Geotechnical Risk and Safety: Proceedings of the 2nd International Symposium on Geotechnical Safety and Risk (IS-Gifu 2009) 11-12 June, 2009, Gifu, Japan - IS-Gifu2009

GEOTECHNICAL RISK AND SAFETY

PROCEEDINGS OF THE 2ND INTERNATIONAL SYMPOSIUM ON GEOTECHNICAL SAFETY & RISK, GIFU, JAPAN, 11–12 JUNE, 2009

Geotechnical Risk and Safety Editors Y. Honjo Department of Civil Engineering, Gifu University, Gifu, Japan

M. Suzuki Center for Structural Safety and Reliability, Institute of Technology, Shimizu Corporation, Tokyo, Japan

T. Hara Department of Civil Engineering, Gifu University, Gifu, Japan

F. Zhang Department of Civil Engineering, Nagoya Institute of Technology, Nagoya, Japan

Cover photo: Traditional cormorant fishing at the Nagara River, Gifu City, Japan Courtesy of Gifu Sightseeing Association

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Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Table of Contents

Preface

IX

Organization

XI

Sponsors

XIII

Wilson Tang lecture Reliability of geotechnical predictions T.H. Wu

3

Keynote lectures Risk assessment and management for geohazards F. Nadim

13

Risk management and its application in mountainous highway construction H.W. Huang, Y.D. Xue & Y.Y. Yang

27

Recent revision of Japanese Technical Standard for Port and Harbor Facilities based on a performance based design concept T. Nagao, Y. Watabe, Y. Kikuchi & Y. Honjo

39

Special lecture Interaction between Eurocode 7 – Geotechnical design and Eurocode 8 – Design for earthquake resistance of geotechnical structures P.S. Sêco e Pinto

51

Special sessions Reliability benchmarking Reliability analysis of a benchmark problem for 1-D consolidation J.Y. Ching, K.-K. Phoon & Y.-H. Hsieh

69

Study on determination of partial factors for geotechnical structure design T.C. Kieu Le & Y. Honjo

75

Reliability analyses of rock slope stability C. Cherubini & G. Vessia

83

Reliability analysis of a benchmark problem for slope stability Y. Wang, Z.J. Cao, S.K. Au & Q. Wang

89

Geotechnical code drafting based on limit state design and performance based design concepts Developing LRFD design specifications for bridge shallow foundations S.G. Paikowsky, S. Amatya, K. Lesny & A. Kisse

V

97

Limit States Design concepts for reinforced soil walls in North America R.J. Bathurst, B. Huang & T.M. Allen

103

Loss of static equilibrium of a structure – Definition and verification of limit state EQU B. Schuppener, B. Simpson, T.L.L. Orr, R. Frank & A.J. Bond

111

Geotechnical criteria for serviceability limit state of horizontally loaded deep foundations M. Shirato, T. Kohno & S. Nakatani

119

Reliability-based code calibration of piles based on incomplete proof load tests J.Y. Ching, H.-D. Lin & M.-T. Yen

127

Sensitivity analysis of design variables for caisson type quay wall G.L. Yoon, H.Y. Kim, Y.W. Yoon & K.H. Lee

135

Evaluating the reliability of a levee against seepage flow Y. Shimizu, Y. Yoshinami, M. Suzuki, T. Nakayama & H. Ichikawa

141

Determination of partial factors for the verification of the bearing capacity of shallow foundations under open channels A. Murakami, S. Nishimura, M. Suzuki, M. Mori, T. Kurata & T. Fujimura

147

Application of concept in ‘Geo-code21’ to earth structures M. Honda, Y. Kikuchi & Y. Honjo

155

Limit state design example – Cut slope design W.K. Lin & L.M. Zhang

159

Probabilistic charts for shallow foundation settlements on granular soil C. Cherubini & G. Vessia

165

Resistance factor calibration based on FORM for driven steel pipe piles in Korea J.H. Park, J.H. Lee, M. Chung, K. Kwak & J. Huh

173

An evaluation of the reliability of vertically loaded shallow foundations and grouped-pile foundations T. Kohno, T. Nakaura, M. Shirato & S. Nakatani

177

Study on rational ground parameter evaluation methods for the design and construction of large earth-retaining wall Y. Yamamoto, T. Hirose, M. Hagiwara, Y. Maeda, J. Koseki, J. Fukui & T. Oishi

185

System reliability of slopes for circular slip surfaces J.-Y. Ching, Y.-G. Hu & K.-K. Phoon

193

Correlation of horizontal subgrade reaction models for estimating resistance of piles perpendicular to pile axis Y. Kikuchi & M. Suzuki

201

Risk management in geotechnical engineering The long and big tunnel fire evacuation simulation based on an acceptable level of risk and EXODUS software S.-Q. Hao, H.-W. Huang & Y. Yuan

211

Risk based decision support system for the pumping process in contaminated groundwater remediation T. Hata & Y. Miyata

217

VI

A risk evaluation method of countermeasure for slope failure and rockfall with account of initial investment T. Yuasa, K. Maeda & A. Waku Risk assessment on the construction of interchange station of Shanghai metro system Z.W. Ning, X.Y. Xie & H.W. Huang Challenges in multi-hazard risk assessment and management: Geohazard chain in Beichuan Town caused by Great Wenchuan earthquake L.M. Zhang

221

229

237

General sessions Design method (1) A study of the new design method of irrigation ponds using sheet materials M. Mukaitani, R. Yamamoto, Y. Okazaki & K. Tanaka

247

Research on key technique of double-arch tunnel passing through water-eroded groove Y. Chen & X. Liu

251

Safety measures by utilizing the old ridge road and potential risks of land near the old river alignments M. Okuda, Y. Nakane, Y. Kani & K. Hayakawa Bearing capacity of rigid strip footings on frictional soils under eccentric and inclined loads K. Yamamoto & M. Hira

257

265

Uncertainty Reliability analysis of slope stability by advanced simulation with spreadsheet S.K. Au, Y. Wang & Z.J. Cao Optimal moving window width in conjunction with intraclass correlation coefficient for identification of soil layer boundaries J.K. Lim, S.F. Ng, M.R. Selamat & E.K.H. Goh

275

281

Soil variability calculated from CPT data T. Oka & H. Tanaka

287

Reducing uncertainties in undrained shear strengths J.Y. Ching, Y.-C. Chen & K.-K. Phoon

293

A case study on settlement prediction by spatial-temporal random process P. Rungbanaphan, Y. Honjo & I. Yoshida

301

Construction risk management Reliability analysis of a hydraulic fill slope with respect to liquefaction and breaching T. Schweckendiek, G.A. van den Ham, M.B. de Groot, J.G. de Gijt, H. Brassinga & P. Hudig

311

A case study of the geological risk management in mountain tunneling T. Ikuma

319

Guideline for monitoring and quality control at deep excavations T.J. Bles, A. Verweij, J.W.M. Salemans, M. Korff, O. Oung, H.E. Brassinga & T.J.M. de Wit

327

A study on the empirical determination procedure of ground strength for seismic performance evaluation of road embankments K. Ichii & Y. Hata

VII

333

Geo Risk Scan – Getting grips on geotechnical risks T.J. Bles, M.Th. van Staveren, P.P.T. Litjens & P.M.C.B.M. Cools

339

Reduction of landslide risk in substituting road of Germi-Chay dam H.F. Aghajani & H. Soltani-Jigheh

347

Risk assessment Probabilistic risk estimation for geohazards: A simulation approach M. Uzielli, S. Lacasse & F. Nadim

355

A research project for deterministic landslide risk assessment in Southern Italy: Methodological approach and preliminary results F. Cotecchia, P. Lollino, F. Santaloia, C. Vitone & G. Mitaritonna

363

Reliability-based performance evaluation for reinforced railway embankments in the static loading condition M. Ishizuka, M. Shinoda & Y. Miyata

371

Maximum likelihood analysis of case histories for probability of liquefaction J.Y. Ching, C. Hsein Juang & Y.-H. Hsieh

379

Suggestions for implementing geotechnical risk management M.Th. van Staveren

387

Design method (2) Framework for evaluation of probability of failure of soil nail system I.S.H. Harahap & W.P. Nanak

397

Reliability analysis of embankment dams using Bayesian network D.Q. Li, H.H. Liu & S.B. Wu

405

Identification and characterization of liquefaction risks for high-speed railways in Portugal P.A.L.F. Coelho & A.L.D. Costa

411

Field characterization of patterns of random crack networks on vertical and horizontal soil surfaces J.H. Li & L.M. Zhang

419

Stochastic methods for safety assessment of a European pilot site: Scheldt M. Rajabalinejad, P.H.A.J.M. van Gelder & J.K. Vrijling

425

A report by JGS chapter of TC23 limit state design in geotechnical engineering practice Code calibration in reliability based design level I verification format for geotechnical structures Y. Honjo, T.C. Kieu Le, T. Hara, M. Shirato, M. Suzuki & Y. Kikuchi

435

Author index

453

VIII

Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Preface

IS Gifu (2nd International Symposium on Geotechnical Risk and Safety) which is held on 11 and 12 June, 2009 at Nagara International Convention Center in Gifu, Japan, is a symposium held as part of a series of conferences organized by a group of people interested in geotechnical risk and safety. These conferences include LSD2000 (November 2000, Melbourne, Australia), IWS Kamakura (April, 2002, Tokyo and Kamakura, Japan), LSD2003 (June, 2003, Cambridge, USA), Georisk 2004 (November, 2004, Bangalore, India), Taipei2006 (November, 2006, Taipei), and the 1st International Symposium on Geotechnical Risk and Safety (1st ISGSR, October, 2007, Shanghai). Besides these events, this group has organized technical sessions in many international and regional conferences from time to time. The major themes of this symposium are: • • • • •

Evaluation and control of uncertainties concerning geotechnical structures. Performance based specifications, RBD and LSD of geotechnical structures, and design code developments. Risk assessment and management of geo-hazards. Risk management issues concerning large geotechnical construction projects. Repair and maintenance strategies of geotechnical structures.

IS Gifu is sponsored by ISSMGE, JGS and GEOSNet. Two technical committees now working in ISSMGE are taking lead in this symposium, namely, TC 23 ‘Limit state design in geotechnical engineering practice’ (chair Y. Honjo) and TC 32 ‘Risk assessment and management in geotechnical engineering practice’ (chair F. Nadim). The organizers greatly appreciate the support provided by the Japanese Geotechnical Society (JGS) on this symposium. ASCE Geo-Institute RAM (Risk Assessment and Management Committee) has also been involved in promoting this symposium. GEOSNet (Geotechnical Safety Network) is a topic-specific international platform to facilitate and promote active interaction on topics related to geotechnical safety and risk among the members, particularly between researchers and practitioners. GEOSNet was formed at Taipei 2006 in view of the increasing interest and momentum to rationalize risks in new design codes using reliability and other methods. GEOSNet is expected to take over this activity and become a permanent body to organize this series of ISGSR conferences. For this reason, we call IS Gifu also the 2nd International Symposium on Geotechnical Safety and Risk (2nd ISGSR). One of the important events related to GEOSNet in this symposium is the initiation of Wilson Tang Lecture series. The lecture is named to recognize and honour the seminal contributions of Professor Wilson Tang, who is one of the founding researchers in geotechnical reliability and risk. GEOSNet plans to host the Wilson Tang Lecture as the key presentation in future ISGSR events to honour distinguished peers and their achievements. The first Wilson Tang lecture is delivered by Professor T.H. Wu of Ohio State University, who is also one of the founding researchers in this domain. Finally, the organizers are grateful to all those who have helped and contributed to the organization of this event. A large part of the credit for the proceedings goes to the authors and reviewers. The publication cost of the proceedings is supported by Grant in Aid for Scientific Research, Scientific Research (A) entitled “Development and promotion of performance based design and reliability based design of geotechnical structures” (Grant No. 19206051, Y. Honjo as the representative researcher). The organizers are deeply indebted for this financial support. Yusuke Honjo Makoto Suzuki Takashi Hara Feng Zhang June 2009, Gifu, Japan

IX

Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Organization

ISSMGE TC23 Limit State Design in Geotechnical Engineering Practice Honjo, Y. (Chair) Zhang, L.M. (Secretary) Becker, D.E. (Core Members) Matsui, K. (Core Members) Paikowsky, S. (Core Members)

Phoon, K.K. (Core Members) Schuppener, B. (Core Members) Simpson, B. (Core Members) Steenfelt, J. (Core Members)

ISSMGE TC32 Engineering Practice of Risk Assessment and Management Nadim, F. (Chair) Fenton, G.A. (Secretary) Bekkouche, A. (Core Members) Bolle, A. (Core Members) Ho, K. (Core Members) Jaksa, M. (Core Members)

Leroi, E. (Core Members) Manfred Nussbaumer, E.H. (Core Members) Pacheco, M. (Core Members) Phoon, K.K. (Core Members) Roberds, B. (Core Members)

GEOSNet Board Members Phoon, K.K. (Chair) Becker, D.E. Chin, C.T. Faber, M.H.

Honjo, Y. Horikoshi, K. Huang, H.W. Simpson, B.

Organizing Committee Honjo, Y. (Chair) Hara, T. Honda, M. Horikoshi, K. Kikuchi, Y. Kimura, T. Kobayashi, K. Kobayashi, S. Kusakabe, O. Maeda, Y. Matsui, K. Mizuno, H. Murakami, A. Nishida, H.

Nishimura, S. Ogura, H. Oishi, M. Okumura, F. Ohtsu, H. Rito, F. Satake, M. Shirato, M. Suzuki, H. Suzuki, M. Ueno, M. Yamamoto, K. Yamamoto, S.

Scientific Committee Suzuki, M. (Chair) Hara, T.

Kieu Le, T.C. Zhang, F.

XI

Local Advisory Committee Asaoka, A. Ohtani, T. Daito, K. Okumura, T. Hara, T. Rokugo, K. Hinokio, M. Sato, T. Honjo, Y. Sawada, K. Itabashi, K. Shibuki, M. Kamiya, K. Sugii, T. Kodaka, T. Sugito, M. Kojima, S. Tsuji, S. Ma, G. Yamada, K. Maeda, K. Yashima, A. Nakai, T. Yasuda, T. Nakano, M. Yoshimura, Y. Narita, K. Yoshio, O. Noda, T. Zhang, F. Nojima, N. International Review Panel Akutagawa, S. Becker, D.E. Calle, E. Ching, J.Y. Coelho, P. Cotecchia, F. Fujita, M. Furuta, H. Han, J. Hara, T. Harahap, I.S.H. Heidari, S. Honda, M. (Makoto) Honda, M. (Michinori) Horikoshi, K. Huang, H. Ichii, K. Karlsrud, K. Katsuki, S. Kikuchi, Y. Kitahara, T. Kobayashi, A. Kobayashi, S. Kojima, K. Kusakabe, O. Lee, S.R. Li, D. Li, X.Z. Lo, R. Maeda, K. Maruyama, O. Miyata, Y. Mori, Y. Moriguchi, S. Mukaitani, M.

Murakami, A. Nadim, F. Nagao, T. Nishida, H. Nishimura, S. Notake, H. Ohdo, K. Orr, T. Otani, J. Paikowsky, S. Qunfang, H. Rajabalinejad, M. Saito, T. Scarpelli, G. Schuppener, B. Schweckendiek, T. Shirato, M. Staveren, M. Sutoh, A. Suzuki, H. Tafazzoli, N. Taghavi, A. Takada, T. Thomson, R. Uzielli, M. Vessia, G. Wakai, A. Wang, Y. Yamaguchi, Y. Yamamoto, S. Yoon, G.L. Yoshida, I. Yoshinami, Y. Zhang, J. Zhang, L.

XII

Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Sponsors

organized by the Japanese Geotechnical Society

under the auspices of the International Society for Soil Mechanics and Geotechnical Engineering

with support of geotechnical safety network (GEOSNet)

XIII

Wilson Tang lecture

Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Reliability of geotechnical predictions Tien H. Wu The Ohio State University, Columbus, Ohio, USA

ABSTRACT: This paper reviews the use of probabilistic and statistical methods in reliability analysis. Results from reliability estimates are compared with observed performance to provide a measure of the reliability of the methods and improve understanding of the parameters. Case histories of failures in clays are examined in detail.

1

RELIABILITY AND GEOTECHNICAL DESIGN

The concepts of risk and uncertainty are familiar to geotechnical engineers. Since predictions are not perfect there is always the possibility of failure or unsatisfactory performance. Structures are designed so that the risk of failure is acceptably small. The two principle components of geotechnical design are the “calculated risk” (Casagrande 1965) and the observational method. The first is described by Casagrande as (1) “the use of imperfect knowledge to estimate the possible ranges for all pertinent quantities that enter into a solution…” and (2) “the decision on an appropriate margin of safety, or degree of risk taking into consideration …losses that would result from failure”. Where the consequence of failure is large and a conservative design is expensive, Terzaghi proposed the use of “the observational method”, which is described by Peck (1969) as, "Base the design on whatever information can be secured. Make a detailed inventory of all the possible differences between reality and the assumptions. Then, compute on the basis of original assumptions, various quantities that can be measured in the field. …On the basis of the results of such measurements, gradually close the gaps in knowledge and, if necessary, modify the design during construction." These concepts can be matched with well known relations in reliability and decision making as illustrated in Figure 1 and 2. In Figure 1, Part (1) “estimate the possible range…” is represented by the probability density function f (s), where s = the shear strength. In Part (2), the “decision” is based on minimizing the expected cost E(C), given as Eq. (1). In Part (3), “an appropriate margin of safety” corresponds to Pf and “losses that would result from failure to Cf in Part (4). Figure 2 shows the relationship between the observational method and Bayes’ theorem, Eq. (2). Element (1), “Compute on the basis of original assumptions, various quantities that can be measured in the field”, is analogous to P[zi |xj ], where z = performance and x = soil property. In Element (2), “the original

Figure 1. The calculated risk.

assumptions” is analogous to P
[xj ], the prior probability. Element (3), “on the basis of the results of such measurements, gradually close the gaps in knowledge”, corresponds to P

[xj |zi ], the posterior probability or updated information. Element (4), “if necessary, modify the design”, is a decision process as described in Fig. 1. The following sections review methods for estimating the failure probability and updating by Bayes’ theorem.

2

UNCERTAINTIES IN GEOTECHNICAL DESIGN

Uncertainties in design parameters and methods lead to errors, which may be random or systematic. Soil variability is the most important source of random error and inaccuracies or simplifications in material and analytical models are the common sources of systematic errors. The result is errors in predictions, represented by the bias N , which is the ratio of the correct answer to the prediction. N has mean N , standard deviation σ[N ] and coefficient of variation [N ]. Soil variability due to spatial variations is represented by (x), where x = property.There is a wide range in (x), from (su ) = 0.10–0.50 for the undrained shear strength to (K) = 2.0–3.0 for permeability (Lumb, 1974). The variability of the permeability coefficient is the largest and can range over more than one order of magnitude within a soil deposit.

3

Figure 2. The observational method.

over FOSM is the use of response surface, or firstorder-reliability method (FORM). More elaborate are simulation and stochastic methods. Simulation has been done with stability analysis and FEM and stochastic FEM. It is instructive to compare results of reliability analysis with observed performance. This is presented in the following sections for failure in clays.

However, in geotechnical engineering practice, uncertainty about the subsoil stratification is often the major issue. Terzaghi’s writings (e.g. Terzaghi 1929) are full of warnings about complications in site conditions. A well known example is the soil profile at Chicopee Dam, MA, shown in Fig. 3a. Much less known is Fig. 3b, which shows the data Terzaghi used to construct Fig. 3a. The uncertainties involved in the extrapolation are obvious. Terzaghi recognized the difficulty of predicting the in-situ permeability at Chicopee Dam and, in an early example of the observational method, provided specific instructions on measurement of the seepage from the dam. Errors in stratification inferred from site exploration data can be considered as mapping and classification problems (Baecher and Christian 2003).The major obstacle is the difficulty of obtaining the necessary geologic parameters. A soil property model is often used to transform results of laboratory or in-situ tests to the property used for design to represent in-situ behavior of the structure. Transformation models, or material models, are approximate and contain errors. Analytical models which include limit equilibrium methods and finite element methods (FEM) also contain errors because of simplifications. Both are model errors and are systematic. Reliability analysis provides a rational method of evaluating the safety of a structure that accounts for all the uncertainties. The origin of reliability-based design can be traced to partial safety factors. Taylor (1948) explained the need to account for different uncertainties about the cohesional and frictional components of soil strength and Lumb (1970) used the standard deviation to represent the uncertainty and expressed the partial safety factors in terms of the standard deviations. In reliability analysis the failure probability is

3

FAILURE IN CLAYS

Stability of slopes on soft to medium clay under the undrained condition is a widely studied problem because it is simple and also because slopes failures in clay are perhaps the most common among failures in geotechnical construction. Many case histories are available and various reliability analyses have been made. 3.1 Soil Variability Models for soil variability range from simple parameters to stochastic fields. A common model represents the mean by a trend, usually taken as a function of depth z, and random departures from the trend by a standard deviation, σ(s), or a coefficient of variation (COV), (s). Soil variability is spatially correlated with correlation distances δx , δz for horizontal and vertical directions. To account for spatial correlation a variance reduction A is used and the average of s over a region A has mean and COV, sA = s, (sA ) = A (s), respectively (Vanmarcke 1977). For generic soil types, Rojiani et al (1991) and Phoon and Kulhawy (1999a) have summarized known data on (s) and δx , δz . There is ample evidence (Wu 2003, Wang and Chiasson 2006) that the trend is not constant even within a small region. Examples of soil variability are given in Table 1. There is a large range in δ. One should note that data on δx and δz were very limited until the 1980’s and Tang et al’s (1976) estimate was based on results from block samples. If δ = 2 m (Phoon and Kulhawy 1999a), then (sA ) ≈ 0.10. Also, because of the small number of samples, there is an uncertainty about the mean value, given as o . The large δ for the James Bay site is to account for the large segment of the slip surface that passes through a layer of lacustrine clay. This illustrates the significance of δ. Also shown are the values

Freudenthal (1947) may be the first to provide a comprehensive formulation of Pf for structures. Since the functions are complex, numerical integration is required. The use of first-order-second-moment (FOSM) method is more convenient. An improvement

4

from Phoon and Kulhawy (1999a) for clays in general. Uncertainty about soil stratification, or the subsoil model, is not included because of inadequate data. 3.2 Model Errors Model errors are systematic and include errors in the soil properties model and the analytical model. Bias in the property model has been investigated by laboratory and in-situ tests that compared the properties measured by different tests. Examples include the estimate of su from results of unconfined compression tests, vane shear tests or cone penetration tests. Transformation models and their reliabilities are summarized in Phoon and Kulhawy (1999b). The engineer must evaluate the results and exercise judgment in estimating the mean and COV of the model error. It is subjective; the true model error is of course unknown. Table 2 gives some examples of estimated errors of strength models. During earlier times the unconfined compression test was the common test used to measure the undrained shear strength of soft to medium clays. The two estimates in Table 2 differ in the factors considered and in the bias N m , and (Nm ). The estimate for vane shear test was based on the laboratory studies by Lefebvre et al (1988) on the same soil. Bias in analytical models has been investigated by comparison of results of simple models used in practice with those of more sophisticated ones. For limit equilibrium analysis of slope stability, the simple models range from the Fellenius method to the Morgenstern-Price method. Sophisticated methods include FEM (Zou et al 1995) and limit analysis (Yu et al 1998). Examples of estimated model errors for four sites are given in Table 3. The estimated error for limit equilibrium analysis is N a ≈ 1.0, (Na ) ≈ 0.05. If the Fellenius method is included, a ≈ł1.14, (Na ) ≈ 0.05. Another factor is the difference between the plane-strain analysis and threedimensional analysis. The first two cases in Table 3 have slide masses of limited width, where the 3-d effect is more important, while the embankment at James Bay is long and a plane-strain failure is likely.The landfill at Kettlement Hills has a complicated geometry. A comparison for an embankment on Bangkok Clay is given in Case 3, Table 4. Despite the different site conditions and the time span between the estimates, the estimated model errors are not very different. There is very little difference between limit equilibrium and limit analyses for example slopes with 30◦ < α < 45◦ .

(a) Permeability Profile at Chicopee Dam, MA. (Terzaghi and Peck 1948) Reprinted with permission from John Wiley and Sons.

3.3

Combined Uncertainty

The combined uncertainty represents the error of the prediction model

(b) Data used by Terzaghi to construct (a)

Using the upper and lower limits of the values in Tables 1–3, the combined prediction error is estimated

Figure 3. Chicopee Dam, MA.

5

Table 1.

Uncertainties due to Data Scatter.

Site

Soil

s kPa

(s)

0

δ(m)

(sA )

Ref.

Chicago

upper clay middle clay lower clay lacustrine clay slip surface∗∗

51.0 30.0 37.0 31.2

0.51 0.26 0.32 0.27 0.14 0.10–0.55

0.083 0.035 0.056 0.045

0.2 0.2 0.2 40∗ 24 1–6

0.096 0.035 0.029

Tang et al. 1976

James Bay Generic ∗

clay

0.063

deGroot and Baecher 1993 Christian et al. 1994 Phoon and Kulhawy 1999

δx , ∗∗ For circular arc slip surface and H = 12 m.

Table 2.

Uncertainties due to Errors in Strength Model.

sample disturbance

Model stress state

Errors,

N mi sample anisotropy size

Site,

Test

Detroit clay

unconf. 1.15, 0.08 comp.

Chicago upper clay middle clay lower clay

unconf. a) 1.38, 0.024 1.05, 0.03 1.00, 0.03 comp. b) 1.05, 0.02 a) 1.38, 0.024 1.05, 0.03 1.00, 0.03 b) 1.05, 0.02 a) 1.38, 0.024 1.05, 0.03 1.00, 0.03 b) 1.05, 0.02

Labrador field clay vane

X

1.00, 0.03 0.86, 0.09

1.00, 0.15

X

(Nmi ) strain rate

progress. failure

X

X

N m, (Nm ) Total

Refer.

0.99, 0.12 Wu & Kraft 1970

0.75, 0.09 0.80, 0.14 0.93, 0.03

Tang et al. 1976

0.93, 0.05 0.80, 0.14 0.97, 0.03 0.93, 0.05 0.80, 0.14 0.97, 0.03 1.05, 0.17

X

X

X

X

1.00,0.15

Christian et al. 1994

(a) stress change, (b) mechanical disturbance Table 3.

Errors in Analytical Model.

Detroit, Cut Chicago, cut James Bay, embankment Kettlement Hills, landfill Example

Analysis

Model 3-D

Error Slip surf.

N ai , (Ni ) Numerical

N a , (Na ) Total

Ref.

φ=0 φ=0 φ=0 c
, φ
φ=0

1.05,0.03 X 1.1,0.05 1.1,0.16 limit eq.

0.95,0.06 X 1.0,0.05 X limit analysis

X X 1.0,0.02 X 0.9, 0.10 for failures. The uncertainty about soil strength, (sA ), for these sites is approximately 0.01. The largest combined uncertainty (N ) = 0.24. When these are used

7

Table 5. Type A Predictions Hp mean 70.6 ft

(Hp ) 0.10

N 1.03

(N ) 0.08

Malaysia Hf = 5.4 m

4.0 m

0.14

1.12

0.07

the information given to the predictors at the two symposia that are worth noting. At the MIT symposium, observed embankment performance during Stages 1 and 2 were known and predictors used it to calibrate their models before making the prediction of the additional height required to produce failure. However, the shear strength at the end of stage 2 was not known and had to be estimated. Table 5 shows the observed and predicted embankment heights at failure. Only the seven predictions that used rational models to estimate the shear strength are shown in Table 5. Most predictors used limit equilibrium analysis and a few used FEM. Despite different prediction models and assumptions, the results are very consistent with N = 1.03 and (N ) = 0.08. However, although the site conditions are considered to be well defined, Leonards (1982) suggested the probable presence of a weak layer. Depending on the strength of this layer and the failure surface, the safety factor could be between 0.35–1.20, which would imply that N ≈ 1.3 and (N ) ≈ 0.25. This is one more example of the importance of the subsoil stratification and its influence on the failure mode. In the Malaysian symposium, the embankment construction took 100 days and this was not known to the predictors. All predictors used the initial undrained shear strengths. The five invited predictors all predicted heights smaller than the observed, with N = 1.12. The underestimate of Hf is likely because the predictors did not account for the strength gain during construction. However, (N ) = 0.07, which is small considering the different methods and assumptions used. These numbers may serve as a measure of the uncertainty under the most favorable design scenario. These prediction errors are not much larger than those for Type C predictions and those estimated in Table 3. The above results show that, for the case histories reviewed, the simple methods used in design and reliability analysis are generally satisfactory. However, it must be emphasized that the cases represent very small spectrum of those in geotechnical practice and that results from simple cases cannot always be generalized. As an example, if one extends the problem to include long-term stability, then the pore pressure must be estimated. For slopes on unsaturated soils, the suction is strongly dependent on the soil-water characteristics (SWC). Studies by Chong et al (2000) and Zhang et al (2005) show that uncertainties about SWC alone can result in a (Fs ) as large as 0.2. This is about equal to the combined uncertainty given in Sec. 3.3.

Figure 4. Pf versus Fs solid dots denote failures.

are not the same as the cases in Table 4, which pertain to failure in the undrained state, or immediately or shortly after construction. 4.2

MIT Hf = 71.7 ft

Prediction of failures

There are many well-documented case histories of failures, especially of slopes on clays. The observed factor of safety of a failure is 1.The ratio of observed to calculated factors of safety provides an empirical measure of the prediction bias N and (N ) is a measure of uncertainty. A distinction should be made on the type of “prediction” as defined by Lambe (1973). Type A predictions are those made before observations Type B predictions are those made during observations and Type C predictions are those made after observations. Consider first Type C predictions. Bishop and Bjerrum (1960) summarized 27 slope and bearing capacity failures in clays and values of Fs calculated with su as measured by the unconfined compression test. The prediction error or bias, N = 1/Fs , has mean and COV of N = 1.01, and (N ) = 0.06 respectively. The prediction error (N ) is much smaller than the range given in Sec. 3.3. Tavenas and Lerouil (1980) summarized almost 60 slope failures and the Fs calculated with su measured by the vane shear test. Their results give N = 1.03, (N ) = 0.17. These are closer to the range given in Sec. 3.3. Good examples of the reliability of Type A predictions are the symposia at Massachusetts Institute of Technology (1975) and at Kuala Lumpur, Malaysia (Malaysian Highway Authority 1989), 14 years later. In each case, well respected predictors were asked to predict the height Hp at failure of a test embankment on clay. The actual height at failure, Hf , was unknown to the predictors. The observed safety factor is 1.0 and the model bias is N = Hf /Hp . The values of N and (N ) for the two symposia are given in Table 5. There are differences between

8

5

and i = 1 = failure, P[zj |xi ] = pdf of β as determined from investigations for failed slopes, and β = reliability index for the specific slope under investigation. To apply Bayesian updating, Eq. (2) is rewritten as,

COMPLEX PROBLEMS

Most design problems are far more complex than those examined in Sec. 3 and 4. Besides the subsoil stratification model, boundary conditions are usually difficult to determine. For slopes on unsaturated soils, surface infiltration may control stability and the change in pore pressure depends not only on the SWC but also on rainfall characteristics. Another complex boundary condition is the displacement of the support system in braced excavations. FEM analyses can predict the pressure distribution well under idealized conditions, but details of construction processes, which are difficult to predict, can have important effect on displacements and stresses. Other complex boundary conditions include wave loadings on offshore structures and ground motion from earthquakes. Evaluation of errors in many of the input data is beyond the scope of soil mechanics. Where the uncertainty predicted by reliability methods may be too large to be useful for design decisions, the observational method provides an attractive alternative to evaluate the safety. There have been many examples of the successful use of the observational method since the Chicopee Dam.

6

The results are used to formulate a slope maintenance strategy for Hong Kong.

7

SUMMARY AND CONCLUSIONS

The review of reliability methods emphasizes the comparison of reliability analysis with observed performance. Failure in soft to medium clays is examined in detailed with well documented case histories. The calculated failure probabilities of slopes on clay with simple subsoil profiles are in good agreement with observed performance and provide some confidence in the methods. It is also clear that for more complex subsoil stratifications, modeling the failure mechanism is critical. Complex boundary conditions where statistical data are often insufficient will require more input in the form of subjective probability based on judgment. For a comprehensive review of this topic, see Baecher and Christian (2003). For very complex design conditions, the observational method is often used to achieve a successful design. Bayesian updating provides an analytical model for the observational method. Two recent examples are given to indicate the potential applications of Bayesian updating.

BAYESIAN UPDATING

The important role of the observational method in solving complex design problems has already been mentioned. Bayesian updating provides a valuable model to evaluate observed performances. It can combine information from different sources including site investigation data, observations, and analytical results. Early examples include Tang (1971), and Matsuo and Asaoka (1978). Eq. (2) can be extended to solve problems with several performance modes (z) and properties (x) (Wu et al 2007). Two recent applications serve to illustrate the potentials of this approach to complex design problems. Gilbert et al (1998) used updating to evaluate the mobilized shear strength of the clay-geosynthetic interface at the Kettlement Hills landfill. The probability that the strength is xi given that the slope has failed is given by P[xi |zj ] in Eq (2), Fig. 2, where P
[xi ] = prior probability that the strength xi , P[zj |xi ] = probability that the slope fails given the strength is xi , P[zi ] = probability that the slope fails. The evaluation accounts for various uncertainties in laboratory tests that contribute to P
[xi ] and inaccuracies in the stability analysis that contribute to P[zj |xi ]. Regional records of slope performance, when related to some significant parameter, such as rainfall intensity, are valuable as an initial estimate of failure probability. Cheung and Tang (2005) collected data on failure probability of slopes in Hong Kong as a function of age and rainfall. This was used as prior probability in Bayesian updating to estimate the failure probability for a specific slope. The failure probability based on age is P[xi ] where i=0 = stable slope

ACKNOWLEDGEMENTS The author thanks the Organizing Committee for the opportunity to make this presentation, Prof. Y. Honjo for advice and help in the preparation of this paper, and Prof. B F. Low and Prof. G. A. Fenton for informative discussions about their FEM analyses. REFERENCES Baecher, G.B., and Christian, J.T. 2003. Reliability and Statistics in Geotechnical Engineering. Chichester: John Wiley and Sons. Bergado, D. T., Long, P.V., Lee, C.H., Loke, K.H., and Werner, G. 1994a. Performance of reinforced embankment on soft Bangkok clay with high-strength geotextile reinforcement. Geotextiles and Geomembranes. 13: 403–420. Bergado, D.T., Patron Jr, B.C., Youyongwatana, W., Chai, J-C., and Yudhbir, 1994b. Reliability-based analysis of embankment on soft Bangkok clay. Structural Safety 13:247–266. Bishop, A. W., and Bjerrum, L. 1960. The relevance of the triaxial test to the solution of stability problems. In Proc. Research Conf. on Shear Strength of Cohesive Soils. 437–501, New York: ASCE.

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Casagrande, A. 1965. Role of the “calculated risk” in earthwork and foundation enmgineering. J. Soil Mechanics and Foundation Division ASCE, 91:1–40. Chai, J., and Bergado, D.T. 1993. Performance of reinforced embankment on Muar Clay deposiot. Soils and Foundations, 33 (4):1–17. Cheung, R. W. M., and Tang, W. H. 2005. Realistic assessment of slope stability for effective landslide hazard management. Geotechnique 55:85–94. Chong, P. C., Phoon, K. K., and Tan, T. S. 2000 Probabilistic analysis of unsaturated residual soil slopes. In R. E. Melchers and M. G. Stewart (eds.) Applications of Statistics and Probability, 375–382. Rotterdam: Balkema. Christian, J. T., Ladd, C. C., and Baecher G. B. 1994. Reliability applied to slope stability analysis. J. of Geotechnical Engineering, 120:2180–2207. DeGroot, D. J., and Baecher, G. B. 1993. Estimating autocovariance of in-situ soil properties. J. Geotechnical Engineering, 119:147–167. El-Ramly, H., Morgenstern, N.R., and Cruden, D.M. 2002. Probabilistic slope stability for practice. Canadian Geotechnical J., 39 :665–683. Freudenthal, A.M., 1947. The safety of structures. Trans. ASCE, 112:125–180. Gilbert, R. B., Wright, S. G., and Liedke, E. 1998 Uncertainty in back analysis of slopes: Kettleman Hills case history. J. Geotechnical and Geoenvironmental Engineering, 124:1167–1176. Griffith, V. D., and Fenton, G. A. 2004. Probabilistic slope stability analysis by finite elements. J. Geotechnical and Geoenvironmental Engineering, 130:507–518. Lafleur, J., Silvestri, V., Asselin, R., and Soulie, M. 1988. Behaviour of a test excavation in soft Champlain Sea clay. Canadian Geotechnical J. 25:705–715. Lefebvre, G, Ladd, C.C., and Pare, J-J. 1988. Comparison of field vane and laboratory undrained shear strengths in soft sensitive clays. In Vane Shear Testing in Soils: field and laboratory studies. STP 1014, 233–246. Philadelphia: ASTM. Lambe, T. W. 1973. Predictions in soil engineering. Geotechnique, 23:149–202. Leonards, G. A. 1982. Investigation of failures. J. Geotechnical Engineering, 108:222–283. Low, B. F. 2008. Practical reliability approach using spreadsheet. In K-K. Phoon (ed.) Reliability-Based Design in Geotechnical Engineering. London: Taylor and Francis. Low, B.F., and Tang,W.H. 1997. Reliability analysis of reinforced embankment on soft ground. Canadian Geotechnical J. 34:672–685. Lumb, P. 1970. Safety factors and the probability distribution of strength. Canadian Geotechnical J., 7:225–242. Malayasian4 HighwayAuthority 1989. In (eds.) R. R. Hudson, C. T. Toh, and S. F. Chan. Proc. Intern. Symp. on Trial Embankments on Malayasian Marine Clays. Kuala Lumpur, Malayasia. Massachusetts Institute of Technology 1975. Proc. Foundatiions Deformation Prediction Symp. Washington, DC: Federal Highway Administration. Matsuo, M. andAsaoka,A. 1978. Dynamic design philosophy of soils based on the Bayesian reliability prediction. Soils and Foundations 18(4):1–17 Meyerhof, G. G. 1970. Safety factors in soil mechanics. Canadian Geotechnical J. 7:333–338. Peck, R. B. 1969. Advantages and limitations of the observational method in applied soil mechanics, Ninth Rankine Lecture. Geotechnique, 19:171–187.

Phoon, K. K., and Kulhawy, F. H. 1999a. Characterization of geotechnical variability. Canadian Geotechnical J. 36: 612–624. Phoon, K. K., and Kulhawy, F. H. 1999b. Evaluation of geotechnical property variability. Canadian Geotechnical J. 36:625–639. Rojiani, K. B., Ooi, P.S.K., and Tan, C.K. (1991) Calibration of load factor design code for highway bridge foundations, Geotechnical Engineering Congress, Geotechnical Special Publication No. 217, 2:1353–1364. New York: ASCE. Silva, F. Lambe, T.W., and Marr, W.A. 2008. Probability and risk of slope failure. J. Geotechnical and Geoenvironmental Engineering, 134:1691–1699. Tang, W. H. 1971. A Bayesian evaluation of information for foundation engineering design. In P, Lumb (ed.) Statistics and Probability in Civil Engineering, 173–185, Hong Kong: Hong Kong Univ. Press. Tang, W. H. 1971. A Bayesian evaluation of information for foundation engineering design. In P, Lumb (ed.) Statistics and Probability in Civil Engineering, 173–185, Hong Kong: Hong Kong Univ. Press. Tang, W. H., Yucemen, M.S., and Ang, A. H-S. 1976. Probability-based short term design of soil slopes. Canadian Geotechnical J. 13:201–215. Tavanas, F., and Leroeil, S. 1980. The behavior of embankments on clay foundations. Canadian Geotechnical J. 17:236–260. Taylor, D. W. 1948. Fundamentals of Soil Mechanics, New York: John Wiley and Sons. Terzaghi, K. 1929 Effect of minor geologic details on the safety of dams. Technical Pub. 215, 31–44, American Institute of Mining and Metallurgical Engineering, New York. U.S. Army, Corps of Engineers 1995. Introduction to probability and reliability methods for use in geotechnical engineering. Technical letter 1110-2-547, Washington, DC Vanmarcke, E. H. 1977. Probabilisic modeling of soil profiles. J. Geotechnical Engineering Division, ASCE, 103:P1227-1246 Wang, Y-J., and Chiasson, P. 2006. Stochastic stability analysis of a test excavation involving spatially variable subsoil. Canadian Getechnical J. 43:1074–1087. Wu, T.H. 2003. Variation in clay deposits of Chicago. In E. Vanmarcke and G. A. Fenton, (eds.) Probabilistic Site Characterization at the National Geotechnical Test Sites. Geotechnical Special Pub. 121. Reston: ASCE. Wu, T.H., Kraft, L.M. 1970 Safety analysis of slopes. J. Soil Mechanics and Foundations Division, ASCE, 96:609–630 Xu, B., and Low, B. F. 2006. and Zou, J-Z., Williams, D. J., and Xiong, W-L. 1995. Search for critical slip surfaces based on finite element method. Canadian Getechnical J. 32:233 Yu, H.S., Salgado, R., Sloan, S.W., and Kim, J.M. 1998. Limit Analysis versus limit equilibrium for slope stability. J. Geotechnical and Geoenvironmental Eng. 124:1–11. Zhang, L. L., Zhang, L. M., and Tang, W. H. (2005) Rainfall-induced slope failure considering variability of soil properties, Geotechnique, 55:183–188. Zou, J-Z., Williams, D.J. and Xiong, W-L. 1995. Search for critical slip surfaces based on finite element method. Canadian Geotechnical J. 32:233–246.

10

Keynote lectures

Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Risk assessment and management for geohazards F. Nadim International Centre for Geohazards (ICG) / Norwegian Geotechnical Institute (NGI), Oslo, Norway

ABSTRACT: Each year, natural disasters cause countless deaths and formidable damage to infrastructure and the environment. In 2004–5, more than 300,000 people lost their lives in natural disasters. Material damage was estimated at USD 300 billion. Many lives could have been saved if more had been known about the risks and possible risk mitigation measures. The paper summarizes the state-of-the-art in the assessment of hazard and risk associated with landslides, earthquakes and tsunamis. The role of such assessments in a risk management context is discussed and general recommendations for identification and implementation of appropriate risk mitigation strategies are provided.

1

INTRODUCTION

Table 1. Natural disasters in the period 1991–2000 (Source: IFRC 2001).

“Geohazards”, i.e. natural hazards that are driven by geological features and processes, pose severe threats to humans, property and the natural and built environment. During 2005, geohazards accounted for about 100,000 deaths worldwide, of which 84% were due to October’s Pakistan earthquake. In that year, natural disasters affected 161 million people and cost around US$ 160 billion – over double the decade’s annual average. Hurricane Katrina accounted for three quarters of this cost. During the period 1996 to 2005, natural disasters caused nearly one million lives lost, or double the figure for the previous decade, affecting 2.5 billion people across the globe (World Disaster Report, 2006). When the trend of fatalities due to natural hazards is studied over the last 100 years, it appears that the increase in the known number of deaths is due to the increase in the exposed population in this time scale and the increased dissemination of the information, and not to an increase in the frequency and/or severity of natural hazards. The economic consequences of geohazards show an even more dramatic increasing trend (Munich Re, 2007). Some of the reasons for this increase are obvious, others less so. The post-disaster effects can be especially severe in a vast, densely-populated area where sewers fail and disease spreads. Slums spring up in disaster-prone areas such as steep slopes, which are prone to landslides or particularly severe damage in an earthquake. Many of the world’s fastest growing cities are located on coastal land or rivers where climate variability and extreme weather events, from cyclones to heat waves to droughts, pose increasing risks of disaster. Several well-documented studies have shown clearly that developing countries are more severely affected by natural disasters than developed countries, especially in terms of lives lost (UNDP 2004, ISDR

Country classification

No. of disasters

No. of lives lost

Low and medium developed countries Highly developed countries

1838

649,400

719

16,200

2004 and International Federation of Red Cross and Red Crescent 2004). Table 1 shows the data compiled by IFRC (2001) for the decade 1991–2000. Of the total number of persons killed by natural disasters in this period, the highly developed countries accounted for only 5% of the casualties. In absolute numbers, the material damage and economic loss due to natural hazards in highly developed countries by far exceed those in developing nations. However, this reflects the grossly disproportionate values of fixed assets, rather than real economic vulnerability. Mitigation and prevention of the risk posed by natural hazards have not attracted widespread and effective public support in the past. However, the situation has changed dramatically during the past decade, and it is now generally accepted that a proactive approach to risk management is required to reduce significantly loss of lives and material damage associated with natural hazards. The wide media attention on major natural disasters during the last decade has clearly changed people’s mind in terms of acknowledging risk management as an alternative to emergency management. A milestone in recognition of the need for natural disaster risk reduction was the approval of the “Hyogo Framework for Action 2005–2015: Building the Resilience of Nations and Communities to Disasters” (ISDR 2005). This document, which was approved by 164 UN countries during the World Conference on Disaster

13

•

Reduction in Kobe, January 2005, clarifies international working modes, responsibilities and priority actions for the coming 10 years. The first step in any decision-making process for disaster risk reduction is the quantitative assessment of the risk. This paper provides an overview of the state-of-the-art for hazard and risk assessment for landslides, earthquakes and tsunamis, and discusses possible risk mitigation strategies for these geohazards.

• • • • •

2

In the following sections, the methodologies for answering one or more of these questions for landslides, earthquakes and tsunamis will be discussed.

RISK ASSESSMENT FRAMEWORK

The terminology used in this paper is generally consistent with the recommendations of ISSMGE Glossary of Risk Assessment Terms (listed on TC32 web page: http://www.engmath.dal.ca/tc32/). The important terms used in the context of this paper are: Danger (Threat): Natural phenomenon that could lead to damage, described by geometry, mechanical and other characteristics. Description of a threat involves no forecasting. Hazard: Probability that a particular danger (threat) occurs within a given period of time. Risk: Measure of the probability and severity of an adverse effect to life, health, property, or the environment. Mathematically, risk is defined as Risk = Hazard × Potential worth of loss. Vulnerability: The degree of loss to a given element or set of elements within the area affected by a hazard. It is expressed on a scale of 0 (no loss) to 1 (total loss). In UNISDR terminology on Disaster Risk Reduction (2009), “disaster” is defined as “a serious disruption of the functioning of a community or a society causing widespread human, material, economic or environmental losses which exceed the ability of the affected community or society to cope using its own resources. The term “natural disaster” is slowly disappearing from the disaster risk management terminology because without the presence of humans, one is only dealing with natural processes. These only become disasters when they impact a community or a society. Quantitatively risk can be evaluated from the following expression:

3

LANDSLIDES

3.1 Landslide threat Landslides represent a major threat to human life, property and constructed facilities, infrastructure and natural environment in most mountainous and hilly regions of the world. Statistics from The Centre for Research on the Epidemiology of Disasters (CRED) show that landslides are responsible for at least 17% of all fatalities from natural hazards worldwide. The socio-economic impact of landslides is underestimated because landslides are usually not separated from other natural hazard triggers, such as extreme precipitation, earthquakes or floods.This underestimation contributes to reducing the awareness and concern of both authorities and general public about landslide risk. As a consequence of climate change and increase in exposure in many parts of the world, the risk associated with landslides is growing. In areas with high demographic density, protection works often cannot be built because of economic or environmental constraints, and is it not always possible to evacuate people because of societal reasons. One needs to forecast the occurrence of landslide and the hazard and risk associated with them. Climate change, increased susceptibility of surface soil to instability, anthropogenic activities, growing urbanization, uncontrolled land-use and increased vulnerability of population and infrastructure as a result, contribute to the growing landslide risk. According to the European Union Strategy for Soil Protection (COM232/2006), landslides are one of the main eight threats to European soils. Water plays a major role in triggering of landslides. Figure 1 shows the relative contribution of various landslide triggering events factor in Italy. Heavy rainfall is the main trigger for mudflows, the deadliest and most destructive of all landslides. Many coastal regions have cliffs that are susceptible to failure from sea erosion (by undercutting at the toe) and their geometry (slope angle), resulting in loss of agricultural land and property. This can have a devastating effect on small communities. For instance, parts of the north-east coast cliffs of England are eroding at rates of 1 m/yr.

where R = risk associated with a particular danger H = hazard V = vulnerability of elements at risk E = expected cost of total loss of elements at risk Several risk assessment frameworks have been proposed, and Düzgün and Lacasse (2005) list a large number of these. The frameworks have the common objective of answering the following questions (modified from Lee & Jones, 2004): •

How often do the dangers of a given magnitude occur? [Hazard Assessment] What are the elements at risk? [Elements at Risk Identification] What is the possible damage to the elements at risk? [Vulnerability Assessment] What is the probability of damage? [Risk Estimation] What is the significance of the estimated risk? [Risk Evaluation] What should be done? [Risk Management]

What are the probable dangers and their magnitude? [Danger Identification]

14

factor of safety is defined as the ratio of the characteristic resistance (resisting force) to the characteristic load (driving force). The approach does not address the uncertainty in load and resistance in a consistent manner. The choice of “characteristic” values allows the engineer to implicitly account for uncertainties by using conservative values of load (high value) and resistance parameters (low value). The choice is somewhat arbitrary. Duncan (1992 and 1996) provided an overview of deterministic slope stability analysis method. The overview included the factor of safety approach, equilibrium methods of slope stability analysis (Janbu’s generalized method of slices, Bishop’s method, Spencer’s method, Morgenstern and Price’s method among others), techniques for searching for the critical slip surface, both circular and non-circular, three-dimensional analyses of slope stability, analyses of the stability of reinforced slopes, drained and undrained conditions, and total stress and effective stress analyses. Slopes with nominally the same factor of safety could have significantly different safety margins because of the uncertainties involved. Duncan (2000) pointed out that “Through regulation or tradition, the same value of safety factor is often applied to conditions that involve widely varying degrees of uncertainty. This is not logical.” To evaluate the hazard associated with the failure of a specific slope, the stability assessment must be put into a probabilistic format using one of the techniques mentioned earlier (FOSM, FORM, MCS, etc.). An overview of the available methods for doing probabilistic slope stability assessment for individual slopes is provided in Nadim et al. (2005).

Figure 1. Landslide triggers in Italy. Source: CNR-GNDCI AVI Database of areas affected by landslides and floods in Italy.

As a consequence of climatic changes and potential global warming, an increase of landslide activity is expected in the future, due to increased rainfalls, changes of hydrological cycles, more extreme weather, concentrated rain within shorter periods of time, meteorological events followed by sea storms causing coastal erosion and melting of snow and of frozen soils in high mountain regions like the Alps and the Himalayas. The growing landslide hazard and risk, the need to protect people and property, the expected climate change and the need to manage the risk have contributed to set the agenda for the profession to assess and mitigate the landslide risk. 3.2 Landslide hazard assessment for specific slopes Hazard assessment for a specific slope usually involves a probabilistic analysis of the slope, while hazard assessment for a region generally requires the computation of frequency of the landslides in the region. For regional analyses, data to be collected are in the form of maps related to geomorphology, geology, land-use/cover and triggers. For specific slopes, the required data for hazard analysis include slope geometry such as height, width, inclination of slope and potential failure plane, shape and length of failure plane etc., strength parameters data for possible trigger such as rainfall intensity, water level, severity of dynamic loads e.g. earthquake magnitude, acceleration and/or other characteristics. The probabilistic models used for a specific slope vary depending on the failure mechanism (e.g. flows, falls or slides) and the slope-forming material (e.g. soil or rock). Analyses of specific slopes use deterministic (factor of safety, numerical analyses) and/or probabilistic methods, e.g. first order, second-moment (FOSM), first order reliability method (FORM), point estimate methods, and Monte Carlo Simulation (MCS) (Ang & Tang 1984). Recent trends combine different approaches for an improved model of the hazard(s). An uncertainty analysis is essential prior to the calculation of slope failure probability as it allows a rational calculation of total uncertainties associated with different sources of uncertainty (e.g. in parameters and models). The quantification and analysis of uncertainties play a critical role in the risk assessment. The stability situation for natural and man-made slopes is often expressed by a factor of safety. The

3.3

Regional landslide hazard assessment

Landslide hazard and risk assessment is often required on a regional or national scale and it would not be feasible to do a stability assessment for all potentially unstable slopes in the study area. Therefore other techniques based on Geographical Information Technology (GIT) are employed in these situations. An example of this type of hazard assessment is the study done by Nadim et al. (2006) in the Global Hotspots study for the ProVention Consortium. That model, which is currently being updated for the Global Risk Update project of ISDR, assesses the landslide hazard by considering a combination of the triggering factors and susceptibility indicators. The principles of the model are demonstrated in Figure 2. In the latest version of the model, a landslide hazard index was defined using six parameters: slope factor within a selected grid cell, lithology (or geological conditions), soil moisture condition, vegetation cover index, precipitation factor, and seismic conditions. For each factor, an index of influence was determined and the relative landslide hazard level Hlandslide was obtained by multiplying and summing the indices. The landslide hazard indices were then calibrated against the databases of landslide events in selected (mostly European) countries to obtain the frequency of the

15

Figure 2. Schematic approach for landslide hazard and risk evaluation (Nadim et al., 2006). Figure 3. Landslide hazard map for parts of Latin America (Nadim et al., 2006).

landslide events, i.e. the landslide hazard. Figure 3 shows the landslide hazard map for parts of Latin America obtained by Nadim et al. (2006). 3.4

Landslide risk assessment

The most complete description of the possible losses (or risk) is quantitatively in terms of a “probability distribution”, which presents the relative likelihood of any particular loss value or the probability of losses being less than any particular value. Alternatively, the “expected value” (i.e., the probability weighted average value) of loss can be determined as a single measure of risk. A general scenario-based risk formulation is given by Nadim & Glade (2006):

Figure 4. Procedure for risk assessment of slopes.

where C is particular set of losses (of collectively exhaustive and mutually exclusive set of possible losses), S is particular scenario (of comprehensive and mutually exclusive discrete set of possible scenarios), P[S] is probability of occurrence of scenario S, P[C | S] is the conditional probability of loss set C given that scenario S has occurred, and E[Loss] is the “expected value” of loss. “Loss” may refer to any undesirable consequence, such as loss of human life, economic loss, loss of reputation, etc., in terms of its direct and indirect effects (e.g. local damage of railway tracks and related interruption of industrial traffic), its effects on different social groups (e.g. individuals, community, insurance, government) as well as its short- and long-term influences on a society (e.g. fatalities could include all children of a community, the tourist industry might collapse). Most often the focus is on the loss of human life. Calculation of the terms in the above equation is not trivial.The hazard term in the above equation (i.e. P[S]) is not constant with time. Moreover, the expected number of fatalities depends on many factors, for example on which week-day and what time of the day the landslide occurs, whether a warning system is in place and working, etc. The potentially affected population could be divided into groups based on for example the temporal exposure to the landslide: people living in houses

that are in the path of the potential landslide, locals in the area who happen to be passer-bys and tourists and/or workers who are coincidentally at the location during certain periods of the day of the year. Figure 4 summarizes a general procedure for risk assessment for slides. The key issue is the identification of potential triggers and their probability of occurrence, the associated failure modes and their consequences. The triggering mechanisms could be natural, such as earthquake, tectonic faulting, rainfall, temperature increase caused by climate change, excess pore pressures or man-made. Generally, one should consider several scenarios of plausible triggers, estimate the run-out distance and extent triggered by these events, and estimate the upper and lower bounds on the annual probability of occurrence of the scenarios (Roberds, 2005). This scenario-based approach involves the following steps: • •

Define scenarios for landslide triggering Compute the run-off distance, volume and extent of landslide for each scenario • Estimate the loss for the different landslide scenarios • Estimate the risk and compare it with tolerable or acceptable risk levels

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4 4.1

EARTHQUAKES

1) specification of the seismic-hazard source model; 2) specification of the ground motion model (attenuation relationship); and 3) the probabilistic calculation. The seismic-hazard source model is a description of the magnitude, location, and timing of all earthquakes (usually limited to those that pose a significant threat). For example, a source model might be composed of N total earthquake scenarios, where each has its own magnitude, location, and annual rate of occurrence. The ground motion model used in PSHA consists of the source model and an attenuation relationship. The latter describes how rapidly a particular ground motion parameter decays with distance from the source. Given the typically large number of earthquakes and sites considered in an analysis, attenuation relationships must be simple and easy to apply. The most basic attenuation relationships give the ground motion level as a function of magnitude and distance, but many have other parameters to allow for a few different site types (e.g., rock vs. soil) or styles of faulting. Different relationships have also been developed for different tectonic regimes. All are developed by fitting an analytical expression to observations (or to synthetic data where observations are lacking). With the seismic-hazard source model and attenuation relationship(s) defined, the probabilistic-hazard calculation is conceptually simple. In practice, however, things can get messy. Besides the non-triviality of defining the spatial distribution of small earthquakes on large faults, there is also the problem that different attenuation relationships use different definitions of distance to the fault plane. The logic tree approach is a fundamental and wellestablished tool in PSHA aimed at capturing the epistemic uncertainties (uncertainties related to our lack of knowledge), primarily associated with seismic sources and with ground motion modelling (Kulkarni et al., 1984; Coppersmith andYoungs, 1986). The logic tree approach, which has been state-of-the-art in PSHA for many years, can also be described as a means by which one can include subjective information in an objective way. The use of experts is a fundamental component in the judgments that are needed in order to model epistemic uncertainties. To this end the state-of-the-art methodology is that developed by SSHAC (1997), which has been summarized in a more easily available way in a review by NRC (1997). McGuire (2004) explained how seismology, geology, strong-motion geophysics, and earthquake engineering contribute to the evaluation of seismic risk. He provided detailed description of the methods used for development of consensus probabilistic seismic hazard maps, an important prerequisite for the assessment of earthquake risk.

Earthquake threat

Earthquakes can be especially devastating when they occur in areas with high population density. The risk posed by earthquakes to large cities and other densely populated areas is by far greater than all other geohazards combined (Nadim & Lacasse, 2008). Similar to other natural hazards, the global fatality count from earthquakes continues to rise. This has occurred despite the adoption of earthquake-resistant building codes in most countries. In the past five centuries, the global death toll from earthquakes has averaged 100,000 per year, a rate that is dominated by large infrequent disasters, mostly in the developing nations (Bilham, 2004). Just in the past few years, two of the most catastrophic earthquakes in history have occurred in Asia (Pakistan in October 2005 and Sichuan, China in May 2008). The increase in earthquake-induced fatalities is mainly due to the steady growth in global population. At the same time, there is a decline in the fatality rate expressed as a percentage of instantaneous population. It is tempting to attribute this observation to the application of earthquake-resistant construction code in new city developments. A more pessimistic, and more realistic, interpretation is, however, that the apparent decline in risk is a statistical anomaly and future extreme earthquake disasters in some of the world’s megacities may arrest, or reverse, the current trend. 4.2

Earthquake hazard assessment

Seismic hazard analysis methods have a wide range of applications, from broadly based zonations aimed essentially only at describing and delineating the seismicity, to site-specific analyses aimed for design of specific structures. Within both fields the analyses range from relatively cursory to highly detailed, with the level of detail for design purposes being dependent on the sensitivity of the structure. Prior to 1970, the assessment of seismic hazard was based on a deterministic approach that considered the most likely scenarios for earthquakes that could affect a particular location. The seminal paper of Cornell (1968) introduced the methodology behind a Probabilistic Seismic Hazard Assessment (PSHA) changed the way most engineering seismologists did their hazard analyses. Traditionally, the peak ground acceleration (PGA) has been used to quantify the ground motion in PSHA. Today the preferred parameter is Response Spectral Acceleration (SA), which gives the maximum acceleration experienced by a damped, single-degree-of-freedom oscillator (a crude representation of building response). The oscillator period is chosen in accordance with the natural period of the structure and damping values are typically set at 5% of critical. The PSHA methodology for estimating the annual probability of occurrence of a ground motion characteristic is the same for both the PGA and the SA. In both situations, PSHA involves three steps:

4.3

Earthquake risk assessment

The most comprehensive work towards earthquake risk calculation to date is condensed in HAZUS, a software system prepared for use in the United States by the Federal Emergency Management Agency (FEMA, 2003).

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Figure 7. Probability of a structure with spectral displacement dp on Figure 6 being in different states of damage after the earthquake.

between different building types, and also between different regions, reflecting on building code regulations and local construction practice. The HAZUS methodology includes standard methods for:

Figure 5. Flow chart of earthquake loss estimation methodology (HAZUS Technical Manual, Federal Emergency Management Agency, 2003).

1. Inventory data collection based on census tract areas 2. Using database maps of soil type, ground motion, ground failure, etc. 3. Classifying occupancy of buildings and facilities 4. Classifying building structure type 5. Describing damage states 6. Developing building damage functions 7. Grouping, ranking and analyzing lifelines 8. Using technical terminology 9. Providing output. The HAZUS approach is attractive from a scientific/technical perspective. However, the fact that it is tailored so intimately to the US situations and specific GIS software makes it difficult to apply in other environments and geographical regions. Aware of the need for a more internationally accessible tool for seismic risk estimation, the International Centre for Geohazards (ICG), through NORSAR and the University of Alicante, has developed a Matlab™based tool in order to compute the seismic risk in urban areas using the capacity spectrum method, SELENA (SEimic Loss EstimatioN using a logic tree Approach, see web page http://www.norsar.no/pc-35-68-SELENA.aspx). SELENA can compute the probability of damage in each one of the four damage states (slight, moderate, extensive and complete) for defined building types. SELENA is a stand-alone software package that can be applied anywhere in the world. It includes a logic treebased weighting of input parameters that allows for the computation of confidence intervals. The loss estimation algorithm in SELENA is based on the HAZUS methodology, and 144 predefined vulnerability curves detailed in the HAZUS manual (see e.g. Figure 8) can be applied in SELENA.

Figure 6. Estimation of earthquake-induced damage using the capacity-spectrum method.

The methodology used in HAZUS for earthquake loss estimation is outlined in Figure 5. The HAZUS approach is based on the so-called the capacity-spectrum method (see Figures 6 and 7). It combines the ground motion input in terms of a response spectrum (spectral acceleration versus spectral displacement) with the building’s specific capacity curve. The philosophy behind this approach is that any building is structurally damaged by the earthquakeinduced permanent horizontal displacement, and not by the acceleration per se. For each building and building type the interstorey drift is a function of the applied lateral force that can be analytically determined and transformed into building capacity curves (capacity to withstand accelerations without permanent displacements). Building capacity curves naturally vary

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Figure 9. Historic tsunamis in the world from 17th century until today (from Tsunami Laboratory Novosibirsk, http://tsun.sscc.ru/tgi_1.htm). Different circle sizes and colors indicate different tsunami intensities (proportional to the average tsunami run-up).

Figure 8. Fragility curves for small refineries with unanchored components (HAZUS Technical Manual, FEMA 2003).

As input to SELENA, the user must supply built area or number of buildings in the different model building types, earthquake sources, attenuation relationships, soil maps and corresponding ground motion amplification factors, capacity curves and fragility curves corresponding to each of the model building types and finally cost models for repair or replacement. This probability is subsequently used with the built area or number of buildings to express the results in terms of damaged area (square meters) or number of damaged buildings. Simple models for computing economic damages and casualties are also included. 5 TSUNAMIS

Tsunamis constitute a serious natural hazard for the environment and populations in exposed areas. Future catastrophes can be mitigated or prevented by tsunami hazard evaluation from statistics and geological analysis, by risk analyses from studies of slide dynamics, tsunami propagation and coastal impact; and by risk mitigation measures such as tsunami warning systems, sea walls and dykes, area planning, evacuation routes to safe elevated areas, and education, preparedness and awareness campaigns. Moreover, tsunami predictions are fundamental in engineering design and location of coastal installations, dams, submerged bridges, offshore constructions, aquaculture, etc.

5.1 Tsunami threat

5.2 Tsunami hazard assessment

Tsunamis are gravity waves set in motion by large sudden changes of the sea water, having characteristics intermediate between tides and swell waves. Although they are infrequent (ca. 5–10 events reported globally pr. year), tsunamis represent a serious hazard to the coastal population in many areas, as demonstrated by the devastating effects of the 2004 Indian Ocean tsunami. Earthquakes are the most important mechanism of tsunami generation, causing more than 75% of all tsunamis globally. The generation mechanism is typically dominated by the co-seismic dip-slip fault movement, as strike-slip fault movements are generally less important for wave generation. Submarine landslides are also becoming increasingly recognized as an important trigger as well. Other sources of tsunamis include rock slides into bodies of water, collapsing/exploding volcanoes, and asteroid impacts. Tsunamis generated by large earthquakes in subduction zones along the major plate boundaries (so called convergent plate boundaries) contribute most to the global tsunami hazard. Such important areas of generation includes the “ring of fire” along the Pacific Rim, the Sunda Arc including Indonesia and the Philippines, Makran south of Pakistan, the Caribbean Sea, the Mediterranean Sea, and the fault zones off the Portuguese coastline. Figure 9 shows the historical tsunamis recorded worldwide since 1628.

Following the catastrophic Indian Ocean tsunami in December 2004, several research groups have started work on the development of a theoretical framework for Probabilistic Tsunami Hazard Assessment (PTHA). The PTHA methodologies are closely related to well-established Probabilistic Seismic Hazard Assessment (PSHA) and we define PTHA, consistently with the definition of PSHA, as the probability of exceeding a given tsunami size (either in terms of tsunami height or inundation) at a given location and in a given time interval. In this respect, the tsunami problem can (again in analogy with PSHA) be divided into three parts: the source (for example the earthquake generating a tsunami), the path (propagation from the source to some short distance from the coast line) and the site effects (inundation distance and height based on the local bathymetry and topography). In traditional PSHA, the sources are described through a zonation, which is characterized by activity rates in terms of a Gutenberg-Richter relationship. This is also the most common approach to follow for PTHA, with the difference that also distant tsunami sources must be accounted for in the PTHA. The path effects in traditional PSHA are described through simple attenuation relations giving the ground shaking level as a function of earthquake magnitude and distance from the rupturing fault. This approach cannot

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based on earthquake mechanics, which can be as simple as magnitude/area relations but can also include physically-based constraints in addition to empirical data such as earthquake locations. Uncertainties in source parameters, such as slip rate and maximum possible earthquake on a source, were included using logic tree analysis. Tsunami hazard assessment methodologies are one of the main research topics within the project TRANSFER (Tsunami Risk and Strategies for the European Region, http://www.transferproject.eu/). TRANSFER aims at improving the understanding of tsunamis in the Euro-Mediterranean region, including hazard and risk assessment and strategies for risk reduction.

be applied for PTHA due to the strong influence of bathymetry on the tsunami propagation. It is therefore necessary to perform full wave propagation modeling to include the path effects in PTHA. This is the largest difference between PSHA and PTHA, though it should be noted that PSHA methodologies are currently being developed, based on full ground shaking scenarios rather than simple attenuation relations. However, because the computation time required for the solution of the path problem may limit its practical applicability, a more efficient and practical PTHA (but less accurate) approach would be to use approximate “amplification functions” for the tsunami maximum inundation or run-up heights (analogous to “attenuation functions” for peak ground acceleration in PSHA), which depend on the profile of the sea floor from a certain water depth and up to the site. Thio et al. (2007) presented a method for Probabilistic Tsunami Hazard Analysis (PTHA) based on the traditional Probabilistic Seismic Hazard Analysis (PSHA). In lieu of attenuation relations, their method uses the summation of finite-difference Green’s functions that have been pre-computed for individual sub-faults. This enables them to rapidly construct scenario tsunami waveforms from an aggregate of subfaults that comprise a single large event. For every fault system, it is then possible to integrate over sets of thousands of events within a certain magnitude range that represents a fully probabilistic distribution. Because of the enclosed nature of ports and harbors, effects of resonance need to be addressed as well. Their method therefore focuses not only on the analysis of exceedance levels of maximum wave height, but also of spectral amplitudes. As in PSHA, these spectral amplitudes can be matched with the spectral response of harbors, and thus allow a comprehensive probabilistic analysis of tsunami hazard in ports and harbors. As mentioned earlier, Probabilistic Seismic Hazard Analysis (PSHA) is based on methodology originally proposed by Cornell (1968) and is well documented in many references (e.g. SSHAC, 1997). The majority of tsunamis are caused by earthquake-induced displacement of the seafloor. Most of the world’s largest tsunamis, which have caused damage at locations thousands of miles away, have been caused by megathrust (subduction interface) earthquakes around the Pacific Rim and Indian Ocean. These include the 1960 Chile earthquake, the 1964 Alaska earthquake and the 2004 Sumatra-Andaman earthquake. On a local scale, smaller earthquakes can cause significant tsunamis as well, but usually the hazard from these events is lower because of their localized impact. A crucial element in PTHA is the estimation of the frequency of occurrence and maximum magnitudes of large tsunami-generating earthquakes in each source region. Due to the very short historical record for mega-thrusts and other large earthquakes in relation to their recurrence times, it is not possible to base such constraints directly on the observed seismicity. Thio et al. (2007) therefore used models that were partly

5.3 Tsunami risk assessment Tsunami vulnerability and risk assessment is a relatively unexplored discipline, and few reliable models exist. The Tsunami Pilot Study Working Group (2006) lists the following tsunami parameters as possible impacts metrics that may enter as parameters in tsunami vulnerability models (i.e. mortality, building damage, forces on structures): • • • •

Tsunami flow depth Wave current speed Wave current acceleration Wave current inertia component (product of acceleration and flow depth) • The momentum flux (product of squared wave current speed and flow depth). In many circumstances this is the best “damage indicator”. The above mentioned parameters are important in determining the mortality of the tsunami, as well as the wave forces on structures. The selection of the flow depth is obvious, being a direct measure of the thickness of the flowing water; the flow depth is also related to the current velocity. In a national tsunami risk evaluation for New Zealand, Berryman et al. (2005) suggested an empirically derived mortality model solely based on the flow depth of the tsunami (Figure 10), however, we note that such an approach is most likely too simplistic (see discussion below). The fluid force on a structure is proportional to the momentum flux, as well as impact forces of flotsam, and hence also a natural possibility as an impact metric. Perhaps more surprising is the inclusion of the wave current acceleration. A tsunami wave that runup on the beach will often accelerate when it hits the shoreline after breaking (Synolakis, 1987), and this effect may be counterintuitive for a lay person observing the tsunami, leading to a misinterpretation of the escape time. Tsunami risk evaluation is the combination of the tsunami hazard, tsunami exposure, and vulnerability as described above. A risk evaluation may focus on different elements at risk, for instance mortality or destruction of buildings or installations. For a proper evaluation, it is therefore crucial to determine the correct damage metrics. Generally, the population,

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Figure 10. Empirical vulnerability (mortality) model of Berryman et al. (2005).

buildings etc. exposed to tsunamis are found by combining flood maps with population density maps, infrastructure maps and building maps in a GIS framework. Regional and global hazard evaluations aim at rough quantification of effects of tsunami inundation, and simple damage metrics and measures of exposure should preferably be used. The tsunami flood maps may be found using available computational tools. However, approximate methods for near-shore wave amplification usually have to be applied for large regions. In theory, mortality risk may then be obtained using relations similar to the one in Figure 10. In practice however, the regional analysis is limited to the hazard or at most, the population exposure. This is because mortality models are too simplistic, leaving out a number of important factors for mortality such as local evaluation of tsunami velocity and momentum flux, tsunami travel time, effects of warning systems, time of tsunami attack (which season, what time during the day, …) etc., and hence add little value to the analyses. Local risk evaluations on the other hand, can be done in detail and provide insight into appropriate local risk mitigation strategies. In a local analysis, run-up simulations may be done for smaller regions, which allow for a more accurate description of both the flow field and the inundated area. Furthermore, mapping of the different vulnerability parameters may be performed in far more detail than in regional evaluations, enabling the possibility of mapping population and building vulnerability at a high level of accuracy.

