicted values of Su/avo'(M.o.) by modified Cam-Clay theory of Roscoe and Burland [97].

The statistical results can be used to empirically adjust the theoretical relationships in one of several ways: (/) inclusion of a cohesion intercept term (c '), (2) inclusion of an attraction term (a ') as proposed by Van Eekelen and Potts [50\, or {3) adjusting the value of the friction parameter M (alter ' by approximately 2 or 3 deg) as suggested by Schofield and Wroth [96]. It should also be noted that the majority of the undrained strengths were measured using the triaxial apparatus. The commonly accepted method of determining shearing rates as proposed by Bishop and Henkel [107\ assume only 95 percent of pore pressure equalization at failure. Possibly, the theory is correct and the experimental data are in error.


422


Stress-Strain Behavior The Cam-Clay models also provide simple analytical representations of undrained shear behavior to failure for normally consolidated soils. Soils which occur at stress states below the current yield surface are assumed to deform as elastic materials. The model presented in this paper deviates from the original theories in that plastic strain concepts are also assumed to apply during overconsolidated conditions. For isotropic consolidation, the stress ratio {q/P') to failure as a function of strain (e) is assumed to be unique for a given soil, independent of OCR. By adopting the expression presented by Schofield and Wroth [96] and substituting an average value of C^ = C^. (1 — A^) from Eq 6, the stress ratio varies with axial strain by -exp

^/^' = M H

M(l+e)log,(10) C,A„(1-A„) '

(14)

where e is the void ratio prior to shear. The current value of mean normal effective stress (P') is determined by extending Eq 8 to represent overconsolidated behavior: P ' = />„ '(e-' OCR)'^" exp A„(l - log, OCR)

(«?/P') M

(15)

The deviator stress q = (ai — a3) may then be expressed as a function of strain by qîq/P')P'

(16)

The stress-strain function can be obtained in closed-form solution by substituting Eq 14 into Eq 15, and then Eqs 14 and 15 into Eq 16. This "extended Cam-Clay" model can be used to represent the undrained stressstrain behavior for clays as well as provide simplified stress paths to failure. Only three soil constants are required to model this behavior: 0', Cf, and A„. q^ MP/OCR^"exp{A„l(l

- lnOCR)(exp7?6) - 1]}(1 -expRe)

(17)

where ^ ~

Mil +ejln,(10) CrA„(A„ - 1)

The application of the "extended" model to predict undrained stressstrain response is illustrated in Figs. 6 and 7 for several different soils. The model is shown to give very reasonable representations of the deformational characteristics of clay soils using only a minimal amount of information. In Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


q(kPa)

SPeSTONE KAOLIN [18] Ao'0.704 0' 'tS.S'

BOSTON BLUE [8] A,'0.703

0' =ie. f

400

423

Cc

C, =0M$

=0.693

zoo xperimehtal data

o q(kPa)

WEALD [105] A, =0.485 0' = 22.8' Cc =0.114

EAST ATCHAFALAYA [85] A.'0.580 f 'SI.7' Cf =0.445

400

200

15

€/%) FIG. 6—Undrained stress-strain behavior for Boston Blue Clay, Spestone Kaolin, East Atchafalaya, and Weald Clay using extended Cam-Clay theory; experimental (solid lines) and predicted {dotted lines).

general, an "attraction" of approximately 11 percent was added to the value of P ' to account for experimental-theoretical differences. Pore Pressure Response The versatility of the critical-state pore pressure parameter for both total and effective stress analyses has been demonstrated. The "extended" theory can also be used to give a simplified representation of pore pressure response during undrained shear to failure for isotropically consolidated soils: u=P'

+ P'

(q/P')

- 1

(18)

as shown in Fig. 8 for Newfield Clay [15]. By substituting Eqs 14 and 15 into Eq 18, the pore pressure is predicted as a function of strain. The authors believe that a more rational and promising critical-state theory which can Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

424


qfkPa) 400

200 0

q(kPa) 400

KAWASAKI I ^t'0.842 g'=35S' Cc =0.668

ILLITE [7]

[44]

A, = 0.491 g'=Z4.S' Cc =0.408 OCR

200

— a

10

15

0

e,(%)

10

15

€,(%)

FIG. 7—Undrained stress-strain behavior for Simple clay, Keuper Marl, Kawasaki, and lllite using extended Cam-Clay theory; experimental {solid lines) and predicted (dotted lines).

better model the pore pressure behavior of overconsolidated soils has been presented by Pender [103]. The approach by Pender, however, is more sophisticated, thus requiring a computer to facilitate computations. The statistical findings presented herein can be used to estimate P' at the criticalstate failure (Pes') for use in Pender's model. The critical-state parameter A^ can also be used to predict the effective stress friction angle (') from total stress strength data. Returning to the theory of Schofield and Wroth [96], it is derived that sin 0 ' = {1/3 + [5'„/ff^'(n.c.)exp(A„)]-'}-'

(19)

Based on the available data, the prediction is again different from experimental values by approximately 12 percent. A linear regression best fit line (b = 0) for the relationship shown in Fig. 9 is 0 '(measured) = 0.871 0 '(predicted)

(20)

with r = 0.82. The recommended procedure for determining the value of A^ for a specific Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


425

250 ii(kPa) 200 OCR = I equation

150

(18)

A/

100

Newfield Clay [15] after Sangrey, Henkel aEsrig (1959)

/

-I

10 w Q. (I> w. O Q.

50

7

f 0

•^

• OCR = 6

-50

6,(%) -100 0

1

2

3

4

5

6

7

8

axial strain FIG. 8—Measured and predicted pore pressure response for Newfield Clay.

clay or silt soil is illustrated by Fig. 2. A set of two or more consolidatedundrained shear tests, conducted at different confining stress levels where a'„ < a\max 's required for this approach. Alternatively, if a SHANSEP approach is employed, the results of only one CIU or CK„\J test are required: logJ(2/M)(5„/a,/(o.c.))] logJOCR] - 1

(21)

An average "attraction" of about 11 percent should be added to a\„ to account for the observed differences between experimental results and CamClay theory. Conclusions The critical-state pore pressure parameter has been shown to be independent of OCR, KQ test conditions, and level of shear to failure, and thus should be considered a basic soil constant. The critical-state parameter has been statistically verified as versatile and applicable to general geotechnical engineering practice. Simple analytical expressions requiring only two soil constants (A,, and 0') can be used to accurately predict the undrained strength of normally consolidated and overconsolidated clay soils. One addiCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

426


60 Note; Numerals correspond to soils and references listed in Table I.

50

40

30

20 •Q.

10 -best fit line ( b=o) r = 0.82

60

30

0' predicted

from total stress dota

FIG. 9- -Relufionship between experimental and predicted values of the effective stress frictiim angle.

tional constant (C^) is needed in order to provide reasonable stress-strain relationships and pore pressure response during undrained shear to failure. Acknowledgments The authors extend gratitude to C. Peter Wroth, University of Oxford, for his inspiration, and to Donna Reese and Anne Bethoun, Law Engineering Testing Company, for their assistance in preparing this study. Refefences [I] Henkel, D. J. in Shear Strength of Cohesive Soils, American Society of Civil Engineers (ASCE), New York, 1960, pp. 533-554.



427

[2] Amerasinghe, S. F. and Parry, R. H., Journal of the Geotechnical Engineering Division, ASCE, Vol. 101. No. GT 12, Dec. 1975, pp. 1277-1293. [3] Mitchell, J. K., Fundamentals of Soil Behavior. Wiley, New York, 1976, pp. 283-339. HI See Ref/. 15] Brown, S. F., Lashine, A. and Hyde, A., Geotechnique. Vol. 25, No. 1, March 1975, pp. 95-114. [6] Ladd, C. C. and Foott, R., Journal of the Geotechnical Engineering Division, ASCE, Vol. 100, No. GT 7, July 1974, pp. 786-793. |7] France, J. and Sangrey, D. A.. Journal of the Geotechnical Engineering Division, ASCE, Vol. 103, No. GT 7, July 1977. pp. 769-785. [S] See Ref 6. 191 See Ref 6. [10] Simons, N. E. in Shear Strength of Cohesive Soils, ASCE. New York. 1960. pp. 744-763. [11] Skempton, A. W. in Proceedings, 5th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Dunod Press, Paris, 1961, pp. 351-357. 1/21 Togrol, E. in Proceedings, 6th International Conference on Soil Mechanics and Foundation Engineering, Vol. 2, University of Toronto Press, 1965, pp. 382-384. 1/Jl Skempton, A. W. and Henkel, D. J. in Proceedings, 3rd International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Swiss Organizing Committee, Zurich, 1953, pp. 302-312. 1/41 Mesri, G. and Olson, R., Geotechnique, Vol. 20, No. 3, Sept. 1970, pp. 261-270. 1/51 Sangrey, D. A., Henkel, D. J., and Esrig, M. I., Canadian Geotechnical Journal, Vol. 6, No. 3, Aug. 1%9, pp. 241-252. 1/61 Hvorslev, M. J. in Shear Strength of Cohesive Soils, ASCE. New York, 1960, pp. 169-273. 1/71 Swanson, P. G. and Brown, R. E.. "Triaxial and Consolidation Testing of Cores from the 1976 Atlantic Margin Coring Project," Open File Report No. 78-124 to the United States Geological Survey, Law Engineering Testing Company, Washington, D.C., Nov. 1977. [IS] Parry, R. H. and Nadarajah, V., Geotechnique, Vol. 24, No. 3. March 1973. pp. 345-358. 1/9] Shibata, T. and Karube, D. in Proceedings, 7th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1969, pp. 361-368. 1201 See Ref 16. [21] See Ref 6. 1221 Moh, Z., Nelson, J., and Brand. E. in Proceedings. 7th International Conference on Soil Mechanics and Foundation Engineering. Vol. 1. Sociedad Mexicana de Mecanica de Suelos, Mexico, 1969, pp. 287-295. [23] Croce, A., Japelli, R., Pellegrino, A., and Viggiani, C. in Proceedings. 7th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1969, pp. 81-89. 1241 Olson, R., Geotechnique, Vol. 12, No. I, March 1%2, pp. 23-43. 125] Lo, K. Y.. Geotechnique, Vol. 12. No. 4. Dec. 1962, pp. 303-318. 1261 Simons. N. E. in Shear Strength of Cohesive Soils, ASCE. New York. 1960, pp. 727-745. 127] Whitman, R. V. in Shear Strength of Cohesive Soils, ASCE, New York, 1960. pp. 581-614. [28] Raymond, G. P. \n Performance of Earth and Earth-Supported Structures, Vol. 1, Part 1, ASCE, New York, 1972, pp. 319-340. 129] Simon. R. M., Christian, J. T. and Ladd, C. C. in Analysis and Design in Geotechnical Engineering, Vol. I. ASCE. New York. June 1974, pp. 51-84. [30] Gibbs. H. J. et al in Shear Strength of Cohesive Soils, ASCE, New York, 1960. pp. 102-115. [31] Koutsoftas. D., Fischer. J.. Dette, J., and Singh, H., "Evaluation of the Vibracorer as a Tool for Underwater Geotechnical Explorations," Offshore Technology Conference. OTC Paper 2629, Houston, May 1976. 1J21 deGraft-Johnson, J. W. S., Bhatia, H. S., and Gidigasu, D. M. in Proceedings, 7th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1969, pp. 165-172. [33] Taylor, P. and Bacchus. D. in Proceedings, 7th International Conference on Soil


