Оглавление
Jean Sulem. Instabilities Modeling in Geomechanics
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Instabilities Modeling in Geomechanics
Introduction
1. Multiphysics Role in Instabilities in Geomaterials: a Review
1.1. Introduction
1.2. General remarks
1.3. Solid phase material criteria
1.4. Material sample stability: experimental
1.5. Boundary value problems: uniqueness and stability at the field scale. 1.5.1. Landslides
1.5.2. Thermal pressurization problem
1.5.3. Localization during drying of geomaterials
1.6. Conclusion
1.7. References
2. Fundamentals of Bifurcation Theory and Stability Analysis
2.1. Introduction
2.2. Bifurcation and stability of dynamical systems
2.2.1. Definition of stability
2.2.2. Linear systems of ODEs
2.2.3. Nonlinear systems of ODEs
2.2.4. An example of LSA
2.3. Stability of two-dimensional linear dynamical systems
2.3.1. Classification of fixed points
2.3.2. Love mechanics: Romeo and Juliet
2.4. Common types of bifurcations
2.4.1. Saddle-node bifurcation
2.4.2. Transcritical bifurcation
2.4.3. Supercritical and subcritical pitchfork bifurcation
2.4.4. From one to two dimensions – limit cycles
2.4.5. Bifurcations in two dimensions – supercritical and subcritical Hopf bifurcation
2.4.6. Mathematical bifurcations in PDEs
2.5. From ODEs to PDEs
2.5.1. Deformation bands and the acoustic tensor
2.5.2. Deformation bands as an instability problem
2.6. Summary
2.7. Appendix
2.8. References
3. Material Instability and Strain Localization Analysis
3.1. Introduction
3.2. Shear band model
3.2.1. Strain localization criterion
3.2.2. Strain localization, loss of ellipticity and vanishing speed of acceleration waves
3.3. Shear band formation in element tests on rock. 3.3.1. Drucker–Prager model
3.3.2. Non-coaxial plasticity
3.3.3. Cataclastic shear banding
3.3.4. Postlocalization behavior
3.4. Strain localization in fluid-saturated porous media. 3.4.1. Strain localization criterion in fluid-saturated porous media
3.4.2. Stability analysis of undrained shear on a saturated layer
3.5. Conclusion
3.6. References
4. Experimental Investigation of the Emergence of Strain Localization in Geomaterials
4.1. Introduction
4.2. Methods
4.2.1. Digital image correlation
4.2.2. X-ray computed tomography
4.2.3. Experimental devices for in situ full-field measurements. 4.2.3.1. A plane strain apparatus for soils
4.2.3.2. A true triaxial cell for rocks
4.2.3.3. An X-ray transparent triaxial cell
4.3. Selected materials. 4.3.1. Hostun sand
4.3.2. Caicos ooids sand
4.3.3. Vosges sandstone
4.3.4. Callovo–Oxfordian clayey rock
4.4. Strain localization in sands
4.4.1. Plane strain compression by FRS
4.4.2. Triaxial compression by X-ray CT and DIC
4.4.3. Triaxial compression by X-ray CT, the critical void ratio
4.5. Strain localization in porous rocks
4.5.1. Strain localization in Vosges sandstone
4.5.2. Strain localization in a clayey rock
4.6. Conclusion
4.7. References
5. Numerical Modeling of Strain Localization
5.1. Introduction
5.2. Cosserat continuum. 5.2.1. Governing equations
5.2.2. Finite element formulation of Cosserat model
5.2.3. Material parameters
5.2.4. Failure in thick-walled cylinder test
5.2.5. Stability analysis of elliptical shape perforations
5.3. Gradient elastoplasticity. 5.3.1. Governing equations
5.3.2. Finite element formulation
5.3.3. Material model
5.3.4. Modeling of the biaxial test
5.3.5. Modeling cavity expansion
5.4. Conclusion
5.5. Acknowledgments
5.6. References
6. Numerical Modeling of Bifurcation: Applications to Borehole Stability, Multilayer Buckling and Rock Bursting
6.1. Introduction
6.2. Borehole stability
6.2.1. Primary loading path
6.2.2. Hole failure
6.2.3. Simulation of hollow cylinder experiments
