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Instabilities modeling in geomechanics

Stefanou, Ioannis.

Instabilities modeling in geomechanics

Stefanou, Ioannis.

9781119755203

9781119755180

London : ISTE, Ltd. ; Hoboken, NJ : Wiley, 2021.

1 online resource (361 pages)

Mechanics, Geomechanics

Mechanics--computational mechanics. Geomechanics.

4.7. References.

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 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

Instabilities Modeling in Geomechanics describes complex mechanisms which are frequently met in earthquake nucleation, geothermal energy production, nuclear waste disposal and CO2 sequestration. These mechanisms involve systems of non-linear differential equations that express the evolution of the geosystem (e.g. strain localization, temperature runaway, pore pressure build-up, etc.) at different length and time scales. In order to study the evolution of a system and possible instabilities, it is essential to know the mathematical properties of the governing equations. Therefore, questions of the existence, uniqueness and stability of solutions naturally arise. This book particularly explores bifurcation theory and stability analysis, which are robust and rigorous mathematical tools that allow us to study the behavior of complex geosystems, without even explicitly solving the governing equations. The contents are organized into 10 chapters which illustrate the application of these methods in various fields of geomechanics.

John Wiley and Sons

Geodynamics.

Geophysics.

Faults (Geology)

Géodynamique.

Géophysique.

Failles (Géologie)

faults.

Geodynamics

Geophysics

Stefanou, Ioannis.

Sulem, Jean.

https://onlinelibrary.wiley.com/doi/book/10.1002/9781119755203