Constitutive Modeling of Soils and Rocks

447 Pages·2008·7.764 MB·English

by  Pierre-Yves Hicher, Jian-Fu Shao

Constitutive Modeling of Soils and Rocks
Constitutive Modeling
of Soils and Rocks

Edited by

Pierre-Yves Hicher
Jian-Fu Shao
First published in France in 2002 by Hermes Science/Lavoisier entitled “Modèles de comportement des
sols et des roches Vol.1 et 2”
First published in Great Britain and the United States in 2008 by ISTE Ltd and John Wiley & Sons, Inc.

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The rights of Pierre-Yves Hicher and Jian-Fu Shao to be identified as the authors of this work have been
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Library of Congress Cataloging-in-Publication Data

[Modeles de comportement des sols et des roches. English] Constitutive modeling of soils and rocks /
Edited by Pierre-Yves Hicher Jian-Fu Shao.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-84821-020-2
1. Engineering geology--Mathematical models. 2. Soil mechanics--Mathematical models. I. Hicher,
Pierre-Yves. II. Shao, Jian-Fu. III. Title.
TA705.M6113 2008
624.1'51015118--dc22
2007046228

British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN: 978-1-84821-020-2
Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire.
Table of Contents
Preface to the English Edition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Preface to the French. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Chapter 1. The Main Classes of Constitutive Relations . . . . . . . . . . . . . . . . . 1
Félix DARVE
1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. The rheological functional. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3. Incremental formulation of constitutive relations. . . . . . . . . . . . . . . . . . . 5
1.4. Rate-independent materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.1. Non-linearity of G and H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.2. Anisotropy of G and H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.3. Homogenity of degree 1 of G and H . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5. Notion of tensorial zones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.6. The main classes of rate-independent constitutive relations . . . . . . . . . . 11
1.6.1. Constitutive relations with one tensorial zone. . . . . . . . . . . . . . . . . 11
1.6.2. Constitutive relations with two tensorial zones. . . . . . . . . . . . . . . . 12
1.6.3. Constitutive relations with four tensorial zones. . . . . . . . . . . . . . . . 19
1.6.4. Constitutive relations with n tensorial zones (n > 4) . . . . . . . . . . . . 23
1.6.5. Constitutive relations with an infinite number of tensorial zones . . . 23
1.6.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.7. The main constitutive relations for rate-dependent materials. . . . . . . . . . 25
1.7.1. First class of incremental strain decomposition. . . . . . . . . . . . . . . . 25
1.7.2. Second class of incremental strain decomposition. . . . . . . . . . . . . . 26
1.8. General conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.9. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Chapter 2. Mechanisms of Soil Deformation . . . . . . . . . . . . . . . . . . . . . . . . 31
Jean BIAREZ and Pierre-Yves HICHER
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2. Remolded soil behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
vi Constitutive Modeling of Soils and Rocks
2.3. Relationships between discontinuous and continuous medium . . . . . . . . 44
2.3.1. Granular materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.3.2. Remolded clayey materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3.3. Granular materials with intergranular glue. . . . . . . . . . . . . . . . . . . 51
2.4. Natural soils. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.6. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Chapter 3. Elastoplastic Modeling of Soils: Monotonous Loadings. . . . . . . . 77
Philippe MESTAT, Emmanuel BOURGEOIS and Philippe REIFFSTECK
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.2. Elastoplasticity equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2.1. Basic concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2.2. Yield surface and elastic domain. . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.2.3. Plastic flow rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.2.4. Incremental relations for one plastic mechanism model. . . . . . . . . . 81
3.2.5. Incremental relationships for multi-mechanism elastoplasticity . . . . 83
3.3. Constitutive laws and laboratory tests. . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.4. Characterization of natural cohesive soil behavior. . . . . . . . . . . . . . . . . 86
3.4.1. Analysis of triaxial test results . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.4.2. Analysis of oedometer tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.4.3. Elasto-viscoplasticity or elastoplasticity?. . . . . . . . . . . . . . . . . . . . 88
3.5. Characterization of frictional soil behavior . . . . . . . . . . . . . . . . . . . . . . 88
3.5.1. Analysis of triaxial test results . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.5.2. Elastoplasticity framework for frictional soils. . . . . . . . . . . . . . . . . 91
3.6. Principles for the derivation of elastoplastic models. . . . . . . . . . . . . . . . 92
3.6.1. Elastic behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.6.2. Estimation of the plastic behavior . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.6.3. Failure surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.6.4. Total and plastic strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.6.5. Plastic potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.6.6. Yield surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.7. Three-dimensional aspect of the models and calculation of geotechnical
works. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
3.8. Examples of perfect elastoplastic models . . . . . . . . . . . . . . . . . . . . . . 117