6 6.1

Figure 11. Risk estimation, analysis and evaluation as part of risk management and control (NORSOK Standard Z-013, 2001).

management process is a systematic application of management policies, procedures and practices to the tasks of communicating, consulting, establishing the context, identifying, analyzing, evaluating, monitoring and implementing risk mitigation measures (Draft ISO / IEC 31010 Ed. 1.0: Risk Management – Risk Assessment Techniques). As depicted in Figure 11, risk assessment is an important component of risk management. In the context of geohazards, Fell et al. (2005) provide a comprehensive overview of the state-of-the-art in landslide risk management. A large body of literature on earthquake risk management also exists. However, tsunami risk management is a relatively now topic and very few references specifically address this issue. 6.2 Acceptable risk One of the most difficult tasks in risk assessment/ management is the selection of risk acceptance criteria. As guidance to what risk level a society is apparently willing to accept, one can use ‘F-N curves’. The F-N curves relate the annual probability of causing N or more fatalities (F) to the number of fatalities, N. The term “N” can be replaced by other quantitative measure of consequences, such as costs. The curves can be used to express societal risk and to describe the safety levels of particular facilities. Figure 12

GEOHAZARDS RISK MANAGEMENT Risk management framework

Risk management broadly refers to coordinated activities to assess, direct and control the risk posed by geohazards to the society. It integrates the recognition and assessment of risk with the development of appropriate strategies for its mitigation. The risk

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Figure 12. F-N curves (Proske, 2004). Figure 13. Hong Kong criteria (GEO, 2001).

presents a family of F-N-curves. Man-made risks tend to have a steeper curve than natural hazards in the F-N diagram (Proske, 2004). F-N curves give statistical observations and not the acceptable or tolerable thresholds. Who should define acceptable and tolerable risk level? The potentially affected population, government, or the design engineer? Societal risk to life criteria reflect the reality that society is less tolerant of events in which a large number of lives are lost in a single event, than if the same number of lives is lost in a large number of separate events. Examples are public concern to the loss of large numbers of lives in airline crashes, compared to the much larger number of lives lost in road traffic. Figure 13 presents an interim risk criterion recommendation for natural hillsides in Hong Kong (GEO, 1998). Acceptable risk refers to the level of risk requiring no further reduction. It is the level of risk society desires to achieve. Tolerable risk presents the risk level which one compromises to in order to gain certain benefits. A construction with a tolerable risk level requires no action/expenditure for reduction, but it requires proper control and risk reduction if possible. Risk acceptability depends on several factors such as voluntary vs. involuntary situation, controllability vs. uncontrollability, familiarity vs. unfamiliarity, short/long-term effects, existence of alternatives, type and nature of consequences, gained benefits, media coverage, availability of information, personal involvement, memory, and level of trust in regulatory bodies. Voluntary risk levels tend to be higher than involuntary risk levels. Once the risk is under personal

control (e.g. driving a car), it is more acceptable than the risk controlled by other parties. For landslides, natural and engineered slopes can be considered as voluntary and involuntary risk. Societies experiencing frequent geohazards may have different risk acceptance level than those experiencing them rarely. Informed societies can have better preparedness for natural hazards. Although the total risk is defined by the sum of specific risk, it is difficult to evaluate its sum, since the units for expressing each specific risk differ. Individual risk has the unit of loss of life/year, while property loss has the unit of loss of property/year (e.g. USD/yr). Risk acceptance and tolerability have different perspectives: the individual’s point of view and the society’s point of view or societal risk.

6.3 Risk mitigation strategies The strategies for the mitigation of risks associated with geohazards can broadly be classified in six categories: 1) land use plans, 2) enforcement of building codes and good construction practice, 3) early warning systems, 4) community preparedness and public awareness campaigns, 5) measures to pool and transfer the risks and 6) construction of physical protection barriers. The first five strategies are referred to as non-structural measures, which aim to reduce the consequences of geohazards; while the last strategy comprises active intervention and engineering works, which aim to reduce the frequency and severity of the geohazards.

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As a consequence the focus on Early Warning System (EWS) development should take into account climatic changes and/or exceptional situations.

Identification of the optimal risk mitigation strategy involves: (1) hazard assessment (how often do the geohazards happen?), 2) analysis of possible consequences for the different scenarios, (3) assessment of possible measures to reduce and/or eliminate the potential consequences, (4) recommendation of specific remedial measure and if relevant reconstruction and rehabilitation plans, and (5) transfer of knowledge and communication with authorities and society. 6.4

Pillar 3: Strengthen national coping capacity. Most of the developing countries lack sufficient coping capacity to address a wide range of hazards, especially rare events like tsunamis. International cooperation and support are therefore highly desirable. A number of countries have over the last decade been supportive with technical resources and financial means to assist developing countries where the risk associated with natural hazards is high. A key challenge with all projects from the donor countries is to secure that they are need-based, sustainable and well anchored in the countries’ own development plans. Another challenge is coordination which often has proven to be difficult because the agencies generally have different policies and the implementation periods of various projects do not overlap. A subject which is gaining more and more attention is the need to secure 100% ownership of the project in the country receiving assistance. The capacity building initiatives should focus on institutions dealing with disaster risks and disaster situations in the following four policy fields:

Reducing the geohazards risk in developing countries

One can observe a positive trend internationally where preventive measures are increasingly recognized, both on the government level and among international donors. There is, however, a great need for intensified efforts, because the risk associated with natural disasters clearly increases far more rapidly than the efforts made to reduce this risk. Three key pillars for the reduction in risk associated with natural hazards in developing countries are suggested (modified from Kjekstad, 2007): Pillar 1: Identify and locate the risk areas, and quantify the hazard and the risk Hazard and risk assessment are the central pillar in the management of the risk associated with natural hazards. Without knowledge and characteristics of hazard and risk, it would not be meaningful to plan and implement mitigation measures.

•

Risk assessment and communication, i.e. the identification, evaluation and possibly quantification of the hazards affecting the country and their potential consequences, and exchange of information with and awareness-raising among stakeholders and the general public; • Risk mitigation, i.e. laws, rules and interventions to reduce exposure and vulnerability to hazards; • Disaster preparedness, warning and response, i.e. procedures to help exposed persons, communities and organizations be prepared to the occurrence of a hazard; when hazard occurs, alert and rescue activities aimed at mitigating its immediate impact; • Recovery enhancement, i.e. support to disasterstricken populations and areas in order to mitigate the long-term impact of disasters.

Pillar 2: Implement structural and non-structural risk mitigation measures, including early warning systems Mitigation means implementing activities that prevent or reduce the adverse effects of extreme natural events. In a broad prospective, mitigation includes structural and geo-technical measures, effective early warning systems, and political, legal and administrative measures. Mitigation also includes efforts to influence the lifestyle and behavior of endangered populations in order to reduce the risk. The Indian Ocean tsunami of 2004, which killed at least 230,000 people, would have been a tragedy whatever the level of preparedness; but even when disaster strikes on an unprecedented scale, there are many factors within human control, such as a knowledgeable population, an effective early warning system and constructions built with disasters in mind. All these measures can help minimize the number of casualties. Improved early warning systems have been instrumental in achieving disaster risk reduction for floods and tropical cyclones. Cuba has demonstrated that such reduction is not necessarily a question of expensive means. However, the recent tropical cyclone Nargis is a sad reminder that much remains to be done in decreasing the risk to tropical cyclones. Meteorological forecast in region where cyclones generally occur is quite effective, but early warning and response remains insufficient in unexpected regions (e.g. Catarina 2004 for South Atlantic Ocean).

In each of these fields, institutions can operate at local, regional, national or international levels.

7

CONCLUDING REMARKS

Management of the risk associated with geohazards involves decisions at local, regional, national and even transnational levels. Lack of information about the risk appears to be a major constraint to providing improved mitigation in many areas. The selection of appropriate mitigation strategies should be based on a futureoriented quantitative risk assessment, coupled with useful knowledge on the technical feasibility, as well as costs and benefits, of risk-reduction measures. Technical experts acting alone cannot choose the “appropriate” set of mitigation and prevention measures in many risk contexts. The complexities and technical details of

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Duncan, J.M. 1996. Soil slope stability analysis. Landslides: investigation and mitigation. Ed. By Turner & Schuster. Washington 1996 TRB Report 247. Duncan, J.M. 2000. Factors of safety and reliability in geotechnical engineering, J. of Geotechnical and Geoenvironmental Engineering 126(4): 307–316. Düzgün, S. & Lacasse, S. 2005. Vulnerability and acceptable risk in integrated risk assessment framework. Landslide Risk Management, Hungr, Fell, Couture & Eberhardt (eds), Taylor & Francis, London: 505–515. Federal Emergency ManagementAgency 2003. HAZUS-MH MR3 Technical Manual – Earthquake Model. Web site: http://www.fema.gov/plan/prevent/hazus/index.shtm Fell, R., Ho, K.K.S., Lacasse, S. & Leroi, E. 2005. “A framework for landslide risk assessment and management – State of the Art Paper 1”. Landslide Risk Management, Hungr, Fell, Couture & Eberhardt (eds), Taylor & Francis, London: 3–25. GEO (Geotechnical Engineering Office) 1998. Landslides and Boulder Falls from Natural Terrain: Interim Risk Guidelines. GEO Report 75, Gov. of Hong Kong SAR. IFRC (International Federation of Red Cross and Red Crescent Societies) 2001. World Disaster Report, Focus on Reducing Risk. Geneva, Switzerland, 239 pp. IFRC (International Federation of Red Cross and Red Crescent Societies) 2004. World Disaster Report. ISDR (International Strategy for Disaster Reduction) 2005. Hyogo Framework for Action 2005–2015, 21 pp. Kjekstad, O. 2007. The challenges of landslide hazard mitigation in developing countries. Keynote Lecture presented at 1st North-American Landslide Conference, Vail, Colorado 3–8 June 2007. Kulkarni, R.B., Young, R.R. & Coppersmith, K.J. 1984. Assessment of confidence intervals for results of seismic hazard analysis. Proc. Eighth World Conf. on Earthquake Engineering, San Francisco, Vol. 1, pp. 263–270. Lacasse, S. & Nadim, F. 2008. Landslide risk assessment and mitigation strategy. Invited Lecture, State-of-the-Art. First World Landslide Forum, Global Landslide Risk Reduction, International Consortium of Landslides, Tokyo. Chapter 3, pp. 31–61. Lee, E.M. & Jones, D.K.C. 2004. Landslide Risk Assessment. Thomas Telford, London. McGuire, R. 2004. Seismic Hazard and Risk Analysis. EERI monograph (MNO-10), ISBN: 0-943198-01-1, 221 p. Munich Re Group 2007. NatCat Service 2007 – Great natural disasters 1950–2007. Nadim, F. 2004. Risk and vulnerability analysis for geohazards. Glossary of Risk Assessment Terms. ICG Report 2004-2-1, NGI Report 20031091-1, Oslo Norway. Nadim, F. Einstein, H.H. & Roberts, W.J. 2005. Probabilistic stability analysis for individual slopes in soil and rock – State of the Art Paper 3. Landslide Risk Management, Hungr, Fell, Couture & Eberhardt (eds), Taylor & Francis, London: 63–98. Nadim, F. & Glade, T. 2006. On tsunami risk assessment for the west coast of Thailand, ECI Conference: Geohazards – Technical, Economical and Social Risk Evaluation 18–21 June 2006, Lillehammer, Norway. Nadim, F., Kjekstad, O., Peduzzi, P., Herold, C. & Jaedicke, C. 2006. Global landslide and avalanche hotspots. Landslides, Vol. 3, No. 2, pp 159–174. Nadim, F. & Lacasse, S. 2008. Effects of global change on risk associated with geohazards in megacities. Keynote Lecture, Development of Urban Areas and Geotechnical Engineering, St. Petersburg, Russia, 16–19 June 2008. NORSOK standard Z-013 2001. “Risk and emergency preparedness analysis”, Rev. 2, www.standard.no

managing geohazards risk can easily conceal that any strategy is embedded in a social/political system and entails value judgments about who bears the risks and benefits, and who decides. Policy makers and affected parties engaged in solving environmental risk problems are thus increasingly recognizing that traditional expert-based decision-making processes are insufficient, especially in controversial risk contexts. Risk communication and stakeholder involvement has been widely acknowledged for supporting decisions on uncertain and controversial environmental risks, with the added bonus that participation enables the addition of local and anecdotal knowledge of the people most familiar with the problem. Precisely which citizens, authorities, NGOs, industry groups, etc., should be involved in which way, however, has been the subject of a tremendous amount of experimentation. The decision is ultimately made by political representatives, but stakeholder involvement, combined with good riskcommunication strategies, can often bring new options to light and delineate the terrain for agreement. The human impact of geohazards is far greater in developing countries than in developed countries. Capacity building initiatives focusing on organizations and institutions that deal with disaster risks and disaster situations could greatly reduce the vulnerability of the population exposed to natural disasters. Many of these initiatives can be implemented within a few years and are affordable even in countries with very limited resources.

ACKNOWLEDGEMENT The author wishes to thank his colleagues at ICG for their direct and indirect contributions to this paper. Special thanks are due to Prof. Hilmar Bungum of NORSAR (earthquake), and Drs Carl Harbitz (tsunami), Finn Løvhølt (tsunami) and Suzanne Lacasse (landslide and risk management) of the Norwegian Geotechnical Institute. REFERENCES Ang, A.H-S. & Tang, W.H. 1984. Probability Concepts in Engineering Planning and Design I & II, John Wiley & Sons, New York. Berryman, K. et al. (editors) 2005. Review of tsunami hazard and risk in New Zealand. Geological and Nuclear Sciences (GNS) report 2005/104. 140 p. Bilham, R. 2004. Urban earthquake fatalities: A safer world or worse to come? Seism. Res. Lett., December 2004. Coppersmith, K.J., & Youngs, R.R. 1986. Capturing uncertainty in probabilistic seismic hazard assessment within intraplate tectonic environments. Proc. Third US Natl. Conf. on Earthquake Engineering, Earthquake Engineering Research Institute, Vol. 1, pp. 301–312. Cornell, C. A. 1968. Engineering seismic risk analysis. Bull. Seism. Soc. Am 58, pp. 1583–1606. Duncan, J.M. 1992. State-of-the-art: Static stability and deformation analysis. Stability and performance of slopes and embankments-II, 1: 223–266.

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Proske, D. 2004. Katalog der Risiken. Eigenverlag Dresden. 372 p. Roberds, W.J. 2005. Estimating temporal and spatial variability and vulnerability – State of the Art Paper 5. Landslide Risk Management, Hungr, Fell, Couture & Eberhardt (eds), Taylor & Francis, London: 129–158. SSHAC (Senior Seismic Hazard Analysis Committee) 1997. Recommendations for Probabilistic Seismic Hazard Analysis: Guidance on Uncertainty and Use of Experts, US Nuclear Regulatory. Commission report CR-6372, Washington DC. Synolakis, C.E. 1987. The run-up of solitary waves, J. Fluid Mech., 185, pp. 523–545. Thio, H.K., Somerville, P. & Ichinose, G. 2007. Probabilistic Analysis of Strong Ground Motion and Tsunami Hazards

in Southeast Asia. Proceedings from 2007 NUS-TMSI Workshop, National University of Singapore, Singapore, 7–9 March. Tsunami Pilot Study Working Group 2006. Seaside, Oregon Tsunami Pilot Study—Modernization of FEMA flood hazard maps. NOAA OAR Special Report, NOAA/OAR/PMEL, Seattle, WA, 94 pp. +7 appendices. UNDP (United Nations Development Programme) 2004. Reducing Disaster Risk – A Challenge for Development, Bureau for Crisis Prevention and Recovery, New York, 146 pp. UNISDR (2009). Terminology on Disaster Risk Reduction. http://www.unisdr.org/eng/library/UNISDR-terminology2009-eng.pdf World Disaster Report 2006. http://www.redcross.ca

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Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Risk management and its application in mountainous highway construction H.W. Huang & Y.D. Xue Key Laboratory of Geotechnical & Underground Engineering, Ministry of Education Department of Geotechnical Engineering, Tongji University, Shanghai, P.R. China

Y.Y. Yang Chief Engineering Office, Shanghai HuShen Highway Construction Development Co., Ltd. Shanghai, P.R. China

ABSTRACT: More and more highways will be constructed in mountainous areas of western China. The mountainous highway projects are subject to more risk than other constructions because they entail intricate site conditions and inhere so many uncertainties. Risk management is an effective approach to reduce and control the risks reasonably for achievement of project objectives. How to put the risk management techniques into practice in the highway projects is on the focus in this paper. Based on the study of the risk mechanism, an integrated project risk management framework is put forward. The organization of a risk management team is very important and each member should be selected suitably. Risk identification should be imposed with more efforts because its results have significant influence to the risk management aims. A synthetical rock tunnel risk identification method based on Fault Tree Analysis (FTA) is proposed and named as RTRI. The risk identification process is generally conducted in an iterative cycle which keeps step with the construction. Risk database is important and useful to risk management which is discussed in detail in another paper. The proposed risk management model for mountainous highway projects is practiced in Shuifu-Maliuwan Highway in Yunnan Province, China. The risks of construction time delay, cost overrun, poor quality and worker safety are assessed carefully. The results are proved relevant and help the decision-maker to deal with the risks effectively.

1

INTRODUCTION

of an industry accepted model of risk analysis may be one factor that limits the implementation of risk management (Lyons & Skitmore 2004). Along with the rapidly economic development, more and more highways will be constructed in mountainous region. The characteristics of these projects include complex geology, poor transport condition, bad weather, earthquake and so on. On the other hand, these projects always include more engineering types: tunnel, bridge, slope, subgrade and road surface. The potential risks include tunnel collapse, water burst, landslide, rockfall, injury, explosion, etc. It’s evident that the mountain area highway construction is faced with significant risks. This paper aims to supply a practicable risk management framework, and describe the process of each step. At last, a case study is conducted.

In general, the highway construction projects are always very complex and dynamic (Akintoye & MacLeod 1997, Carr & Tah 2001). Each project involves a variety of organizations and a larger number of people. It is known that all participants of a construction project are continuously faced with a variety of unexpected or unwanted situations. The projects have an abundance of risk due to the nature of construction. It is recognized that risk is built into any actions of people. In a construction project, the risk is perceived as events that influence the project objectives of cost, quality, time, safety and environment. To reduce or control the project risk, most people agree that project risk management (PRM) is suitable (Wideman 1986). Lyons & Skitmore (2004) had surveyed that the use of risk management in the Queensland engineering construction industry is medium to high. It has been a critical part of integrated project management system. Even though most people think risk management play a crucial role in project management and numerous papers on such subject have been printed, the actual use of risk management in practice is limited. Lack

2

GENERAL RISK MANAGEMENT

Risk management is a system which aims to identify and quantify all risks to which the project is exposed so that a conscious decision can be taken on how to manage the risks (Roger & George 1996,

27

3 Risk Identification

MOUNTAINOUS HIGHWAY CONSTRUCTION

3.1 Features In China, with the rapidly economic development, more and more highways are constructed or planned in mountainous areas. The engineering environments and conditions are far from the plain area. The main characteristics of mountain area highway can be summarized as: • High mountain • inconvenient transportation • bad weather • unfavorable geology • limited construction methods • long tunnels • long bridges with high pier • deep cut slope • construction material shortage • earthquake and • so on. In general, the main engineering types include rock tunnel, bridge, cutting/ nature slope, subgrade and road surface. According to the results of surveys and statistics to most accidents related with mountain road engineering in the last decade, the slope failure accidents are the most frequent and severest no matter in quantity or loss. The next one is long tunnel which is always suffered to poor geological condition. Then the risk is high pier bridge. New techniques and materials are widey used in bridge construction. This situation hints potential severe risks. The accidents about roadsubgrade and road surface are most faced in operation phase, seldom in construction phase.

Risk Classification

Risk Analysis Risk Attitude Risk Response Figure 1. The risk management framework (Roger & George 1996).

Eskesen et al. 2004, MOHURD 2007). It includes a series of processes. The Association of Project Managers defines nine phases of risk management: define, focus, identify, structure, ownership, estimate, evaluate, plan, and manage (APM Group 1997, Chapman 1997). Chapman (2001) think that all the process of risk analysis and management is composed of two stages, risk analysis and risk management. Roger defines some general stages are: risk identification, risk classification, risk analysis, risk attitude and risk response. The risk management framework is illustrated in Figure 1. The definition of project risk is important before it can be managed. Wideman defines project risk “as the chance of certain occurrences adversely affecting project objectives”. Chapman (2001) defines it as “an event, which should it occur, would have a positive or negative effect on the achievement of a project’s objectives”. The main difference is that whether or not consider the risk chance. In general, construction project risk has two types: pure risk and speculative risk. In this paper, the risk is defined as “a function of potential adverse event’s occurrence probability and consequence”. It is clear that only the pure risk concept is used in the highway construction project risk management. Risk identification is the most important stage in risk management. Unidentified risks may hide severe threats to a project’s objectives. Categorization of the source of risk is helpful to risk identification. British Standard 6079 considers that risks or adverse events generally fall into one of the following five categories: technological, political, managerial, sociological and financial. Zayed et al. (2008) divided the highway construction risks into two areas: company (macro) and project (micro) levels. In the micro hierarchy, emerging technology usage, contracts and legal issues, resources, design, quality, weather, etc. are included. Technological risk assessment is in general the main section of construction risk management.

3.2

Risk mechanism

There is abundant severe potential risk inherent with highway construction under such bad conditions. For the sake of effective risk management, the risk mechanism should be studied at first. A simple risk mechanism is obtained based on project management experience and theoretical studies. The mechanism of risk development is illustrated in Figure 2. Figure 2 can help people to understand the nature of construction risks. Activities, materials, tools and all kinds of equipments related with human can be considered as internal causes of risk event. Related surrounding environment can be thought as external causes of risk event. Through a careful screening of the project, the most risk factors can be identified. The risk effects mainly include economic loss, time delay, casualty, quality loss, environment loss, etc.According to the aim of risk assessment, the risk effects can be categorized differently. 4

MOUNTAIN HIGHWAY CONSTRUCTION RISK MANAGEMENT

It is known that there are numerous project risk management methods in different engineering areas. A risk

28

Internal environmental factors

Safety

Effect

Economic loss Time delay

Quality Casualties

Project decision-making

Project risk Geology and hydro-geology

Construction technology, Machinery, Operation, and etc.

Vulnerbility

Risk

External environmental factors

Risk surroundings

Riskfactors

Cost

Quality loss

Time

Ecological environment loss

Environment

Figure 2. Risk mechanism diagram. • •

management framework for mountain highway construction is proposed. It will also be accepted as a basic risk management structure in Guideline of Risk Assessment & Control for Safety Construction of Road Tunnel in China. 4.1

in construction phase: • • • • •

Risk management flowchart

The whole phase of a road construction project includes project development stage, construction contract procurement stage, design stages, construction stage and operation stage (ITIG 2006). Most people agree that the risk management should be used through the whole life cycle to reduce the risk. At present, risk management application in the execution and planning stages of the project life cycle is higher than in the conceptual or termination phases (Lyons & Skitmore 2004). In this paper, the main project phases include preliminary design, construction documents design and construction. The flowchart of risk management is illustrated in Figure 3. 4.2

principal designer or representative, contractor representative, consultant engineer, supervisor representative and other related personnel.

4.2.2 Scope, objective and strategy The scope of risk management defines the benchmark information such as client’s objective, why conduct the risk assessment, who will execute and control the process, when and how to assess the risk, anticipated achievement and other critical issues. The scope should be documented as task instruction document. General objective of a construction project risk management is identify and quantify all risks and consciously manage them. For risk management is time-person-cost-consuming, it is not reasonable to pay much attention to all low level risks. The detail of objective and client’s circumstance will influence the depth of risk analysis. The objective of mountain highway construction is dealing with the risks as low as reasonably practicable (known as ALARP principle). The mountain highway construction risk management strategy include:

Risk management

4.2.1 Risk management team To a new project/phase, an organization of risk management team should be established as the first task of the risk management. A risk analysis specialist plays a crucial role in the team organization, and this will significantly influence the following risk management processes. The team members are dynamic, and will change in different phases or special risk issues. To a risk management team, risk specialist, experienced project managers and client representatives are core members. Other members maybe include,

• • • • •

in design phase: • •

consultant engineer and other related personnel.

representatives of the core design team, design team representative,

29

carry out risk assessment through out the whole project construction process clarify the risk share of the various parties involved in the project a plan of dynamic risk assessment a training of risk view point to all persons involved a standard risk document format, including risk register and risk measures

Project phases Client Preliminary design phase

Construction documents design phase

Risk management specialist

Scope Objectives Strategy

Risk management team

Engineering type or area

Contractor and others

Risk identification

Construction phase Risk evaluation Risk acceptance criteria Risk response and monitor

Risk document and database

Figure 3. Risk management flowchart.

4.2.3 Engineering types or areas A typical mountain highway construction project is always so complex that risk management is very hard. Separation is an effective solution to complex problem. So it is used here to separate a project into a set of base elements for structuring the management. It is natural and reasonable to separate project according to its engineering types. In general, a mountain highway construction project can be separated into tunnel, bridge, slope, subgrade, road surface, etc. A typical kind engineering is usually complex, too. It can be separated into sub-engineering according to engineering areas futures.A tunnel project can be separated into tunnel portal section, poor geology section and other section depends on the nature of the tunnel engineering. A bridge will be separated into superstructure, substructure and connection section. A slope can be categorized as nature slope, cutting slope, rock slope and soil slope.

project. A survey result shows that risk identification and risk assessment are the most often used risk management elements ahead of risk control and risk documentation. The quality of identification results is greatly dependent on the team’s professional experience and knowledge. At the same time, the identification technique plays an important role. Risk identification methods generally include brainstorming, risk checklists, expert analysis/ interviews, modelling and analyzing different scenarios and analyzing project plans. Brainstorming and expert questionnaire (Ahmad & Minkarah 1988) are the most common risk identification techniques used in road construction project in China. Based on the Fault Tree Analysis method, a synthetical identification method (named RTRI) is used effectively in many tunnel construction projects. Its operation structure is illustrated in Figure 4. The key of this method is that severe and general risk events are distinguished. It is easy to control the risk identification depth, and can help to understand the internal logic relation of different risks. It is necessary to build up a risk database and register all the risks identified. The database is very useful and helpful to identify risk of a new analogous project.

4.2.4 Risk identification Risk identification is the most important step in the overall process of risk management. Unidentified and therefore unmanaged risks are clearly unchecked threats to a project’s objectives, which may lead to significant overruns. Floricel & Miller (2001) got that regardless of a thorough and careful identification phase, something unexpected occurred in every

4.2.5 Risk evaluation After the risks have been identified, they must be evaluated in terms of the probability of occurrence and

30

Figure 4. Rock tunnel construction risk identification method (RTRI). Table 1.

Risk occurrence probability ranking.

Ranking

Occurrence probability

Table 2.

1

2

3

4

5

Impossible P < 0.01%

Seldom 0.01% ≤ p < 0.1%

Occasional 0.1% ≤ p < 1%

Possible 1% ≤ p < 10%

Frequent P ≥ 10%

Risk impact ranking.

Ranking

1

2

3

4

5

Impact

Insignificant

Considerable

Serious

Severe

Disastrous

evaluation matrix (Table 3). For easy use, a colored standing for risk ranking is made as list in Table 4. The mountain highway construction risk acceptance criterion is described in Table 5. The criteria can aid the decision maker to deal with the risk.

impact. In practice, the risk probability and impact can be analyzed based on the historic statistic data. But for mountain highway construction project, the data are always very scarce. In this paper, probability and impact ranking is listed in Table 1 and Table 2 (MOHURD 2007) .The risk impact ranking is variable with different risks and client risk attitude. When the risk occurrence probability and impact is defined, the risk can be rated according to the risk

4.2.6 Risk response and monitor Risk response is a strategy taken to manage the identified risks. In general, there are four basic forms of

31

Table 3.

Risk evaluation matrix (risk ranking). Impact

Risk

Impossible Seldom Occasional Possible Frequent

Table 4.

Considerable

Serious

Severe

Disastrous

1 I I II II III

2 I II II III III

3 II II III III IV

4 II III III IV IV

5 III III IV IV IV

Colored standing for risk rank.

Risk ranks

Table 5.

Probability 1 2 3 4 5

Insignificant

Logo

Table 6.

Colour

Proposal for risk status definitions.

Risk status Identified Assessed Responses implemented Occurred Avoided Closed out

Risk acceptance criteria.

be communicated effectively among all parties. Risk communication is a key point to successful risk management. A software based on database technique has been developed for standard implementation of risk management in mountainous highway construction project. response or control strategies which can be used in risk management. The four types of risk response are acceptance, mitigation, transfer and avoidance. The decision of risk response should consider the risk acceptance criteria (Fig. 5). When a risk is identified and evaluated, the undertaker should take specific actions to control it. Any actions or measures should be analyzed carefully in order to achieve the project objectives. As an important part of risk response, project contingency arrangement should be established for critical risk. It includes the risk action schedules: • • • •

5

CASE STUDY

5.1 Project introduction Shuifu-Maliuwan Highway (shorted as Shui-Ma Highway) locates in the adjacent area of the Yungui Plateau and Liangshan mountain, which is in northeast of Yunnan Province in China. The total length of the highway is 135.55 km with three years’ construction time and the total general estimate of project investment is 92 billion RMB. Owing to Yanshan and Himalayan tectonic movement, the tectonic deformation is heavy. There are high mountains, steep gorges with heavy erosion, rapid rivers and saw-cuts everywhere. There are 39 tunnels with a total length of 27.21 km, 365 bridges with a total length of 91.4 km and many cut slopes and talus slopes along this highway in the whole project. The whole project was formally commenced with 28 bidding contracts in March 2005. Some characteristics of this project are illustrated in Figures 6 to 8.

Actions required (what is to be done); Resources (what and who); Responsibilities (who) and Timing (when).

Once the risk responses have been defined, the project risk source should be monitored in time throughout the construction. The states of risk are logged into the risk database. The risk status can be defined as Table 6.

5.2 Shui-Ma Highway construction risk management

4.2.7 Risk document and database The risk management is a systematic process.All materials related with the process should be documented. The materials include all kinds of memos, statistical data, photos, design and construction specifications, etc. A comprehensive risk register form logs the risks’ status and information. Formatted risk information can

According to the aforementioned method, the risk management is carried out for the Shui-Ma Highway construction project, including risk identification, risk evaluation, risk response and risk documentation. The risks are categorized into time, cost, quality and human

32

Risk acceptance criteria

Negligible risk

Acceptable risk

Unwantedrisk

Unacceptable risk

Risk acceptance

Risk mitigation

Risk transfer

Risk avoidance

Risk response Figure 5. The approximate relation between risk response and acceptance criteria.

Figure 6. Photo of construction of Guanhe bridge. Figure 8. Hazard of rock fall.

Table 7. No.

Risk events

P

C

R

R10 R11

Inconvenient traffic conditions Poor weather condition result in short effective construction time Poor social environment including the government mismanagement and the backwardness of people idea Delay of the design alteration, design change and the design approval Supplement of the unified supply materials are not in time Narrow construction site and poor construction conditions result in difficult transportation Power supply is not in time and the supply is unstable The treatment and influence of unfavorable geology Unreasonable resource preparing result in run-idle

3 5

2 3

II IV

2

2

II

3

2

II

3

2

II

4

2

III

2

3

II

3

3

III

3

3

III

R12 Figure 7. The panorama of the ancient landslide.

R13 R14

safety. Because this project is very long and complex, the project is separated into 28 sections according to the bidding contracts. As an example of the risk management, the risks of Contract 11 were evaluated. The occurrence probability ranking of risk event is decided according to Table 1 based on historic events statistic or experience of highway construction specialists. The impact ranking is decided according to Table 2. The Risk evaluation matrix (Table 3) is used for risk ranking. The results are listed in Table 7 ∼ Table 10 (P

R15 R16 R17 R18

33

Risk evaluation results of time delay.

Table 8.

Risk evaluation results of cost overrun.

Table 10.

Risk evaluation results of human safety.

No.

Risk events

P

C

R

No.

Risk events

P

C

R

R20

Insufficient credit level of the insurance company The price rising of raw materials, fuel and labor cost Natural disasters including flood and debris flow Owner improves the quality standard and contractor underestimates the exist risks Unfavorable geology including landslide, rock heap and rock fall Inconvenient traffic conditions result in the increasing of the materials transportation cost Construction contract risks Poor human environment Design risks (design alteration results in the increasing of investment) Narrow construction site results in the increasing of the spoil cost

3

2

II

R40 R41

3 3

3 3

III III

4

4

IV

4

4

IV

2

3

II

3

5

IV

R42 R43 R44 R45 R46 R47 R48

3 2 3 1 1 3 2

2 1 2 2 2 3 3

II 1 II I I III II

3

3

III

R49

Unfavorable geology Insufficient safety consciousness of constructors Improper construction protection Improper equipments manipulate High altitude construction Contact of injurant Road traffic accident Natural disasters Custody of initiating explosive device and blasting construction Power failure when the construction of the digging pile and the overturn of the bridge machine

1

5

III

3 1 2

3 2 4

III I III

2

4

III

R21 R22 R23 R24 R25 R26 R27 R28 R29

Table 9. No.

data, and the supporting parameters can be changed if necessary. The major quality risk is contract which is quoted with unreasonable low-price bid. Another major factor is unreasonable project schedule and time. The worker safety risk is acceptable. Risk education and reminder are effective management approaches to improve safety. Shi rock tunnel project is the key sub-project of Contract 11, and there are so many uncertainties in its construction that the potential risks are very big. The risk management system must be applied to achieve the final objectives.

Risk evaluation results of poor quality.

Risk events

R30 Construction contract risks (short construction period and low bid price) R31 Poor quality of equipments and materials R32 Protection risks (incorrect construction of anti-slide pile and shot Crete and anchor) R33 Site personnel quality R34 Technology risks of tunnel construction R35 Technology risks of subgrade and pavement construction R36 Technology risks of bridge construction R37 Unfavorable geology R38 Poor weather condition

P C R 5 3

IV

1 2 2 3

I II

3 3 2 4 3 3

III III III

4 1 2 4 4 2

II III III

5.3 Shi rock tunnel construction risk management Shi tunnel is a separated two-single-tunnel situated in Contract 11. Its left tunnel is approximately 4,75 2m in length, and the cover depth varies from 1.5 m to 352 m. The right tunnel is approximately 4,755 m in length and depth varies from 0 m to 357 m. The tunnel cross-sections are 11.7 m wide and 7 m high. Traditional Drill and Blast method is employed in the tunnel excavation. The conditions of the portal section are even worse which contains faults and fragment zones.

in the tables means probability, C means impact and R means risk rate). The risks of time delay (Table 7) show that the poor weather condition is a critical risk factor to the schedule. The adverse factor is mainly raining in the project area. There are almost 2/3 days raining in a year, and the effective workdays are limited. Because the weather condition is uncontrolled, the better risk response should be drawing a good plan which arranges the project processes thinking of weather influence. Table 8 shows that the major cost risks include price rising of materials, natural disasters and geo-hazards. The materials cost risk should be considered in the tendering. Different natural disasters risks should be assessed in detail. Then the contractor has a meeting to propose practicable risk control measures and emergency plans. To reduce the geohazards risk, the design of rock reinforcement should be certificated base on the new geological survey

5.3.1 Risk identification and assessment Based on in-situ investigation, tunnel construction design and other related materials, the main risks and general risks are identified with RTRI. The tunnel risk breakdown structure is listed in Figure 9. When all the risks are identified, Delphi method is employed to evaluate the risk rating. The risk evaluated results are given in Table 11. From Table 10, the manager can easily grasp and understand the risk profile of the tunnel project. Then the key points of risk management transported to all project parties. Because the Shi tunnel is very long and its geological conditions change greatly along the tunnel alignment, the tunnel is separated into several sections according to the geological conditions. The risks of each section are evaluated and diagramed in Figure 10.

34

Risks of Shi Tunnel during construction

Environmental impacts

Construction time delay

Waterflooding accidents

Gas accidents

Fire accidents

Harmful gases poisoning

High falling accidents

Machine accidents

Electric shock accidents

Blasting accidents

Rip spalling and floor heave

General risks

Surrounding rock large deformation

Tunnel collapse

Water or mud bursting

Tunnel portal slop failure

Main risks

Figure 9. Possible risks of Shi tunnel during construction.

Table 11.

cyclical footage and advanced support, etc. are much more important factors which will result in large deformation. The risk control methods of main risks and general risks are proposed accoding to the results of risk identification, risk assessment, analysis of risk factors, and the actual conditions of Shi tunnel. In the mean time, emergency plans against the possible risks are also put forward. The risk management should be implemented throughout the life of the project and keep all risks under control.

Risk evaluation results.

6

CONCLUSIONS

The mountainous highway construction projects are generally very complex, costly and time-consuming. Inevitably, there are a lot of potential risks which may hinder the project development and often result in poor performance with increasing costs and time delays. Most people agree that the risk management is very useful in project management of complex systems, but few people analyze the risks in highway construction practice other than by using intuition and experience. The major factors that limit the implementation of risk management maybe the lack of risk awareness and the lack of accepted risk assessment method. In this paper, a systematic risk management framework is proposed and practiced in Shui-ma highway construction project. The practice proved that the risk evaluation results can help the decision maker with more confidence. In the risk management process, the risk identification, risk evaluation, risk monitoring and risk database are key steps as well as project experience. The risk identification is the most important phase. This paper proposes a FTA based synthetical identification method which has been used in more than 10 road tunnels. Quantitative or semi-quantitative risk analysis method for complex mountainous highway construction project should be developed in future.

5.3.2 Sub-risk factors analysis For risk control, the sub-risk factors of main risk events are analyzed with specialist questionnaire method. From Figure 11 we can find that supporting quality, overburden, excavation method, etc. are the main factors that result in the occurrence of collapse, so during the construction, special attention should be paid to these factors in order to reduce the probability of collapse occurrence. Figure 12 shows that advanced geological forcast, construction organization design,undergroundwater disposal, etc. affect the water bursting and mud surging significantly. Special attention should be paid to these factors during the construction. Figure 13 shows that the excavation method, blasting method and advanced supporting influence the tunnel portal stability significantly. As a system risk control measure, the rock slop reinforcement quality and portal sunrrounding rock supporting paramaters must satisfy the design documents (Yang et al. 2006, Pine & Roberds 2005). From Figure 14, we can find that excavation method, blasting method,

35

36

II III IV

[BQ]=255

Middle risk, acceptable High risk, unwanted Extremely high risk, unacceptable

Depth:154~350m, rock: blastopsammite, less integrity,[BQ]=370

Fault effect area

Figure 10. Diagram of critical risks rating along the tunnel alignment.

Portal Collapse Water bursting Deformation

[BQ]=230

Shuikou Fault

Depth:170m,,[BQ]=340

Fault effect area,fragmentized

Depth:101~176m,,blastopsammite,,[BQ]=360

ACKNOWLEDGEMENTS The authors wish to acknowledge the support of National Natural Science Foundation of China (No.40772179) and Western Science & Technology Project of Ministry of Transport of China (No.2006318799107). REFERENCES Ahmad, I. & Minkarah, I. 1988. Questionnaire survey on bidding in construction. Journal of Management in Engineering 3(4): 229–243. Akintoye, A. & MacLeod, M. 1997. Risk analysis and management in construction. International Journal of Project Management 15(1): 31–38. APM Group. 1997. Project risk analysis and management. http://www.eurolog.co.uk/apmrisksig/publications/ minipram.pdf. Bao, H.L. & Huang, H.W. 2008. Risk assessment for the safe grade of deep excavation. In Ng C.W.W. et al. (eds), Geotechnical Aspects of Underground Construction in Soft Ground: 507–512. London: Taylaor & Francis. Carr, V. & Tah, J. 2001. A fuzzy approach to construction project risk assessment and analysis construction project risk management system. Advances in Engineering Software 32: 847–857. Chapman, C. 1997. Project risk analysis and managementPRAM the generic process. International Journal of Project Management 15(5): 273–281. Chapman, R.J. 2001. The controlling influences on effective risk identification and assessment for construction design management. International Journal of Project Management 19: 147–160. Eskesen, S.D. et al. 2004. Guidelines for tunnelling risk management: InternationalTunnellingAssociation, Working Group No. 2. Tunnelling and Underground Space Technology 19(3): 217–237. Floricel, S. & Miller, R. 2001. Strategizing for anticipated risks and turbulence in large scale engineering projects. International Journal of Project Management 19: 445–455. Huang, H.W. et al. 2006. Risk analysis of building structure due to shield tunneling in urban area. In Zhu H.H. et al. (eds), Underground construction and ground movement; Proc. of sessions of Geoshanghai, Shanghai, 2–4 June 2006. New York:ASCE. Lyons, T. & Skitmore, M. 2004. Project risk management in the Queensland engineering construction industry: a survey. International Journal of Project Management 22: 51–61. MOHURD. 2007. Guideline of Risk Management for Construction of Subway and Underground Works. Beijing: China Architecture & Building. MTPRC. 2004. Code for design of road tunnel. Chinese Standard: JTG D70-2004: 62–65. Pine, R.J. & Roberds, W.J. 2005. A risk-based approach for the design of rock slopes subject to multiple failure modes—illustrated by a case study in Hong Kong. International Journal of Rock Mechanics & Mining Sciences 42: 261–275. Roger, F. & George, N. 1993. Risk Management and Construction. London: Blackwell science Ltd. The International Tunnelling Insurance Group (ITIG). 2006. A code of practice for risk management of tunnel works.

Figure 11. Diagram of influence factors to tunnel collapse risk.

Figure 12. Diagram of influence factors to water bursting and mud surging.

Figure 13. Diagram of influence factors to tunnel portal slope failure.

Figure 14. Diagram of influence factors to tunnel large deformation.

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http://www.munichre.com/publications/tunnel_code_of_ practice_en.pdf Wideman, R.M. 1986. Risk management. Project Management Journal 17(4): 20–26. Yang, Z.F. et al. 2006. Research on the Geo-hazards of Sichuan-Tibet Road and its Prevent and Control. Beijng: Science Press of China.

Yao, C.P. & Huang, H.W. 2008. Risk assessment on environmental impact in Xizang Road tunnel. In Ng C.W.W. et al. (eds), Geotechnical Aspects of Underground Construction in Soft Ground:601–606. London: Taylaor & Francis. Zayed T. et al. 2008. Assessing risk and uncertainty inherent in Chinese highway projects using AHP. International Journal of Project Management 26: 408–419.

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Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Recent revision of Japanese Technical Standard for Port and Harbor Facilities based on a performance based design concept T. Nagao National Institute for Land and Infrastructure Management, Yokosuka, Japan

Y. Watabe & Y. Kikuchi Port & Airport Research Institute, Yokosuka, Japan

Y. Honjo Gifu University, Gifu, Japan

ABSTRACT: The purpose of this paper is to introduce the revision of the Technical Standards for Port and Harbor Facilities (TSPHF) which was recently revised in April 2007. It is thought that the TSPHF is one of the first cases of a revision of a design code based on a performance based design/specification concept. First, the reason why a performance based design concept was introduced to the TSPHF is explained. Then, the philosophy of providing a performance concept is explained. The standard verification procedure in the TSPHF guidelines is explained using an example. The policy for determining the geotechnical parameters used for the performance based design concept is introduced. Finally, the adequateness surveillance system introduced is explained. This kind of organization is inevitably required for the new design system in order to achieve higher levels of transparency and fairness.

1

2

INTRODUCTION

The Japanese government published the first guidelines for port and harbor facilities in 1930. These were something like a collection of design case histories. Engineers at that time designed port facilities by themselves with the aid of such design examples. In 1967, the Port and Harbor Bureau published the Standards for Port and Harbour Facility Design. These standards were the basis of the standards for approximately 40 years. However, at that time, such standards had no concrete legal background. In 1973, the Port and Harbor Law was revised to provide a legal background for these standards. In 1979, standards and commentaries were revised to suit the law. The Port and Harbour Bureau then revised them twice during the period up until 1999. In these revisions, the concept of the standards was the same as those in 1967. In 2007, new technical standards were presented. The concept of these standards was different from the former standards. These standards were formulated in order to coincide with the WTO/TBT agreement. This paper presents the features of the new Japanese Technical Standard for Port and Harbor Facilities (TSPHF).

JAPANESE GOVERNMENT POLICY ON TECHNICAL STANDARDS AND ACCREDITATIONS

Since 1995 (the year in which the WTO/TBT agreement came into effect.), the Japanese government has adopted a policy of deregulation with regard to a variety of laws and rules related to economic activities and trade. In March 1998, the Three-Year Program for Promoting Deregulation was determined as a result of a cabinet decision, and the following tasks were delineated: 1 All economic regulations should be eliminated in principle, and social regulations should be minimized. 2 Rationalization of regulation methods. For example, testing can be outsourced to the private sector. 3 Simplification and clarification of the contents of the regulations. 4 International harmonization of the regulations. 5 Speeding up of regulation related procedures. 6 Transparency in regulation related procedures. Following the above plan, the Three-Year Plan for the Promotion of Regulatory Reform was determined

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Table 1.

Revision of Port and Harbor Law.

Article 56 Item 2-2 (Before revision) Those port and harbor facilities, such as navigation channels and basins, protective facilities for harbors, and mooring facilities, should comply with the law that specifies such matters if such a law exists. In addition, their construction, improvement and maintenance should comply with the Technical Standards for Port and Harbor Facilities that have been specified as a ministerial ordinance by the Ministry of Land, Infrastructure and Transportation. (After revision) Those port and harbor facilities, such as navigation channels and basins, protective facilities for harbors, and mooring facilities (termed facilities covered by the TSPHF), should comply with the law that specifies such matters if such a law exists. In addition, construction, improvement and maintenance concerning the performance of facilities covered by the TSPHF should comply with the Technical Standards for Port and Harbor Facilities that have been specified as a ministerial ordinance by the Ministry of Land, Infrastructure and Transportation.

parliament, which made a proclamation in September 2006, and was implemented on 1 April 2007. The item that influenced the revision of the standards, Article 56 Item 2-2, is shown in Table 1. In the revision, rather than prescribing the specifications of design details, the performances of facilities are regulated. Based on the revised Port and Harbor Law, the TSPHF was fully revised. The main points of the revision summarized here are from two aspects, namely, the system for the performance based specifications, and the performance verification. Previously established comprehensive design codes (MLT, 2002; JSCE, 2003; JGS, 2004) provided foundations for the revision of these technical standards.

as a result of a cabinet decision in March, 2001. This plan consisted of the objectives shown below: 1 Realization of sustainable economic development through the promotion of economic activities. 2 Realization of a transparent, fair and reliable economic society. 3 Secure diversified alternative lifestyles. 4 Realization of an economic society that is open to the world. In order to realize such objectives, the promotion of essential and active deregulations in various administrative services was planned. In the field of standards and accreditations, the following basic policies were implemented.

3.1 Performance based specifications system

– Essential reviews of standards and accreditations in order to check the necessity of the involvement of the government. – In cases where administrative involvement was still required, administrative roles should be minimized, and self-accreditation or self-maintenance of standards and accreditations by the private sector should be promoted. – The international harmonization of standards, performance based specifications and the elimination of multiple examination procedures in accreditation processes should be promoted.

The basic system for the TSPHF is that the required performances of the structures are given as mandatory items in three levels, i.e. objectives, performance requirements and performance criteria, whereas the performance verification methods are not mandatory but are given in the annex or in the reference documents as some of the possible methods (Figure 1). The objectives state the necessity of the structures, whereas the performance requirements state the functions of the structures that need to be implemented in the structures in order to satisfy the objectives in plain language from the view point of accountability. The performance criteria restate the performance requirements from technical view points, thus making each performance requirement verifiable. The performance requirements are classified into basic requirements and other requirements (Table 2), where the former specifies structural performances against various actions and their combinations, and the latter specifies structural dimensional requirements arising from usage and conveniences. The basic requirements are further classified into serviceability, reparability and safety requirements as defined in Table 2. The basic requirements should be combined with the actions considered in the design, which are summarized in Table 3. The combinations of performance requirements and actions are termed design situations, where performance verification of the structure should be carry out for each design situation. The actions are classified into accidental and

The third item had a very strong impact on the revision of design standards and codes for civil structures. The Ministry of Land, Infrastructure and Transportation (MLIT) started a program entitled the Restructuring of Public Works Costs in March, 2003, and which includes the tasks shown below: – Revision of common specifications for civil works. – Review of the Highway Bridge Specifications. – Revision of the Technical Standards for Port and Harbor Facilities (TSPHF) to performance based. The revision of the TSPHF was started around this time with the goal of achieving harmonization between the standards and the international agreement. 3

REVISION OF THE TSPHF

Based on the background explained in the previous section, the Port and Harbor Law was revised in

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Figure 1. Performance based specifications for the TSPHF. Table 2.

Performance requirements in the TSPHF.

Classification

Definition

Basic requirement

Performance of structural response (deformation, stress, etc.) against actions. The function of the facility would be recovered with minor repairs. The function of the facility would be recovered in a relatively short period of time after some repairs. Significant damage would take place. However, the damage would not cause any loss of life or serious economic damage to the hinterland. Performance requirements for structural dimensions concerning usage and convenience of the facilities.

Serviceability Reparability Safety

Other requirements

Table 3.

Figure 2. Classifications of performances, actions and frequency.

The objectives and the performance requirements are prescribed in the MLIT ministerial ordinance part of the TSPHF, whereas the performance criteria are specified in the MLIT declaration part of the TSPHF that defines the details of the TSPHF. In this way, the hierarchy of the performance specifications is maintained. Table 4 shows an example of the provisions in the new TSPHF. This example is for a protective facility. A breakwater is a representative protective facility. Figure 3 shows the cross section of a caisson-type breakwater. Table 5 shows the provisions for breakwaters in the former TSPHF. In the new TSPHF, objectives, performance requirements, and performance criteria are written clearly in accordance with the hierarchy shown in Figure 1. However, these were not clearly described in the former TSPHF. With regard to verification, this was mandatory in the former TSPHF, but is not mandatory in the new TSPHF. As performance verification in accordance with TSPHF is Approach B verification shown in Figure 1, the recommended verification method is presented in the guidelines, but is not mandatory.

Summary of the basic requirements.

Design situation Persistent Situation Transient Situation Accidental Situation

Definition Permanent actions (self weight, earth pressures) are major actions. Variable actions (waves, level 1 earthquakes) are major actions. Accidental actions (tsunamis, level 2 earthquakes) are major actions.

Performance Requirements Serviceability Serviceability – Serviceability – Reparability – Safety

permanent/variable actions employing an annual occurrence rate of approximately 0.01 (i.e. a return period of 100 years) as a threshold value. For both permanent and transient design situations, serviceability needs to be satisfied, whereas in accidental situations, either of the three performance requirements needs to be satisfied depending on the importance and functions of the structure under design. This concept is further illustrated in Figure 2. It should be noticed that the performance of a structure may not be verifiable in accidental situations in some cases.

3.2

Performance verifications

In order to harmonize the TSPHF with international standards such as ISO2394 and introduce newly developed verification methods using more sophisticated design calculation methods such as seismic response

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Table 4.

Example of provisions in the new TSPHF. Mandatory situation

Level

Definition

Objectives

The reason why the facility is needed

Mandatory (Port and Harbor Law)

Performance requirements

Levels of performance facilities are required to possess

Mandatory (Port and Harbor Law)

Performance criteria

Concrete criteria which represent performance requirements

Mandatory (Notification)

Performance verification

Performances should be verified using engineering procedures

Not Mandatory (Guidelines are presented as references)

Example for breakwaters The calmness of navigation channels and basins should be maintained in order to safely navigate and moor ships, to handle cargo smoothly, and to safely maintain buildings and other facilities located in ports. Law Article 14 Damages due to the actions of self weights, waves, and level 1 earthquakes should not affect the objectives of the breakwater and its continuous usage. Law Article 14 -Serviceability requirements-Notification Article 351st Danger of the possibility of sliding failures of the ground under persistent situations in which the main action is self weight should be lower than the limit level. 2nd Danger of the possibility of sliding and rotation failures of gravity structures and of failures of the ground due to insufficient bearing capacity under variable situations in which the main actions are waves or level 1 earthquakes should be lower than the limit level. (Guidelines present the standard procedure for performance verifications for reference purposes)

tolerable limit values for the design in order for the users of the revised TSPHF to understand the intentions of the code writers. For this purpose, it is judged appropriate to provide the information in the form of an annex and supporting documents. Figure 4 shows the verification procedures for the sliding safety of a caisson type breakwater shown in the former and new TSPHF guidelines. For the design of a breakwater in a persistent situation where the major action is waves, it is recommended to employ RBD based on force equilibrium. Level I RBD is adopted, and recommended partial factors are provided in tables in the annex. In the case of a caisson-type breakwater on a rubble embankment, serviceability is required for a wave force with a 50 year return period (a variable action), and partial factors are provided which are determined based on the annual failure probability of 0.01 or below for sliding, overturning and bearing capacity failure.

Figure 3. Typical caisson type breakwater.

analyses, the following verification methods are introduced in the revised TSPHF (Table 6): – Reliability based design (RBD) methods, mainly level I partial factor approach. – Numerical methods (NM) capable of evaluating structural response properties. – Model tests. – Method based on past experiences.

3.3 Geotechnical parameters The soil parameters of the ground and the quality parameters of industrial products are completely different in terms of their treatments. Statistical treatments suitable for geotechnical parameters are strongly required in consideration of non-uniform sedimentary structures, investigation errors, testing errors, and limited numbers of data entries, etc. In the new TSPHF, a simplified and reasonable method, which pursues practical usability by simplifying statistical treatments, to determine soil characteristic values was introduced. Details have been published by Watabe et al. (2009a; 2009b). The method is briefly introduced in the following sections.

The performance verification implies design procedures to verify for the structures in order to satisfy the specified performance requirements and/or the performance criteria. In principal, the revised TSHPF does not specify any concrete allowable values for strength nor displacement. In order to perform the tolerable failure probability, safety indices and characteristic values for basic variables in the design are introduced. These are all decided by designers. However, it is considered necessary to provide standard verification methods together with the minimum

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Table 5.

Example of provisions in the former TSPHF.

Objectives and performance requirements

Contents

Provisions in former TSPHF

Function

Protective facilities for harbors should maintain their functions under all natural situations such as geographical, meteorological, and marine phenomena, etc. (Law Article 7) Protective facilities should be safe against self weight, water pressure, wave forces, earth pressure, an earthquake forces, etc. (Law Article 7) The wave force acting on a structure shall be determined using appropriate hydraulic model experiments or design methods in the following procedure. (Notification Article 5) Examinations of the safety of the members of reinforced concrete structures shall be conducted as standard using the limit state design method. (Notification Article 34) Examinations of the stability of upright sections of gravity type breakwaters shall be based on the design procedures using the safety factors against failures. (Notification Article 48)

Safety Performance verifications (also described in notifications)

Calculation of forces Safety verification of members Stability check

of the general design code, in which the characteristic value is generally the expected value of the derived values.

Table 6. Summary of basic performance verification methods. Design situation

Major actions

Recommended performance verification procedures

3.3.1 Principle of soil parameter determination JGS4001: Principles for foundation design grounded in the performance-based design concept were published in 2004 by the Japanese Geotechnical Society. These are guidelines for determining soil parameters for performance-based reliability design in Japan. Figure 5 shows the flowchart in the TSPHF for determining soil parameters used for performance verifications. This flowchart was modified for the new TSPHF, but reflects the purpose of JGS4001. The measured value is the value directly recorded in a field or laboratory test. The derived value is the value obtained by using the relationship between the measured value and the soil parameter. The characteristic value is the representative value obtained by modeling the depth profile of the data by taking into account the variation of the estimated values. The value must correspond to the critical state for the performance considered in the design. Taking account of the application range of either the verification equation or the prediction equation, the characteristic value is converted into the design value by multiplying with an appropriate partial safety factor. The partial safety factors for each facility are listed in the design code corresponding to both the variation and sensitivity of the soil parameter in the design verification. The characteristic value of the geotechnical parameters in Eurocode7 is also defined following the same concept as JGS4001. In the case of industry products, the characteristic value is generally defined as 5% fractile corresponding to Equation 1, e.g. in Eurocode0 (EN 1990, 2002).

Persistent and Self weight, RBD transient earth and water situations pressures, live loads, waves, wind, ships, etc. Level 1 Non-linear response earthquakes analyses taking into consideration soil structure interactions RBD Pseudo-static procedures (e.g. seismic coefficient method) Accidental Level 1 Numerical procedure to situations earthquakes, evaluate displacements tsunamis, ship and damage extents collisions, etc.

For example, it is well known that undrained shear strengths obtained through unconfined compression tests are more variable than those obtained as a result of triaxial tests, indicating that the reliability of the former is much smaller than that of the latter (Tsuchida, 2000; Watabe and Tsuchida, 2001). In each design procedure, however, it is difficult to take account of data variations which are dependent on testing methods. Consequently, the method in the new TSPHF has adopted a concept in which the characteristic value is corrected in correspondence with the reliability of the testing method. This concept aims to use the partial safety factor, which is independent of the testing method. Therefore, the concept in the case of a large number of data entries is slightly different from that

where µ(x) is the average of x, and σ(x) is the standard deviation of parameter x. This kind of characteristic

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Figure 4. Example of the verification of persistent and transient situations for caisson-type breakwaters.

Ovesen (1995) proposed a simple equation expressed as Equation (2) in order to obtain the lower limit of the 95% confidence level.

where n is the number of data entries. Schneider (1997) proposed a more simplified equation for n = 11.

When n is larger than 12, Schneider’s equation gives a more conservative value than Ovesen’s equation. The new TSPHF adopted a more practical method, which uses the outline of both Schneider’s and Ovesen’s equations and is partly consistent with JGS4001, in order to determine the characteristic value. Because an engineer who performs geotechnical investigations and an engineer who performs facility design are usually different engineers, the engineer who performs facility design cannot determine an appropriate partial safety factor taking into account data variations for soil parameters in association with the investigation and testing methods. In addition, it is virtually impossible to determine each partial safety factor taking into account data variations derived from the heterogeneity of the ground itself reflecting the soil locality. Therefore, it is ideal that the reliability of the soil parameters is always guaranteed to remain at the same level when the geotechnical information is transmitted from the geotechnical engineer to the facility

Figure 5. Flowchart for the determination of soil parameters in TSPHF.

value is applicable to structural materials; however, it is not applicable to soil parameters because they vary significantly. If we consider ground failure, for example, we have to treat the whole ground failure, not the failure in each element. From this background, Eurocode7 adopted the value corresponding to the 95% confidence level instead of the 5% fractile (Orr, 2006). In JGS4001, the characteristic value is described in the same manner as Eurocode7, but the confidence level is not fixed at 95%.

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Table 7. Values for correction factor b1 .

design engineer. Consequently, the partial safety factor as a general value listed in the design code can be used.

Correction factor b1

3.3.2 Characteristic value determination with correction factors In the new TSPHF guidelines, the partial safety factor γ is determined from the empirical calibration taking into consideration the data variation. Because the data variation is a given condition in most cases, any efforts, e.g. examinations designed to obtain the most appropriate depth profile, adopting a reliable laboratory testing method, brushing up skills for site investigations and laboratory testing, designed to decrease the data variation are not rewarded. Consequently, we prefer to use conventional investigation methods. The new TSPHF guidelines aim to solve these kinds of issues. In JGS4001, because the confidence interval range narrows with increases in the numbers of data entries, the characteristic value is coincident with the mean value when the number of data entries becomes large. In the new TSPHF guidelines, because the characteristic value is determined according to the data variation, efforts to reduce the data variation are rewarded in the design. Because the derived value is influenced by the sampling method, laboratory testing method, sounding method, and empirical/theoretical equation, etc., the design values must reflect these influences. For example, it has been well known that the reliability of the undrained shear strength obtained using the unconfined compression test is much lower than that obtained using the recompression triaxial test. However, it is very difficult to take account of this fact in design. The method in the new TSPHF guidelines adopted the concept in which the characteristic value is corrected according to the reliability level of the testing method. The coefficient of variation (COV) is introduced to represent the data variation. To reflect the data reliability in the characteristic value, the estimated value is corrected according to the COV. Consequently, we can establish a design code with a common partial safety factor by using the characteristic value determined using this method, even though the derived value of the soil parameter has been obtained from a different soil test. A larger number of data entries is more desirable in order to reduce the COV. However, 10 data entries are sufficient in practice, because the number of data entries is generally very limited. In fact, in most cases the COV converges on a certain value when the number of data entries is more than 10. It is known that the COV for derived values obtained by highly skilled technicians is less than 0.1 (Watabe et al., 2007). In other words, the variation at this level is inevitable due to ground heterogeneity and laboratory testing errors. Ground heterogeneity, sample disturbances, inappropriate soil tests, and inappropriate modeling of depth profiles, etc., result in large COV values. In such cases, it is reasonable to conservatively

Coefficient of variation COV

Parameter for safe side

Parameter for unsafe side

COV < 0.1 0.1 < COV < 0.15 0.15 < COV < 0.25 0.25 < COV < 0.4 0.4 < COV < 0.6 0.6 < COV

1.00 1.00 0.95 1.05 0.90 1.10 0.85 1.15 0.75 1.25 Reexamination of the data/ Reexamination of the soil test

determine characteristic values by taking uncertainties into account. In order to calculate the characteristic value ak from the estimated value a∗ , the correction factor b1 is introduced as a function of the COV, then ak is defined as Equation (4).

When the soil parameter a contributes to either the resistance moment in the safety verification (e.g. the shear strength in the stability analysis) or the safety margin in the prediction (e.g. the consolidation yield stress pc ; the coefficient of consolidation cv in the consolidation calculation), the correction factor is defined as Equation (5).

On the other hand, when it contributes to either the sliding moment in the safety verification (e.g. the unit weight of the earth fill in the stability analysis) or the unsafe factor in the prediction (the compression index Cc ; coefficient of volumetric compression mv in the consolidation calculation), the correction factor is defined as Equation (6).

In these definitions, the characteristic values correspond to either 30% or 70% of the fractile value. Because the aim of this method is simplification, the values listed in Table 7 are to be used instead of the correction factors with detailed fractions. When the COV is larger than 0.6, it is judged that the reliability of the soil parameter is too low for the design. In this case, the test results are reexamined; i.e. the depth profile is remodeled if necessary. In some cases, the ground investigation may be performed again. In JGS4001 or Eurocode7, the characteristic value is defined as the upper/lower boundary of a certain confidence level (95% in most cases) as mentioned above. The new TSPHF guidelines using a simplified

45

method without real statistical treatment are partly consistent with JGS4001. The characteristic value is defined as 30% or 70% of fractile values which correspond to a 95% confidence level when the number of data entries n is 10 and the data variation COV is 0.1. If the number of data entries is not sufficient for statistical treatment, another correction factor b2 is introduced to correct b1 . Then, the characteristic value is expressed as Equation (7).

Approximately 10 or more data entries in the depth profile can be thought to be sufficient to reliably calculate COV. In cases with less than 10 data entries, when the soil parameter contributes to either resistance moment in the stability verification or safety margin in the prediction, the correction factor is defined as Equation (8).

Figure 6. Design verification surveillance system.

to the TSPHF. On the other hand, for verification results obtained using Approach B, it is necessary to certify that the verification results are evaluated adequately. Technical standards or verification procedures in public construction works in Japan are authorized by operating bodies such as railways, roads, or ports. In the existing system, evaluations of design results are performed by such operating bodies. This system seems to be less transparent or fairness viewing from outside of concerned group. In order to avoid this problem, a third party for certifying design verification results is required. This surveillance organization is required to satisfy the items required for an adequateness evaluation organization provided by ISO/IEC guide #65. When a design verification surveillance organization issues a certification for the adequateness of a design, it is responsible for conducting a survey designed to show that the design results are free from faults. It is also required to prepare a discharge of liability for any damages arising from a misevaluation. To perform this certification, the TSPHF has a rule that design results for important facilities will be checked by a governmental institution or a third party institution which is authorized by the government (Figure 6).

On the other hand, when it contributes to either the sliding moment in the stability verification or the unsafe factor in the prediction, the correction factor is defined as Equation (9).

Here, b2 for cases with only one data entry is set at 0.5 or 1.5, and the reliability is assumed to rapidly increase with the number of data entries. In this regard, however, the correction factor b1 cannot be obtained in the case of n = 1, because the COV cannot be calculated. This indicates that more than two data entries are required in this method. In the new TSPHF guidelines, the correction factor b2 is introduced when the number of data entries is less than 10. However, this number can be varied by each design guideline. Note here that b1 = 1 and b2 = 1 are used for soil parameters that contribute equivalently to both action and counteraction.

4 3.4

Institution for surveillance of adequateness to the TSPHF

CONCLUSION

The purpose of this paper is to introduce the revision of the Technical Standards for Port and Harbor Facilities (TSPHF) which was recently revised in April 2007. It is thought that the TSPHF is one of the first cases of a revision of a design code based on a performance based design/specification concept. First, the reason why a performance based design concept was introduced to the TSPHF is explained in this paper. Then, the philosophy of providing a performance concept is explained. The standard verification procedure in the TSPHF guidelines is explained using an example consisting of the sliding failure of a caisson type breakwater. The policy for determining the geotechnical parameters used for the performance based design concept

The new TSPHF admits designs which are not completely verified by the guidelines. There are two procedures for design verification. One procedure is to use Approach A in Fig. 1, which is a verification approach with designer’s original consideration certificating the satisfaction of the requirement of performance criteria provided in TSPHF. The other procedure is to use Approach B, which is a verification approach in accordance with recommended procedures in the guidelines. Even in Approach B, designers can make their own decisions in the verification procedures. For verification results using Approach A, it is necessary to certify that the verification results conform

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Orr, T.L.L. (2006): Development and implementation of Eurocode 7, Proceedings of the International Symposium on New Generation Design Codes for Geotechnical Engineering Practice – Taipei 2006, CDROM, 1–18. Ovesen, N.K. (1995): Eurocode 7 for geotechnical design, Proceedings Bengt B. Broms Symposium on Geotechnical Engineering, Singapore, 333–360. Schneider, H.R. (1997): Definition and determination of characteristic soil properties, Proceedings 12th International Conference on Soil Mechanics and Geotechnical Engineering, Hamburg, Vol. 4, 2271–2274. The Japan Port and Harbour Association (2007): Technical standards, and commentaries for port and harbour facilities. (in Japanese) Tsuchida, T. (2000): Evaluation of undrained shear strength of soft clay with consideration of sample quality, Soils and Foundations, 40 (3), 29–42. Watabe, Y. and Tsuchida, T. (2001): Comparative study on undrained shear strength of Osaka Bay Pleistocene clay determined by several kinds of laboratory tests, Soils and Foundations, 41 (5), 47–59. Watabe, Y., Shiraishi, Y., Murakami, T. and Tanaka, M. (2007): Variability of physical and consolidation test results for relatively uniform clay samples retrieved from Osaka Bay, Soils and Foundations, 47 (4), 701–716. Watabe, Y., Tanaka, M. and Kikuchi, Y. (2009a): Soil parameters in the new design code for port facilities in Japan, Proceedings of the International Foundation Congress & Equipment Expo’09: IFCEE’09. (in print) Watabe, Y., Tanaka, M. and Kikuchi, Y. (2009b): Practical determination method for soil parameters adopted in the new performance based design code for port facilities in Japan, Soils and Foundations. (in print)

is introduced. The TSPHF guidelines introduce a simplified determination method allowing for ease of use for the practitioner, and with this determination procedure innovative geotechnical investigation methods and laboratory testing methods can be easily introduced. Finally, the adequateness surveillance system introduced is explained. This kind of organization is inevitably required for the new design system in order to achieve higher levels of transparency and fairness. Engineers in the field are experiencing a certain degree of confusion with regard to application of the new TSPHF. Misunderstandings of the concept is one of the reasons for this confusion, with the result that the introduction of a brand new concept is inevitable. As code writers we also intend to work hard to improve the design code. REFERENCES EN 1990: 2002: Eurocode 0, Basis of structural design. EN 1997-1: 2004: Eurocode 7, Geotechnical design –Part 1: General rules. JGS (2004), JGS-4001-2004: Principles for Foundation Designs Grounded on a Performance-based Design Concept (nickname ‘Geocode 21’). JSCE (2003), Principles, Guidelines and Terminologies for drafting design codes founded on performance based design concept (nickname ‘code PLATFORM ver.1’), Japan Society of Civil Engineers. MLIT (2002); Basis for design of civil and building structures, Ministry of Land, Infrastructure and Transportation.

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Special lecture

Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Interaction between Eurocode 7 – Geotechnical design and Eurocode 8 – Design for earthquake resistance of geotechnical structures P.S. Sêco e Pinto Faculty of Engineering, University of Coimbra, National Laboratory of Civil Engineering (LNEC), Lisbon, Portugal

1

INTRODUCTION

country to choose the safety level defined in each National Document of Application. The global safety of factor was substituted by the partial safety factors applied to actions and to the strength of materials. This invited lecture summarises the main topics covered by Eurocode 7 and the interplay with Eurocode 8 and also identify some topics that need further implementation. In dealing with these topics we should never forget the memorable lines of Lao- Tsze, Maxin 64 (550 B.C.):

The Commission of the European Communities (CEC) initiated a work in 1975 of establishing a set of harmonised technical rules for the structural and geotechnical design of buildings and civil engineers works based on article 95 of the Treaty. In a first stage would serve as alternative to the national rules applied in the various Member States and in a final stage will replace them. From 1975 to 1989 the Commission with the help of a Steering Committee with the Representatives of Member States developed the Eurocodes programme. The Commission, the Member states of the EU and EFTA decided in 1989 based on an agreement between the Commission and CEN to transfer the preparation and the publication of the Eurocodes to CEN. The Structural Eurocode programme comprises the following standards: EN 1990 Eurocode – Basis of design EN 1991 Eurocode 1 – Actions on structures EN 1992 Eurocode 2 – Design of concrete structures EN 1993 Eurocode 3 – Design of steel structures EN 1994 Eurocode 4 – Design of composite steel and concrete structures EN 1995 Eurocode 5 – Design of timber structures EN 1996 Eurocode 6 – Design of masonry structures EN 1997 Eurocode 7 – Geotechnical design EN 1998 Eurocode 8 – Design of structures for earthquake resistance EN 1999 Eurocode 9 – Design of aluminium alloy structures The work performed by the Commission of the European Communities (CEC) in preparing the “Structural Eurocodes” in order to establish a set of harmonised technical rules is impressive. Nevertheless, due the preparation of these documents by several experts, some provisions of EC8 with the special requirements for seismic geotechnical design that deserve more consideration will be presented in order to clarify several questions that still remain without answer. The actual tendency is to prepare unified codes for different regions but keeping the freedom for each

“The journey of a thousand miles begins with one step”.