428


Mechanics and Foundation Engineering, Vol. 1, Sociedad Mexicana de Mecanica de Suelos. Mexico, 1969, pp. 401-409. \34\ Ladd, C. C , "Stress-Strain Behavior of Saturated Clay and Basic Strength Principles," Report No. R64-17 to the U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., April 1964. [35] Sherif, M. A., Wu, M. J., and Bostrum, R. C , "Reduction in Soil Strength Due to Dynamic Loading," Microzonatioii Conference. Vol. II, National Science Foundation and ASCE, Nov. 1972, pp. 439-454. [36] Tavenas, F., Blanchet, R., Garneau, R., and Leroueil, S., Canadian GeotechnicalJournal, Vol. 15, No. 2, May 1978, pp. 283-305. \37\ Olson, R. and Hardin, J. in Proceedings. 2nd Panamerican Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1963. pp. 204-218. \38\ Perloff, W. H. and Osterberg, J. O. in Proceedings. 2nd Panamerican Conference on Soil Mechancis and Foundation Engineering, Vol. I, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1963, pp. 103-128. [39] daCruz, P. T. in Proceedings, 2nd Panamerican Conference on Soil Mechanics and Foundation Engineering, Vol. I, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1963, pp. 73-102. \40] Lambe, T. W. in Proceedings, 2nd Panamerican Conference on Soil Mechanics and Foundation Engineering, Vol. H. Sociedad Mexicana de Mecanica de Suelos, Mexico, 1963, pp. 257-308, [41] Ladanyi, B. et al, Canadian GeotechniculJoumal. Vol. 2, No. 2, May 1965, pp. 60-89. [42] See Ref 6. [43] Wu, T. H., Chang, N., and Ali, E. M., Journal of the Geotechnical Engineering Division, ASCE, Vol. 104, No. GT 7, July 1978, pp. 889-905. [44] Ladd, C. C. and Lambe, T. W. in Laboratory Shear Testing of Soils, ASTM STP 361, American Society for Testing and Materials, 1963, pp. 342-371. [45[ Wesley, L. D., Journal of the Geotechnical Engineering Division, ASCE, Vol. 100, No. GT 5, May 1974, pp. 503-522. [46] D'Appolonia, E. D., Alperstein, R., and D'Appolonia, D. J. in Performance of Slopes and Embankments, ASCE, New York, 1966, pp. 489-518. [47] Egan, J. A., "A Critical State Model for the Cyclic Loading Pore Pressure Response of Soils," Ph.D. thesis, Cornell University, Ithaca, New York, June 1977. [48] See Ref 47. [49] See Ref 44. [50] Van Eekelen, H. and Potts, D. M., Geotechnique. Vol. 28, No. 2, May 1978, pp. 173-196. [51] Raymond, G. P., Highway Research Board Bulletin. No. 463, 1973, pp. 1-17. [52] Ladd, C. C , discussion on "Use of Stress Loci for Determination of Effective Stress Parameters" by R. Yong and E. Vey, Highway Research Board Bulletin. No. 342, 1962, pp. 49-51. [53] Wissa, A,, Ladd, C. C , and Lambe, T. W. in Proceedings, 6th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, University of Toronto Press, 1965, pp. 412-416. [54] Adams, J. in Proceedings, 6th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, University of Toronto Press, 1965, pp. 3-7. 155] Kenney, T. and Watson, G. in Proceedings, 5th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Dunod Press, Paris, 1961, pp. 191-195. [56] Bjerrum, L. and Simons, N. in Shear Strength of Cohesive Soils, ASCE, New York, 1%0, pp. 711-726. [57] Leathers, F. D. and Ladd, C. C , Canadian Geotechnical Journal. Vol. 15, No. 2, May 1978, pp. 250-268. |5«1 Hanzawa, H., Soils and Foundations, Vol. 17, No. 4, Dec. 1977, pp. 17-30. [59] Alberro, J. and Santoyo, E. in Proceedings, 8th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1.1, USSR National Society on Soil Mechanics and Foundation Engineering, Moscow, 1973, pp. 1-9.



429

\60] Mitachi. T. and Kitago, S., Soils and Foundations. Vol. 16, No. 1, March 1976, pp. 45-58. [6/] See Ref 60. [62] See Ref 60. \b3\ Hanzawa, H., Soils and Foundations, Vol. 17, No. 4, Dec. 1977, pp. 1-15. [64] Tavenas, F., Leroueil, S., LaRochelle, P., and Roy, M., Canadian Geotechnicid Journal. Vol. 15, No. 3, Aug. 1978, pp. 402-423. {64b] Tavenas, F. A. et al in In Situ Measurement of Soil Properties, Vol. 1, ASCE, New York, 1975, pp. 450-476. 165) Yudhbir and Varadarajah, A., Soils and Foundations, Vol. 14, No. 4, Dec. 1974, pp. 1-12. 166) See Ref 65. |67] Sketchley, C. J. and Bransby, P. L. in Proceedings, 8th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, USSR National Society on Soil Mechanics and Foundation Engineering, Moscow, 1973. pp. 377-384. [68] Broms, B. and Casbarian, A. in Proceedings, 6th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, University of Toronto Press, 1965, pp. 179-183. 169] Ladd, C. C , "Laboratory Determination of Soil Parameters for Excavation and Shallow Foundations," Field and Laboratory Determinations of Soil Parameters, ASCE, National Capital Section, Washington, D.C., 1976. ]70] Montgomery, M. W., "Geotechnical Investigation - Gas Centrifuge Enrichment Plant. Portsmouth, Ohio," Law Engineering Testing Company, Report No. MK 7502, April 1978. [71] Fischer, K. P., Anderson, K. H., and Mourn, J., Canadian Geotechnical Journal, Vol. 15, No. 3, Aug. 1978, pp. 322-331. [72] Korhonen, K. H. in Proceedings, 9th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Japanese Society of Soil Mechanics and Foundation Engineering, Tokyo, 1977, pp. 165-168. [73] Wu, T., Douglas, A. and Goughnour, R., Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 90, No. SM 3, June 1962, pp. 1-32. [74] Broms, B. and Ratnam, M., Journal of the Soils Mechanics and Foundations Division, ASCE, Vol. 89, No. SM 6, Nov. 1963, pp. 1-26. 175] Karlsson, R. and Pusch, R. in Proceedings, Geotechnical Conference, Oslo, Vol. 1, Norwegian Geotechnical Institute, 1967, pp. 35-42. 176] Sridharan, A., Rao, Narasimha S. and Rao, Venkatappa, G., Soils and Foundations, Vol. 11, No. 3. Sept. 1971, pp. 1-22. 177] See Ref 76. [78] Crooks. J. H. and Graham, J., Geotechnique, Vol. 26, No. 2, 1976, pp. 293-315. [79] Gangopadhyay, C , Som, N. and Roy, S., Indian Geotechnical Journal, Vol. 4, No. 2, Jan. 1974, pp. 140-160. [80] Widger, R, A. and Fredlund, D. G., Canadian Geotechnical Journal, Vol. 16, No. 1, Feb. 1979, pp. 140-151. [81] Swanson, P. G. and Brown, R. E., "Triaxial and Consolidation Testing of Cores from the 1976 Atlantic Margin Coring Project," Open File Report No. 78-124 to the United States Geological Survey, Law Engineering Testing Company, Nov. 1977. ]82] Saxena, S., Hedberg, J. and Ladd, C. C , Geotechnical Testing Journal. Vol. 1, No. 3. Sept. 1978, pp. 148-161. [83] Abeyesekera, R. A., Geotechnical Testing Journal, Vol. 2, No. 1, March 1979, pp. 11-19. [84] Singh, Ram and Gardner, William in Soil Dynamics in the Marine Environment. Proceedings of ASCE, Preprint 3604, April 1979. [85] Donaghe, R. T. and Townsend, F. C., Geotechnical Testing Journal. Vol. 1, No. 4, Dec. 1978, pp. 173-189. [86] See Ref 85. [87] Akai, K. and Adachi, J. in Proceedings. 6th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, University of Toronto Press, 1965, pp. 146-150. [88] Costa Filho, L., Wemeck, M., and Collet, H. in Proceedings. 9th International Con-


430


ference on Soil Mechanics and Foundation Engineering, Vol. I, Japanese Society of Soil Mechanics and Foundation Engineering, Tokyo, 1977, pp. 69-72. \S9] Sparrow, R. W., Swanson, P. G.. and Brown, R. E., "Report of Laboratory Testing of Gulf of Alaska Cores," Open File Report to the United States Geological Survey, Law Engineering Testing Company, March 1979. [90] Crawford, C , Canadian GeotechnicalJournal, Vol. 1, No. 4, Nov. 1964, pp. Ill-US. [91] Poulos, H. G., Geutechnical Testing Journal, Vol. I, No. 2, June 1978, pp. 102-106. [92] Henkel, D. J. and Sowa, V. A. in Laboratory Testing of Soils. ASTM STP36I, American Society for Testing and Materials, 1964, pp. 280-291. [93] Duncan, J. M. and Seed, H. B., Journal of Soil Mechanics and Foundations Division. ASCE, Vol. 92, No. SM 5, May 1966, pp. 21-50. [94] Wroth, C. P. and Loudon, P. A. in Proceedings. Geotechnical Conference, Oslo, Vol. 1, 1%7, pp. 159-163. [95] Mahar, L. J. and Ingram, W. B.. "Geotechnical Investigation for a Field Study of Pile Group Action," FUGRO GULF, Inc., Report No. 78-161-1 for the Federal Highway Administration, Oct. 1979. [96] Schofield, A. N. and Wroth, C. P., Critical-State Soil Mechanics, McGraw-Hill, London, 1968, pp. 134-206. ]97] Roscoe, K. H. and Burland, J. B. in Engineering Plasticity, Cambridge University Press, 1%8, pp. 535-609. [98] Skempton, A. W., Geotechnique, Vol. 4, 1954, pp. 143-147. [99] Henkel, D. J. and Wade, N. H., Journal oj Soil Mechanics and Foundations Division, ASCE. Vol. 92, No. SM 6, June 1%6, pp. 67-80. [100] Ladd, C. C , Foott, R., Ishihara, K., Schlosser, F., and Poulos, H. G. in Proceedings, 9th International Conference on Soil Mechanics and Foundation Engineering, Vol. 2, Tokyo, 1977, pp. 421-495. [lOI] Atkinson, J. H. and Bransby, P. L., The Mechanics of Soils, McGraw-Hill, London, 1968, pp. 329-333. ]I02] Mesri, G., Ullrich, C . and Choi, Y., Geotechnique, Vol. 28, No. 3, Aug. 1978, pp. 281-307. [103] Pender, M. J., Geotechnique, Vol. 28, No. 1, March 1978, pp. 1-25. [104] Mayne, P. W., Geotechnical Testing Journal, Vol. 2, No. 2, June 1979, pp. 118-121. [105] Mayne, P. W., Journal of the Geotechnical Engineering Division, ASCE, Vol. 106, No. GTU.Nov. 1980, pp. 1219-1242. [106] Butterfield, R., Geotechnique, Vol. 29, No. 4, Dec. 1979, pp. 469-479. [107] Bishop, A, W. and Henkel, D. J., The Measurement of Soil Properties in the Triaxial Test, Edward Arnold, London, 1957.