3.8.1. The Mohr-Coulomb model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.8.2. The Drücker-Prager model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.9. Examples of elastoplastic models with hardening . . . . . . . . . . . . . . . . 124
3.9.1. University of Cambridge models (Cam-Clay models). . . . . . . . . . 124
3.9.2. Nova model (1982 version). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.9.3. Mélanie model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
3.10. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Table of Contents vii
3.11. Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
3.12. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Chapter 4. Elastoplastic Modeling of Soils: Cyclic Loading . . . . . . . . . . . . 143
Bernard CAMBOU and Pierre-Yves HICHER
4.1. Soil behavior under drained loading. . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.1.1. Isotropic and oedometric cyclic loading. . . . . . . . . . . . . . . . . . . . 143
4.1.2. Cyclic triaxial loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.1.3. Influence of rotating principal axes . . . . . . . . . . . . . . . . . . . . . . . 148
4.2. Isochoric triaxial tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
4.3. Modeling soil cyclic behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
4.3.1. Difficulties involved in the modeling of the soil cyclic behavior in
the framework of elastoplasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.3.2. The Masing model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.4. Models based on one or several independent yield surfaces . . . . . . . . . 160
4.4.1. The CJS model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
4.5. Models based on nested yield surfaces . . . . . . . . . . . . . . . . . . . . . . . . 166
4.5.1. Models with nested yield surfaces: the Mroz model . . . . . . . . . . . 167
4.5.2. Model with infinite yield surfaces: the Hujeux model. . . . . . . . . . 168
Deviatoric mechanisms (k = 1, 2, 3). . . . . . . . . . . . . . . . . . . . . . . . . . . 169
4.5.3. Models with two yield surfaces: the Dafalias model . . . . . . . . . . . 176
4.5.4. Models with two yield surfaces: the Hashigushi model. . . . . . . . . 178
4.5.5. Models with two yield surfaces: CJS 4 model. . . . . . . . . . . . . . . . 179
4.6. Generalized plasticity models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
4.7. Parameter identification for cyclic plasticity models . . . . . . . . . . . . . . 182
4.8. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
4.9. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Chapter 5. Elastoplastic Behavior of Ductile Porous Rocks . . . . . . . . . . . . 187
Jian-Fu SHAO and Shou-Yi XIE
5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
5.2. Review of typical mechanical behavior of porous rocks. . . . . . . . . . . . 188
5.3. Formulation of the constitutive model. . . . . . . . . . . . . . . . . . . . . . . . . 192
5.3.1. Plastic pore collapse model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
5.3.2. Plastic shearing model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
5.4. Examples of numerical simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 198
5.5. Influence of water saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
5.6. Creep deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
5.7. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
5.8. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
viii Constitutive Modeling of Soils and Rocks
Chapter 6. Incremental Constitutive Relations for Soils. . . . . . . . . . . . . . . 211
René CHAMBON, Félix DARVE and Farid LAOUAFA
6.1. Incremental nature of constitutive relations. . . . . . . . . . . . . . . . . . . . . 211
6.2. Hypoplastic CloE models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
6.2.1. Irreversibility in hypoplasticity. . . . . . . . . . . . . . . . . . . . . . . . . . 214
6.2.2. Limit states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
6.2.3. A simple example: the 2D Mohr-Coulomb model. . . . . . . . . . . . . 219
6.2.4. Use in boundary value problems. . . . . . . . . . . . . . . . . . . . . . . . . 221
6.2.5. Explicit criterion of localization . . . . . . . . . . . . . . . . . . . . . . . . . 222
6.2.6. Induced anisotropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
6.2.7. Extension to media with internal length. . . . . . . . . . . . . . . . . . . . 225
6.2.8. Examples of application. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
6.3. Incrementally non-linear constitutive relations . . . . . . . . . . . . . . . . . . 229
6.3.1. Formalism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
6.3.2. Continuous transition between non-linear and octo-linear
interpolations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
6.3.3. Significant degenerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
6.3.4. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
6.3.5. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
6.4. General conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
6.5. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
Chapter 7. Viscoplastic Behavior of Soils. . . . . . . . . . . . . . . . . . . . . . . . . . 261
Pierre-Yves HICHER and Isam SHAHROUR
7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
7.2. Laboratory testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
7.2.1. Strain rate influence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
7.2.2. Creep tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
7.3. Constitutive models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
7.3.1. Modeling framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
7.3.2. Perzyna’s formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
7.4. Numerical integration of viscoplastic models . . . . . . . . . . . . . . . . . . . 280
7.5. Viscoplastic models for clays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
7.5.1. Choice of the viscoplastic mechanisms . . . . . . . . . . . . . . . . . . . . 281