2 2.1

EUROCODE 7 – GEOTECHNICAL DESIGN Introduction

The Eurocode 7 (EC7) “Geotechnical Design” gives a general basis for the geotechnical aspects of the design of buildings and civil engineering works. The link between the design requirements in Part 1 and the results of laboratory tests and field investigations run according to standards, codes and other accepted documents is covered by Part 2” EN 1997 is concerned with the requirements for strength, stability, serviceability and durability of structures. Other requirements, e.g. concerning thermal or sound insulation, are not considered.

2.2

EUROCODE 7 – Geotechnical Design – Part 1

The following subjects are dealt with in EN 1997-1 Geotechnical design: Section 1: General Section 2: Basis of Geotechnical Design Section 3: Geotechnical Data Section 4: Supervision of Construction, Monitoring and Maintenance Section 5: Fill, Dewatering, Ground Improvement and Reinforcement Section 6: Spread Foundations Section 7: Pile Foundations Section 8: Anchorages

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Where relevant, it shall be verified that the following limit states are not exceeded:

Section 9: Retaining Structures Section 10: Hydraulic failure Section 11: Overall stability Section 12: Embankments

– Loss of equilibrium of the structure or the ground, considered as a rigid body, in which the strengths of structural materials and the ground are insignificant in providing resistance (EQU); – Internal failure or excessive deformation of the structure or structural elements, including footings, piles, basement walls, etc., in which the strength of structural materials is significant in providing resistance (STR); – Failure or excessive deformation of the ground, in which the strength of soil or rock is significant in providing resistance (GEO); – Loss of equilibrium of the structure or the ground due to uplift by water pressure (buoyancy) or other vertical actions (UPL); – Hydraulic heave, internal erosion and piping in the ground caused by hydraulic gradients (HYD).

2.2.1 Design requirements The following factors shall be considered when determining the geotechnical design requirements: – Site conditions with respect to overall stability and ground movements; – Nature and size of the structure and its elements, including any special requirements such as the design life; – Conditions with regard to its surroundings (neighbouring structures, traffic, utilities, vegetation, hazardous chemicals, etc.); – Ground conditions; – Groundwater conditions; – Regional seismicity; – Influence of the environment (hydrology, surface water, subsidence, seasonal changes of temperature and moisture).

The selection of characteristic values for geotechnical parameters shall be based on derived values resulting from laboratory and field tests, complemented by well-established experience. The characteristic value of a geotechnical parameter shall be selected as a cautious estimate of the value affecting the occurrence of the limit state. For limit state types STR and GEO in persistent and transient situations, three Design Approaches are outlined. They differ in the way they distribute partial factors between actions, the effects of actions, material properties and resistances. In part, this is due to differing approaches to the way in which allowance is made for uncertainties in modeling the effects of actions and resistances. In Design Approach 1 partial factors are applied to actions, rather than to the effects of actions and ground parameters, In Design Approach 2 approach, partial factors are applied to actions or to the effects of actions and to ground resistances. In Design Approach 3 partial factors are applied to actions or the effects of actions from the structure and to ground strength parameters. It shall be verified that a limit state of rupture or excessive deformation will not occur. It shall be verified serviceability limit states in the ground or in a structural section, element or connection.

Each geotechnical design situation shall be verified that no relevant limit state is exceeded. Limit states can occur either in the ground or in the structure or by combined failure in the structure and the ground. Limit states should be verified by one or a combination of the following methods: design by calculation, design by prescriptive measures, design by loads tests and experimental models and observational method. To establish geotechnical design requirements, three Geotechnical Categories, 1, 2 and 3 are introduced. Geotechnical Category 1 includes small and relatively simple structures. Geotechnical Category 2 includes conventional types of structure and foundation with no exceptional risk or difficult soil or loading conditions. Geotechnical Category 3 includes: (i) very large or unusual structures; (ii) structures involving abnormal risks, or unusual or exceptionally difficult ground or loading conditions; and (iii) structures in highly seismic areas. 2.2.2 Geotechnical Design by calculation Design by calculation involves: – Actions, which may be either imposed loads or imposed displacements, for example from ground movements; – Properties of soils, rocks and other materials; – Geometrical data; – Limiting values of deformations, crack widths, vibrations etc. – Calculation models.

2.2.3 Design by prescriptive measures In design situations where calculation models are not available or not necessary, the exceedance of limit states may be avoided by the use of prescriptive measures. These involve conventional and generally conservative rules in the design, and attention to specification and control of materials, workmanship, protection and maintenance procedures.

The calculation model may consist of: (i) an analytical model; (ii) a semi-empirical model; (iii) or a numerical model.

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– The type of samples (category, etc) to be taken including specifications on the number and depth at which they are to be taken, – Specifications on the ground water measurement, – The types of equipment to be used, – The standards that are to be applied.

2.2.4 Design by load tests and experimental models When the results of load tests or tests on large or small scale models are used to justify a design, the following features shall be considered and allowed for: – Differences in the ground conditions between the test and the actual construction; – Time effects, especially if the duration of the test is much less than the duration of loading of the actual construction; – Scale effects, especially if small models are used. The effect of stress levels shall be considered, together with the effects of particle size.

The laboratory test programme depends in part on whether comparable experience exists. The extent and quality of comparable experience for the specific soil or rock should be established. The results of field observations on neighbouring structures, when available, should also be used. The tests shall be run on specimens representative of the relevant strata. Classification tests shall be used to check whether the samples and test specimens are representative. This can be checked in an iterative way. In a first step classification tests and strength index tests are performed on as many samples as possible to determine the variability of the index properties of a stratum. In a second step the representativeness of strength and compressibility tests can be checked by comparing the results of the classification and strength index tests of the tested sample with entire results of the classification and strength index tests of the stratum. The flow chart shown below demonstrates the link between design and field and laboratory tests. The design part is covered by EN 1997-1; the parameter values part is covered by EN 1997-2.

Tests may be carried out on a sample of the actual construction or on full scale or smaller scale models. 2.2.5 Observational method When prediction of geotechnical behaviour is difficult, it can be appropriate to apply the approach known as “the observational method”, in which the design is reviewed during construction. The following requirements shall be met before construction is started: – The limits of behaviour which are acceptable shall be established; – The range of possible behaviour shall be assessed and it shall be shown that there is an acceptable probability that the actual behaviour will be within the acceptable limits; – A plan of monitoring shall be devised which will reveal whether the actual behaviour lies within the acceptable limits. The monitoring shall make this clear at a sufficiently early stage and with sufficiently short intervals to allow contingency actions to be undertaken successfully; – The response time of the instruments and the procedures for analysing the results shall be sufficiently rapid in relation to the possible evolution of the system; – A plan of contingency actions shall be devised which may be adopted if the monitoring reveals behaviour outside acceptable limits. 2.3

3

EUROCODE 8 – DESIGN OF STRUCTURES FOR EARTHQUAKE RESISTANCE

3.1

Introduction

The Eurocode 8 (EC8) “Design of Structures for Earthquake Resistant” deals with the design and construction of buildings and civil engineering works in seismic regions is divided in six Parts. The Part 1 is divided in 10 sections: Section 1 – contains general information; Section 2 – contains the basis requirements and compliance criteria applicable to buildings and civil engineering works in seismic regions; Section 3 – gives the rules for the representation of seismic actions and their combination with other actions; Section 4 – contains general design rules relevant specifically to buildings; Section 5 – presents specific rules for concrete buildings; Section 6 – gives specific rules for steel buildings; Section 7 – contains specific rules for steel-concrete composite buildings; Section 8 – presents specific rules for timber buildings; Section 9 – gives specific rules for masonry buildings; Section 10 – contains fundamental requirements and other relevant aspects for the design and safety related to base isolation.

EUROCODE 7 – Part 2

EN 1997-2 is intended to be used in conjunction with EN 1997-1 and provides rules supplementary to EN 1997-1 related to the: – Planning and reporting of ground investigations, – General requirements for a number of commonly used laboratory and field tests, – Interpretation and evaluation of test results, – Derivation of values of geotechnical parameters and coefficients. The field investigation programme shall contain: – A plan with the locations of the investigation points including the types of investigations, – The depth of the investigations,

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Further Parts include the following: Part 2 contains relevant provisions to bridges. Part 3 presents provisions for the seismic strengthening and repair of existing buildings. Part 4 gives specific provisions relevant to tanks, silos and pipelines. Part 5 contains specific provisions relevant to foundations, retaining structures and geotechnical aspects. Part 6 presents specific provisions relevant to towers, masts and chimneys. In particular the Part 5 of EC8 establishes the requirements, criteria, and rules for siting and foundation soil and complements the rules of Eurocode 7, which do not cover the special requirements of seismic design. The topics covered by Part 1 – Section 1 namely: seismic action, ground conditions and soil investigations, importance categories, importance factors and geotechnical categories and also the topics treated in Part 5 slope stability, potentially liquefiable soils, earth retaining structures, foundation system, topographic aspects are discussed. 3.2

Figure 1. Elastic response spectrum (after EC8).

In EC 8, in general, the hazard is described in terms of a single parameter, i.e. the value ag of the effective peak ground acceleration in rock or firm soil called “design ground acceleration” (Figure 1) expressed in terms of: a) the reference seismic action associated with a probability of exceeding (PNCR ) of 10% in 50 years; or b) a reference return period (TNCR ) = 475. These recommended values may be changed by the National Annex of each country (e.g. in UBC (1997) the annual probability of exceedance is 2% in 50 years, or an annual probability of 1/2475).

Seismic action

The definition of the actions (with the exception of seismic actions) and their combinations is treated in Eurocode 1 “Action on Structures”. Nevertheless the definition of some terms in EN 1998-1 further clarification of terminology is important to avoid common misunderstandings and shortcomings in seismic hazard analysis as stressed by Abrahamson (2000). In general the national territories are divided by the National Authorities into seismic zones, depending on the local hazard.

where: Se (T) elastic response spectrum, T vibration period of a linear single-degree-offreedom system, αg design ground acceleration, TB , TC limits of the constant spectral acceleration branch, TD value defining the beginning of the constant displacement response range of the spectrum,

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S soil parameter with reference value 1.0 for subsoil class A, η damping correction factor with reference value 1.0 for 5% viscous damping.

Table 1. Values of the parameters describing the Type 1 elastic response spectrum*. Ground type

S

TB (s)

TC (s)

TD (s)

The earthquake motion in EC 8 is represented by the elastic response spectrum defined by 3 components. It is recommended the use of two types of spectra: type 1 if the earthquake has a surface wave magnitude Ms greater than 5.5 and type 2 in other cases. The seismic motion may also be represented by ground acceleration time-histories and related quantities (velocity and displacement). Artificial accelerograms shall match the elastic response spectrum. The number of the accelerograms to be used shall give a stable statistical measure (mean and variance) and a minimum of 3 accelerograms should be used and also some others requirements should be satisfied. For the computation of permanent ground deformations the use of accelerograms recorded on soil sites in real earthquakes or simulated accelerograms is allowed provided that the samples used are adequately qualified with regard to the seismogenic features of the sources. For structures with special characteristics spatial models of the seismic action shall be used based on the principles of the elastic response spectra.

A B C D E

1.0 1.2 1.15 1.35 1.4

0.15 0.15 0.20 0.20 0.15

0.4 0.5 0.6 0.8 0.5

2.0 2.0 2.0 2.0 2.0

3.3

Table 2. Values of the parameters describing the Type 2 elastic response spectrum*. Ground type

S

TB (s)

TC (s)

TD (s)

A B C D E

1.0 1.35 1.5 1.8 1.6

0.05 0.05 0.10 0.10 0.05

0.25 0.25 0.25 0.30 0.25

1.2 1.2 1.2 1.2 1.2

Subsoil S 2 – deposits of liquefiable soils, of sensitive clays, or any other soil profile not included in types A–E or S1 . For the five ground types the recommended values for the parameters S, TB , TC , TD , for Type 1 and Type 2 are given in Tables 1 and 2. The recommended Type 1 and Type 2 elastic response spectra for ground types A to E are shown in Figures 2 and 3. The recommended values of the parameters for the five ground types A, B, C, D and E for the vertical spectra are shown in Table 3. These values are not applied for ground types S1 and S2. The influence of local conditions on site amplification proposed by Seed and Idriss (1982) is shown in Figure 4. The initial response spectra proposed in the pre-standard EC8 based in Seed and Idriss proposal was underestimating the design levels of soft soil sites in contradiction with the observations of the last recorded earthquakes. Based on records of earthquakes Idriss (1990) has shown that peak accelerations on soft soils have been observed to be larger than on rock sites (Figure 5). The high quality records from very recent earthquakes Northridge (1994), Hyogo-ken-Nambu (1995), Kocaeli (1999), Chi-Chi (1999) and Tottoriken (2000) have confirmed the Idriss (1990) proposal. Based on strong motions records obtained during Hyogoken-Nanbu earthquake in four vertical arrays sites and using and inverse analysis Kokusho and Matsumuto (1997) have plotted in Figure 6 the maximum horizontal acceleration ratio against maximum base acceleration and proposed the regression equation:

Ground conditions and soil investigations

For the ground conditions five subsoil classes A, B, C, D and E are considered: Subsoil classA – rock or other geological formation, including at most 5 m of weaker material at the surface characterised by a shear wave velocity Vs of at least 800 m/s; Subsoil class B – deposits of very dense sand, gravel or very stiff clay, at least several tens of m in thickness, characterised by a gradual increase of mechanics properties with depth shear wave velocity between 360–800 m/s, NSPT > 50 blows and cu > 250 kPa. Subsoil class C – deep deposits of dense or medium dense sand, gravel or stiff clays with thickness from several tens to many hundreds of meters characterised by a shear wave velocity from 160 m/s to 360 m/s, NSPT from 15–50 blows and cu from 70 to 250 kPa. Subsoil class D – deposits to loose to medium cohesionless soil (with or without some soft cohesive layers), or of predominantly soft to firm cohesive soil characterised by a shear wave velocity less than 180 m/s, NSPT less than 15 and cu less than 70 kPa. Subsoil class E – a soil profile consisting of a surface alluvium layer with Vs, 30 values of type C or D and thickness varying between about 5 m and 20 m, underlain by stiffer material with Vs, 30 > 800 m/s. Subsoil S 1 – deposits consisting – or containing a layer at least 10 m thick – of soft clays/silts with high plasticity index (PI > 40) and high water content characterised by a shear wave velocity less than 100 m/s and cu between 10–20 kPa.

This trend with a base in a Pleistocene soil is similar to the Idriss (1990) proposal where the base was in rock.

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ground classification of EC8 follows a classification based on shear wave velocity, on SPT values and on undrained shear strength, similar to UBC (1997) that is shown in Table 4. Based on the available strong-motion database on equivalent linear and fully nonlinear analyses of response to varying levels and characteristics of excitation Seed et al. (1997) have proposed for site depending seismic response the Figures 7 and 8, where A0 , A and AB are hard to soft rocks, B are deep or medium depth cohesionless or cohesive soils, C, D soft soils and E soft soils, high plasticity soils. Comments: The following comments are pointed: (i) as seismic cone tests have shown good potentialities they should also be recommended; (ii) the EC 8 (Part 5) stress the need for the definition of the variation of shear modulus and damping with strain level, but doesn’t refer to the use of laboratory tests such as cyclic simple shear test, cyclic triaxial test and cyclic torsional test. It is important to stress that a detailed description of laboratory tests for the static characterisation of soils is given in EC 7 Part 2 and the same criteria is not adopted in EC 8 – Part 5.

Figure 2. Recommended Type 1 elastic response spectrum (after EC8).

3.4 Importance categories, importance factors and geotechnical categories The structures following EC 8 (Part 1.2) are classified in 4 importance categories related with its size, value and importance for the public safety and on the possibility of human losses in case of a collapse. To each importance category an important factor γI is assigned. The important factor γI = 1,0 is associated with a design seismic event having a reference return period of [475] years. The importance categories varying I to IV (with the decreasing of the importance and complexity of the structures) are related with the importance factor γI assuming the values [1,4], [1,2], [1,0] and [0,8], respectively. To establish geotechnical design requirements three Geotechnical Categories 1, 2 and 3 were introduced in EC 7 with the highest category related with unusual structures involving abnormal risks, or unusual or exceptionally difficult ground or loading conditions and structures in highly seismic areas. Also it is important to refer that buildings of importance categories [I, II, III] shall generally not be erected in the immediate vicinity of tectonic faults recognised as seismically active in official documents issued by competent national authorities. Absence of movement in late Quaternary should be used to identify non active faults for most structures. It seems that this restriction is not only very difficult to follow for structures such as bridges, tunnels and embankments but conservative due the difficult to identify with reability the surface outbreak of a fault. Anastapoulos and Gazetas (2006) have proposed a methodology to design structures against major fault ruptures validated through successful Class A predictions of centrifuge model tests and have recommended some changes to EC8 – Part 5.

Figure 3. Recommended Type 2 elastic response spectrum (after EC8). Table 3. Recommended values of the parameters for the five ground types A, B, C, D and E. Spectrum

αvg /αg

TB (s)

TC (s)

TD (s)

Type 1 Type 2

0.9 0.45

0.05 0.05

0.15 0.15

1.0 1.0

The downhole arrays are useful: (i) to understand the seismic ground response; and (ii) to calibrate our experimental and mathematical models. Following the comments proposed by Southern Member States the actual recommended elastic response spectrum of EC8 incorporates the lessons learnt by recent earthquakes. The soil investigations shall follow the same criteria adopted in non-seismic areas, as defined in EC 7 (Parts 1, 2 and 3). The soil classification proposed in the pre-standard of EC8, based only on the 3 ground materials and classified by the wave velocities was simpler. The actual

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Figure 4. Influence of local soil conditions on site response (after Seed and Idriss, 1982).

Figure 5. Influence of local soil conditions on site response (after Idriss, 1990).

valleys as well as of deeper geologic structures in determining site response was shown from the analysis of records in Northridge and Kobe earthquakes.

Comments: The following comments are presented: (i) no reference is made for the influence of strong motion data with the near fault factor (confined to distances of less than 10 km from the fault rupture surface) with the increases of the seismic design requirements to be included in building codes; (ii) also no reference is established between the ground motion and the type of the fault such as reverse faulting, strike slip faulting and normal faulting; (iii) EC8 refers to the spatial variation of ground motion but does not present any guidance; (iv) basin edge and other 2D and 3D effects were not incorporated in EC8. The importance of shapes of the boundaries of sedimentary

3.5

Potentially liquefiable soils

Following 4.1.3.(2) – Part5 – EC8 “An evaluation of the liquefaction susceptibility shall be made when the foundations soils include extended layers or thick lenses of loose sand, with or without silt/clay fines, beneath the water level, and when such level is close to the ground surface”.

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Figure 6. Maximum horizontal acceleration ratio plotted against maximum base acceleration (after Kokusho and Matsumoto, 1997). Table 4.

Ground profile types (after UBC, 1997).

Ground profile type

Shear wave velocity Vs(m/s)

SPT test

Undrained shear strength (kPa)

1500 760–1500 360–760

– – >50

– – >100

180–360 1 means stable slope. 2) Strain. Failure is defined by onset of strains great enough to prevent safe operation of the slope, or that the rate of movement exceeds the rate of mining in an open pit. 3) Probability of failure. Stability is quantified by probability distribution of difference between resisting and displacing forces (Safety Margin), which are each expressed as probability distributions. 4) LRFD (load and resistance factor design). Stability is defined by the factored resistance being greater than or equal to the sum of the factored loads.

for the factor of safety (FS) have been investigated (De Mello 1988):

where P is the wedge weight; T is the anchor pull; β is the anchor and the slope inclination; α is the sliding surface inclination and φ is the internal friction angle. Such factor of safety values can be compared with some target values proposed by Terzaghi and Peck (1967) and by Canadian Geotechnical Society (1992) that for earthworks vary between 1.3 and 1.5. The upper value applies to usual loads and service conditions while the lower value applies to maximum loads and the worst expected geological conditions. Therefore, apart from the ambiguity in computing procedure, the factor of safety is affected by uncertainties and variability which cannot be avoided.

In order to investigate the stability of a rock slope wedge involved in sliding mechanism, the equilibrium method is usually employed and the factor of safety is computed. In the case studied the presence of an anchorage force has been considered (see Fig. 1). Here, according to Mohr-Coulomb failure criterion for the rock mass behaviour, two different expressions

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Table 1. Variable values for benchmark.

The study performed below focuses on reliability approach for computing the safety of the slope by accounting for random variables to describe rock resistance parameters.

Variable Sliding surface slope α [◦ ] Rock face slope β [◦ ] Friction angle φ [◦ ] Unit weight γ [kN/m3 ] Slope height H[m]

2 THE CASE STUDIED 2.1

Uncertainties in rock mass characterization

Strength of a rock mass is characterized by strength of intact rock and of discontinuities. Depending on number, orientation and condition of joints the rock mass behaviour is affected by anisotropy and weakness which can lead to the failure when slopes are concerned. Moreover human activity and weathering processes may contribute to increase failure prone conditions by means of increasing acting forces or reducing rock mass resistance. Besides, the first step in rock slope stability study is the mechanical characterization of rock mass by means of classification systems. Then, after a good analyses of discontinuities and their shear resistance the type of sliding movement can be forecast. In the proposed case study a rock slope sliding along sliding prone discontinuities is considered (see Fig. 1) where the slope is the rock face one of an open quarry reinforced by an anchorage. The friction angle of a joint in a rock mass, can be computed as Barton and Choubey (1977):

Mean value

Standard deviation value

40 7.5

4

Characteristic value 38

–

7.5

35

10.5

29.8

23

0.5

22.8

5 10 15

–

–

determined by means of structural investigations and consequently affected by human errors. Therefore, for α a normal probability distribution with a mean value of 40◦ is considered a coefficient of variation equal to 10%. 2.2 Factor of safety method The commonest approach to stability studies is based on the computation of the factor of safety. According to the equilibrium method and Mohr-Coulomb soil behaviour, the safety factor is computed by means of different expressions, namely Eq. (1) and (2): such two cases arise from different interpretation of the pull component along the sliding surface direction. As a matter of fact, it can be taken as a stabilizing force or as a negative contribution to the sliding weight component. The choice between the two approaches can be rationally undertaken considering a parametric deterministic and probabilistic study where anchorage pull and the height of the slope are varied. Table 1 shows values of variables used in such a benchmark. Three values for slope height have been investigated: 5, 10 and 15 m. According to anchor pull increasing the two factors of safety increase with a different trend as can be seen in Fig. 2. The expression Eq. (1), indicated as FS+ increases linearly although slope decreases when height increases. So that, the factor of safety is stronger affected by anchorage pull for smaller height of the slope. On the contrary, expression Eq. (2), reported as FS− , shows a parabolic trend with a rapid increase as anchor pull increases. Such a trend provides obviously negative values as the contribution of anchorage pull got higher than the weight component on the weak plane. Accordingly, FS− won’t be discussed further on.

where σn is the vertical effective stress acting on discontinuity wall; JRCn is the joint roughness coefficient for joint of actual length; JCSn is the joint wall compression strength for joint of actual length; φr is the residual friction angle that can be drawn experimentally and “i” is the roughness of discontinuity at large scale. JRCn and JCSn are calculated by Bandis et al.’s formulation (1981), that is:

where JCS0 and JRC0 are joint wall compression strength and joint roughness coefficient respectively computed for reference joint length L0 of 10cm; Ln is the actual joint length. JCS0 can be provided by reference tables whereas JRC0 can be drawn from Schmidt’ hammer test. As explained before, the evaluation of φ for a joint in a rock mass is affected by variability and uncertainty. Here, the friction angle probability distribution is modelled as lognormal with the coefficient of variation equal to 30, 40 and 50%. Nonetheless, the sliding plane inclination, named α, can be considered also as a random variable. It is

2.3 Reliability method As the FS− fails, only expression Eq. (1) can be considered for the safety factor. Then, it is worthy to compare

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Figure 3. Reliability index versus anchorage pull for CVφ = 30%.

Figure 2. Variation of safety factor (Eq. 1) with the anchor pull. Table 2.

Variable

Random variable distribution type. Distribution Variation type coefficient

Sliding surface Normal slope α [◦ ] Rock face Uniform slope β [◦ ] Friction angle Lognormal φ [◦ ] Unit weight Normal γ [kN/m3 ] Anchorage pull Constant T [kN] Slope height Constant H[m]

Min Max value value

10% –

5

10

30, 40, 50% 2% – Figure 4. Reliability index versus anchorage pull for CVφ = 40%.

–

Results from FORM and SORM techniques coincide, thus just FORM are reported in the following. At first, reliability index is reported versus the anchorage pull, as already done for the Factor of safety (Fig. 2). Then, reliability index is compared with the safety factor for the same anchorage pull values. Fig. 3 shows curved trends of reliability index versus anchorage pull. For the case of slope height equal to 5 m, as anchorage pull varies from 100 to 150 kPa the reliability index increases from 2 to 4 when the friction angle coefficient of variation CVφ is 30%. Such trend can be seen for other two height values but with a slope reduction as the height increases: this means that when height increases an higher anchorage pull increase is needed for stabilizing the slope as in the case of the factor of safety. Such evidence is true also when CVφ increases (Figs. 4–5). So that, when the variability of friction angle increases the safety level of the slope reduces and much higher anchorage pull increments are needed for improving stability condition. Accordingly, Figure 6 shows, for the slope height equal to 5 m the safety factor and the reliability index values corresponding to the same anchorage pull for the three CVφ values. Hence, when the reliability index varies between 2 and 4 the safety factor increases its values according to the CVφ . As a matter of fact, in order to get a reliability index equals to 2.5, the factor of safety should be increased from 1.8 to 2.2.

the safety factor with the reliability index computed by means of a random variable approach. Such a parameter is strictly related to the probability of failure. Many studies have been performed on the allowable values of the probability of failure of the engineering project accepted by people. In the case of slope stability values of reliability index about 2-4 are suggested by Baecher (1982). Accordingly, in this analysis such interval will be investigated. Table 1 summarizes mean and standard deviation values for random variables while Table 2 shows the assumption about probability distribution for such provided variables. As the unit weight γ is concerned, it is can be assumed as a random variable with a small variability, proved by literature (Cherubini 1997). In this case it is considered normally distributed with a coefficient of variation equal to 2%. In this benchmark FORM, SORM and Monte Carlo methods are performed in order to evaluate the reliability index by means of COMREL code (1997). In this case, the performance function considered is:

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2.4 LRFD method Finally, an interesting comparison is proposed between reliability index and the partial factor design method suggested by Eurocode 7 (1997) and by Italian Technical Building Code (TU 14/01/2008). The combination of factors suggested for the global stability analysis is named as Combination 2, where load factors (A2), resistance factor (M2) and global factor (R2) are considered as follows:

Figure 5. Reliability index versus anchorage pull for CVφ = 50%.

In Eq. (7), design variables values employed are characteristic values: such values are introduced by the Eurocode for limit state design but no suggestions are provided about the way to compute them. Characteristic values for reinforced concrete compression strength is commonly assumed as the value corresponding to the 95% probability to be exceeded. Assuming it is normally distributed we have:

where xm is the mean value and s is the standard deviation of the concrete compression strength. Such an assumption could be too much conservative in the case of geotechnical random variables. As a matter of fact, let’s consider the friction angle, with mean value equal to 35◦ and standard deviation equal to 10.5◦ ; its characteristic value is 14.4◦ , which is too much conservative value. Here the expression from Schneider (1997) reported also by Cherubini and Orr(1999) is used:

Figure 6. Factor of safety (Eq. 1) versus reliability index for CVφ = 30%, 40% and 50% and H = 5 m.

where CV is the coefficient of variation; xm is the random variable mean value. Three cases are then considered according to the CVφ variation. In this case, the friction angle characteristic value is 30◦ . Moreover, as Eq. (7) is concerned, building code requests that such difference is higher than zero although no minimum value suggests. Hence, Figs. 8–10 show the positive difference between resistance and action according to the expression Eq. (7) versus the anchorage pull values. The trend, for each slope height, is not linear and it shows a decrease of slope as height increases. The three values of CVφ do not affect the slopes of the trend while affect the magnitude of anchorage pull needed: when CVφ increases the anchorage pull must be increased in order to have the same positive difference between resistance and action. A meaningful correlation can be observed in Fig. 11 where reliability index is related to the positive difference between resistance and action for the same anchorage pull value. Each graph corresponds to different CVφ values for the case of 5 m slope height.

Figure 7. Reliability index computed by MCS versus anchorage pull for CVφ = 30, 40 e 50%: H = 5 m (continuous lines); H = 10 m (dotted lines); H = 15 m (dashed lines).

Therefore, the reference values 1.3–1.5 suggested for the factor of safety are definitively inadequate when φ variability is taken into account. As the other two slope height cases (H = 10 m and 15 m) are concerned they give the same results as coincident curves are provided. Results from MCS with an adaptive sampling scheme have been investigated: 30000 samples are needed for the case studied and reliability index values drawn are the same as FORM. Fig. 7 shows the same evolution of reliability index curves from MCS.

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Figure 11. Combination for sliding condition in LRFD versus reliability index for slope height H = 5 m and CVφ = 30%, 40% and 50%. Figure 8. Combination for sliding condition in LRFD versus anchorage pull for CVφ = 30%.

considered increases as friction angle variability increases. This means that, in such a case, simply considering: 1) resistance just higher than actions; 2) characteristic values and partial safety factors; it cannot give a constant reliability level. These changes are related both to anchorage pull values, slope height and variability. Hence, when variability of the friction angle is enlarged higher differences between resistance and loads are needed but these values vary according not only to CVφ but also to slope height variation. 3

CONCLUDING REMARKS

A benchmark has been proposed to investigate stability of an anchored rock slope according to three different methods: the factor of safety, the reliability index and the load and resistance partial factor. Results show that, when variability of those random variables which govern the limit equilibrium of a rock slope has taken into account:

Figure 9. Combination for sliding condition in LRFD versus anchorage pull for CVφ = 40%

1 it causes a safety reduction which depends on variability magnitude; 2 target values for safety factor shall be increased according to variability magnitude; 3 the difference between factorized resistance and load must be increased according to the variability magnitude and the height of the slope. REFERENCES Bandis, S.C., Lumdsden, A.C. & Barton, N. 1981. Experimental studies of scale effects on the shear behaviour of rock joints. Int. Journal of Rock Mech. Min. Sci. and Geoch. Absts. 18: 1–21. Baecher G.B. 1982. Simplified geotechnical data analysis. Reliability theory and its application in structural and soil engineering. Thoft-Christensen P. (ed.), Dordrecht: Reidal Publishing. Barton, N. & Choubey, V. 1977. The shear strength of rock joints in theory and practice. Rock mechanics 10(1): 1–54.

Figure 10. Combination for sliding condition in LRFD versus anchorage pull for CVφ = 50%.

From Fig. 11 the LRFD differences between 30 and 60kPa correspond to the reliability index varying between 2 and 4 for the case of CVφ = 30%. Such difference shall be the same for higher variability although the lower boundary of the range

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Canadian Geotechnical Society 1992. Canadian Foundation Engineering Manual. Vancouver, Canada: BiTech Publishers Ltd. Cherubini, C. 1997. Data and consideration on the variability of geotechnical properties of soils. In Proceedings of the ESREL’97 International Conference on Safety and Reliability, Lisbon: 1583–1591. Cherubini, C. & Orr, T.L.L. 1999. Considerations on the applicability of semiprobabilistic Bayesian methods to geotechnical design. In Atti del XX Convegno Nazionale di Geotecnica, Parma:421–426. COMREL 1997. Reliability Consulting Programs RCP GmbH, Munchen, Germany. De Mello, Victor F.B. 1988. Risks in geotechnical engineering: conceptual and practical suggestions. Geotechnical Engineering 19(2): 171–208.

Eurocodice 7, Progettazione geotecnica – Parte 1: Regole generali, UNI ENV 1997 – 1- Aprile 1997. Schneider, H.R. 1997. Definition and determination of characteristic soil properties contribution to discussion. In XIV ICSMFE, Hamburg: Balkema. Terzaghi, K. & Peck, R. 1967. Soil mechanics in Engineering Practice. New York: John Wiley and Sons. Testo Unitario 2008. D.M. Infrastrutture 14 gennaio 2008. Nuove Norme Tecniche per le Costruzioni. Ministero delle Infrastrutture, Ministero del’Interno, Dipartimento della Protezione Civile. Wyllie, Duncan C. & Mah, Christopher W. 2004. Rock slope engineering. London and New York: Spon Press.

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Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Reliability analysis of a benchmark problem for slope stability Y. Wang, Z.J. Cao, S.K. Au & Q. Wang Department of Building and Construction, City University of Hong Kong, Hong Kong, China

ABSTRACT: This paper presents a benchmark study for slope stability analysis using the Swedish Circle method in conjunction with general procedure of slices. The purpose is to illustrate implementation of spatial variability of soil properties (i.e., undrained shear strength Su ) in the analysis. The study reveals that different reliability analysis methods use different critical slip surfaces. The pitfalls of using different slip surfaces in different methods are discussed.

1

INTRODUCTION

Limited published studies/implementation examples are believed as one reason for geotechnical practitioners’ reluctance to apply reliability methods to slope stability analysis. In view of this aspect, this paper provides a benchmark example that illustrates implementation of reliability methods in slope stability analysis. The example focuses on spatial variability of soil properties and different critical slip surfaces used in different reliability analysis methods. After this short introduction, a simple slope stability example is described, together with the random variables and solution methods used in the example. Then, the analysis results are presented, and difference among the results from different solution methods are highlighted. Finally, the pitfalls of using different critical slip surfaces in different methods are discussed.

2 2.1

Figure 1. Slope stability example.

segment, and an angle αi between the base of the slice and the horizontal. The factor of safety is then given by

where the minimum is taken over all possible choices of slip circles, i.e., all possible choices of (x, y) and r. Note that li , Wi , and αi change as (x, y) and/or r change (i.e., geometry of the ith slice changes). In addition, the Wi is a function of the clay total unit weight γ. Therefore, for a given choice of (x, y) and r, FS only depends on Sui and γ. The performance function P of this slope stability problem can be expressed as

BENCHMARK EXAMPLE Description of the example

Figure 1 shows a clay slope with a height and slope angle of 5 m and 45◦ , respectively. Stability of the slope is assessed using the Swedish Circle method in conjunction with general procedure of slices (Duncan and Wright 2005). The factor of safety FS is defined as the critical (minimum) ratio of resisting moment to the overturning moment, and the slip surface is assumed to be a circular arc centered at coordinate (x, y) and with radius r. The overturning and resisting moments are summed about the center of the circle to calculate the factor of safety, as shown in Figure 1. For moment calculations the soil mass above the slip surface is subdivided into a number of vertical slices, each of which has a weight Wi , circular slip segment length li , undrained shear strength Sui along the slip

Note that the mathematical operation of “min” in Equations (1) and (2) makes the performance function implicit and non-differentiable. 2.2 Input variables This example considers the spatial variability of soil properties, and the soil between the upper ground

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Table 1. The values and distributions of the input variables. Variable Su γ ∗

Distribution Log-Normal (30 entries in the vector are iid.) Deterministic

Table 2.

Primary analysis results.

Solution method

β

Pf (%)

Relative error in Pf

FOSM FORM MCS with Slope/W MCS with Excel Subsim with Excel

4.74 3.89 4.34 2.95 3.04

1.1 × 10−4 5.1 × 10−3 7.0 × 10−4 1.6 × 10−1 1.2 × 10−1

−99.9% −96.8% −99.6% N/A −25.0%

Statistics Mean = 20 kPa Cov∗ = 20% 18 kN/m3

“Cov” stands for coefficient of variation.

surface and 15 m below is divided into 30 equal layers with a layer thickness of 0.5 m. A vector Su = [Su (1), Su (2), . . . , Su (30)]T is defined for the values of Su in these 30 layers. Then, Sui for the ith slice is average of the entries in Su that correspond to the depths of slip segment of the ith slice. All entries in Su are taken as independent and identically-distributed (i.e., iid) log-normal random variable with a mean and coefficient of variation (i.e., COV) of 20 kPa and 20%, respectively. The total unit weight of clay γ is taken as deterministic with a value of 18 kN/m3 . The values and distributions of these basic input variables are summarized in Table 1.

is developed for generating a random sample (realization) of the random variables Su . Starting with uniform random numbers provided by the built-in function ‘Rand()’ in Excel, transformation is performed to produce the random samples of desired distribution. Available VBA subroutines in Excel are used to facilitate the uncertainty modeling. From an input-output perspective, the uncertainty modeling worksheet takes no input but returns a random sample of Su as its output whenever a re-calculation is commanded. Then, the uncertainty model worksheets are ‘linked’ together with the deterministic slope stability analysis spreadsheet through their input/output cells to produce a probabilistic analysis model of the slope stability problem. The value of Su shown in the deterministic analysis worksheet is equal to that generated in the uncertainty modeling worksheet, and so the FS value calculated in the deterministic analysis worksheet is random. In other words at this stage one can perform a direct Monte Carlo simulation of the problem by repeatedly executing the built-in function ‘Rand()’ in Excel. In addition, a VBA code for Subset Simulation is developed that functions as an Add-In in Excel and can be called by selecting from the main menu ‘Tools’ followed by ‘SubSim’. A user form appears upon invoking of the function, and the Subset simulation can be performed accordingly. More details on the Excel spreadsheets and VBA functions/Add-In are referred to Au et al. (2009).

2.3 Solution methods For a given choice of (x, y) and r, FS is calculated by implementing Equation 1 in an Excel spreadsheet where each row represents a particular slice and each column represents the variables and terms in Equation 1. A VBA code has been written to calculate the ratio of resistant to overturning moment for different values of (x, y) and r and then pick the minimum value as the factor of safety. As a reference, the nominal value of FS that corresponds to the case where all Su values equal to their mean values of 20 kPa is equal to 1.25. For the critical slip surface, r = 15 m and (x, y) = (2.7 m, 8.8 m). The calculation results are found to be consistent with results from the commercial slope stability analysis software Slope/W (GEO-SLOPE International Ltd. 2008). Consequently, the Excel spreadsheet model is validated and used in the reliability analysis. The reliability methods employed in this study include the First-Order Second Moment (FOSM) with a given critical slip surface (Ang and Tang 1984, Tang et al. 1976, Wu 2008), First-Order Reliability Method (FORM) using the object-oriented constrained optimization tool in the Excel spreadsheet (Low and Tang 1997, Low 2003, Low and Tang 2007), direct Monte Carlo simulation (MCS) using commercial software Slope/W and the Excel spreadsheet, and Subset simulation using the Excel spreadsheet (Subsim) (Au and Beck 2001). The MCS in Slope/W uses the Swedish Circle method and general procedure of slices. Therefore, the performance function defined by Equation (2) is also applicable. To facilitate direct Monte Carlo simulation and Subset simulation using the Excel spreadsheet, a package of spreadsheets and VBA functions/Add-In are developed in Excel. An uncertainty model spreadsheet

2.4 Analysis results Table 2 summarizes the analysis results from different reliability methods. Totally 5,000,000 samples are taken in MCS with Slope/W, as the Pf obtained is extremely small. For MCS with Excel, the number of samples is 10,000. For Subsim with Excel, three levels of simulation are performed with 500 samples taken in each level. The second and third columns of Table 2 show the equivalent reliability index β = −1 (1 − Pf ) and its corresponding probability of failure Pf from FOSM, FORM, MCS with Slope/W, MCS with Excel and Subsim with Excel, respectively. The Pf from FOSM and MCS with Slope/W is on the order of magnitude of 10−4 %. In contrast, the Pf from MCS and Subsim with Excel is on the order of magnitude of 10−1 %, and the Pf from FORM falls between 10−4 % and 10−1 % (i.e., on the order of magnitude of 10−3 %). If the Pf from MCS with Excel is used as the reference

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for comparison, the relative error in Pf is about 100% for FOSM, FORM, and MCS with Slope/W. The Pf from Subsim with Excel is reasonably accurate with a significant increase of computational efficiency (i.e., decreasing number of samples needed). The substantial difference between the Pf from FOSM and MCS with Slope/W and that from MCS and Subsim with Excel might seem surprising at the first glance. Detailed examinations show that the difference can be attributed to different critical slip surfaces used in different reliability methods, which are discussed in the next section. Figure 2. Critical slip surface in Slope/W.

3

PITFALL OF CRITICAL SLIP SURFACE

3.1 FOSM with a given critical slip surface FOSM is based on the first order approximation and uses the first terms of a Taylor series expansion of performance function P. Therefore, the mean of FS is estimated by setting all Su values equal to their mean values of 20 kPa and searching for critical slip surface. The resulting mean of FS is 1.25, and the corresponding critical slip surface has a r = 15 m and (x, y) = (2.7 m, 8.8 m). For this given critical slip surface, the standard deviation of FS is estimated as 0.053. Note that, for the given critical slip surface, Equation 1 only involves linear operation (i.e., summation) of random variables Su , and high-order partial derivative of the Equation is zero. The solution from FOSM is therefore reasonably accurate if only one given critical slip surface is concerned. 3.2

Figure 3. Examples of critical slip surfaces obtained from MSC with Excel.

3.3 MCS with slope/W

Form

Table 2 shows that the Pf from MCS with Slope/W is on the same order of magnitude as that from FOSM. In Slope/W, the MCS only takes into consideration the variability of soil properties, and it uses a critical slip surface that is first determined based on the mean values of the random variables. Figure 2 shows the critical slip surface obtained in Slope/W using the mean values of Su . The critical slip surface in Slope/W is quite consistent with the one used in FOSM. As a result, it is not surprising to find that the Pf from FOSM and MCS with Slope/W agrees well with each other. However, as the variation of potential critical slip surfaces is not properly accounted for in either method, their results are biased.

A practical object-oriented constrained optimization approach proposed by Low (2003) is used in this work to calculate the Hasofer-Lind reliability index. The approach is implemented in an Excel spreadsheet and uses the built-in optimization tool “Solver” to obtain the minimum distance between the performance function and center of an expanding equivalent dispersion ellipsoid in the original space of the random variables as the reliability index. The searching for critical slip surface is accounted for in the approach by including (x, y) and r as additional optimization variables and adding a constraint for FS (i.e., FS = 1) in the optimization for the minimum distance. Variation of potential critical slip surfaces is implicitly factored in the analysis. Consequently, as shown in Table 2, the Pf from FORM is more than one order of magnitude larger than that from FOSM which only one given critical slip surface is used. On the other hand, when compared with the Pf from MCS with Excel which includes the variation of critical slip surface explicitly, FORM significantly underestimates the Pf . The poor performance of FORM might be attributed to the inadequate linear approximation of the failure criterion (i.e., Equation 1), particularly when the variation of potential critical slip surfaces is accounted for.

3.4

MCS and Subsim with Excel

MCS in Excel starts with generation of random samples (realizations) for the random variables Su . Then, for each random sample of Su , critical slip surface is searched, and the minimum FS is obtained accordingly. Figure 3 show examples of different critical slip surfaces obtained from different random samples of Su . It is obvious that the critical slip surface changes significantly as the spatial distribution of Su changes for different random samples. As a reference, the critical

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Table 3. Ranges of center coordinates and radius for critical slip surfaces obtained from MCS with Excel.

4

Parameter

Minimum

Maximum

Range

Coordinate x (m) Coordinate y (m) Radius r (m)

1.0 6.0 9.0

3.0 9.6 16.0

2.0 3.6 7.0

When spatial variability of soil properties is taken into consideration in reliability analysis of slope stability problem, variation of potential critical slip surfaces has a profound impact on the calculated Pf or β. Similar to FOSM with a given critical slip surface, MCS in Slope/W relies on a given critical slip surface obtained from deterministic analysis with mean values of soil properties, and hence, the impact of variation of critical slip surfaces is not accounted for in the analysis. Their results are therefore biased. The FORM approach considers implicitly the variation of potential critical slip surfaces. However, it significantly underestimates the Pf due to the inadequate linear approximation of the failure criterion (i.e., Equation 1), particularly when the variation of potential critical slip surfaces is accounted for. Therefore, the use of MCS or Subsim with explicit consideration of critical slip variation is recommended. Such consideration can be implemented in the analysis with relative ease, as illustrated in this paper.

Table 4. Comparison of simulation results with different critical slip surfaces. Relative error in Pf (%)

Solution method

β

Pf (%)

MCS with Slope/W and fixed critical slip MCS with Excel and fixed critical slip MCS with Excel and changing critical slip Subsim with Excel and fixed critical slip Subsim with Excel and changing critical slip

4.34 7.0 × 10−4

−99.6%

4.38 6.0 × 10−4

−99.6%

2.95 1.6 × 10−1

N/A

4.53 3.0 × 10−4

−99.8%

−1

−25.0%

3.04 1.2 × 10

5

RECOMMENDED RELIABILITY METHODS

CONCLUDING REMARKS

This paper presents a benchmark example for slope stability analysis using the Swedish Circle method in conjunction with general procedure of slices. Spatial variability of soil properties are taken into consideration in the reliability analysis, and the effect of variation of potential critical slip surfaces is highlighted. Several reliability methods are implemented to investigate their feasibility and efficiency. Similar to FOSM with a given critical slip surface, MCS in Slope/W does not account for the variation of potential critical slip surfaces and only uses a given critical slip surface obtained from deterministic analysis with mean values of soil properties. Their results are therefore biased. The variation of potential critical slip surfaces is implicitly considered in the FORM approach proposed by Low and his collaborators. However, it significantly underestimates the Pf due to the inadequate linear approximation of the failure criterion. MCS or Subsim with explicit consideration of variation of critical slip surfaces are implemented in an Excel spreadsheet environment. They are shown to provide reasonable results, and hence, their use is recommended at the expense of computation time/efforts.

slip surface #4 in Figure 3 is the one obtained from deterministic analysis with mean Su values and used in the FOSM and MCS in Slope/W. Table 3 summarizes ranges of (x, y) and r for critical slip surfaces obtained from MCS with Excel. The r varies from 9.0 m to 16.0 m and has a range of 7.0 m. When the variation of potential critical slip surfaces is considered explicitly in the simulation, the Pf from MCS with Excel is three order of magnitude larger than that from FOSM and MCS with Slope/W which use a given critical slip surface. To further illustrate the effect of variation of critical slip surfaces on the Pf , MCS is also performed in Excel using the critical slip surface #4 in Figure 3, which is obtained from deterministic analysis with mean Su values and used in the FOSM and MCS in Slope/W. As shown in Table 4, the resulting Pf is on the order of 10−4 % and agrees well with those from FOSM and Slope/W which uses the same/similar critical slip surface. The comparison summarized in Table 4 confirms that the substantial difference among Pf from different methods is mainly attributed to the variation of critical slip surfaces. Subsim is carried out in Excel with either a fixed critical slip surface (i.e., #4 in Figure 3) or searching for critical slip surfaces for different random samples of Su . As shown in Table 4, the results agree well with those from MCS with Excel. The Pf from Subsim is reasonably accurate with increasing computational efficiency (i.e., decreasing number of samples needed).

ACKNOWLEDGEMENTS The work described in this paper was supported by General Research Fund [Project No. 9041327 (CityU 110108)] and Competitive Earmarked Research Grant [Project No. 9041260 (CityU 121307)] from the Research Grants Council of the Hong Kong Special

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GEO-SLOPE International Ltd. 2008. Stability Modeling with Slope/W 2007 Version, GEO-SLOPE International Ltd, Calgary, Alberta, Canada. Low, B. K. 2003. Practical probabilistic slope stability analysis. Proceedings of Soil and Rock America, MIT, Cambridge, MA, June 2003, Verlag Gluckauf GmbH Essen, Germany, Vol. 2, 2777–2784. Low, B. K. and Tang, W. H. 1997. Efficient reliability evaluation using spreadsheet. Journal of Engineering Mechanics, 127(7): 149–152. Low, B. K. and Tang, W. H. 2007. Efficient spreadsheet algorithm for first-order reliability method. Journal of Engineering Mechanics, 133(2): 1378–1387. Tang, W. H., Yucemen, M. S., and Ang, A. H.-S. 1976. Probability-based short term design of soil slopes. Canadian Geotechnical Journal, 13: 201–215. Wu, T. H. 2008. Reliability analysis of slopes. ReliabilityBased Design in Geotechnical Engineering: Computations and Applications, Chapter 11: 413–447, Edited by Phoon, Taylor & Francis.

Administrative Region, China. The financial supports are gratefully acknowledged.

REFERENCES Ang, A. H.-S. and Tang, W. H. 1984. Probability Concepts in Engineering Planning and Design, Vol. II, Wiley, New York. Au, S. K., Wang, Y., and Cao, Z. J. 2009. Reliability analysis of slope stability by advanced simulation with spreadsheet. Proceeding of the 2nd International Symposium on Geotechnical Safety and Risk (IS-Gifu2009), June 2009, Gifu, Japan (submitted). Au, S. K., and Beck, J. L. 2001. Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics, 16(4): 263–277. Duncan, J. M. and Wright, S. G. 2005. Soil Strength and Slope Stability, John Wiley & Sons. Inc. New Jersey, 2005.

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Geotechnical code drafting based on limit state design and performance based design concepts

Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Developing LRFD design specifications for bridge shallow foundations S.G. Paikowsky Geotechnical Engg Research Lab, University of Massachusetts, Lowell, Massachusetts, USA & Geosciences Testing and Research Inc., N. Chelmsford, Massachusetts, USA

S. Amatya Geotechnical Engg Research Lab, University of Massachusetts, Lowell, Massachusetts, USA

K. Lesny & A. Kisse University of Duisburg-Essen, Essen, Germany

ABSTRACT: An ongoing project, supported by the National Cooperative Highway Research Program, NCHRP Project 24–31 is aimed to develop LRFD procedures and to modify the current AASHTO design specifications for Ultimate Limit State (ULS) design of bridge shallow foundations. The current study utilizes a comprehensive database of 549 cases of shallow foundation load tests under various loading conditions (i.e. vertical-centric, vertical-eccentric, inclined-centric and inclined-eccentric). In this paper, the procedure to establish the LRFD design adopted in the research study is introduced. The design methods used for ULS design of bridge shallow foundations are presented and the uncertainty in the estimation of the ultimate bearing capacity has been expressed in terms of a bias, defined as measured over calculated capacities. The biases in the estimation of the ultimate bearing capacity have been appraised based on the database. Typical bridge foundation loadings and their uncertainties are defined and utilized along with the resistance uncertainties to establish resistance factors. The investigations lead to the conclusion that one single resistance factor for the bearing capacity is not sufficient, as different loading conditions result in different levels of uncertainties. Hence, different resistance factors have been established based on the First Order Second Moment (FOSM) method, and the Monte Carlo simulations (MCS), each for the vertical-centric, vertical-eccentric, inclined-centric and inclined-eccentric loading conditions. The recommended preliminary resistance factors thus obtained in the study are presented. 1

INTRODUCTION

reliability. The challenges for the requirement of the second objective include overcoming generic difficulties applying the LRFD methodology to geotechnical applications, i.e. the evaluation of uncertainty in the geotechnical model incorporating e.g. indirect variability (site or soil parameters interpretation), load dependency of the geotechnical resistance (especially in the case of shallow foundations, where a strict separation between load and resistance is not possible), judgment (e.g. a previous experience), and other similar factors.

An ongoing project, NCHRP Project 24–31: LRFD design specifications for shallow foundations, is aimed at developing LRFD procedures and modifying the current AASHTO design specifications for the Ultimate Limit State (ULS) design of bridge shallow foundations. It is supported by the National Cooperative Highway Research Program (NCHRP) under the Transportation Research Board (TRB) of the National Academy of Science (NAS). The AASHTO specifications are traditionally observed as a National Code of the US highway practice on all federally aided projects, hence, they influence the construction of highway bridge and other structure foundations across the USA. The current AASHTO specifications as well as other existing codes based on Load and Resistance Factor Design (LRFD) principles were calibrated using a combination of reliability theory, fitting to ASD (allowable stress design) and engineering judgment. The main objectives of this project therefore are the compilation of a database of load tests on shallow foundations and the calibration of resistance factors based on the reliability analysis of the data to obtain more rational designs with consistent levels of

2 2.1

EVALUATION OF BEARING CAPACITY UNCERTAINTY Database

This research study utilizes a comprehensive database of load tests on shallow foundations, UML-GTR ShalFound07, for the evaluation of uncertainties in bearing capacity (BC) estimation. It contains 549 cases of load tests, mostly performed in Germany and the USA. It has been compiled from various publications noticeably using four major sources: (a) ShalDB Ver5.1 (Briaud & Gibbens 1997), (b) Lutenegger

97

Table 1.

Summary of UML-GTR ShalFound07 database. Predominant soil type

Foundation type Plate load tests B ≤ 1 m Small footings 1 1. However, this may not be possible if the underlying deterministic model is poor. This has been the case for current design methods for geosynthetic reinforced soil walls that use the tie-back wedge method (Miyata and Bathurst 2007, Bathurst et al. 2008). Fortunately, the prediction of load for steel-reinforced soil walls is reasonably accurate as demonstrated by Bathurst et al. (2008, 2009). The following equation can be used as a starting point to estimate the load factor, if load bias statistics are available:

where nσ is a constant. For a given value of nσ , the probability of exceeding any factored load is about the same. The greater the value of nσ , the lower the probability the measured load will exceed the predicted nominal load. A value of nσ = 2 for the strength limit state was used in the development of the Canadian Highway Bridge Design Code and AASHTO LRFD Bridge Design specifications (Nowak 1999, Nowak and Collins 2000). This value is used in the example computations to follow. Using load bias statistics reported in the previous section gives 1.87 as a starting point. Bathurst et al. (2008) reported values from 1.73 to 1.87 depending on various minor adjustments to the selection of load and resistance normal statistics. A value of 1.75 is selected here. A visual check on the reasonableness of the

Once the load factor is selected, the resistance factor can be estimated through iteration to produce the desired magnitude for β, using Equations 9 and 10 (as applicable), a design point method based on the Rackwitz-Fiessler procedure (Rackwitz and Fiessler 1978), or the more adaptable and rigorous Monte Carlo method demonstrated later. Here, the example described earlier in the paper is continued using Equation 10 rewritten as follows:

Using the normal statistics for best fit-to-tail, load factor γQ = 1.75 and a target reliability index value of β = 2.33 (probability of failure pf ∼ 1/100) gives a resistance factor of ϕ = 0.612. From a practical point of view, ϕ = 0.60 is convenient and sufficiently accurate. If the resistance data is parsed and restricted to the middle range of data points in Figure 3, then the computed resistance factor is 0.81 (Bathurst et al. 2008). Clearly judgment is required in any calibration effort of the type described here. 4.6 Trial and error approach using Monte Carlo simulation An alternative approach to select the resistance factor is to carry out a Monte Carlo simulation. It is

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computationally convenient to assume a nominal (mean) value of Tmax = 1 kN/m, then according to Equation 5, the nominal (mean) value for resistance must be equal to (γQ /ϕ) × 1 kN/m. The variation of Tmax values is lognormal and can be quantified using the normal statistics for load bias (µQ , COVQ ) and for the factored resistance values using (γQ /ϕ)µR and COVR computed from resistance bias values. Recall that normal statistics can be used to compute lognormal distributions with suitable accuracy. The factored limit state equation is now expressed as:

Random values of Ri and Qj can be computed using:

and

An advantage of Monte Carlo simulation is that normal and lognormal distributions can be used together. In fact, any fitted distribution function can be used to calculate random values of Ri and Qi in the example used here.

5

CONCLUSIONS

This paper has demonstrated some fundamental concepts for LSD calibration of geotechnical structures. An attempt has been made here to break through the obscure language that has traditionally been used in LSD practice. The paper has highlighted the need to carry out LSD calibration using model bias statistics in order to capture the accuracy of the underlying deterministic models on LSD load and resistance factors. Finally, the paper illustrates how simple Excel spreadsheets can be used to carry out calibration, treat data outliers and avoid hidden dependencies between variables.

REFERENCES

where, zi and zj are random values of the standard normal variable. Random pairs of Ri and Qj are then used to compute a set of g values. These values are then sorted in increasing order and a CDF plot constructed as shown in Figure 6. The calculations can be easily carried out using an Excel spreadsheet. Different values of γQ and ϕ can be tried until the value of the CDF plot intersects g = 0 at the target value of β although the general approach is to fix the load factor (which is often prescribed) and then adjust ϕ. In the example here, the numerical approach gives β = 2.35 which is very close to the target value of 2.33 used in the closed-form solution to compute ϕ = 0.60 assuming a resistance factor of 1.75. 5

standard normal variable, z

4 3 2 1 0 –1 –2

     

–3 –4 –5 –3 –2 –1 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

g (kN/m)

Figure 6. Monte Carlo simulation for the pullout limit state, using the AASHTO Simplified Method of design (steel grid walls only – lognormal distribution assumed for Tmax and Tpo , γQ = 1.75, and ϕR = 0.60, and 10,000 values of g generated).

AASHTO. 2007. LRFD Bridge Design Specifications, American Association of State Highway and Transportation Officials, Fourth Edition, Washington, D.C., USA. AASHTO. 2002. Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials, 17th Edition, Washington, D.C., USA, 686 p. Allen, T.M., Bathurst, R.J., Holtz, R.D., Lee, W.F. & Walters, D.L. 2004. A new working stress method for prediction of loads in steel reinforced soil walls, ASCE Journal of Geotechnical and Geoenvironmental Engineering, Vol. 130, No. 1, 1109–1120. Allen, T.M., Christopher, B.R., Elias, V. & DiMaggio, J. 2001. Development of the simplified method for internal stability of Mechanically Stabilized Earth (MSE) walls, Washington State Dept of Trans, Report WA-RD 513.1, 108 p. Allen, T.M., Nowak, A.S. & Bathurst, R.J. 2005. Calibration to Determine load and resistance factors for geotechnical and structural design, Transportation Research Board Circular E-C079, Washington, DC. Bathurst, R.J., Miyata, Y., Nernheim, A. & Allen, T.M. 2008. Refinement of K-Stiffness method for geosynthetic reinforced soil walls, Geosynthetics International, Vol. 15, No. 4, 269–295. Bathurst, R.J., Allen, T.M. & Nowak, A.S. 2008. Calibration concepts for load and resistance factor design (LRFD) of reinforced soil walls, Canadian Geotechnical Journal, Vol. 45, 1377–1392. Bathurst, R.J., Nernheim, A. & Allen, T.M. 2008. Comparison of measured and predicted loads using the Coherent Gravity Method for steel soil walls, Ground Improvement, Vol. 161, No. 3, 113–120. Bathurst, R.J., Nernheim, A., Miyata, Y. & Allen, T.M. 2009. Predicted loads in steel reinforced soil walls using the AASHTO Simplified Method, ASCE Journal of Geotechnical and Geoenvironmental Engineering, Vol. 135, No. 2, 177–184. Bathurst, R.J., Miyata, Y., Nernheim, A. & Allen, T.M. 2008. Refinement of K-Stiffness method for geosynthetic

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reinforced soil walls, Geosynthetics International, Vol. 15, No. 4, 269–295. Becker, D.E. 1996. Eighteenth Canadian Geotechnical Colloquium: Limit states design for foundations. Part I. An overview of the foundation design process, Canadian Geotechnical Journal, Vol. 33, 956–983. CFEM. 2006. Canadian Foundation Engineering Manual (4th Ed). Richmond, BC, Canada. CSA. 2006. Canadian Highway Bridge Design Code (CHBDC), CSA Standard S6-06, Canadian Standards Association, Toronto, Ontario, Canada. Christopher, B.R., Gill, S.A., Giroud, J.-P., Juran, I., Mitchell, J.K., Schlosser, F. & Dunnicliff, J. 1989. Reinforced soil structures, Vol. II Summary of research and systems information, FHWA Report FHWA-RD-89-043, 158 pp. D’Appolonia. 1999. Developing new AASHTO LRFD specifications for retaining walls, Report for NCHRP Project 20-7, Task 88, Transportation Research Board, Washington, DC., USA 63 p. Eurocode 7, 1995, ENV 1997-1 Eurocode 7, Geotechnical design, Part 1: General rules (with the UK National Application Document), British Standards Institution, London. Geoguide 6, 2002, Guide to reinforced fill structure and slope design, Geotechnical Engineering Office, Hong Kong, China. Miyata,Y. & Bathurst, R.J. 2007. Development of K-stiffness method for geosynthetic reinforced soil walls constructed with c-φ soils, Canadian Geotechnical Journal, Vol. 44, No. 12, 1391–1416.

Nowak,A.S. 1999. Calibration of LRFD Bridge Design Code, NCHRP Report 368, Transportation Research Board, Washington, DC, USA. Nowak, A.S. & Collins, K.R. 2000, Reliability of Structures, McGraw Hill, New York, NY. NRC, 2005. National Building Code. NRC of Canada, Ottawa, Ontario, Canada. Paikowsky, S.G., Birgisson, B., McVay, M., Nguyen, T., Kuo, C., Baecher, G., Ayyub, B., Stenersen, K., O’Malley, K., Chernauskas, L. & O’Neill, M. 2004, Load and resistance factor design (LRFD) for deep foundations, NCHRP Report 507, Transportation Research Board of the National Academies, Washington, D.C., 126 p. Phoon, K-K. & Kulhawy, F.H. 2003. Evaluation of model uncertainties for reliability-based foundation design. Applications of Statistics and Probability in Civil Engineering (Der Kiureghian, Madanat and Pestana (eds). Millpress, Rotterdam, Netherlands. Rackwitz, R. & Fiessler, B. 1978. Structural reliability under combined random load sequences, Computers and Structures, Vol. 9, 484–494. RTA 2003, Design of Reinforced Soil Walls, QA Specification R57, Roads and Traffic Authority of New South Wales, Australia. Withiam, J.L., Voytko, E.P., Barker, R.M., Duncan, J.M., Kelly, B.C., Musser, S.C. & Elias, V. 1998, Load and Resistance Factor Design (LRFD) for Highway Bridge Substructures, FHWA HI-98-032, Federal Highway Administration, Washington, DC, USA.

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Loss of static equilibrium of a structure – Definition and verification of limit state EQU B. Schuppener Federal Waterways Engineering and Research Institute, Karlsruhe, Germany

B. Simpson Arup Geotechnics, London, UK

T.L.L. Orr Trinity College, Dublin University, Ireland

R. Frank Université Paris-Est, Ecole nationale des ponts et chaussées, Navier-CERMES, Paris, France

A.J. Bond Geocentrix, Banstead, Surrey, UK

ABSTRACT: In order to satisfy the essential requirements for construction works, the Eurocodes require that structures fulfil the design criteria for both serviceability and ultimate limit states. Three ultimate limit states are of particular importance in geotechnical design: loss of static equilibrium (EQU), failure or excessive deformation of the structure (STR), and failure or excessive deformation of the ground (GEO). This paper is concerned with EQU. The problems relating to the use of GEO in geotechnical design are described in this paper and alternative views are presented. The authors have sought, by means of a number of illustrative examples, to examine these problems and clarify issues relating to the application of EQU.

1

2

INTRODUCTION

In order to satisfy the essential requirements for construction works, the Eurocodes require that structures fulfil the design criteria for both serviceability and ultimate limit states (SLSs and ULSs). It is a principle of the Eurocodes that “ultimate limit states shall be verified as relevant”. Three ultimate limit states are of particular importance in geotechnical design: loss of static equilibrium (EQU), failure or excessive deformation of the structure (STR), and failure or excessive deformation of the ground (GEO). This paper is concerned with EQU, which the authors have debated at length how to apply in geotechnical design, encountering problems which are also relevant to structural design. Particular difficulties arise when the stability required by EQU has to be augmented by structural or ground resistance. The problems relating to the use of GEO in geotechnical design are described in this paper and alternative views are presented. The authors have sought, by means of a number of illustrative examples, to examine these problems and clarify issues relating to the application of EQU.

DEFINITIONS

Ultimate limit states STR and GEO are described in Eurocode Basis of design (EN 1990) and Eurocode 7 Geotechnical design Part 1 General rules (EN 1997-1) by the following definitions: STR: Internal failure or excessive deformation of the structure or structural members, including footings, piles, basement walls, etc., where the strength of construction materials of the structure governs [EN 1990] (or) …where the strength of structural materials is significant in providing resistance [EN 1997-1]. GEO: Failure or excessive deformation of the ground, in which the strength of soil or rock is significant in providing resistance. In the verification of both STR and GEO, it must be shown that in every section, member and connection, the design value Ed of the effect of actions (such as internal force, moment or a vector representing several internal forces or moments) does not exceed the design value Rd of the corresponding resistance of the structure or the ground:

111

Inserting partial factors, this may be expanded to:

where: Frep is the representative value of an action, derived from individual characteristic actions taking account of combination of variable actions (in the case of variable actions Q, Frep = Qrep = ψ·Qk where ψ is a factor for converting the characteristic value to the representative value; in the case of permanent actions, Frep = Grep = Gk ) Xk is the characteristic value of a ground property anom is the nominal value of geometrical data (i.e. dimension) γE and γF are partial factors for effects of actions and actions, respectively γM and γR are partial factors for ground properties and ground resistance, respectively a is a safety margin or tolerance (Note: all γ values are usually ≥ 1 and a is typically zero.) Limit state EQU is described in EN 1990 and EN 1997-1 by two slightly different definitions: EN 1997-1, 2.4.7.1(1)P gives: “Loss of equilibrium of the structure or the ground, considered as a rigid body, in which the strengths of structural materials and the ground are insignificant in providing resistance” EN 1990, 6.4.1(1)P gives: “Loss of static equilibrium of the structure or any part of it considered as a rigid body, where: •

minor variations in the value or the spatial distribution of actions from a single source are significant, and • the strengths of construction materials or ground are generally not governing.” The concept of a ‘single source’ is important: EN 1990 notes (see Note 3 in Table A.1.2 (B) of Annex A.1): “For example, all actions originating from the self weight of the structure may be considered as coming from one source; this also applies if different materials are involved.” As the definitions state that the strength of the materials or the ground either plays no part in the verification or is not governing, the expression for EQU is different from Equation (1). For equilibrium, it must be verified that the design value Ed,dst of the effect of destabilising actions does not exceed the design value Ed,stb of the effect of stabilising actions:

where: Frep,dst and Frep,stb are representative destabilising and stabilising actions, respectively γF,dst and γF,stb are partial factors for destabilising and stabilising actions, respectively and the other symbols are as defined for Equation (1a) above Alternatively, partial factors may be applied to the effects of actions instead:

where γE,dst and γE,stb are partial factors for destabilising and stabilising effects of actions, respectively. In Annex A.1 of EN 1990 for buildings, the following partial factors are recommended in NOTE 1 of Table A1.2 (A): γG,dst = γG,sup = 1.1 for destabilising permanent actions Gdst , γG,stb = γG,inf = 0.9 for stabilising permanent actions, and γQ,dst = 1.5 for destabilising variable actions Qdst . In situations where the expression for EQU cannot be satisfied, EN 1990 also allows the introduction of additional stabilising terms in Equation (2) resulting from “for example, a coefficient of friction between rigid bodies” (EN 1990, 6.4.2 (2)). These “additional terms” are an important issue for this paper. For such situations, NOTE 2 of Table A1.2 (A) in Annex A.1 of EN 1990 also allows an alternative procedure, subject to national acceptance, in which the two separate verifications of STR/GEO and EQU are replaced by a combined EQU + STR/GEO verification with recommended partial action factor values of γG,dst = 1.35, γG,stb = 1.15, and γQ,dst = 1.50 (provided that applying γG,dst = γG,stb = 1.0 does not give a more unfavourable effect) combined with the relevant STR/GEO partial material and resistance factors from Design Approaches DA 1 (Combination 1), DA 2 and DA 3. EN 1997-1 requires verification of a limit state of static equilibrium or of overall displacements of the structure or ground (EQU) by:

and a note is added: “Static equilibrium EQU is mainly relevant in structural design. In geotechnical design, EQU verification will be limited to rare cases, such as a rigid foundation bearing on rock, and is, in principle, distinct from overall stability or buoyancy problems. If any shearing resistance Td is included, it should be of minor importance.” In discussions between the authors, two ‘concepts’ for the interpretation and application of ENs 1990 and 1997-1 have been developed. •

Inserting partial factors, this may be expanded to:

112

Concept 1 proposes verifying only EQU in those cases where loss of static equilibrium is physically possible for the structure or part of it, considered as a rigid body. Similarly Concept 1 proposes verifying only STR/GEO in situations where the strength

of material or ground is significant in providing resistance. • Concept 2 proposes verifying EQU in all cases; it is interpreted as a load case. Where minor strength of material or ground is involved, the combined EQU/STR/GEO verification may be used, if allowed by the national annex. Further discussion involves the term “Td ” in expression EN 1997-1 2.4, particularly with the use of Concept 1: it might be regarded either as a resistance (Concept 1-R) or as an action (Concept 1-A). Using Concept 1-R, the design resistance of the anchor is:

and a similar approach is generally used with Concept 2. If load factors can be applied directly to action effects, Rd is given directly as:

where EQ,rep,dst is E{Qrep,dst }. Using Concept 1-A and substituting the characteristic value of a stabilising action Ak,stb (assumed to be permanent, from, for example, an anchor), expression EN 1997-1 2.4 becomes:

Hence:

and Ak is then used in a STR/GEO verification to show that the design stabilising action Ad can be provided by the resistance Rd of, for example, an anchor:

Figure 1. Balanced structure on piled foundation.

that are different from those of STR/GEO. In contrast, no values are given for EQU for partial factors for geotechnical resistances, and none are offered for structural materials or resistances in EN 1990; it might be inferred that these unspecified material and resistance factors will be the same for EQU as for STR/GEO. The following examples show how these differing concepts lead to different results in practical design situations.

3

EXAMPLE 1: BALANCED STRUCTURE ON PILED FOUNDATION

3.1 General When variable actions are significantly larger than the permanent actions, this simplifies to:

Figure 1 shows a balanced structure sitting on a piled foundation. In the verifications it is assumed that: •

which is more onerous than ‘normal’ GEO design for which Rd ≥ EQ,rep,dst γQ,dst . The difference between Concepts 1-R and 1-A lies in the ratio γG /γG,stb (compare equations 3a and 4b), where γG is the load factor in a STR/GEO verification. Example 4, given below in section 6, illustrates this difference. EN 1997-1 allows national standards bodies to set values of partial factors for soil strength in EQU

• • • •

the representative values of the two forces W are equal (=Wr ). the column and footing are assumed to be weightless all structural components are of reinforced concrete the structure consists of a single beam, one column and two piles and there is no transfer of bending moment to the piles.

