Constitutive Modeling of Soils and Rocks

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

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

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

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 model 284

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

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 Quasibrittle 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

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