J. H. Prevost^

Nonlinear Anisotropic Stress-StrainStrength Behavior of Soils

REFERENCE: Prevost. J. H., "Nonlinear Anisotropic Stress-Strain-Strengtii Beliavior of Soils," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 431-455. ABSTRACT: Soils consist of an assemblage of particles witli different sizes and shapes which form a skeleton whose voids are filled with various fluids. The stresses carried by the soil skeleton are conventionally termed "effective stresses" in the soil mechanics literature, and those in the fluid are called the "pore-fluid pressures". In cases in which some flow of the pore fluid can take place, there is an interaction between the skeleton strains and the pore-fluid flow. The solution of these problems therefore requires that soil behavior be analyzed by incorporating the effects of the flow (transient or steady) of the pore fluid through the voids, and thus requires that a multiphase continuum formulation be available for soils. Such a theory was first developed by Biot (1955) for an elastic porous skeleton. However, it is observed experimentally that the stress-strain behavior of the soil skeleton is strongly nonlinear, anisotropic, elastoplastic, and path-dependent. An extension of Biot's theory into the nonlinear anelastic range is therefore necessary in order to analyze the transient response of soil deposits. Such an extension of Biot's formulation is proposed herein by viewing soil as a multiphase medium consisting of an anelastic porous skeleton and viscous fluids, and by using the modem theories of mixtures developed by Green and Naghdi (1965) and Eringen and Ingram (1965). In order to relate the changes in effective stresses carried by the soil skeleton to the solid rate of deformation tensor, a general analytical model is used which describes the nonlinear, anisotropic, elastoplastic, stress and strain dependent, stress-strain-strength properties of the soil skeleton when subjected to complicated three-dimensional and, in particular, cyclic loading paths. The theory falls within the general framework of the formalism of classical plasticity theory. It combines properties of isotropic and kinematic plasticity, and allows for the adjustment of the plastic hardening rate to any kind of experimental hardening law by using a collection of nested yield surfaces. It is shown that the model parameters required to characterize the behavior of any given soil can be derived entirely from the results of conventional soil tests. The model's extreme versatility and accuracy is demonstrated by applying it to represent the behavior of both cohesive and cohesionless soils under both drained and undrained, monotonic and cyclic loading conditions. The use of the proposed formulation for solving boundary value problems of interest in soil mechanics is illustrated. KEY WORDS; consolidation, constitutive equations, diffusion, finite elements, geotechnical engineering, plasticity, porous media 'Assistant Professor of Civil Engineering, Princeton University, Princeton, N.J. 08544.

Copyright by Downloaded/printed Copyright 1981 University of

by

431 ASTM Int'l (all rights by A S T M International www.astm.org British Columbia Library

reserved); pursuant

Sun to

Dec License

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Agreement

432


Soil consists of an assemblage of particles with different sizes and shapes which form a skeleton whose voids are filled with various fluids. The stresses carried by the soil skeleton are conventionally termed "effective stresses" [1]^ in the soil mechanics literature, and those in the fluids are called the "porefluid pressures". In cases in which some flow of the pore fluids takes place, there is an interaction between the skeleton strains and the pore-fluid flow. The solution of these problems therefore requires that soil behavior be analyzed by incorporating the effects of the flow (transient or steady) of the pore fluids through the voids, and thus requires that a multiphase continuum formulation be available for soils. Such a theory was first developed by Biot [2] for an elastic porous skeleton. However, it is observed experimentally that the stress-strain behavior of the soil skeleton is strongly nonlinear, anisotropic, elasto-plastic, and path-dependent. An extension of Biot's theory into the nonlinear anelastic range is therefore necessary in order to analyze the transient response of soil deposits. Such an extension of Biot's formulation [3] is adopted herein. The resulting coupled field equations [3] obtained by viewing soil as a multiphase medium consisting of an anelastic porous skeleton and viscous fluids, and by using the modem theories of mixtures developed by Green and Naghdi [4] and Eringen and Ingram [5], are presented. In order to relate the changes in effective stresses carried by the soil skeleton to the skeleton rate of deformations, a general analytical model is used [6] which describes the nonlinear, anisotropic, elastoplastic, stress and strain dependent, stress-strain-strength properties of the soil skeleton when subjected to complicated three-dimensional and, in particular, cyclic loading paths [7]. A brief summary of the model's basic principle is included and the constitutive equations are provided. It is shown that the model parameters required to characterize the behavior of any given soil can be derived entirely from the results of conventional soil tests. The model's extreme versatility and accuracy are demonstrated by applying it to represent the behavior of both cohesive and cohesionless soils under both drained and undrained, monotonic and cyclic loading conditions. The use of the proposed formulation for solving boundary value problems of interest in soil mechanics is thereafter illustrated by applying it to analyze (7) the one-dimensional and two-dimensional consolidation of a linear elastic porous medium, and (2) the time-dependent response of a rigid footing resting on top of a soil deposit and loaded at various loading rates.

Field Equations For a saturated soil consisting of a macroscopically perfect fluid and a piecewise-linear time-independent porous skeleton wherein both the pore ^The italic numbers in brackets refer to the list of references appended to this paper.


PREVOST ON NONLINEAR ANISOTROPIC BEHAVIOR OF SOILS

433

fluid and the solid grains are incompressible, the coupled field equations take the following forms [3]: div[ff'' + a'' div v^] - div[(p„, + p„, div v^l] + div[D : L'] + p„,divv^b - a") + pb = p'a' + p"'a»' (1) •k"'^ • (grad/j„, - p„,b + pâ") + div v» = 0

— div

(2)

Pw

where D ahcd

1 [1 = 0, P = Q; consequently the C-tensor possesses the major symmetry. The yield function is selected of the form [6] / = ^ ( s ^ - a) : (s^ -a)

+ C^(p'» - ^)2 - ^2 = 0

(20)

where s* is the deviatoric stress tensor (that is, s* = a '^ — p '* 1, p '* = '/3 trace a ' 0 ; a and |3 are the coordinates of the center of the yield surface in the deviatoric stress space and along the hydrostatic stress axis, respectively; k is the size of the yield surface; and C is a material parameter called the yield surface axis ratio. In order to allow for the adjustment of the plastic hardening rule to any kind of experimental data (for example, data obtained from axial or simple shear soil tests) a collection of nested yield surfaces is used. A plastic modulus is associated with each of the yield surfaces, and


436


where h ' is the plastic shear modulus, and {h' + B') and (h' — B') are the plastic bulk moduli associated with / which are mobilized in consolidation tests upon loading and unloading, respectively. The projections of the yield surfaces onto the deviatoric stress subspace thus define regions of constant plastic shear moduli. The yield surfaces' initial positions and sizes reflect the past stress-strain history of the soil skeleton, and in particular their initial positions are a direct expression of the material "memory" of its past loading history. Because the a's are not necessarily all equal to zero, the yielding of the material is anisotropic. Direction is therefore of great importance and the physical reference axes ix,y,z) are fixed with respect to the material element and specified to coincide with the reference axes of consolidation. For a soil element whose anisotropy initially exhibits rotational symmetry about the j-axis, a^ = a^ = — a^/2, and Eq 20 simplifies to [{a, •' - a, •') - aY + C^ (p '' - &Y - k^ = 0

(22)

where a = 3a^/2. The yield surfaces then plot as ellipses in the axisymmetric stress plane {a^'^ — a,'^) as shown in Fig. 1. Points C and E on the outermost yield surface define the critical state conditions (that is, H ' = 0) for axial compression and extension loading conditions, respectively. It is assumed that the slopes of the critical state lines OC and OE remain constant during yielding. The yield surfaces are allowed to change in size as well as to be translated

(a;-a;)

3p'»(aj;*2a;)

FIG. I—Field of yield surfaces in axial stress plane.



437

by the stress point. Their associated plastic moduli are also allowed to vary and, in general, both k and H' are functions of the plastic strain history. They are conveniently taken as functions of invariant measures of the amount of plastic volumetric strains and/or plastic shear distortions, respectively [7]. Complete specification of the model parameters requires the determination of (1) the initial positions and sizes of the yield surfaces together with their associated plastic moduli, (2) their size or plastic modulus, or both, change as loading proceeds, and (3) the elastic shear, G, and bulk, B, moduli. The soil's anisotropy originally develops during its deposition and subsequent consolidation which, in most practical cases, occurs under no lateral deformations. In the following, the >'-axis is vertical and coincides with the direction of consolidation; the horizontal jcz-plane is thus a plane of material's isotropy and the material's anisotropy initially exhibits rotational symmetry about the vertical ji-axis. The model parameters required to characterize the behavior of any given soil can then be derived entirely from the results of conventional monotonic axial and cyclic strain-controlled simple shear soil tests [6.7.10,11]. This will now be explained and further discussed. Determination of Model Parameters In order to follow common usage in soil mechanics, compressive stresses and strains are considered positive. All stresses are effective stresses unless otherwise specified and, in order to simplify the notation, the superscript s is omitted hereafter. As explained previously, for a material which initially exhibits crossanisotropy about the vertical j-axis, the initial position in stress space of the yield surfaces is defined by the sole determination of the two parameters a*"'' andfi^"'^(m — 1, . . . , p), and Eq 22 simplifies to \q - a'""]^ + C2 [p ' - /^("•'p - [A;("'>]2 = 0

(23)

for axial loading conditions (that is, a^' = oj and i^ = T^, = j ^ — 0), where q — {Oy' — a^'). The yield surfaces then plot as circles in the q versus £p ' plane (referred to as the axial stress plane hereafter) as shown in Fig. 2. A^hen the stress point reaches the yield surface,/„,, q = a*"'' + ;fc*"'> sin d

(24a)

p ' = /3 sin 6c

(40) (41)

^^^^

(43)

t (m)

/3,»"')=pc'exp(-Xe,C)

^cos^c

(44)

where TC = sin 6c + Cyc cos 6c

(45a)

TE = sin 6E + CyE cos 6^

(4Sb)

The yield surface,/], is chosen as a degenerate yield surface of size A / " = 0. Further, in order to get a smooth transition from the elastic into the plastic regime, ^ i ' = oo; so that the material behavior inside/2 is elastic. The elastic shear, Gi, and bulk, 5 ) , moduli are then determined from the steepest slopes observed at the origin of the plots q versus e, andp ' versus e^ of the axial compression/extension soil test results, respectively. At the critical state, Xc = x^ = 0; and the stress point is on the outermost yield surface/^. From Eqs 39 and 40, it is apparent that ftp' = 0 in that case.



441

Interpretation of Monotonic Unchained Axial Compression and Extension Soil Test Results In undrained tests, 4^ = 0, and (from Eq 37)yc= yg — " B\ in that case. The model parameters associated with the yield surface /„, are again determined by the condition that the slopes q/T are to be the same in axial compression and extension tests when the stress point has reached the yield surface /„,. As noted previously, the corresponding values dc and d^ are determined from Eqs 33 and 34, in which RCE-C''''''''

(46)

Knowing B^ and B^, the model parameters associated with /„, are computed using Eqs 39 to 45 in which e^^ = e,,^ = 0. Note that the sole use of undrained axial soil test results for the determination of the model parameters does not allow the determination of the parameter \ . Interpretation of Simple Shear Soil Test Results In simple shear soil tests, e^ = e^ — e^ = 0. The necessary algebra for the determination of the model parameters is considerably simplified in that case if the elastic contributions to the normal strains are neglected. Equations 17 to 21 then yield a^' — a.',

«('") = ( a / - a / )

(48)

fcv

a

H

'

0

0

0

—

0• c—

—

•

-

o 1=1.5

0

0

0

I

0

.6\ j

Analyticol

.4 --

-

0 0

.2

-

\ ^

0

1 10-3

5—i

10-2

10-1 b

4

r^^ lot

lOl

T-Cv^:

H»

8/H

(a) Finite element mesh (b) Degree of consolidation versus time (c) Settlement versus time FIG. 8—One-dimensional elastic consolidation.

numerical solution accurately predicts the increase in excess pore-fluid pressure which occurs at the early times of consolidation. This phenomenon is characteristic of the coupled theory [2.21-24] and is referred to as the Mandel-Cryer effect. Figure 9c shows the computed dimensionless settlement, 6, of the center point of the strip load as a function of the dimensionless time, T, for various h/fi^ ratio. The curves again show that the larger the h/n" ratio, the more drastic is the difference between finite and small deformation results. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.


