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Record Nr. |
UNINA9910555254003321 |
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Titolo |
Instabilities modeling in geomechanics / / coordinated by Ioannis Stefanou, Jean Sulem |
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Pubbl/distr/stampa |
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London : , : ISTE Ltd |
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Hoboken, NJ : , : John Wiley & Sons, Inc., , 2020 |
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ISBN |
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1-119-75520-4 |
1-119-75518-2 |
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Descrizione fisica |
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1 online resource (xiii, 341 pages) : illustrations |
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Collana |
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Sciences. Mechanics, Geomechanics |
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Disciplina |
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Soggetti |
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Rock mechanics - Mathematics |
Stability - Mathematical models |
Rock mechanics - Mathematical models |
Bifurcation theory |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- 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. Commmon 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 |
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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 rocks -- 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 -- 4.3. 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 -- 7.4.2. Coupled finite element formulation -- 7.4.3. Two-dimensional specimen under compression -- 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 |
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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 -- EULA. |
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