6.3. Folding of elastic media as a bifurcation problem
6.3.1. Buckling of a layer under initial stress
6.3.2. Eigen-displacements and tractions at layer boundaries
6.3.3. Buckling of a layer system – the transfer matrix technique
6.3.4. Buckling of layered half-space
6.4. Axial splitting and spalling
6.4.1. Buckling of a half-space with surface parallel cracks
6.5. Conclusion
6.6. Acknowledgments
6.7. References
7. Numerical Modeling of Multiphysics Couplings and Strain Localization
7.1. Introduction
7.2. Experimental evidences of strain localization
7.3. Regularization methods
7.3.1. Enrichment of the constitutive law
7.3.2. Enrichment of the kinematics
7.4. Coupled local second gradient model for microstructure saturated media
7.4.1. Balance equations for microstructure poromechanics. 7.4.1.1. Local second gradient model for a monophasic medium
7.4.1.2. Second gradient constitutive equation
7.4.1.3. Coupled local second gradient model
7.4.2. Coupled finite element formulation. 7.4.2.1. Numerical implementation
7.4.2.2. Linearization of the field equations
7.4.2.3. Spatial discretization
7.4.2.4. Global solution
7.4.3. Two-dimensional specimen under compression
7.4.3.1. Classical medium
7.4.3.2. Microstructure enhanced medium
7.4.3.3. Non-uniqueness of the solution
7.4.3.4. Bifurcation criterion for the second gradient model
7.5. Coupled local second gradient model for an unsaturated medium
7.5.1. Partial saturation conditions
7.5.2. Anisotropy of the intrinsic permeability
7.5.3. Compressibility of the solid grains
7.6. Modeling of a gallery excavation
7.6.1. Numerical model
7.6.2. Influence of stress and permeability anisotropies
7.6.3. Influence of second gradient boundary condition
7.6.4. Influence of Biot’s coefficient
7.6.5. Influence of gallery ventilation
7.7. Conclusion
7.8. References
8. Multiphysics Couplings and Strain Localization in Geomaterials
8.1. Introduction
8.2. Thermo-chemo-chemical couplings and stability of shear zones. 8.2.1. Problem statement
8.2.2. Stability of adiabatic undrained shear
8.2.3. Chemical weakening and earthquake nucleation
8.3. Dissolution weakening and compaction banding. 8.3.1. Multiscale modeling of strong chemo-poro-mechanical coupling
8.3.2. Compaction banding in oedometric compression
8.4. Conclusion
8.5. References
9. On the Thermo-poro-mechanics of Chemically Active Faults
9.1. Introduction
9.2. Time-independent formation of shear zones from solid mechanics
9.2.1. Shear zone thickness at boundary temperature conditions
9.2.2. Shear zone thickness at elevated temperature
9.3. Time-dependent evolution of shear zones
9.3.1. Energy considerations
9.3.2. The Taylor–Quinney coefficient
9.3.3. Chemical reactions
9.4. Postfailure evolution of a shear zone
9.4.1. Analysis of the system’s response
9.4.2. Time scales of the system
9.5. Comparison to field observations
9.6. Application to ETS sequences
9.6.1. Regular sequences – Cascadia ETS sequence
9.7. Discussion
9.8. Appendix: poro-chemical model
9.9. References
10. Analysis of Instabilities in Faults
10.1. Introduction
10.2. Description of the model
10.2.1. Cosserat continuum theory
10.2.2. Constitutive equations for a Cosserat continuum
10.2.3. Mass balance equation
10.2.4. Energy balance equation
10.3. Bifurcation analysis. 10.3.1. LSA for a Cosserat continuum with THM couplings
10.3.2. Localization conditions for a fault zone
10.3.3. Shear band thickness evolution in a fault zone
10.4. Numerical analysis
10.4.1. Regularization of the mesh dependency
10.4.2. Response and shear band thickness of a fault gouge
10.5. Conclusion
10.6. Bibliography
List of Authors
Index. A, B
C
D
E
F, G
H, I
L
M
N, O, P
S
T, U
W, X
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