451

Hh 111 nil

K.I. ((.(•RaflKUd louKMrir

T.eyt/B* y».o

10-3

lO-J

10-1

lOO

lOt

102

(a) Finite element mesh (b) Pore-fluid pressure versus time at depth Z = B/2 (c) Midpoint settlement versus time FIG. 9—Two-dimensional elastic consolidation. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

452


•2 ^

00

m

cd a:

V)

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3 o ffi T3

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o


453

Two-Dimensional Elasto-Plastic Consolidation [18] The finite element mesh and problem description are shown in Fig. 10a. A rigid permeable strip footing of width IB is resting on the surface of a soil layer with drainage occurring at the top surface only. The mechanical properties of the soil to be considered in this example are described by the axial compression and hydrostatic consolidation stress-strain curves shown in Figs. 3 and 4. Table 1 gives the model parameter values which characterize the behavior of this soil. The parameter values have been normalized by dividing them by a^^ '^ — vertical effective consolidation stress. The soil deposit is assumed to be normally consolidated, and &„. ''^ = y '^z where z is the depth measured from the top surface of the deposit and 7'^ = (1 — «»)p,. Here «»' = 0.7, p/p„. - 2.82, andfe™= 2.10'*'. The transient response of soil deposit under the footing load is dependent upon the rate of loading, w,

^^

1 dh H' dT

where T = Cj/B^ as previously, and n^ is selected to be the initial (at time f = 0) shear modulus at depth Z = 5 / 2 , (that is, /x* = 120.0). At very slow loading rates (that is, w -> 0) the soil deposit's response is fully drained, whereas when the loading rate becomes large (that is, w — 00), the deposit behaves in an undrained (that is, constant volume) fashion. This is illustrated in Fig. lOb, which shows the computed load/settlement curves for various loading rates. These calculations were performed by neglecting changes in geometry (that is, small strains/displacement) and by including the effects of gravity. The numerical results shown in Fig. \0b were obtained by taking At,, = ^ Ar„_, with jS = 1.1, so that loading could be achieved in 16 steps only. Use of the proposed formulation for solving other boundary value problems of interest in soil mechanics has also been demonstrated by applying it to analyze the interaction of an offshore gravity structure with its soil foundation when subjected to cyclic wave forces [25,26], the penetration of marine pipelines into their soil foundation [26], and the localization of deformations into shear bands in soil media [27].

Smnmary and Ctmclusions The coupled field equations that govern the behavior of anelastic porous media are presented. A general analytical model that describes the nonlinear, anisotropic, hysteretic stress-strain behavior of the soil skeleton is proposed. The accuracy and versatility of the model are demonstrated. The


454


use of the proposed formulation in solving boundary value problems of interest in soil mechanics is demonstrated. Acknowledgments Computer time was provided by Princeton University Computer Center. References [/] Terzaghi, K., Theoretical Soil Mechanics, Wiley, New York, 1943. [2] Biot, M. A., Journal of Applied Physics, Vol. 26, 1955, pp. 182-185. [3] Prevost, J. H., International Journal of Engineering Science, Vol. 18, No. 5, 1980, pp. 787-800. [4\ Green, A. C. and Naghdi, P. M., International Journal of Engineering Science. Vol. 3, 1%5, pp. 231-241. [5] Eringen, A. C. and Ingram, J. D., International Journal of Engineering Science. Vol. 3, 1965, pp. 197-212, and Vol. 5, 1967, pp. 289-322. [6] Prevost, J. H., Journal of the Engineering Mechanics Division, American Society of Civil Engineers, Vol. 104, No. EMS, 1978, pp. 1177-1194. [7) Prevost, J. H., International Journal of Numerical Analytical Methods in Geomechanics, Vol. 1, No. 2, 1977, pp. 195-216. [8\ Hill, R., Journal of the Mechanics and Physics of Solids, Vol. 6, 1958, pp. 236-249. [9] McMeeking, R. M. and Rice, J. R., International Journal of Solids and Structures, Vol. 11, 1975, pp. 601-616. [10] Prevost, J. H., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, Vol. 104, No. GTS, 1978, pp. 1075-1090. [//] Prevost, J. H. in Proceedings, 3rd International Conference on Numerical Methods in Geomechanics, Aachen, Germany, Vol. 1, 1979, pp. 347-361. [12] Richard, F. E., Woods, R. D., and Hall, J. R., Vibrations of Soils and Foundations. Prentice-Hall, Englewood Cliffs, N.J., 1970. \I3] Roscoe, K. H. and Burland, J. B. in Engineering Plasticity. Heyman and Leckis, Eds., Cambridge University Press, Cambridge, England, 1%8, pp. 535-609. [14] Forrest, J. H. et al, "Experimental Relationships between Moduli for Soil Layers Beneath Concrete Pavements," Report No. FAA-RD-76-206, 1976. [15] Anderson, K. H. in Proceedings. BOSS 76 Conference, Tronheim, Norway, Vol. 1, 1976, pp. 392-403. [16] Zienkiewicz, O. C , The Finite Element Method. McGraw-Hill, New York, 1977. [IT] Hughes, T. J. R. and Prevost, J. H., "DIRT II — A Nonlinear Quasi-static Finite Element Analysis Program," California Institute of Technology, Pasadena, Calif., August 1979. [18] Prevost, J. H., Journal of the Engineering Mechanics Division. American Society of Civil Engineers, Vol. 107, No. EMI, 1981, pp. 169-186. [19] Malkus, D. S. and Hughes, T. I. R., Computer Methods of Applied Mechanical Engineering. Vol. 15, No. 1, 1978, pp. 63-81. [20] Scott, R. F., Principles of Soil Mechanics. Addison-Wesley, New York. 1963. [21] Chen, A. T. -F., "Plane Strain and Axi-Symmetric Primary Consolidation of Saturated Clays," Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, N.Y., 1%6. [22] Cryer, C. W., Quarterly Journal of Mechanics and Applied Mathematics. Vol. 16, 1963, pp. 401-412. [23] Mandel, J., "Etude Mathematique de la Consolidation des Sols," Actes du Colloque International de Mechanique. Poitier, France, Vol. 4, 1950. pp. 9-19. [24] Mandel, J., Geotechnique. Vol. 3, 1953, pp. 287-299. [25] Prevost, i. H., Hughes, T. J. R., and Cohen, M. F., "Analysis of Gravity Offshore Structure Foundations,"/owrna/o/Perrotewm Technology, Feb. 1980, pp. 199-209.



455

\26] Prevost, J. H. and Hughes, T. J. R., "Finite Element Solution of Boundary Value Problems in Soil Mechanics," in Proceedings. International Symposium on Soil under Cyclic and Transient Loading, Swansea, U.K., Jan. 1980, pp. 263-276. 127\ Prevost, J. H. and Hughes, T. J. R., Journal of Applied Mechanics, American Society of Mechanical Engineers, Vol. 48, No. 1, 1981, pp. 69-74.


/. H. Schmertmann^

A General Time-Related Soil Friction Increase Phenomenon

REFERENCE: Schmertmann, J. H., "A General Time-Related SoU Friction Increase Phenomenon," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and P. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 456-484. ABSTRACT: Various laboratory treatments of clay specimens produced an increase in the frictional component of their ability to mobilize shear resistance. These treatments included compression after isotropic normal consolidation, compression after isotropic overconsolidation, anisotropic normal consolidation, chemically induced dispersion, changing pore fluid, decreasing rate-of-strain, increasing time for secondary compression, and allowing time for creep. The paper shows how increasing clay fabric dispersion in these treatments relates directly to an increased friction capability. The author then suggests that the dispersion shifts the external shear load to stiffer and stronger aggregates of particles in the fabric. This produces a stiffer and stronger clay due to its increased frictional capability. The practical aspects of this behavior include a better understanding of various laboratory specimen aging effects such as increasing modulus and the quasi-preconsolidation effect, recognizing it as a frictional and not a bonding behavior, and the desirability of including such behavior in the laboratory or computer simulation of in situ performance. KEY WORDS: soils, soil tests, shear properties, clays, fabric, compressibility, aging, time effects, friction

Nomenclature A Ag c' Cf c/j D E

Pore pressure parameter = [AM/A(CTI ' — oj')] Net value of A during quasi-preconsolidation (2-4 ESP in Fig. 12) Empirical Mohr-Coulomb cohesion intercept in terms of effective stress Early notation for /^ Alternative expression for the D-component, = AT/ACT' Component of mobilized shear resistance seemingly linearly dependent on effective stress, a', at constant structure Young's modulus

'Principal, Schmertmann and Crapps, Inc., Gainesville, Fla. 32601.


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SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

ESP G Gj iNC iOC / /f IDS-test /„, IQ KQ NC OC Pc Po Apcq PI R ^2 S4 u wi Wp Wj X^ j3 A 6 a a' ai' oi' 03' <Ti 'h Oi'( T

457

Effective stress path Shear modulus Specific gravity of soil solids Isotropically normally consolidated Isotropically overconsolidated Component of mobilized shear resistance seemingly independent of effective stress, a', at constant structure. Note I + D — T Notation for / to emphasize that component is a function of strain, value of / at strain e Experimental procedure for determining the / and D components of T as functions of strain. Usually done with e and u control Maximum value of / determined from a graph of / versus strain Mobilized shear resistance when a ' = 0, the bond shear resistance Ratio of (J3 Vffi' during virgin consolidation Normally consolidated Overconsolidated Preconsolidation pressure Normal consolidation pressure Increment of apparent p^. due to quasi-preconsolidation effect Atterberg plasticity index Overconsolidation ratio Value of [(1 — Ko)/{l + KQ)] before secondary compression aging Value of [(1 — /Co)/(I + KQ)] at start of new increment of virgin consolidation Pore water pressure Atterberg liquid limit Atterberg plastic limit Atterberg shrinkage limit Fraction of /3-strength increase mobilized during secondary aging Parameter relating /-component to effective stress [1]^ Denotes "an increment of" Strain Total normal stress Effective normal stress, = a — u Major principal effective stress Average value of a^' (bar denotes average value) Minor principal effective stress Higher effective stress level in an IDS-test Lower effective stress level in an /D5-test Mobilized shear resistance

The italic numbers in brackets refer to the list of references appended to this paper.


458

(j>' are needed. Note that c and / are shear strength parameters that are obtained through the application of the two-parameter failure theory. Their direct relationship to the actual physics of the problem (that is, shear resistance mechanisms) is obtained when the soil response performance is properly modelled. In other soils where overconsolidation effects or strong bonding forces, or both, exist, it has been observed that in several instances the application of a simple yield or failure criterion, normally used for c-<j> soils, may not adequately represent the actual situation. An example of such an inadequacy is shown in Fig. 3 where a bonded sensitive clay from St. Jean Vianney is tested at effective normal pressures/?' below the preconsolidation pressure PciPc ~ 100 psi = 689.5 kPa). The shear strength s = (a| - (Tj)/! from consolidated undrained (CU) triaxial tests is shown at peak and residual levels. It may be seen that a curved envelope would better fit peak shear strength as opposed to a straight Mohr-Coulomb envelope. Further discussion of this problem is given later in the section on Conflict Resolution. Violations of Fitted Criteria It is not unusual to observe some deviations between predicted shear strength and response performance from an analytical model on the one hand and measured strength and observed performance on the other hand. When such deviations or disagreements occur, one might observe that the fitted criterion, in a deterministic context, could be violated. Violations may be attributed either to shortcomings of the analytical model or to inadequacy of the STT. In the second-order envelope fitted to peak shear strength in Fig. 3, for example, this envelope represents the average shear strength s mobilized at a given p '. The actual measurements obtained show violations both on the safe and unsafe sides of the fitted failure envelope. Note that the unsafe side Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