The details and the results of some verifications proposed by the authors are in presented in Table 1. Concept 1 only requires limit states STR and GEO to be considered, since failure can only occur from

113

a lack of strength in the structure or in the ground surrounding the piles. There is no possibility of loss of equilibrium, provided the structure and foundations are strong enough. It might be useful in such a situation to introduce the load case given by the factors of EQU as an additional STR verification. Alternatively, other provisions of ENs 1992 and 1993 might dominate this problem (e.g. geometric allowances etc). Concept 2 requires the spatial distribution of actions from the self weight of the horizontal element (a single source) to be considered, so additionally EQU must be verified. 3.2 Verification of limit states STR and GEO If there are no wind or snow loads to be considered the column will only carry the vertical load of the self weight 2Wr of the horizontal beam. The partial factor for permanent actions of γG = 1.35 must be applied to Wr to determine the design value of the effects of actions for the pile design. Clause 5.2(1)P of EN 1992-1-1 states that the “unfavourable effects of possible deviations in the geometry of the structure and the position of loads shall be taken into account in the analysis of members and structures”. For isolated members, such as that shown in Figure 1, a vertical lean of approximately 1/200 should be included in the calculation of moments. 3.3 Verification of limit state EQU via Concept 2 According to the notes of Annex A of EN 1990 two alternative procedures with two sets of partial factors Table 1.

to be applied to the self weight of the horizontal beam may be used to design the structure: Note 1: γG,dst = 1.1 and γG,stb = 0.9 Note 2: γG,dst = 1.35 and γG,stb = 1.15 (not shown in Table 1 – the results are as for Note 1). 3.4 Conclusions From the results of the verifications in Table 1, it can be seen that the design values of the different verifications depend to a large extent on the ratio a/b (width a between the forces relative to the width b between the piles). Comparing the different EQU-verifications it can be seen that in this example the EQU-verifications do not represent a separate ultimate limit state but a different set of partial factors on actions to account for a special design situation – here the possibility of the variance in the spatial distribution of the self weight of the horizon-tal concrete beam. In effect, the design values of the actions taken from EQU are applied when verifying limit state STR for the concrete of the column and piles and when verifying limit state GEO for the piles’ ground bearing resistance. 4

EXAMPLE 2: TOWER SUBJECT TO A VARIABLE ACTION

4.1 General The second example shown in Figure 2 is a tower subjected to a variable action. Here not only the structural design and Eurocode 7’s three Design Approaches for the verification of the ground bearing capacity need to

Results of the verifications of example 1 – balanced structure on piled foundation.

Concept

1, 2

2

1(1)

Source of factor values

EN1990 Table A1.2(B)

EN1990 Table A1.2(B)

Values of factors

γG = 1.35

Design value(s) of the bending moment M for structural design of the bottom of the column Design values of the forces F1 and F2 (compression > 0) for geotechnical design of the pile Design values of the force F1 and F2 (tension 0) for structural design of the pile Design values of the force F1 and F2 (tension 1.5 1.2–1.5 0.8–1.2 0.6–0.8 “acceptable risk”, it would suggest a high risk that the population exposed will develop cancer. Individual(for a single chemical) acceptable risk was set to 1 × 10−5 (carcinogen compounds); acceptable Hazard Quotient (HQ, single chemical, noncarcinogen effects) was set to 1.0 as well as the Hazard Index (HI ), these values were established according to ASTM recommendations. 5

4

HUMAN RISK CALCULATION BASED ON REFERENCE-DOSE MODEL

4.1 Human health risk assessment model To perform Human health risk assessment, the four steps described in the introduction were followed. For

NEW DECISION SUPPORT SYSYTEM WITH FUZZY-RISK CALCULATION MODEL

The goal of a Pump and Pump and Treat remediation work should be to protect human health for decision making. We developed the new decision support system for groundwater remediation by using Pump and treat method. This DSS can potentially be a reasonable

219

Table 2.

Parameter of risk evaluation.

Non Carcinogens

Carcinogens

Parameter

Value

Unit

Reference∗

Referential dose (RfD0) Body weight (BW) Averaging time for noncarcinogens (ATn) Ingestion rate of water (IRw) Exposure duration (ED) Exposure frequency (EF) Body weight (BW) Averaging time for carcinogens (ATc) Slope factor (SF0) Ingestion rate of water (IRw) Exposure duration (ED) Exposure frequency (EF)

0.006 50 30

mg/(kg day): TCE kg year

U.S.EPA (1996) JEA (1999) JEA (1999)

2 30 10 350 50 70

L/day year days/year kg year

JEA (1999) Assumed in this study JEA (1999) JEA (1999) JEA (1999)

0.011 2 30 10 350

[mg/(kg day)]−1 : TCE L/day year Days/year

U.S.EPA (1996) JEA (1999) Assumed in this study JEA (1999)

*USEPA: U.S. Environmental Protection Agency, JEA: Japan Environmental Agency

fuzzy inference. The proposed method may contribute for low-cost and low-risk remediation works. Application to actual site and modification of basic concept should be needed to further development. REFERENCES

Figure 4. Flow of a decision support system.

remediation work and protecting human health. Concept of decision support system is shown in Fig. 4. Human health risk assessment was calculated based on the ASTM RBCA model. And, environmental risk and rational pumping rate is expressed by fuzzy membership functions. The samples of the risk calculation parameters are shown in Table 2.

6

ASTM (2000) Standard guide for risk-based corrective action, ASTM E 2081-00. Japan Environmental Agency (1999) Survey and countermeasure guidelines for soil and groundwater contamination, Geo-Environmental Protection Center. Mamdani, E.H. (1974) Applications of fuzzy algorithms for control of simple dynamic plant, Proc. IEE, 121, 12, 1588. Mamdani, E.H. (1976) Advances in the linguistic synthesis of fuzzy controller, Int. J. Man-Machine Studies, Vol.8, No.6, pp. 669–679. Morisawa, S. (1991) Optimum allocation of monitoring wells around a solid-waste landfill site using precursor indicators and fuzzy utility functions, Journal of Contaminant Hydrology, Vol.7, pp. 337–370. U.S. Environmental Protection Agency (1996) Soil screening guidance technical background document, EPA/540/ R95/128. Zadeh, L.A. (1968) Fuzzy algorithms, information and control, Vol.12, pp. 94–102. Zadeh, L.A. (1973) Outline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on SMC, SMC-3, Vol.1, pp. 28–44.

SUMMARY

The concept of new fuzzy inference model, which is effective for groundwater contaminated with low levels of VOCs, was proposed. In this remediation technique, remediation efficiency and environmental impact are considered in the remediation period by

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Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

A risk evaluation method of countermeasure for slope failure and rockfall with account of initial investment T. Yuasa & K. Maeda Graduate School of Civil Engineering, Nagoya Institute of Technology, Japan

A. Waku Ltd. Takashima technology central adviser, asset management department general manager

ABSTRACT: In Japan, with the asset management and the advancement of risk management research, soil structures, such as slopes, are now being taken into consideration as infrastructure properties. In order to execute effective countermeasure for slope failure and rockfall, it is necessary to quantity effects of countermeasure by numerical analysis, such as DEM rockfall simulation. And, at present, method for evaluating the initial investment in countermeasures has not yet been established. To allow for the determination of an appropriate investment, we propose a new method of calculating the investment based on slope risk in this paper.

1

INTRODUCTION

In Japan, with the development of risk management technology, earth structures, such as slopes and tunnels, are now being taken into consideration as infrastructure properties. In this framework, there are circumstances in which it is necessary to execute slope measures more efficiently. This is because local governments face strict financial limitations, while the number of dangerous slopes is increasing due to expanding road networks in mountain areas. Slope risk management presumes the slope risk value beforehand, and supports the execution of strategic measures corresponding to the slope risk value. Some risk quantification techniques have been proposed, and in part, these have been studied increasingly for business use with GIS. However, many large problems should be addressed. The first problem is improving the precision of slope risk value. This is particularly the case with the countermeasures; it is necessary to adequately reflect their positive effect in the slope risk. At present, this effect has not been quantified and an evaluation technique to quantify the above effect has not been established. Second, an evaluation technique for calculating the investment for new slope measures has not been established. In a lot of infrastructure properties, investment appraisal is executed, including cost-benefit analysis (B/C). However, a method to evaluate the validity of slope measure cost has not been determined. This is a critical problem for efficient investment. The purpose of this paper is, first, improving the precision of slope risk quantification with slope measures. Second, the paper proposes a new method to evaluate the validity of the slope measure cost.

In this study, deal with slope failure and rock fall as a slope collapse disaster at the same time. Probability distributions are used in a mechanical stability analysis model to quantify the slope risk after each occurring mechanism is presumed. Moreover, we use the rockfall simulation DEM (Discrete Element Method) to quantify the effect of counter measures. 2 2.1

QUANTIFICATION OF SLOPE RISK Definition of slope risk

In order to quantify the slope risk R, R is defined as follows. This shows the expected value of amount lost.

where p is the probability of slope disaster, D is the amount lost due to disaster. 2.2 Calculation of occurrence probability We indicate the calculation method for each probability in this section because the occurring mechanism is different between slope failure and rockfall. (1) Probability of slope failure The calculation method for slope failure probability is divided roughly into a statistical and a mechanical technique. Here, we will use the mechanical model that Ohtsu proposed the method which is used slope stability analysis. In this method, first, rainfall is assumed to be an exogenous factor of slope disaster. We calculate the slope failure probability pa from the excess probability of annual probable rainfall ψ(α) in rainfall intensity

221

Figure 2. Types of rockfall. Figure 1. Infinite slope model.

α and the slope failure probability pf in case of that probable rainfall. If it is supposed that the rainfall hazard follows the Gumbel distribution, the excess probability ψ(α) will be the following.

In this equation, a and b are constant numbers obtained from the rainfall history. Next, it is supposed that a collapse type is infinity slope model (Fig. 1) in order to calculate the pf . Then, the safety factor of the slope stability analysis is indicated as follows.

where γ is the soil unit weight, γw is the unit weight of water, H is the thickness of the sliding layer, Hw is groundwater level, θ is the slope angle, c and ϕ are the soil strength parameters. Moreover, it is necessary to relate α and Hw , so we decided to use Eq. (4) from reference. (JCCA kinki, 2006)

Now, to quantify slope failure probability, we calculate the probability of “F < 1” because this shows the unstable (collapse) condition. To do this, we assume the soil cohesion c and inter friction angle φ to be random variables according to a normal distribution as in Eq. (5). This shows the uncertainly of soil parameters in physical terms.

As a result, the slope failure probability pf is calculating from the following equation.

Therefore, the slope failure probability pa is as follows.

The feature of this method is that probability distribution is taken into the mechanical stability analysis model. However, it is difficult to determine the volatility of the random variable. In addition, it is necessary to note that we use a simple equation for ease of calculation, though it is known that the occurring mechanism is influenced by the saturation, groundwater level, and so on. (2) Probability of rockfall The occurring mechanism of rockfall is very complex and has not yet been clarified. However, the calculation method for rockfall probability is also roughly divided into a statistical and a mechanical technique. We use the mechanical model that Okimura proposed. Fig. 2 shows the cases of the overhang type and fall off type of rockfall, and the safety factor equation for each type. Then, the random variables c and ϕ are taken into these equations. It is assumed that the probability from F number of falls below one (N
) is divided into the number of all trials (N) by Monte Carlo simulation. This mechanical model is very simple, so it is easy to execute. On the other hand, it seems that endogenous factors such as geological situation and exogenous factors such as rainfall, snow, freeze-thaw, wind, and earthquakes cannot be reflected in the model. Therefore, these points will become research topics in the future. 2.3 Calculation of loss amount due to disaster It this study, we define D as the sum of D1, the personal loss; D2, the road restoration cost; and D3, the traffic detour loss. In addition, the loss amount is changed by whether there are existing countermeasures or not. However, this section does not deal with the effects of countermeasures; these details will be given in section 4. Collapse types, which are needed to calculate D1, are modeled as in Fig. 3.

222

Figure 3. Type of collapse.

(1) Personal loss, D1 In case of slope failure, it called a “buried case” when sand exceeds the height of a car; the “buried case” seems to result in death, incurring the human loss I (yen) in this case. The loss amount decreases linearly in relation to the reduction of the disaster level. In case of rockfall, it seems that the case of being situated “right under the falling rock” results in death, and this is calculated in the same manner as before (Fig. 3). The number of victims is calculated from the daily traffic volume of the object road and the average number of passengers. Furthermore, the number of victims is calculated separately in relation to compact cars and large-sized cars in order to reflect the difference in the cars’ height. Incidentally, the human loss used is I = 29,764,000 (yen), as obtained from the survey of the Japanese Cabinet Office. (2) Road restoration cost, D2 In each case of slope failure and rockfall, we use Eq. (9) to calculate D2 (Yen). This equation is a regression function between the restoration cost and the archived volume of sand V (m3 ) based on past disaster records. (PWRI, 2004)

Figure 4. Relationship between collapse volume and recovery time (Kohashi, H et al. 2007).

Table 1. Slope no.

1

2

3

4

5

V (m3 ) φ (deg.) θ (deg.) γ (kN/m3 ) c (kN/m2 ) H (m) Traffic volume (/days) Mix rates of large-sized car (%) Distance of original/ detour road (km) Speed of original/ detour road (km/h)

2,100 30 41 18 16.7 3.5 4,502

600 35 38 18 2.7 1 4,502

900 30 43 18 10.4 2 4,502

800 35 36 18 4.5 1.5 4,502

1,500 25 38 18 13.2 2.5 4,502

10

10

10

10

10

3

(3) Traffic detour loss, D3 The traffic detour loss refers to the closing of roads when slope failure or rockfall occurs, and D3 consists of two kinds of loss, the “Cost loss of time” generated by increases of running time and the “Running cost loss” generated by increases in mileage. These can be calculated according to the mileage distance and the daily traffic volume. Recovery time has a big influence on the detour loss, and Fig. 4 shows relations between the recovery time N (days) and the collapse volume V (m3 ). In this study, we use the regression function as given in Eq. (10) However, it seems that extensive losses that are not reflected in the equation occur if there is no detour or the event occurs near an isolated village, so it is necessary to evaluate D3 in each slope for these cases.

Slope failure conditions.

20/40 10/25 15/25 15/50 15/50 50/30 50/30 50/30 50/30 50/30

RESULTS OF CASE STUDY

In this section, the calculations of slope risk using the above method are shown. In this paper, we set the 10 slope conditions as inTable 1.These are not real slopes, but we can assess what factors influence the results. In addition, probable rainfall is based on rainfall history for 1945–2006 in the Takayama Gifu observatory. Previously, there were no methods of indicating a slope risk which is expressed by the monetary value in terms of slope failure and rockfall at the same time. Now, however, we indicate that each type of slope risk can be evaluated simultaneously by the index of slope risk. Moreover, it is understood that the collapse probability by use of stability analysis that has been used does not necessarily correlate the slope risks. This is because the risk includes not only an index that shows the danger of slope collapse but also that considers the amount loss when the disaster will occur. For instance, comparing slope No. 3 and No. 9, the collapse probability is almost at the same level. However, it is understood that slope No. 3 has double or more the risk of slope No. 9 (Fig. 5).

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Table 2.

Rockfall conditions.

Slope no.

6

7

8

9

10

Type of collapse* Weight of rock W (kN) Angle of sliding surface α (deg.) Length of sliding surface Y (m) Length of crack Y (m) φ (deg.) c (kN/m2 ) Traffic volume (/days) Mix rates of large-sized car (%) Distance of original/ detour road (km) Speed of original/ detour road (km/h)

(ov) 12.9

(ov) 2.76

(rf) 6.9

(rf) 86.3

(rf) 4.1

80

95

65

50

55

0.8

0.4

0.5

2.5

0.2

0.0

0.2

–

–

–

35 35 35 35 35 15 15 15 15 15 4,502 4,502 4,502 4,502 4,502 10

10

10

10

10/25 20/30 20/70 5/20

Figure 6. Priority of executing slope measures.

addition, it seems that slope risk can be used as a means of determining the accountability for residents as to when slope measures will be executed under the budget reductions.

10 10/30

50/30 50/30 50/30 50/30 50/30

4

*(ov)…Overhang Type (rf)…Rock off Type.

Table 3.

In this section, it described how to quantify the effects of countermeasure that either exist or will be built up. In this study, it pays attention to the rockfall disaster; the effect of countermeasure is quantified by calculating a rockfall behavior using two-dimensional DEM.

Results of slope risk analysis.

Slope no.

pa

D1

D2

D3

D

R

1 2 3 4 5 6 7 8 9 10

0.0621 0.9960 0.2001 0.3384 0.1041 0.3870 0.4650 0.0200 0.2050 0.0350

1,446 57 803 0 1,307 566 566 566 566 566

2,157 714 1,002 906 1,580 137 136 136 140 136

2,258 807 761 1,437 2,719 485 463 976 466 549

5,862 1,578 2,567 2,343 5,605 1,188 1,165 1,678 1,172 1,252

364 1,571 515 793 583 460 542 34 240 44

QUANTIFICATION OF SLOPE MEASURE EFFECT

4.1 Concept of DEM rockfall simulation

Figure 5. Results of slope risk and failure probability.

A methodology to determine the priority level of slope measures had not been clarified. However, it is thought that these priority levels can be decided more reasonably by arranging slopes in order in terms of slope risk value. (Fig. 6) This also means that we can order slopes in terms of their impact on society. In

DEM is a numerical analysis method used to solve each element progressively in an independent motion equation. At present, this method is most commonly used for rockfall simulations, in Japan. The ground slope is an actual section of a real site, and ground surface is approximated by a single layer of some particles. Often, ground slope is expressed by particle assembly. In this study, only one layer was used because it reduces the lengthy analytical time required to calculate many cases. Details will be provided later. Based on preliminary surveys, the location of rockfall generation was determined. To simplify calculations, rock particle was assumed to have a circular shape. Furthermore, the shape and location of countermeasure, such as a retaining wall, is set up arbitrarily. This represents the situation of how to establish a new countermeasure. To quantify the effect of slope measure, it is necessary to judge whether the road would be struck as a result of rockfall simulation. Two cases are thought to serve as judgment standards, and are represented in Fig. 7 and Table 4. In case (B), the judgment standard is presumed to be an amount greater than the possible absorption energy of the countermeasure. In order to describe uncertain rockfall behavior, caused by initial conditions, the generation location is regularly changed and rockfall simulation is executed 38 times. As a result, the probability of being struck by

224

Figure 8. Results of simulation (wall height = 2.0 m).

Figure 7. Judgment standards for road being struck. Table 4.

Judgment standards for road being struck.

(A) A rock exceeds the retaining wall (B) A rock destroys the retaining wall

Table 5. Analytical parameters of DEM. Spring constant (normal) Spring constant (shear) Damping factor (normal) Damping factor (shear) Coefficient of particle friction

5.0 × 106 5.0 × 106 × 1/4 0.3 0.3 0.477

Figure 9. Results of simulation (wall height = 2.5 m).

the rockfall is calculated as the number of times either judgment standard (A) or (B) is met divided into the total number of simulations. It is also possible to verify rockfall behavior width. In addition, another method of describing uncertain rockfall behavior exists. It is the probability distribution that takes into analytical parameters of rockfall simulation. Because the influence of analytical parameters on falling rock behavior has not yet been clarified, the former method described is used in this study. 4.2

Results of DEM rockfall simulation

Analytical parameters DEM are set according to Table 5. Fig. 8 represents one example of a simulation result. The solid line shows tracks of two or more falling rocks. The figure’s scales are equivalent to the actual site. In order to determine the number of times judgment standards (A) or (B) are filled, it is necessary to obtain two numbers. First, the number of times rockfall height exceeds the retaining wall height of 2.0 m; and, second, the number of times that rockfall energy exceeds the possible absorption energy of the retaining wall. To be more specific, the possible absorption

energy is set at 300 kJ, and it is assumed the countermeasure is destroyed if it received more than 300 kJ of kinetic energy in the x-direction. In this study, that number was 21; therefore, the probability of being struck by rockfall is estimated to be 55%. Next, it is necessary to calculate the risk decrease rate in order to correlate this result to the slope risk. In this case, risk decrease rate is estimated at 45%, calculated as (100–55)%. In addition, rockfall simulation may be used not only to examine the effects of countermeasures, but also to decide the best scale and shape for them. For instance, Fig. 9 represents the results of changing the height of the retaining wall, by only 0.5 m, when exactly the same simulation as before was executed. As a result, the risk decrease rate increased to 70%. The risk decrease rate, relative to the arbitrary scale and shape, is estimated by DEM rockfall simulation both in existing and newly measured cases. 4.3 Assignment of rockfall simulation DEM is used most commonly for rockfall simulations; however, it is not clear how much it is influenced by analytical parameters, the effects of talus, and rock shape so forth. Especially, the effects of talus which is deposited materials or weathered slope surfaces when

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Figure 10. Meaning of slope risk.

Figure 11. Comparison of the two types of LCC (w = 65%).

falling rock is digging into them, how breakage of falling rock when the rock is crushed and other important elements have on rockfall behavior. Moreover, when a falling rock is modeled as a circle in 2D, or a sphere in 3D, the influence of shape and interaction between rotational and translational motion needs to be considered. The points that have been described so far represent problems to simulate rockfall behavior adequately. At the same time, however, energy dissipation effects such as rock crushing and digging into the talus, for instance, must be considered when designing effective, natural countermeasures. Therefore, it is important to continue to improve the precision of categorizing falling rock behavior to be able to achieve more effective yet inexpensive measures. It will also be possible to measure the effect of slope and to evaluate investment decisions by using the risk decrease rate. This is described further in the next section. 5

EVALUATION METHOD OF INVESTMENT FOR COUNTERMEASURES

In this section, we propose an evaluation method for the initial investment for countermeasures. At present, a technique for evaluating the validity of countermeasure cost has not yet been established. The biggest reason for this is that it is quite difficult to forecast the degrees of loss when a disaster occurs and to quantify the effect of damage reduction by countermeasures. However, as seen up to now, it is becoming feasible to use ‘slope risk’ for the former and ‘quantification of slope measure effect’ for the latter. Thus, we propose an evaluation method for the validity of an initial investment for countermeasures based on slope risk. 5.1

the slope risk is the slope’s cost per year. Therefore, slope LCC can be calculated by integrating slope risks for the use period. In addition, it is possible to adjust the evaluation techniques related to investment amount that have been developed with general infrastructures by the concept of slope LCC. Therefore, slope LCC is defined as follows.

where Ri is the slope risk of the ith year, N is the use period, C0 is the initial investment, w is the risk decrease rate by investment, and r is the Japanese social discount rate (4%). The OM cost (operation and maintenance cost) is not included in Eq. (11) because we assume that slope check and research costs can be disregarded compared with slope risk. In addition, it is necessary to presume w based on the DEM simulation result indicated in section 4, because this differs depending on the type of measurement and scales in each slope. 5.2 Evaluation index of investment, W In order to examine the amount of the investment, it is necessary to compare LCC
in case of making the initial investment (countermeasure is executed) to LCC in the case of not making it (unmeasured). If LCC
< LCC, it will be judged that “It is necessary to execute the project.” This means that the standard of the evaluation has to do with the relationship between both LCCs, as shown in Fig. 11. Therefore, we propose a new index W as in Eq. (12) that pays attention to the ratio of both LCCs in order to simplify investment decisions.

Slope LCC (Life Cycle Cost)

To examine the amount of investment, we must consider the cost generated during the use period, and the concept of LCC is necessary for this, as well as a general infrastructure. The damage cost on the slope is generated only at the disaster points, as shown in Fig. 10(Left). On the other hand, slope risk shows the expected value per year of the cost that may be generated, as shown in Fig. 10(Right). In other words, it can be assumed that

With the index of W , the project can be judged “It is necessary to execute it” if W is positive, or can be judged “Should not execute it” if W is negative. Table 6 shows the example of investment decisions when some measures plan is shown. The decisionmaker can determine the most effective plan by choosing the plan in which W has the biggest value. In this case, Plan (B) is the most effective investment plan.

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Table 6.

Example of investment judgment for each plan. Non Plan (A)

Measures cost 0 100 Risk decrease 0 50% rate (%) LCC or LCC
500 350 (100 + 250) W (%) – +20

Plan (B)

Plan (C)

200 65%

400 90%

375 350 (200 + 175) (400 + 50) +25 +10

Table 7. Volatility factors in the future slope risk. Volatility of probability Volatility of loss amount

Figure 13. Result of Slope LCC.

(A) Volatility of probable rainfall (B) Volatility of geometrical parameter (C) Volatility of traffic volume

Figure 14. Relationship decision-maker.

Figure 12. Traffic volume prediction by use of “Arithmetic Brownian motion”.

And, for the further discussion, we call initial investment when becoming W = 0 “Amount of the limit investment”, Csup .

5.3

Evaluation of investment amount considering the risk volatility

In the previous section, the slope risk volatility is not considered. However, it is necessary to consider the risk volatility according to passage of time in the use period when we calculate slope LCC. Then, we describe the investment amount evaluation in the condition of uncertainty. The risk volatility factors are shown in Table 7, but the governing factor is (C). Therefore, in this study, we assume that (C) is the only volatility factor in the future slope risk. Then, it is necessary to model the traffic volume in the future. This estimation is usually carried out according to the some scenario based on forward road planning, but this has been criticized in that there is uncertainty in prediction and a constant width in the predictive value. Because of this, we considered the annual volatility of traffic volume to be “Arithmetic Brownian motion,” which is used in the field of the Financial Engineering; this is expressed using

between

W and

C0

for

the Monte Carlo simulation. Fig. 12 shows one example of these results. In addition, the feature of the arithmetic Brownian motion is its accordance with the Markov process in that the following present term traffic volume depends only on the traffic volume before one term. LCC can be fined when the traffic volatility is given; the result is shown in Fig. 13. The result demonstrates that LCC50 shows distribution with a certain width that centers on the mean value. Here, we consider the confidence interval of distribution to be 90%, DownSide and it is assumed that LCC50 when the cumuDownSide lative probability is 5% and LCC50 when the cumulative probability is 95%. From this, we can calculate the “Amount of the limit for investment.” With this result, the W and initial investment C0 relation are led as in Fig. 14. It can be determined whether the initial investment under examination is in the safety zone or in a dangerous zone, and the width of the middle zone generated by the uncertainty of the traffic can also be understood. For instance, if it was proposed to build newly countermeasure from 150,000 thousand yen, decision-maker can evaluated that this proposal is not economical but is not far apart from Csup . And if it was proposed more expensive plan, they might require to change this measure plan fundamentally. From this, it is believed that the investment evaluation for uncertain conditions will become possible by the index of W .

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6

REFERENCES

CONCLUSION

In this paper, it has been made clear that slope risk can be quantified both in terms of slope failure and rockfall when slope risk management is executed. Furthermore, it has been demonstrated that it is possible to reasonably determine the priority level of countermeasures by slope risk. Moreover, in order to quantify the slope measure effect, rock fall simulation by DEM is an effective method. And it is able to calculate risk decrease rate of countermeasure by judging the road struck in many calculations. We have proposed a new method for evaluating the validity of an initial investment by leveraging the index W based on the concept of slope LCC. In addition, this method will be able to support decision making under uncertain conditions, as it has built in the risk volatility of traffic volume in the future. Future tasks include determining how to treat the statistical and mechanical error margin for each model. Furthermore, the required risk precision is different in the steps of risk management as compared to those of decision-makers, so it is necessary to construct a complete system of risk management. For instance, the decisions of measuring priority level are based on relative risk evaluations; on the other hand, investment decisions are based on an absolute risk value. In this case, a high level precision is needed. Briefly, it is necessary to clarify the risk quantification technique corresponding to the necessary risk precision. In addition, in relation to the rock fall simulation DEM, etc., future research to improve its precision is necessary.

Cundall, P.A. 1971. A computer model for simulating progressive large scale movements in blocky rock system, Proceedings of the Symposium of the International Society of Rock Mechanics (Nancy, France), Vol. 1, No II-8 Japanese civil engineering consultants association Kinki branch, JCCA kinki, July 2006. Introduction of deterioration concept for slope stability evaluation. (in Japanese) Japanese Society of Civil Engineers, 2003, Guidebook on Traffic Demand Forecasting, Vol. 1 (in Japanese) Kohashi, H., Kato, S., Ishihara, H & Furuya, A. September 2007. Evaluation of recovery time of road slope disaster, JSCE 2007 Annual meeting, Hiroshima: 877–878 (in Japanese) Komura, T., Muranishi, T., Nishizawa, K. & Masuya, H. 2001. Impact of falling rock on field slopes used in rock-fall simulation method, Journal of Structural Engineering, JCSE, VI-47A: 1613–1620. (in Japanese) Okimura, T., Torii, N., Hagiwara, S. & Yoshida, M. 2002. A proposal for risk evaluation method for rock fall on road slope, Journal of the Japan Landslide Society, Vol. 39, No. 1, June: 22–29 (in Japanese) Otsu, H., Onishi,Y., Nishiyama, S. & Takeyama,Y. 2002. The Investigation of Risk Assessment of Rock Slopes Considering the Socioeconomic Loss due to Rock Fall, Journal of JSCE, No.708/III-59: 187–198. (in Japanese) Otsu, H., Supawiwat, N., Matsuyama, H. & Takahashi, K. 2005. A Study on Asset Management of Road Slopes Considering Performance Deterioration of Groundwater Counter-measurement System, Journal of JSCE, No.784/VI-66: 155–169. (in Japanese) Public works research institute, PWRI. 2004. Manual that supports risk analysis and management for road slope disaster (idea). (in Japanese) Usiro, T. 2001. Rockfall numerical simulation software DRSP, Kochi Prefecture bridge association. (in Japanese)

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Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Risk assessment on the construction of interchange station of Shanghai metro system Z. W. Ning, X. Y. Xie & H. W. Huang Key laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, P. R. China Department of Geotechnical Engineering, Tongji University, Shanghai, P. R. China

ABSTRACT: As the rapid growing of Shanghai metro system, risks along with the construction of interchange station are given great concerns. In this paper, an overview of interchange station in 2012 Plan is first presented by thorough statistics. Then both the objective and the subjective risk factors of the construciton of interhchange station are well analyzed. Finally a risk assessment model is established by using the Fuzzy Synthetic Evaluation Method and the Analytic Hierarchy Process to evaluate the risk level of the 4-line Century Avenue interchange station. 1

INTRODUCTION

The Shanghai metro system which currently operates 8 lines with a total length of 228.4 km is one of the fastest growing metro systems in the world. According to the plan, the system will include 13 lines with a total length over 500 km in 2012. Therefore, Shanghai metro system has stepped into a period of network-scale construction from previous single-line scale construction, which inevitably raises new risk issues. Among those, the risks along with the construction of interchange stations are given great concerns. Generally speaking, their more complicated configuration compared with normal stations would increase the chances of failure when excavation, and therefore cause severe consequences as they are normally located on central spots of the city. Moreover, a large potion of interchange stations are constructed by expanding or reconstructing the existing stations, which brings about great threatens to the safety of the operating metro lines. Apart from these technical concerns, poorly risk management in site, lack of experienced contractor and qualified personnel as well as equipment problems are all the potential causes for accident or delay in the process of interchange station construction.

2

STATISTIC OF INTERCHANGE METRO STATION IN SHANGHAI 2012 PLAN

According to the 2012 Plan, nearly 60 interchange stations will be built. Before risk analysis, we conducted statistic study to obtain an overview of these interchange stations in some aspects as station scale, interchange mode and construction mode.

Figure 1. Distribution of interchange stations with different scale.

2.1 Statistic study on station scale There are 59 interchange stations according to the 2012 Plan. Among those, there are 43 2-line interchange stations, 15 3-line interchange stations and 2 4-line interchange stations, making up 73%, 25% and 2% respectively in total. Figure 1 shows the distribution of interchange stations with different scale among all the 13 metro lines. It is found that Line 4 has the most interchange stations as it is a circular line that intersects with many other lines. The early built lines (Line 1 to Line 4), which make up of the framework of the Shanghai metro system, consist of more large scale stations (3-line and 4-line) than those newly built or in plan. It indicates that, in the following few years, there are many stations in old lines need to be expanded or reconstructed for interchange function.

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Figure 2. Distribution of interchange pairs with different interchange modes.

Figure 3. Distribution of interchange stations with different construction modes.

2.2

to different lines are built at different stages. For the built at one time mode, it literally means the sessions belong to different lines within an interchange station are built at one time. Among all the interchange stations, there are 24 stations of reconstruction mode, 23 stations of built at stages mode and 12 stations of built at one time mode, making up 41%, 39%, 20% respectively in total. Figure 3 shows the distribution of interchange stations with different construction modes among all the 13 metro lines. Figure 3 demonstrates high percentage of reconstruction mode in early built lines as Line 1, Line 2, Line 3 and Line 4. It is also for the reason that there was less consideration for future network expansion when these stations were designed. As to interchange stations in new lines, excepting for those intersect with existing lines, they are mostly built at stages or built at one time with an overall interchanging design concept.

Statistic study on interchange mode

In Shanghai metro system, there are three interchange modes as: parallel-interchange, cross-interchange and passage-interchange (interchanging via passage connecting separate stations of different lines). For every pair of two different lines in an interchange station, they belong to a type of interchange mode. Thus, when we calculating the number of interchange modes, there are Cnn−1 interchange pairs for a n-line interchange station. Among all the interchange pairs in those interchange stations, there are 18 pairs of parallel-interchange mode, 34 pairs of crossinterchange mode and 42 pairs of passage-interchange mode, making up 19%, 36% and 45% respectively in total. Figure 2 shows the distribution of interchange pairs with different interchange modes among all the 13 metro lines. From Figure 2, high percentage of passageinterchange mode is found in Line 1, Line 2 and Line 3. That is because a complete metro network had not formed yet in early age of metro construction and less considerations for future interchanging needs in design. Under this circumstance, passage-interchange becomes a low cost and low risk option for existing lines to connect with new lines. In those newly built lines or lines still in plan, the parallel-interchange and the cross-interchange modes are widely adopted with higher efficiency and more convenience for passengers. 2.3

3

RISK ANALYSIS OF INTERCHANGE STATION CONSTRUCTION

In this paper, the authors divide the risk factors of interchange station construction into two categories: objective risk factors and subjective risk factors. The former are commonly recognized as technical or natural issues which add inherent difficulties and uncertainties to proposed projects while the latter are usually related to human errors or organizational deficiency in management, which may lead to failure or delay of projects.

Statistic study on construction mode

As old saying goes that, Rome was not built in one day, it is impossible to build all the metro lines simultaneously. Besides, the alignment of lines could be adjusted after original planning. Therefore, there are currently three different construction modes for interchange stations as: reconstruction, built at stages and built at one time. For the reconstruction mode, it refers to reconstructing or expanding a station without interchanging function to an interchange station. As to the built at stages mode, it means the interchange station is designed as a whole complex while the sections belong

3.1 Objective risk factors of interchange station construction From previous statistic study on the interchange stations of Shanghai metro system, it can be found that the complicated configuration and various construction modes are unique features of interchange station compared with normal station. To a great extent, they would affect the risk level of projects. Besides, as ground-related project, the geological conditions and the surrounding environments should always be taken into consideration as objective risk factors as well.

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3.1.2 Construction mode A unique feature of interchange station construction that differs from normal station is the possible interval between the construction of different parts within a whole station. Therefore, the risks accompanied with each construction mode as defined in session 2 should be analyzed.

Table 1. Risk level of interchange station construction in terms of station configuration Risk level

Low

Interchange mode

Passage

Parallel

Cross

shallow/ medium normal regular

medium/ deep large regular

deep

Depth Area Layout

High

medium complicated

3.1.1 Station configuration Unlike the uniform configuration of normal metro stations, the interchange stations are distinct in excavation depth, excavation area and plan layout due to different interchange modes. The relationship between station configuration and construction risk will be discussed in terms of three different interchange modes stated above. 1 Cross-interchange As to the cross-interchange mode, because the platforms of different metro lines should be located at different levels, the stations are normally threestory or even four-story with excavation depth ranging from 20 m to 25 m in Shanghai. Such deep excavation would increase the chances of failure of the retaining structure and excess displacement of the adjacent ground. Besides, the plan layout of cross-interchange stations tend to be irregular, which is likely to result in poor arrangement of bracing and weak joints in the corners of retaining walls. Finally, if the station is not built at one time, the later-built line has to go up-through or downthrough the existing line. That would inevitably bring great threaten to the safety of the operating line. 2 Parallel-interchange For the parallel-interchange mode, though the plan layout of stations are usually rectangular, the excavation area are double or even triple of normal station, which would bring higher level of risk in excavation. However, the excavation depth could be well controlled less than 20 m as the platforms of different lines could be arranged at the same level. Similarly, if the station is not built at one time, risk will increase due to a very close distance between the existing line and the later-built line. 3 Passage-interchange Because the station of passage-interchange mode actually consists separate stations connected by passage, its construction risks are the same with normal station. Even when new lines will be incorporated later, the impact will be relatively low due to a far distance between different lines. The risk level of interchange station in terms of station configuration is summarized in Table 1.

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1 Reconstruction Regarding to the reconstruction mode, the existing station will be partially reconstructed or expanded to incorporate new lines. Thus, there must be loading or unloading effects on the existing structure induced by any construction activities operated above, beneath or aside it, which would consequently cause certain response of the early built station. According to the protecting requirements for operating metro in Shanghai, neither vertical nor horizontal displacement of the station is allowed to exceed 20 mm. Therefore, extraordinary high risks exist in the reconstruction projects of interchange station, especially in shanghai’s high sensitive and saturated soft clay ground condition. Moreover, rare experience in similar projects multiplies the potential risks. Up to now, there have been some successfully completed reconstruction projects of interchange stations in Shanghai of various type as: Century Avenue Station (parallel/up-through), Shanghai Indoor Stadium Station (down-through) and People’s Square Station (parallel). More details will be presented in session 5. 2 Built at stages Due to the limit of available contractors, labor force and equipments as well as the endurability of the environment and the public, the number of metro projects carried out during the same period should be controlled. So there are a number of interchange stations could not be built at one time. However, for built at stages mode, the needs for future expansion and measures to reduce the impacts of later-built lines are taken into consideration in structural design phase. Besides, the joint areas connecting different lines are usually built and carefully treated in advance with the first-built line. Moreover, the bid for different lines within an interchange station usually goes to the same contractor to make sure an overall organization and smooth handover between separated construction stages. For all these reasons, though there still would be impacts of the later-built line to the existing one, the risk of built at stages mode is relatively lower than the reconstruction mode. According to the statistic above, this mode is now widely adopted in new lines under construction. 3 Built at one time The construction of interchange station of built at one time mode in Shanghai is the typical deep excavation project in soft clay areas. Generally speaking, its risk is lower than the previous two modes with similar scale under identical geological and environmental conditions.

The risk level of interchange station in terms of constructioin mode is summarized in Table 2. 3.1.3 Geological conditions In Shanghai the soft clay layers are widely distributed with low strength, large compressibility and high water content. The weakest  silty clay layer and  clay layer are distributed among 7 to 20 m underground where most metro stations are located. It greatly increases the chance of failure of the retaining structure and excess ground movement during excavation. The confined water is another important risk source for deep excavation in Shanghai. It will lead to soil up-rush at the bottom when its pressure is close to the gravity of the above soils. Also, seepage may occur around the foot of retaining walls due to the water pressure and high permeability of the fine sand layer. There are three confined water layers which might affect the construction of metro station in Shanghai as follows: the sub-confined water in  sandy silt layer, the 1st confined water in  silty fine sand layer and the 2nd confined water in  sand layer. Table 2. Risk level of interchange station construction in terms of construction mode.

3.1.4 Surrounding environments As the metro network grows rapidly in downtown areas in Shanghai, it increasingly become a threaten to the safety of surrounding environments such as buildings or infrastructures during construction. The construction of interchange station bears especially high risk as they are usually located near the commercial center or other important city spots. There is a control criterion of environment protection in excavation of metro construction based on the engineering experience in Shanghai , which could be adopted as a reference to the risk assessment for the interchange station construction (Specification for Excavation in Shanghai Metro Construction, 2000). In this specification, three environment protection grades are set concerning the importance of the adjacent objects as well as the distance between the objects and the construction site. 3.2 Subjective risk factors of interchange station construction

Interchange mode Construction mode

Passage

Parallel

Cross

Built at one time Built at stages Reconstruction

low low medium

low/medium medium/high high

medium high high

Table 3.

Based on the depth and the relationship between different confined water layers, it is divided into five confined water zones in Shanghai (Liu, 2008). Risk varies in these zones for the construction of the interchange stations as shown in Table 3

Indeed, objective risk factors like technical difficulties and ground uncertainties increase the chances of project failure. However, whether the failure will occur or not is to a large extent affected by subjective factors like management and personal expertise. Both Sowers (1993) and Bea (2006) have studied

Risk level of interchange station construction in terms of geological conditions.

Risk level

Low

Confined water zone

Zone I

Zone II

Zone III

Zone IV

Zone V

thin or missing sub-confined water layer. 1st confined water −40 m to −50 m. layer locates at

1st confined water layer locates at around −30 m. 1st and 2nd confined water is connected.

1st confined water layer locates at around −30 m. water is connected.

1st confined water layer is located at shallow level.

thick sub-confined water layer. 1st and 2nd confined

Description

Table 4.

High

Risk level of interchange station construction in terms of environmental conditions.

Risk level Protection grade Environmental conditions

Low 1st-grade There are metro, municipal common trenches, gas pipes, main water pipes, important buildings or structures within the range of 0.7H* from the excavation.

2nd-grade There are important pipe lines, buildings or structures within the range of H ∼ 2H from the excavation.

*H: excavation depth.

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High 3rd-grade There is no important pipelines, buildings or structures within the range of 2H from the excavation.

a large number of well-documented cases of failing civil engineering projects. Though there is a long time span between their studies, they got similar findings that approximately 80% of the failures are caused by subjective factors like human or organizational shortcomings. As follows, functioning of risk management system, contractor experience, personnel qualification and equipment condition are discussed.

problems, it often leads to a delay in construction procedures. Subject to the pressures of a tight schedule of metro construction plan in Shanghai, overuse and insufficient maintenance of equipments are widely found among contractors.

3.2.1 Functioning of risk management system A well established and effectively functioning risk management system is essential for risk control especially in construction phase. Very important are short and efficient communication channels in conjunction with clearly defined responsibilities (Savidis, 2007). And the management of all information such as monitoring data is the core of risk management system of geotechnical projects. Unfortunately, only a part of contractors realize the importance of risk management system and are willing to put their resources into it. In many cases, careless inspection of monitoring data or slow response to emergency in poor risk management system led to serious accidents.

In this general risk assessment model for the construction of interchange station, a primary risk value Fo is first introduced concerning the objective risk factors. Then, in order to consider the impact of subjective factors, an adjustment coefficient α is deduced as well. The final risk value is obtained as follow:

3.2.2 Contractor experience Underground projects present distinct regional features because different geological conditions require different construction methods and parameters. Therefore, contractors with less experience in soft clay areas might bring about higher risk than local contractors in Shanghai. Moreover, contractors with affluent experience are more sensitive with signs of potential hazards. Thus effective measures can be timely carried out to prevent the accidents from happening or at least minimize the negative consequences as much as possible. Whereas, for the reason that the experienced local contractors are not enough for large-scale metro construction in Shanghai, imports of contractors with less experience is inevitable.

4.1

4

RISK ASSESSMENT MODEL

Both Fo and α are calculated by applying the Fuzzy Synthetic Evaluation Method and the Analytic Hierarchy Process (AHP) (Liang, 2001).

3.2.3 Personnel qualification The metro projects are mostly ground-related with high risk and strict technical requirements, which can only be done by specially trained staffs. According to the terms of relevant codes in China, certificates are compulsory for staffs participating in construction projects. For large-scale project like the interchange metro station discussed here, the project manager should have the 1st-class manager qualification and the proportion of senior professional personnel should be higher than 10% in managing group. However, due to the booming development of the metro in China, the shortage of excellent project managers and qualified technical staffs become an urgent issue. There are situations where contractors employ unqualified staffs or appoint inexperienced managers, which are reported to be the direct or indirect causes for lots of metro construction accidents in China. 3.2.4 Equipment condition Compared with other factors, although less structure failures or casualty are directly caused by equipment

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Calculation of primary risk value Fo

1 factor set The factor set for Fo is:

Where u1 is ‘station configuration’, u2 is ‘construction mode’, u3 is ‘geological conditions’ and u4 is ‘surrounding environments’. 2 weight set The weight set for each factor is:

It can be determined by AHP method. 3 comment set The comment set for Fo is:

Where v1 is ‘very high’, v2 is ‘high’, v3 is ‘medium’ and v4 is ‘low’. The value assigned to v1 , v2 , v3 , v4 is ‘4’, ‘3’, ‘2’ and ‘1’ respectively for quantification of the assessment result. 4 evaluation matrix The evaluation matrix or Fo expresses as:

Where rij is the degree of membership of factor ui to risk level vj . RF can be obtained by membership function, statistic or referring to pre-defined relationship between U and V. 5 primary risk value Fo The evaluation vector BF is calculated as:

Table 5.

Risk level of interchange station construction.

Risk Level

I

II

III

IV

Description Risk value

low 3.5

It gives the degree of membership of the target project to different risk levels. Then primary risk value Fo is:

Figure 4. Overview of Century Avenue interchange station.

4.2

Calculation of adjustment coefficient α

1 factor set For the calculation of α, The factor set is:

5

CASE STUDY

5.1 Project introduction Where u1 is ‘functioning of risk management system’, u2 is ‘contractor experience’, u3 is ‘personnel qualification’ and u4 is ‘equipment condition’. 2 weight set The weight set for each factor is:

It is determined by AHP method as well. 3 comment set The comment set is:

Where v1 is ‘poor’, v2 is ‘medium’, v3 is ‘excellent’. The value assigned to v1 , v2 , v3 is ‘1.3’, ‘1’ and ‘0.7’ respectively for quantification of the assessment result. 4 evaluation matrix The evaluation matrix for α expresses as:

5 adjustment coefficient α The evaluation vector Bα is first calculated as: It gives the degree of membership of the combining condition of subjective risk factors to different levels. Then the adjustment coefficient α is:

Century Avenue station is a 4-line interchange station for Line 2, Line 4, Line 6 and Line 9. The platforms of Line 2, Line 4 and Line 9 are parallel with the platform of Line 6 go across them above. The construction of this station is divided into three phases. Line 2 was firstly built and put into operation early in 1999. Line 4 was built years later and put into operation in 2005. Line 6 and Line 9 are now being built synchronously. The risk of construction phase 2 will be assessed in the following part. The excavation for the station of line 4 is 20.8 m in depth with an area of about 4300 m2 . The minimum distance between the retaining wall and the operating line 2 station is only 5.4 m. Because no future expansion was considered in previous design of line 2, part of the station have to be reconstructed for the connection with the new line. As to the ground profile, the soft clay is widely distributed 30 m below the ground. The 1st confined water layer is found about 8 m to the bottom of the excavation with a pressure head about 20 m. Except for the existing metro line, there are some commercial buildings and municipal pipelines near the excavation within a range of 5 to 10 m. The contractor who carried out this project holds the top qualification and has accumulated affluent experience in the underground projects in Shanghai. A web-based multilevel field monitoring and information management system was applied to this project.

5.2 Risk assessment

4.3

Calculation of risk value F

After the primary risk value Fo and the adjustment coefficient α are both obtained, The risk value F is determined by equation (1). The final risk level could refer to Table 5 as follows.

5.2.1 Risk assessment of object risk factors The statuses and rough risk levels of relevant object risk factors are summarized in Table 6 referring to the previous analysis. In order to get the weight set and the evaluation matrix, a survey was conducted among 15 experts engaged in the geotechnical engineering.

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Table 6.

Risk level of interchange station construction.

Risk factors

Status

Risk level

Station configuration

medium medium regular reconstruction zone III 1st grade

medium

Depth Area Layout Construction mode Geological Condition Surrounding environment

The evaluation vector Bα was calculated according to equation (4):

The adjustment coefficient α was calculated according to formula (5):

high medium/high high

So the overall condition of the subjective factors is ‘excellent’. The weight set AF was determined by the AHP method as follows:

The evaluation matrix RF was determined in a way that, if n experts consider the risk level of factor ui is vj , then rij is n/15. For example, after the risk evaluation of ‘station configuration (u1 )’, the number of experts who gave the comment of ‘very high (v1 )’, ‘high (v2 )’, ‘medium (v3 )’, and ‘low (v4 )’ is 1, 5, 8 and 1 respectively. So, the evaluation vector R1 is (1/15, 5/15, 8/15, 1/15). In this way, evaluation matrix RF was obtained as:

5.2.3 Final assessment result Since the primary risk value Fo and the adjustment coefficient α are both obtained, the risk value F is calculated according to equation (1):

Thus, the risk level of this project is ‘medium’ but very close to ‘high’. From the overall risk assessment, it is found that, though the risk level is ‘high’considering the objective factors, the overall risk level was effectively reduced to ‘medium’ by ‘excellent’ combining condition of subjective factors, regarding experienced contractor, effective monitoring and risk management in field. 6

The evaluation vector BF was calculated according to equation (2):

The primary risk value Fo was calculated according to equation (3):

So, referring to Table 5, the risk level is ‘high’ based on the assessment of objective factors. 5.2.2 Risk assessment of subjective risk factors The weight set Aα was determined by the AHP method as well:

The evaluation matrix Rα was obtained in a similar way to RF :

COMMENTS ON RISK COUNTERMEASURE

By the risk assessment model developed in the foregoing session, all the interchange metro stations to be built could be classified in terms of risk level. However, the ultimate target of risk assessment, which is for better decision-making to avoid or minimize the risks by corresponding countermeasures has not been touched. Here the authors provides brief comments on this concerns The risk assessment can be carried out in selecting the suitable contractors during the tendering procedure. For projects with ‘low’ or ‘medium’ risk level only considering the objective risk factors, average contractors are qualified. While for projects with ‘high’ or ‘very high’ risk level in objective view, top contractor with excellent risk management should be required to adjust the overall risk to a lower level. When the risk assessment is carried out during construction, special attentions should be given to projects with ‘high’ and ‘very high’ risk level. For ‘high’ risk, evaluation of construction methods and intensified monitoring are required. The ‘very high’ risk is generally unacceptable. Under this circumstance, temporary cease of the project may be necessary until sound countermeasures are achieved by special technical meetings or researches. 7

CONCLUSIONS

There are a large number of interchange stations going to be built according to the plan of Shanghai metro

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system in the following few years. Unlike the normal metro station, the interchange station features in complicated configuration, various construction modes, which greatly increase the risks in construction phase. The risk factors that affect the risk level of interchange station construction can be divided into objective factors and subjective factors. ‘station configuration’, ‘construction mode’, ‘geological conditions’ and ‘surrounding environments’ are four main objective factors while ‘functioning of risk management system’, ‘contractor experience’, ‘personnel qualification’, ‘equipment condition’ are four main subjective factors. From the risk assessment on Century Avenue 4-line interchange station by using Fuzzy Synthetic Evaluation Method and the Analytic Hierarchy Process (AHP), it is found that, the risk level of interchange station is generally high concerning the objective risk factors. However, a qualified and experienced contractor with effectively functioning risk management system would well decrease the overall risk level of the project. The results of risk assessment can be used for contractor selection and better decision-making to reduce or minimize the risk during the construction of interchange metro stations.

REFERENCES Bea, R. 2006. Reliability and human factors in geotechnical engineering. Journal of Geotechnical and Geoenvironmental Engineering. May 2006: 631–643. Chapman, T.J.P. & Van Staveren, M.Th. et al. 2007. Ground risk mitigation by better geotechnical design and construction management. Proc. ISGSR2007 First International Symposium on Geotechnical Safety and Risk, Shanghai, 18–19 Oct. Liang, S. & Bi, J.H. 2001. Fuzzy synthetic evaluation method of construction engineering quality grade. Journal of Tianjin University 34(5): 664–669. Liu, J & Pan, Y.P 2008. Guideline of Confined Water Risk Control in Rail Transit Construction. Shanghai: Tongji University Press. Sowers, G.F. 1993. Human factors in civil and geotechnical engineering failures. Journal of Geotechnical Engineering. 119(2): 238–256. Savidis, S.A. 2007. Risk management in geotechnical engineering projects by means of an internet-based information and cooperation platform. Proc. ISGSR2007 First International Symposium on Geotechnical Safety and Risk, Shanghai, 18–19 Oct. Wang, Q.G. 2008. Research on Deformation Prediction and Construction Control in Deep Excavation of Expansion Project near Existing Metro Transfer Station. Shanghai: Tongji University.

ACKNOWLEDGEMENTS The work presented in this paper was supported by Shanghai Shentong Group Co., Ltd. The authors gratefully acknowledge this support.

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Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Challenges in multi-hazard risk assessment and management: Geohazard chain in Beichuan Town caused by Great Wenchuan Earthquake Limin Zhang Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Hong Kong

ABSTRACT: The Great Wenchuan Earthquake of Ms 8.0 in Richter scale on 12 May 2008 triggered approximately 15,000 landslides. This paper starts with an overview of the disaster chain caused by the earthquake. It then describes four episodes of geohazards occurred during and shortly after the earthquake in Beichuan Town, a small county town in north Sichuan. In Episode I, the fault rupturing and the earthquake caused the collapse of 80% of the buildings in the town. In Episode II, one large landslide (Wangjiayan Landslide) and one rock avalanche (Jingjiashan Landslide) were triggered by the earthquake, which together buried a significant part of the town and caused the death of more than 2300 people. In Episode III, on 10 June 2008, the flood from the breaching of Tangjiashan Landslide Dam, which is located approximately 3.5 km upstream of Beichuan, flushed the town. The dam-breaching flood was greater than a 200-year return period flood. In Episode IV, on 23-25 September 2008, the loose landslide deposits near and inside the town turned into severe debris flow torrents amid a storm. The debris flowed into the town and buried much of the old town that was not affected by the two landslides and the Tangjiashan flood occurred earlier. Finally, several challenges to geotechnical risk assessment and management are posed based on the observed disaster chain.

1

INTRODUCTION

A great earthquake of magnitude 8 in Richter scale occurred in Sichuan on 12 may 2008. The strikeslip rupturing started near Yingxiu and developed towards the northeast along the Yingxiu-BeichuanQingchuan fault zone. The rupture zone was approximately 300 km long (Fig. 1, Chen 2008). The epicenter depth was between 10–20 km. Latest investigations (Huang 2008; Xie et al. 2008) show that approximately 15,000 landslides were triggered during the earthquake. The earthquake caused a casualty of approximately 80,000, of these 19,065 were students. One quarter of the total casualty was caused by earthquake-induced landslides. I am deeply saddened because all these happened in the place I lived for many years. What further touches me is the degree of damage to a single site by a chain of geohazards. It is well known that a particular site may be affected by multiple hazards, such as rockfalls, landslides, and debris flow. The Great Wenchuan Earthquake posed new challenges: multiple geohazards not only occurred at a particular site, but also developed over time as a disaster chain. Hence assessment of the risks associated with such a disaster chain becomes a dynamic problem. This paper starts with an overview of the disaster chain caused by the Wenchuan earthquake. Then four episodes of catastrophes occurred during and after

Figure 1. Rupture zone in the Great Wenchuan Earthquake and location of Beichuan. (After Chen 2008).

the earthquake in a single place, Beichuan Town, are described. Finally, several challenges to geotechnical risk assessment and management are raised based on the observed disaster chain.

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2

DISASTER CHAIN CAUSED BY GREAT WENCHUAN EARTHQUAKE

3

Figure 2 summarizes some observed disaster/event chains along the time line caused by the Great Wenchuan Earthquake. Focusing on geohazards only. Five typical types of geohazards occurred during the earthquake, namely, landslides, topplings, ejected deposits, loosened or cracked soil/rock masses, and peeled terrains covered by loose dry debris. These geohazards became more severe few days after the main shocks, caused by numerous aftershocks with eight of these larger than magnitude 6 in Richter scale. The landslides also blocked rivers and formed over 100 landslide dams. The water levels in these lakes started to rise after the earthquake. By one to three weeks after the earthquake, 34 large landslide lakes had formed and posed enormous risks to the public both downstream and upstream of the dams. While many of these landslide dams overtopped naturally, emergent engineering division measures had to be carried out for several very large ones. The Tangjiashan landslide dam is an example in which a division channel was excavated at extremely difficult conditions to reduce the risks to over one million people. The collapse of large landslide dams along Mianyuan River and Jianjiang River also caused floods larger than raininduced, 50 year-return floods, which inundated towns and cut off some major highways. Then in July and September 2008, severe storms occurred in the earthquake zone and the widespread dry landslide debris caused by the earthquake turned into wet debris flow. Such debris flow caused not only losses of lives and property, but also fundamental transformation of the natural environment. Such transformation is expected to last for many years.

MULTI-HAZARDS AT BEICHUAN CAUSED BY GREAT WENCHUAN EARTHQUAKE

3.1 Episode I, fault rupture and building collapse Beichuan Town is located in northern Sichuan (Fig. 1). By the end of 2006, the population of Beichuan County was 160,156 (Beichuan County Government 2008). Beichuan Town (Qushan Town), where the county government is located, was a quiet and beautiful town surrounded by green mountains and the Jianjiang river (Fig. 3). During the Wenchuan earthquake, which occurred at 2: 28 pm, 12 May 2008, the earthquake rupture went across the entire town (Fig. 4). The ground seismic intensity reached the 11th degree. The earthquake caused devastating damage to buildings (Figs. 4–6). In fact, 80% of the buildings in Beichuan Town collapsed and almost all of the remaining buildings were severely damaged (Fig. 5). Approximately 15,640 people in the county lost their lives (9.8% of the

Figure 3. Beautiful Beichuan Town surrounded by green mountains and a meandering river before the Great Wenchuan earthquake. (After Beichuan County Government 2008).

Figure 2. Observed disaster/event chains caused by the Great Wenchuan Earthquake.

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population) and 4,412 people were reported missing (CCTV 2008). The most tragic of all was the collapse of two five-storey classroom buildings at the Beichuan Middle School (Fig. 6, loss of more than 1000 young students (Beichuan Middle School 2008)) and the burial of the entire New Beichuan Middle

School (loss of over 700 young students and teachers, to be described later). 3.2 Episode II, Landslides After a moment of time delay, one large landslide and one rock avalanche occurred. The landslide, Wangjiayan Landslide shown in Fig. 7, is about 10 million m3 in volume. The scar is steep, wide and very high, showing the features of a typical landslide that detached from the scar as a whole piece under tensile stresses and the detached materials slid down at a high speed. The landslide debris buried a large part of a government office area in the old town. As the debris advanced, it pushed many buildings, which were already shattered by the earthquake but not buried, forward for a distance, turning these buildings in ruins (Fig. 8). The scraping power of such high speed debris was such that the shallow foundation of a building was seen to have been brought to the debris surface (Fig. 9). This landslide caused the loss of about 1600 lives: the most amount of casualty in a single geohazard event.

Figure 4. The fault zone across the entire town and severe building damage. (After Huang 2008). The extents of two large landslides can also been seen, which affected a significant part of the town.

Figure 5. Beichuan Town shortly after the earthquake. (After Xinhua News Agency, 16 June 2008).

Figure 6. Ruins of Beichuan Middle School after the earthquake. Over 1000 young students lost their lives.

Figure 7. Wangjiayan Landslide in Beichuan Town, which killed 1600 people. (After Yang et al. 2008).

Figure 8. Wangjiayan Landslide in Beichuan Town. The landslide debris not only buried numerous buildings but also pushed a number of buildings forward for a distance.

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Figure 9. The high-speed debris from Wangjiayan Landslide brought the shallow foundation of a building to the debris. Figure 12. Tangjiashan Landslide, Tangjiashan Landslide Lake, and Beichuan Town. (After Yang et al. 2008).

Figure 10. Jingjiashan Landslide in Beichuan Town, which buried the Beichuan Middle School, killing approximately 700 people, mainly young students.

Figure 13. Tangjiashan Landslide, which is 30 million m3 in volume. (After Yang et al. 2008).

Beichuan Middle School, leaving approximately 700 young students and their teachers in the darkness.

3.3 Episode III, flooding from breaching of Tangjiashan landslide dam

Figure 11. Jingjiashan Landslide in Beichuan Town. Large rock blocks are seen in this picture, three blocks being sufficient to fill a basketball court.

The rock avalanche, Jingjiashan Landslide, was also about 10 million m3 in volume (Figs. 4 and 10). The rock avalanche is characterized by the falling of a large quantity of rock blocks with diameters larger than 5 m (Fig. 11). The avalanche buried the New

The end of earthquake was not yet the end of geohazards exposure. During the earthquake, a large landslide occurred at Tangjiashan, about 3.5 km upstream of Beichuan Town (Fig. 12). Similar to the Wangjiayan landslide, the Tangjiashan landslide is a whole-piece, high-speed landslide detached from a wide and steep scar (Figs. 12 and 13), with the materials falling down for a vertical distance of approximately 500 m. The landslide deposit measures 611 m along the sliding direction and 803 m in the perpendicular direction, and approximately 20.4 million m3 in volume (Liu 2008). The landslide cut off the Jianjiang river and formed a large landslide dam 82–124 m high (Figs. 12 and 13). In the three weeks following the earthquake, the landslide lake was filled at a rate of approximately 110 m3 /s. By 9 June 2008, the lake volume reached 247 million m3 (water level = 742.58 m). When full the lake capacity would be 316 million m3 (Liu 2008).

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Figure 14. Breaching of Tangjiashan Landslide Dam on 10 June 2008. The peak flow rate reached 6500 m3 /s at 11:30 am and the corresponding lake water level was 735.81 m. (After Gang Li, Xinhua News Agency, 10 June 2008).

Figure 16. Remains from the flood from the breaching of Tangjiashan Landslide Dam in Beichuan Town. The watermarks can be clearly seen on the third floor of a building.

Figure 15. The flood from the breaching of Tangjiashan Landslide Dam passed Beichuan Town, 12 noon, 10 June 2008. The peak flow rate reached 9780 m3 /s; the flood water level was 629.54 m. (After Gang Li, Xinhua News Agency, 10 June 2008).

The lake posed enormous risks to 1.2 million people downstream. A well organized emergency division program was implemented under the leadership of Mr. Ning Liu, Chief Engineer of the Ministry of Water Resources, during 25 May–11 June 2008. Meanwhile, approximately 250,000 people downstream were evacuated. The dam finally breached in a controlled manner on 10 June 2008 (Fig. 14). The peak flow rate reached 6500 m/s, which was similar to a flood of 200-year return level (6970 m3 /s) (Huaxi Metropolitan News 2008). When the dam-breaching flood reached Beichuan Town, the peak flow rate reached 9780 m3 /s, which was larger than a 200-year return flood. The old town was severely flooded (Figs. 15–17). In particular, the Jianjiang river makes a turn inside the town, creating a higher flood water level on the side of the old town (Fig. 15). The water marks can be clearly seen on the third floor of a building in Fig. 16. The flood inundated much of the old town, flushing building debris into the town. The debris jammed completely the roadway, which was open and played a critical role during the rescue period (Fig. 17).

Figure 17. Building debris that was brought into Beichuan Town by the flood from the breaching of Tangjiashan Landslide Dam. Also shown in this figure are the building damage by the earthquake and a rock avalanche front on the right. Quake collapse, landslide and flooding debris in the same scene: what else could possibly be more?

Fortunately, all the people in the town who survived through the earthquake were evacuated about two weeks after the earthquake for infective disease and biological control; hence no casualty was resulted from the flood. 3.4 Episode IV, debris flow The earthquake in May 2008 caused numerous landslides and rock avalanches. Much of the landslide or avalanche deposits spreading on the hilly terrains are at a marginally stable condition, and are highly erodible. On 23–25 Sept. 2008, a severe storm brought about 190 mm of rainfall, which caused widespread debris flow torrents. A severe debris flow from Weijiagou, a gully in the southwest of the town, as well as that originated from the Wangjiayan landslide deposit (Fig. 13), bursted into the old town. A large part of the old town that was not affected by the landslides and the Tangjiashan dam-breaching flood, was now buried

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Figure 20. Timeline of geohazards in Beichuan Town.

Figure 18. Beichuan Town after the massive debris flow on 24 Sept. 2008.The buried part was planned as a Memorial Site to memorize those who lost their lives. (After China News Agency, 25 September 2008).

deposits and loosen terrains is likely to continue in years to come. Experiences with the Ch-Chi earthquake (ML = 7.3) in Taiwan in 1999 (Lin et al. 2008) show that the occurrence of major debris flow torrents during two typhoon events after the Chi-Chi earthquake was more than doubled compared with that prior to the earthquake. Transformation of the river system took place in the course of debris flow and general soil erosion. It appears that our ability to identify possible hazard scenarios is still limited and that we have to live with the unexpected. May peace upon the ceased. 4.2 Risk assessment The risk assessment process answers three questions (e.g. Ayyub 2008): (1) What can go wrong? (2) What is the likelihood that it goes wrong, (3) What are the consequences it will go wrong. The question ‘What can go wrong’ is addressed in hazards identification. The risk associated with multiple hazards can be expressed as

Figure 19. Beichuan Town after the massive debris flow on 24 Sept. 2008. The debris is seen to have contributed from Wejiagou Gully behind the town and Wangjiayan Landslide. (After China News Agency, 25 September 2008).

(Figs. 18 and 19).Again no casualty was resulted inside the town because all the people were evacuated in later May. 4 4.1

CHALLENGES TO GEOHAZARDS RISK ASSESSMENT AND MANAGEMENT Hazards Identification

A first lesson learned through the Great Wenchuan Earthquake is the need to re-assess risks faced by cities and communities located in high seismic zones or exposed to high-risk geohazards. A critical task in risk assessment is the identification of possible hazards that may affect the elements under concern. The time line for the four scenarios of geohazards reported in the above sections is shown in Fig. 20. Is the debris flow in Episode IV the end of hazards for Beichuan Town? Obviously, unexpected geohazards may occur in the future: the four episodes reported in this paper were largely unexpected years ago. Smaller earthquakes can occur in the foreseeable future. Some large landslides may reactivate due to rainfall infiltration or other triggers. Debris flow from the landslide

where pi is the occurrence probability of an hazard event i out of n possible events; vi is the vulnerability of the element at risk to the ith hazard; and ci is the element at risk given the occurrence of the ith hazard. The Beichuan Town hazard scenarios show that: (1) The hazard events are highly correlated. The outcome of one event (e.g. landslide) is the cause of other events (formation of landslide dams, dam breaching, debris flow etc.), the lead cause being the strong earthquake. (2) The events do not necessarily occur at the same time. They evolve as a disaster chain (Figs. 2 and 20). (3) The vulnerability to each event may be different. For example, the earthquake and landslide scenarios came without any warning and thus resulted in enormous loss of life, whereas dam-breaching flood and debris flow caused little casualty due to the sufficiently early warning and evacuation of the population at risk. (4) The selection of a proper benchmark recurrence period for a hazard type is an important decision for risk analysis. The occurrence probability of the root cause (strong earthquake) is extremely small (approximately 2000-year return period in the case of the Great Wenchuan earthquake). If a systematic risk analysis were conducted considering the

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possible run-down distances of the two large landslides (Figs. 4, 7 and 10) and the debris flow (Figs. 18 and 19), the safe distance to the fault rupture (Fig. 4), and the zone susceptible to flooding (Figs. 15–17), then almost the entire town would not be inhabitable. Note that the Chinese Code for Geotechnical Engineering Investigation GB50021-94 (Ministry of Construction 1995) recommends the following safe distances to strongly active faults with the potential to cause earthquakes greater than magnitude 7 in Richter scale: 3000 m for designs to 9th degree intensity, and 1000–2000 m for designs to 8th degree intensity. The Code also recommends that important constructions should not be on the upper plate near the rupture. Similar situations in many towns in the quake zone make decisions on reconstruction planning very difficult.

4.3 Risk management The risk management answers the questions of (1) what can be done to reduce or control risk and (2) what are the impacts of any proposed solutions on the risk profile of the system (e.g. Ayyub 2008). The first question can be answered through the reduction of one or more of the three risk components: occurrence probability of hazard, vulnerability, and element at risk. Several issues or challenges in dealing with the two questions are as follows: (1) Reducing the occurrence probability of hazards requires the identification and strengthening of a large number of natural or manmade slopes to a tolerable level. While some landslide hazards will certainly be mitigated and some slopes will be stabilized, it is not likely a great number of features can be identified and strengthened. (2) Again the selection of a proper benchmark hazard recurrence period for engineering design is a difficulty decision. A large area suffered from damage of 8th-11th degree during the Wenchuan earthquake (2000-year event), while the original design seismic intensity was mostly 7th degree based on a hazard level that has a 10% probability of exceedance in a 50-year exposure period (475year return period). Although a design intensity of 8th degree has been adopted for reconstruction works, there is still a shortfall. A cost analysis often does not allow the use of the severe earthquake event actually happened as a benchmark for design. There must be a trade-off between risk and costs. The construction of the New Orleans Hurricane Protection System offers an example. While Hurricane Katrina in August 2005 was a 400-year event, the new system is designed for 100-year level events from a cost-benefit point of view (USACE 2006). (3) Now that the hazard occurrence probability cannot be reduced significantly due to economic concerns, a more effect way to risk mitigation is the

lowering of vulnerability. Since earthquake disasters may not be forecasted in a near future and the people are to live with disasters in high-risk zones, measures for vulnerability reduction at the community level (safe islands etc.) are called for. While forecasting of earthquakes is a formidable task, it is possible to monitor and predict the development of after-quake disaster chains (Figs. 2 and 20). The mitigation of Tangjiashan Landslide Dam risks (Figs. 12–17) is a successful example. (4) When risks cannot be reduced to a tolerable level or cost-benefit cannot be justified, there is a need to reduce the elements at risk, i.e., to relocate permanently the residents in areas susceptible to nearfuture disaster chains. This is often proved not quite viable considering various negative social impacts (e.g., separation of family members, loss of familiar communities, job market etc.). (5) There is a need for effective risk education and communication on several issues during the reconstruction period: (a) Cost-benefit evaluation of new design intensity when it is smaller than that actually happened; (b) Keeping earthquake vulnerability in mind in city planning; (c) Relocation or reconstruction at it is; (d) Use of potentially more dangerous new sites.

5

SUMMARY

The geohazard chain in Beichuan Town, particularly four episodes of catastrophes during and shortly after the Great Wenchuan Earthquake is described in this paper. The hazard events did not occur at the same time; instead these events evolved as a disaster chain with possibly unknown future events. The hazard events are highly correlated. The outcome of one event (e.g. landslide) is the cause of other events (formation of landslide dams, dam breaching, debris flow etc.), the lead cause being the strong earthquake. The earthquake actually happened was an extreme event (approximately 2,000-year event) that caused the loss of 80,000 people. The public has witnessed the cruel fact but has yet to accept smaller hazard events for future design and construction. All these raise challenges to risk assessment and management in a multi-hazard environment.

ACKNOWLEDGMENTS The author would like to acknowledge the assistance from Prof. Chang-Rong He of Sichuan University, who arranged a trip for the author to visit Beichuan shortly after the Great Wenchuan Earthquake. Profs. RunQiu Huang of Chengdu University of Technology and Wei-Lin Xu of Sichuan University provided valuable information. Mr. Yao Xu, Miss Melissa Zhang, and Ms Jinhui Li proof read the manuscript. The financial support from the Research Grants Council of Hong Kong (Project No. 622207) and the Hong Kong

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University of Science and Technology (Project No. RPC06/07.EG19) is also gratefully acknowledged. REFERENCES Ayyub, B.M. (2008). A risk-based framework for multihazard management of infrastructure. Proc. International Workshop on Frontier Technologies for Infrastructures Engineering, 23–15 Oct. 2008, National Taiwan University of Science and Technology, Taipei, S.S. Chen and A. H-S. Ang (eds.), 209–224. Beichuan County Government. (2008). Beichuan county population statistics. http://beichuan.my.gov.cn/bcx/ 16581690 87802474496/20080617/305295.html. Beichuan Middle School (2008). Earthquake relief for Beichuan Middle School. Online: http://bczx.changhong. com/. CCTV (2008). Beichuan casualty statistics. The China Central Television. 23 June 2008. Chen, Y.T. (2008). Mechanisms of Wenchuan earthquake. Keynote lecture, Forum on Earthquake Relief and Science and Technology, Chinese Academy of Sciences, Chengdu, 25 July 2008. China News Agency. (2008). 25 September 2008. Huang, R.Q. 2008. Preliminary analysis of the developments, distributions, and mechanisms of the geohazards triggered by the Great Wenchuan Earthquake. State Key Laboratory of Geohazards Prevention and Geological Environment Protection, Chengdu University of Technology, Chengdu, China.

