Constitutive Modeling of Soils and Rocks

Pierre-Yves Hicher lectures at L'Ecole Centrale, Nantes, France. Jian-Fu Shao is a Professor at the University of Science and Technology, Lille, France.

• Preface to the English Edition xiPreface to the French xiiiChapter 1. The Main Classes of Constitutive Relations 1Félix DARVE1.1. Introduction 11.2. The rheological functional 31.3. Incremental formulation of constitutive relations 51.4. Rate-independent materials 61.4.1. Non-linearity of G and H 71.4.2. Anisotropy of G and H 71.4.3. Homogenity of degree 1 of G and H 81.5. Notion of tensorial zones 91.6. The main classes of rate-independent constitutive relations 111.6.1. Constitutive relations with one tensorial zone 111.6.2. Constitutive relations with two tensorial zones 121.6.3. Constitutive relations with four tensorial zones 191.6.4. Constitutive relations with n tensorial zones (n > 4) 231.6.5. Constitutive relations with an infinite number of tensorial zones 231.6.6. Conclusion 241.7. The main constitutive relations for rate-dependent materials 251.7.1. First class of incremental strain decomposition 251.7.2. Second class of incremental strain decomposition 261.8. General conclusions 271.9. References 28Chapter 2. Mechanisms of Soil Deformation 31Jean BIAREZ and Pierre-Yves HICHER2.1. Introduction 312.2. Remolded soil behavior 322.3. Relationships between discontinuous and continuous medium 442.3.1. Granular materials 472.3.2. Remolded clayey materials 482.3.3. Granular materials with intergranular glue 512.4. Natural soils 552.5. Conclusion 732.6. References 73Chapter 3. Elastoplastic Modeling of Soils: Monotonous Loadings 77Philippe MESTAT, Emmanuel BOURGEOIS and Philippe REIFFSTECK3.1. Introduction 773.2. Elastoplasticity equations 783.2.1. Basic concepts 783.2.2. Yield surface and elastic domain 793.2.3. Plastic flow rule 803.2.4. Incremental relations for one plastic mechanism model 813.2.5. Incremental relationships for multi-mechanism elastoplasticity 833.3. Constitutive laws and laboratory tests 843.4. Characterization of natural cohesive soil behavior 863.4.1. Analysis of triaxial test results 863.4.2. Analysis of oedometer tests 873.4.3. Elasto-viscoplasticity or elastoplasticity? 883.5. Characterization of frictional soil behavior 883.5.1. Analysis of triaxial test results 883.5.2. Elastoplasticity framework for frictional soils 913.6. Principles for the derivation of elastoplastic models 923.6.1. Elastic behavior 923.6.2. Estimation of the plastic behavior 963.6.3. Failure surface 973.6.4. Total and plastic strains 1023.6.5. Plastic potential 1033.6.6. Yield surface 1073.7. Three-dimensional aspect of the models and calculation of geotechnical works 1163.8. Examples of perfect elastoplastic models 1173.8.1. The Mohr-Coulomb model 1173.8.2. The Drücker-Prager model 1213.9. Examples of elastoplastic models with hardening 1243.9.1. University of Cambridge models (Cam-Clay models) 1243.9.2. Nova model (1982 version) 1293.9.3. Mélanie model 1313.10. Conclusions 1363.11. Notations 1383.12. References 138Chapter 4. Elastoplastic Modeling of Soils: Cyclic Loading 143Bernard CAMBOU and Pierre-Yves HICHER4.1. Soil behavior under drained loading 1434.1.1. Isotropic and oedometric cyclic loading 1434.1.2. Cyclic triaxial loading 1444.1.3. Influence of rotating principal axes 1484.2. Isochoric triaxial tests 1494.3. Modeling soil cyclic behavior 1544.3.1. Difficulties involved in the modeling of the soil cyclic behavior in the framework of elastoplasticity 1554.3.2. The Masing model 1574.4. Models based on one or several independent yield surfaces 1604.4.1. The CJS model 1614.5. Models based on nested yield surfaces 1664.5.1. Models with nested yield surfaces: the Mroz model 1674.5.2. Model with infinite yield surfaces: the Hujeux model 168Deviatoric mechanisms (k = 1, 2, 3) 169 4.5.3. Models with two yield surfaces: the Dafalias model 1764.5.4. Models with two yield surfaces: the Hashigushi model 1784.5.5. Models with two yield surfaces: CJS 4 model 1794.6. Generalized plasticity models 1814.7. Parameter identification for cyclic plasticity models 1824.8. Conclusion 1834.9. References 183Chapter 5. Elastoplastic Behavior of Ductile Porous Rocks 187Jian-Fu