492


-^

c

:::) u

I ^ .^

0:0

q, e / (Si) -

, s 4)6u9j(s

Jesi(5

Ol


YONG AND TABBA ON RANDOM ASPECT OF SHEAR STRENGTH

493

is in actual fact inadmissible or imaginary from the theoretical point of view, since points in this region cannot exist. Violations due to shortcomings of the analytical model are expected in the following cases: 1. When anisotropic soils are represented by isotropic analytic models. 2. When a strain-softening or work-hardening soil is represented by models assuming perfectly plastic behavior. 3. When the velocity field is assumed normal to the stress-increment field using plasticity analyses. 4. Extrapolation of fitted yield criterion beyond the range of available data, as, for example, at the lower end of the envelopes of Fig. 3. This is a well-known phenomenon in regression analysis, where the confidence level in the mean is reduced towards the two extremities of the data range [9]. Violations due to the inadequacy of the sampling and testing techniques (STT) can occur under the following circumstances: 1. If biased shear strength measurements are used for prediction without the necessary corrections for inherent bias, as shown by Tabba and Yong [7]. Such bias might be due to the created stress field and boundary conditions, sample orientation, sample disturbance and storage, stress relief, scale effects, strain rate, drainage conditions, pore-pressure development, volume change, etc. 2. When sample size (that is, number of tests) is too small to warrant prediction with reasonable confidence levels. 3. Where measurements are improperly distributed within the zone of interest to the project. Conflict Resolution It is apparent from the preceding discussions that two main drawbacks may be cited with regard to the present practice: 1. Failure to accommodate the random aspect of soil shear strength, including the spatial trend and scatter associated with a certain sampling and testing technique STT. This is a direct consequence of use of deterministic yield/failure criteria. 2. Failure to compare and/or combine test results belonging to different STT. It is noted that in addition to better and more careful testing techniques, improvement in one's capability for prediction of shear strength must also rely on the resolution of the aforementioned deficiencies. The wide range of soil types encountered in practice, and the increasingly numerous sampling and testing techniques available to the profession, require that proper attention Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

494


be paid to the recognition of the aforementioned deficiencies and to a resolution of the "conflict". Modelling of Shear Strength The basic requirement for resolution of the aforementioned conflict recognizes the random aspect of shear strength. The simplest representation of such a random phenomenon will identify the spatial trend as well as the scatter with respect to it, plus any autocorrelation that may exist in the data. Probabilistic modelling procedures of shear strength have been proposed earlier by several researchers, Wu and Kraft [10], Alonso [3], Lumb [//], Yucemen et al [12], Yong et al [13], Van Marcke [14], among others. Many of these models, however, are by and large difficult to use in practical situations where data points are few, are irregularly spaced, and come from different STT. For practical purposes, it suffices to deal with first-order probability approximation, where the random shear strength at each point in the soil deposit is represented by its mean, variance, and covariance. Higher-order probability parameters will not be useful in general, since a limited number of data points does not allow for any meaningful estimation of such parameters. An analytical model of mapping and prediction of random soil properties was suggested by Tabba and Yong [7], where the measured property (shear strength) Pj at any point i was resolved into a deterministic spatial trend component Pfand a random scatter component e, with respect to Pf, or Pi = P*+ e,

(1)

It was shown that the random scatter component denoted by e, combined uncertainty due to the soil's intrinsic nature with that due to the sampling and testing techniques. Two types of data are distinguished depending on the sampling technique used: block sampling which denotes a cluster of data at one point in space, and borehole sampling which denotes one piece of data at each point sampled. Distinction is also made according to the testing technique used between biased and unbiased data. The unbiased data set is defined as that which corresponds to the STT judged to be the most appropriate or accurate as a measurement of shear strength. Note that the judgement of "accuracy" of test result as a means of comparison of test information from two or more tests is purely one of relative measure of level of confidence in the test result obtained. The higher one's level of confidence in a particular test technique and the results obtained thereby, the greater is one's assessment of the "accuracy" of the results. It follows then that other types of STT providing a lesser degree of confidence in accuracy of measurements would be considered as biased data. Note that different test and research laboratories might differ


YONG AND TABBA ON RANDOM ASPECT OF SHEAR STRENGTH

495

insofar as "good sophisticated" test equipment and techniques are concerned. Thus, while one laboratory might consider the triaxial test to produce unbiased test results, another might consider the unconfined compression test or the direct shear test as "unbiased". With a set of measurements -P, from a borehole sampling program, irregularly distributed within the zone of interest to the project, one can associate each Pi with the physical location of point / (x,, yij, Zj) with respect to a global coordinates system (x.y.z). A trend function is then fitted to data points i = 1, 2, . . . n, using matrix formulation of the Maximum Likelihood theorem [15], Residuals are examined and their variance and autocorrelation function are derived. When two or more data sets, corresponding to biased and unbiased STT, are available for the same soil deposit, calibration is carried out to evaluate various parameters characterizing the spatial trend and scatter of shear strength. Of particular interest to this study are two parameters e and X, defined by Tabba and Yong [7] in the following manner: !• e, defined as the mean bias, represents the average relative bias of the biased data set with respect to the unbiased one. In other words, it is the average amount of bias by which biased shear strength measurements are different from the unbiased ones, the latter being considered as datum for comparison purposes. 2. X, defined as the bias of variance, is the ratio between variances of the biased and the unbiased shear strength measurements, which represent the amount of bias in the variance of scatter e, brought about by the biased STT as compared with the unbiased STT. Both e and X exclude the effect of spatial trend and can be calculated for a variety of mapping situations. To illustrate the application of biased and unbiased test results, reflecting one's assessment of the level of confidence of test measurements obtained, the analytical model of mapping and prediction was applied by Tabba and Yong [16] to the analysis of a landslide at St. Jean Vianney, Quebec, Canada [4], Mapping of undrained shear strength of the landslide area was carried out using four data sets corresponding to different STT, namely, field vane, laboratory vane, UC on recovered borehole samples, and UC from undisturbed blocks identical to those mentioned earlier. Various mapping combinations were calibrated and the amounts of bias e and X calculated. Considering the UC results from borehole samples as unbiased data set (see footnote to Table 2), e and X associated with the other three STT are shown in Table 2. It is seen, for example, that undrained shear strength measurements using field vane are on the average higher than those of UC (borehole) by 68.2 kPa (1425 psf), and the associated scatter is also higher by a ratio of 2.35 to 1.0. Thus UC on undisturbed block samples provides, on the average, the highest shear strength \e = 124.1 kPa (2590 psf)] of the four STT while it maintains a low scatter (X = 1.03). Meanwhile, the


496


TABLE 2—Comparison of undraimd shear strength from different samioling and testing techniques. Sensitive clay - St. Jean Vianney. Quebec [from Tabba and Yong IRef 16)]. Unbiased Test"

Mean bias e, psf kPa Bias of variance X

Biased Tests

UC Borehole''

Laboratory Vane''

Field Vane''

UC Blocks''

0 0 1

1025 49.1 2.0

1425 68.2 2.35

2590 124.1 1.03

"The choice of UC resuHs from borehole samples as unbiased data is used here for comparison purposes only and does not reflect any belief by the authors that it is the most appropriate or accurate method to measure the undrained shear strength of sensitive clays. *Unconfined compression on disturbed borehole samples using Shelby tubes, sample size 38 by 76 mm (1.5 by 3 in.). "•Laboratory vane on disturbed borehole samples using Shelby tubes, vane size 13 by 13 mm ('/2 by '/2 in.) down to 30 m (100 ft) depth, then 17 by 8.5 mm (2/3 by '/3 in.) downward. ''Field vane in boreholes, vane size 51 by 102 mm (2 by 4 in.). ••Unconfined compression on undisturbed blocks recovered from Trench T2, sample size 38 by 76 mm (1.5 by 3 in.). For sample stress-strain curves see Fig. 1.

lowest shear strength measurements are obtained from UC on borehole samples (e = 0), which provided the lowest variance of the four STT as well (X = 1.0). These results regarding the mean bias e are in general agreement with published data given by La Rochelle and Lefebvre [6] for sensitive clays of eastern Canada, and reflect the degree of disturbance due to the STT. One can conclude that for the St. Jean Vianney sensitive clay, UC on borehole samples created the highest disturbance while the lowest is offered by UC from block samples; the scatter of results is kept as low as possible in both techniques. On the other hand, field and laboratory vane created medium disturbance, but caused more scatter in test results. To implement shear strength mapping, one, two, or more parameters are needed to define the yield or failure criteria at each point in the soil deposit. As in the example of St. Jean Vianney cited here, the undrained shear strength of cohesive soils may be adequately described by one parameter s„ as in the Tresca yield criterion 5„ = •/2(a, - (T3)

(2)

Therefore, in such cases, mapping is carried out using individual measurements Sui at various points i. In cases where the shear strength is attributed to pure friction, s may be assumed as the product of the effective normal pressure p ' = '/2((Ji' + a^) and tan (/>, the friction coefficient. For soils where shear resistance is obtained through a combination of cohesion and friction, utilization of the Mohr-Coulomb failure criterion as s =" c + p' tan i V ear shee s

10

FIG. 15—Stress-strain curves from loading tests on loose sand with induced anisotropy (ti'datafrom 16 points).


ARTHUR ET AL ON STRESS PATH TESTS

2.0 5

1.6

-; 1.4

O

• o V

R =4

-

-

a

@

-

\© o -

/o

0.8

o

c

-

(3)

1.2 --

S 10 „

1

-

V>

UJ

O" — I —

1.8 RODRIGUEZ

j"

1—— 1 —

•

MIT

535

~

o/

0.6 0.4

-

O/a

-

0.2 T

0

i

l

l

1

10 20 30 40

50

1

1

1

60 70

1

80 90

6 (degrees) FIG. \b—Stniiii ratio versus rotation angle for loose sand with induceJ anisotropy.

5

1

1

1

„.

1

1

1

• ^

4

*

Test No

S/mbol

V

LI 0

^>-

7°

L I 40

—D—

3°

LtSO

--0--

-5°

L I 70,

-A--

•7°

L I 702 .-V—•

-6°

L I 90, . . - 0 - .

•2°

3

L I 902

2
and c values were indicative of drained test conditions. The close agreement of ' and c ' . Comparison with laboratory direct shear and triaxial tests showed that BST results fell in between. Results of comparative studies with conventional laboratory results have been reported by various investigators [1,7-10], A summary of available data for friction angle is shown in Fig. 4. The soil materials tested ranged from cohesionless sands (SW) to cohesive clays (CH). Although a considerable amount of scatter is indicated and BST results fall between drained and undrained, it is of interest to note that, with the exception of one point, all undrained laboratory tests give values lower than BST. In many cases, BST results tend to compare better with drained laboratory results, particularly at higher values of 0. It should be emphasized, however, Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

570


NORMM, STRESS

FIG. 3—Stage testing BST modified shear plates.

that no clear-cut relation exists for all materials. Wineland [10] has suggested that plasticity might be used as a qualitative indication of the drainage conditions; that is, high-plasticity clays may behave more as undrained and lowplasticity soils as drained. This appears to have some merit. The problem of positive pore pressures generated during shear appears to remain a difficult point. In saturated clays, if the soil is sheared at a faster rate than it drains, or if drainage is prohibited, positive pore pressure develops. In sands, or dry cohesive soils, this does not appear to present a problem, and results compare better with drained tests. Positive pore pressures are generally detected by a flattening of the failure envelope. This flattening can also be caused if the shear head is fully expanded, in that the normal stress on the control console can be increased without a further increase in applied normal stress on the shear plates. One method to detect if the flattening is caused by pore pressure is to repeat the test point with increased consolidation time. At present, no provision is made for detecting negative pore pressure. The problem of test drainage must be viewed from an individual test standpoint; saturated clays which have very low permeability should probably be treated as undrained, which would be on the safe side for design. As an example, consider the data shown in Fig. 5 for a very clay-rich shale. With initial void ratio e^ = 0.36 and saturation 5 = 100 percent, these results would no doubt be considered undrained, since the pore water has no means of escape. In some cases, the initial portion of a test may give data which could be considered drained, with the latter portion indicating undrained conditions, as in Fig. 6. For this test data, up to about 193 kPa (28 psi) normal stress, = 31.7 deg, c = 27 kPa (3.9 psi); after 193 kPa (28 psi), = 0 and using undrained shear strength Su', (2) for active slides, shear strength may be determined directly in the zone of shear to give the most realistic values for calculations; (3) if the area will not allow a drill rig to take samples, the use of a lightweight field test becomes necessary; and (4) measurement of soil creep. Rock Borehole Shear Test (RBST) The concept of Borehole Shear has been extended into in situ rock testing by the developers of the soil device [17] and while perhaps beyond the scope of this discussion it is worthy of mention. The RBST is nearly identical in operation to the BST, with the exception that the equipment has greater

.SANDY CLAY LOAM

600

_a^ " 6 psi (41.4 kPa)

(39 kPa)

J

l__L

J I I_J L I .L I 1 2 1 8 2 4 3 0 3 6 TIME (minutes)

VTfe-

FIG. 8—BST creep curves (modified from Ref 16).


