**Constitutive Modeling of Soils and Rocks by Pierre-Yves Hicher and Jian-Fu Shao**

## Contents of Constitutive Modeling of Soils and Rocks

**Chapter 1. The Main Classes of Constitutive Relations**- The rheological functional
- Incremental formulation of constitutive relations
- Rate-independent materials
- Non-linearity of G and H
- Anisotropy of G and H
- Homogenity of degree of G and H
- Notion of tensorial zones
- The main classes of rate-independent constitutive relations
- Constitutive relations with one tensorial zone
- Constitutive relations with two tensorial zones
- Constitutive relations with four tensorial zones
- Constitutive relations with n tensorial zones (n > )
- Constitutive relations with an infinite number of tensorial zones
- The main constitutive relations for rate-dependent materials
- First class of incremental strain decomposition
- Second class of incremental strain decomposition
**Chapter 2. Mechanisms of Soil Deformation**- Remolded soil behavior
- vi Constitutive Modeling of Soils and Rocks
- Relationships between discontinuous and continuous medium
- Granular materials
- Remolded clayey materials
- Granular materials with intergranular glue
- Natural soils
**Chapter 3. Elastoplastic Modeling of Soils: Monotonous Loadings**- Basic concepts
- Yield surface and elastic domain
- Plastic flow rule
- Incremental relations for one plastic mechanism model
- Incremental relationships for multi-mechanism elastoplasticity
- Constitutive laws and laboratory tests
- Characterization of natural cohesive soil behavior
- Analysis of triaxial test results
- Analysis of oedometer tests
- Elasto-viscoplasticity or elastoplasticity?
- Characterization of frictional soil behavior
- Analysis of triaxial test results
- Elastoplasticity framework for frictional soils
- Principles for the derivation of elastoplastic models
- Elastic behavior
- Estimation of the plastic behavior
- Failure surface
- Total and plastic strains
- Plastic potential
- Yield surface
- Three-dimensional aspect of the models and calculation of geotechnical works
- Examples of perfect elastoplastic models
- The Mohr-Coulomb model
- The Drücker-Prager model
- Examples of elastoplastic models with hardening
- University of Cambridge models (Cam-Clay models)
- Nova model ( version)
- Mélanie model
- Notations
**Chapter 4. Elastoplastic Modeling of Soils: Cyclic Loading**- Soil behavior under drained loading
- Isotropic and oedometric cyclic loading
- Cyclic triaxial loading
- Influence of rotating principal axes
- Isochoric triaxial tests
- Modeling soil cyclic behavior
- Difficulties involved in the modeling of the soil cyclic behavior in
- the framework of elastoplasticity
- The Masing model
- Models based on one or several independent yield surfaces
- The CJS model
- Models based on nested yield surfaces
- Models with nested yield surfaces: the Mroz model
- Model with infinite yield surfaces: the Hujeux model
- Deviatoric mechanisms (k = , , )
- Models with two yield surfaces: the Dafalias model
- Models with two yield surfaces: the Hashigushi model
- Models with two yield surfaces: CJS model
- Generalized plasticity models
- Parameter identification for cyclic plasticity models
**Chapter 5. Elastoplastic Behavior of Ductile Porous Rocks**- Review of typical mechanical behavior of porous rocks
- Formulation of the constitutive model
- Plastic pore collapse model
- Plastic shearing model
- Examples of numerical simulations
- Influence of water saturation
- Creep deformation
- Constitutive Modeling of Soils and Rocks
**Chapter 6. Incremental Constitutive Relations for Soils**- Incremental nature of constitutive relations
- Hypoplastic CloE models
- Irreversibility in hypoplasticity
- Limit states
- A simple example: the D Mohr-Coulomb model
- Use in boundary value problems
- Explicit criterion of localization
- Induced anisotropy
- Extension to media with internal length
- Examples of application
- Incrementally non-linear constitutive relations
- Formalism
- Continuous transition between non-linear and octo-linear
- interpolations
- Significant degenerations
- Applications
- Conclusions
- General conclusion
**Chapter 7. Viscoplastic Behavior of Soils**- Laboratory testing
- Strain rate influence
- Creep tests
- Constitutive models
- Modeling framework
- Perzyna’s formulation
- Numerical integration of viscoplastic models
- Viscoplastic models for clays
- Choice of the viscoplastic mechanisms
- Viscoplastic models derived from the elastoplastic Cam-Clay model
- Cyclic viscoplastic modeling
**Chapter 8. Damage Modeling of Rock Materials**- Modeling of damage by mesocracks and induced anisotropy
- Preliminaries: damage variables and some micromechanical bases
- Anisotropic damage model (basic model – level (i))
- Comments on the identification of the model’s parameters and on its prediction capability
- Taking into account mesocrack closure effects: restitution of moduli and
- complex hysteretic phenomena
- Normal unilateral effect
- Introduction of friction
- Numerical integration and application examples – concluding notes
**Chapter 9. Multiscale Modeling of Anisotropic Unilateral Damage in Quasibrittle Geomaterials: Formulation and Numerical Applications**- Homogenization of microcracked materials: basic principles and
- macroscopic energy
- Formulation of the multiscale anisotropic unilateral damage model
- Constitutive equations
- Friction-damage coupling and evolution laws
- Computational aspects and implementation of the multiscale damage
- model
- Determination of the tangent matrix
- Local integration of the model
- Illustration of the model predictions for shear tests
- Model’s validation for laboratory data including true triaxial tests
- Validation by comparison with conventional triaxial compression
- tests
- Simulations of true triaxial compression tests
- Application on an underground structure: evaluation of the excavation
- damage zone (EDZ)
**Chapter 10. Poromechanical Behavior of Saturated Cohesive Rocks**- Fundamentals of linear poroelasticity
- Fundamentals of poroplasticity
- Damage modeling of saturated brittle materials
- Experimental characterization
- Constitutive Modeling of Soils and Rocks
- Numerical modeling
**Chapter 11. Parameter Identification**- Analytical methods
- Correlations applied to parameter identification
- Optimization methods
- Numerical formulation
- Examples of parameter identification by means of laboratory
- testing
- Parameter identification from in situ testing