7.5.2. Viscoplastic models derived from the elastoplastic Cam-Clay model284
7.5.3. Cyclic viscoplastic modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
7.6. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
7.7. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Chapter 8. Damage Modeling of Rock Materials . . . . . . . . . . . . . . . . . . . . 299
André DRAGON
8.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
Table of Contents ix
8.2. Modeling of damage by mesocracks and induced anisotropy . . . . . . . . 302
8.2.1. Preliminaries: damage variables and some micromechanical bases. 302
8.2.2. Anisotropic damage model (basic model - level (i)) . . . . . . . . . . . 306
8.2.3. Comments on the identification of the model’s parameters and on
its prediction capability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
8.3. Taking into account mesocrack closure effects: restitution of moduli and
complex hysteretic phenomena. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
8.3.1. Normal unilateral effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
8.3.2. Introduction of friction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
8.4. Numerical integration and application examples – concluding notes . . . 336
8.5. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
Chapter 9. Multiscale Modeling of Anisotropic Unilateral Damage in Quasi-
brittle Geomaterials: Formulation and Numerical Applications. . . . . . . . . 347
Djimédo KONDO, Qizhi ZHU, Jian-Fu SHAO and Vincent PENSEE
9.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
9.2. Homogenization of microcracked materials: basic principles and
macroscopic energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
9.3. Formulation of the multiscale anisotropic unilateral damage model. . . . 354
9.3.1. Constitutive equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
9.3.2. Friction-damage coupling and evolution laws. . . . . . . . . . . . . . . . 358
9.4. Computational aspects and implementation of the multiscale damage
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
9.4.1. Determination of the tangent matrix . . . . . . . . . . . . . . . . . . . . . . 360
9.4.2. Local integration of the model . . . . . . . . . . . . . . . . . . . . . . . . . . 361
9.5. Illustration of the model predictions for shear tests . . . . . . . . . . . . . . . 363
9.6. Model’s validation for laboratory data including true triaxial tests. . . . . 364
9.6.1. Validation by comparison with conventional triaxial compression
tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
9.6.2. Simulations of true triaxial compression tests. . . . . . . . . . . . . . . . 367
9.7. Application on an underground structure: evaluation of the excavation
damage zone (EDZ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
9.8. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
9.9. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
Chapter 10. Poromechanical Behavior of Saturated Cohesive Rocks . . . . . 377
Jian-Fu SHAO and Albert GIRAUD
10.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
10.2. Fundamentals of linear poroelasticity . . . . . . . . . . . . . . . . . . . . . . . . 378
10.3. Fundamentals of poroplasticity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
10.4. Damage modeling of saturated brittle materials. . . . . . . . . . . . . . . . . 385
10.4.1. Experimental characterization. . . . . . . . . . . . . . . . . . . . . . . . . . 386
x Constitutive Modeling of Soils and Rocks
10.4.2. Numerical modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
10.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
10.6. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
Chapter 11. Parameter Identification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
Pierre-Yves HICHER and Jian-Fu SHAO
11.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
11.2. Analytical methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
11.3. Correlations applied to parameter identification. . . . . . . . . . . . . . . . . 407
11.4. Optimization methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
11.4.1. Numerical formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
11.4.2. Examples of parameter identification by means of laboratory
testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416
11.4.3. Parameter identification from in situ testing. . . . . . . . . . . . . . . . 418
11.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
11.6. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
Preface to the English Edition
The French version of this book appeared in 2002 as part of the “Material
Mechanics and Engineering” series. The objective of this book was to create as
complete as possible a corpus of knowledge and methods in this field.
In designing this book on the mechanical behavior of soils and rocks, we
gathered together a number of internationally known specialists, who each brought a
significant contribution to the knowledge of the experimental behavior of these
materials, as well as their constitutive modeling. Our goal was to cover as far as
possible the theories at the basis of the different approaches of modeling, and also to
address the most recent advances in the field.
In translating this book into English, we hope to make available to a wider
scientific and engineering public the approaches and school of thought which have
dominated the field of geomaterial mechanics in France over the past few decades.
We have put together present-day knowledge of mechanical behavior and their
theoretical bases in order to construct an original, analytical framework which, we
hope, will give readers a useful guide for their own research. Most of the chapters
have been updated in order to include the most recent findings on the respective
topics.
Finally, we wish to dedicate this book to the memory of Professor Jean Biarez,
who not only played a ground-breaking role in the history of soil mechanics in
France, but remains a source of inspiration to many of us today.
Pierre-Yves Hicher
Jian-Fu Shao