576


12

SANDY CLAY LOAM w = 20.41 10 t-a^ = 5 p s i

2 O H

A 20 min

' even if interface friction is the mechanism of failure, unless that friction is local to the gage face. For the case of local friction, the method yields only the interface friction angle 6. Experimental results are encouraging, and the method is being studied for application to a deepwater wire-line device for in situ determinations of S and (j)'. KEY WORDS: angle of internal friction, clays, deepwater, friction angle, geotechnical engineering, in situ testing, interface friction, marine soils, penetrator, radial stress, shear strength, shear stress, soils, static strength, strength angle, stress gage, wire line

Experience is showing, as offshore work moves into deeper water, that conventional methods of determining in situ soil strengths are in some cases inadequate. The situation is expected to worsen as even deeper waters are explored over the next decade. Soil strengths are presently measured by boring/sampling/laboratoty testing or by in situ testing. The first procedure is often unsatisfactory, especially if the water is deep or the soils contain gas or clathrates, because of pressure release, temperature change, and sample disturbance. The in situ methods consist mainly of Standard Penetration Tests (SPT), cone-penetration tests, and vane-shear tests. The SPT is an impact-dynamic test which relies solely on empirical correlations to yield an estimate of soil strength, 'Technical staff member. Sandia National Laboratories, Albuquerque, N.M. 87185. 579 Copyright by Downloaded/printed Copyright 1981 University of


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580


and its results can be substantially in error, especially in cohesive soils. There are many types of cone-penetration tests, all of which rely either on empirical correlations or on modifications to or adaptations of bearing-capacity theory to yield estimates of soil strength. Cones are simple to use because they require only a pushing motion. They are widely used in marine exploration. The vane-shear test requires a twisting motion in addition to the pushing motion, but it measures soil strength directly by mobilizing that strength on an assumed cylindrical surface of shear. Existing cone and vane devices are designed for a few hundred feet of water; it is expected that considerable modification, and even redevelopment, will be required to operate in a few thousand feet of water, which is where much of the activity will be in the next decade. In most practical engineering problems, it is necessary to know not only a soil's present strength, but also how that strength and other properties will change in response to the future stresses which will be imposed on the soil. The SPT and the cone-penetrometer and vane-shear tests offer no direct information on how a soil's strength will change. Estimates of such information are presently obtained by laboratory testing, which consists of applying the anticipated stresses and measuring the soil's response to them in order to determine the soil's strength angle (t>'. This procedure, however, has the serious flaws of pressure release and sample disturbance, and confidence in the results is often quite low. It is therefore generally agreed among practitioners and researchers that there is a clear need to develop new and improved in situ methods for determining soil strength and effective strength angle, especially for deepwater situations. In an attempt to solve these problems, Texas A&M University has developed and used for about one year, a pressurized core barrel [1],^ which acquires samples preserved at their in situ pressure. The samples are sealed at their in situ pressures, raised to the surface, transported to a special pressurized laboratory chamber, and tested while the in situ pressure is maintained. The core barrel has been proved to depths of about 300 ft of water, the limit at which laboratory technicians can work in the special pressurized laboratory chamber. Work is underway to develop a core barrel for deeper water with an associated high-pressure testing facility. It is presently expected that the testing capability will initially be limited to vaneshear or unconfined tests, performed remotely within the high-pressure testing facility. Sandia National Laboratories is working to develop deepwater in situ testing instruments to be made available to government and industry. The first version of these, a pilot project to evaluate concepts and identify opportunities, is the Geotechnically Instrumented Seafloor Penetrator [2]. The present version, an instrument test platform, is a static penetrator which ^The italic numbers in brackets refer to the list of references appended to this paper.


MCNEILL AND GREEN ON A SHEAR-NORMAL GAGE

581

penetrates to a given depth, measures pore pressures continuously as a function of time, and transmits its data, on command, acoustically to a small boat on the surface. It is clear from the work to date that one promising way to estimate soil strength and its changes with time is by using penetrators [3], both static and dynamic. This paper has as a background the general notion of a small cylindrical static penetrator that is to be handled by wire line and pushed by the drill bit. This work is intended to provide insight into soilstrength phenomenology for purposes of guiding further theoretical and instrumentation developments, and for purposes of designing field and laboratory experiments. Valuable insight into the expected performance of penetrators can be gained by studying the results of pile-load tests, which are the reverse of a penetrator strength test. The soil's strengths are determined by conventional means, and then are integrated along the pile's skin area to calculate the load the pile can carry. The calculated load is then compared with the actual load as measured in the pile-load test. Experience shows that in most cases this procedure results in a calculated load which is higher than the actual load [4]. These experiences seem to indicate that (/) the true mechanism of stress transfer and strength mobilization is not accurately accounted for in the calculational procedure; or (2) sliding friction, at a value less than the soil strength, is playing some role in the mechanism; or (J) both. Studies have been presented that seek to account for both factors in a rigorous way using the theory of an expanding cavity [5,6]. Those studies are not yet complete. The work presented in this paper bypasses the fundamental mechanisms of the insertion of a penetrator. Instead, the effect of the insertion upon the soil is postulated, and the opportunities for novel instrumentation to measure soil properties are investigated. Finally, the derived principles are tested against data from the literature. Concepts The developments presented here assume that the cavity made by a static penetrator develops under the near-simultaneous applications of the surfacetraction shear of the downward-moving penetrator, and of the increased radial stresses required to expand a cavity in the soil. After the penetrator nose has passed, the conditions at the face of the penetrator are postulated to be as shown on the upper left-hand side of Fig. 1: (/) the shear stress at the face of the penetrator in the r-v plane is Sp-, and (2) the largest stress in the planes normal to or tangential to the face of the penetrator is the radial stress, a / (in this paper, all normal stresses are effective stresses, assuming that any static penetrator would have a pore-pressure measuring capability). The radial stress a/ is not, however, the largest possible normal stress, as shown by the limit equilibrium circle on the right-hand side of Fig. 1: the largest normal stress is the major principal stress, a / , which is inclined


582


b

S 'SS3J(S JDSMS

I I

O



583

radially off the vertical into the penetrator axis, as shown on the lower left of Fig. 1. Both of the a^'-a^' planes are probably actively failing, as shown, and, for a rough penetrator, the actual soil-shear failure surface is probably in the soil and some distance out from the penetrator. Thus, if a thin skin of soil is postulated to be adhering to the face of the penetrator, the shear stress at the face of the penetrator, Sp, is larger than the shear strength of the soil, Ss, and that shear stress could be approximately equal to the maximum shear, S,„; see Fig. 1. This point is studied with experimental data at the end of the section on Experimental Study. Inspection of the limit-equilibrium Mohr's circle in Fig. 1 indicates that, if it were possible to measure Sp and a/ while the penetrator is loaded andCTI' when the penetrator is unloaded, it should in principle be possible to calculate the effective strength angle,
\ .

(1)

I

Aa2 + Sp^ where ACT = O)' —CT^',as shown in Fig. 1. The derivation of Eq 1 is given in Fig. 2. The values of Sp and a/ could be measured by a gage that simultaneously measures shear and normal stresses [7,8]. The value a,' would be the normal-stress measurement on that gage when the penetrator is not loaded, if one assumes that the large cavity-expansion radial stress maintains the soil in the critical state [9]. Thus, referring to Fig. 1, it is in principle possible to calculate the strength angle, 0 ' , from a load-unload cycle on a rough penetrator, which forces the shear failure to occur in the soil. Then, using <j>' and the measuredCTJ', the shear strength of the soil {S^) and the maximum shear (S„,) can be calculated. It is in principle possible to do the same thing even if the penetrator is smooth so that the failure occurs in interface friction. Figure 3 has been prepared to aid in this discussion of possible friction failure. In this case, failure will occur at the face of the penetrator. If the friction strength (S/) is close to the value of the soil shear strength, (S^), then the soil will be at or near its limit-equilibrium state (Fig. 3). For overall failure in friction along the entire penetrator, or at least an appreciable length of it, the maximum value of the interface friction Sf is S^= a/ tan 6

(2)

Thus, if the shear Sf and radial a/ stresses are measured, it is in principle possible to calculate the value of 5 for that soil and that penetrator surface. If the value of oi' is also available, the value of =arcsin /•

2Ti'^^T

VA '

*

o d a> u o

•^ «> _c fO

d

\

\ N\ ^0\

\ \

( \ \

\ \ ^

CVJ

b

\

k^

{

b

^

^ "viBSS^ 1

k

' s / *s ouoy



b

587

I? I

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4

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>

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I

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o

tSONflOdl 30M0J HvaHS


604


ooro

SZO'O

•t-oso*o 00

KO'O „

s?

in

hOSO'O-

-J I O in

ol U P y]

H Z £ W <J W HJ - i J ^ iJ 0. £ O)

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in o O

WI'O-

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9

^

(SQNnOdl 30aOJ avans


MIEDEMA ET AL ON SHEAR STRENGTH OF NESPELEM CLAY

605

so.o

..^y.

30.0

k—,^' is the friction angle of the normally consolidated clay. Should a sample of the overconsolidated clay be removed from the ground, the stress path will be along EO in Fig. 4b. Upon reloading in a onedimensional consolidation test, the stresses a/,' and o^' will vary along OIGH. The segment 01 corresponds to the clay response during Phase I and its slope is given by KQ. For the Lachute clay, KQ = 0.23 in this region. It should be noted at once that KQ measured during Phase I is not equal to the in situ value of KQ, since, as discussed previously, the in situ value of ATo is given by the slope of the line OE, which is not equal to that of 01. As a consequence,. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SILVESTRI ON GUY BEHAVIOR IN KQ-TRIAXIAL TESTS

627

it is not possible to measure in the laboratory the_in situ value of KQ since, as shown previously, one measures the value of KQ during recompression. In order to measure the in situ value of KQ, one must use field tests, as pointed out also by Wroth [5]. At point /, the preconsolidation pressure of the clay is reached and the clay structure collapses. At point G, once again, the clay becomes normally consolidated, and the stresses Of,' and a^' will vary along the Iinei3'i8'. Prediction of Ky and B During Phase I For the sensitive clays of Eastern Canada, a considerable number of studies have shown that deformations are essentially of an elastic nature so long as the shearing stresses are less than the shearing strengths [7.14]. In addition, it has been shown that these clays behave as anisotropic elastic materials having different elastic properties in the vertical and horizontal direction [75.76]. By applying the theory of anisotropic elasticity [77] it can be easily shown that 7^0 is given by

where Hyi, = Poisson's ratio for the strain in the horizontal direction due to a vertical stress, ÂA = Poisson's ratio for the strain in the horizontal direction due to a horizontal stress, £/,=Young's modulus in the horizontal plane, and £",,=Young's modulus in the vertical direction. Even though the parameters n^^, /i/,/,, Ef,, and E^ were not evaluated for the Lachute clay used in this study, it is possible to extrapolate to this soil the results obtained for other sensitive clay of Eastern Canada. Thus, for a sensitive clay from Ottawa, Wong and Mitchell [18] report an average value of Poisson's ratio equal to 0.25 which, when introduced into Eq 1, yields KQ = 0.33, by assuming £"/, = E^. Such a value of KQ is very close to the value of 0.30 measured in a TiCo-triaxial test for the same clay [7]. In addition, by applying the experimental data obtained by Lo etâl [76] on another sensitive clay of Eastern Canada, an average value of KQ equal to 0.23 is obtained. Finally, for the St. Louis (P. Q.) clay studied by Yong and Silvestri [75], n^f, = 0.35, MA/, = 0.20, EH -_A.3\ MPa, andf^ = 6.90 MPa, which, when introduced into Eq 1, yield KQ = 0.27. As the measured value of KQ for the Lachute clay which is equal to 0.23 falls in the range of values predicted earlier for a number of sensitive clays of Eastern Canada, it appears reasonable to assume that the theory of Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

628


anisotropic elasticity may be applied also to the Lachute clay used in this investigation. By using this theory, it is possible to arrive at a mathematical expression for the pore water pressure parameter^. This parameter is given by [19]:

where ni,y = Poisson's ratio for the strain in the vertical direction due to a horizontal stress. As the pore water pressure coefficient B is related to A by the following expression [20]: 5-Zo + (l-ôM

(3)

substitution of Eq 2 into Eq 3 yields

B = Ko + {l-Ko)-

^Ji^:'^""Eh'Ey + 2-

.