Huaxi Metropolitan News. (2008). Tangjiashan division channel can pass floods of 200 year-return period. 25 June 2008. Lin, M.L., Wang, K.L., and Kao, T.V. (2008). The effects of earthquake on landslides – A case study of Chi-Chi earthquake, 1999. Landslides and Engineered slopes, Chen et al. (eds.0, Taylor & Francis Group, London, 193–201. Liu. N. (2008). Landslide dams in Wenchuan earthquake and risk mitigation measures. Keynote lecture, Forum on Earthquake Relief vs. Science and Technology, Chinese Academy of Sciences, 25 July 2008, Chengdu, China. Ministry of Construction. 1995. Commentary – Code for Investigation of Geotechnical Engineering, GB50021-94. Ministry of Construction, Beijing. United States Army Corps of Engineers (USACE). 2006. Performance Evaluation of the New Orleans and Southeast Louisiana Hurricane Protection System. Draft Final Report of the Interagency Performance Evaluation Task Force, Volume I – Executive Summary and Overview. 1 June 2006. Xie, H.P., Deng, J.H., Tai, J.J., He, C.R., Wei, J.B., Chen, J.P., and Li, X.Y. (2008). Wenchuan large earthquake and postearthquake reconstruction-related geological problems. Chinese Journal of Rock Mechanics and Engineering, Vol. 27, No. 9, pp. 1781–1791. Xinhua News Agency. (2008). 10 June 2008. Xinhua News Agency. (2008). 16 June 2008. Yang, X.G., Li, S.J., Liu, X.N., and Cao, S.Y. (2008). Key techniques for emergent treatment of earthquake induced landslide dams. State Key Laboratory of Mountain Rivers and Environment, Sichuan University, Chengdu, China.

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General sessions Design method (1)

Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

A study of the new design method of irrigation ponds using sheet materials M. Mukaitani, R. Yamamoto & Y. Okazaki Takamatsu National College of Technology, Takamatsu, Japan

K. Tanaka Naruto surveying & designing co., ltd., Naruto, Japan

ABSTRACT: There are two hundred ten thousand of ponds in Japan. Most of all ponds became too old, damaged by natural disastars and spread of house building. When we repair the pond’s dike, we can not get soil materials from nearby mountains. Nobody is permitted to get from mountain’s soil with license, because of environmental problems. Many types of industrial sheets are developed after 1970’s. We must make the new design method of pond dike using sheet materials. Most pond dike’s slope failures are caused by the shear strength on between main slip layer’s soil and sheet material. Then, the shearing mechanisms of dike’s soils on sheet material are important. This paper treats the considerations of dike’s slope by viewpoint of the infinite slope method, application for the in-situ case study, a comparative study of ordinary design methods and progress of seepage line. Firstly, we considered the infinite slope method on simple type of slope stability and clarified the safety factor’s relation between the proposal method and traditional slope stability. We formularized the seepage line of progress of soil on the sheet material. We clarified that the seepage line is described a parabola.

1

INTRODUCTION

This paper treats the new design method of irrigation ponds using sheet materials. There are 210 thousand of ponds in Japan. If the pond is repaired against too old or the earthquake-resistant, we must seek dike’s materials. The dike of the irrigation pond is consisted of the covered soil, the filter soil and the core soil. It seems that we can’t get dike’s materials so easily. Top 5 prefectures make up over 50% of the irrigation ponds in Japan. These are Hyogo, Hiroshima, Kagawa, Yamaguchi and Osaka prefecture. The newly construction method of pond is made by the center core type. The old pond is improved by the front core type. The front core type pond needs lot of dike’s materials. From environmental view point, it is difficult to get newly dike’s materials from the near-by mountain area. In solitary island and island area, it is more difficult to get them. Because of above mentioned reasons, we must investigate the dike improvement method with low-cost and using low volume of newly materials. The dike improvement work is not used large scale construction machines in country area, where the irrigation pond does not have the big volume. We have been used the waterproof sheet material which made in factories after 1960’s. There are many kinds of waterproof sheet materials. These are imported from other countries and lot of types of structural design by each company. It is needed that the proper design method and the check system are clarified against the pond’s improvement work

(Tanaka (2007), Mukaitani (2008a, b and c)). When we designed the improvement work of the old pond, design problems are experimentally solved in each engineer. In this paper we would like to give our opinion about the newly design method of the old pond using the waterproof sheet material which has lately become a subject of special interest. 2

SUMMARY OF THEORETCAL ANALYSIS

Fundamental formula of theoretical analysis is based on the infinite slope stability. In this section, we make the assumption that the soil condition of the dike on the waterproof sheet material is as well as the infinite slope. R. M. Koener and D. E. Daniel (1997) proposed the dike’s analysis using the finite slope method including the waterproof sheet material. Manufacturing companies show lots of technical notes and the soil sliding model with consideration of the material’s tensile strength. We proposed the newly infinite slope stability which can be considered the parallel submergence ratio called PSR, the back side seepage pressure, the seepage pressure and the cohesion of the soil. The PSR and horizontal submergence ratio called HSR are determined by Koener et al. For example, when the PSR is zero, the groundwater level is equal to the bottom of the slope soil column on the waterproof sheet material. If the value of PSR is one, it means that the groundwater level is equal to the top of the slope soil column.

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Figure 2. Schematic diagram of a typical case study. Figure 1. Schematic diagram of infinite slope stability.

When water is filled in the pond, the value of PSR is over one. In slope stability, most dangerous groundwater condition shows that the value of PSR is greater than zero and less than one. We determined the general equation of the safety factor of the infinite slope above considered problems as follows;

where PSR = hw /h, Z is the vertical height of the covered soil layer, α is the coefficient of the back side seepage pressure which determined by c
/(γw · h · tanϕ
) , β is slope angle of waterproof sheet material, and c
and ϕ
are strength parameters of the covered soil. The α indicates the value from zero to one. We had better adopt the α less than 0.5. The seepage water pressure fh is determined as follows;

3 A TYPICAL CASE STUDY OF FAILURED DIKE In this case, c
and α are equal to zero because of the conventional analysis. Figure 2 shows the schematic diagram of the failure dike. The failure of the pond dike was occurred by the continuous rainy days and the high level water of near river, which made the seepage pressure in the slope’s soil layer on the waterproof sheet material. When the value of PSR is zero, the safety factor from equation (1) is given 1.019. When the value of PSR is 0.5, the safety factor is given 0.714. When the value of PSR is one, the safety factor is given 0.483. If the pond is filled with water, the safety factor is recovered to 1.019. The pond which is filled with water is most stabilized. We investigated that the influence on the safety factor of the slope length between the conventional infinite analysis and Koener’s method.

Figure 3. Relation between safety factors and slope length.

Figure 3 shows relation between safety factors and slope length. In this paper the safety factor by Koener’s analysis is called F. The safety factor of Fs by our infinite method show constant value of 1.019 against the change of the slope length. The safety factor by Koener’s method decreases with the slope length growing. The relation between the safety factor by our infinite method and Koener’s F is determined as follows;

We compare the margin of error by each method on 10 m of the slope length. The safety factor by Koener’s method is 6.6% greater than our one. Our conventional infinite method gives the low value of the safety factor. We can get a little safety designing against the changes of environment immediately. Figure 4 shows the relation between the safety factor by our proposed infinite method and PSR under variation of the α from zero to 0.3. This figure shows that the safety factor is affected by the existence of the back side seepage pressure or the groundwater level in the soil layer on the waterproof sheet material. We think that many slope failure using the sheet materials were affected by the existence of α or seepage water pressure. When the bottom of pond is partially saturated, the possibility of slope failure rises up. The drainage system is needed against the groundwater nearby the bottom of pond.

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Figure 5. Schematic diagram of seepage line on the slope soil layer by rainfall.

Figure 4. Relation between Fs and PSR under variation of α.

The covered soil on the waterproof sheet material has low value of cohesion. The covered soil has ten blows of the standard penetration test value by compaction work at the dike slope. The 5 kN/m2 of cohesion is needed by our infinite analysis against the normal slope of the pond dike. The cohesion on the slope is raised using the cement mixing method. We proposed that the cohesion under wet condition of unsaturated soil is equal to the thickness of the slope. This investigation will treat another paper. 4

COMPARISON WITH TECHNICAL NOTES BY MATERIAL’S COMPANIES

There are two groups of companies of the waterproof sheet materials. One is made by the rubber sheet. Another is made by the bentonite sheet. 4.1 Finite slope satiability using the mixed analysis This method is adopted by companies of the rubber sheet. After the countermeasure of bottom soil’s improvement is treated, they calculate the resistance based on the passive earth pressure. This view point is similar to the calculation of the cantilever retaining wall. The tensile strength of sheet is not considered. The fatal defect of this concept is not considered the changing of water level in the slope soil layer. 4.2 Infinite slope satiability considering with reinforced sheet and soil layer

5

CALCULATION OF SEEPAGE LINE IN THE POND’S DIKE UNDER RAINFALLL

We focused two points before calculations of seepage line in the pond’s dike under the rainfall. One is needed conventional assumptions and that formula is abele to be adapted to the general slope problems. Another is needed that it is easily calculated safety factor in the construction work at pond’s dike. Figure 5 shows the schematic diagram of the seepage line on the slope soil layer under the rainfall. We focused the column on the slope. In the following, it shall be assumed against the analysis of the seepage line; 1) The sedimentary condition is assumed the horizontal deposit. 2) The coefficient of horizontal permeability; kh is greater than the coefficient of vertical permeability; kv . The coefficient of storage in the covered soil layer is determined by (1 − 1/a). Therefore, if the value of inflow is one, the value of outflow is 1/a. 3) The anisotropy of permeability is assumed that kh /kv is normally 25 by the Japanese recommendation for design of irrigation tanks (2006). 4) The value of the seepage velocity by rainfall; v is assumed from 2 to 3 mm/hr. The seepage velocity by rainfall and the rainfall intensity have a simple proportional relation. The volume of inflow is assumed about 26% for decomposed granite soil. We will explain this in the Figure 5, the coordinate origin is decided at the top of slope. The seepage line in the slope on the waterproof sheet material is calculated as follows;

This method is adopted by companies of the bentonite sheet. The safety factor is calculated with the tensile strength of sheet on the slope. If the sheet has the open area like the geogrid, the soil penetrates to the sheet material. The fatal defect of this concept is not considered the changing of water level in the slope soil layer, too. In this case Koener’s method gives 1.26 of the safety factor.

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where D is output water level, Z0 is input water level and Xmax is the peak value of water level in the slope. The Xmax is calculated by following formula;

The equation shows that the Xmax is affected by D, β and L. We must above mention the seepage line to our proposed PSR. PSR is calculated by following formula;

where Dmax is the thickness of covered soil layer on the waterproof sheet material. The area under seepage line is calculated by the integration of equation (4). 6

CONCLUSIONS

Many small scale irrigation ponds must be repaired. It is necessary to calculate easily at in-situ and economically. This paper proposed the conventional analysis using the infinite slope stability. The pond’s dike will repair using the waterproof sheet materials. The soil layer’s stability on the waterproof sheet material must be reconstructed more carefully. In Japan, heavy rainfall will be happened in one year. The accident in dike’s construction must be preventing as much as possible. The seepage pressure makes the slope failure which

is not so filled in soil layer. The effects of the bench cut under the sheets and the taper of covered soil’s layer on the sheet are must be investigated. These items are often considered in slope works. We continue the applications against in-situ problems and the failure slope data. REFERENCES Koerner, R.M & Daniel, D.E. 1997. Final Covers for Solid Waste Landfills and Abandoned Dumps, Thomas Telford Ltd. Tanaka, K. & Mukaitani, M. 2007. The new design method of irrigation ponds using sheet materials (part 1), Proc. of domestic annual conference for geotechnical engineering, JGS of Shikoku brunch, 87–88. (in Japanese) Mukaitani, M. & Tanaka, K. 2008a. The new design method of irrigation ponds using sheet materials (part 2), Proc. of domestic conference on disaster prevention engineering, JSCE of Shikoku brunch, 55–60. (in Japanese) Mukaitani, M. & Tanaka, K. 2008b. The new design method of irrigation ponds using sheet materials (part 3), Proc. of domestic annual conference for civil engineering, JSCE of Shikoku brunch, 212–213. (in Japanese) Mukaitani, M. & Tanaka, K. 2008c. The new design method of irrigation ponds using sheet materials (part 4), Proc. of domestic symposium for geotechnical problems and environment, JGS of Shikoku brunch & Ehime Univ., 63–68. (in Japanese) Recommendation for design of irrigation tanks, 2006 The Japanese society of irrigation, drainage and rural eng. (in Japanese)

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Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Research on key technique of double-arch tunnel passing through water-eroded groove Y. Chen Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, China

X. Liu School of Civil and Architectural Engineering, Central South University, China

ABSTRACT: In excavation of double-arch tunnel, there exists a big water-eroded groove. The method of elastic foundation beam is used to cope with the situation. According to the relationship of foundation beam with tunnel structure and scene case, the mechanical behaviour of double-arch tunnel passing through water-roded groove is studied by using finite element numerical simulation method. The research result shows that the interface of two different foundation mediums is worst point of foundation beam, cutting damage and ripping damage easily happen here; the physics property of filling matter in water-eroded groove has distinct influence to the foundation beam, to consider fully the carrying capacity of filling matter is reasonable; setting invert is good to improve internal force state of tunnel structure, but the action is no big to share the load of foundation beam. 1

GENERAL INSTRUCTIONS

Since there is a big water-eroded groove in excavation of tunnel, the choice of traversing method becomes critical. In practical tunneling engineering, the existence, location and size of water-eroded groove is difficult to be judged because of the limitation of geologic investigation, so relevant traversing method according to the actual condition is only when the problem happens instead of a design special for big water-eroded groove. This way is available to single tunnel because of its simple structure. However, to double-arch tunnel, a special design is necessary, considering the difficulty in the excavation caused by the complicated structure and more important, the influence to the stability by the construction. Therefore, taking the structure characteristics of double-arch tunnel in water-eroded groove into account, the writer get the available solution by calculation and analysis for setting foundation beam combined with the design and construction of practical engineering.

2 THE RELATION BETWEEN DESIGN AND CONSTRUCTION OF DOUBLE-ARCH TUNNEL In the construction, a middle pilot heading is finished firstly in order to support the arch ring at both sides. The middle wall is at a disadvantage stress state since its two sides is not tight to the surrounding rocks thus causing independent deformation. Commonly, it is not

Figure 1. Construction steps of double-arch tunnel.

suitable to construct the both tunnels at the same time in order to avoid long-span at the same cross-section that influences the stability of surrounding rock. So the idea of construction scheme is that excavate the one-side single span firstly. As a consequence, the horizontal force of the first-finished arch ring makes the middle wall bear marked bias, which is disadvantage to the middle wall without lateral rock resistance. Apparently, the middle wall is the key in this kind of tunnel construction. Construction steps are showed in fig 1. From the view of design, there are two kinds of structural stress state in the construction of doublearch tunnel, namely single span state and double span state.The middle wall is under a disadvantage bias condition in the first-finished single span lining and this

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bias disappears since the final-finished double span lining is a balanced construction, so apparently the single span state is the most disadvantaged condition. In the design and construction should reflect this characteristic to ensure the safety. So the emphasis in the design is the state of single span. 3

the width of the wall bottom by 15 cm to 35 cm. 5 m is remained on the both end of the beam to put on the bedrock(IV grade wall rock) and the middle piece of the beam is put on the groove’s filler. So this is a elastic foundation beam setting on different foundation. 3.2 Design of tunnel’s support structure and load of elastic foundation beam

DISCUSSION OF ENGINEERING CASE

Tong you Mountain tunnel, major project in GuangXi South 2 belt highways, is 445 m in length. The area is in karsts developing district where limestone is widely distributed and dissolution groove and crack is common. Dissolution geode is commonly seen in dolomite which form anomalistic cast groove along the joint plane. Being limited by landform and landmark, the tunnel is designed as double-arch structure, meeting the demand of connection of road at the tunnel opening, which is excavated at a clear width of 28.56 m and a clear height of 8.92 m. In the part of K2 + 312 ∼ +332 of the tunnel, there is a big water-eroded groove, 20 m in longitudinal width, displaying an oblique tunnel axis along the direction northeast-southwest and it is passed through by the cross section of the double-arch tunnel. The part of water-eroded groove, belonging to shallow-buried segment, is about 20 m in buried depth. Its cover is clay adding detritus in which 20–40% belongs to dolomitic limestone whose corrosion surface is clear. The clay, having delicate and plastic structure, obviously is the filling of the groove and this kind of filling is compacting and its bearing capacity is about 150–180 Kpa. Its natural unit weight is γ = 16 ∼ 17 kN/m3 and there is no influence on groundwater. To prove the influence range of the bottom of the groove, we drilled to 17 m under the tunnel’s bottom and stopped since it is also bottomless. 3.1 Water-eroded groove span scheme and elastic foundation design The main method of water-eroded groove crossing is filling or span etc[13,14] . The range of this tunnel’s groove is deep, so the technical requirement to the filler of grouting reinforcement is high and objective effect cannot be guaranteed easily. Through careful research, the way of erecting beam crossing is decided to adopt. This method can ensure that there is no longitudinal or transverse crack along the lines caused by the weakening of the bearing strength of the basement in the structure of double-arch tunnel thus creating condition to guarantee the high quality of the tunnel. To make the tunnel pass safely, there is a strip reinforced concrete beam (foundation beam for short) across the groove in the base of right wall, left wall and middle wall. The beam is 30 m-long and 1 m-high. To detract the stress on the base of the wall, the width of the foundation beam in the side-wall is designed to 1.3 m and that of middle wall is 2.7 m, all go beyond

The tunnel’s support structure is compound lining. Initial support is a combined support including wire mesh, anchor and shotcrete. Double level of φ6 mat reinforcement is set in the whole cross section of the arch wall. The space between the mat reinforcement is 25 cm * 25 cm. The anchor arm is 3 m-long 22 reinforcement and its longitudinal space is 1 m and 1.2 m in ring space. The shot Crete is C20 concrete and it is 25 cm thick[15] . In order to make the surrounding rock stable (especially the clay filling of the water-eroded groove), advanced small pipe grouting support is set, 4.5 mlong φ42 steel pipe is arranged along the tunnel arch ring, one ring every longitudinal 2 m and the ring distance is 35 cm. Meanwhile “I” 18-type steel arch timbering and the longitudinal distance is 0.5 m. Secondary lining design is determined by analysis of load-structure model calculation. Considering that primary support is under a certain load of surrounding rock and also small duct grouting is taken in the assisting construction measures that help to reduce the stress of surrounding rock, so 80% of the overlying soil weight is used as the vertical load of secondary lining and the lateral pressure is comparatively treated. But there is no lateral pressure in the middle wall in the altitude rang of middle pilot heading. According to the actual situation, the most unfavorable loading state is taken namely single-span structure calculation as shown in fig 2. After the calculation of lining structure, the result of foundation pressure (per running meter) is 2460 kN in middle wall and 2200 kN in side wall. The load on the foundation beam is 2460/(2.7 × 1.0) = 911 kN/m2 in the middle wall whose foundation beam’s width is 2.7 m and 2200/(1.0 × 1.0) = 2200 kN/m2 in side wall whose foundation beam’s width is 1.0 m.

Figure 2. Lining counting sketch.

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3.3

Counting and analysis of elastic foundation beam

Since the water-eroded groove’s filling and bedrock on the end of the foundation beam is two completely different medium, it is a problem about solving elastic foundation beam basing on different foundation. Finite element displacement method programming calculation is adopted and the assumption of simulation foundation’s sedimentation deformation by Winkler. fig 3 is the calculation graphic formulas and Table 1 is the calculation parameter. Put the max internal force and deflection of the foundation beam into the Table 2. Take the middle wall as an example and the internal force and deflection is listed in the Picture 4. From the result of calculation, it can be seen that the max shearing force happen at the fifth point, the point of intersection between the bedrock and the filling of the groove, according to the Fig. 3 and it shows that this has the greatest possibility of shear failure.Absolute maximum moment happen at the forth point and also at the junction. What’s more, it is negative moment which may make the superior margin of the beam have tension failure. All these should be paid to great attention in the reinforcement design. The max deflection happens at the mid span of the beam. However, this cannot form dangerous crosssection since the moment and shearing force are both very little. It should be illustrated that the length of foundation beam on the base rock of the two ends has great impact on the internal force state of the beam, long indwelling leading to waste and short to unsafe and both over long and over short can make the internal force unreasonable distribution. Since the groove should be treated as soon as possible to avoid collapse accident, there is no time for further analysis. Optimization treatment of proportion between indwelling length of the beam on the base rock and aspect of cross section is suggested in similar project. From the table 2, it can be known that the max positive and negative moment is separated by 19% that means further adjustment of the length of the whole beam or proportion of the aspect of the cross section is allowed. However, that in the middle wall is only 1.4% showing the reasonable design parameter.

3.4 Discussion about invert Invert and lining is divided into first done and later done. If do the invert later, the foundation beam will bear all the overlying pressure and the structure calculation is without the invert. If do the invert first, part of the pressure is separated make the stress on the beam decreased and now, the invert is involved in the calculation. To ensure the actual influence of this kind of Table 2. The max internal force and flexibility of the foundation beam. Mmax /(kN.m) Point 4 Point 4

−1662 −1663

Point 8 Point 8

1410 1687

Notice: points in the table see figure 5; Mmax – Absolute Maximum Moment, Qmax – Absolute Maximum Shear, Wmax-Maximum Deflection; A positive/negative bending moment causes compression/extension of the top fibres of a beam; a positive shear will tend to rotate each portion of the beam clockwise with respect to its other end, otherwise is negative.

Figure 3. Counting pattern of elastic foundation beam. Table 1.

In order to discuss the influence of fillings to the internal force state of the foundation beam, comparing calculation is taken among different fillings. Take the middle wall as an example, after regression treatment, and the result is shown in fig 5. Shown in the fig 5, there is a higher-correlation power function relationship between the max positive and negative moment and elastic coefficient of the fillings, namely value K. When the value K becomes small, the growth speed of the max moment gets higher. Especially when the value K becomes small to some degree (30 MPa/m), the max moment increases dramatically and the negative moment becomes more obvious than the positive moment. No matter how the elastic coefficient changes, the action point of the max negative moment is always on the fourth point, namely the edge of the groove. Therefore the junction of two different foundations medium is the easiest to damage place and the superior margin of the beam is easier to damage. And with the decrease of the value K, the max positive moment gradually moves to the mid span and eventually happens at the mid span. This shows that the groove fillings have important impact on the adjustment of the distribution of the moment of the whole beam.

Counting parameters of foundation beam.

Location of beam

The section of beam (m) (long × high)

Side wall Middle wall

1.0 × 1.0 2.7 × 1.0

Elastic foundation coefficient (MPa/m) Rock of grade IV

Cave clay medium

Elastic modulus (MPa)

Unit weight (kN/m3 )

Vertical load (kN/m2 )

350 350

100 100

2.85 × 104 2.85 × 104

25 25

2200 911

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Figure 4. Internal force and flexibility of the beam under meddle wall.

4

Figure 5. Influence of different fillings to max moment of foundation beam. Table 3. The influence of invert to foundation beam load. Location of beam

Setting Pressure Acting load Load decrement(%) invert (kN) (kN/m2 )

Middle Yes wall No Side wall Yes No

2390 2460 1840 2200

885 911 1840 2200

2.8 16

groove filling to the beam, comparative calculation is taken in this case. The result turns out that the main effect of the invert is to improve the intern force state of the lining structure. Take the vault node as an example, the moment is decreased by about 70% when invert is set but it do little to reduce the load function to the beam especially to the middle wall beam, only 2.8% is reduced. It is slightly inconsistency to the initial estimate that the invert bears the most foundation beam load. After analysis, it turns out that lining structure mainly taken by the foundation beam since the invert is located on the flabby groove filling and the lining’s wall corner is located on the solid foundation beam that causing a tremendous difference in their nature leading to subsidence of the invert. Therefore, when this kind of foundation beam is designed, the foundation of the invert cannot be magnified. The influence of invert to the foundation beam is listed in table 3.

CONCLUSION

(1) When the groove is filled, it should be regarded as elastic foundation rather than simple overhead beam. By analysis, we know that even completely not considering the filling’s bearing capacity, the effect to the intern force of the beam is obvious. Comparing the foundation elastic coefficient k = 5 MPa/m and k = 0 MPa/m, it turns out that the max moment of the beam is 29745 kN.m and 70230 kN.m respectively, having a difference of 2. Therefore, when meeting the groove, we should earnestly find out the filling’s compactness and bearing capacity and also the groundwater condition. If possible, we should do our best to think about its bearing capacity to reduce the cost of the engineering. What’s more, appropriate grouting and exchanging filling can be combined with to enhance the bearing capacity artificially and then erecting beam and span. It is more economical than the method totally without the calculation of foundation beam capacity. (2) Generally speaking, since the uncertainty of the surround rock around the tunnel, the load to the foundation beam has its fuzziness. However to shallow-buried tunnel, this kind of fuzziness becomes much smaller. Therefore, there is certain reasonability to reach the effect on the foundation beam by the way mentioned in this context. (3) The junction where two different kinds of base medium meet is the most dangerous point of the foundation beam, shear and tension crack easily occurring there. (4) The function of the invert is mainly to improve the intern force state of the lining structure. However, turn to the sharing the stress of the beam, its function is changing with the bearing capacity of the filling. When the filling is very weak, the load sharing by the invert is very small.

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(5) The middle wall is weakest part in the engineering and horizontal blanking level brace should be set to improve the stress state. REFERENCES [1] PENG Ding-chao,YUANYong, ZHANGYong-wu. Spatial effects on mid-partition due to excavation of a double-arched runnel[J]. Modern Tunnelling Technology, 2002, 39(1):47–53. [2] LU Yao-zong, YANG Wen-wu. Ressearch on construction scheme of Lianhuashan double-arch tunnel[J]. China Journal of Highway and Transport, 2001, 14(2):75–77. [3] LIU Hong-zhong, HUANG Lun-hai. Overview of design and construction of tunnel with multiple arch[J]. West China Exploration Engineering, 2001, 68((1):54–55. [4] XIA Cai-chu,LIU Jin-lei. Study on the middle wall stress of Xiangsilin doubled arch tunnel[J]. Chinese Journal of Rock Mechanics and Engineering, 2000, 19(Supplement):1116–1119. [5] LIU Zhi-kui, LIANG Jing-cheng, ZHU Shou-zeng, et al, Stability analysis of rock foundation wihth cave in karst area [J]. Chinese Journal of Geotechnical Engneering, 2003, 25(5):630–633. [6] ZHAO Ming-jie, AO Jian-hua, LIU Xu-hua, et al. Study on deformation character of the surrounding rock masses concerning the influence of karst caves in the bottom of tunnel[J]. Journal of Chogqing Jiaotong University, 2003, 22(2):20–23.

[7] ZHOU Yu-hong, ZHAO Yan-ming, CHENG Chonguo. Optimum analysis on the construction process for joint a arch tunnels in partial pressure. Chinese Jounal of Rock Mechanics and Engineering, 2002, 21(5):679–683. [8] LI De-hong. Construction monitoring of multi-arch tunnel and its result analysis[J], 2003, 40(1):59–64. [9] QI Zhi-fu, SUN Bo. Construction of multi-arch tunnels with twin large spans by NATM[J]. Journal of Railway Engineering Society, 2002(1):62–65. [10] LIU Gui-ying, WANGYu-xing, CHENG Jian-ping, et al. Structure analysis and working optimization of the double-arch tunnel of the expressway[J]. Geological Science and Technology Information, 2003, 22(10):97–100. [11] CHEN Shao-hua, LI Yong. Structural analysis for a joined roof tunnel[J]. China Journal of Highway and Transport, 2000, 13(1):48–51. [12] HAN Chang-ling. Structure design of double -arch integrity type tunnel[J]. Haiway, 2000(11):79–81. [13] The Second Survey and Design Institute of China Railway. Design technique handbook for railway engineering

Tunnel [M]. Beijing: Press of China railway, 1995: 426–438. [14] The Second Engineering Burean of China Railway. Construction technique handbook for railway engineering

Tunnel, the next volume[M]. Beijing:Press of China railway, 1995: 323–329. [15] ZHANG De-he. Design and construction of tunnel crossing cavern with accumulations[J], Underground Space, 1999, 19(2):93–100.

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Safety measures by utilizing the old ridge road and potential risks of the land near old river alignments M. Okuda Okuda Construction: Nagoya, Japan

Y. Nakane Showa Concrete Industries Co., Ltd, Nagoya, Japan

Y. Kani Nippon Concrete Industries Co., Ltd, Nagoya, Japan

K. Hayakawa Ritsumeikan University, Kusatsu, Japan

ABSTRACT: This is a study paper from the historical viewpoints on the safety measure and the potential risks of ridge road and old river site respectively. Many old roads in the mountainous area are the road along the crest of the mountain ridge. Since the ridge road is located far away from the river and located on the top of mountainous slope, the old ridge road can be used for the people coming and going during the blockade period of the modern riverside road due to calamity. It can be proved by the examinations of the existence of old facilities with a long and distinguished history, which are the old temple, old traveler’s guardian deity, Goddess stone, statue of Mercy, etc. The old ridge roads have been steadily existed for a long period after the experiences of historical calamities. Therefore, the old ridge road can be utilized as the fail-safe path during the time of calamity. This is also proved by the experiences of the recent calamity of flood and earthquake. The alignments of old Kiso River in the Nobi Plain were investigated through the literatures at first. It was found that there were many offshoots of old Kiso River in the Nobi Plain. The place-names near the old Kiso River and offshoots are also the useful information to judge the alignments of old river flow. The ground reconnaissance was made along the alignments of old Kiso River. Many sections of the old offshoot’s alignments have been already reclaimed and developed as the residential area, farmland, road, irrigation channel, etc. Such a developed land has no more retained what it used to be. Those developed places will have the potential risks of flood and the damages by earthquake due to the lower land, the existence of shallow groundwater and the existence of shallow and loose sandy layer, which will have a liquefaction risk.

1

INTRODUCTION

flow are shown respectively from the historical viewpoints in this study.

This is a qualitative study presenting the safety measures by utilizing the old ridge road as the fail-safe path during the time of calamity. Akiha Old Road is selected as a case study of old ridge road and also presented here three examples of old ridge road utilized during the time of calamity. Also, this study is presenting the potential ground risks of flood and liquefaction occurring along the old offshoot’s alignment of Kiso River in the Nobi Plain. The ground reconnaissance along the old offshoots of Kiso River was made. The findings of the safety measures by utilizing the old ridge road and the potential risks along old river

2 2.1

OLD MOUNTAINOUS ROADS Status of old road in the mountainous area

Many mountainous old roads in the Tokai area are the road along the crest of the mountain ridge, which have been utilized since the Japanese Warring State Period (16 Century) or before. Also, the said mountainous old roads used to being located far away from river and located on the top of mountainous slope.

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Photo 1. Gateway at the entrance to the Akiha Shrine in Hamamatsu City.

Photo 2. A Stone Guidepost along Akiha Old Road.

The distinguish history of an old mountainous road, Akiha Old Road, is introduced hereinafter as an example to the long history of old ridge road. 2.2

History of Akiha Old Road

The distinguished history of Akiha Old Road can be proved by the existences of old shrines, old temple, stone statues, stone image of Buddha, etc. along the alignment of Akiha Old Road as follows: i) Shuyo Temple; This temple has been famous for a fire festival, located about 700 m above sea level and founded by Gyoki Bodhisattva about 1300 years ago, ii) Akiha Shrine; This shrine had been integrated with the Shuyo Temple up to the end of the Edo era (1868). The shrine is located at 885 m above sea level and has been also famous for fire prevention and metallurgy. The shrine holds about 400 Japanese swords dedicated by Samurais. Famous dedicated swords are “Masamune” by Shingen Takeda and “Osafune” by Kansuke Yamamoto in 1534. iii) Stone statues; The letters of the Bunka era (1804– 1818) are chiseled on the stone statues of Jizo. The years of 1760, 1787, etc. are also chiseled on the stone guideposts. iv) Yamazumi Shrine; This shrine has been famous for wolf and war, located about 1100 m above sea level and founded about 1300 years ago. A pair of stone guardian wolves is provided at the entrance of Yamazumi Shrine. Thus, Akiha Old Road has been utilized by the people for 1300 years or more as a road of life, belief in Akiha, transportation of volcanic glass as well as salt and a road for military operation. Those evidences of long history have been spread over the alignment of Akiha Old Road. 2.3

Historical Calamity occurred near Akiha Old Road

The main part of Akiha Old Road is located in the Haruno town in Hamamatsu City. According to a book

Photo 3. A Pair of Stone Guardian Wolves at the Entrance of Yamazumi Shrine.

written by Kishita (1984), there is no description about the disaster occurred along the Akiha Old Road, but describes the following calamities occurred along the rivers: i) An earthquake occurred in 715 caused landslide and the slid materials blocked the flow of Tenryu River for several months, ii) A flood occurred in 1715. It was the serious flood in 180 years, iii) An earthquake occurred in 1854. 1400 houses in the county were completely destroyed, iv) Bridges were washed away due to the heavy rain occurred in 1904. The historical calamities have occurred near the river in Haruno Town, but might be not often along the ridge road as Akiha Old Road. Furthermore, the above-mentioned long history of Akiha Old Road indicates also that the ridge road has been relatively safe and stable. 2.4 Recent examples of old ridge roads utilized during the time of calamity Example 1; Heavy rain attacked on Obara & Fujioka village of Toyota City in July 1972. The rainfall of downpour was 85 mm/hour and the death toll from the heavy rain climbed to 67. Next day after the downpour, an old ridge road was passable, but the prefectural road near river was not passable as shown in Figure 2.

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Figure 3. Passable Old Roads inYamakoshiVill. of Nagaoka City After the 2004 Mid Niigata Prefecture Earthquake.

Figure 1. Alignments of Old Akiha Road in Hamamatsu City. (after Nakane).

Figure 4. Provision Road for Disaster and An Old Ridge Road in Okazaki City.

Figure 2. Passable Ridge Road at Obara Village of Toyota City after Heavy Rain in 1972.

Example 2; The 2004 Mid Niigata Prefecture Earthquake of thrust type earthquake occurred on October 23, 2004 at near Nagaoka City in Niigata prefecture. The maximum magnitude was 6.8 (JMA) and the death toll from the earthquake climbed to 68. The main lifeline roads in Yamakoshi village of Nagaoka City were not passable due to damages from earthquake at that time. However, some old ridge roads were passable as shown in Figure 3 and they were utilized as the access road just after the occurrence of earthquake. Example 3; A provision road against disaster in Kobu town of Okazaki City had been provided by the Okazaki city authority in 2005. This road alignment was selected near and parallel to the alignment of an old ridge road (= Zemanjo Road) as shown in Figure 4.

259

Figure 6. Typical Sectional Dimensions of Okakoizutsumi Dike (after Nishida).

Figure 5. Main Offshoots of Old Kiso River (after “Kisogawa Town History”, 1981).

2.5

Merit of ridge road

The reasons why many mountainous roads have been chosen the ridge alignment and sustained for long period are as follows: i) War operation at the ridge road has an advantage over enemy, ii) Safe from dangers of wild animals, harmful insect and viper, because the animal path is not overlapped with ridge road, iii) Less chance across river and swamp, iv) Good visibility, v) Less obstruction of falling stone. 3

OFFSHOOT ALIGNMENT OF OLD KISO RIVER

3.1 Search for old offshoots shown in literatures Old Kiso River ran along Sakai River and jointed with Nagara River up to 1586. It was noted that there were seven offshoots of old Kiso River after “Study on the Place-name of Owari Clan, 1916”. Other literatures describe not only seven offshoots of old Kiso River but also eight offshoots and twelve offshoots of old Kiso River. (for example, after “Asahi Village Journal, 1963”) Therefore, it can be understood that there had been many offshoots of old Kiso River, but not specific number of offshoots. According to a report of the resources investigation committee belonging to the Prime Minister’s Office, there were three main offshoots of old Kiso River at the beginning of the Edo period (1603–1867) as indicated in the Figure 5. The 1st offshoot, 2nd offshoot and 3rd offshoot of old Kiso River was identified as Ishimakura River, Hannya River and Azai River, respectively. Furthermore, Kuroda River and Ajika River were also the

Photo 4. Signboard of Okakoizutsumi along present Kiso River in Konan City.

offshoots of old Kiso River. It was also known that Saya River was a main flow of old Kiso River. The Owari Clan, who had ruled the left side territory of Kiso River during the Edo period, had constructed the left dike of about 48 km in length along old Kiso River from Inuyama City to Yatomi City between the years 1608 and 1609 in order to protect his territory against flood attacked by the old Kiso River. The left dike of old Kiso River has been called as “Okakoizutsumi”. The typical sectional dimensions of Okakoizutsumi dike are shown in Figure 6. The Okakoizutsumi dike had been constructed only along the left bank of old Kiso River. Therefore, the right bank area of old Kiso River had been often affected by flooding. Also, all flows of offshoot except Saya River had been blocked off the forks from old Kiso River by the embankment of Okakoizutsumi. It can be noticed from Figure 6 that some trees were planted on the dike though the modern Japanese river code does principally not allow to plant trees on the outer slope of embanked dike. Planting tree on the outer dike, however, could be said a Japanese traditional method. Because, the article 17 of the Yozenryo (= a regulation of building & repairs) in the Taihoritsuryo (= old Japanese regulation established in 701) specified that the trees (= elm, willow, etc.) should be planted on the dike. 3.2 Ground reconnaissance on alignment of old Kiso river Some dike sections of Okakoizutsumi still exist along the present Kiso River and also along the left bank of the abandoned Saya River.

260

Figure 7. An Existing Sectional Dimension of Okakoizutsumi Dike at Futago Town in Aisai City (after Nakane). Photo 5. Trace of 1st Offshoot, Aoki River at Kashiwamori.

Photo 6. Trace of 2nd Offshoot, Hannya River at Konan City.

Figure 8. Soil Profile along Okakoizutsumi Dike from Sobue area to Tatsuta area (after Nakane).

An existing sectional dimension of abandoned dike of Okakoizutsumi at Futago Town in Aisai City is shown in Figure 7. The soil profile along Saya River as determined from three boring data is shown in Figure 8. The boring point A, point B and point C is located along old Saya River offsetting from Kiso River around 30 km, 26 km and 20 km upper from the present Kiso River mouth, respectively. The strata name of soil profile are complied with the description shown in the literature of “Ground of Inazawa” because the order of strata has likeness to the soil profile of western Inazawa City presented in this literature. After the blockage of branch forks in 1610, some sections of the abandoned offshoot have gradually reclaimed and developed as the residential area, farmland, road, irrigation channel, etc. The Saya River has been also blocked off the fork from Kiso River in 1900 due to the dike burst at Utasu of Aisai City in 1897 and developed along the abandoned Saya River.

Photo 7. Trace of 3rd Offshoot, Nikko River at Inazawa City.

The developed land along old offshoot has no more retained what it used to be as shown above. Aoki River is the present name of Ishimakura River which is identified with the 1st offshoot of old Kiso River. The place-name indicates also the trace of old Kiso River alignment. For example, the place-name “Kotsu” at the fork of 1st offshoot indicates the timberland of drift-timber. “Kura” of Ishimakura River (= 1st offshoot) indicates the narrow ground between rivers. Hannya of Hannya River (= 2nd offshoot) called originally “Haniya”,

261

Figure 9. Zero-meter Area in Nobi Plain (after Society of Tokai-three-Pref. Ground Settlement Investigation).

Figure 10. Flooding Simulation Map of Aoki River in 40 min. after Burst of Aoki River Dike at 2.2 km (after Inazawa City H.P.).

which indicates the dried up land of mud flow. Azai of Azai River (= 3rd offshoot) indicates the swampy area and/or the existence of shallow groundwater. Also, the minor place-names related with river and swamp can be found along the offshoot areas of old Kiso River, such as Furukawa (= old river), Sunaba (= Sandy ground), Kawahara (= riverbed), Hatagawa (= old river name), Hasuike (= old swamp name), etc. These grounds which have the minor place-name related with river and swamp used to be lower than the surrounding ground. 3.3

Potential risks of flood at the lower ground

The Nobi Plain spreads over about 1,300 km2 and has the gentle slope from northeast to southwest. The Nobi Plain is also known with “zero-meter area” at the south part of the plain. Zero-meter area spreads over about 274 km2 (after Committee of Ground Subsidence at theTokai Three Prefectures, 1988) which occupy about 21% of Nobi Plain area. Most parts of the zero-meter area had been flooded at the time attacked by the Vera Typhoon (= Isewan Typhoon) in 1959. This zero-meter area in Nobi Plain is the largest zero-meter ground in Japan and has a potential risk of flooding. Some local governments have announced the potential risk of flooding areas near the offshoot of old Kiso River, which information are available in the home page of local government via internet. An example of flooding simulation along Aoki River (= 1st offshoot) is shown Figure 10. Thus, the zero meter area and some areas near the offshoot alignment of old Kiso River have a potential risk of flooding. The said flooding risk can be also recognized by the following map which is overlapped Figure 5 (after KisogawaTown) inArticle 3.1 and a map of anticipated

Figure 11. Anticipated flooding area and the offshoots of old Kiso River (after Aichi Pref. 1978 and Kisogawa Town).

flooding area when the right dike of Kiso River is bursted at Yamana in Fuso Town (after “Flood Control Plan of Aichi Prefecture”, 1978). 3.4 Potential risks of liquefaction near the offshoots of old Kiso River The authority of Aichi prefecture announced officially the prediction degree and zone of liquefaction against the future mega-earthquake as shown in Figure 12. In order to check the liquefaction potential along the alignment of Okakoizutsumi, four sandy soil samples

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Figure 12. Prediction degree and zone of liquefaction against the future Tonankai Earthqueke (Aichi pref. H.P.). Table 1.

Figure 13. Gradations of soil samples obtained from Okakoizutsumi and the liquefaction potential zone specified in JMSDC.

Criteria of Liquefaction Potential by JBFDC, 1974.

Item

JBFDC Criteria

Okakoizutsumi

Finer than #200 sieve D50 Uc

1/6, qb,min will be negative, which means that tension will develop. Since soil cannot take any tension, there will be a separation between the footing and the soil. Then, the shape of the pressure distribution will become a triangle, described by Eq. (2). It is currently considered that the exact distribution of contact pressures is difficult to estimate. In Fig. 4(a), which is the case of centered, vertical loading (e/B = 0 and α = 0◦ ), the distribution is symmetrical with respect to the center of

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Figure 2. Typical finite element mesh for FEM.

Figure 3. Relationship between qb /γB and vertical displacement/B from FEM (φ = 35◦ , α = 0◦ ).

the footing, and the maximum value of the distribution is obtained at the center of the footing. Note that the tension is positive for the contact normal stress below the footing. As the eccentricity-to-width ratio (e/B) increases beyond 1/6, the FEM shows that the extent of the contact stress distributions and the maximum values become smaller, consistent with the loss of contact between the footing and the soil at the trailing edge of the footing. Accordingly, qb /γB also decreases. From Fig. 4, the maximum value of the distribution obtained from the FEM occurs almost at the point of application of the load Q. For the case of e/B = 1/3 and α = 0◦ shown in Fig. 4(d), it is observed that the area of contact between the soil and the footing is entirely located on the left side of the footing. As shown in Fig. 4, both the distribution shapes and the maximum values of contact normal stress are in good agreement between FEM and the linear distribution. Figure 5 shows the distribution of contact shear stress below the footing from FEM corresponding to Fig. 4. In Fig. 5(a), which corresponds to Fig. 4(a), the distribution of contact shear stress is symmetrical. Regarding the sign of the contact shear stress below the footing, the clockwise direction is positive. Like the distribution of contact normal stress shown in Fig. 4, the distribution and the value of contact shear stress become smaller, as e/B increases. The point of application of the load, at which the value of contact shear stress equals zero, separates negative shear stresses on the right from positive shear stresses on the left. When e/B increases, the point at which the contact shear stress changes from positive to negative migrates in the same direction as the eccentricity e. In the case

of e/B = 1 / 3 and α = 0◦ , the contact shear stresses is mobilized at the left side of the footing as shown in Fig. 5(d). In the case of eccentric and vertical loading, the variations of the distributions of contact normal and shear stresses below the footing are more remarkable at the direction of the eccentricity. The tendency where the zigzag is appeared in the distributions can be found in Frydman & Burd (1997). This would be due to the effect of the discretization of continuum in finite element method, the interpolation from the integration points of elements and the average value for the nodes constituting several elements. Figures 6 and 7 show the distributions of contact normal and shear stresses below the footing under centered and eccentric, inclined loadings. Like the tendency shown in Figs. 4 and 5, when e/B increases, the extent of the contact stresses distributions and the maximum values become smaller. qb /γB also decreases. The zigzag in the distributions is not much observed at the direction of the applied (inclined) loading, comparing with that of the opposite side. In Fig. 7, the areas where negative shear stresses work, increase when the angle of load inclination is positive (the clockwise direction from the vertical), comparing with Fig. 5. Figure 8 shows the relationship between qb /γB and eccentricity-to-width ratio (e/B) for the cases of φ = 30◦ , 35◦ and 40◦ . In this figure, the solution obtained from FEM and the solutions calculated using Meyerhof’s and Hansen’s bearing capacity equation are presented. The bearing capacity equations proposed by Meyerhof (1963) and Hansen (1970) are:

where B is the footing width; e is the eccentricity; α is the angle of the load acting on the footing with respect to the vertical; φ and γ are the internal friction angle and unit weight of the soil; Nγ in Eqs. (3) and (4) is the bearing capacity factor given by Meyerhof (1963) and Hansen (1970), respectively; and B − 2e is Meyerhof’s effective footing width. Regarding the Nγ value, it is observed that the solution obtained from FEM agrees well with Meyerhof’s solution. The values qb /γB obtained from Eq. (3) are always larger than those obtained from FEM, except when e/B = 0, when they nearly match the FEM

267

Figure 4. Contact normal stress distribution on footing base from FEM (φ = 35◦ ).

Figure 5. Contact shear stress distribution on footing base from FEM (φ = 35◦ ).

values. Also, the values qb /γB obtained from Eq. (4) are larger than those from FEM for e/B > 1/12. It is observed that the Meyerhof’s solution is always larger than Hansen’s solution. When the internal friction angle increases, the difference between Meyerhof’s and Hansen’s solutions become large particularly for e/B = 0. However, when the eccentricity-to-width

ratio (e/B) increases, the difference gets smaller gradually. These observations suggest that Meyerhof’s and Hansen’s Eqs. (3) and (4) tend to overestimate the bearing capacity when e/B becomes large (e/B > 1/6). This fact agrees well with that derived by Michalowski & You (1998). They examined Meyerhof’s concept of an effective width (Meyerhof 1953), and showed that

268

Figure 6. Contact normal stress distribution on footing base from FEM (φ = 35◦ ).

its use may lead to upper bounds that are large for cohesionless soils. The following equation is proposed not to overestimate the bearing capacity in large eccentricities.

Figure 7. Contact shear stress distribution on footing base from FEM (φ = 35◦ ).

where Nγ is the bearing capacity factor given by Hansen (1970); and the key of Eq. (5) is that B − 2.5e is used instead of B − 2e. It is observed that the proposed equation is well corresponded to Hansen’s value for e/B ≤ 1/12 and is similar to those from FEM for e/B > 1/12.

269

Figure 8. Relationship between qb /γB and eccentricityto-width ratio (e/B) for various friction angles and α = 0◦ .

Figure 9 shows the relationship between qb /γB and inclination angle α for φ = 35◦ . It is observed that Meyerhof ’s and Hansen’s solutions are larger than the FEM values for α = 0◦ in Fig. 9(b) and α = 0◦ , 5◦ , 10◦ and 15◦ in Figs. 9(c) and (d). Particularly for the case for e/B = 1/3 (Fig. 9(d)), the values obtained from Meyerhof’s and Hansen’s Eqs. (3) and (4) are much larger than the FEM values, when α is small. In Fig. 9(a), the proposed equation agrees well with Hansen’s value when α = 0◦ . Also, the equation gets closer to the FEM values when α increases. In Figs. 9(b)–(d), it is observed that the equation is similar to the FEM values comparing with

Figure 9. Relationship between qb /γB and the load inclination angle α for φ = 35◦ .

Meyerhof’s and Hansen’s solutions. As a result, we can state that the solutions obtained from Meyerhof’s and Hansen’s Eqs. (3) and (4) are not accurate and tend to overestimate the bearing capacity when the eccentricity is large (e/B ≥ 1/3).

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4

REFERENCES

CONCLUSIONS

The bearing capacity of a rough, rigid strip footing on purely frictional soil subjected to eccentric and inclined loads was analyzed using finite element method. The bearing capacities obtained from the finite element method were compared with those calculated from the bearing capacity equation proposed by Meyerhof (1963) and Hansen (1970). The conclusions drawn in this paper are summarized as follows: (1) The finite element analysis produces contact stress distribution and maximum contact stress values that are in better agreement with the corresponding values for the linear stress distribution. (2) The bearing capacities calculated using the Meyerhof (1963) and Hansen (1970) equations, which is expressed in terms of a effective width B − 2e, are not accurate and tend to overestimate the bearing capacities, particularly when the eccentricity is large (e/B ≥ 1/3). The Meyerhof’s solution is always larger than Hansen’s solution. When the eccentricity-to- width ratio (e/B) or the inclination angle increases, the difference between the Meyerhof ’s and Hansen’s solutions become small gradually. In general, foundation design avoids large eccentricities, so this deficiency in the Meyerhof (1963) and Hansen (1970) solutions are not usually present in a significant way. (3) The bearing capacity equation is proposed not to overestimate the bearing capacity in the large eccentricities. It is shown that the proposed equation can give the reasonable bearing capacity even in the large eccentricities.

Abbo, A. J. & Sloan, S. W. 1995. A smooth hyperbolic approximation to the Mohr-Coulomb yield criterion, Comput. Struc., 54(3): 427–441. Frydman, S. & Burd, H. J. 1997. Numerical studies of bearingcapacity factor N γ, J. Geotech. Geoenviron. Eng., ASCE, 123(1): 20–29. Hanna, A. M. & Meyerhof, G. G. 1981. Experimental evaluation of bearing capacity of footings subjected inclined loads, Can. Geotech. J., 18: 599–603. Hansen, J. B. 1961. A general formula for bearing capacity, Danish Geotech. Inst. Bull., 11: 38–46. Hansen, J. B. 1970. A revised and extended formula for bearing capacity, Danish Geotech. Inst. Bull., 28: 5–11. Meyerhof, G. G. 1953. The bearing capacity of foundations under eccentric and inclined loads, Proc. of 3rd ICSMFE, Zürich, 1: 440–445. Meyerhof, G. G. 1963. Some recent research on the bearing capacity of foundations, Can. Geotech. J., 1(1): 16–26. Michalowski, R. L. & You, L. 1998. Effective width rule in calculations of bearing capacity of shallow footings, Comput. Geotech., 23(4): 237–253. Peck, R. B., Hanson, W. E. & Thornburn, T. H. 1953. Foundation Engineering, John Wiley & Sons, Inc., New York. Prakash, S. & Saran, S. 1971. Bearing capacity of eccentrically loaded footings, J. Soil. Mech. And Found. Engrg. Div., ASCE, 97(1): 95–117. Purkayastha, R. D. & Char, A. N. R. 1977. Stability analysis for eccentrically loaded footings, J. Geotech. Engrg. Div., ASCE, 103(6): 647–651. Saran, S., Prakash, S. & Murty, A. V. S. R. 1971. Bearing capacity of footings under inclined loads, Soils Found., 11(1): 47–52. Saran, S. & Agrawal, R. K. 1991. Bearing capacity of eccentrically obliquely loaded footing, J. Geotech. Eng., ASCE, 117(11): 1669–1690.

271

Uncertainty

Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Reliability analysis of slope stability by advanced simulation with spreadsheet S.K. Au, Y. Wang & Z.J. Cao Department of Building and Construction, City University of Hong Kong, Hong Kong, China

ABSTRACT: This paper develops a package of EXCEL worksheets and functions/Add-In to implement an advanced Monte Carlo method called Subset Simulation in the EXCEL spreadsheet and applies it to reliability analysis of slope stability. The deterministic slope stability analysis and uncertainty modeling and propagation are deliberately decoupled so that they can proceed separately by personnel with different expertise and in a parallel fashion. An illustrative example demonstrates application of the EXCEL package to a slope with uncertainty on undrained shear strength and highlights computational efficiency of Subset Simulation for the slope stability problem. 1

INTRODUCTION

The reluctance of geotechnical practitioners to apply reliability methods to slope stability analysis is attributed, among other factors, to the sophistication of advanced probabilistic assessment/modelling methods, limited published studies/worked examples illustrating the implementation, and lack of user-friendly tools. From an implementation point of view, the less information required from the engineers regarding the probabilistic assessment or reliability computational algorithm, the smaller hurdle the engineer will face in properly using the algorithm, and the more likely it will be implemented. Therefore, it is desirable to decouple the process of deterministic slope stability analysis and reliability analysis so that the work of reliability analysis can proceed as an extension of deterministic analysis in a non-intrusive manner. It is also desirable to implement the reliability analysis algorithm in a software platform with whom the engineers are familiar. From this perspective, the ubiquitous Microsoft EXCEL spreadsheet is particular of interest. Low (2008) showed that geotechnical analysis and the expanding ellipsoidal perspective of the HasoferLind reliability index can be readily implemented in a spreadsheet environment. The Hasofer-Lind reliability index can be obtained using the object-oriented constrained optimization tool in the Excel spreadsheet (Low and Tang 1997, 2007). The approach has been applied to obtain the reliability index of conventional bearing capacity problem (Low 2008), anchored sheet pile design (Low 2005a&b), slope stability analysis (Low et al. 1998, Low 2003). This paper implements an advanced Monte Carlo method called Subset Simulation (Au and Beck 2001) in the EXCEL spreadsheet and illustrates its application to reliability analysis of slope stability. After this introduction, the Subset Simulation algorithm will be

briefly discussed, followed by developments of Subset Simulation tool and slope stability analysis worksheets in EXCEL.Then, an example of slope stability reliability analysis will be presented to illustrate the analysis process using the EXCEL spreadsheets. 2

SUBSET SIMULATION ALGORITHM

Subset Simulation is an adaptive stochastic simulation procedure for efficiently computing small tail probabilities (Au and Beck 2001, 2003). Originally developed for dynamic reliability analysis of building structures, it stems from the idea that a small failure probability can be expressed as a product of larger conditional failure probabilities for some intermediate failure events, thereby converting a rare event simulation problem into a sequence of more frequent ones. During simulation, conditional samples are generated from specially-designed Markov chains so that they populate gradually each intermediate failure region until they reach the final target (rare) failure region. Let Y be a given critical response for which P(Y > y) is of interest, let 0 < y1 < y2 < · · · < ym = y be an increasing sequence of intermediate threshold values. It should be noted that considering a single critical response leads to little loss of generality because multiple failure criteria can be incorporated into a single one (Au and Beck 2001). By sequentially conditioning on the event {Y > yi }, the failure probability can be written as

The raw idea is to estimate P(Y > y1 ) and {P(Y > yi |Y > yi−1 ): i = 2,…,m} by generating samples of  conditional on {Y () > yi ): i = 1,…,m}.

275

Figure 1. Schematic diagram of Subset Simulation procedure.

In implementations, y1 , …, ym are generated adaptively using information from simulated samples so that the sample estimate of P(Y > y1 ) and {P(Y > yi |Y > yi−1 ): i = 2,…,m} always correspond to a common specified value of the conditional probability p0 . The efficient generation of conditional samples is highly-nontrivial but pivotal in the success of Subset Simulation, and it is made possible through the machinery of Markov Chain Monte Carlo (MCMC) simulation (Roberts & Casella 1999). Markov Chain Monte Carlo is a class of powerful algorithms for generating samples according to any given probability distribution. It originates from the Metropolis algorithm developed by Metropolis and co-workers for applications in statistical physics (Metropolis et al. 1953). In MCMC, successive samples are generated from a specially designed Markov chain whose limiting stationary distribution tends to the target PDF as the length of the Markov chain increases. An essential aspect of the implementation of MCMC is the choice of ‘proposal distribution’ that governs the generation of the next sample from the current one. The efficiency of Subset Simulation is robust to the choice of the proposal distribution, but tailoring it for a particular class of problem can certainly improve efficiency. For robustness in applications, the standard deviation of the proposal distribution for each random variable is set equal to that of the conditional samples of the current simulation level. The Subset Simulation procedure for adaptively generating samples of  conditional on {Y () > yi : i = 1,…,m} corresponding to specified

target probabilities {P(Y () > yi ) = pi0 , i = 1,…,m} is illustrated schematically in Figure 1. First, N samples {0,k : k = 1,…,N } are simulated by direct Monte Carlo simulation (MCS), i.e., they are i.i.d. as the original PDF. The subscript ‘0’ here denotes that the samples correspond to ‘conditional level 0’ (i.e., unconditional). The corresponding values of the tradable variable {Y0,k : k = 1,…,N } are then computed. The value of y1 is chosen as the (1 − p0 ) · N -th value in the ascending list of {Y0,k : k = 1,…,N }, so that the sample estimate for P(F1 ) = P(Y > y1 ) is always equal to p0 . Due to the choice of y1 , there are p0 · N samples among {0,k : k = 1,…,N } whose response Y lies in F1 = {Y > y1 }. These are samples at ‘conditional level 1’ and are conditional on F1 . Starting from each of these samples, MCMC is used to simulate an additional (1 − p0 ) · N conditional samples so that there is a total of N conditional samples at conditional level 1. The value of y2 is then chosen as the (1 − p0 ) · N -th value in the ascending list of {Y1,k : k = 1, . . . , N }, and it defines F2 = {Y > y2 }. Note that the sample estimate for P(F2 |F1 ) = P(Y > y2 |Y > y1 ) is automatically equal to p0 . Again, there are p0 · N samples lying in F2 . They are samples conditional on F2 and provide ‘seeds’ for applying MCMC to simulate an additional (1 − p0 ) · N conditional samples so that there is a total of N conditional samples at ‘conditional level 2.’ This procedure is repeated for higher conditional levels until the samples at ‘conditional level (m − 1)’ have been generated to yield ym as the (1 − p0 ) · N -th value in the ascending list of {Ym−1,k : k = 1,…,N } and that ym > y so that there are

276

enough samples for estimating P(Y > y). Note that the total number of samples is equal to N + (m − 1) · (1 − p0 ) · N .Approximate formulas have been derived for assessing the statistical error (in terms of coefficient of variation) that can be estimated using samples generated in a single run. The Subset Simulation algorithm has been applied to a variety of complex systems in structural (Au and Beck 2003), aerospace (Thunnissen et al. 2007) and fire (Au et al. 2007) engineering. Probabilistic sensitivity and failure analysis have also been carried out using Subset Simulation (Au 2004, Au and Beck 2003). 3

SIMULATION TOOLS IN EXCEL SPREADSHEET

equilibrium calculations and then returns the value of FS as the output. No probability/reliability concept is involved in the deterministic worksheet and so it can be developed by personnel without reliability background. To allow a seamless integration with Subset Simulation, the deterministic analysis worksheet is specially designed to be fully automated and does not involve any human intervention. This is necessary for automated calculation of the FS during Subset Simulation. E.g., if calculating the response requires clicking a button, then such button will need to be clicked as many times as the number of samples used in the simulation, which could be in the order of a thousand and is not acceptable in the simulation. 3.2

A package of EXCEL worksheets and functions/AddIn are developed, with the aids of Visual Basic for Applications (VBA) in EXCEL, to implement the Subset Simulation algorithm in a spreadsheet environment and apply it reliability analysis of slope stability. A software architecture is proposed that clearly divides the package into three parts: 1) deterministic analysis of slope stability, 2) modeling of uncertainty in slope stability problem, and 3) uncertainty propagation by Subset Simulation. It is of particular interest to decouple the process of developing the deterministic slope stability analysis worksheets and the VBA functions/Add-In for uncertainty modeling and uncertainty propagation (Subset Simulation) so that the work of uncertainty modeling and propagation can proceed as an extension of deterministic analysis in a non-intrusive manner. The deterministic analysis of slope stability and uncertainty modeling and propagation can be performed separately by personnel with different expertise and in a parallel fashion. Therefore, minimum information is required from the engineers regarding the reliability computational algorithm. 3.1 Deterministic slope stability analysis worksheets Deterministic analysis of slope stability is the process of calculating the factor of safety FS for a given ‘nominal’ set of values of the system parameters θ. The system parameters generally include geometry and stratigraphy of the slope, soil properties (e.g., soil unit weight, undrained shear strength, friction angle, cohesion, and pore water pressure) and other relevant information. Limit equilibrium analysis procedures (e.g., Ordinary Method of Slices, Simplified Bishop, Simplified Janbu, Spencer, Morgenstern and Price, Chen and Morgenstern procedures) are implemented in a series of worksheets and VBA functions for the FS calculation. The deterministic analysis using limit equilibrium procedures are organized into one or a set of worksheets, although for discussion purposes it is referred as a single worksheet. From an input-output perspective, the deterministic analysis worksheet takes a given θ as input, performs limit

Modeling of uncertainty in slope stability problem

Uncertainty in slope stability analysis arises from the system parameters θ, such as soil properties (e.g., soil unit weight, undrained shear strength, friction angle, cohesion, and pore water pressure). Therefore, these soil properties are treated as random variables in the analysis, although different limit equilibrium analysis procedures may have slightly different sets of random variables. Note that this paper focuses on the uncertainties arising from soil properties and does not account for other uncertainties, such as calculation model uncertainties. The spatial variability of soil properties within a given layer of soil is modeled by homogeneous random fields with an exponentially decaying correlation structure. An uncertainty model spreadsheet is developed for generating a random sample (realization) of the uncertain parameters θ. Starting with uniform random numbers supported by EXCEL, transformation is performed to produce the random samples of desired distribution. Available VBA subroutines in EXCEL is used to facilitate the uncertainty modeling. The uncertainty model worksheet is developed in parallel with development of deterministic analysis worksheet. From an input-output perspective, the uncertainty modeling worksheet takes no input but returns a random sample of θ as its output whenever a re-calculation is commanded (e.g., by pressing ‘F9’ in EXCEL). Similar to the deterministic analysis worksheets, the uncertainty model worksheet is specially designed to be fully automated and does not involve any human intervention. In addition, the uncertainty modeling is implemented in a single worksheet for the convenience of Subset Simulation. The Subset Simulation VBA code instructs EXCEL to re-calculate only the uncertainty model worksheet to generate a sample of θ, avoiding re-calculation of deterministic analysis worksheets which is not needed and which is often most time-consuming. 3.3

Uncertainty propagation by subset simulation

After the deterministic analysis and uncertainty model worksheets are developed, they are ‘linked together’

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Figure 2. Schematic diagram of link between deterministic and uncertainty modeling worksheet.

Figure 4. Slope stability example.

Figure 3. Subset Simulation Add-In.

through their input/output cells to produce a probabilistic analysis model of the slope stability problem. As illustrated by Figure 2, linking simply involves setting the cell reference for the nominal values of θ in the deterministic analysis worksheet to be the cell reference for the random sample in the uncertainty model worksheet. After this task, the value of θ shown in the deterministic analysis worksheet is equal to that generated in the uncertainty modeling worksheet, and so the FS value calculated in the deterministic analysis worksheet is random. E.g., pressing the ‘F9’ key in EXCEL generates a random value of the FS. In other words at this stage one can perform a direct Monte Carlo simulation of the problem by repeatedly pressing the ‘F9’ key. When the deterministic analysis and uncertainty model worksheets are completed one is ready to make use of the Subset Simulation algorithm for uncertainty propagation that can provide better resolution at the distribution tail (i.e., low failure probability levels). A VBA code for Subset Simulation is developed that functions as an Add-In in EXCEL and can be called by selecting from the main menu ‘Tools’ followed by ‘SubSim’. A user form appears upon invoking of the function, as shown in Figure 3. The user should input the cell reference of the uncertain parameters θ and

system response Y = 1/FS in the uncertainty modeling worksheet. Other inputs include the following algorithm-specific parameters: p0 (conditional probability from one level to the next), N (number of samples per level), m (number of levels to perform). As a basic output, the program produces complementary CDF of the driving variable versus the threshold level, i.e., plot of estimate for P(Y > y) versus y. In general the CDF, histogram or their conditional counterparts can be produced.

4

ILLUSTRATIVE EXAMPLE

As an illustration, the worksheets and VBA functions/Add-In are applied to assess reliability of the slope shown in Figure 4. The factor of safety FS is defined as the critical (minimum) ratio of resisting moment to the overturning moment, and it is calculated using the Swedish Circle method in conjunction with general procedure of slices (Duncan and Wright 2005). The slip surface is assumed to be a circular arc centered at coordinate (x, y) and with radius r. The overturning and resisting moments are summed about the center of the circle to calculate the factor of safety, as shown in Figure 4. For moment calculations the soil mass above the slip surface is subdivided into 24 vertical slices, each of which has a weight Wi , circular slip segment length li , undrained shear strength Sui along the slip segment, and an angle αi between the base of

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the slice and the horizontal. The factor of safety is then given by

where the minimum is taken over all possible choices of slip circles, i.e., all possible choices of (x, y) and r. A VBA code has been written to calculate the ratio of resistant to overturning moment for different values of (x, y) and r and then pick the minimum value as the factor of safety. As a reference, the nominal value of FS that correspond to the case where all Su values equal to their nominal value of 20 kPa, is equal to 1.2. Undrained shear strength of soil is treated as random variable, and the undrained shear strength at locations with the same depth is assumed to be fully correlated. The spatial variability with depth is modeled by a homogeneous Lognormal random field with an exponentially decaying correlation structure. The correlation structure is described through the logarithm of the undrained shear strength. That is, let Su (z) be the value of undrained shear strength at depth z. Then the correlation between log Su (zi ) and log Su (zj ) is given by Rij = exp (−2|zi − zj |/λ), where λ is the effective correlation length. The values of Su at different depths are simulated through transformation of i.i.d. uniform random variables. The generation of the latter is provided by the built-in function ‘Rand()’ in EXCEL. Specifically, let S = [Su (z1 ), Su (z2 ), . . . , Su (zn )]T be a vector of Su values at depths z1 , . . . , zn . Then

where u and s are Lognormal parameters equal to the mean and standard deviation of log Su (z); 1 is a column vector of length n with all entries equal to 1; Z is an n-dimensional standard Gaussian vector; L is a lower triangular matrix obtained from Cholesky factorization of the correlation matrix R = [Rij ] such that LLT = R. Note that each component of Z can be generated using the inverse of the standard Gaussian cumulative distribution function (‘NORMINV’ in EXCEL) of a uniform random variable. A combination of u = 2.976 and s = 0.198 is adopted in this example so that the mean and spatial variability are approximately equal to 20 kPa and 4 kPa (i.e., 20% coefficient of variation), respectively. The effective correlation length λ is assumed to be 2 m. The soil between the upper ground surface and 15 m below is divided into 30 equal layers. In the context of Subset Simulation, the set of uncertain parameters is  = Z, which contains 30 i.i.d. Gaussian random variables that are used for characterizing the spatially varying random field for Su . By default, Subset Simulation drives the samples to the upper tail of the distribution of the response Y . As the lower tail of the distribution of the factor of safety (i.e., the unsafe zone) is of interest, the response Y is defined as the reciprocal of FS, i.e., Y = 1/FS = the ratio of the overturning to resistant moment.

Figure 5. Simulation results.

Subset Simulation is performed in EXCEL with the following parameters: p0 = 10%, N = 200 samples per level, m = 3 simulation levels. This means that the results for P(Y > y) shall be produced from a probability level of 1 down to 0.001. Figure 5 shows a typical estimate of the complementary CDF for Y = 1/FS, i.e., P(Y > y) versus y, estimated by Subset Simulation with a total of 200 + 180 + 180 = 560 samples (i.e., calculations of FS). For comparison the estimate by direct Monte Carlo with the same number of samples is also plotted. It is seen that the CDF curve by direct Monte Carlo is not accurate at low probability levels, while the Subset Simulation estimate provides consistent results even in the low probability level regime. The observed computational efficiency of Subset Simulation for the slope stability problem is typical of those structural reliability problems (Au et al. 2007). As mentioned before, the nominal factor of safety (i.e., ignoring soil uncertainty) is equal to 1.2. For this configuration in the presence of soil uncertainty described the failure probability P(FS < 1) = P(Y > 1) is about 8%. This corresponds to an effective reliability index of −1 (92%) = 1. 41. Note that this value depends on the level of soil uncertainty assumed. E.g., had a larger spatial variability been assumed, the failure probability will be larger and the corresponding effective reliability index will be smaller. Nevertheless the nominal factor of safety remains the same as it does not address uncertainty. The actual value of spatial variability used should of course be consistent with the site characteristics. 5

CONCLUDING REMARKS

This paper developed a package of EXCEL worksheets and VBA functions/Add-In to implement an advanced Monte Carlo method called Subset Simulation in the EXCEL spreadsheet and illustrated its application to reliability analysis of slope stability. A software architecture is proposed that clearly divides the package into three parts: 1) deterministic analysis

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of slope stability, 2) modeling of uncertainty in slope stability problem, and 3) uncertainty propagation by Subset Simulation. The process of developing the deterministic slope stability analysis worksheets and the VBA functions/Add-In for uncertainty modeling and uncertainty propagation (Subset Simulation) are deliberately decoupled so that the work of uncertainty modeling and propagation can proceed as an extension of deterministic analysis in a non-intrusive manner. The deterministic analysis of slope stability and uncertainty modeling and propagation can be performed separately by personnel with different expertise and in a parallel fashion. Therefore, minimum information is required from the engineers regarding the reliability computational algorithm. The illustrative example demonstrated the application of Subset Simulation to slope stability reliability analysis that involves a large number of random variables characterizing a spatially varying random field and highlighted computational efficiency of Subset Simulation for the slope stability problem. ACKNOWLEDGEMENTS The work described in this paper was supported by General Research Fund [Project No. 9041327 (CityU 110108)] and Competitive Earmarked Research Grant [Project No. 9041260 (CityU 121307)] from the Research Grants Council of the Hong Kong Special Administrative Region, China. The financial supports are gratefully acknowledged. REFERENCES Au, S. K. 2004. Probabilistic failure analysis by importance sampling Markov chain simulation. Journal of Engineering Mechanics, 130(3): 303–311. Au, S. K., and Beck, J. L. 2001. Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics, 16(4): 263–277.