SHAO and Shou-Yi XIE5.1. Introduction 1875.2. Review of typical mechanical behavior of porous rocks 1885.3. Formulation of the constitutive model 1925.3.1. Plastic pore collapse model 1945.3.2. Plastic shearing model 1955.4. Examples of numerical simulations 1985.5. Influence of water saturation 2005.6. Creep deformation 2045.7. Conclusion 2065.8. References 207Chapter 6. Incremental Constitutive Relations for Soils 211René CHAMBON, Félix DARVE and Farid LAOUAFA6.1. Incremental nature of constitutive relations 2116.2. Hypoplastic CloE models 2136.2.1. Irreversibility in hypoplasticity 2146.2.2. Limit states 2166.2.3. A simple example: the 2D Mohr-Coulomb model 2196.2.4. Use in boundary value problems 2216.2.5. Explicit criterion of localization 2226.2.6. Induced anisotropy 2246.2.7. Extension to media with internal length 2256.2.8. Examples of application 2266.3. Incrementally non-linear constitutive relations 2296.3.1. Formalism 2296.3.2. Continuous transition between non-linear and octo-linear interpolations 2346.3.3. Significant degenerations 2386.3.4. Applications 2406.3.5. Conclusions 2556.4. General conclusion 2556.5. References 257Chapter 7. Viscoplastic Behavior of Soils 261Pierre-Yves HICHER and Isam SHAHROUR7.1. Introduction 2617.2. Laboratory testing 2627.2.1. Strain rate influence 2627.2.2. Creep tests 2657.3. Constitutive models 2777.3.1. Modeling framework 2777.3.2. Perzyna’s formulation 2787.4. Numerical integration of viscoplastic models 2807.5. Viscoplastic models for clays 2817.5.1. Choice of the viscoplastic mechanisms 2817.5.2. Viscoplastic models derived from the elastoplastic Cam-Clay model 2847.5.3. Cyclic viscoplastic modeling 2947.6. Conclusion 2957.7. References 296Chapter 8. Damage Modeling of Rock Materials 299André DRAGON8.1. Introduction 2998.2. Modeling of damage by mesocracks and induced anisotropy 3028.2.1. Preliminaries: damage variables and some micromechanical bases 3028.2.2. Anisotropic damage model (basic model - level (i)) 3068.2.3. Comments on the identification of the model’s parameters and on its prediction capability 3148.3. Taking into account mesocrack closure effects: restitution of moduli and complex hysteretic phenomena 3228.3.1. Normal unilateral effect 3228.3.2. Introduction of friction 3298.4. Numerical integration and application examples – concluding notes 3368.5. References 342Chapter 9. Multiscale Modeling of Anisotropic Unilateral Damage in Quasibrittle Geomaterials: Formulation and Numerical Applications 347Djimédo KONDO, Qizhi ZHU, Jian-Fu SHAO and Vincent PENSEE9.1. Introduction 3479.2. Homogenization of microcracked materials: basic principles and macroscopic energy 3499.3. Formulation of the multiscale anisotropic unilateral damage model 3549.3.1. Constitutive equations 3549.3.2. Friction-damage coupling and evolution laws 3589.4. Computational aspects and implementation of the multiscale damage model 3609.4.1. Determination of the tangent matrix 3609.4.2. Local integration of the model 3619.5. Illustration of the model predictions for shear tests 3639.6. Model’s validation for laboratory data including true triaxial tests 3649.6.1. Validation by comparison with conventional triaxial compression tests 3659.6.2. Simulations of true triaxial compression tests 3679.7. Application on an underground structure: evaluation of the excavation damage zone (EDZ) 3699.8. Conclusions 3739.9. References 374Chapter 10. Poromechanical Behavior of Saturated Cohesive Rocks 377Jian-Fu SHAO and Albert GIRAUD10.1. Introduction 37710.2. Fundamentals of linear poroelasticity 37810.3. Fundamentals of poroplasticity 38210.4. Damage modeling of saturated brittle materials 38510.4.1. Experimental characterization 38610.4.2. Numerical modeling 39410.5. Conclusion 40110.6. References 402Chapter 11. Parameter Identification 405Pierre-Yves HICHER and Jian-Fu SHAO11.1. Introduction 40511.2. Analytical methods 40711.3. Correlations applied to parameter identification 40711.4. Optimization methods 41311.4.1. Numerical formulation 41411.4.2. Examples of parameter identification by means of laboratory testing 41611.4.3. Parameter identification from in situ testing 41811.5. Conclusion 43011.6. References 430List of Authors 433Index 437