(4)

Hhh- 4iu„

For the St. Louis (P. Q.) clay [15], fi^y = 0.24 which, when introduced with the other parameters given above into Eqs 3 and 4, yields/4 = 0.12 and B — 0.36. For the Ottawa clay studied by Lo et al^/6], an average value for B equal to 0.32 is obtained. These values of B are consistent with those reported by Leroueil et al [2/] for a considerable number of case histories related to embankment loadings on sensitive^lay deposits. For the St. Alban (P. Q.) test fills [21], the observed values of B vary for the most part between 0.23 and 0.53, with an average of about 0.35. On the basis of the results presented in this section it may be stated that while the predictive ability of this approach cannot be fully assessed in view of the limited data reported, a preliminary evaluation appears to indicate general consistency in the prediction of both the coefficient of incremental pressure at rest, ATQ, and the pore water pressure parameter B. Conclusions For the specific materials discussed in this paper, the following conclusions have been reached: 1. A clay model has been proposed and found satisfactory to describe the mechanisms by which lateral stresses are mobilized in overconsolidated clay deposits. On the basis of this model it is shown that the in situ values of ATQ cannot be measured in the laboratory; instead one measures the value of KQ during recompression. 2. The response of the Lachute clay analyzed in this paper is characterized


SILVESTRI ON CLAY BEHAVIOR IN KQ-TRIAXIAL TESTS

629

by three distinct phases of behavior: Phase I linked to a pseudo-elastic response; Phase II related to a critical shear strength; and Phase III related to the normally consolidated clay response. 3. The value of Kg during recompression in Phase I is remarkably constant and has an average value of 0.23 for the Lachute clay. 4. The value of ô during Phase III is constant and equal to 0.55, from which a friction angle of 26.7 deg is obtained by application of Jaky's expression KQ = I — sin (j)'. 5. Application of the theory of anisotropic elasticity permits one to predict the values of both KQ and B during Phase I. The calculated values of KQ are consistent with that measured for the Lachute clay. It is also shown that the pore water pressure coefficients B calculated by means of the theory of anisotropic elasticity are consistent with experimental data obtained from in situ measurements. Acknowledgments The author wishes to express his appreciation to the National Research Council of Canada for Grant A-6110, under which this study is being carried out. References |/] Bishop, A. W., "Test Requirements for Measuring the Coefficient of Earth-Pressure at Rest," Brussels Conference on Earth Pressure Problems, Brussels, 1958, Vol. 1, pp. 2-14. \2] Brooker, E. W. and Ireland. H. C , Canadian GeotechnicalJoumal. Vol. 2, No. I, 1965, pp. 1-15. \3\ Campanella, R. G. and Vaid, Y. P.. Canadian GeotechnicalJoumal. Vol. 9, No. 3, 1972, pp. 249-260. \4\ Schmidt, B., Canadian GeotechnicalJoumal. Vol. 3, No. 4, pp. 239-242. (5| Wroth, C. P. in Proceedings. American Society of Civil Engineers (hereafter cited as ASCE] Specialty Conference on /« Situ Measurement of Soil Properties, Raleigh, N.C., 1975, Vol. II, pp. 181-230. (6] Simons, N. E. and Som, N. N. in Proceedings. 7th International Conference on Soil Mechanics and Foundations Engineering, Mexico, 1%9, Vol. 1, pp. 369-377. [7] Mitchell, R. J., Sangrey, D. A., and Webb, G. S. in Proceedings. ASCE "Foundations in the Crust of Sensitive Clay Deposits", Specialty Conference on Performance of Earth and Earth-Supported Structures, Lafayette, Ind., 1972, Vol. 1, Part 2, pp. 1051-1072. [8] Berre, T. and Bjerrum, L. in Proceedings, 8th International Conference on Soil Mechanics and Foundations Engineering, Moscow, 1973, Vol. 1.1, pp. 39-49. (9] Bjerrum, L. in Proceedings. 8th International Conference on Soil Mechanics and Foundations Engineering, Moscow, 1973, Vol. 3, pp. 111-159. [10] Bishop, A. W. and Henkel, D. J., The Measurement of Soil Properties in the Triaxial Test. Arnold, London, 1957, p. 190. [//] Chandler, R. J. in Proceedings. Geotechnical Conference, Oslo, 1967, Vol. 2, pp. 177-178. [12] Bjerrum, L. and Andersen, K. H. in Proceedings. 5th European Conference on Soil Mechanics and Foundations Engineering, Madrid, 1972, Vol. 1, pp. 11-20. |/J] Leroueil, S., Tavenas, F. A., and Brucy, ¥., Journal of the Geotechnical Engineering Division. ASCE, Vol. 105, No. GT6, 1979, pp. 759-778. [14] Tavenas, F. A., Chapeau, C , LaRochelle, P., and Roy, M., Canadian Geotechnical Journal. Vol. 11, No. 1, 1974, pp. 109-141.


630


[IS] Yong, R. N. and Silvestri, V., Canadian GeotechnicalJournal. Vol. 16, No. 2, 1979, pp. 335-350. [/61 Lo, K. Y., Leonards, G. A., and Yuen, C , Norwegian Geotechnical Institute, Publication No. 117, Oslo, 1977, pp. 1-16. [17] Hearmon, R. F. S., An Introduction to Applied Anisotropic Elasticity, Oxford University Press, Oxford, 1%1. [18] Wong, P. K. K. and Mitchell. R. J., Geotechnique. Vol. 25, No. 4, 1975, pp. 763-782. [791 Pickering, D. J., Geotechnique. Vol. 20, No. 3, 1970. pp. 271-276. 120] Wu, T. H., Soil Mechanics, Allyn and Bacon, Boston, 1966, p. 431. [21] Leroueil, S., Tavenas, F., Mieussens, C , and Peignaud, M., Canadian GeotechnicalJournal, Vol. 15, No. 1, 1978, pp. 66-82.


Discussions


Suzanne Lacasse^ and Mladen Vucetic^

Discussion of "State of tine Art: Laboratory Strength Testing of Soils"

REFERENCE: Lacasse, Suzanne and Vucetic, Mladen, "Discussion of 'State of the Art: Lalioratoiy Strengtii Testing of Soils'," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 633-637. ABSTRACT: Saada and Townsend, in their state-of-tlie-art paper on laboratory strength testing of soil, present very severe criticisms of the simple shear testing method and the apparatuses presently in use. The discussers do not share this point of view. A fair assessment of a piece of equipment and of the testing procedure calls not only for an enumeration of its shortcomings, but also for a careful evaluation of the significance of these deficiencies on the measured parameters. Saada and Townsend questioned the overall usefulness of the testing method in geotechnical engineering problems. KEY WORDS: direct simple shear test, size effect, test procedures, undrained shear strength, clay

Saada and Townsend, in their state-of-the-art paper on laboratory strength testing of soils,^ present very severe criticisms of the simple shear testing method and the apparatuses presently in use. The discussers do not share this point of view. A fair assessment of a piece of equipment and of the testing procedure calls not only for an enumeration of its shortcomings, but also for a careful evaluation of the significance of these deficiencies on the measured parameters. Saada and Townsend questioned the overall usefulness of the testing method in geotechnical engineering problems. Nonunifonn Stress Distribution The configuration of the simple shear specimen expectedly leads to nonuniformity of stresses. The SGI/NGI apparatus does not provide complementary shear stresses on the vertical sides of the specimen. During shear 'Research Fellow, Norwegian Geotechnical Institute, Oslo, Norway. This publication, pp. 7-77.


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distortion, the soil specimen experiences a nonuniform shear stress distribution over the top and bottom faces and normal stresses develop on all faces Prevost and Heeg [/] investigated theoretically the effects of slippage on the normal and shear stress distribution on the upper and lower faces and edges of the test specimen. Figure 1 illustrates the stresses on the upper and lower faces for conditions of "no slippage" (X = 0) between the top and bottom plates and the soil. The figure also shows the stress distribution for the unlikely condition of X = 0.5, that is, where slippage is such that the center point on the top and bottom faces of the specimen moves by only one half of the horizontal displacement at the edges of the specimen. The analyses, for a height-to-diameter ratio (h/D) of 0.25, show zones of large stress variations at the edges of the specimen. But the data represent the extreme case of stress concentration, as Prevost and Heeg, to produce that figure, used an isotropic elastic soil model. For an elastic-plastic soil, the end effect will be greatly reduced as yield occurs. One can minimize slippage with the insertion of short pins or fins on the faces of the specimen or with a coating of the soilcap interfaces with an epoxy-sand mixture (for testing sands). In most cases, one can detect slippage by studying the experimental stress-strain curve. If in doubt, one can carry out the simple shear test to large strains and observe any differential displacement between top and bottom caps and specimen. In a thorough investigation of the Cambridge and NGI simple shear apparatuses, Budhu and Wood [3] showed that the (average) ratio of shear stress to normal stress on the top and bottom horizontal boundaries underestimated the stress ratio in the center of the sample by about 12 percent in static loading. This average stress ratio is that measured by the NGI apparatus.

New Experimental Results Concerning Specimen Size Effect One means to investigate the boundary effects consists in testing specimens of different diameters while keeping the specimen height constant. In the presence of significant nonuniform stresses on the faces and within the cross section of the specimen, changing of the height-to-diameter ratio of the specimen should lead to different measured values of stiffness and average horizontal shear stress at failure. Figure 2 summarizes the results of simple shear tests recently conducted at NGI on undisturbed specimens of Haga clay Up = 15 percent, S, = 6), sampled in 200-mm-diameter tubes. The investigation looked into the effects of sample size at two overconsolidation ratios (OCR). The overconsolidation ratio of 10 was achieved by rebound of the specimens consolidated under a The italic numbers in brackets refer to the list of references appended to this paper.


LACASSE AND VUCETIC ON STATE-OF-THE-ART PAPER

635

T - average horizon-tal shear stress applied on the specimen.

FIG. 1—Distribution of shear and normal stresses on top face of specimen [1].

maximum vertical stress of 400 kPa. The test program included tests on specimens with cross-sectional areas of 20, 50, and 104 cm^. Thin specimens of large diameter presumably have a more uniform stress distribution than short thick specimens. The experimental results show very little, if any, size effect on either the measured maximum horizontal shear stress or the stress-strain curve and hence modulus of Haga clay. The differences in measured horizontal shear stress amount to less than the expected scatter in results due to nonhomogeneity of undisturbed soil specimens. Further tests with the 104-cm2 specimens are underway [4]. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

636


g

104 5 0 ^ ^

100

20 j

Cross-sectional areo ( c m ' ) OCR=1

I _ 80 I/) rM

peo S z

OCR= O v e r c o n s o l i d a t i o n r a t i o

N X.

OCRÎO

il40 £

t->

h

E

3

20

f o r all t e s t s =• 1 6 m m

Max.

consol. stress^ °„'

0.2 Height-

(a)

0.4

diameter

ratio,

Maximum h o r i z o n t a l

= 400

kN/m'

0.6 ^/D

shear s t r e s s

100

% —

.—}

0.3 2

0.20 0.14

(b) FIG. 2—Effect

Stress - strain curves

of height-to-diameter ratio on direct simple shear test results.