Au, S. K., and Beck, J. L. 2003. Subset simulation and its applications to seismic risk based on dynamic analysis. Journal of Engineering Mechanics, 129(8): 1–17. Au, S. K., Ching, J. and Beck, J. L. 2007.Application of Subset Simulation methods to reliability benchmark problems. Structural Safety, 29(3): 183–193. Au, S. K., Wang, Z.W. and Lo, S. M. 2007. Compartment fire risk analysis by advanced Monte Carlo method. Engineering Structures, 29(9): 2381–2390. Duncan, J. M. and Wright, S. G. 2005. Soil Strength and Slope Stability, John Wiley & Sons. Inc. New Jersey, 2005. Low, B. K. 2003. Practical probabilistic slope stability analysis. Proceedings of Soil and Rock America, MIT, Cambridge, MA, June 2003, Verlag Gluckauf GmbH Essen, Germany, Vol. 2, 2777–2784. Low, B. K. 2005a. Reliability-based design applied to retaining walls. Geotechnique, 55(1): 63–75. Low, B. K. 2005b. Probabilistic design of anchored sheet pile wall. Proceedings of 16th International Conference on Soil Mechanics and Geotechnical Engineering, 12–16 Septermber 2005, Osaka, Japan, Millpress, 2825–2828. Low, B. K. 2008. Practical reliability approach using spreadsheet. Reliability-based Design in Geotechnical Engineering, Edited by Phoon, K. K. Taylor & Francis, London and New York. Low, B. K., Gilbert, R. B., and Wright, S. G. 1998. Slope reliability analysis using generalized method of slices. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 124(4): 350–362. Low, B. K. and Tang, W. H. 1997. Efficient reliability evaluation using spreadsheet. Journal of Engineering Mechanics, 127(7): 149–152. Low, B. K. and Tang, W. H. 2007. Efficient spreadsheet algorithm for first-order reliability method. Journal of Engineering Mechanics, 133(2): 1378–1387. Metropolis, N., Rosenbluth,A., Rosenbluth, M., and Teller,A. 1953. Equations of state calculations by fast computing machines, Journal of Chemical Physics, 21(6): 1087– 1092. Roberts, C. and Casella, G. 1999. Monte Carlo Statistical Methods, Springer. Thunnissen, D. P., Au, S. K., and Tsuyuki, G. T. 2007. Uncertainty quantification in estimating critical spacecraft component temperatures. AIAA Journal of Thermal Physics and Heat Transfer, 21(2): 422–430.

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Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Optimal moving window width in conjunction with intraclass correlation coefficient for identification of soil layer boundaries J.K. Lim & S.F. Ng Universiti Teknologi MARA Pulau Pinang, Pulau Pinang, Malaysia

M.R. Selamat & E.K.H. Goh Universiti Sains Malaysia, Pulau Pinang, Malaysia

ABSTRACT: The identification of layer boundaries and demarcating the soil profile into homogeneous layers are often much more complicated than one expected when dealing with highly variable complex natural material. The quantitative approaches reported in geotechnical literatures are limited, varies and mostly restricted to case or project specific basis. In this study, the performance of intraclass correlation coefficient (RI) in conjunction with various suggested window widths are investigated using three fairly different CPT soundings obtained from the database of National Geotechnical Experimental Sites. RI appears to be a powerful, robust and persistent tool and the corresponding optimal window width was proven as a function of average distance between boundaries which could be determined from autocorrelation analysis. The empirical criterion of 0.7 was found useful in guiding the researcher to decide whether a peak is significant enough to be considered as a valid boundary.

1 1.1

INTRODUCTION Background of research

A major uncertainty in geotechnical engineering is the inherent spatial variability of soil properties. The importance of recognizing uncertainties and taking them into account in geotechnical design have been propagated by numerous leaders since 1960s (Casagrande 1965; Peck 1969; Wu 1974; Leonards 1982; Tang 1984; Morgenstern 1995; Whitman 2000; Christian 2004). Probability theory and statistics provide a formal, scientific and quantitative basis in assessing risk and uncertainties and have been sprouted in geotechnical engineering research in recent years. In line with the development, characterization of soil properties has been advanced onto the functions of the deterministic mean and its stochastic characters, comprises of coefficient of variation and scale of fluctuation in modeling the inherent soil variability as a random field (Vanmarcke 1977; DeGroot and Baecher 1993; Jaksa et al. 1997; Phoon and Kulhawy 1999; Fenton 1999). Compliance to stationarity or statistical homogeneity criterion is imperative in any soil data analyses. A random function which used to modeled the variability of soil is considered stationary, or weakly stationary if (Brockwell and Davis 2002): (1) the mean of the function is constant with distance, i.e. no trend in the data, (2) the variance of the function is constant with distance, i.e. homoscedastic, (3) there are no seasonal variations, (4) there are no apparent changes in behaviors, and (5) there are no outlying observations.

In other words, a stationary series is essentially a function of their separation distance, rather than their absolute locations. In geotechnical characterization undertaking, the first step usually involves demarcating the soil profile into layers or sections which are homogeneous so that the result of subsequent analysis is not biased. A homogeneous layer comprises uniform soil material that has undergone similar geologic history and possesses with certain distinctive behaviors. The identification of boundaries and thus demarcation process are often much more complicated than one expected when dealing with this highly variable complex natural material. The variability exists not only from site to site and stratum to stratum, but even within apparently homogeneous deposits at a single site (Baecher and Christian 2003). 1.2

Problem statement

It would be rather useful to supplement the existing procedures with a quantitative systematic approach. The conventional method, which is based on visual observation, gives less accuracy and substantial subjectivity to the identification of actual boundary of soil. Existing statistical tools are not widely explored, well-calibrated and properly defined, thus generally result in unsatisfactory outcome. This paper intends to resolve the above problem for better characterization of soil properties. Reported useful statistical tools would be compared in terms of their effectiveness and the existing procedures are revamped for further improvement.

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Cone Penetration Test (CPT) is widely used in soil characterization in view of its ability to provide almost continuous profile, widely correlated and highly repeatable (Robertson 1986; NCHRP 2007). In this study, the CPT soundings, in particular the cone tip resistance, qc , were used for detail illustration. The data were selected on the basis of their spacing, extensiveness and difference between each other which best yield the thorough examination on the performance of statistical tools in soil boundary demarcation. 2

STATISTICAL APPROACHES

2.1 General Classical and advance statistical approaches for testing similarity or dissimilarity of univariate or even multivariate records are believed to be substantial. Some of the established analytical tools have potential to be applied in the field of geotechnical engineering with modification to suit the nature of geotechnical parameters. Nevertheless, the cross-disciplinary collaboration undertaking is surprisingly little. Many geotechnical engineers are unfamiliar with the underlying concepts of statistics and probability and remain skeptical and reluctant even to make an attempt. In this paper, two statistical methods which are relatively common and simple in identifying the soil layer boundaries are presented. 2.2 Intraclass correlation coefficient Intraclass Correlation Coefficient (RI) was reported by Campanella and Wickreseminghe (1991) as a useful statistical method for detecting soil layer boundaries using CPT soundings. For identification of layer boundaries, a moving window width, Wd , is first specified and the window is divided into two segments. The RI profile is then generated by moving two contiguous segments over a measurement profile and the computed index is plotted corresponding to the midpoint of the window. RI will always lie between zero and unity and a relatively high value of RI is likely to indicate the presence of a layer boundary. The RI together with its pooled combined variance (sw2 ) and the between class variance (sb2 ) are defined as:

where n1 and n2 are the sample size of two equal segments, above and below the middle line of the window, s12 and s22 being the variances of the sample for the two segments, x¯ and s2 are the sample mean and variance

within the designated window. The equation can also be written as follow (Zhang and Tumay 1996) for the two segments with equal sample size of m and their sample mean of x¯ 1 and x¯ 2 , respectively.

Judging whether an index value is high enough to indicate a boundary in a relative sense by visual observation is fairly subjective and would result in inconsistency. Zhang and Tumay (1996) suggested that the peak value of RI which is equal to or larger than 0.7 can be empirically determined as the boundary line. Hegazy et al. (1996) proposed the critical value as the (mean + 1.65 standard deviation) with a level of significance of 5%. However, Phoon et al. (2003) commented that the above critical values are not depending on the underlying correlation structure of the profile. 2.3 Window width As all these statistical methods incorporate with the concept of moving windows, the width of the sampling window becomes an important parameter which could have substantial influence on the result of analysis. Generally, too narrow a window will result in undesirable effect of high noise level with too many peaks appear. On the other hand, too wide a window will oversmoothen the statistics till missing out the possible boundaries due to excessive perturbation region. Webster (1973) proposed a method to determine the boundaries on transects automatically and has found that the suitable width for the calculation window is approximately two thirds of the expected distance between boundaries where the spacing between boundaries does not differ widely. The expected distance or average spacing between boundaries could be determined from an autocorrelation analysis. The technique is said reasonably sensitive but found little affected by window width. Campanella and Wickremesinghe (1991) elaborated in detail the statistical methods for determination of window width and recommended that it is rather to adopt an incorrect narrower window width than wider window width to avoid missing out the possible layer boundaries. Two case studies, namely McDonald farm Site and Haney Site have been illustrated and the window widths selected were 1.5 m and 2.0 m, respectively. To the other extent, window width that less than 1.0 m should not be selected due to normal distribution restriction on the samples (Wickremesinghe 1989). Zhang and Tumay (1996) based on the finding of previous research that the standard 10 cm2 electric cones may require minimum stiff layer thickness of 36 cm to 72 cm to ensure full tip resistance and concluded that the value of the window width could be conservatively taken to be 150 cm or 75 cm for half of the window. Nevertheless, they reported that primary

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layering usually does not provide satisfactory results due to uneven soil layers. The big difference of layer thicknesses will result in too many layers in thick zone and too little in the thin causing a bias in making a judgment. Cafaro and Cherubini (2002) used the same procedure as proposed by Webster (1973) in analyzing a stiff overconsolidated clay at a test site in Taranto, Southern Italy and obtained a fairly wide window width of 6.8 m for qc , fs and Ic profiles. The width was reduced to 4.8 m and the variation in the RI profile was found negligible on both the position (depth) and the value of the peaks. The geostatistical boundary was found not always correspond well to the geolithological boundary thus suggested the possible offset to be accounted for. Kulatilake and Um (2003) introduced a new procedure to detect statistical homogeneous layers in a soil profile. In examining the cone tip resistance data for the clay site at Texas A&M University, a window width of 0.4 m which contains 10 data points in each section has been used. Due to the short section adopted, four possible combinations for the mean soil property (either constant or with linear trend) were considered. The distance between the lower and upper sections was calculated and subsequently generated along the depth for evaluation of the statistical homogeneity at different levels. Phoon et al. (2003) adopted the lower limit of permissible window width, that is 1.0 m in generating the RI and Bstat profiles. Both profiles manage to capture the primary layer boundaries in consistent with visual inspection, of which the Bstat peaks were much more prominent. Considerable noises were observed and 3 fault boundaries were identified (no obvious soil boundaries can be seen in the qt record) in the RI profile when comparing to the critical value of 0.7.

coefficient will decrease more or less steadily with increasing lag distance from around 1 to some minimum value near zero and fluctuate thereafter. The lag distance over which this decay occurs can be taken as the average distance between boundaries which could be used as guidance in selection of suitable window width. 3 3.1

NUMERICAL EXPERIMENTS Selected case studies

For the present study, established database for National Geotechnical Experimental Sites (NGES) (http://www.unh.edu/nges/) funded by the Federal Highway Administration (FHWA) and National Science Foundation (NSF) of America were explored. The performance and usefulness of several approaches (in terms of window width and the statistical tool) that have been used by other geotechnical researchers in identifying layer boundaries were thoroughly examined. Typical CPT profiles from three sites representing different parts of North America were selected. These sites have been classified as Level I and II sites that are most closely fit the combined criteria of research areas as of significant national importance. These CPT soundings were closely spaced, extensive and fairly different between each other which best suit for this examination. The selected sites are 1) Treasure Island Naval Station in the San Francisco Bay area (CATIFS), 2) University of Massachusetts, Amherst campus (MAUMASSA), and 3) Northwestern University Lake Fill Site in Evanston (ILNWULAK). 3.2 Examination of Existing Approaches

2.4 Autocorrelation analysis The Webster’s intuition that the suitable window width should be equal to or somewhat less than the average distance between boundaries has led to the exploitation of autocorrelation analysis (Webster 1973). The result of his study showed that the optimize width is around two thirds of the expected distance although larger width up to the full expected distance could still be useful (main peaks appeared in the same positions but with different relative heights) for those area with marked changes. The autocorrelation coefficient at lag k was expressed as

where n is the number of sampling points in the series, k is the lag and u is the deviation from the series mean at the tth (or t + kth) point. In the correlogram, i.e. the plot of autocorrelation coefficient, rk against lag, k, the autocorrelation

Intraclass correlation coefficient (RI) which was reported to be useful in geotechnical literatures are examined here. Since the method is used in conjunction with moving window averaging concept, the sensitivity of the window width in generating the most optimize profiles which would discriminate the ‘true’ boundaries is of great concern. Several criteria in determining suitable window width deduced from previous researchers’ works are incorporated in this study as follows: i) Two thirds of the average distance between boundaries determined by using autocorrelation analysis (Webster 1973; Campanella and Wickremesinghe 1991), ii) The conservative assumption for full tip resistance of 1.5 m (Zhang and Tumay 1996), and iii) The minimum width of 1.0 m due to normal distribution restriction on samples (Wickremesinghe 1989; Phoon et al. 2003). In reality, perfect result is almost not possible as the actual soil data could be really erratic. However, the analytical approach (combination of a statistical

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Figure 1. Identification of soil layer boundaries using RI of varying Wd for CATIFS site: Wd1 = 1.0 m, Wd2 = 1.5 m and Wd3 = 1.9 m.

tool with an optimize window width) could be deemed satisfactory from at least two practical aspects. The approach should avoid missing out possible prominent layer boundaries and at the same time, able to capture as many major boundaries as possible at one time. And it is evident from past literatures that the boundaries indicated by these statistical tools are often slightly offset probably due to variation in the upper and lower segments as moving the sampling window over the soil profile. Therefore, note that the tools could serve as a useful indicator, but yet final adjustment and decision have to be made with regards to the original profile, geological background and not forgotten engineering judgment. 3.3

Results of analysis

The results of analysis for CATIFS, MAUMASSA and ILNWULAK sites are presented in Fig. 1, Fig. 2 and Fig. 3, respectively. For each set of results, 3 different window widths as delineated above (i, ii and iii) have been incorporated with RI and presented side-by-side for comparison.

Figure 2. Identification of soil layer boundaries using RI of varying Wd for MAUMASSA site: Wd1 = 1.0 m, Wd2 = 1.5 m and Wd3 = 2.4 m.

Case 1: CATIFS Site From the cone tip resistance profile in Fig. 1 (CATIFS site), the heterogeneity of soil from 7.0 m to 9.0 m as compared to others is readily observed through visual examination. The RI profile manages to capture these peaks at both 7.0 m and 9.0 m locations, and another one at approximately 2.1 m. The above three main peaks were found persist for all the tested widths of 1.0 m, 1.5 m and 1.9 m (Wd1 to Wd3 ) with quite a number of noises appear exceeding the empirical value of 0.7 for window widths of 1.0 m and 1.5 m (Wd1 and Wd2 ). Thus, inference could be made from the results that the optimal window width should be around 1.9 m in this case. Limitation of the approach on missing out the information at both ends of the profile is noted. The apparent boundary of cone tip resistance at 1.26 m for instance is basically out of the coverage area of the generated output as the computed index is plotted against the midpoint of the moving window. In addition, the identification of a potential boundary around the depth of 2.1 m using RI profile indicated that the tool able

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Case 3: ILNWULAK Site Results of the third case study of ILNWULAK site are presented in Fig. 3. The cone tip resistance profile seems to exhibit higher resistance values at both ends, i.e. depths before 1.0 m and after 7.0 m, and an interbedded heterogeneous layer at approximately 3.3 m to 4.3 m. RI profiles for all the tested widths of 1.0 m, 1.5 m and 1.3 m (Wd1 to Wd3 ) as presented in Fig. 3 show a very good agreement where the four expected boundaries were managed to detect. The main peaks persist as the window width changes and more noises can be noticed at smaller widths particularly for window width of 1.0 m (Wd1 ). Similar inference could still be reasonable drawn where the suitable width for this boundaries demarcation exercise ranges at approximately 1.3 m, obtained from the autocorrelation analysis. 3.4

Figure 3. Identification of soil layer boundaries using RI of varying Wd for ILNWULAK site: Wd1 = 1.0 m, Wd2 = 1.5 m and Wd3 = 1.3 m.

to detect a considerable sharp change along the profile which suggested two quasi-linear portions to be divided.

Case 2: MAUMASSA Site MAUMASSA site (Fig. 2) was the second case study where the cone tip resistance profile exhibits apparent heteroscedasticity characteristic with gradual change of gradient around the potential boundary. As shown in Fig. 2, the generated RI profiles for window widths of 1.0 m and 1.5 m (Wd1 and Wd2 ) are basically some noises inferring that the windows are too narrow. As the window width increased to 2.4 m (Wd3 ), which is approximately two thirds of the average distance between boundaries, the ‘true’ main peaks appeared, one at approximate depth of 4.4 m and another one at 3.0 m. Generated profile at both ends tends to be less reliable as shown by two erroneous peaks thus should not be considered. In this case, 2.4 m can be considered as the suitable width when intraclass correlation coefficient is used.

Discussion

In general, RI appears to be a powerful tool as it can capture most of the prominent major boundaries at one time fairly accurately. Besides, it is reasonably robust which could persistently detect the main peaks at the same positions even with window widths that are fairly different from the optimize configuration. Webster’s suggestion (1973) to determine the suitable window width as a function of average distance between boundaries using autocorrelation analysis was validated. The difference for profiles generated using smaller window widths is that many undesired peaks or noises may appear, whereas larger widths tend to hidden the necessary boundaries. The empirical criterion of 0.7 (Zhang and Tumay, 1996) to guide the worker in deciding whether a peak is significant enough to be considered as a valid boundary is very useful. The criterion was found performing pretty well in most circumstances as illustrated through various distinctive case studies in this paper. Observing the results of analysis, the authors presumed that these statistical tools are likely to well perform in identifying boundaries at which each divided layer is constituted of linear trend. Nonetheless, the presumption on this limitation does not restrict the worker to combine two or more layers in the subsequent analyses as far as they possess very similar variation characteristics, i.e. scale of variance and the autocovariance distance (or scale of fluctuation). The modeling which reasonably simplifies the soil profile into fewer layers within the same geological formation and at the same time remains most of the important information is always of great interest from the pragmatic stand. Note that statistical tools do not appreciate explicit soil type classification nor engineering behaviors, thus final evaluation and decision still lie with sound engineering judgment. Note that actual soil profile could be extremely erratic and complex, thus adopting any statistical method without incorporating engineering judgment could be unsatisfactory. One of the difficulties as mentioned by Webster (1973) and Zhang and Tumay (1996)

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was solving the profile with layer thicknesses differ widely. To reduce the complication, the worker must first be clear on what he expects and properly plan before one starts the analysis. For instance, if in the first place, the rough approximate average thickness between layers is by visual seemed to be about 3.0 m, then the optimize window width would probably be around that value or somewhat slightly smaller. Any attempt that far too small or far too large from that value would be fruitless. Often, one time demarcation might not be adequate; on the other extent, excessive subdivision and modeling which has no practical value should be avoided. In the case whereby a homogeneous layer is of clear evident, for instance the clay layer from approximately 12.0 m depth to the end of exploration of about 30.0 m at the CATIFS site, that section of profile should not be mixed together with other relatively thinner layers at upper depth in the analysis (note that the clay layer from 12.0 m to 30.0 m had been excluded in the first case study here). Or else, any possible erroneous peaks appear within that section should be discarded after incorporated with visual observation and engineering judgment. For verification, the demarcated sections should be examined using stationarity tests, e.g. Kendall’s τ test, run test, sign test, etc. which are not covered in this paper. Every method has its own limitations and the underlying concepts must be well understood in order to fully exploit it appropriately. Please note that statistical tool is by mean to assist but not to confuse. 4

CONCLUSIONS

Generally, statistical tools can be utilized in identifying layer boundaries satisfactorily. RI appears to be a powerful one as it can capture most of the prominent major boundaries at one time fairly accurately. Also, it is robust and persistent which could detect the main peaks at the same positions even with fairly different window widths. Results from the analysis carried out shows that the lower limit of 1.0 m tends to create plenty of unnecessary noises which might complicate the interpretation. The resistance zone of 1.5 m appears to be too restrictive and may only apply to certain specific soil profile horizons. The conclusion obtained from previous research using 1.0 m and 1.5 m window widths are likely to be coincident. The average distance between boundaries from autocorrelation analysis seems to be most relevant, flexible and useful. The empirical criterion of 0.7 was consistently well performed in guiding the researcher to decide whether a peak is significant enough to be considered as a valid boundary. REFERENCES Baecher, G.B. & Christian, J.T. 2003. Reliability and statistics in geotechnical engineering. England: John Wiley & Sons. Brockwell, P.J. & Davis, R.A. 2002. Introduction to time series and forecasting. 2nd Ed., New York: SpringerVerlag New York.

Cafaro, F. & Cherubini, C. 2002. Large sample spacing in evaluation of vertical strength variability of clayey soil. Journal of Geotechnical and Geoenvironmental Engineering 128(7): 558–568. Casagrande, A. 1965. Role of the ‘calculated risk’ in earthwork and foundation engineering. Journal of Soil Mechanics and Foundation Division 91(SM4): 1–40. Christian, J.T. 2004. Geotechnical engineering reliability: How well do we know what we are doing? Journal of Geotechnical and Geoenvironmental Engineering 130(10): 985–1003. DeGroot, D.J. & Baecher, G.B. 1993. Estimating autocovariance of in-situ soil properties. Journal of Geotechnical Engineering 119(1): 147–166. Hegazy, Y.A., Mayne, P.W. & Rouhani, S. 1996. Geostatistical assessment of spatial variability in piezocone tests. Uncertainty in the geologic environment: from theory to practice (GSP 58): 254–268, New York: ASCE. Jaksa, M.B., Brooker, P.I. & Kaggwa, W.S. 1997. Inaccuracies associated with estimating random measurement errors. Journal of Geotechnical and Geoenvironmental Engineering 123(5): 393–401. Kulatilake, P.H.S.W. & Um, J. 2003. Spatial variation of cone tip resistance for the clay site at Texas A&M University. In Probabilistic Site Characterization at the National Geotechnical Experimentation Sites, New York: ASCE. Leonards, G.A. 1982. Investigation of failures. Journal of Geotechnical Engineering 108(GT2):185–246. Morgenstern, N.R. 1995. Managing risk in geotechnical engineering. The 3rd Casagrande Lecture. Proceedings of the 10th Pan-American Conference on Soil Mechanics and Foundation Engineering Vol. 4: 102–126, Guadalajara. NCHRP Synthesis 368 2007. Cone Penetration Testing. A Synthesis of Highway Practice. National Cooperative Highway Research Program, Washington D.C: Transportation Research Board of the National Academies. Peck, R.B. 1969. Advantages and limitations of the observational method in applied soil mechanics. Geotechnique 19(2): 171–187. Phoon, K.K. & Kulhawy, F.H. 1999. Characterization of geotechnical variability. Canadian Geotechnical Journal 36: 612–624. Phoon, K.K., Quek, S.T. & An, P. 2003. Identification of statistically homogeneous soil layers using modified Bartlett statistics. Journal of Geotechnical and Geoenvironmental Engineering 129(7): 649–659. Robertson, P.K. 1986. In-situ testing and its application to foundation engineering. Canadian Geotechnical Journal 23(3): 573–587. Vanmarcke, E.H. 1977. Probabilistic modeling of soil profiles. Journal of the Geotechnical Engineering Division 103(GT11): 1227–1246. Webster, R. 1973. Automatic soil boundary location from transect data. Mathematical Geology 5(1): 27–37. Wickremesinghe, D. & Campanella, R.G. 1991. Statistical methods for soil layer boundary location using the cone penetration test. Proc., ICASP6: 636–643, Mexico City. Wickremesinghe, D.S. 1989. Statistical characterization of soil profile using in-situ tests. PhD thesis, Univ. of British Columbia, Vancouver, Canada. Wu, T.H. 1974. Uncertainty, safety and decision in soil engineering. Journal of the Geotechnical Engineering Division 100(GT3): 329–348. Zhang, Z.J. & Tumay, M.T. 1996. The reliability of soil classification derived from cone penetration test. Uncertainty in the geologicenvironment: From theory to practice (GSP 58): 383–408, New York: ASCE.

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Soil variability calculated from CPT data T. Oka & H. Tanaka Graduate School of Engineering, Hokkaido University, Japan

ABSTRACT: The design method based on reliability has extensively used for construction of civil engineering structures, even in foundation design. Since the ground is not artificially but naturally created, the reliability method for conventional structures such as steel or concrete cannot be directly to the foundation design. This is because variability in soil properties may be different from that in other civil engineering materials. It is necessary to establish data base for showing variability in various grounds. In this present study, using data measured by Cone Penetration test (CPT), statistical analyses are carried out for selected 11 sites.

1

2 TESTED SITES AND METHOD OF CPT

INTRODUCTION

The design method based on reliability was introduced and has been gradually used for construction of civil engineering structures, including design of foundations. However, there are a lot of problems in this method when applying it to geotechnical engineering. For example, soil properties are different from those of other civil engineering materials, such as concrete and steel. Because the ground is naturally deposited except for compacted or improved soils, variability in soil properties is completely different from artificially manufactured materials whose properties are strictly controlled. In addition to this inherent difference, human errors at measurement of soil parameters should be taken account. Sample disturbance is one of key issues to obtain reliable soil parameters at laboratory test. Although in situ tests do not need to consider the sample disturbance, measured values are strongly influenced by the drilling method and/or the testing method. In Standard Penetration Test (SPT), for example, the method for dropping the hammer affects the N value. Cone Penetration Test (CPT) has been gradually used even in Japan. The most advantage feature of the CPT over other in situ tests may be that measured values are nearly free from human factors, because it does not require a borehole and its testing procedures are relatively simple. In addition, the CPT can obtain geotechnical information nearly continuously to depth. In this study, using CPT data measured at various 11 sites in Japan as well as overseas, variability in soil parameters is examined. Also, for comparison, variability in N value for sandy ground and the unconfined compressive strength (qu ) for clayey ground is investigated.

Statistical analyses were carried out for 11 sites, whose main features and location are indicated in Table 1 and Fig. 1 (excluding overseas sites), respectively. From Hachirogata to Amagasaki sites in Table 1, the ground consists of normally consolidated clayey soil. The burden pressure at Hachirogata and Busan sites does not so much change (except for fluctuation of the ground water table), while sites of Singapore and Amagasaki were recently reclaimed, but consolidation due to the filling is considered to be completed. From Kagoshima to Tomakomai, investigated grounds consist of granular materials. Material at Kagoshima, Nakasibetsu and Tomakomai sites is volcanic ash. At Kagoshima site, volcanic ash was transported and deposited by rivers at Kagoshima

Figure 1. Testing Sites in Japan.

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Table 1.

Features for tested sites and Analyzed results from CPT data.

Site

Soil Type

Hatchirogata Busan

Clay Clay

Depth (m) a (MPa/m) b (MPa/m) β1

10∼37 5∼23 5∼23 Singapore Clay 18∼30 Amagasaki1 Clay 11∼19 Amagasaki2 Clay 11∼19 Kagoshima Volcanic Ash 5∼30 Yodogawa Sand 5∼20 Nakashibetsu Volcanic Ash 4∼10 Kemigawa Sand 6∼20 Higashiohgishima Filling (sandy) 5∼20 Tsuruga Filling 4∼16 (Crush Rock) Tomakomai Volcanic Ash 13∼20 sand no sand

β2

σ (MPa) Reference

−0.08 0.044 0.041 0.33 −0.32 −0.3 9.23 12.1 −8.61 −8.4 4.4 3.2

0.03 0.022 0.022 0.037 0.091 0.088 −0.0096 0.15 2.18 1.41 −0.092 0.3

0.0067 2.89 0.02 1.8 10.82 0.028 0.000062 2.63 0.024 0.00033 2.73 0.024 0.052 3.32 0.04 0.066 2.59 0.043 0.0986 3.87 1.35 0.061 2.93 3.74 0.78 1.98 4.61 0.33 3.1 1.94 2.16 5.18 1.92 0.0064 3.26 2.54

7.48

−0.0037

1.23

site (secondary deposition), while at the site of Nakashibetsu and Tomakomai, the ash was directly deposited by wind at the eruption (primary deposition). Yodogawa and Kemigawa sites are located in the riverside (“gawa” means river in Japanese), and their ground consists of mainly sandy material. Higashiougishima and Tsuruga sites are on a reclaimed land by sand and crushed gravel, respectively. More detail information on soil properties for sites are available in literatures indicated in Table 1. CPT was conducted following the specification of the international reference test procedure proposed by the ISSMFE technical committee on penetration testing (1988): the apex angle of the cone is 10 cm2 (the diameter is 35.7 mm); the apex angle of the cone is 60◦ ; the location of the filter for measuring pore water pressure is the shoulder behind the cone and the speed of the penetration is 2 cm/s. The point resistance (qt ) is corrected by the effective area and takes into account pore water pressure acting on the filter. 3 ANALYSES OF CPT DATA 3.1 A trend function due to increase in burden pressure qt measured by CPT may be broken down into a trend function [t(z1 . . . zn )] and set of residuals to the trend [ξ(z1 . . . zn )]: i.e., qt = qt (t) + qt (ξ). As a typical example of CPT result from clayey soil, Fig. 2 shows qt distribution at the site of Busan. In this example, qt values clearly increases with depth. The qt can be expressed by the following equation:

where, Nkt , Su and σvo are the cone factor, the undrained shear strength and the total burden pressure, respectively. σvo increases with depth and for normally consolidated ground, Su also increases with depth because of increase in consolidation pressure. Therefore, it is

Tanaka, 2006 Tanaka et al., 2001a Tanaka et al., 2001b

Mimura, 2003 Tanaka, 1999

4.05 0.85

Figure 2. (a) Measured and trend qt at Busan site. (b) Residuals at Busan site.

anticipated that qt linearly increases with depth (z), especially for the normally consolidated soil layer. On the other hand, for sandy soil, in another word, where the penetration of CPT is performed under drained condition, it is well known that qt does not increase lin
0.5 early with σvo , but with σvo . However, in this study, as a preliminary study, it is assumed that qt values from CPT have a trend function of the following linear equation:

where z is depth. Constants of a and b are calculated by the least square regression method. The calculated trend line at Busan site is shown in Fig. 2. In this site, depths for obtaining the trend line are restricted from 5 m to 23 m. Fig. 3 shows observed qt values and the trend line at the site of Kagoshima, which is covered by thick volcanic ash that was transformed by river from “Shirasu” terrace. Constants of a and b for other areas are

288

Figure 3. (a) Measured and trend qt at Kagoshima site. (b) Residuals at Kagoshima Site.

Figure 4. Pearson chart from CPT.

indicated in Table 1. For clayey ground, constant of b is related to increment of Su because unit weight of soil (γt ) does not so much vary in sites. It is shown that b for Amagasaki is clearly larger than that for other sites. For granular ground, b constants are completely different among sites, and those in some sites indicate negative values: see for example, Kagoshima, as shown in Table 1 and Fig. 3.

3.2

are plotted, and β1 and β2 are defined by the following equations.

where, Csk and Cku are skewness and kurtosis, respectively, and these equations are given as follows:

Residuals

Residuals (qt (ξ)) are a difference between measured qt and calculated from the trend line qt (t) at the same depth. Distribution of qt (ξ) is shown in Figs 2(b) and 3(b), for Busan and Kagoshima sites, respectively. It is thought that qt (ξ) consists of two components: measurement error and variation caused by heterogeneity of the objective layer. It is interested to note that qt (ξ) does not increase in depth but nearly constant for both Busan (clay) and Kagoshima (volcanic ash). This indicates that qt (ξ) is not influenced by magnitude of qt . In another word, qt (ξ) is not suitable to treat as normalized such as coefficient of variation, qt (ξ)/qt (t), since qt (ξ)/qt (t) decreases in depth. Standard deviation of qt (ξ) is indicated in Table 1 (its symbol is σ). As expected, σ for clayey ground is definitely smaller than that for granular ground, and its difference is as much as 100 times. This means that variation in qt is smaller than that for granular grounds, in addition to small qt itself for clayey ground. For studying properties of qt (ξ), it may be useful to know what shape of the qt (ξ) distribution is suitable. If qt (ξ) is formed by measurement errors, qt (ξ) should follow the normal distribution. In this study, Pearson chart (see Fig. 4) will be used for examination of qt (ξ) distribution. Pearson developed an efficient system for the identification of suitable probability distributions based on third and forth moment statistics of a data set, as shown in Fig. 4 (Baecher & Christian). In his chart, β1 for the horizontal axis and β2 for vertical axis

where, n, ϕi , mϕ , sϕ are sample numbers, residuals, sample mean, sample standard deviation, respectively. mϕ , sϕ are given as follows.

The values of β1 and β2 at various sites are indicated in Table 1. For clayey ground, β1 is relatively small compared with granular ground, except for Busan. β1 as well as β2 at the Busan site is extremely large, even in comparison of those for granular grounds. The reason for large these values at the Busan site may be attributed to the existence of sand layers. As shown in Fig. 2, at depths of 10 and 16 m, qt suddenly increases. From the data showing the pore water pressure, it was revealed that sand layers exist in these depths. When qt data at these sand layers are omitted, both β1 and β2 are dramatically changed, as shown in Table 1. Especially β1 was changed from 1.8 to 0.000062. However, the trend function (see a and b in the table) is not changed (though a little change in a), but σ is also slightly changed only from 0.028 to 0.024 (MPa). The distribution of qt (ξ) with sand layer and without sand

289

Figure 6. Measured values and trend line from UCT at Busan Site.

Figure 5. Histogram of residuals at Busan Site.

layer are compared in the histogram of Fig. 5. It can be seen that the shape of the histogram for both cases are almost same each other, except for a few data exceeding 80 kPa, which corresponds to qt at sand layers. The existence of these extreme values, though its frequency is very small, significantly β1 and β2 values. β1 and β2 of qt (ξ) for investigated sites in this paper are plotted in Pearson’s chart, as shown in Fig. 4. It can be seen that β1 and β2 relation for clayey and most granular grounds are distributed along “log Normal distribution” line and β1 values are nearly zero. Therefore, it can be judged that qt (ξ) for clayey and most granular grounds “follow normal distribution”. Some granular grounds (Kemigawa, Higashiougishima and Nakashibetsu) may follow Beta distribution.

4 ANALYSIS OF SPT AND UCT DATA Although CPT has gradually used in Japan, the most conventional testing method is SPT for granular soils and the unconfined compression test (UCT) for clayey soil. The same analysis is carried out for data from SPT and UCT. Figs 6 and 7 show qu /2 and N values for Busan and Kagoshima sites, respectively, with superimposed trend lines calculated by the regression method. It is interested to note that the trend line for the Kagoshima site also has a negative slope, similarly to that for CPT (see Fig. 4). Analyzed results are indicated in Table 2.

Figure 7. Measured values and trend line from SPT at Kagoshima Site.

For granular grounds, the slope of the trend line (i.e., b value) is compared for SPT and CPT in Fig. 8. It can be seen that there is a good relation between them. Fig. 9 shows the relation between σ obtained by SPT and CPT. It is also found that when σ for CPT is large, σ for SPT is also large. This fact indicates that the variation from the trend line may be caused mainly

290

Table 2. Analyzed results from UCT & SPT.

Site

Soil Type

Hatchirogata Busan Singapore Kagoshima Yodogawa Nakashibetsu Kemigawa Higashiohgishima

Clay Clay Clay Volcanic Ash Sand Volcanic Ash Sand Filling (sandy) Filling (Crush Rock) Volcanic Ash

Tsuruga Tomakomai

Testing Method

Sample Number

a (MPa/m)

b (MPa/m)

β1

β2

σ (Mpa)

UCT UCT UCT SPT SPT SPT SPT SPT

28 15 7 35 20 10 22 13

0.012 0.028 −0.016 21.46 21.16 −11.11 −21.04 −1.18

0.00072 0.0029 0.0032 −0.28 0.17 2.96 3.21 0.75

1.02 9.67 0.46 0.091 0.18 0.003 1.54 0.47

4.83 14.04 1.41 1.95 4.74 3.08 4.76 3.07

0.0047 0.029 0.0019 3.64 5.55 3.59 4.64 4.19

SPT

24

3.09

0.66

0.19

2.67

4.78

SPT

26

9.65

−0.024

1.21

3.75

1.98

Figure 8. Comparsion between SPT and CPT for b value.

Figure 10. (a) Comparsion between SPT and CPT for β1 value. (b) Comparsion between SPT and CPT for β1 value. Figure 9. Comparsion between SPT and CPT for σ value.

by heterogeneity in the ground, not by measurement error. Unlike σ or b, β1 and β2 for Pearson’s chart do not have dimension so that these values are comparable for grounds measured by SPT and UCT. β1 and β2 are calculated from SPT or UCT data and plotted in the Peason’s chart of Fig. 10. Compared with Peason’s chart from CPT, points from SPT and UCT are much

scattered, especially β2 values are larger. β1 and β2 are compared in Fig. 10(a) and (b). Though any meaningful relation for β1 can be hardly identified, it seems that there exists a weak relation for β2 . 5

CONCLUSIONS

Using CPT data, soil variability was examined for 11 different sites, consisting of various soil materials: i.e.,

291

clay, volcanic ash, sand and crushed gravel. Measured qt values are broken down into trend function and residuals, assumed that the trend is expressed by a linear line to depth. Properties of residuals are analyzed and the main conclusions are as follows: 1) The distribution of residuals from CPT at most sites follows the normal distribution. However, some granular grounds (Kemigawa, Higshiohgishima, Nakashibetsu) follow Beta distribution. 2) Statistical parameters such as σ, β2 calculated from SPT or UCT have relatively good relation to those from CPT. REFERENCES Baecher, B. & Christain, T. 2003. Reliability and Statistics in Geotechnical Engineering. England: Wiely

Mimura, M. 2003. Characteristics of some Japanese natural sands-data from undisturbed frozen samples, Characteristation and Engineering Properties of Natural Soils–Tan et al.(eds), (2): 1149–1168. Tanaka, H. 2006. Goetechnical properties of Hachirogata Clay. Characterization and Engineering Properties of Natural Soils, Vol. 3: 1831–1854. Tanaka, H., Mishima, O. & Tanaka, M. 1999. Applicability of CPT and DMT for grounds consisting of large granualar particles, Journal of Japanese Society for Civil Engineerings, III–49: 273–283, (in Japanese). Tanaka, H., Mishima, O., Tanaka, M., Park, S. Z, Jeong, G. H. & Locat, J. 2001a. Characterization of Yangsan clay, Pusan, Korea, Soils and Foundations, Vol. 41(2) : 89–104. Tanaka, H., Locat, J., Shibuya, S.,Tan,T. S. & Shiwakoti, R. D. 2001b. Characterization of Singapore, Bangkok and Ariake clays, Canadian Geotechnical Journal, 38: 378–400.

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Reducing uncertainties in undrained shear strengths Jianye Ching National Taiwan University, Taipei, Taiwan

Yi-Chu Chen National Taiwan University of Science and Technology, Taipei, Taiwan

Kok-Kwang Phoon National University of Singapore, Singapore

ABSTRACT: Undrained shear strengths (su ) play important roles in geotechnical designs. In the context of geotechnical reliability-based design, reducing uncertainties in su can be an important research topic. There are at least two ways of reducing uncertainties in su : conduct laboratory or in-situ tests to obtain indices or parameters to correlate su indirectly. The way of reducing uncertainties in su can be challenging. The challenge lies in the fact that the so-obtained indices and parameters, e.g. CPT value, cannot be directly used to estimate su but can estimate su only through correlations. Above all, there is a challenge in combining information: how to reduce uncertainties in su when there are multiple sources of information? In this paper we will address the aforementioned challenges and propose a probabilistic framework to handle these difficulties. Sets of simplified equations will be obtained through the probabilistic analysis for the purpose of reducing uncertainties: the inputs to the equations are the results of in-situ or laboratory tests and the outputs are the updated mean values and coefficients of variation (c.o.v.) of the desirable undrained shear strengths. The uncertainties in su will decrease when the number of inputs increase, i.e. more information is available. The results of this research may be beneficial to geotechnical reliability-based design. 1

INTRODUCTION

Uncertainties are commonly encountered in geotechnical engineering. Possible sources of uncertainties include inherent variabilities, measurement errors, modeling uncertainties, etc. More economical geotechnical designs can be achieved by reducing the uncertainties in soil shear strengths through site investigation. 1.1 Reducing uncertainties by correlations In practice, it is already well-known that field or laboratory test data, denoted as “test indices” from hereon, can be combined to reduce the uncertainties in undrained shear strengths through correlations. For instance, given the field SPT-N test data, it is possible to infer first-order estimates of the mean value and coefficient of variation (c.o.v.) of the undrained shear strength (Su ) of the clay under consideration. This process of pairwise correlation is illustrated in Figure 1 – for a given observed SPT-N value (N), the corresponding mean value and c.o.v. of the undrained shear strength can be estimated. In the literature, such pairwise correlations between various test indices and undrained shear strengths have been widely studied. Table 1 lists examples of previous research studying such correlations. In particular,

Figure 1. Su versus SPT-N relationship.

Kulhawy and Mayne (1990) and Phoon (1995) both contain fairly comprehensive reviews about the pairwise correlations between various test indices and undrained shear strengths. 1.2 Graphical model for clayey soils The undrained shear strength (Su ) considered is the undrained shear strength determined by CIUC

293

Table 1. Previous research studying pairwise correlations between various test indices and undrained shear strengths.

2

Correlation pair

Examples of previous research

2.1 Database

Standard penetration test (SPT-N) Cone penetration test (CPT) Pressure meter test (PMT) Dilatometer test (DMT) Vane shear test (VST) Plasticity index (PI)

Terzaghi and Peck (1967); Hara et al. (1974) Keaveny and Mitchell (1986); Konrad and Law (1987) Mair and Wood (1987) Lacasse and Lumme (1988) Bjerrum (1972); Mersi (1975) Skempton (1957); Chandler (1988) Ladd et al. (1977); Jamiolkowski et al. (1985)

Probabilistic models for the pairwise correlations between undrained shear strengths and the chosen test indices are necessary for the Bayesian analysis. Therefore, efforts were made in compiling a correlation database, e.g. the Su vs. SPT-N data points shown in Figure 1, from the literature to estimate the probabilistic models for the pairwise correlations. For the database, it is always a concern whether the compiled data points are enough to cover a wide range of possible scenarios. The following guidelines are followed to mitigate this concern: (a) Unless mentioned explicitly, data points in the database do not include those from special clays, e.g. fissured and organic clays. Therefore, the corresponding correlations should not be applied to those soils; (b) In the case that all data points of a particular correlation are from the same geographical region, that correlation may be only applicable to that region. In general, the applicability to other regions is questionable. Bayesian updating will not reduce the physical limitations inherent in existing pairwise correlations. It merely provides a more rational and systematic method for combining information that will serve as a useful complement to engineering judgment. The following strategy is adopted to obtain the probabilistic models for the pairwise correlations given the pairwise-correlation data points:

Overconsolidation ratio (OCR)

Figure 2. Graphical model for clayey soils.

(isotropically consolidated undrained compression) tests. Figure 2 presents the graphical model adopted for clays in this paper. For the model of Su of clayey soils, the adopted test indices are limited to the following: (a) overconsolidation ratio (OCR); (b) energy-ratio corrected SPT-N value (N60 ); (c) adjusted CPT reading qT

= qT − σv0 , where σv0 is the total vertical stress, and qT is the CPT reading corrected with respect to the pore pressure behind the cone. The underlying assumptions of this model are: (a) OCR is the main factor influencing the undrained shear strength, which in turn influences SPT-N and CPT values, i.e. the undrained shear strength is treated as the consequence of OCR, and SPT-N and CPT values are treated as consequences of the undrained shear strength; (b) given the undrained shear strength of a clay, its SPT-N and CPT values are independent of OCR, i.e. the undrained shear strength serves as a sufficient statistics of the SPT-N value and CPT reading: once the undrained shear strength is known, OCR does not contain further information of SPT-N and CPT values; (c) given the undrained shear strength, its SPT-N value and CPT reading are mutually independent. In other words, the SPT-N value and CPT reading are treated as two pieces of independent information for the undrained shear strength. This model is deemed to be reasonable for unstructured unfissured inorganic clays. The first two moments of the following quantities are needed for the Bayesian analysis: (a) Su conditioning on OCR; (b) N60 conditioning on Su ; (c) qT

conditioning on Su . Details are given below.

PROBABILISTIC MODELS FOR PAIRWISE CORRELATIONS

– (a) In the case that the pairwise data points for a certain correlation are sufficient, the data quality will be verified through empirical correlations in the literature. Only those data points that are consistent with the literature will be later used to derive the probabilistic model for that correlation. – (b) In the case that the pairwise data points for a certain correlation are insufficient, the empirical correlation provided by literature that best matches the data points will be adopted to derive the probabilistic models for that correlation. If the c.o.v. of the adopted empirical correlation is not available in the literature, it will be estimated from the data points at hand. – (c) In the case that the pairwise data points for a certain correlation are absent, the empirical correlation provided by literature will be adopted. 2.2 Probabilistic models for pairwise correlations in clays Recall that the first two moments [mean and coefficient of variation (or standard deviation)] of the following quantities are needed: (a) Su conditioning on OCR; (b) N60 conditioning on Su ; (c) qT

conditioning on Su . The derivations of the first two moments are presented in detail below.

294


Figure 3. Su /σv0 vs. OCR correlation, and the mean value and 95% confidence interval proposed by this research.

2.2.1 First two moments of Su conditioning on OCR Overconsolidation ratio OCR is assumed to be the main basic index affecting Su . Mayne (1988) compiled
a set of Su /σv0 vs. OCR data (the Su data points were all from CIUC tests), shown in Figure 3. Based on the data, a least-square method is taken to obtain the following correlation:

Figure 4. The mean value of 95% confidence interval proposed by this research.

where εSu is the prediction error term. Its standard deviation is found to be around 0.237. Therefore,

and the standard deviation of this correlation is 0.237. Figure 3 shows the mean value and 95% confidence interval of this equation and the comparison with the actual data. In the case that the OCR information is not available, the prior c.o.v. for Su is taken to be a very large number. 2.2.2 First two moments of N60 conditioning on Su The correlation between Su of clayey soils and the SPT-N value is well known. Figure 4 compiles the pairwise data for this correlation summarized by Hara et al. (1974) (also see Phoon (1995) and Kulhawy and Mayne (1990)), where the undrained shear strengths are determined by UU tests. Note that all data points here are from clays in Japan. The following equation was proposed:

where SuUU denotes the undrained shear strength determined by a UU test; N is uncorrected SPT-N value; the standard deviation of ε1 is roughly 0.15 (Phoon 1995). The SPT-N energy ratio is roughly 78% in Japan (Chen 2004); therefore, the N value in (3) is roughly 1.3 N60 . In other words,


Figure 5. ln(SuUU /Su ) vs. ln(Su /σv0 ) correlation, and the mean value of 95% confidence interval proposed by this research.

Equation (4) can be used to obtain the first two moments of SuUU conditioning on N60 ; however, our goal here is to derive the first two moments of N60 conditioning on Su . With the same data set in Figure 4, a least-square method is taken to obtain the following equation:

where the standard deviation of ε2 is 0.407, and the unit of SuUU is in kPa. The 95% confidence interval of this new equation is shown in Figure 4 for comparison. Moreover, according to the database presented in Chen and Kulhawy (1993) (see Figure 5), the correlation between undrained shear strength determined by UU and CIUC tests are as follows:

where the standard deviation of ε3 is roughly 0.167,
and σv0 is the effective vertical stress. The mean value of 95% confidence interval together with the database

295

3

presented in Chen and Kulhawy (1993) are plotted in Figure 5. Equations (5) and (6) imply that


where Su and σv0 are both in the unit of kPa, and the standard deviation of εN is (0.4072 + 1.2302 · 0.1672 )0.5 = 0.456 = 0.456. Therefore,

and the standard deviation of this correlation is 0.456. 2.2.3 First two moments of q

T conditioning on Su The correlation between undrained shear strength and the CPT reading has been studied in several literature, e.g. Hanzawa (1992) (direct shear test), Tanaka and Sakagami (1989) (CIUC test), Fukasawa et al. (2004) (vane shear and unconfined compression tests) and Anagnostopoulos et al. (2003) (UU tests). The following correlation equation is commonly adopted (e.g. Lunne et al. (2002), Kulhawy and Mayne (1990)):

where Nk is called the cone bearing factor. Theoretical studies showed that Nk ranges from 7 to 18. Several experimental studies indicated that the measured Nk can vary wildly from 4.5-75, probably due to inconsistent reference strengths, mixing of different types of cones, need for correction on pore water pressure, etc. (Kulhawy and Mayne 1990). On the other hand, Phoon (1995) reported that:

for CIUC test results. This corresponds to Nk = 12.7, which agrees well with the theoretical results (Nk ranging from 7 to 18). Phoon (1995) further reported that the uncertainty of (10.) is roughly 35%. The probabilistic version of (10) is therefore

In the case that only a single piece of information is available, updating the mean value and c.o.v. of undrained shear strength is not difficult. For instance, given that SPT-N value of a clay sample is 10, from Figure 1 it is concluded that the updated mean value of Su is roughly 160kPa, and c.o.v. is roughly 30%. The same principle can be used to update mean and c.o.v. of undrained shear strength based on another single piece of information. However, in the case that multivariate test data is available, e.g.: SPT-N and OCR of a clay sample are available, updating the mean value and c.o.v. of the Su is less straightforward. Bayesian analysis is a natural way of handling multivariate information, even conflicting information. The basic Bayes’ rule consists of the following equation:

where x and y can be both vectors; y is the uncertain variable of interest, while x is the observed variable. f (y) is called the prior PDF of y, quantifying the uncertainties in y before observation on x is made, and f (x|y) is called the likelihood function of y given x. f (y|x) is the updated or posterior PDF of y conditioning on the information of x. As an example, let y be the logarithm of the undrained shear strength. In the case that OCR is given, f (ln(Su )|ln(OCR)) then serves as the prior PDF f (y). If the observed variable x is the corrected SPT-N value N60 , f (ln(N60 )|ln(Su )) serves as f (x|y). Then

represents the updated (posterior) PDF of the undrained shear strength given the multivariate information {N60 ,OCR}. In this paper, we have implemented the aforementioned model assumption that conditioning on Su , N60 is independent of OCR. 4

where ε4 is zero-mean with standard deviation equal to 0.34, corresponding to the 35% uncertainty of (10.). A simple Bayesian argument can transform the above equation into:

where εqT is also zero-mean with standard deviation equal to 0.34. Therefore,

BAYESIAN INFERENCE WITH MULTIVARIATE TEST DATA

MAIN RESULTS

If the variable of interest and the observed variable are jointly Gaussian, it is possible to derive all relevant conditional means and conditional variances in closed-form. Using these results, the updated mean and variance of the logarithm of the undrained shear strengths conditioning on various combination of multivariate test data are listed in the following with detailed derivations: Conditioning on OCR:

and the standard deviation of this correlation is 0.34.

296

Table 2.

Conditioning on N60 :

Conditioning on qT

:

Conditioning on OCR, N60 :

qT

1 (kPa)

11.3 12.8 14.8 16.1 17.1 17.8 18.3 20.2 20.2 20.9 22.7 24.0 26.6

43.1 76.5 82.4 88.7 58.4 85.8 93.8 106.2 111.2 115.7 101.9 121.3 139.8

628.9 577.1 459.9 420.0 454.9 479.0 495.4 543.5 544.6 561.5 636.7 772.8 1047.3

CK0 U UU VST UU CK0 U UU VST UU UU VST VST UU UU

1.6 1.4 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0

9.1 9.1 12.8 14.6 17.5 18.9 18.5 17.3 17.3 16.8 16.0 16.2 13.8

4.0 3.0 3.3 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.8 5.6 7.2

206.4 233.4 270.2 293.6 312.0 324.7 334.7 368.4 369.2 381.1 413.9 437.4 485.4

115.5 128.0 144.9 155.6 164.0 169.9 174.5 190.0 190.3 195.8 210.9 221.7 243.7

835.3 810.5 730.1 713.6 766.8 803.7 830.0 911.9 913.7 942.6 1050.6 1210.2 1532.6

Strictly speaking, this is not qT

because the CPT reading was not corrected against the pore pressure behind the cone.

Conditioning on N60 and qT

:

Conditioning on OCR, N60 , qT

:

The above results provide estimates for the first two moments of ln(Su ). Let us denote the estimated mean value and standard deviation of ln(Su ) by m and s, respectively, then the mean value and c.o.v. of Su are exp(m + s2 /2) and [exp(s2 ) − 1]0.5 , respectively, by assuming lognormality.

5.1

Depth Test (m) type

Equiv. Test indices CIUC
Su value PI σv0 σv0 qc (kPa) OCR (%) N60 (kPa) (kPa) (kPa)

1

Conditioning on OCR, qT

:

5

In-situ test data and indices for the Taipei case.

CASE STUDIES Clays in a deep excavation site of Taipei

A deep excavation site is extracted from Ou (2006). SPT-N and CPT tests were conducted at this site. The soil profile includes three thick clayey layers and three thin sandy layers. The water table is 2 m below the surface. Cone penetration and vane shear test results were taken to estimate the undrained shear strength of the clays. Moreover, several undisturbed clay samples are

extracted from the site, and laboratory tests, including UU and CK0 U tests, were taken to determine the undrained shear strengths. In principle, undrained shear strengths from different test types cannot be directly compared. Therefore, attempts are made to convert all undrained shear strengths into their equivalent CIUC values through empirical transformations suggested by Kulhawy and Mayne (1990) for CK0 UC to CIUC, suggested by Chen and Kulhawy (1993) for UU to CIUC and suggested by Ladd et al. (1977) for VST to field value (closer to DSS value; the DSS values are further converted to CIUC values by the transformation equations suggested by Kulhawy and Mayne (1990)). Table 2 summarizes the tested undrained shear strengths and their equivalent CIUC values as well as the other in-situ test indices of the clay at various depths. Notice that qT data is not available for this site since the behind cone pore pressure was not documented. As a result, qc data is directly taken to compute qT

for this case study, i.e. qT

= qT − σv0 . Because qT is always greater than qc , the actual qT

values should be larger than the qT

value reported in the table to a certain degree. Based on these data and the formulas provided in the previous section, the updated mean values and 95% confidence intervals (±2 standard deviations) with respect to depth are plotted in the left column in Figure 6 for various combinations of test indices D (Cases 1-7 in the figure). The mean values E(Su |D) and standard deviations Var(Su |D)0.5 are both normalized with respect to the measured equivalent CIUC values Sum , so mean = 1 indicates the updated mean is the same as the measured equivalent CIUC value. It is evident that the updated standard deviation of Su decreases as more information is taken for the updating. Let us take Cases 1, 2 and 4 as examples: When only one piece of information is involved (Case 1 for OCR and Case 2 for N60 ), the confidence intervals

297

Figure 6. Updated mean values and 95% confidence intervals of Su with respect to depth (normalized with respect to the measure Su ) for the Taipei case.

seem large, manifesting more uncertainties. When the OCR and N60 information is combined (Case 4), the confidence intervals start to shrink; moreover, although the confidence intervals become smaller, most of them still contain 1, i.e.: the measured equivalent CIUC value Sum still lies within the intervals. When all information is implemented, i.e. Case 7, the c.o.v. of the undrained shear strength is as low as 0.16. Compared to the c.o.v.s for Cases 1-3 that ranges from 0.24 to 0.34, the 0.16 c.o.v. is a major improvement: the uncertainty in Su is effectively reduced by incorporating multivariate data. Notice that relatively larger biases are found in the estimated Su values for Cases 3, 5 and 6. This can be clearly seen in the plots for Cases 3, 5 and 6, where the estimated mean values E(Su |D) deviate from 1. These are the cases where qT information is incorporated. These biases are obviously due to the fact that the employed qc values here are less than the actual qT values, so the estimated mean values of Su are significantly less than their actual CIUC values. However, by also incorporating OCR and N60 information, i.e. Case 7, the bias is significantly reduced. Therefore, incorporating more information not only reduces uncertainties but also reduces bias. Obviously, if the data is judged to be incomplete such as qT , it is preferable not to include these data, even if bias

can be reduced by including more sources of information. In other words, we do not recommend including all sources of information indiscriminately. Engineering judgment is still important in this interpretation process. The performance of the proposed Bayesian method is further compared with the level-1 T.E.A.M. approach (Technical Expert Averaging Method, Briaud et al. (2002)). The level-1 TEAM approach is an intuitive way of combining multivariate information. Taking Case 7 as an example: there are 3 prediction methods (predictions based on OCR, N60 and qT

) over 13 measured events {Sum j , j = 1, . . . , 13}, and the i-th method gives prediction E(Suj |Di ) for Sum j . The ratio rij = E(Suj |Di )/Sum j is treated as a measure of performance of the i-th prediction method over the j-th measured event; it has standard deviation = σi , which is estimated as the sample standard deviation of {rij : j = 1, . . . , 13}. The TEAM ratio rTEAM ,j for the j-th measured event is simply the arithmetic average (r1j + r2j + r3j )/3. The TEAM standard deviation is simply σTEAM ,j = [(σ12 + σ22 + σ32 )/3]0.5 – it is not a function of j and hence we drop j from the subscript from hereon. Note that the TEAM standard deviation σTEAM is estimated based on the ratios {rij : j = 1, . . . , 13}, which in turn based on the measured data {Sum j , j = 1, . . . , 13}. The TEAM 95% confidence intervals for the j-th measured event can then be plotted as rTEAM ,j ± 2 σTEAM . The estimated TEAM ratios and their 95% confidence intervals are plotted in the right column in Figure 6. For the cases not involving qT

, i.e.: Cases 1, 2 and 4, the performance is similar to those from the Bayesian method proposed in this paper (see left column). It is reassuring that the proposed Bayesian method does agree with the empirical rule-of-thumb observed in numerous foundation capacity prediction exercises that “averaging” seems to improve predictions. It is noteworthy that the proposed Bayesian method can also be applied to improve estimation of foundation capacities by combining laboratory and in-situ based formulae. The Bayesian method is admittedly more analytically involved than simple averaging, but it does provide a more general and rigorous framework for deriving practical approximate results such as Eqs. (16.) to (22.). In addition, the Bayesian method will serve to validate the theoretically correctness of “averaging”. Furthermore, it is quite significant that the Bayesian method gives similar standard deviations to the TEAM method for Cases 1, 2 and 4: the standard deviations given by the former are completely independent of the Su values of the 13 data points (the standard deviations are actual fixed numbers as seen in Eqs. (16.) to (22.)), while those estimated by the latter depend on the Su values of the 13 data points. In this sense, the comparison between the Bayesian and TEAM methods is already inequitable, because the latter uses very valuable new information, i.e.: the Sum j , values of the 13 data points, that is usually not available before site investigation is taken. The consistency between the Bayesian

298

and TEAM results suggests that the Bayesian method can effectively predict standard deviations close to their actual values. For the cases involving qT

, i.e.: Cases 3, 5, 6 and 7, the TEAM standard deviations are obviously smaller than those estimated by the Bayesian method although the TEAM ratios are obviously biased. The TEAM standard deviation is small because it is purely the sample standard deviation of the observed ratios {rij : j = 1, . . . , 13}: when these ratios are consistently biased – as seen in Cases 3, 5, 6 and 7 – their sample standard deviation will be small. However, the standard deviation of the Bayesian method is estimated purely from the training database (data from past correlations), not from the observed ratios. In fact, one can see that the variances from Eqns (16.) to (22.) are independent of the observed ratios. In this sense, the standard deviation estimated by the Bayesian method seems to be robust against the bias in the ratios. 5.2

Clays in various regions of the world

Ten soil profiles are extracted from Rad and Lunne (1988); they are located around the world, including Norway, North Sea, Norwegian Sea, England, Brazil and Canada. In these soil profiles, both OCR and qT data are available; moreover, the actual values of Su are known from either CIUC or CK0 UC tests. Similarly, the CK0 UC values are converted to their equivalent CIUC values before comparisons are made. Three scenarios of site investigation information are considered: Case 1: only OCR information is known; Case 2: only qT information is known; Case 3: OCR and qT are both known. The updated mean values and 95% confidence intervals, both normalized with respect to the measured equivalent CIUC Su , are shown in the first column in Figure 7. The analysis results show that the uncertainties are effectively reduced by incorporating more information: when OCR and qT information is both implemented, i.e. Case 3, the c.o.v. of the undrained shear strength is as low as 0.195. Compared to the c.o.v.s for Cases 1 and 2 that ranges from 0.237 to 0.337, the 0.195 c.o.v. is a major improvement. Furthermore, although the confidence intervals for Case 3 are small, they still mostly contain 1, indicating that the analysis performs satisfactorily. For all cases, the performance of the proposed Bayesian method is again compared with the level-1 T.E.A.M. approach (the second column). Unlike the deep-excavation example, they are similar to the results of the multivariate Bayesian analysis probably because in the current example, the systematic bias in the TEAM ratios does not exist. Again, it is quite significant that the Bayesian method gives similar standard deviations to the TEAM method for all cases: the Bayesian method can effectively predict standard deviations close to their actual values.

Figure 7. Updated mean values and 95% confidence intervals of Su (normalized with respect to the measure Su ) for the ten sites.

5.3 Discussions for the case studies – For both case studies, the updated mean values and confidence intervals (i.e. c.o.v.s) are consistent to

299

–

–

–

–

the actual Su data points except the cases in the first example where CPT information is involved, including Cases 3, 5 and 6, where large biases are found in the prediction. However, such biases can be understandable: qc rather than qT was used for the analysis. Therefore, it is expected that the predicted Su values would be conservative since qc is always less than qT . It seems helpful in reducing bias to incorporate more information. As we have seen from Cases 3, 5 and 6 in the first example: there are significant biases due to the incorrect use of qc . Nonetheless, when all available information is implemented in Case 7, the bias is obviously reduced. Incorporating more information also help to reduce uncertainties, i.e. make the confidence intervals smaller. This is obvious from the analysis results in Figures 6 and 7. Judging from the analysis results, Eqs. (16.) to (22.) seem to provide results that are consistent to actual Su data. Moreover, this consistency seems to be independent of the location of the site of interest. It is possible to reduce the c.o.v. of Su down to 0.16 if OCR, qT and N60 information are all implemented. This reduction in c.o.v. is significant: the c.o.v. of the inherent variability of Su can be as large as 0.3-0.4. In fact, with only information of OCR and qT , the c.o.v. is already reduced to 0.195.

– The TEAM approach seems to provide similar results to the Bayesian method proposed in this paper when there is no systematic bias in the estimation. This is quite significant since it indicates that the Bayesian method can effectively predict standard deviations close to their actual values. When there is systematic bias, the TEAM approach may give a small standard deviation. Nonetheless, the standard deviation estimated by the Bayesian method is based on the training database (data from past correlations) and is robust against the bias in the estimation. 6

CONCLUSION

A new framework is proposed to update the first two moments of undrained shear strengths of clayey soils based on in-situ and laboratory test data and indices, e.g., overconsolidation ratio, SPT-N value and CPT reading. This new method is based on pairwise correlations developed by literature, but it implements the Bayesian analysis to accommodate multivariate correlations to update the moments. The main product of this paper is a set of equations whose inputs are the observed multivariate test index values and outputs are the updated mean values and coefficients of variation (c.o.v.) of the undrained shear strength. One real case study are employed to verify the consistency of the proposed framework in predicting shear strengths of clays. The results show that the proposed framework offers satisfactory estimations of the undrained shear strengths. REFERENCES Anagnostopoulos, A., Koukis, G., Sabatakakis, N., and Tsiambaos, G. (2003). Empirical correlations of soil parameters based on cone penetration tests for Greek soils. Geotechnical and Geological Engineering, 21, 377–387. Bjerrum, L. (1972). Embankment on Soft Ground. Proceedings of ASCE Specialty Conference on Performance of Earth and Earth-Supported Structures, Lafayette. Briaud, J.L., Goparaju, K. and Dahm, P.F. (2002). The T.E.A.M. approach in geotechnical engineering. ASCE Geotechnical Special Publications No. 116 (Deep Foundations 2002), Vol. 2, 976–992. Chandler, R.J. (1988). The in-situ measurement of the undrained shear strength of clays using the field vane. Vane Shear Strength Testing in Soils: Field and Laboratory Studies (DTP1014), ASTM, Philadelphia, 13–44. Chen, J.R. (2004). Axial Behavior of Drilled Shafts in Gravelly Soils. Ph.D. Dissertation, Cornell University. Chen, Y.J. and Kulhawy, F.H. (1993). Undrained strength interrelationships among CIUC, UU, and UC tests. Journal of Geotechnical Engineering, 119(11), 1732–1750.

Fukasawa, T., Mizukami, J., and Kusakabe, O. (2004). Applicability of CPT for construction control of seawall on soft clay improved by sand drain method. Soils and Foundations, 44(2), 127–138. Hanzawa, H. (1992). A new approach to determine soil parameters free from regional variations in soil behavior and technical quality. Soils and Foundations, 32(1), 71–84. Hara,A., Ohta, T., Niwa, M., Tanaka, S., and Banno, T. (1974). Shear modulus and shear strength of cohesive soils. Soils and Foundations, 14(3), 1–12. Jamiolkowski, M., Ladd, C.C., Germaine, J.T., and Lancellotta, R. (1985). New developments in field and laboratory testing of soils. Proceedings of the 11th International Conference on Soil Mechanics and Foundation Engineering, San Francisco. Keaveny, J.M. and Mitchell, J.K. (1986). Strength of finegrained soils using the piezocone. In Use of In-Situ Tests in Geotechnical Engineering (GSP-6), Ed. S. P. Clemence, ASCE, New York. Konrad, J.M. and Law, K.T. (1987). Undrained shear strength from piezocone tests. Canadian Geotechnical Journal, 24(3), 392–405. Kulhawy, F.H. and Mayne, P.W. (1990). Manual on Estimating Soil Properties for Foundation Design, Report EL-6800, Electric Power Research Institute, Palo Alto. Lacasse, S. and Lunne, T. (1988). Calibration of dilatometer correlations. Proceedings of the 1st International Symposium on Penetration Testing (ISOPT-1), Orlando. Ladd, C.C., Foote, R., Ishihara, K., Schlosser, F. and Poulos H.G. (1977). Stress-deformation and strength characteristics. Proceedings of 9th International Conference on Soil Mechanics and Foundation Engineering, Tokyo. Lunne, T., Robertson, P.K. and Powell, J.J.M. (2002). Cone Penetration Testing in Geotechnical Practice. Spon Press, London. Mair, R.J. and Wood, D.M. (1987). Pressuremeter Testing. Butterworths, London. Mayne, P.W. (1988). Determining OCR in clay from laboratory strength. ASCE Journal of Geotechnical Engineering, 114(1), 76–92. Mersi, G. (1975). Discussion of “New design procedure for stability of soft clays”. ASCE Journal of Geotechnical Engineering, 101(4), 409–412. Ou, C.Y. (2006). Deep excavation engineering, Scientific & Technical Publishing Co. Ltd. Phoon, K. K. (1995). Reliability-based Design of Foundations forTransmission Line Structures. Ph.D. Dissertation, Cornell University, Ithaca, NY. Robertson, P.K. and Campanella, R.G. (1989). Guidelines for Geotechnical Design Using the Cone Penetrometer Test and CPT with Pore Pressure Measurement. Hogentogler Co., Inc (1989). Skempton, A. W. (1957). Discussion of “Planning and design of new Hong Kong airport”. Proceedings of Institution of Civil Engineers, 7, 305–307. Tanaka, Y. and Sakagami, T. (1989). Piezocone testing in underconsolidated clay. Canadian Geotechnical Journal, 26, 563–567. Terzaghi, K. and Peck, R.B. (1967). Soil Mechanics in Engineering Practice. A Wiley International Edition, 729 p.

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Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

A case study on settlement prediction by spatial-temporal random process P. Rungbanaphan & Y. Honjo Gifu University, Gifu, Japan

I. Yoshida Musashi Institute of Technology, Tokyo, Japan

ABSTRACT: A systematic procedure for spatial-temporal prediction of settlement is proposed. The method is based on Bayesian estimation by considering both prior information of the settlement model’s parameters and the observed settlement to search for the best estimates of the parameters. By taking into account the spatial correlation structure, all observation data can be used for rational estimation of the model parameters at any location and any time. The system error can be considered by Kalman filter including process noise. A procedure to estimate auto-correlation distance of the parameters and the observation-model error based on the maximum likelihood method is also proposed. The Kriging method is considered to be a suitable approach for determining the statistics of the estimated model parameters at any arbitrary location. A case study on the secondary compression settlement of the alluvial soil due to preloading work is carried out. The y ∼ log (t) method is chosen as a basic model for settlement prediction. It is concluded that, while the strong spatial correlation is required for significant improvement of the settlement prediction by taking into account the spatial correlation structure, the proposed approach gives the rational prediction of the settlement at an arbitrary point with quantified uncertainty. In addition, including process noise in the calculation can improve the estimation but care should be taken to assign an appropriate level of this system error. 1

INTRODUCTION

So far, all methods of predicting future settlement using past observations are based solely on the temporal dependence of their quantity. However, the fact that soil properties tend to exhibit a spatial correlation structure has been clearly shown by several studies in the past, e.g. Vanmark (1977), DeGroot & Baecher (1993). It is therefore natural to expect that the accuracy of the settlement prediction can be improved by taking into account the spatial correlation of ground properties, by which the observed settlement data from all of the different observation points can be simultaneously utilized. Furthermore, by introducing spatial correlation, it is possible to estimate the future settlement of the ground at any arbitrary point by considering the spatial-temporal structure. This study is actually an attempt to search for such an approach.

model is considered to be rational and practical for prediction of the secondary compression (Bjerrum 1967, Garlanger 1972, Mesri et al. 1997, etc.). The equation is given by

where yk = settlement at kth step of observation; m0 and m1 = constant parameters; tk = time at kth step of observation; εk = observation model error.