Kovacs [5], whom Saada and Townsend cite to support their arguments, presented very puzzling results with respect to the effects of specimen size on the simple shear cyclic shear modulus of resedimented kaolinite. Saada and Townsend's conclusions differ from those of Kovacs. We also believe that their comments based on Kovacs's results from "unconfined" cyclic shear tests do not constitute a basis for severe criticism of simple shear testing as usually performed. Woods [6], in a careful evaluation of the available apparatuses for measuring dynamic soil properties, recognized the usefulness of the simple shear test despite its shortcomings. He arrived at this conclusion mainly on the basis of good correlations with other reliable data, with has accrued significance in terms of cyclic results.


LACASSE AND VUCETIC ON STATE-OF-THE-ART PAPER

637

Sununaiy

The design of any experimental device will always be a compromise between the theoretically possible and the practically feasible. Both soil characteristics and equipment features condition the selection of an appropriate testing method for a given problem. It is believed that the advantages of the simple shear test, including the simplicity in setting up the specimen and in carrying out the test, are significant. Soil specimens may be prepared in their undisturbed state, a feature not available for more complex and research oriented tools, which are limited to the testing of redeposited or sedimented specimens. The back pressuring capability in the newer versions of the simple shear apparatus provides added flexibility to the testing method. The possibility of relating stress ratio on the horizontal plane and the inclination of the principal axes of stress exists [3], and the quantity of available evaluated experience for a variety of soils, encourages further use of the equipment. Even in consideration of its shortcomings, some of which appear to have relatively minor effects on the measured parameters, the direct simple shear test is believed to yield very useful results. It represents one of the valuable tools available to define the complex stress-strain-strength behavior of soils in engineering practice. References [/] Prevost, J. H. and Heeg, K., Canadian Geotechnical Journal, Vol. 13, No. 4, 1976, pp. 418-429. [21 Shen, C. K., Sadigh, K., and Herrmann, L. R. in Dynamic Geotechnical Testing. ASTM STP 654. American Society for Testing and Materials, 1978, pp. 148-162. [3\ Budhu, M. and Wood, D. M., "A Study of the Simple Shear Test," Engineering Department, Cambridge University, England, April 1979. [4\ Vucetic, M., "The Influence of Height versus Diameter Ratio on the Behaviour of Haga Clay in the NGI Simple Shear Device," Internal Report 56204-9, 1981, Norwegian Geotechnical Institute, Oslo, Norway. [5] Kovacs, W. D., "Effect of Sample Configuration in Simple Shear Testing," Symposium on Earth and Earth Structures under Earthquake and Dynamic Loads, Roorkee, India, 1973, pp. 82-86. [6] Woods, R. D., "Measurement of Dynamic Soil Properties," Specialty Conference on Earthquake Engineering and Soil Dynamics, American Society of Civil Engineers, Pasadena, Calif., 1978, Vol. I, pp. 91-178.


J. T. Christian^

Discussion of "State of tiie Art: Laboratory Strength Testing of Soils"

REFERENCE: Christian, J. T., "Discussion of 'State of tlie Art: Laboratory Strengtii Testing of Soils'," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 638-640. ABSTRACT: Finite element analyses of the direct simple shear sample do account for the three-dimensional state of displacement, strain, and stress. Three independent analyses indicate substantial uniformity of stress in the central region of a linearly elastic sample, but stress concentrations at the edges may make the device unsuitable for very sensitive soils or for investigation of progressive failure. The results of photoelastic investigations described in the report include unsymmetric distributions of stress that are mathematically anomalous and are probably caused by inadequate restraints at the boundaries. KEY WORDS: direct shear tests, simple shear tests, finite elements, photo-elasticity

This author must take exception to the comments in the state-of-the-art (SOA) paper by Saada and Townsend^ regarding the analysis of the Norwegian Direct Simple Shear device performed by Lucks et al (SOA Ref 37), and the expanded version of these remarks presented in an earlier paper partially authored by one of the reporters (SOA Ref 40). The photoelastic experiments described in the report may also be in error. Lucks et al described two independent analyses whose results were combined into one technical note. One analysis, performed by H6eg and Brandow, used three-dimensional finite elements. The lateral boundaries were stress free, the bottom was fixed and rigid, and the rough, rigid top boundary was constrained to move uniformly in the X-direction. The horizontal shear stresses on the midplane from this analysis appear to be the ones identified in SOA Fig. 26 as "finite element" results. Clearly, this analysis does not prescribe plane strain deformations. ' Senior consulting engineer. Stone & Webster Engineering Corporation, Boston, Mass. 02107. ^This publication, pp. 7-77.


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CHRISTIAN ON STATE-OF-THE-ART PAPER

639

The second analysis, performed by Lucks and Christian, used a finite element model of an axially symmetric body loaded unsymmetrically. The technique involves expansion of the loads and displacements in a Fourier series in terms of the cylindrical coordinate angle theta. It can express any arbitrary three-dimensional state of stress and strain, provided the material is linearly elastic and has at least two axes of symmetry, the geometry is axially symmetric, and the boundary conditions are expressed in a Fourier series. It happens that for the case of a uniform horizontal displacement of the top platen, the Fourier series degenerates to one term for each component of displacement. Details of this approach were described by Wilson^ and are to be found in standard texts on the finite element method (for example, by Zienkiewicz''). The boundary conditions used by Lucks and Christian were the same as those used by Hoeg and Brandow. The analyses reported by Lucks et al showed substantial uniformity of stress throughout the sample. They also showed significant concentrations of normal stress at the comers of the vertical section of the sample. Some six years later, Shen et al (SOA Ref 39), using the same type of Fourier expansion technique, with a mesh of essentially the same fineness, performed a more comprehensive parametric analysis, incorporating the membrane in the finite element model and including the nonuniform stress distributions due to initial vertical loading. They showed distributions of horizontal shear strain that were in some instances quite nonuniform and in others reasonably close to the pattern of shear stress reported by Lucks et al. Shen et al made the point that much of the nonuniformity is due to the initially imposed vertical displacement and that "a large horizontal displacement... seems to have overriding effect in minimizing the nonuniform shear distribution due to vertical displacement". It should be noted that the extreme instance of nonuniform distribution of shear stress occurred when Poisson's ratio was 0.49 for both the vertical compression and the shear loading. This is, in effect, a case in which the initial vertical load is applied under undrained conditions, which is a very unlikely situation for most testing programs. Both of these analyses are limited to isotropic, elastic materials with rough, rigid end platens. They show that there are concentrations of stress and strain near the comers of the sample, but for most cases the distribution of stress and strain is substantially uniform over the central portion of the sample. These facts indicate that the device is suitable for testing the behavior of most clays under monotonic loading, as described by Ladd.^ They also indicate that the device is not suitable for finding the peak strength of very sensitive clays, as is confirmed by La Rochelle's experience with Leda clays. Wilson, E. L., American Institute of Aeronautics and Astronautics Journal, Vol. 3, No. 12, 1965, pp. 2259-2274. ''zienkiewicz, O. C , The Finite Element Method. 3rd ed., McGraw-Hill, London, 1977, especially Ch. 15. This publication, pp. 643-652.


640


Cyclic loading on sands is another type of test in which progressive failure is important, and Shen et al pointed out that this may be a serious problem when the Norwegian device is used for dynamic testing. Saada and Townsend describe the results of photoelastic experiments. The results, plotted in SOA Figs. 25 and 26, show at least one anomaly. Figure 26 shows the horizontal shear stresses unsymmetrically distributed about the center of the sample. This is found in none of the finite element analyses and is impossible for an isotropic, elastic, axially symmetric body loaded by displacing a rigid top platen uniformly vertically or horizontally in the X-direction. The photoelastic model replaces the rigid platens with blocks of photoelastic material of about the same thickness as the sample. Despite all efforts to restrain these ends, they cannot guarantee a uniform displacement of the top surface of the cylindrical sample. The resulting vertical strains in the sample are probably the cause of the anomaly obtained by the photoelastic method.


Panelists' Reports


C. C. Ladd'

Discussion on Laboratory Shear Devices

REFERENCE: Ladd, C. C , "Discassion on Laboratmy Shear Devices," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 643-652. ABSTRACT: This discussion starts with a general assessment of the capabilities of several types of laboratory shear devices and their corresponding suitability for use in specialized design practice and for basic research into the constitutive stress-strainstrength relationships of soils. It then focuses in greater depth on two specific topics: use of the Geonor Direct Simple Shear (DSS) device for design practice involving soft clays, and experimental requirements needed to reliably measure stress-strain-strength behavior in cross anisotropic soils. KEY WORDS; anisotropy, clay, deformation, laboratory test equipment, sand, shear modulus, shear strength, shear tests

General Assessment of Laboratory Shear Devices Devices and Criteria Table 1 lists the devices considered, using a slightly different terminology than employed in the SOA paper. (SOA denotes the state-of-the-art paper by Saada and Townsend.2) The devices are further described as follows: 1. Triaxial—a conventional triaxial cell having a solid circular specimen and subdivided as either "standard" triaxial compression cells or "special" cells with frictionless end platens, ability to readily achieve /fo-consolidation and/or perform both triaxial compression and extension tests, etc. 2. Direct Simple Shear—the Geonor Direct Simple Shear (DSS) device as described in SOA Ref 11. 3. Plane Strain—devices primarily designed for plane strain compression ' Professor of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass. 02139. ^This publication, pp. 7-77.


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has been suggested by Hvorslev and explains part of the nonuniformity of the stresses within the sample. Conclusion Following his own observations and experience, the author cannot find any real advantage to the use of the DSS device: it is not appreciably simpler to use than the triaxial apparatus; it does not yield a strength value comparable to the peak strength obtained in the triaxial test; it gives no reliable information on the shear or deformation moduli; even the volumetric moduli obtained in the NGI apparatus on samples of overconsolidated sensitive clays may be adversely influenced by the poor confinement of the reinforced membrane; and for the same reason, the value of the preconsolidation pressure obtained during the consolidation stage in that device can be seriously questioned. For sensitive clays, the maximum values of shear strength determined with the DSS devices seem to correspond to the strength measured with the direct shear test or obtained at large strain in the triaxial test; moreover, the strain developed in the DSS devices is not large enough to allow the determination of the residual strength parameters. It is thus apparent that the DSS devices present no real improvement over


LA ROCHELLE ON DIRECT SIMPLE SHEAR TEST DEVICES

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drained compression and extension strengths are only two points on the more general yield envelope. Therefore normalization with respect to preconsolidation pressure should be applicable to the entire yield envelope. In the upper half of Fig. 7 are plotted the yield envelopes determined from samples at various depths throughout the Belfast clay deposits [14], If the stress states at yield along the individual stress paths used to determine these yield envelopes are normalized with respect to Pc, a general yield envelope range for the entire deposit can be determined as shown in the lower portion of Fig. 7. It is of interest to compare the shape of this general range of normalized yield envelope for Belfast clay with published data for other material types. In the upper portion of Fig. 8 are plotted triaxial compression and extension strengths normalized with respect to preconsolidation pressure for a number of different soil types. While there is clearly scatter in the data, the general Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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ranges in Su/pc for compression and extension tests, together with the location of Pc as shown in the lower half of Fig. 8, would indicate a yield envelope shape which corresponds well with the normalized yield envelope range obtained for the Belfast clays. Further, it is also noted that for this general yield envelope shape, the ratio of p^ and/>„o (that is, the p '-value at which the yield envelope crosses the q = o axis) is about 1.6 which is the average value for 23 natural clays as reported by Tavenas and Leroueil [15]. In the initial interpretation of yield from laboratory tests on the Belfast Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

696


COMPRESSION DATA FOR : - SCANDANAVIAN CLAYS - EASTERN CANADIAN CLAYS -BANGKOK CLAY -BELFAST CLAY

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deposits, the definition of yield was varied depending on stress path direction [2], Thus, along a constantffoctstress path, little volumetric strain occurred and yield was defined using a\ versus ei plots. However, along a constant shear stress path, a clear definition of yield could only be obtained from the

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