This implies the temporally independent characteristic of εk . 2.2 Bayesian estimation considering spatial correlation structure

2 2.1

SPATIAL-TEMPORAL UPDATING AND PREDICTING PROCESS Settlement prediction model

The basic model used for settlement prediction in this paper is the linear relationship between logarithm of time and the settlement, i.e. y ∼ log (t) method. The

In order to improve the estimation and to enable local estimation, utilization of Bayesian estimation considering spatial correlation is proposed in this paper. This approach uses prior information of the parameters and the observed settlement data from all observation points to search for the best estimates of the unknown parameters, i.e. model parameters

301

(m1 and m0 ), auto-correlation distance (η), and the variance of the observation-model error (σε2 ). The formulation consists of two statistical components, namely, the observation model and the prior information model. These two models will then be combined by Bayes’ theorem to obtain the solution. 2.2.1 Observation model This model relates the observation data to the model parameters. At a specific time step k, let Yk denote the observed settlement at n observation points, x1 , x2 , …, xn , where

The state vector, θ, is defined as the estimates of model parameters (m∗1 , m∗0 ) at the n observation points, as follows:

2.2.2 Prior information model By assuming two multivariate stochastic Gaussian fields for m1 and m0 , the prior information has the following structure:

where

m∗1,0 (xi ) and m∗0,0 (xi ) denote the prior mean at observation point xi of m1 and m0 , respectively. δ is the uncertainty of the prior mean with E[δ] = 0 and E[δδT ] = Vθ,0 . Vθ,0 is a prior covariance matrix. By introducing the spatial correlation structure in the formulation of Vθ,0 , we have

Consequently, the model in Eq. (1) can be rewritten in the following matrix form 2 2 where 0n,n denotes an nx n zero matrix. σm1,0 and σm0,0 represent the prior variance of m1 and m0 , respectively. ρ(|xi − xj |) denotes the auto-correlation function. The exponential type auto-correlation function is chosen for the current study because it is commonly used in geotechnical applications (e.g. Vanmarcke 1977). The function is given as

where

In,n denotes an n × n unit matrix. ε is a Gaussian observation-model error vector with E[ε] = 0 and E[εεT ] = Vε . Vε is a covariance matrix, the components of which are

It should be emphasized that σε2 is both spatially temporally independent. Furthermore, this error is also defined as the combination of the observation error and the model error. These two kinds of errors cannot be separated in practice, and so are assumed to be integrated in the model as shown in Eq. (8). Given θ and σε2 , the predicted settlement distribution at any time t can be represented by the following multivariate normal distribution

where xi , xj = spatial vector coordinate, and η = autocorrelation distance. It should be noted that, for the sake of simplification, there are two important assumptions about the correlation structure for formulating the above covariance matrix. Firstly, m1 and m0 are assumed to be independent of one another. Secondly, the correlation structures of these two parameters are identical, meaning that they share the same auto-correlation distance. Given η, prior means, and prior variances of m1 and m0 , the prior distribution of the model parameters is also a multivariate normal distribution of the following form

It is clear from this formulation that the spatial correlation of soil properties is included in the form of the spatial correlation of m1 and m0 . The settlements themselves are not correlated spatially. The authors believe that this is the most suitable way to introduce the spatial correlation structure to the settlement prediction model since it is soil properties that are spatially correlated, not the settlement.

302

2.2.3 Bayesian estimation Suppose that the set of observations Yk at the time tk for k = 0, 1, . . . , K has already been obtained. By employing Bayes’ theorem, the posterior distribution of the state vector θ can be formulated as

where Y denotes the set of all observed data, i.e. Y = (Y1 , Y2 , . . . , YK ). By substituting Eq. (9) and (15) into the above equation, a likelihood function can be defined, with the given values of σε2 and η, as follows:

The Bayesian estimator of θ, i.e. θ ∗ , is the one that maximizes the above function. Therefore, it is equivalent to minimizing the following objective function

has two distinct phases: time updating and observation updating. The time updating phase uses the state estimate from the previous time step to produce an estimate of the state at the current time step by considering process noise. In the observation updating phase, measurement information at the current time step is used to refine this prediction in order to arrive at a new state estimate. In fact, it can be proved that, without process noise, the Kalman filter gives the same results as the previously proposed approach, i.e. Bayesian estimation (Hoshiya & Yoshida 1996 and 1998). For the estimation of the soil parameters, the unknown parameters is considered to be stationary, then the Time updating process is expressed by

where Qk denotes covariance matrix of process noise; suffix k stands for the kth step of processing; k/k − 1 represents the kth step estimation conditioned on processing observation data up to the k − 1th datum To systematically define the value of process noise, we assume that Qk are given based on a priori information, as follows (Hoshiya & Yoshida, 1998):

where c is a constant parameter representing the level of system error, i.e. process noise. From (22) and (23), we have By differentiating the above equation with respect to the state vector, we obtain For Observation updating process, the updating is given by

By trial and error, the values of σε2 , η, and the corresponding θ ∗ that give the maximum value of the likelihood function (L) can be obtained. These values are actually the Bayesian estimators for the current problem. 2.3

Process noise consideration by Kalman filter method

In the previous section, the batch procedure by which all of the observations are treated equally for parameters updating was proposed. In practice, it is natural to give higher weight to the more recent observations. This can be done by considering an uncertainty parameter, so called ‘process noise’, through a sequential procedure, Kalman filter (Kalman 1960, Kalman & Bucy 1961, Jazwinski 1976). The Kalman filter

by defining the Kalman gain

where suffix k/k, similarly, represents the kth step estimation conditioned on processing observation data up to the kth datum. It should be emphasized that θ0/0 and Vθ,0/0 need to be defined in the same way as θ0 and Vθ,0 in Eq. (11) and (13), in order to take into account the prior information of the model parameters together with the spatial correlation structure. With its ability to sequentially update the estimation and systematically take into account process noise, this method is used in estimation of the unknown parameter, θ, while σε2 and η are estimated by Bayesian estimation described in Section 2.2

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2.4

Local estimation by the Kriging Method

Based on the calculated statistical inferences of the model parameters at the observation points and the estimated auto-correlation distance, the statistics of the model parameters at any arbitrary locations can be determined by the ordinary Kriging method (Krige 1966, Matheron 1973, Wackernagel 1998).This method provides an unbiased and least error estimator built on the data from a random field. It is also assumed that the random field is second-order stationary. Based on the estimated model parameters (m∗1 , m∗0 ) at the n observation points x1 , …, xn , the value of m∗1 and m∗0 , at an arbitrary point x0 can be estimated by the following equations:

where Figure 1. Soil condition.

wi (i = 1, …, n) are the weights attached to the data at each of the observation points. µ is the Lagrange multiplier used for minimizing the Kriging error, and x0 denotes the spatial vector coordinate at x0 . ρ|xi − xj |) represents the auto-correlation function as defined in Eq. (14). 3

Figure 2. Surcharge thickness and settlement vs. time.

CASE STUDY

3.1 Description of the case The site is a residential land development project located in suburb area of Tokyo, Japan. This area is covered by a thick alluvial deposit which can be classified as a surface layer of peats followed by a very soft clay layer down to the thickness of about 17 meters (Fig. 1). Below these layers, the layers of medium dense sand and silt are found. In order to avoid the large amount of settlement due to the thick soft soil layer at the surface, the soil condition is improved by preloading prior to the construction. As shown in Figure 2, the preloading surcharge was filled up to the maximum thickness of about 6 m during the preloading period of, approximately, 900 days. The settlement observations were performed at both during the preloading period by the settlement plates and after removal of the surcharge by measuring settlement of the boundary stone around the housing lots. The settlement after removal of the surcharge, which is used in this study, was observed at about every 600 m2 with the total number of observation points of 42. The location plan of these observation points is shown in Figure 3, while all of the observation data are shown

Figure 3. Location plan of the observation points and surcharge area.

as semi-logarithmic plots of settlement and time in Figure 4. Various techniques have been proposed by several authors for predicting the future settlement using the observed settlement, for example, hyperbola method (Sridharan et. al. 1987, Tan 1994), y ∼ log (t) method (Bjerrum 1967, Mesri et al. 1997), and Asaoka’s method (Asaoka 1978). In this study,

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By this treat, the missing data can be initially assumed within a reasonable range and it will then be ignored from the calculation by the influence of matrix Vε . As can be seen from Figure 5, the early part of the observed data clearly shows disagreement with the previously described y ∼ log (t) model. This is due to the fact that the settlement observed in this period, which is expected to result from the secondary compression, was still strongly influenced by the rebound effect from the removal of preloading surcharge. In order to implement the model to these sets of observation data, a part of the data need to be ignored. By investigating the settlement data of all the observation point, the data before the day 103th are discarded from the calculation by judgment. Choosing appropriate prior statistics of the unknown parameters (m1 and m0 ) is also an important issue. What has been done in the current research is that the prior mean of m1 and m0 were assumed to be equal to the value of slope and the intercept of the trend line resulting from the linear regression analysis of settlement vs. time plotting considering the data from all of the observation points. On the other hand, the prior variances are selected by trying several values of prior coefficient of variation (COV) and choosing the one which is relatively insensitive to the changes of prior means. Based on this approach, the prior means of m1 and m0 , which are assumed to be identical at every observation points, are assigned as 109.7 cm and −204.1 cm, respectively, while the prior COV is set as 0.4 for calculating prior variance of both parameters.

Figure 4. Observed settlement vs. time (after surcharge removal) for all observation points.

Figure 5. Observed settlement vs. time (after surcharge removal) and trend line at point A (see Figure 3).

y ∼ log (t) method is considered to be the most suitable approach due to the fact that the primary consolidation is expected to be completed before the surcharge removal, thus the settlement occurring afterward should result from the secondary compression process. Figure 5 shows an example of the y ∼ log (t) plot at an observation point. It can be seen that, by excluding a part of data in the early period of observation, within which the secondary compression is considered to be influenced by the rebound effect due to surcharge removal, this semi-logarithmic relationship fits quite well with the observation data. 3.2

Practical problems and solutions

To deal with the field observation result, the incompleteness of the data is, of cause, unavoidable. The example of the observed data shown in Figure 5 is illustrated a relatively complete set of data, but it is not always the case. Several observation points suffer the missing of settlement data at some observation steps.The problem is that, for both Bayesian estimation and Kaman filter, the data from all of the observation points are required at every time steps. It is clear form Eq. (17), (20) and (25) that every components of Yk is needed for every time steps k = 1 to K. To cope with this problem, the components of Vε which correspond to the observation points with the missing data at that time step are replaced by the extremely high numbers.

3.3 Estimation of the auto-correlation distance and observation-model error It was proposed in Section 2.2.3 that auto-correlation distance (η) and the standard deviation of the observation-model error (σε ) can be estimated by an optimization procedure based on Bayesian estimation. Considering the observation data together with the prior information of the model parameters, the likelihood values (L) for each pairs of η and σε can be determined by Eq. (17). The values of η and σε that give the maximum value of L will be served as the Bayesian estimators of these parameters. Figure 6 shows the contour of L in η and σε space for the case that all of the settlement data until the last step of observation, i.e. the day 1017th, is considered. In this case, the Bayesian estimators of η and σε are 32 m and 6.75 cm, respectively. Obviously, the estimated values of η are more likely to be changeable than those of σε . In practice, the observation data is collected stepwise for a period of time. Therefore, it is natural to sequentially update the estimation once the new sets of observation are provided. Figure 7 illustrates the plots of the estimated values of η and σε vs. observation time, until which the observation data are used in estimation. It can be observed that the estimated values of auto-correlation distance tend to decrease with the observation time, while those of the

305

Figure 6. Contour of likelihood values (L), using observation data until the last step of observation (the day 1017th).

Figure 8. mean absolute error of settlement prediction at the last observation time step(the day 1017th) vs. observation time.

points can be calculated, considering prior information of the parameters and observation data. Using these parameters, the settlement at any specific time can be estimated by y ∼ log (t) model. This can be compared with the observed data at this point to discover the estimation error. For quantitatively describing the estimation error, the term ‘mean absolute error’ is defined as follows:

Figure 7. Estimated values of auto-correlation distance (η) and the standard deviation of the observation-model error (σε ) vs. observation time.

observation-model error tend to increase, depending on the characteristic of the observed data. Both of these estimations seem unstable at the early stage of the observation, indicating insufficiency of the observation data for the calculations. However, they become more stable as the observation data accumulates. 3.4

Settlement prediction and estimation

Based on the procedure proposed in Section 2.2, the estimates of model parameters at each observation

where Xest,i and Xtrue,i denote the estimated value and true value, respectively, of the parameter to be estimated at each observation point. Nx represents the total number of estimated values. In this case, the estimated value is the estimated settlement, while the true value is the observed settlement. Nx is the total number of observation points, i.e. Nx = n. Figure 8 shows the plots of the ‘mean absolute error’ for prediction of settlement at the last observation time step (the day 1017th) vs. observation time. For comparison purpose, the case that the spatial correlation is ignored is also presented. For this case, the observation data at each point are used to update the model parameters of that point itself, i.e. η = 0. It should be noted that, for the case with considering spatial correlation, the estimated values of auto-correlation distance, as shown in Figure 7, are used in the calculations. As might be expected, the prediction error decreases with the increase of the available observation data. However, for the current set of observation data, considering the spatial correlation do not significantly improve the estimation in terms of the mean error. This may be due to the fact that the auto-correlation distance is relatively short in comparison with the spacing between the observation points. To further investigate the efficiency of the proposed method in dealing with the space-time problem, the observation data at each selected observation point are removed and the settlement estimations, or predictions, at this point are performed using the rest of the observations. Firstly, the estimates of model

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Figure 9. Comparison between the estimated and the observed settlement at the day 430th, using data from the day 103th to 403th.

parameters at each observation points are calculated. Then, the parameters at the removed observation point are determined by Kriging method using the estimated auto-correlation distance (see Section 2.4). Comparison between the settlement estimated by these parameters and the actually observed one reveals the estimation error. Figure 9 shows the comparison between the estimated and the observed settlement of all 42 observation points at the day 430th. The observation data from the day 103th to the day 430th are used in the calculation. Obviously, for the case that the relatively weak spatial correlation is assumed, i.e. assuming η = 10 m (Fig. 9a), the estimation tends to be uniform and is not likely to be able to represent the variation of ground settlement. On the other hand, for the case that the estimated value of auto-correlation distance, η = 52 m, is used (Fig. 9b), the estimation gives relatively more realistic pattern of settlement in the area. It should be noted that the observation data at some points are missing due to the common imperfection of the field observation. Only the estimated values are shown at these points. In fact, this illustrates one of the practical advantages of the proposed method, i.e. the ability to perform estimation at a specific point without any observed information. Figure 10 shows the plots of mean absolute error (Eq. (30)) of settlement estimation at the removed observation points vs. observation time. Two cases of calculations are presented: Case A and B. Case A is an attempt to avoid the temporal error resulting from prediction of future settlement; therefore, the estimated settlement and the observed settlement are compared at that observation time, i.e. the same way as the calculations shown in Figure 9. Case B is the comparison between the predicted settlement at the last observation time step (the day 1017th) and the observed settlement at that time. It should be emphasized that the estimated values of auto-correlation distance and the observation-model error, which are varied with the

Figure 10. Mean absolute error of settlement estimation at the removed observation points vs. observation time. Case A presents the settlement observation at that day. Case B presents the settlement prediction at the day 1017th.

observation time as shown in Figure 7, are used for all calculations. It can be seen that, for the both cases, the estimation errors are decreased with the observation time. In other words, the estimation can be improved if more observation data are given. However, Case B gives the lower estimation error, even though the future prediction is performed in this case. This may be the result of the cancellation of error during the settlement prediction. 3.5 Effect of process noise consideration As mentioned in Section 2.3, higher weight should be given to the more resent data than to the previous one. This can be done by assigning appropriate values of process noise, i.e. system error, during the time updating process in Kalman filter procedure. According to Eq. (23), the level of this system error can be controlled by assigning an appropriate value of the constant parameter, c. By performing the same calculation as what is shown in Figure 8, but with the different values of c, the effect of process noise to the settlement prediction can be investigated. Figure 11 presents the prediction error of settlement at the last observation time step (the day 1017th) at different observation time. In fact, for the case that c = 0, i.e. no process noise, this is the same with the one plotted in Figure 8, for considering spatial correlation case. It can be concluded from Figure 11 that, to some extend, the settlement prediction can be improved by considering the system error. Especially for estimation at last time step (the day 1017th), at which all observation data until the target day for the prediction are include in the calculations, the mean absolute error reduce dramatically from about 9.8% to 0.3%. However, this is not always the case. At some stage of prediction, assuming too high value of process noise may mislead the prediction and the error become higher instead. This can be seen in Figure 11 when c = 2.0 are assigned. Therefore, the optimization of this process noise coefficient is required. This is, however, out of scope of the current research.

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taken in assigning appropriate value of this parameter to avoid additional error due to including too high value of process noise.

REFERENCES

Figure 11. Mean absolute error for prediction of settlement at the last observation time step (the day 1017th) vs. observation time under different levels of process noise.

4

CONCLUSION

A methodology was presented for observation based settlement prediction with consideration of spatial correlation structure. The spatial correlation is introduced among the model parameters and the settlements at various points are spatially correlated through these parameters, which naturally describe the phenomenon. A case study on the secondary compression of alluvial deposits due to ground improvement by preloading was carried out using the proposed approach. It was found that the estimation of auto-correlation distance is relatively unstable and insufficient amounts of observation data may mislead the estimation. Furthermore, even though it seems that the auto-correlation distance of the soil parameter is relatively short in comparison with the observation point’s spacing, the proposed method provides the rational estimation of the settlement at any time and any location with quantified error. Including system error, i.e. process noise, into the calculation can give the improvement on the settlement estimation to some extend. However, care should be

Asaoka, A. 1978. Observational procedure of settlement prediction. Soil and Foundations 18(4): 87–101. Bjerrum, L. 1967. Engineering geology of Norwegian normally consolidated marine clays as related to settlement of buildings. Géotechnique 17(2): 81–118. DeGroot, D. J. & Baecher, G. B. 1993. Estimating autocovariance of in-situ soil properties. Journal of Geotechnical Engineering 119(1): 147–166. Garlanger, J.E. 1972. The consolidation of soils exhibiting creep under constant effective stress. Géotechnique 22(1): 71–78. Hoshiya, M. & Yoshida, I. 1996. Identification of conditional stochastic gaussian field. Journal of Engineering Mechanics, ASCE 122(2): 101–108. Hoshiya, M. & Yoshida, I. 1998. Process noise and optimum observation in conditional stochastic fields. Journal of Engineering Mechanics, ASCE 124(12): 1325–1330. Krige, D. G. 1966. Two dimensional weighted moving averaging trend surfaces for ore evaluation. Proc., of Symp. on Math., Statistics and Comp. Appl. for Ore Evaluation. Matheron, G. 1973. The intrinsic random functions and their applications. Adv. in Appl. Probab. 5. Mesri, G. et al. 1997. Secondary compression of peat with or without surcharging. Journal of the Geotechnical Engineering Division, ASCE 123(5): 411–421. Sridharan, A., Murthy, N. S. & Prakash, K. 1987. Rectangular hyperbolar method of consolidation analysis. Géotechnique 37(3): 355–368. Tan, S. A. 1994. Hyperbolic method for settlements in clays with vertical drains. Canadian Geotechnical Journal 31: 125–131. Vanmarcke, E. H. 1977. Probabilistic modeling of soil profiles. Journal of the Geotechnical Engineering Division, ASCE 103(GT11): 1227–1246. Wackernagel, H. 1998. Multivariate Geostatistics: An Introduction with Applications. 2nd ed. Germany: SpringerVerlag Berlin Heidelberg.

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Construction risk management

Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Reliability analysis of a hydraulic fill slope with respect to liquefaction and breaching T. Schweckendiek Deltares, unit Geo-engineering & TU Delft, Delft, The Netherlands

G.A. van den Ham & M.B. de Groot Deltares, unit Geo-engineering, Delft, The Netherlands

J.G. de Gijt & H. Brassinga Public Works Rotterdam, Rotterdam, The Netherlands

P. Hudig Gate Terminal B.V.

ABSTRACT: A recently reclaimed site in the Port of Rotterdam will serve as location and foundation of an LNG terminal. LNG (Liquefied Natural Gas) is recognized as hazardous material and underlies strict safety requirements. As part of the safety assessment of the entire installation, a specific analysis had to be carried out concerning the geotechnical aspects. The paper describes the probabilistic approach that was chosen to verify the required level of safety of the hydraulic sand fill regarding (static) liquefaction, slope failure and breaching processes. Several reliability analyses using the respective physical process models were carried out and the results combined using a fault tree or scenario approach, leading to upper bounds of the failure probability. 1 1.1

INTRODUCTION Project outline

The paper describes an approach for a geotechnical reliability analysis problem in a real life project in 2007. For an LNG terminal to be built in the Port of Rotterdam, hydraulic sand filling was used to extend an existing artificial terrain in order to create space for 4 large LNG tanks (Fig. 1).

The original design contained slopes with angles of 1:2.5, protected mainly against erosion and wave action by steel slag dams. Initially, it was thought that compaction would not be required until a rough analysis of the liquefaction potential cast this assumption into serious doubt. Subsequent more thorough analyses led to several design modifications, the most important of which were to use a shallower slope angle of 1:3 and to compact the entire slope itself up to the height of the tanks to be built by means of vibro-flotation. The final representative cross section in Figure 2. Note that due to the construction process and the last-minute design amendments, some portions of the hydraulic fill could not be compacted and remained in a relatively loose state. These areas in combination with the still relatively steep slope caused some uncertainty about the chance of the occurrence of a liquefaction flow slide with subsequent damage to the foundation of the LNG-tanks. This uncertainty was the focus of the analysis described in this paper.

1.2

Figure 1. Overview LNG terminal.

Design requirements

For the LNG installation, as for other activities with hazardous materials, the safety requirements were formulated in terms of risk respectively an acceptable probability of failure, failure being defined as some the occurrence of an unwanted event or accident. The

311

Figure 2. Representative cross-section.

safety criterion for the geotechnical aspects treated in this paper was derived from the overall safety requirement, being: “The probability of a slope failure, including liquefaction and breaching, affecting the foundation safety of the LNG-tanks must not exceed Pf ,adm = 10−6 in the planned life time of the structure (50 years)”. Note that this criterion involves several potential failure mechanisms. 1.3 Probabilistic approach For the evaluation of the probability of failure stated in the previous section, the complex failure mechanism was split into basically three sub-mechanisms, which were tractable for structural reliability analysis. A choice for a dominant failure scenario did not seem appropriate, mainly due to the fact that multiple failure mechanisms were involved. To this end several failure scenarios were defined in order to ensure to not miss significant contributions. The results of the sub-mechanisms and the scenarios were combined by means of fault tree analysis in order to obtain the (upper bound of the) overall probability of failure, which was then compared to the acceptability criterion. Section 2 treats the physical process models applied in the analysis, whilst section 3 focuses on the reliability analysis aspects. 2 APPLIED PHYSICAL PROCESS MODELS 2.1 Liquefaction flow slide and subsequent breaching Under certain circumstances, loose, saturated sand elements in a slope may be sensitive to liquefaction or, more precisely formulated, may be in a ‘meta-stable’ state, which means that they will liquefy and loose their strength under any quick loading if they are free to undergo shear deformation. In case most adjacent sand elements in a slope have a much more stable state, no liquefaction will occur because these more stable elements will prevent the shear deformation of their meta-stable neighbors. However, in a slope with sufficient large pockets of meta-stable elements a

liquefaction flow slide may occur. The conditions for meta-stability mainly concern the soil state in terms of density and stresses which will be discussed in section 2.2. Whether the pockets of meta-stable elements are sufficiently large to enable a liquefaction flow slide will be studied by a traditional slope stability analysis in which the originally meta-stable elements are supposed to have liquefied (section 2.3). The final question is whether a liquefaction flow slide will result in failure of the foundation of the tanks. In case of a relatively shallow flow slide, this will only be the case if a breach in the unprotected sand created by the flow slide will progress over a sufficient large distance. The breaching process will be discussed in section 2.4. 2.2 Meta-stability or sensitivity to liquefaction The model that was used in this study for the undrained behavior of saturated (loose) sand is based on the theory presented in Stoutjesdijk et al (1998), which is also the basic theory used in the software SLIQ2D, mainly used by GeoDelft in the Netherlands during the last two decades. Whilst SLIQ2D only uses an instability or metastability criterion based on material parameters and the soil state (porosity and stresses) according to Molenkamp (1989), the approach in this study uses more information from the modeled undrained behavious respectively the stress path. For a given in-situ stress point, the undrained stress path is derived as a function of relative density from extensive laboratory tests. This path allows us two extract two types of information that helps us to judge the liquefaction potential and the residual strength after liquefaction:

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1 whether the in-situ density is higher or lower than the wet critical density (WCD, see Figure 5). If ID < WCD, the undrained stress path exhibits a decreasing deviatoric or shear stress. This is the most important necessary, however not sufficient, condition for meta-stability and thus for the occurrence of instability and static liquefaction. 2 the maximum generated excess pore pressure respectively the minimum isotropic effective stress

p
min , which can be used to estimate the (“worst case”) strength reduction due to liquefaction. Both definitions are definitely conservative respectively will lead to upper limits of failure probabilities. We will come back to this question in section 3. 2.3

Slope stability

The slope stability was treated by conventional Bishop slip circle analyses using the MStab software by GeoDelft (since 2008 Deltares). Two non-standard features had to be included:

Figure 3. Equilibrium profile after flow slide.

1 The slope stability analysis had to reflect the situation, given that liquefaction occurred in the liquefaction-sensitive parts of the slope. In the deterministic setup, the reduction in isotropic effective stress was used as measure for the reduction of shear capacity, expressed in form of a reduced friction angle:

2 The Rotterdam area is not typically earthquakeprone, however, due to the low required failure probability, also very low occurrence frequency seismic loads were considered. An option in MStab to account for vertical and horizontal peak accelerations in the slope stability analysis was applied (Delft GeoSystems 2006). 2.4

Figure 4. Undrained stress path of loose sand.

Breaching

If slope instability occurs, a liquefaction flow slide will start, which means that the instable soil mass starts to slide over a shear surface. It will continue to do so until it finds a new equilibrium. The flow process will in this case probably take not more than several seconds to a minute, as follows from calculations in which inertia is incorporated. That time is not long enough to cause significant reduction of the excess pore pressure in the liquefied sand pockets. Consequently, the shape of the new profile can be estimated by using Bishop calculations and the new slope profile is characterized by a relatively steep slope just above the soil mass, that flowed down. Its location can be characterized by L1 as defined in Figure 3. This steep slope consists of sand and is not likely to be covered by slags or other parts of any slope protection. Part of the steep slope is situated under water, as indicated in Figure 3. This part of the slope may start breaching. Breaching is a process in which a steep under water slope, “breach”, remains temporary stable under the influence of dilation induced negative pore pressures, and gradually moves backwards while sand grains fall down from the surface and mix with water to create an eroding, turbulent sand water mixture. The process stops when the height of the under water part of the breach is reduced to zero. The resulting profile is sketched in Figure 6.

Figure 5. Definition Wet Critical Density (WCD).

Figure 6. Equilibrium profile after breaching process.

The breaching process is described by Mastbergen & van den Berg (2003) and can be modelled by the computer code HMBREACH. Given grain size distribution, relative density and initial height of the under

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water part of the steep slope, sbh, the model calculates the change in this height as a function of the horizontal distance, from which the total distance of breach progress L2 (Fig. 6) can be derived. The slope of the part above the water is determined by the common shearing process and can be assumed to equal 1:1.5. Now the length (L2 − L1 ) of the damaged area follows. It is assumed, supported by indicative calculations, that no significant damage to the foundation of the tanks will occur as long as (L2 − L1 ) < 22.5 m, which is the distance between the foundation and the slope crest.

3

Figure 7. Upper and lower bounds of Pf vs. the design criterion.

RELIABILITY ANALYSIS

The previous section gave a concise overview of the concepts and methods used for deterministic evaluation of the sub-mechanisms playing a role in the present safety assessment problem. In this section we will discuss how an assessment of the criterion stated in section 1.2 was made in a probabilistic manner. First of all, we are dealing with the verification of a design criterion. That implies that it is sufficient to show that the upper bound of the estimate of the failure probability Pf ,sup fulfills the requirement:

Figure 8. Sequence of mechanisms in Failure mode.

Figure 9. Sequence of mechanisms leading to top event.

Thus, we can start with rough, conservative (upper bound) approaches and apply refinements, if necessary, as illustrated in Figure 7. Such refinements can either concern the probabilistic analysis itself (e.g. treatment of correlations) or more realistic physical process models. Such an approach was applied in the project, though for sake of readability in the following only the analysis that led to the successful outcome is described.

Figure 10. Sequence of mechanisms in Failure mode.

3.1 System definition As described in 2.1, the principal contemplated failure mode is a sequence of three mechanisms. To reiterate the sequence shortly, liquefaction of substantial, uncompacted volumes in the slope part of the fill may cause a flow slide respectively slope failure. The residual profile is common steep in the upper part and a breaching process may be initiated that could endanger the foundations of the installation in question. For the reliability analysis, this sequence is modeled by a parallel “sub-system” in a fault tree, consequently combined by and AND-gate (Fig. 10). Given the large uncertainties, it is not trivial to determine a dominant or representative scenario as we are used to do in deterministic approaches. For different combinations of parameters or properties, in some cases liquefaction and slope failure in the upper part may lead to the worst consequences, in other cases failures in the lower part or deeper sliding surfaces.

Figure 11. Schematic representation of two scenarios.

One way to circumvent the problem of choosing one scenario, is the definition of several scenarios. Two examples of such scenarios are presented schematically in Figure 11. The main difference in this

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Figure 12. Fault tree.

discrete distinction of possibilities is the assumption of which of the uncompacted volumes liquefy and how many at a time, with all the due consequences. All the defined scenarios are integrated in a fault tree (Fig. 12). For sake simplicity, the “conservative”, i.e. upper bound assumption of independence (actually even mutually exclusivity) is made (see 3.6). 3.2

Parameters and uncertainties

The in-situ relative densities of the hydraulic fill were determined by means of the empirical CPT correlation function of Baldi e.a. (1982) which correlates the density index ID to the cone penetration value qc as a function of the vertical effective stress. A total of over 50 CPT’s were available. Accounting for both spatial variability and uncertainty of the correlation function the expected value of ID was found to be 39% with a standard deviation of 10%. These values concern the average of ID over a potential liquefiable area or failure surface. By means of several drained (CD) and dry triaxial tests on a number of representative (disturbed) samples, taken from the hydraulic fill, the parameters for the constitutive model (see 2.2) were determined. Influence of soil state was assessed by performing the tests at different stress conditions and porosities. Statistical analysis of the test results and considerations on spatial variability, lead to probability distribution functions of the important material model parameters for further use in the probabilistic analysis. In order to check the calibrated parameter set, a number of undrained (CU) triaxial tests was executed on the same samples and simulated with the model. Measurements and prediction fitted reasonably well (Fig. 13). 3.3

Meta-stability or sensitivity to liquefaction

The probability of meta-stability or the sensitivity to liquefaction Pliq of each area with non-compacted sand was evaluated by determining the probability of the in-situ sand being in a state below the WCD (see 2.2),

Figure 13. Comparison stress path (CU) between test and calibrated model.

given a representative stress point in the area and the uncertainties in the material properties:

with x being a vector containing all random variables. Pliq was determined by means of Monte-Carlo analysis. Per scenario, n = 105 realizations of the state, material and model parameters were produced and propagated through the model (undrained stress path, Fig. 4). Consequently the estimator for Pliq is:

where xi is the ith realization of x and IC (x) is the indicator function for condition C. Considering the definition of WCD, being a necessary not sufficient condition for static liquefaction, this is clearly a conservative approach leading to an upper bound estimate of the probability of liquefaction. In fact, the results in section 4 show that the estimate based on this method usually lead to very high probabilities that intuitively do not reflect the judgment of most experts. For the assessment of the probability of sensitivity to liquefaction, it is definitely desirable to

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Figure 14. MStab reliability module. Table 1.

Peak acceleration values.

amax [m/s2 ]

P{amax > ámax } [1/year]

P{amax > ámax } [1/50year]

0.20 0.40

1/475 1/10000

1-(1-1/475)ˆ50 = 0.1 1-(1-1/10000)ˆ50 = 0.005

Figure 15. GEV distribution of amax .

use an approach that includes also the “distance” from instability or a critical-state model. This was not realized in the course of this project, but is one of our goals for the future. It is also noted that seismic action was neglected in this step. Due to the very low intensity the contribution was found to be insignificant. 3.4

Slope stability, given liquefaction

The second step respectively sub-mechanism in the contemplated chain of events is slope failure, given liquefaction has occurred in one or more of the problematic uncompacted zones. A total of 6 critical failure modes could be identified. The slope reliability analysis is carried out using the reliability module of MStab, which is essentially FORM applied to a Bishop slip circle analysis using average properties of the soil shear resistance properties as the main basic random variables, thus with implicit treatment of averaging effects in the probability distributions for the shear resistance (see JCSS 2001). As mentioned earlier, seismic loading was not considered in the initiation of liquefaction, i.e. the implicit assumption is that a trigger is always present with high probability. However, seismic action was taken into account in the slope stability analysis. For the considered area, two values of peak acceleration amax are given for the return periods of 10,000 years and 475 years (see Table 1). In order not to use the heaviest condition as deterministic value, a Generalized Extreme Value (GEV) distribution corresponding to the given quantiles was used to integrate the seismic loads in a probabilistic manner. The resulting GEV-distribution is shown in Figure 15.

Since the used software did not allow us to include the uncertainty in amax in the Bishop-FORM analysis, several of these form analyses were carried out for a set of deterministic values of the peak acceleration. Subsequently, the results in terms of the reliability index β, conditional on amax , can be integrated numerically to solve the following integral:

This is practically done by an external FORM-loop respectively design point search, for details refer to (Delft GeoSystems 2006). 3.5 Breaching, given slope failure By carrying out an uncertainty analysis on the initial breach height sbh and the value of L1 , based on the
uncertainties in the strength of liquefied sand (φred ) and the strength of the non-liquefied and (critical state) probability distribution functions for these variables were established. The breach length L2 proved to be very insensitive to L1 , reason to give it a conservative deterministic value: L1 = 5 m (again simplified upper bound approach). The uncertainty in sbh, however, is expressed as a lognormal distribution with an expected value of 1m and a standard deviation of 1 m. The results of a large series of HMBREACH calculations could be approximated by the following equation (response surface):

where C1 and C2 are model parameters with lognormal distributions, expected values 1 and standard deviations 0.1 and 0.3, respectively. A reliability analysis on this response surface of the breach model resulted in: P{(L2 − L1 ) > 22.5m|slopeinstability) = 1.3 10−7

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and an expected value of E(L2 ) = 7.8 m and a standard deviation σ(L2 ) = 3.7 m. It should be noticed that the applied models for the breaching process, given slope instability, are very rough. Even conservative assumptions, however, make clear that no large damage is to be expected here in the unlikely cased that slope instability occurs. This is due to the shallow location of the uncompacted areas. In other cases of liquefaction slope failures, the length L2 − L1 of the damaged area may reach values of up to 100 m or even more, as experience shows. Research in the field of the breaching process and the interaction between liquefaction and breaching is needed to improve the models and develop a practical tool to predict the length L2 − L1 of the damaged area.

3.6 Total failure probability As mentioned earlier, but emphasized again at this point, the results presented here in terms of the failure probability concern an upper bound. By definition, the value of this probability is expected to be lower. Various assumptions have led to a value “on the safe side”. These assumptions can be roughly classified in two categories: 1. Assumptions in probabilistic approach: a. The soil properties in the constitutive models are essentially independent and therefore treated as such. b. For combining the scenarios, it is assumed that they are mutually exclusive, thus the total probability is the sum of the probabilities of scenarios i (serial system):

b. In the slope stability analysis, the theoretical minimum of the shear strength according to the material model is assigned to the zones that are assumed to be liquefied. It is likely that not the entire affected volumes undergo the total strength reduction and that excess pore pressures diminish, i.e. that the shear strength is recovered at least partially. At the same time, the assumptions made, indicate where there is certainly significant potential for refinements in the applied method. More sophisticated mechanical and constitutive models are in principle available for coupled analysis in academia, but not yet easily applicable in consultancy work. There is a challenge for the applied sciences community to further develop these methods and tools closer to application in practical problems. 4

For the project itself, it was shown that some design amendments were necessary, such as the compaction of mainly the slope part pf the hydraulic fill and a slightly shallower slope than initially planned in order to fulfill the strict safety requirement. With this amended design it was shown that the total probability of failure (upper bound, see previous section) was in the order of Pf ,sup = 10−7 . But rather than presenting more figures, the type of results that can be produced with such an analysis are illustrated in this section: •

The probability of the top event in the fault tree, in this case the foundations of the installation affected by slope failure, possibly induced by liquefaction and breaching, can be used in higher level risk analyses and reliability analyses of the entire installation. The probabilistic approach therefore provides a comparability with other elements of the system that cannot be achieved otherwise by the classical deterministic methods. • The fault tree contains probabilities on (sub-) mechanism level. That enables the identification of the most relevant mechanisms and scenarios.This information is extremely useful for optimization of the design. • The reliability analyses on (sub-) mechanism level also produce information on the relative importance of the variables involved (e.g. FORM gives influence coefficients αi ). Some of these properties can either be influenced by changes of the design or by acquiring more information and thereby reducing (epistemic) uncertainty, e.g. additional soil investigation.

c. The combination of the sub-mechanism probabilities concerns a parallel system. Here the worst case is total dependence between the submechanisms. This assumptions is probably not even unreasonable since in all mechanisms the same soil properties play a role. Therefore, the maximum value of the sub-mechanism probabilities is used as the upper bound for the scenario probability:

Consequently the top event probability is determined by:

for n scenarios and m sub-mechanisms. 2. Assumptions in the physical-process modeling: a. As mentioned in 3.3, the probability of liquefaction is actually the probability of the material being liquefiable. More conditions in terms of stress state etc. have to be fulfilled for liquefaction to occur.

RESULTS

5

CONCLUSIONS

The work on this paper has lead us to formulate the following three main conclusions: Firstly, the paper demonstrates the applicability of reliability analysis for a rather complex geotechnical problem in a real world design problem. In the course

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of the design verification, the upper bound of the failure probability is lowered step-wise by refinements of either physical process or probabilistic models until it is shown that the design fulfills the rather strict requirements. Secondly, it should be emphasized that such a decomposition of the analyzed failure processes can hardly be done with deterministic approaches. The common safety value, be it a factor, margin or something else, would be very difficult to compose out of the results of the evaluation of the sub-mechanisms. Once again, comparability is one of the major advantages using probabilistic approaches. Finally, of course, a probabilistic approach does not compensate for deficiencies in physical processbased models, it merely provides a consistent manner to deal with the uncertainties. In the illustrated case, the sometimes quite rough upper bound approaches led to a satisfactory answer, namely an acceptance of the design by verifying the required requirements. On the other hand, we are convinced that the use of upper bounds led to a rather conservative assessment. However, carrying out the indicated potential refinements is not a trivial task with the currently available methods. Especially for the initiation of liquefaction, the currently used models are unsatisfactory. Either they are of empirical nature and based on a limited number of (indirect and interpreted) observations, or they combine several physical-process based models with rather restrictive assumptions. There is clearly a need for better in-depth understanding of the physical

processes and their interaction leading to improved models. REFERENCES JCSS (Joint Committee of Structural Safety) 2001. Probabilistic Model Code, Part 3.07 – Soil Properties (last update 08/2006). ISBN 978-3-909386-79-6. Lindenberg, J. & Koning, H.L. 1981. Critical density of sand. Geotechnique 31(2): 231–245. Lunne, T. & Christoffersen, H.P. 1983. Interpretation of cone penetrometer data for offshore sands. In Proceedings of the Offshore Technology conference, Paper no. 4464. Richardson, Texas. Mastbergen, D.R. & Van den Berg, J.H. 2003. Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. In Sedimentology 50: 635–637. Molenkamp, F. 1989. Liquefaction as an instability. In Proceedings Int. Conf. on Soil Mechanics and Foundation Engineering (ICSMFE): 157–163. Delft GeoSystems 2006. MStab 9.9, User Manual, Delft GeoSystems, Delft. Olson, S.M. & Stark, T.D. 2003.Yield Strength Ratio and Liquefaction Analysis of Slopes and Embankments. In Journal of Geotechnical and Geoenvironmental Engineering 129 (8): 727–737. ASCE. Sladen, J.A., D’Hollander, R.D. & Krahn, J. 1985. The liquefaction of sands, a collapse surface approach. In Canadian Geotechnical Journal 22: 564–578. Stoutjesdijk, T.P., De Groot, M.B. & Lindenberg, J. 1998. Flow slide prediction method: influence of slope geometry. In Canadian Geotechnical Journal 35: 34–54.

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A case study of the geological risk management in mountain tunneling T. Ikuma Dia Consultants Co., Ltd, Tokyo, Japan

ABSTRACT: In this tunneling project, a research was conducted on the risk management technique for occurrence prevention of latent geological risks on a mountain tunnel in Japan. The geological consultant played important role about the revaluation for unexcavated section and the proposal of a suitable construction method from geotechnical viewpoint. The geological risk management research of ground evaluation utilizing this experience is continued in other mountain tunnel with the same kind of geological features.

1

INTRODUCTION

Investigation of the prior stage of mountain tunnel with long length and high overburden was conducted for the purpose of clarifying each following item. •

The overall geological structure, distribution of geological features and characteristics of the tunnel section • Ground classification with synthetic technical consideration based on the results of investigation • Topography and geology of portal locations, basic data for a problem and its measure design, and • Basic data for evaluation of face stability, design of support, selection of auxiliary method, selection of excavation method and tunnel driving method Especially in a tunnel design stage, geographical and geological data of high accuracy are required. However, it is difficult to do the highly precise geological survey which covers all the extension of the tunnel as the linear structural object before excavation given the present technical level, and investigation period and current requirement of economic efficiency for geological survey. Moreover, the Japanese Islands belong to the mobile belt through the geological age, and have very complicated geological structure and distribution of geological features. For this reason, recognition of the uncertainty about the geological phenomenon in tunnel construction and the correspondence to them have been an important subject. In tunnel construction, how it grasps in a prior stage has linked to the subject resulting from the latent geological risk by the heterogeneity of the ground, and the uncertainty of geological information with cost and construction period directly. The geological risk in tunnel construction expresses degree and grade of a size of the uncertainty which undesirable phenomenon generates for construction and control of maintenance. This paper describes an example which reduced deviation of ground evaluation in the prior stage and

construction stage in the mountain tunnel built on the steep mountains area, and the future view from the viewpoint of geological risk management.

2

GEOMORPHOLOGICAL FEATURE AND GEOLOGY OF RESEARCHED TUNNEL

This tunnel is planned by steep mountain area with 1200–1400 m altitude, and some mountain streams which have channel in the direction of northeastsouthwest cross tunnel alignment (refer to Figure 1). The direction of these mountain streams is in agreement also with the lineament by an aerial photograph interpretation. Moreover, it is analyzed as low-velocity zone by seismic refraction method, and is geomorphological weak zone.

Figure 1. Locality and geological map of researched tunnel.

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Ground consists of the Nohi Rhyolites (Rhyolitic∼ Dacitic welded tuff) formed at the Cretaceous age and Granite porphyry which intrude them. These welded tuffs have received weathering and hydrothermal alteration, and lithofacies also changes intricately. 3

GEOTECHNICAL PROBLEMS

It became clear that the following geotechnical problems were held from the geological investigation carried out in the prior stage in this tunnel •

Geological outcrops was deficient in land surface as a whole, and it was difficult to grasp in detail about the geological structure of ground in the prior stage. • It was presumed that welded tuffs were distributed over 96.6% of tunnel length, and granite porphyry was distributed to the remaining 3.4% in the tunnel formation level. However, the former has the development of fracture frequency and the extent of alteration in various forms, estimated accuracy for deep bedrock conditions is considerably low. • It is considered that geological boundary between welded tuffs and granite porphyry is a alteration zone with many clayey thin layers, and possibility of being the bed rock which deteriorated is high in the depths also. Therefore, large increase of earth pressure caused by tunnel excavation or sudden water inflow occurs when clayey layer is an impermeable wall at section where overburden exceeds 300 m. In such a case, it has a significant impact on excavating. The ground classification was performed in consideration of the ground conditions on this tunnel based on the tunnel standard for road tunnel-structure (Japan Road Association; 1989). The underground condition of tunnel with large overburden depends on the elastic wave velocity value acquired mainly by seismic refraction method. However, since the depth of not less than about 200 m is a limit of exploration, the reliability of the acquired elastic wave velocity value is considerably low. Therefore, accuracy of the position of low velocity zone and boundary on the class of the ground is also low in the tunnel formation level of these large depth sections. The low velocity zone is considered to be abovementioned alteration zone or shear zone on the ground. In the design phase, the FEM analysis was conducted in large overburden part. As a result, support pattern corresponding to the ground classification was ranked higher about the section where overburden exceeds 300 m. According to prediction the amount of water inflow using hydrogeological conditions and hydraulic formula, it is considered that the amount of steady inflow in this tunnel is about 0.7 m3 /min/km. The amount of concentrated water inflow at stage of construction is presumed to be those about several times. The generating position of concentrated water inflow can consider at the periphery of low velocity zone and directly under a mountain stream in the tunnel formation level.

4

GEOLOGICAL RISK MANAGEMENT

This tunnel is crossing some mountain streams with the right angle or the high angle. An intersection part is in agreement with the position of a low-velocity zone in many cases. In those parts, although the overburden is large, face falling and generating with large amount of water inflow are assumed with construction. In respect of safety of construction, such frequency and quantity pose a problem as the geological risk. The geological risk management about the countermeasure of emergency time or predicting of the geological risk is very important. The example which was able to be reflected in construction is reported using the geological risk management technique. In order to cope with the geological risks and to advance construction more smoothly, the tripartite council which consisted of owner, constructor and geological consultant were established before construction. Since geotechnical information was always shared in the tripartite council, quick investigation was conducted by the geological consultant when collapse of the face and water inflow occurred in tunnel. The geological engineer played important role about the revaluation for unexcavated section and the proposal of a suitable construction method from geotechnical viewpoint. 4.1 Case example (southern section of this tunnel) In southern section, after excavation was started, construction was favorably continued by performing TSP (Tunnel Seismic Prediction) and horizontal core boring as investigation of ahead of the tunnel face. However, from the vicinity of STA338, the deteriorated bed rock came to appear frequently, and the squeezing from a tunnel sidewall also became remarkable. When excavation work advanced to STA.333, the convergence was increased. A maximum of 500 mm displacements by squeezed are found at the lateral side of tunnel at the point of STA.331+15, and excavation was stopped. The cave of about 3 m × 4 m size was checked in the upper part of this face. The amount of spring-water from a cave was 1.3 m3 /min (Figure 2). When an alteration zone appears in tunnel formation level with deep overburden, face falling, expansion of loosen zone accompanying excavation and the increase in lateral pressure are given. Moreover, it became clear that the confined aquifer existed in ahead of the face from result of horizontal core boring. The support pattern accompanied by the high rigid auxiliary method is needed in continuation of excavation judging from these situations. Then, the steel pipe fore-piling as the prevention for face falling, increase of rock bolt as lateral pressure preventive measures and drainage borings as measure against water inflow were proposed, respectively. Although displacement headed for convergence, water inflow was not decreased. Pressure of water inflow also had 1.7 Mpa.

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Figure 2. Base rock and water inflow situation around STA.331.

The geological condition in a tunnel was examined synthetically, and an excavation of drainage was proposed as a prevention which breaks through the confined aquifer with irregular distribution from a viewpoint of construction and economical efficiency. As shown in Figure 2, a drainage drift was excavated. In the point of No.331+16, it encountered the expected artesian aquifer by excavating the drainage drift. At that time, the face fell suddenly, the clayey∼sandy deteriorated bed rock of 80 m3 collapsed, and the water inflow of 2.5 m3 /min was occurred. The drainage drift was blockaded by this collapse. However, the generated water inflow move from the main tunnel to the drainage drift, and the water level and the amount of water inflow have been decreased. The total amount of water inflow of tunnel was ca. 7500 m3 /day. Since it was still generated by large amount water inflow from the face of this tunnel and the steel pipe fore-piling also after that, five more drainage boring were executed with STA.331+5.9. As a result, the amount of water inflow from the face also decreased and continuation of excavation was attained. However, since the deep overburden section will continue and occurring of sudden water inflow is also predicted, management of water inflow processing is needed. For this reason, drainage capability was reexamined and proliferation of the facilities for drainage in always and an emergency was proposed.

From this and other example (northern section of this tunnel), the technique of the geological risk management to construction in the section where deterioration of the bedrock and generating of a large amount of water inflow are summarized in Figure 3.

4.2

Orientation of geological risk

Although generating frequency was low about the sudden water inflow under tunnel construction, it was predicted that a large amount of water inflow was expected at occurred time. The mountain stream which flows through near a portal part is a clear stream, and mountain trout inhabits. Moreover, in the downstream region of southern section, there is a source of tap water using the infiltration water of the river, and it is used as drinking water. It is necessary to care about enough the measure against drainage of the water by which it is generated from the inside of a tunnel also from a viewpoint of social environment. The amount of convergence displacement measured by real construction is settled in the range presumed in the preliminary survey stage. The crack situation of the shotcrete surface was also observed carefully, and lining concrete was placed after checking displacement convergence. Those positioning is shown in Figure 4 about the amount of sudden water inflow and convergence among the geological risks in each stage of tunnel construction.

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Figure 3. Construction flow chart about the face falling section and role of the geological engineer.

Figure 4. Orientation map of the geological risks.

In the maintenance stage, these geological risks are monitor by visual observation and periodical measurement.

4.3

classification is done by using the modification index (i). The modification index (Inoma: 1984) was used to analyze comparison of ground evaluation between initial design stage and actual results quantitatively. Modification index (i) is defined by equation 1.

Quantitative evaluation of ground by modification index

Next, comparison between initial design stage and actual results after excavation stage of the ground

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Table 1. tunnel.

Brief summary of the risk managementin this

Figure 5. Contrast of the ground classification between initial design and excavation stage.

Where, R: Difference of class numbers with corresponding rock mass between each designed and actual case n: Ratio against the total length with each R. This index is a statistical numerical value using root mean square showing distributed condition of a variable. The modification index is calculated through the following process; Procedure 1: First of all, class of ground in original design stage and actual excavation result are compared. Then, it totals for every width of a class about change situation of ground class between the two. And an accumulation curve of the changed width as variable is drawn. Procedure 2: The modification index is calculated by equation 1 by using above-mentioned R and n. The result of comparing the ground classification at initial design stage, ahead of the face investigation stage, and actual results after excavation stage is shown in Figure 5. If the modification index is calculated from the ground classification in the ahead of face investigation stage and excavation stage, it becomes 0.59 and 0.80, respectively. With the general technical level, it is considered i ≤ 1.1 as a standard, and the quite effective face design was completed by the ahead of face investigation.

4.4 Effect of the geological risk management based on case example in this tunnel Management of risks have roots in geological features is predicting appearance of risk in advance, and preventing or avoiding beforehand. Especially, the uncertainty of geological risk in underground construction of our country is high with complexity of geological

features, and it is not easy to straightforwardly classify geological risk management in several patterns. However, geological risk working group of JGCA researched geological risk management pattern recently, and they divided into following three patterns. Type A: Type B: Type C:

A case of avoiding geological risk. A case on which geological risk is actualized. A case of minimizing damage associated with geological risk which was actualized.

Above-mentioned case example belongs to Type A. About southern section, deteriorated ground was expected to some extent from before construction. However, those scale and extension were uncertain. This case confirmed these situations by various explorations ahead of face and prevents geological risks such as face collapse and water-inflow beforehand. In this case, since bed rock deterioration which repeated itself complicatedly, we continued NATM by the observational method. Furthermore, suitable correspondence of heaving and displacement of side wall were completed by geological risk managements such as convergence measurement, reset of control criteria value, and water-inflow management. Brief summary of the geological risk management is shown in Table 1.

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Table 2.

Ground classification of this tunnel.

Figure 6. Ground classification of the planned tunnel with the same kind of geological features.

5

FUTURE VIEW

In the ground where geological and rock mass condition change intricately in tunnel extension and transverse direction like this tunnel, the difference of ground classification between initial design stage and construction stage is remarkable in many cases. About the unexcavated section which poses a problem especially in a construction stage, the ahead of face investigation result by two or more techniques is considered synthetically, and grasp of the threedimensional ground condition of the tunnel extension is needed. However, an applicable exploration method is different according to overburden, geologic structure, and the rockmass condition of the ground. Therefore, the geological management which judges the more effective exploration method appropriately about quality grasp of the unexcavated part of a tunnel is important. In evaluation about deterioration part of the ground consists of the Nohi Rhylolitic rocks like this tunnel, examination of the resistivity value was effective. However, the geological problem about the structure of Granite porphyry remained during construction, and the variation of ground evaluation was caused. Geological outcrop distribution of Granite Porphyry was fragmentary and details of those distribution and geological structure were uncertain in the preliminary investigation stage. In the excavation stage, it became clear that Granite porphyry had several times as many spread compared with a preliminary investigation stage. Petrographically, the extensional shape of Granite porphyry is stock, and widening toward deep. The depth distribution shape of Granite porphyry remained as a residual risk until the excavation stage. A ground classification in the design and construction stage of this tunnel is shown in Table 2. The class of ground of this table is conformed to the ground classification of Japan Road Association (1989). In addition, based on the actual result of the portal part, the ground classification of the general

part of this tunnel in a design stage was changed. Furthermore, the DSC (Different Site Condition) was also considered and a new standard of classification was made. Moreover, the ground classification scheme in the planning stage of A and B tunnel which consists of same geological kind around this tunnel is shown in Figure 6 (refer to next page). These two tunnels are under excavation now. By repeating observation of these tunnel face conditions and comparison of each ground condition, the more practical standard of ground will be built from now on.

6

CONCLUSIONS

It learned from the case of face collapse and squeezing of ground which occurs at northern section of this tunnel, geological risk management about prediction and accident prevention to tunnel deformation, and water inflow in the unexcavated part was carried out. As a result, the modification index (i) became about 0.5∼0.8, concerning the section where occurrence of tunnel deformation and water inflow were predicted, and deviation of the ground evaluation before and after excavation was able to be made considerably small. In general, a large amount of water inflow generated in the tunnel inside is thought to be the geological risk on excavation. However, because it was precious water resources about the fresh water in particular, water analysis was used together about this. Furthermore, separation measures were taken appropriately about fresh and murky water, and it was managed on water inflow. It was possible to manage appropriately ground classification and water inflow using geological risk management technique, this management effect was large also from a standpoint of the excavation cost.

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ACKNOWLEDGMENTS The author expresses his sincere gratitude to Professor Yusuke HONJO of the Gifu University for his encouraging advice. Special thanks are extended to ProfessorTUNEMI WATANABE of the Kochi University of Technology and Mr. Yoshihito SABASE of the CTI ENGINEERING Co.,Ltd. for kind advice. Thanks are due to Mr. Akira TAINAKA of the DIA CONSULTANTS Co., Ltd, who provided suggestion during the preparation of this paper. The author also expresses gratitude to Mrs. Keiko HORIKAWA of the DIA CONSULTANTS Co., Ltd, who cooperated in creation of the figure and table for this paper.

result in Mountain Tunnel, The 36th Japan National Conference on Geotechnical Engineering, The Japanese Geotechnical Society pp.1927–1928. (in Japanese) T. Ikuma 2008. A case study of the geological risk management using suitable investigation in mountain tunneling, Proc. of International Symposium on Society for Social Management Systems 2008, Kochi. Society for Social Management System H. Inoma 1984. Comparison between the Projected Rock Mass Classification at the Initial Design and the Actual Results after the Excavation under NATM Method, Journal of the Japan Society of Engineering Geology, Special Volume: 63–70.(in Japanese with English Abstr.) Japan Road Association, 1989, Technical Standard for Road Tunnels-Structures, 273p. (in Japanese)

REFERENCES T. Ikuma, K. Hatamoto, K. Yamamoto, T.Shindou, T. Ogawa, 2001, Revaluation of the Rock Mass based on Excavated

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Guideline for monitoring and quality control at deep excavations T.J. Bles, A. Verweij, J.W.M. Salemans & M. Korff Deltares, Delft, The Netherlands

O. Oung & H.E. Brassinga Public Works Rotterdam, Rotterdam, The Netherlands

T.J.M. de Wit Geomet BV, Alphen a/d Rijn, The Netherlands

ABSTRACT: Geotechnical monitoring and quality control are often used as a standard approach of deep excavation risk control. However, often the full potential of monitoring is not used and the relation with design and construction processes is delimited to some ground water levels readings and height marks. Monitoring offers much more possibilities when incorporated in the projects risk management and the constructions quality control. That is why a committee of experts from the field is setting up a guideline for the implementation of monitoring and quality control in deep excavations. The guideline helps designers, contractors and clients to determine monitoring benefits for their project and suggests opportunities for successful embedding of monitoring in design, tender, contract and construction. This paper deals with the content of the guideline, which is to be released in 2009. 1

BENEFITS OF QUALITY CONTROL AND MONITORING

3. 4. 5. 6.

1.1 Introduction Failure costs in the construction sector are estimated to be five to ten percent of the total turnover. A large portion of these failure costs is related to underground construction works including deep excavations and pile foundations. The focus of the research done and of this paper is on deep excavations (i.e. an excavation for purpose of building an underground construction with depths of a few meters with a maximum of approximately 30 meters) and accompanying foundation works. In order to reduce failure costs it is necessary to control the risks accompanying underground construction works. Unwanted and unforeseen events frequently occur, resulting in constructional and economical damage and in a negative image of the construction sector. Examples are severe leakages, foundation piles not reaching the required depth, discomfort for the public or even damage to deep excavation or surroundings. As a consequence, ground related risk management has rapidly evolved in recent years. More and more it is used as a fruitful method to reduce geotechnical risks. To give structure on ground related risk management Deltares developed the GeoQ-method (Van Staveren, 2006). GeoQ is based on six generally accepted risk management steps: 1. Determination of objectives and data collection; 2. Risk identification;

Risk classification and quantification; Risk remediation; Risk evaluation; Transfer of risk information to next project phase

Geotechnical risk management is already successfully used in many construction projects. Monitoring and quality control are excellent tools within this approach for deep excavation design and construction. 1.2

Monitoring and quality control

Many definitions are available for geotechnical monitoring such as described by Dunnicliff (1988, 1993). The most important aspects are: – Measurements are performed repeatedly. This is necessary to gain insight in deep excavation behavior over a certain period of time. – Depending on the (failure) mechanism to be observed measurements are performed on (elements of) the construction, in soil and/or on possible surrounding constructions. – Measurements can be executed before, during and after the construction period. – Measurements should create the possibility to foresee unwanted events and facilitate an incentive to take appropriate measures in order to prevent negative consequences. Contractors also perform measurements for quality control. These measurements contribute to building process control. Measurements for quality control are usually performed only once and are usually not

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part of a monitoring plan. Still, many quality control measurements complement traditional geotechnical monitoring. Therefore quality control should be part of deep excavation risk management. 1.3

Objectives of measuring

As Marr (2001) states: “Geotechnical monitoring saves money and lives and/or diminishes risks”. In addition, Marr gives fourteen reasons demonstrating geotechnical monitoring benefits, varying from indicating construction failure to construction process control and increase of state-of-the-art knowledge. In general four types of objectives of measuring and monitoring are identified: 1. Operational/qualitative goals: Decision making with regard to possible occurrence of risks is improved by measuring failure mechanism development. The progress of construction of the deep excavation is controlled and checks are performed on the assumptions made for the design of the deep excavation. Constructive safety of deep excavation and surroundings is also guaranteed. The aim is to reduce uncertainty and gain reliability. In addition, quality control of constructional elements is an operational goal. Examples are load tests on anchors or piles, or torque measurements while installing drilled piles. 2. Communicative goals: Deep excavations are often constructed in densely populated areas. Therefore it is very important to get the public’s support in order to prevent complaints that can slow down the construction process. Monitoring can be efficiently used to demonstrate the construction process is under control. 3. Legal goals: Monitoring can be used to answer questions about liability of building damage. Monitoring can also be a requirement or boundary condition to authorities’ permission for deep excavation construction. 4. Scientific goals: Monitoring can provide excellent data for scientific research to improve understanding of deep excavation (and soil) behavior. 2

industry in the Netherlands (contractors, clients, engineers, monitoring companies and researchers). The result is a CUR guideline for the implementation of quality control and monitoring in deep excavations (CUR is a Dutch civil engineering research institute). The guideline will be available (in Dutch) mid 2009.

RESEARCH AND GUIDELINE

2.1 Research In general practice, monitoring is already used as a standard part of deep excavations risk control. However, often the monitoring potential is not fully used and the relation with design and construction processes is limited. The main reason for this research is to clarify the possibilities to use monitoring more efficiently in practice. We researched the way monitoring can be optimized during the entire construction process, providing a powerful tool within a broad risk management framework for quality control and process optimization. The research has been done together with the construction

2.2 Improvement in monitoring practice After guideline implementation three types of improvements are expected to be achieved in Dutch construction practice. These improvements are: 1. Increase of client’s awareness of monitoring benefits. Monitoring is often mistaken for a time and money consuming activity, necessary for satisfying the authorities’ requirements and clients demands. The guideline underlines monitoring benefits and describes how to maximize monitoring results. 2. Monitoring will become an integral part of the building process. This can be separated in the following aspects: – Facilitation of explicit responsibility allocation for different parties involved in the construction process. – All monitoring activities are based on a risk management approach and are laid down in a standardized monitoring plan. – Monitoring activities are coordinated by one party to prevent fragmentation of monitoring activities. – Measurements are directly adapted to the building process (frequency, reference and end measurements, limit values of measurements, communication and interpretation of data, etc.). 3. Providing an overview of all different measurement techniques applicable for deep excavations. Techniques are coupled with specific risks incorporated in different construction methods in a work break down structure. 2.3 Objectives of the guideline The guideline’s overall-goal is to improve the use of measurements and monitoring, thus improving quality and risk management. Three objectives were formulated: 1. Describe measurement techniques associated with deep excavation construction, coupled to all relevant construction risks and the respective parameters. 2. Present a step-by-step plan and format to set up a solid monitoring plan. 3. Provide opportunities to embed monitoring in tenders and contractual processes. 3

OVERVIEW OF MEASUREMENT TECHNIQUES

Many companies deal with monitoring. They all have their own experience with different monitoring

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Table 1. Standard for describing parameters to be measured; example deals with soil deformations. Parameter

Soil deformation

Measurements(msmt) of

Deformation in x-, y- and z-direction with use of inclination or extenso instruments, leveling Measurement boundary Measurements should be checked values during each construction phase against design values – signal values 80% design value – limit values 100% design value

Figure 1. Structure to identify measurement techniques.

Required accuracy – absolute accuracy – frequency

Depends on design A minimum of one time per construction phase (end msmt is start msmt of next phase). During critical phases more measurements are necessary, especially when time is an important factor – timing of ref. msmt Before starting of activities – demands on reference At least two measurements measurement (similar) – timing of end With time related effects: 3 month measurement after last activity affecting the deformations. Without consolidation: 1 month after last activity affecting the deformations. – demands on end msmt One is sufficient Handling of data – processing of data

Lines of deformation according to time. Check against design value. – necessary speed for Speed of processing depends availability of data at on construction phase and risk; testing company aim for maximal three days. Communication to all parties involved. – necessary speed for Speed of decision making depends decision making when on construction phase and risk; measurement exceeds aim for maximal three days. boundary Communication to all parties involved. Measurements in Monitoring plan quality-control-plan or monitoring-plan

Figure 2. (Part of a) WBS of a deep excavation.

techniques. However, these experiences are not shared among others. In this way the practical knowledge level does not increase and best practice is in fact re-invented at each deep excavation, especially for new and special techniques. For a complete outline of all measurement techniques a risk-based overview of a deep excavation is developed. This overview has the structure as shown in figure 1. The elements of a deep excavation are identified by means of a work-break-down-structure (WBS) of a deep excavation. The WBS can be seen in figure 2. For every element a list of unwanted events has been made. These unwanted events are described to show the relevance. In order to keep an overview, a differentiation has been made for unwanted events affecting

1. single elements of the deep excavation e.g. instability of trench of cemented bentonite wall 2. deep excavation as a whole, a combination of those single elements e.g. bursting/heave of a submerged concrete floor 3. surroundings of the deep excavation e.g. cracks in surrounding buildings caused by vibrating piles For each unwanted event the parameters have been identified which should be taken into account for possible development of the unwanted event. With these parameters it is possible to find a list of specific measurement techniques. Each parameter and technique is described using a standard. Examples of such standards are shown in table 1 and table 2.

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Table 2.

Standard for describing a monitoring technique; example deals with extensometer.

Monitoring technique

Extenso instrument

What is monitored

Vertical displacements (swell caused by excavation, settlement caused by consolidation, relative to strains in concrete constructions) Extenso instruments are used to constantly measure differences in distance between two or more points over the axis of a borehole. This makes it able to determine the vertical displacements of soil layers. In combination with inclino measurements a total view of the displacements can be derived. In practice, an open tube is placed inside a borehole. Fixed points are placed on different depths. The displacements between these fixed points and the head of extenso instruments on the top of the tube are measured. E.g. the instruments can be displacement recorders or potentio instruments.

Functioning of instrument

Photo of instrument Figure of measurements Accuracy of monitoring technique a) sensitivity to installation errors b) sensitivity to errors during operation c) vulnerability of instruments (solidness) Explanation and recommendations

d) Accuracy (absolute) e) Measurement range (absolute) Relevant influencing factors from surroundings Long term behavior (calibration, stability) Procedure of measurements Interpretation of data a) Existing systems for analysis and interpretation b) Ambiguity Maintenance Application 1 Suitability for this application Best practices a) Number of instruments b) Location of instruments Application 2 Application 3

Little sensitive for installation errors Little sensitive for measurement errors Instruments are vulnerable When used for measurements in center of deep excavation, instruments are sensitive for collision with vehicles. Instruments can be protected by installing a casing till 1 meter below excavation level and attaching the casing to a strut. +/− 0,05 mm 100 mm Instruments should be protected in case of placement in an excavation. Depends on specification of instruments. Reference point should be measured regularly. Automatically Absolute and relative displacements can be measured. Unambiguous (interpretation always objective) None Swell (vertical soil displacements) at excavation Very suitable At minimum one location in the center of the deep excavation At minimum one measurement anchor at each soil layer. More accurate results can be obtained by using two anchors per soil layer. Damage to surroundings caused by (densification of sand layers due to) vibrating or hammering sheet piles Deformation of soil and surrounding buildings caused by bending or collapse of wall of the pit

For this example, app. 2 and 3 are not worked out in detail

4

DEVELOPING A MONITORING PLAN

4.1 Table of contents

The guideline presents a step-by-step plan to set up a good monitoring plan. The basis of this plan was formulated in HERMES (2003), but adapted for practical use in construction works. Not all situations ask for the same monitoring intensity and efforts. A large deep excavation in a busy and old city centre will require a much more intense monitoring system than a standard deep excavation outside the city. In addition, the type of construction will lead to a different monitoring strategy. With help of the guideline, the reader can learn which monitoring is necessary, based on the situation and project risks, to provide a good tool for proper risk management.

A good monitoring plan should include at least the elements stated below. The capitals behind the chapters refer to the steps that can be followed in order to get all necessary input for a proper risk based monitoring plan. These steps are described below. 1 1.1 1.2 2 3 4 5

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Introduction Project description and basic assumptions Objectives of monitoring Results from risk analysis Monitoring strategy Operational plan Maintenance plan

A B C D–G H–I J

6 7 8

Measures when measurement limits are exceeded Dismantle plan Communication plan

– Frequency of the measurements; a higher or lower frequency can lead to the choice for other instruments.

K L M

The table of contents is the same for every type of project, big or small, simple or complex. The way it is elaborate can however be different. One has to use the guideline in a pragmatic way. 4.2

Steps to obtain a risk based monitoring plan

4.2.1 Steps A and B, scope and objectives The project needs demarcation in space and time in order to control the scope. Then, the objectives (see different types of objectives in paragraph 1.3 of this paper) for the monitoring are chosen. 4.2.2 Step C, risk analysis Risk management is of key-importance to a good monitoring plan. Monitoring efforts may be an outcome of a risk analysis. Step C therefore includes a go/nogo decision. This decision should be based on the following questions: – Is the risk to be monitored critical (big enough)? – Is monitoring the best option in order to manage the risk? The risk analysis can be technical on operational goals, but can also be more general; for example on communicational goals. A summary from this analysis should be written in the monitoring plan. 4.2.3 Step D, monitoring strategy The effort on monitoring needs to be evaluated, together with the client, by weighing the benefits of measuring (decrease of risk to loose money, time, quality and/or image of the client) to the costs. In this way better understanding of the necessity of the measurements is created. For elaboration one can use the following steps D–G. However, only the determined strategy needs to be reported and further elaborated in the final monitoring plan. 4.2.4 Step E, parameters Determine the parameters to be measured. Are these parameters sensitive enough for all risks that have to be monitored? The scheme in the previous chapter provides background for this step. 4.2.5 Step F, demands Determine the demands on the monitoring: – Signal and limit values of parameters to be measured, making use of the scheme in the previous chapter and/or drawings, norms and literature. – Location of the measurements; is this location sensitive enough in order to have proper measurements? – Sensitivity and range of measurements of each parameter to be measured; this is defined from the risks to be controlled and is a demand for the instruments.

4.2.6 Step G, instruments Based on the previous steps, types of instruments can be selected that fit the given demands. Each type of instrument should have a specific goal for measurements. Instruments without such a specific goal should be left out. Afterwards a specific instrument can be selected from a producer. 4.2.7 Step H, influence from surroundings Effects from activities surrounding the project can disturb the measurements. For example heavy traffic on a neighboring road causes possible vibrations and daily temperature differences cause shrinkage and extension of constructions. This can influence processing of the data and can put high demands on the maintenance plan. Sometimes it is necessary to go back to step F and choose a different instrument. 4.2.8 Step I, planning of operations For each monitoring instrument the following should be clear: – – – –

Location (xy) and depth (z) Demands on reference measurement Measuring frequency Time table for obtaining monitoring data (related to the construction process) – Format of data – Demands on the processing of data – Demands on end measurement 4.2.9 Step J, planning maintenance Planning of necessary calibration and maintenance. 4.2.10 Step K, measures An important step in this risk based process is to decide about measures to be taken when exceeding signal and limit values of measurement. Only with pro-active thinking, measures can be taken in time in order to prevent discussions when immediate action is necessary. However, for each project one has to choose to what depth one wants to elaborate all possible measures. 4.2.11 Step L, dismantling Short description of when and how dismantling of the monitoring system will take place and who is responsible. 4.2.12 Step M, communication When using monitoring it is very important to have proper communication between all parties involved. The processing of the data should be aligned with the project activities. Especially the maximum time span between measurement, processing and taking measures is of importance. When there is no attention for communication, monitoring does not make sense. After all, the purpose of monitoring is to foresee unwanted events and take measures in time.

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However, the client can state process requirements. For example, the client can demand the contractor to formulate the monitoring plan according to the guideline. During the tender phase it is difficult to give specifications within an integrated contract, because a client can not be too specific, allowing the contractor to make the design himself. Risk management is the key to solve this. The client can demand a contractor to use risk management in his design approach and to be specific on the role monitoring will play in the total project’s risk management.

Therefore, it is crucial to have an effective communication plan. This plan should at least give answers to the following questions: – Who is responsible for measurements execution? – Who is responsible for measurement communication? – Who is responsible for measurement processing? – Who is responsible for measurement interpretation? – Who is responsible for taking action after exceeding the boundary values of measurements? How is ensured that these actions really take place? – Who is end responsible for the total program? 5

6

PRACTICAL USE

In the end, monitoring has to be used in practice. However, also when monitoring is considered of much importance, it is often perceived difficult to divide responsibilities between the different parties involved in the construction process. The guideline therefore provides suggestions on how monitoring can be embedded in tenders and contracts and how to spread responsibilities. Distinction is made between traditional contracts (using specifications, design by or through the client) and integrated contracts (i.e. design and construct). Three rules form the basis for dividing the responsibilities: 1. The party that makes a certain choice in the design or construction process is responsible for that choice. 2. This party also takes the consequences accompanying the choice. 3. Accordingly, this responsible party determines the monitoring with regard to this choice and performs the monitoring or assigns a third party to perform the monitoring. Roughly, this results in the following distribution of responsibilities for the different types of contracts: – Traditional: the client determines the extent of monitoring and performs it himself, or assigns a third party to perform the monitoring. The monitoring can be part of the specifications for the contractor. – Integrated: Monitoring is part of the contract with the contractor and the contractor is responsible for determination and performing.

CONCLUSIONS

The guideline’s overall-goal was to improve the use of measurements and monitoring, thus improving quality and risk management. The guideline indeed answers the research questions. The knowledge of Dutch monitoring and construction industry with regard to deep excavations is gathered in order to get an overview of all different measurement techniques. Also a tutorial is given in order to obtain a risk based monitoring plan. Finally, suggestions are shown for implementation in practice. Two case studies have been executed to check the practical use of the guideline with positive results. Last changes are made according to the results of these cases. The guideline will be available from mid 2009. ACKNOWLEDGEMENTS This research was only possible with the contributions of all members of the committee (CUR H416) of experts in the field and Delft Cluster (www.delftcluster.nl). REFERENCES Dunnicliff, J., 1988, 1993, Geotechnical Instrumentation for Monitoring Field Performance, John Wiley & Sons, Inc. HERMES, feb 2003, Het Rationale Monitoring Evaluatie Systeem (The Rational Monitoring Evaluation System), Delft Cluster Marr, A.W., 2001, Why monitor Geotechnical Performance? 49th Geotechnical Conference in Minnesota Staveren, M. van, 2006, Uncertainty and Ground Conditions: A Risk Management Approach, Elsevier Ltd.

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A study on the empirical determination procedure of ground strength for seismic performance evaluation of road embankments K. Ichii Graduate School of Engineering, Hiroshima University, Higashihiroshima, Japan

Y. Hata R&D Center, Nippon Koei Co., Ltd., Tsukuba, Japan

ABSTRACT: Road embankments should have a certain level of seismic performance against a strong earthquake motion. The ground strength parameters (cohesion c and internal friction angle φ) are key factors in the seismic performance assessment of road embankments. However, the procedure to determinate the ground strength parameter is dependent on the experience of the engineers, and it is not well documented. For example, the patterns of in-situ soil test at the embankment (Number of tests and its locations) are not unique. In this study, a questionnaire survey to 76 civil engineers in Japan is conducted to reveal their empirical procedure of parameter determination. The result of the questionnaire clarify the considerable variation of determined ground strength parameters which depending on the experience of engineers.

1

INTRODUCTION

Road embankments should have a certain level of seismic performance against a strong earthquake motion (Japan Society of Civil Engineers (JSCE), 2000). There are many applicable guidelines for the seismic performance evaluation of geotechnical works including road embankments. In the procedure of seismic performance assessment, the ground strength parameters (cohesion c and internal friction angle φ) are most important. However, the procedure to determinate the ground strength parameter is dependent on the experience of the engineers, and it is not well documented. For example, the patterns of in-situ soil test at the embankment (Number of tests and its locations) are not unique. In this study, a questionnaire survey to 76 civil engineers in Japan is conducted to reveal their empirical procedure of parameter determination. The questionnaires consist of 4 questions. The first one is a question for the types of geotechnical investigation to be carried out. The second one is a question for the location and number of in-situ tests. The third one is a question asking parameter identification for a virtual soil profile. The last one is a question for the experience of the respondents. In this paper, the result of the third question is briefly reported. 2

Seismic performance assessments of embankments are requested for the point A and point B, as shown in the Figure 1. The point A is a standard type embankment on horizontally layered bedrock, but the point B is the half-bank shaped embankment on tilted bedrock. The distance between point A and point B is 5 km. These embankments (Embankment A & Embankment B) are both located in Hiroshima Prefecture, Japan, and filled by Masado sand (decomposed granite). The shapes of embankments are summarized in Figure 1 and Table 1. The parameters of embankments shapes, such as slope gradient, height and crest width are also shown in Table 1. The bedrocks are very strong. The ground water level is very low, the possibility of liquefaction is no necessary to be considered.

CONTENTS OF QUESTIONNAIRE

2.1 Assumed background for the questions The following are assumptions for questions. Note it determined by the viewpoint of simplicity.

Figure 1. The targeted embankments.

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Table 1.

Parameters of targeted embankments.

Embankment Parameters

Embankment A (Standard)

Embankment B (Half-bank)

Height H (m) Crest width W (m) Gradient of slope 1:s (deg.) Gradient of base 1:k (deg.) Soil material

12 22 1:1.8 (29.1)

12 22 1:1.8 (29.1)

Horizontal base Masado

Tilted base 1:3.63 (15.4) Masado

and number of in-situ tests. The third one is a question asking parameter identification for a virtual soil profile. The last one is a question for the experience of the respondents. Following is the contents of the third question. ‘Standard penetration tests (SPT) were carried out at the crest of Embankment A and Embankment B. The obtained N values are shown in Figure 2. Based on the obtained data, please identify the shear strength parameters (cohesion c and internal friction angle φ) to carry out the slope stability assessment based on the circular slip method.’ ‘If possible, please mention the method to be used. Furthermore, in addition to the final estimate values of shear strength parameters (cohesion c and internal friction angle φ), please mention the possible range of parameters.’

3

RESULTS OF THE QUESTIONNAIRE

3.1 Characteristics of respondents The questionnaire was sent to total 200 engineers. As a result, the effective response was 76. The characteristics of respondent are shown in Figure 3. As shown in Figure 3(a), the majority of respondents (42) are consultant engineers. The practical working year of the respondents is summarized in Figure 3(b). It is in very wide range. Figure 3(c) shows the qualification of the respondents. Most of the respondent have at least one of big four qualifications (Professional Engineer of Japan in civil engineering field, Professional Engineer of Japan in general technological project management, Doctor of Engineering, 1st grade Engineering works management engineer). Therefore, most of the respondents might have certain level of technological knowledge and experience. Figure 3(d) shows the main business field of respondents. About one-third of the respondents are mainly working on the design of embankment or slope stability assessment.

3.2 Method for cohesion estimation Most of the engineers estimated the cohesion as zero (c = 0), because the Masado soil was used. This is based on the engineers experience and by the engineering judgment considering the safety side. The cohesion of a small quantity is answered by some respondents, as a dummy value to prevent surface failure of slopes in the dynamic FEM analysis. The followings are empirical equations used in the answer (Japan Road Association (JRA), 1996; JRA, 1999). Figure 2. The N values at the sites.

2.2

Questions

Total 4 questions are given in the questionnaire. The first one is about the type of geotechnical investigation to be carried out. The second one is the location

Where, c (kPa) is the cohesion and h (m) is the depth from the crest of embankments.

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Figure 3. The characteristics of respondents.

3.3

Method for internal friction angle estimation

The results of answered method for internal friction angle φ are summarized in Figure 4. There is no great difference in the methods for Embankment A and Embankment B. The answered methods can be classified into 10 types as follows. Method I is the technique proposed by Fukui (Fukui et al., 2000), and it is on the specifications for highway bridges (JRA, 2002).

The conversion of N value into N1 value is as follows.

Where, σv
is the effective overburden pressure (kPa). Method II is the technique which is on the specifications for highway bridges (JRA, 1980). The effect of the confining pressure is not considered in this equation.

Method III is the technique based on the actual values for expressway embankments (e.g. Okubo et al.,

Figure 4. The methods for parameter determination.

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2004). Note a purely empirical decision based on the experience in expressway embankment is also classified as this method. Method IV is the technique proposed by Osaki (Osaki, 1959). This method is based on the soil test results in the Kanto region in Japan.

MethodV is the technique based on the effect of previous studies on the Masado (e.g. Japan Geotechnical Society (JGS), 2004). Method VI is the technique based on the guidelines for design of expressway by NEXCO (Nippon Expressway Co., Ltd, 2006). Method VII is the technique proposed by Hatanaka (Hatanaka & Uchida, 1996). This method is based on the relationship between CD test results and corresponding N value.

The conversion of N value into N2 value considering the effect of effective confining pressure is as follows.

Method VIII is the technique based on the guidelines for road earthwork of the slope engineering and slope stability engineering (JRA, 1999). Method IX is the technique based on the guidelines for railways (Railway Technical Research Institute, 2007). Method X is the technique proposed by Dunham (Dunham, 1954).

Where, A is the coefficient considering the grain size distribution and the grain shape. In Figure 4, “Others” are comments that it is difficult to estimate the internal friction angle only from the N value, and “None” are non-effective answers. About a half respondent adopted the techniques based on the specifications for highway bridges (Method I and Method II). 3.4 Estimated result of cohesion The estimated result of the cohesion is shown in Figure 5. There is no great difference between the estimated cohesion for Embankment A and that for Embankment B. Most of the respondents regard the cohesion as zero (c = 0), and only 15 respondents considered Masado as adhesive material. The main reason of regarding Masado as cohesionless material (c = 0) is to get evaluation on the safety side, though a certain level of cohesion can be observed for the unsaturated soil in usual.

3.5 Estimated result of internal friction angle The estimated result of the internal friction angle is shown in Figure 6. As same as the Figure 5, there is no great difference between the estimated values for Embankment A and Embankment B. The degrees of the dispersion of estimated internal friction angle are about ±4 degrees in the standard deviation, about 0.13 in the variation coefficient. Even if the same method is adopted, the estimated result varies. This is because of the difference in the way of dealing with scattering N values. Some respondent divide the embankment into some layers. Note there is a unique answer which regard Masado as purely adhesive material (frictionless material; φ = 0) because the obtained N values are not increased with the increase of the depth.

4

DISCUSSION

As the effect of variations in estimated ground strength parameters (c, φ), the Mohr-Coulomb’s failure criterion is varied as shown in Figure 7. The influence of the determined cohesion is significant in the lower confining pressure region. However, maybe due to the effect of surface failure which corresponds to the lower confining pressure region, it is reported that the seismic performance of embankments evaluated by FEM is greatly dependent on the level of the apparent cohesion (Hata et al., 2009). Therefore, the obtained variation of the estimated cohesion implies the significant variation on evaluated seismic performance of embankments. In this study, the degree of the dispersion of the estimated internal friction angle is almost 0.1 in the variation coefficient (refer to Figure 6). On the other hand, it is reported that the degree of the heterogeneity of the internal friction angle obtained by laboratory tests for Japanese airport embankments is almost 0.1 in the variation coefficient (Hata et al., 2008). In other words, the degree of the dispersion of internal friction angle based on engineering judgments is almost in a same level of the degree of the heterogeneity of soil itself.

5

CONCLUSIONS

In this study, a questionnaire to 76 civil engineers in Japan to reveal their empirical procedure of parameter determination is carried out. In this paper, the answers for a partial question are briefly reported. The method for the ground strength parameter determination from N values shows a wide range of variety. In addition to the difference of the adopted method, the difference in the way of dealing with scattering N values is also a major reason of the difference of the estimated parameters. As a result, a certain level of variation in the estimated values on shear strength parameters is reported.

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Figure 5. The estimated cohesion.

Figure 6. The estimated internal friction angle.

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Figure 7. The difference of estimated Mohr-Coulomb’s failure criterion.

For example, the degree of the dispersion of internal friction angle based on engineering judgments is almost in a same level of the degree of the observed heterogeneity of soil strength. This kind of knowledge is quite important to discuss the reliability of seismic performance evaluation. A detailed examination of obtained answers and some more detailed survey will be done as a future study. REFERENCES Dunham, J. W. 1954. Pile foundations for buildings, Proc. of ASCE, Soil Mechanics and Foundation Division.

Fukui, J., Shirato, S., Matsui, K. and Okamoto, S. 2002. Relationship between internal friction angle of the sand between N value of the standard penetration test based on the triaxial compression test (in Japanese), Technical note of PWRI, No.3849, 50p. Hata, Y., Ichii, K., Kano, S. and Tsuchida, T. 2008. A fundamental survey on the soil properties in the airport embankments (in Japanese with English abstract), Bulletin of the graduate school of engineering, Hiroshima university, Vol.57, No.1. Hata, Y., Ichii, K., Tsuchida, T. and Kano, S. 2009. A study on the seismic resistance reduction of embankment due to rainfall (in Japanese with English abstract), Jour. of JSCE C, Vol.65, No.1. (in printing) Hatanaka, M. and Uchida, A. 1996. Empirical correlation between penetration resistance and internal friction angle of sandy soils, Soils and Foundations, JGS, Vol.36, No.4, 1–9. Japan Geotechnical Society. 2004. Japanese standards for geotechnical and geoenvironmental investigation methods, Standards and explanations (in Japanese), 889p. Japan Road Association. 1980. Specifications for highway bridges, Part IV Substructure edition (in Japanese), Maruzen Co., Ltd. Japan Road Association. 1996. Specifications for highway bridges, Part IV Substructure edition, 566p, Maruzen Co., Ltd. Japan Road Association. 1999. Guidelines for road earthwork, Slope engineering and slope stability engineering edition, 470p, Maruzen Co., Ltd. Japan Road Association. 2002. Specifications for highway bridges, Part V aseismic design edition, 406p, Maruzen Co., Ltd. Japan Society of Civil Engineers. 2000. The third suggestion and commentary about the civil structure (in Japanese), Chapter 8, Earth structures edition, 29–34. Kitazawa, G., Takeyama, K., Suzuki, K., Okawara, H. and Osaki, Y. 1959. Tokyo ground map (in Japanese), 18–19, Gihodo Shuppan Co., Ltd. Nippon Expressway Company Limited. 2006. Guideline for design of expressway, earthwork edition (in Japanese), 350p. Okubo, K., Hamazaki, T., Kitamura, Y., Inagaki, M., Saeki, M., Hamano, M. and Tatsuoka, F. 2004. A study on seismic performance of expressway embankments subjected to High-level seismic load (part 1) –Evaluation of shear strength of embankment materials- (in Japanese), Proc. of 39th Japan National Conference on Geotechnical Engineering (CD-ROM), No.881, 1759–1760. Railway Technical Research Institute. 2007. Guidelines for railway, Earth structure edition (in Japanese), 703p., Maruzen Co., Ltd.

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Geo Risk Scan – Getting grips on geotechnical risks T.J. Bles & M.Th. van Staveren Deltares, Delft, The Netherlands

P.P.T. Litjens & P.M.C.B.M. Cools Rijkswaterstaat Competence Center for Infrastructure, Utrecht, The Netherlands

ABSTRACT: Ground conditions appear a major source of cost overruns in infrastructure projects, which has been confirmed by recent Dutch research. As an answer to these cost and time overruns, ground related risk management has rapidly evolved in recent years. Deltares for instance developed the GeoQ-method. In the Netherlands, Rijkswaterstaat, the Centre for Public Works of the Dutch Ministry of Public Works and Water Management, is initiator and owner of all federal infrastructure projects. They asked Deltares to perform a Geo Risk Scan on five selected projects of the top 20 largest Dutch infrastructure projects. The Geo Risk Scan proved to be an effective tool for quickly providing information about the degree and the quality of ground related risk management in infrastructure projects. This paper describes the Geo Risk Scan, as well as its application within five projects. The evaluation of the five projects resulted in six main lessons which are further elaborated in 20 recommendations. These lessons may help project owners, engineers, and contractors to manage their construction projects. 1 1.1

INTRODUCTION Successful and unsuccessful projects

What makes the difference between a successful and an unsuccessful construction project? A project that is completed well within budget, time, and its requirements, or not? It can not be its size and complexity, because there are successful and unsuccessful ones, amongst small and large, as well as simple and complex projects. It is also not its location, because every country seems to have its successful and problematic projects. It is even not because of ground conditions, as we all know examples of successful projects that have been completed in very difficult ground conditions. There must be another reason. Perhaps it is the way the management team of a project is able to manage the inherent presence of risk, during all phases of realizing the project.

1.2 Risk management as an answer to failure costs Several studies indicate that failure costs in the construction industry are typically 10 to 30 percent of the total construction costs (Avendano Castillo et al., 2008). This seems to be a worldwide phenomenon. There is also abundant evidence that unexpected and unfavourable ground conditions have a serious stake in these failure costs (Van Staveren, 2006). In the Netherlands, Rijkswaterstaat, the Centre for Public Works of the Dutch Ministry of Public Works and

Water Management, is initiator and owner of all federal infrastructure projects. Therefore, Rijkswaterstaat decided to pay particular attention to the management of ground related risks within their projects.

1.3

Ground related risk management

The development and application of geotechnical risk management gets more attention in recent years. More and more, it is considered an effective and efficient way of work process for controlling all types of ground-related risk. For instance Deltares, formerly known as GeoDelft, developed the GeoQ-method (Van Staveren, 2006), that is already used in many construction projects with good results. The GeoQ approach is in fact an in-depth application of the RISMAN project risk management method. GeoQ focuses on controlling ground-related risks. The method is based on six generally accepted risk management steps: 1. Determination of project objectives and data collection; 2. Risk identification; 3. Risk classification and quantification; 4. Risk remediation; 5. Risk evaluation; 6. Transfer of risk information to the next project phase. These risk management steps should be explicitly taken in all phases of a construction project. Ideally, the ground related risk management process starts in the feasibility phase and is continued during the

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(pre)design phase, the contracting phase, the construction phase and the operation and maintenance phase. Obviously for being effective and efficient, the ground related risk management should be aligned with more general project risk management approaches. Because of the similarity of risk management steps, this should be no problem. The main differentiating feature of ground related risk management, when compared to generic project risk management, is its specific attention to geotechnical risk and its remediation. Therefore, ground related risk management uses conventional risk management approaches, such as qualitative risk assessments, as well as specific geotechnical approaches. The latter includes for example risk-driven site investigations and monitoring programmes. 2 2.1

SET UP OF A GEO RISK SCAN Introduction and objectives

For gaining insight in the degree and quality of geotechnical risk management in projects, Rijkswaterstaat asked Deltares to perform a Geo Risk Scan on five selected projects out of the top 20 largest Dutch infrastructure projects. The main objectives were gaining insight in the type and characteristics of ground related risks, the possible consequences when these risks would occur, and the degree to which risk remediation measures were taken within the projects. Moreover, the results of the Geo Risk Scan would generate a quality judgement about the degree of geotechnical risk management. In order to achieve these objectives the Geo Risk Scan aims to quickly scan both process and content of the ground related risk management within a project. The execution of a well-structured risk management process, by taking the presented six risk management steps, is considered as the main boundary condition for generating effective and efficient geotechnical risk management. If necessary, recommendations to the project organisations are provided in order to improve the project performance and reducing the probability of ground related failure costs. 2.2

Structure of a Geo Risk Scan

The basis of the Geo Risk Scan is the GeoQ approach mentioned above. Using this approach the Geo Risk Scan was executed focussing furthermore on aspects such as: – Deviation between process and content – Within the context of a project, the scan is executed from a more generic analysis to more detailed analyses on specific points of interest for the projects scanned – Any scan starts with a qualitative analysis; quantitative analyses are only performed when considered necessary, based on the qualitative analysis

The following four stages are identified regarding these basic assumptions. The first two stages in fact form the Geo Risk Scan; the latter two stages can be completed within a project, depending on the results of the first two stages. 1. 2. 3. 4.

Geo Quick Scan – qualitative process test; Geo Check – qualitative content and product test; Geo Risk Analysis – quantitative content analysis; Implementation – Geo Risk Management as a routine work process

3

EXECUTION OF A GEO RISK SCAN

3.1

Stage 1: Geo Quick Scan

3.1.1 Execution of a Geo Quick Scan In order to be able to perform this stage, first one has to gain insight in the project objectives and context. Therefore, an interview is planned with the project management team. It is important to have at least an interview with the technical project manager, who is normally responsible for the technical part of a project. For larger projects, it can be of good help to interview the risk manager (when present within the project), project leaders of specific elements of the project and the contract manager. The interview is based on a standardized questionnaire and deals mainly with the GeoQ approach. Examples of questions are: – Is the GeoQ approach recognizable in the scanned project? – Have all six steps been fully elaborated in each project phase? Is everything done in order to get good results from the risk management steps? – Have all six steps been explicitly elaborated in each project phase? It is important to know whether a step is performed explicitly, following a plan or just as some sort of unaware coincidence. In general, when a step is only performed implicitly, it is not guaranteed that in next project phases or in other projects the same risk driven project management is applied. This could cause negative consequences. Further insight is gained by asking for the products available from these steps and the knowledge and tools that have been used in the project to assist in the elaboration of the steps.

3.1.2 Results of Geo Quick Scan Elaboration of the interview and studying of the gathered information make it possible to evaluate the Geo Quick Scan. Scores are based on table 1 (made for each project phase) and the accompanying legend. Moreover, the application of the six main lessons learned (next chapter in this paper) is checked. Besides this score, recommendations are provided for improvement of the ground related risk management process.

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Table 1.

Scoring the Geo Quick Scan.

Step in GeoQ-approach

Degree of explicit execution

Degree of complete execution

1. Setting objectives and data collection 2. Risk identification 3. Risk classification and quantification 4. Risk remediation 5. Risk evaluation 6. Transfer of risk information

Figure 1. Structure of checklists. Table 2.

Risk table.

Risk after implementation of measures Unwanted recommended event Probability Consequence Risk in scan

1 point: step isn’t executed 2 points: implicitly, but not fully elaborated 3 points: explicitly, but not fully elaborated 4 points: implicitly, and fully elaborated 5 points: explicitly, and fully elaborated The total amount of points from table 1 gives the judgement and a ‘report mark’: – 28 excellent 9

3.2

Stage 2: Geo Check

3.2.1 Execution of a Geo Check The work in the Geo Check phase is focussing on the points of attention resulting from the Geo Quick Scan. The Geo Check deals particularly with the content or quality of the projects ground related risk management. Analyses and calculations from the project are checked qualitatively by making use of experienced geotechnical engineers. New calculations are not performed in this stage. The primary focus is checking the work already performed by the project organisation. For example, the following questions should be answered during the Geo Check: – Are correct starting points chosen in relation with boundary conditions of the project? – Are all relevant ground related risks identified? – Are calculations been performed for the relevant identified risks? – Are appropriate models and techniques applied? – Are results of the performed analyses according to expectations? 3.2.2 Checklists Despite the experience of geotechnical experts, it is of major importance to assure all foreseeable risks are indeed identified. Therefore, using standardized checklists is very useful. These checklist have been developed for building pits, roads and dikes for quickly gaining insight in the completeness of the identified ground related risks. These checklists proved to be of good assistance in all performed Geo Risk Scans.

All risks in the checklists are classified as geotechnical risks, geohydrological risks, geo-ecological risks, risks related to objects or obstacles in the ground, risks related to contract requirements or construction risks. All risks are described in terms of causes and consequences. The consequences are by definition unwanted events. By using this structure of the checklists, it is possible to use them on different scales. If the project is still in the feasibility phase, risk identification can be done only on the scale of unwanted events. When more detail is required, one can work from causes to sub causes and estimate the risks accordingly. 3.2.3 Results of Geo Check When a Geo Check is performed, the project organisation gaines insight in the following questions: – Are unacceptable ground related risks present in the project? – Have already risk remediation measures been identified for these risks? (based on expert judgement during the Geo Check) – Which unacceptable risks are still present? Answers on these questions are described as recommendations for improving the in-depth quality of ground related risk management. Besides these recommendations a risk table (table 2) is presented. Such risk tables proved to be a more practical way of displaying the project risks than conventional risk graphs (figure 2), without loosing insight. Finally, the Geo Check is evaluated by giving a ‘report mark’ on a scale of 1 to 10, based on expert judgement. 3.3 Results of Geo Risk Scan After execution of the Geo Quick Scan (process) and the Geo Check (content) a total overview of the degree of a projects ground related risk management is available. Rijkswaterstaat asked for a project portfolio of all scanned projects in order to be able to compare

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used, as well as geotechnical calculations. Examples are the use of an Electronic Board Room for brainstorm/expert sessions, contractual risk allocation by the Geotechnical Baseline Report, model experiments, field monitoring, and so on. This makes it possible to analyse and quantify any remaining unacceptable risks in order to select and execute proper measures. The project team itself can execute work during the Geo Risk Analysis stage. At the end of the Geo Risk Analysis stage, the optimal risk assessment strategy can be chosen. Possibilities are avoiding the risk, reducing risk probability and or consequence, and risk transfer to a third party.

Figure 2. Risk graph.

3.5 Stage 4: Implementation All information gathered and recommendations from the previous stages will not improve the projects work, unless it is implemented in the projects work. Therefore, the implementation can be seen as the most important stage! Implementation has to be done by the project team itself. This stage is beyond the scope of this paper and for instance elaborated in Van Staveren (2009). 4

LESSONS LEARNED

the results of the different project scans. Figure 3 shows the matrix which made this possible. Each scanned project can be placed in the matrix. Content is evaluated as of more importance than process. After all, when the results of a project are good, the project objectives will not be affected. Therefore, projects with bad scores for the Geo Quick Scan still can get a good or moderate overall score. Nevertheless, these projects should keep focus on improving the process of ground related risk management. Maybe, it was only a coincidence that the content part of ground related risk management of the project had good results!

The evaluation of the five scanned projects resulted in six main lessons which are further elaborated in 20 recommendations. All lessons are described in this chapter of the paper. The lessons are subdivided in two main types. The first set of lessons may help to improve the application of well-structured ground related risk management during projects. These lessons are interesting for owners who are responsible for the geotechnical conditions in their projects, as well as for contractors or engineers who have to manage ground conditions towards successful project results. These lessons are referred to as lessons dealing with content (C). The second set of lessons teaches how the coordination and delegation of managing geotechnical risk by owners can be improved. These lessons seem particularly relevant for owners who use innovative design and build type of contracts and are referred to as lessons dealing with process (P).

3.4

4.1 Lesson 1 – Clear risk management positioning

Figure 3. Quality matrix and project portfolio

Stage 3: Geo Risk Analysis

The aim of the Geo Risk Analysis stage is to improve projects ground related risk management, either with focus on process, or with focus on content by performing extensive and if necessary quantitative analyses. Executing the Geo Risk stage, a project in the bottom left corner of the quality matrix in figure 3 should move to the upper right corner of the matrix by executing the Geo Risk stage. Analyses are executed on unacceptable risks as identified in the Geo Check and recommendations of both Geo Quick Scan and Geo Check are elaborated. If necessary, advanced risk management tools can be

Lesson 1 concerns the positioning of ground related risk management within the project. 4.1.1 Ground related risk management should be an integral part of project risk management, but with explicit status (P) In all of the five scanned projects, ground related risks were an integral part of the total risk management. From a project management point of view, this seems a good strategy, because more aspects than only ground related risks are of importance for a project. From a geotechnical specialist point of view, this gives the

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opportunity to give ground related risks the proper attention. However, ground related risks need special attention, having specialists dealing with them and executing specific remediation measures. Most remarkable is that ground related risks have mainly consequences during the construction and maintenance of the project. Consequently, these risks are often not given the attention they need, or thought about as solvable, during the design phase. In each specific project it is recommended that in early stages geotechnical experts determine whether or not this may result in unacceptable risks later on in the project. Therefore, ground related risks need an explicit status in the total risk management. In two of the five scanned projects this approach was used with good results. 4.1.2 All specific ground related risks should be part of a project’s risk register (P&C) All ground-related risks should not only have an explicit status, they should also be part of the project risk register. Often, only imprecise ground-related risks are part of the project risk register. For example, phrases like “soil investigation is insufficient for making a good design”. Such fuzzy descriptions make explicit risk management difficult and probably even impossible. It is unclear which measures have to be taken and what the anticipated effects are. Therefore, it is recommended that the groundrelated risk register is part of the overall project risk register. 4.2

Lesson 2 – Clear risk management responsibility

Lesson 2 highlights the importance that any identified ground related risk needs one or more owners. Otherwise the risk will not get the required attention for adequate remediation. 4.2.1 Appoint a coordinator who is responsible for ground related risk management (P) Scanning the five projects showed the importance of somebody in the project acting as a coordinator of all ground related issues. The quality of the project largely improved by such a coordinator. It is not necessary that this person also is responsible for the ground related risks themselves. The technical manager of a big infrastructural project is usually too busy to give ground related risks the proper attention. The mentioned coordinator should assist the technical manager. 4.2.2 All ground related risk should be allocated contractually to one or more of the parties within a project (P) Because of the inherent ground related uncertainty it is very important to contractually arrange the responsibilities for unwanted events caused by differing soil conditions. At least, it is important to think about

the consequences, when ignoring risks caused by the uncertainty accompanying the soil. One could simply divide all risks to one or the other party, but often partial risk allocation is preferred. For instance the principles and practices of the geotechnical baseline report (GBR) are recommended (Essex, 2007). The main principle is to allocate any risk to the party involved that is best able to manage the risk. Sometimes sharing a risk is preferred, as both parties are (un)able the manage the risk by their own. 4.2.3

Ground related risks, completely allocated to the contractor, needs still evaluation by the client (C) In integrated contracts, many risks are transferred from the client to the contractor. However, the client still bears consequences when the risks occur. This is especially the case for immaterial consequences, like loss of reputation, safety or political risks. The project management team can use monitoring and other quality checks in order to keep control over these risks. These checks should not only be process checks, but should also include in depth analyses of content. 4.3

Lesson 3 – Clear risk communication

Lesson 3 stresses the importance of transparent risk communication between all parties involved in the project, as early in the project as feasible. 4.3.1

Link explicitly the functional and technical level of project organisation to each other (C&P) All five scanned projects used integrated contracts, where the contractor also had to do the design or even finance and maintenance. This implies that the project organisation has to pay much attention to the functional description of project specifications. By this way, all identified risks need to be transformed to the contractor. During scanning of the five projects two handicaps were shown: – (Geo)Technical experts have difficulties in translating their recommendations to this functional level. – On the other hand, project managers have difficulties in translating the technical requirements of the experts to functional requirements. Only one of the five projects excelled in this link between project management and ground related technical experts. This precious link was formed by one person who could ‘speak both languages’. This is recommended for every project. 4.3.2 The risk file of a client should be known by the contractor and vice versa (P) Every project organisation of the five scanned projects had a dilemma about sharing their risk file with the contractor. Many different concepts of sharing this information (or not) were encountered.

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One might think it is desirable to show the contractor all identified (ground-related) risks and vice versa. By doing so, project organisations however feel like attracting responsibility to themselves, because the information given to the contractor can contain misconceptions. Though, this last option is not esteemed to be correct. Risks are only transferred as points of attentions and can not be wrong. Another rationale is that with innovative design and build type of contracts, one might be pushing the contractor in some direction, when exchanging risk information. After all, the intention of an integrated project is to use the knowledge and experience of the contractor for the design and the client should not give implicit directions to a design. Balancing between these both ways, from point of view of a professional client, it is recommended to always exchange risk information between parties; at least after the tender phase. 4.3.3 Tests should be applied on feasibility of requirements with a geotechnical scope (C) Requirements with a direct relation to (geo) technical aspects can be stricter than the maximum accuracy of predictions in the design and construction phase. For example, settlement requirements for roads are often more stringent than can possible be designed and constructed within reason using ‘state-of-the-art’techniques and models. Negative consequences are over dimensioning or relatively big efforts for maintenance. It is therefore recommended to verify the feasibility of those types of requirements.

Figure 4. Need of early risk sessions.

the scanned projects. However, looking back at project activities it always seemed possible to divide them to the six risk management steps. One needs to keep in mind that real risk management is only possible when these steps are taken with an explicit plan. Risk management steps are performed with a cyclic approach. Consequently the steps are not always performed in succeeding order. For example gathering of extra information (executing extra soil investigation) is part of step 1, but can be done as a measure identified in step 4. Therefore, when risk management steps are not performed in succeeding order, there needs to be an induced explanation by the risk management process itself (see previous example).

– – – –

4.4.3 A ground related risk session should be organized in early project phases (P) In early stages of a project little investments are made and steering possibilities are still high. This underlines the importance of risk sessions in the early project phases. However, technical risk sessions are often ignored during the first project stages because project management conceives technical risks as solvable in later project stages. As a consequence of this assumption optimal technical solutions might be overlooked in the early stage of the project. This will require much more effort in later project stages. Therefore also technical risk sessions should be planned in the early stages. One of the scanned projects proved this to be true. From an early risk session one major construction risk was identified. Extra soil investigation was executed and the risk got special attention during the tender phase in which the contractor had to make a plan to show how this specific risk was managed.

4.4.2 All GeoQ steps should be explicitly executed step by step during each project phase (P) Following the six risk management steps will lead to good risk control of a project and hence a correct and complete risks register. This is generally accepted. Therefore, a crucial aspect in all Geo Risk Scans was the examination of the way these steps were followed in

4.4.4 Communication should be explicitly risk based between project and third parties (P) A project organisation can call in the help of third parties (e.g. for soil investigation, monitoring, technical advice, etc.).Third parties are often called in to manage (implicitly or explicitly) identified risks. It is important to communicate these risks as an instruction. This ensures that the right analyses are executed by third parties. The other way around it is also important for the project management to ask the third parties to report identified risks to them.This ensures a more completed

4.4

Lesson 4 – A ground related risk register

Lesson 4 underlines the importance of a correct, complete and up-to-date ground related risk register and gives recommendations for realization. 4.4.1 Description of a risk needs to satisfy basic demands (C&P) This is a general recommendation that is applicable on all types of risks; also ground related risks. It is important to describe a risk in the risk file with at least the following aspects: Cause (in words) of the risk Consequence (in words) of the risk Determination of probability of the risk Determination of amount of consequences of the risk (failure costs, quality loss, delays, loss of image & public confidence, etc.) – Possible remediation measures – Owner of the risk – Responsibility for the risk

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risk file of the project and no important information gets lost. 4.4.5 Explicit guarantee on completeness and correctness of ground related risks and analyses is necessary (P) Experts are of major importance in soil related risk management. Caused by the uncertainty of geotechnique, almost always different interpretations of the same risk can be expected. Guarantee on completeness and correctness of ground related risks therefore is important. One can think of big risk sessions with many experts, colleague checks, second opinions and use of checklists in order to guarantee this. 4.4.6 Checklists are recommended as a check on the completeness of risk files (C) Accompanying the previous point checklists have proven to be of good help in order to check the completeness of risk files. In paragraph 2.4.2 is shown how a good checklist can be implemented and used. 4.5

Lesson 5 – Risk driven site investigations

4.5.1

Site investigation should be explicitly risk based (C) From a good (ground related) implemented risk management process, in situ ground investigation and supporting laboratory research can be identified as a good measure. After all, Performing in situ soil and lab research will gain insight in specific risks. The risk management that let to the performing of the in situ soil and lab investigation should be extended in the plan for the investigation itself. Six basic steps can be used (Staveren, 2006) in order to be sure that the correct information is gathered. In short: 1. Determine ground related constructions; 2. Determine main mechanisms that affect the fit-forpurpose; 3. Determine the risks if the identified mechanisms act adversely; 4. Determine the design techniques for the identified measurements; 5. Determine the most critical ground parameters; 6. Determine the in situ soil and lab investigation considering the ground parameters and the geological heterogeneity. 4.5.2

In situ soil and lab research should be flexible executed (C) By using a flexible approach of site investigation it is possible to adjust to the obtained results during execution. On the one hand more detailed research can be executed if more heterogeneity is encountered as expected. On the other hand the research can be done more broad if there is no reason for more detail. 4.5.3

Quality control of site investigations is necessary (C) Lab and in situ soil research are used in calculations in order to make analyses. It is therefore of great

importance that the parameters derived from lab and in situ soil research are reliable. There can also be contractual consequences when soil investigation results were send to the contractor but are proven to be wrong. Question marks were stated in three out of the five scanned projects regarding the quality of the in situ soil and lab research. Especially with specialized experiments one should critically apply quality control. A geotechnical specialist should be able to perform these checks.

4.6

Lesson 6 – Risk driven field monitoring

4.6.1

Monitoring should be used as a tool for guarantee of quality and control of risks (C) Field monitoring is an excellent tool for controlling ground-related risks during the construction and operation phases of projects. Obviously, these programmes need to be defined according to the risk profile of the project. With integrated contracts, often monitoring is coordinated by the contractor. However, the client should always check the results of the applied monitoring for the key-risks of the project. Monitoring should not only be checked according to the process, but regular in-depth analyses of content should also be applied.

4.6.2

Ground related risks should have an explicit place in a monitoring plan (C) Monitoring can be broader than only measuring for controlling ground related risks. However, ground related risks should have an explicit place in a monitoring plan in order to make sure the measurements make sense for the ground related risks to be monitored.

5

CONCLUSIONS

Unexpected ground conditions appear a major source of cost and time overruns in infrastructure projects, which is confirmed by recent Dutch research. The presented Geo Risk Scan proved to be an effective tool for quickly providing information about the degree and the quality of ground-related risk management in infrastructure projects. Six main lessons and supporting recommendations are derived from using the Geo Risk Scan in five major Dutch projects. The main lessons are: 1. 2. 3. 4. 5. 6.

Clear risk management positioning Clear risk management responsibility Clear risk communication A ground related risk register Risk driven site investigations Risk driven field monitoring

These lessons seem to be generically applicable in construction projects. Ongoing application of these lessons in Dutch projects proves this conclusion.

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ACKNOWLEDGEMENTS The authors are grateful to all professionals who have been interviewed, or who otherwise contributed, during performing the Geo Risk Scans in the five infrastructure projects. REFERENCES Avendano Castillo, J.E., Al-Jibouri, S.H. and Halman, J.I.M., 2008, Conceptual model for failure costs management in construction, Proceedings of the Fifth International Con-

ference on Innovation in Architecture, Engineering and Construction (ACE), Antalya, Turkey, July 23–25. Essex, R.J. (ed.), 2007, Geotechnical Baseline Reports for Construction: Suggested Guidelines. Danvers: ASCE. RISMAN, www.risman.nl Staveren, M. Th. van, 2006, Uncertainty and Ground Conditions: A Risk Management Approach, Elsevier Ltd. Staveren, M.Th. van, 2009, Suggestions for implementing geotechnical risk management, Proceedings of the Second International Symposium on Geotechnical Safety and Risk, Gifu, Japan, June 11–12 (in press).

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Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Reduction of landslide risk in substituting road of Germi-Chay dam H. Farshbaf Aghajani M.Sc in Geotechnical Engineering, Ashenab Consulting Engineers Co., Tabriz, Iran

H. Soltani-Jigheh PhD of Geotechnical Engineering, Technical Faculty, Azerbaijan University of Tarbiyat Moallem, Tabriz, Iran

ABSTRACT: Germi-Chay dam is an earth-fill dam with central clay core that is underconstruction across the Germi-Chay River in Iran. Due to dam construction, part of the main road, that connects East Azerbaijan and Ardabil provinces together, remains within the dam reservoir. Therefore, it is necessary to construct a substituting road, 5 km long, outside of the reservoir. Part of the substituting road is located on the natural ground slope is susceptible to landslide. In this paper, first, the stability of the road slope is verified by performing a back analysis for the slip surfaces. Then, an appropriate scheme is suggested for construction of the road embankment in order to attain permanent stability of the slope. Evaluation of measured deformations show that the slope displacements have decreased considerably and slipping of the slope have stopped after executing the stabilization treatment. 1

2

INTRODUCTION

Landslide is one of the most important geohazards in geotechnical engineering that can be a threat for the stability of the structures. The potential of land sliding may increases when the slope is consisting of a weak texture and also subjected to groundwater rising by locating in vicinity of a waterway. Construction of infrastructures, such as the roads and buildings over the mentioned slopes may increases the geohazard risk, and even can lead to slide of the slope and consequently failure of the constructed structures. To avoid from the unfavorable incidents and to guarantee stability of structures, the landslide risk must be managed and reduced by using the efficient and practical methods as well as with considering of the costs. Some researchers have investigated the risk assessment and management of the landslides by statistical, analytical and geological methods (Lessing et al, 1983; Fell, 1994; Dai et al, 2002). Some of these methods are appropriate for risk assessment of land slide occurrence. However, a few numbers of methods have been presented for hazard risk reduction and treatment of the slipped slope that are performable in practice with low costs. In this research, a practical and efficient method is employed to reduce the landslide risk of a slipped slope, as a subgrade of a road, in Iran. The geological formations, landslide potential, and stability of the slope are first investigated. Then, an appropriate methodology is proposed for construction of the road embankment with considering the necessity of current land slide risk reduction. Also, for examining the efficiency of proposed method, slope deformations are monitored at regular intervals during and after embankment construction.

SUBSTITUTING ROAD OF GERMI-CHAY DAM

Germi-Chay dam is an earth-fill dam with central clay core that is being constructed over the Germi-Chay River, located about 220 km of north-east of Tabriz city in East Azerbaijan province of Iran. The heights of the dam from bed rock and river bed are 82 and 62 m, respectively. Also, length and width of the dam at the crest are respectively 730 and 10 meters. The maximum water level of reservoir is 1460 meters higher than sea level. The main purposes of the Germi-Chay dam are irrigation of farm lands and supplement of urban drinking water. Unfortunately, due to dam construction, a part of the main road, that connects East Azerbaijan and Ardabil provinces together, is located within the dam reservoir. For this reason, a substituting road is being constructed, with the length of 5 km, outside of the reservoir. A part of the substituting road at kilometer 2 + 065 is located in the natural ground slope that is a slipped area and susceptible to landslide. The geological investigation of the area shows that the slope is comprised of weak shale material located on the igneous bedrock. Furthermore, a waterway has been located in the vicinity of subgrade slope. So that during the rainy seasons, ground water rises within the slope and causes to occur slips and tension cracks in the subgrade slope. Field measurements indicate that the values of horizontal and vertical displacements during 9 months are 714 and 346 centimeters, respectively. A view of cracks and slips occurred in the subgrade slope are presented in Figures 1 and 2, respectively. With respect to the importance of substituting road from the view point of linking two provinces

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Figure 3. Geological map of studying area as well as land sliding mass with substituting road axis. Figure 1. Tention cracks near borehole BH 55 due to slipping.

Figure 2. A view of sliped in the subgrade slope as well as substituting road axis.

and its location on the slipped area, the stabilization of the subgrade slope and securing of road safety permanently is concerned in this research.

3

GEOLOGY OF LANDSLIDING AREA

To investigate the geological and geotechnical properties of the studied area, a number of six boreholes, denoted by BH-53, BH-54, BH-55, BH-56, BH-57, and BH-R1, are drilled in the subgrade slope. The results of the subsurface explorations and laboratory tests showed that the geological structure of the subgrade slope consist of the recent alluvium (TR), quarternerary traces (TA), crashed red rhyodacite (RhD), quartz diorite & quartz monzo-diorite (QD & QMD) and alternation of grey shale with yellow sandstone (Sh & S). Details of these formations have been illustrated in Figure 3 (Ashenab, 2005). The recent alluviums have located at the sides of waterway and comprised of silt and sand mixtures. The thickness of this formation is less than 3 meters. The quarternerary traces comprise mixtures of finegrained soils and some sand and gravel.

Sedimentary formations consist of shale and sandstone materials frequently have been repeated with depth within the slipped zone, and exposed at the kilometer 2 + 065 of the substituting road. At deep levels, amount of sandstone mass increases and sometimes the sedimentary layer is alone consisting of sandstone. Shale mass is in the forms of claystone and siltstone. In order to investigate properties of shale material, a number of experimental tests were carried out on the samples obtained from BH-54 and BH-55 boreholes. The results indicated that these materials have low shear strength with average liquid limit (LL) and plasticity index (PI) of 42 and 17, respectively. Also according to Unified Soil Classification System, the majority of samples are categorized as CL (ASTM 1997). Because of weak texture of sedimentary formations, precisely determination of layers strikes and their dips is difficult. However, site explorations show that the slip plane of slope does not coincide to the dip direction of sedimentary layers of shale materials. At the right hand of the waterway, geological formations have been made from the rhyodacite mass. Also, at the upper elevation of subgrade slope, rhyodacite mass with almost 50 meters depth is located over the shale layer. The rhyodacite formation has good quality and strong property which the fragments are used as concrete aggregates. Bedrock formations of quartz diorite & quartz monzo diorite materials have been embedded under the mentioned layers. The bedrock has relatively good quality and high strength with a few joints. According to the site explorations, the depth of bedrock at BH-53, BH-54 and BH-55 boreholes are 10, 14.8 and 3.5 m, respectively. The slope has slipped because of seasonal raining and weak condition of shale mass. Figure 3 illustrates the boundary and direction of slips. Also, a geological longitude profile of the slope along the slip direction (i.e. G-H cross section in Figure 3) is presented in Figure 4. As illustrated in this figure, the slipped area can be divided into two separate portions. The first portion, specified by S.S.1 area, includes the land slips in the upper elevations of the slope occurred due to the movement of rhyodacite mass on the shale layer. The values

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Table 1.

Figure 4. Geological profile of slope (G-H), locations of slip surfaces of 1 and 2 as well ground water level.

Material type

Friction Angle

Cohesion (kPa)

Density (kN/m3 )

Rhyodacite Shale Slip Surface 1∗ Slip Surface 2∗

30 23 15 15

10 100 20 15

22 20 19.5 19.5

*Obtained from the back-analysis

of displacements at benchmarks installed on the rhyodacite mass are about a few centimeters. This fact is due to existence shallow bedrock in front of rhyodacite mass, which withstand against the movements. The second portion of the slips is ground movement in the lower elevation of the slope through the shale material, i.e. S.S.2 area shown in Figures 3 and 4. Field observations indicated that the amount of movements progressively have increased during rainy seasons. Also, subsurface explorations determined the depth of sliding about 10 m. This relatively low depth is related to the non-conforming of shale lamination and slip direction as well as increasing of fraction of sandstone at lower depths. Although the strong sandstone has extended up to considerable depth, the amount of horizontal movements is much more, about 714 centimeters during a period of nine months.

4

Strength parameter of slope materials.

BACK ANALYSIS OF SLIP

Prior to stabilize the subgrade slope, it is necessary to known the mechanical parameters of materials located among the sliping surfaces. The most efficient method for determine these parameters is performing a backstability analysis for slipped slope (Sabatini, 2002). With respect to the progressive movement of the subgrade slope, it can be concluded that the shale material along the slip surface have reached to the residual condition. In this condition, the soil cohesion is negligible and the effective friction angle may be determined by performing a stability analysis assigning safety factor of 1.0 (USACE, 2003). The back-analysis was performed with the limit equilibrium method by using SLOPE/W software. Mohr-Coulomb criterion is utilized for modeling of material. Since the slip surface is known in the field, it must be defined carefully for back-analysis. Therefore, the slip surfaces (S.S.1 and S.S.2) with identified situation are considered as a narrow band made of weak material with unknown friction angle and differ from the other material of slope. It is necessary to note that the SLOPE\W software is unable to model the interfaces between different materials in order to define slip surfaces. Thus, by applying this approach, it is not necessary to reduce the parameters of whole slope. The Mohr-Coulomb parameters of other materials, such as cohesion and friction angle, are obtained from conducting triaxial and direct shear tests on the samples retrieved from boreholes. Density, cohesion and

friction angle of the slope materials are presented in Table 1. Subsurface explorations determined ground water level 2 m below the ground surface. Two dimensional geometry of the slope, materials of layers, locations of slip surfaces as well as ground water level are shown in Figure 4. The values of the friction angle and cohesion of slip surface materials obtained from the back-analysis are presented inTable 1. Comparison between the obtained results and recommended values in literature shows the accuracy of back analysis (Bowles, 1996).

5 A SCHEME FOR SUBGRADE SLOPE STABILIZATION Since the safety of substituting road was threatened by future probable sliding of subgrade mass totally due to large deformations expected in S.S.2 area, it is necessary to seek a remedial treatment for stabilizing of the subgrade slope with considering practical and economical feasibility. In last decades, many approaches and methodologies have been introduced for stabilizing and treatment of the slopes. These methods can be categorized in the following groups: slope geometry modification, control surface water and internal seepage control, provide retention, increase soil strength with injections and soil reinforcement (Hunt, 2007, Cheng & Lau, 2008). Selection of appropriate method is based on several factors such as practical feasibility, economy and available facilities. In Germi-Chay project, utilizing the slope geometry modification method required enormous excavation and thus high cost. Because of slipped and weak texture of shale mass, the efficiency of soil reinforcement also is unconfident. As mentioned in geological description, bedrock embedded under the slope at S.S.1 area has been located at shallow depth. Thus this feature is utilized to construct a retained system along with appropriate drainage capacity. Therefore, to stabilize the slope, it was proposed to excavate the foundation of road embankment up to the bedrock level. Then, the foundation trench was filled with rockfill material to reach to the identified level of road embankment and, finally, the road embankment was completed. It expected that the road embankment plays role as a barrier against slope sliding and

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Figure 5. Geometry of the slope after stabilization and road embankment.

Figure 7. Excavation and filling processes of the strips during construction.

6

Figure 6. Potentially slip surface after stabilization.

decreases the movement of the upper mass because of high strength and stiffness of rockfill material used in the embankment and its appropriate geometry. Figure 5 illustrates the stabilization scheme of subgrade slope after stabilization process as well as road embankment section. The proposed scheme for stabilization was modeled and analyzed using SLOPE/W software for evaluating safety of the slope and road as well as for determining supposed slip surfaces. Also, the factor of safety of S.S.1 surface was determined by stability analysis of the proposed geometry. As indicated in Figure 6, the results of the analysis show that in the presence of the road embankment, the safety factor of S.S.1 surface increases from nearly 1.0 (as a threshold condition in stability analysis) to 2.545. Moreover, the safety factor of the embankment constructed on the bedrock is about of 3.85. Since the embankment material is comprised of rockfill material with high drainage property, the phreatic line locates in a lower level and the safety factor becomes more than theoretical calculation. In addition, a culvert was performed within the road embankment to conduct the surface flows toward downstream; hereby the safety increases from this point of view. For economic evaluation of proposed stabilization method, the costs of this method was calculated and compared with those of the geometry modification method. The results indicated that in proposed method, the volumes of subgrade excavation and foundation filling are 21650 and 16100 cubic meters, respectively. However, for the second method required excavation is 256000 cubic meters as well as 94000 cubic meters of rockfilling for embankment construction to a level higher than the normal water level of reservoir. Thus, the excavation volume of second method is almost 12 times greater than proposed method.

METHODOLOGY OF THE EMBANKMENT CONSTRUCTION

In spite of the current movement of the slope and low strength parameters of shale material, it is expected that the subgrade slope excavation up to the bedrock may lead to instability and hazardous in the slope; particularly that the trench locates at the toe of slope. As a result, in this research, a comprehensive method was proposed to excavate the road trench down to the bedrock level without occurrence of any instability in the slope. In the suggested method, first, the material of embankment basin located in the outside part of the slipped region (S.S.1) was excavated to the bed rock and then immediately filled with the coarse grained material. For excavating road embankment foundation located on the slipped area, it is divided into a number of narrow strips (about 3 meters width) perpendiculars to the longitude axis of road. To avoid any instability within the slope during construction process, each strip was first excavated from downstream to the upstream of the slope and then filled with rockfill material until reaching to original ground level. Then, the adjacent strip was performed similarly. This operation was executed for all strips until the weak shale material of the road subgrade was substituted with the strong rockfill material. Since the least depth of the bedrock located at the east north of the embankment, the excavation and filling processes was commenced from this situation. After completing the excavation and filling of all the strips, the road embankment was constructed safely. Figure 7 shows the excavation and filling processes for one strip of road foundation. Also, the embankment of substituting road after completion is shown in Figure 8. 7

MONITORING OF SLOPE BEHAVIOR

To control the deformations of slope during construction, displacements was surveyed and evaluated

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embankment construction, the displacement of Z21 increases only about 4 centimeters (from May-2008 to Oct-2008). After embankment completion up to now, the movement of benhmark Z21 and subsequently the slips of slope are almost stopped. This consequence indicates the effectiveness of embankment in reduction of landslide risk and attainment of permanent stability of substituting road. 8 Figure 8. Embankment completion.

of

substituting

road

after

CONCLUSIONS

In this paper, to reduce the landslide risk and construction of a substituting road, a practical, most effective and economical method was proposed and constructed. Also, the enormous cost of slope modification was saved by applying the proposed method for risk management. To assure from stability of the slope, as a subgrade of the road, during and after the road construction, it was necessary to monitoring and evaluating the deformations of benchmarks installed on the rhyodacite mass and shale slope (upstream of road embankment). By evaluating the measured data, the slope behavior can be managed and studied continuously, and the critical deformations, led to the hazards, can be predicted. REFERENCES

Figure 9. Measured accumulated displacements at benchmarks located on the slope and construction level of earthfill.

regularly at the benchmarks. The investigations showed that the considerable reduction occurred in the deformations after construction of road embankment. For example, variations of displacements during and after construction at the benchmarks located near the BH-55 borehole and Z21 are presented in Figure 9. In this figure, the horizontal displacement of the benchmark located on BH-55 borehole is 721 cm before the road embankment construction (from Oct.2006 to July-2007). So the average rate of horizontal displacement is equal to 2.38 cm/day. Although during construction of embankment (from July-2007 to Oct.-2007), the displacement of this benchmark shows considerable reduction. Unfortunately, during construction operation, this benchmark is destroyed and inevitably another benchmark (i.e. Z21) was installed in the slip direction and slope behavior was investigated via monitoring displacements in this benchmark. The site surveying during road construction indicated that the accumulative value of displacements in the benchmark Z21 at the similar rainy season is 16 centimeters (from Oct-2007 to May-2008) and its average rate is about 0.7 mm/day. Comparing the displacements of the two benchmarks at similar time intervals indicates that the deformation of subgrade slope has decreased about 34 times. During

Ashenab 2005. Geology Report of Germi-Chay Dam, Ashenab Consults, Tabriz Iran ASTM 1997. Standard practice for classification of soils for engineering purposes (Unified Soil Classification System). ASTM D2487. West Conshohocken, Pa. American Society for Testing and Materials, Bowles, J. E. 1996. Foundation analysis and design”, Fifth Edition. New York, McGraw-Hill Cheng,Y.M. and Lau, C.K. 2008. Slope Stability analysis and stabilization: new methods and insight. New York. Rout ledge Taylor & Francis Group Dai, F.C., Lee, C.F. and Ngai, Y.Y. 2002. Landslide risk assessment and management: an overview, Engineering Geology, 64(1), 65–87 Hunt, R.E. 2007. Geological Hazards: a field guide for geotechnical engineers. New York. Taylor & Francis Group, Fell, R. 1994. Landslide risk assessment and acceptable risk, Canadian Geotechnical Journal, 31(2), 261–272. 1994 Lessing, P., Messina, C.P., and Fonner, R.F. 1983. Landslide risk assessment, Environmental Geology, 5(2), 93–99 Remondo, J., Bonachea, J. and Cendrero, A. 2005. A statistical approach to landslide risk modeling at basin scale: from landslide susceptibility to quantitative risk assessment, Landslide, 2(4), 321–328 Sabatini, P.J., Bachus, R.C., Mayne, P.W. Schneider, J.A. Zettler, T.E. 2002. GEOTECHNICAL ENGINEERING CIRCULAR NO. 5; Evaluation of Soil and Rock Properties, FHWA-IF-02-034, Washington, DC, USACE, 2003, SLOPE STABILITY, EM 1110-2-1902, 31 October 2003, USA

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Risk assessment

Geotechnical Risk and Safety – Honjo et al. (eds) © 2009 Taylor & Francis Group, London, ISBN 978-0-415-49874-6

Probabilistic risk estimation for geohazards: A simulation approach M. Uzielli Georisk Engineering S.r.l., Florence, Italy

S. Lacasse & F. Nadim International Centre for Geohazards, Norwegian Geotechnical Institute, Oslo, Norway

ABSTRACT: Risk estimation for geohazards is inherently characterized by considerable uncertainties in inputs and outputs. Uncertainty-based analysis provides a more robust and complete assessment of risk in comparison with deterministic analysis. A probabilistic framework for the quantitative, uncertainty-based estimation for geohazards is proposed. The framework relies on Monte Carlo simulation of risk through the preliminary definition of its macro-inputs: hazard, vulnerability and the value of elements at risk. The paper provides an operational description of the framework as well as conceptual discussions supporting and motivating each step of the procedure. A calculation example is provided. 1

INTRODUCTION

It is generally accepted that quantitative risk estimation for natural hazards is to be preferred over qualitative estimation whenever possible, as it allows for a more explicitly objective output and an improved basis for communication between the various categories involved in technical and political decision-making. The considerable heterogeneity in conceptual approaches to risk estimation is a well-known fact. No univocal definition is available at present, and the conceptual unification of risk analysis methods currently appears to be a practically unattainable goal. A consistent quantitative risk estimation analysis must rely on a reference risk framework. UNDRO (1979), for instance, proposed the following model, in which risk is calculated as the product of three macro-factors:

To avoid the undesirable consequences of misinterpretations of risk estimates and assessment due to the aforementioned terminological fragmentation, it is essential to provide reference definitions explicitly. In the ISSMGE Glossary of Risk Assessment Terms (e.g. http://www.engmath.dal.ca/tc32/), risk is defined as a “measure of the probability and severity of an adverse effect to life, health, property, or the environment”. Hazard is “the probability that a particular hazardous event occurs within a given period of time”; vulnerability is “the degree of expected loss in an element or system in relation to a specific hazard”. The “elements at risk” macro-component parameterizes the value of vulnerable physical or non-physical assets in a reference system. The measurement units of

elements at risk are not univocal, and depend at least on the reference time frame of hazard, the typology of elements at risk and on the investigator’s perspective. The value of physical assets, for instance, is usually measured and expressed in financial units, while the value of lives has been parameterized using financial and non-financial units (e.g. ‘equivalent fatalities’). Safety and cost-benefit optimization are primary, essential objectives of risk management. The quest for optimum decision-making, which ensures the safety and performance of a physical system while minimizing the cost of risk management and mitigation, can be associated to the concept of minimization of excess conservatism. Conservatism is in itself a positive concept, as it is finalized to the attainment of safety, and to the reduction of the likelihood and risk of undesirable performance of a physical system to a level which is deemed acceptable or tolerable. Excess conservatism, however, should be also avoided as it corresponds to a non-optimal use of resources to attain the aforementioned goals. While the above qualitative reasoning is trivial, the borders between under-conservatism, conservatism and excess conservatism are not easily assessed in risk management for natural hazards practice because of the relevance of uncertainties in the physical environment. Among the main factors contributing to uncertainty are: (a) the difficulty in parameterizing the destructiveness of geohazards; (b) the heterogeneity, spatial and temporal variability of the physical environment; (c) the complexity in the interaction between the hazardous event and the physical system; and (d) the indetermination in mitigation costs. Neglecting uncertainties can introduce unnecessary conservatism or, on the other extreme, lead to mitigation countermeasures which are inadequate in terms of safety and performance. Although mathematical disciplines such as statistical science can

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effectively contribute to quantifying, modeling and processing uncertainties, they are not routinely used in estimating risk for geohazards. With reference to the risk model in Eq. (1), while hazard is usually investigated in an uncertainty-based perspective, vulnerability and elements at risk are almost invariably estimated deterministically.The conventional quantification of risk also ignores the effects of uncertainties, and the term “risk” is often synonymous with the expected value of risk. A truly non-deterministic approach to risk estimation should acknowledge the existence of uncertainties in all risk macro-factors, and address such uncertainties explicitly. This paper illustrates a framework for uncertaintybased, quantitative risk estimation for geohazards by Monte Carlo simulation. Operationally, the emphasis is on practical applicability and robustness. As large uncertainties exist in the parameters and models used for risk estimation, it is not deemed advisable nor significant, in an operational perspective, to employ overly refined techniques for uncertainty modeling and uncertainty propagation analysis, as significantly more complex theoretical frameworks and restrictive conditions on parameters, hardly compatible with the type and quantity of data available in risk estimation practice, would be required. Nonetheless, the methods and criteria adopted in the proposed approach are theoretically sound and well suited for systems with large uncertainties. Uzielli (2008) extended the scope of the framework to include probabilistic decision-making criteria for risk mitigation. The term “Monte Carlo simulation” embraces a wide class of computational algorithms which are effectively capable of simulating complex physical and mathematical systems by repeated deterministic computation of user-defined models using random or pseudo-random values sampled from user-assigned distributions. Despite the vast and heterogeneous character of the algorithms, a common operational sequence consisting of the following steps can be identified: (1) probabilistic modelling of uncertainties in parameters and models; (2) repeated deterministic model simulation by computation on sampled model inputs; and (3) aggregation of results of the individual simulation instances into the analysis output. These steps are developed in the following sections. 2 2.1

UNCERTAINTY MODELLING FOR RISK ESTIMATION Uncertainty: definitions

The uncertainty in risk factors can be seen as the result of the complex aggregation of aleatory and epistemic uncertainties (see e.g. Phoon & Kulhawy 1999). Aleatory uncertainty stems from the temporal and/or spatial variability of relevant parametric attributes of both the hazardous event and vulnerable elements in the reference system. Epistemic uncertainties are a consequence of the practical impossibility

to measure precisely and accurately the physical and non-physical characteristics of the reference system and the hazardous event, and to model their interaction confidently. The absolute and relative magnitudes of the aleatory and epistemic components of total uncertainty are markedly case-specific. The aleatory and epistemic uncertainties addressed herein are conscious uncertainties, in the sense that the analyst is aware of their existence. Unknown uncertainty refers to the knowledge which is not currently attainable by the analyst. The reader is referred to Ayyub (2001) for an interesting discussion of uncertainty categorization. A number of mathematical techniques for modelling and processing uncertainties are available. Here, a probabilistic approach is chosen for a variety of reasons. First, probability theory (most often used in conjunction with statistical theory) provides a widely used, generally well understood and accepted framework for which a vast bulk of theoretical and applicative literature is available. Second, some of the basic concepts in risk analysis (e.g. the definition of hazard) are conceptually linked to probability. Third, enhanced computational capabilities allow extensive use of techniques such as Monte Carlo simulation, which are of greater applicability than other probabilistic techniques such as First-Order Second-Moment approximation, the latter requiring constraints on the degree of linearity of the reference models and on the magnitude of uncertainties in input variables. Fourth, due to the diffusion of probabilistic concepts in the technical disciplines, probabilistic approaches can be implemented with relative ease using general distribution software such as electronic spreadsheets. Fifth, uncertain parameters can be modelled probabilistically using both objective and subjective criteria, thereby allowing greater applicability to risk assessment analyses. The ‘dual nature’ of probability, which includes the objective ‘frequentist’ perspective and the subjective ‘degree of belief’ perspective, is of great practical significance in the context of QRE for geohazards as it is most often necessary to resolve to both objective and subjective modelling. Objective modelling can be performed if results of descriptive statistical analyses on samples of the random variates of interest are available, for instance in the form of frequency histograms. Once a suitable distribution type has been selected by the user, distribution parameters can be retrieved using appropriate inferential statistical techniques involving distribution fitting. A purely objective modelling is seldom feasible in the context of QRE for geohazards, where data are invariably limited in number and quality and the complexity of the interaction between a hazardous event and any reference system exceeds the analyst’s modelling and parameterization capabilities. Moreover, site-specific conditions may require substantial interpretation. A purely subjective modelling relies on the analyst’s experience, prior information, belief, necessity or, more frequently, a combination thereof. Subjective modelling should not be viewed as a surrogate of objective modelling (Vick 2002). In practice, probabilistic modelling is invariably hybrid

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(i.e. both subjective and objective) to some extent. Well-established frameworks such as Bayesian theory allow rigorous merging of subjective and objective probabilistic estimates. Whether the assignment is objective or subjective, it is important to recognise that reducing the magnitudes of the sources of uncertainty requires fundamentally different actions. Epistemic uncertainty can be reduced by increasing the amount and quality of data and refining models. Aleatory uncertainty, however, may remain unchanged or even increase with increases in the quality and quantity of data, because the real degree of scatter in values of relevant parameters may increase if more observations, better measurement tools and more refined models become available. To reduce aleatory uncertainty, it is necessary to increase the resolution of the analysis (e.g. by defining a greater number of more specific categories, or subdividing the reference system into geographical sub-units) as to decrease the intra-category heterogeneity of vulnerable elements. 2.2

Uncertainty-based modelling of risk factors

The character of the interaction between a hazardous event and a vulnerable element depends on the characteristics of both the event and the element. In the technical risk analysis literature, hazard, vulnerability and elements at risk are expressed formally in a variety of ways. Here, risk macro-components are modelled as functions of intensity. In qualitative terms, intensity parameterizes the damaging potential of the hazardous agent. The concept of intensity is not univocally established in a quantitative sense: the diversity and heterogeneity of hazardous events are such that it is difficult to attain a general quantitative definition. Even for any single typology of hazardous event, the literature reveals that different parameterizations of intensity have been identified as most suitable depending on the problem to be investigated. In earthquake risk analyses, for instance, commonly adopted intensity parameters include peak ground acceleration, peak ground velocity, peak ground displacement, spectral acceleration and magnitude. The situation is even more complex for landslides. A reference intensity parameter should be selected by the user with the aim to concisely describe the most relevant damaging characteristic of the event. It depends both on the type of event and vulnerable element, because different vulnerable elements may suffer prevalently from different attributes pertaining to the event. Here, the aforementioned intensity-dependence is formalized by identifying a reference intensity parameter IN for the hazardous event and by subsequently expressing hazard, vulnerability and elements at risk quantitatively as risk factor functions of IN . The framework proposed herein allows the selection of any scalaror vector-valued intensity parameter from which risk macro-factor functions can be defined univocally. Three risk factor functions are defined, namely: the hazard function fH (IN ); the vulnerability function

fV (IN ); and the elements at risk function fE (IN ). Each of these functions can be described analytically if a concise model is available or devised by the user; otherwise, functions can be defined empirically by points at relevant levels of nominal intensity. Risk factor functions are defined in a common domain of nominal intensity values. A nominal value is a representative deterministic value of a non-deterministic parameter. In the subsequent phase, uncertainty must be associated to nominal values. The total uncertainty in risk factors is, in operational terms, an aggregation of parameter and transformation uncertainty. Parameter uncertainty in risk factors is due essentially to the total uncertainty in the reference intensity parameter, which serves as input to the risk factor functions. Epistemic uncertainty in intensity results at least from limited measurement capability of dynamic characteristics (e.g. velocity, momentum, seismic magnitude) and geometric features (e.g. volume, displacement, area, depth) and the uncertainty in the model used to define the reference intensity parameter from available data. Aleatory uncertainty in intensity is due, among other things, to the complexity of the physical media which are mobilised in the course of a hazardous event and to the spatial and/or temporal non-stationarity of the dynamic and geometric characteristics of any hazardous event. As will be shown in Section 3.2, intensity is directly involved in the sampling process of risk factors because sampling distributions of risk factors must account for the uncertainty in intensity. Transformation uncertainty in risk factors stems from the risk functions’ limited capability of modeling and approximating the physical world. Parametrically, transformation uncertainty can include bias and scatter (or dispersion). Bias is related to a function’s precision; scatter is related to its accuracy.

2.3 Uncertainty modeling for simulation In a probabilistic simulation perspective such as the one adopted herein, uncertainty modelling requires the generation of sampling distributions for intensity I and for the risk macro-factors H , V and E. Here, two approaches are proposed for the generation of sampling distributions: the direct approach is applicable if the distribution parameters are known from objective analyses or can be assigned subjectively. Such approach relies on the implementation of the definitions of the selected probability distribution types. The indirect approach requires the preliminary generation of distribution parameters from secondmoment statistics such as standard deviation, variance or coefficient of variation. Experience has shown that a relatively limited set of distributions are able to fit satisfactorily a wide range of observed phenomena. Selected distribution types must be consistent with the definition and properties of the parameters which are being modelled. Different distribution types may be used for the same macrofactor at different intensity levels.

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Hazard has been defined herein as a probability of occurrence of a hazardous event. As probability values are by definition inferiorly and superiorly bounded at 0 (no likelihood of occurrence) and 1 (certainty of occurrence) respectively, any distribution used in modelling hazard must be bounded in the closed interval [0,1]. Vulnerability as defined in Section 1 is also defined in the closed interval [0,1]. Even at the greatest level of generality, it is intuitive that values of Elements at risk must be both non-negative and non-infinite. Hence, inferiorly and superiorly bounded distributions are assumed for all of the risk macro-components. Among commonly used probability distributions which satisfy the conditions of lower- and upperbounding are the uniform distribution and the PERT distribution. These are two special cases of the Beta distribution. The probability density function of the Beta distribution for a continuous random variable θ is given by

in which B(α1 ,α2 ) is the beta function with inputs α1 and α2 ; and

is the range of θ, given by the difference of the two extreme values (upper-bound value θ u and lowerbound value θ l ). The uniform distribution is a special case of the Beta distribution with α1 = α2 = 1. The probability density function of the uniform distribution can also be expressed in simplified form:

subjectively. When distribution parameters are not available and uncertainty is parameterized in terms of second-moment statistics, the indirect approach can be used to estimate lower- and upper-bound values. In descriptive statistical terminology, the coefficient of variation (COV) of a generic parameter ψ is defined as the ratio of the standard deviation of a dataset to its expected (i.e. mean) value:

As the COV provides an effective measure of relative dispersion of a dataset around its mean value, it can be conceptually associated with uncertainty, with higher values attesting for higher levels of uncertainty. It is thus possible to transpose a qualitative judgment on the level of uncertainty in a parameter (or model) quantitatively by associating to it a COV. For instance, a small COV (e.g. COV < 0.10) can be used to represent the belief in a low level of uncertainty. COVs in the range 0.10–0.30 can be regarded as “intermediate”, while higher values attest for high uncertainty. In the indirect approach, the derivation of lowerand upper-bound parameters can be achieved using statistical theory, by which relations between the standard deviation and the range of a random variable are available depending on the known or assumed distribution type. The standard deviation σ(θ), if it is not available directly, can be calculated by inverting Eq. (7) using the modal value as expected value (assuming that the distribution is quasi-symmetric with respect to the modal value). It is then used to calculate the upperand lower-bound values. This is achieved by calculating the range. If the distribution is uniform-type, the range is given by:

In case of PERT-type distributions:

The uniform distribution should be assumed whenever no objective information or subjective motivations are present regarding the existence of values inside the parameter domain which are more likely to occur than others. The PERT distribution is a particular case of a Pearson type-I Beta distribution which requires user specification of the modal value θ m of the distribution and the extremes only. The characteristic parameters of the PERT distribution α1 , α2 are calculated by:

Modal values can be taken as corresponding to nominal values when these are available, or can be assigned

Lower- and upper-bound values are then given, respectively, by subtracting and adding the semi-range to the modal value. It may be necessary to impose constraints on limiting values θ min and θ max :

The inherent boundary values θ min and θ max are parameter-specific: for hazard and vulnerability, for instance, θ min = 0 and θ max =1; for elements at risk, θ min = 0 and θ max