Jean Sulem - Instabilities Modeling in Geomechanics

7 Chapter 7Figure 7.1. Non-local approach on a representative material volumeFigure 7.2. Kinematic degrees of freedom of the Cosserat elastic continuum theor...Figure 7.3. Kinematics of a microstructure continuum: (a) initial configuration ...Figure 7.4. Material system with current configuration Ω and boundary conditions...Figure 7.5. Finite element used for the spatial discretization of the coupled lo...Figure 7.6. Sketch of the plane-strain compression testFigure 7.7. Uniaxial compression: (a) global specimen response curves and (b) Ri...Figure 7.8. Localized patterns represented by the deviatoric deformation for cla...Figure 7.9. Localized patterns represented by the plastic zone for a second grad...Figure 7.10. Example of localized solutions for a compression test obtained afte...Figure 7.11. Schematic representation of the models used for the modeling of a g...Figure 7.12. Imposed total stresses and pore water pressure at the gallery wall ...Figure 7.13. Evolution of strain localization during and after the gallery excav...Figure 7.14. Comparison of the strain localization pattern at the end of the cal...Figure 7.15. Evolution of strain localization during and after the gallery excav...Figure 7.16. Evolution of strain localization during and after the gallery excav...Figure 7.17. Evolution of strain localization after the gallery excavation, with...Figure 7.18. Positions of cross-sections and gallery wall observation points. Fo...Figure 7.19. Evolution of pore water pressure along (a) vertical and (b) horizon...Figure 7.20. Stress paths at the gallery wall, during and after gallery excavati...

8 Chapter 8Figure 8.1. Model of a fault zone as an infinite layer under uniform shear strai...Figure 8.2. Homogeneous layer at 7 km depth T 0= 210°C, p f 0= 70MPa, (σ n= 180MP...Figure 8.3. Wavelength selection: λ is the wavelength of the perturbation normal...Figure 8.4. Growth coefficient (Lyapunov exponent) in terms of perturbation wave...Figure 8.5. Strain localization due to chemical softening in a 5 m thick dehydra...Figure 8.6. Positive feedback process due to dissolution and solid skeleton dama...Figure 8.7. Instability region (shaded) for compaction bands under oedometric co...Figure 8.8. Evolution in time of (a) deformation, (b) the specific surface, (c) ...Figure 8.9. Profile of the vertical deformation at various times and for ℓ c= 4 ...Figure 8.10. Vertical deformation in function of time: at the peak of the compac...Figure 8.11. Stress paths of the point at the peak of the compaction band (ABC2)...Figure 8.12. Profile of the vertical deformation at various times for ℓ c= 16 mm...

9 Chapter 9Figure 9.1. (a) Conceptual model of the internal structure of a fault described ...Figure 9.2. (a) Sketch of the continuum mechanical concept of shear failure as a...Figure 9.3. Summary of the system’s response when equations [9.15] are satisfied...Figure 9.4. Evolution of the core strain rate on line III in Figure 9.3(a). Irre...Figure 9.5. Influence of the characteristics of the reaction. Snapshots of the p...Figure 9.6. (a) Punchball fault from Chester and Chester (1998) featuring two sc...Figure 9.7. Regular ETS sequence in South Vancouver Island, Cascadia, station AL...Figure 9.8. Irregular ETS sequence of Gisborne, New Zealand, station GISB. (a) T...

10 Chapter 10Figure 10.1. Photos of the outcrop of the Glarus Thrust (Switzerland) showing th...Figure 10.2. Representation of the components of the stress and couple-stress te...Figure 10.3. Boundary conditions for the infinite sheared layer modeling a satur...Figure 10.4. Real part of the growth coefficient s as a function of the length o...Figure 10.5. Real part of the growth coefficient s as a function of the length o...Figure 10.6. Bifurcation parameter Hcr (hardening modulus for which a bifurcatio...Figure 10.7. Wavelength of the perturbation with the fastest growth λmax as a fu...Figure 10.8. Selected wavelength λmax as a function of the hardening coefficient...Figure 10.9. Stress–strain response of an infinite sheared layer for Cauchy cont...Figure 10.10. Shear deformation plotted on the deformed mesh with 50 elements an...Figure 10.11. Mesh convergence obtained for the stress-strain response of an inf...Figure 10.12. Cosserat rotation plotted on the deformed mesh with 80 elements an...Figure 10.13. Effect of THM couplings on the stress–strain response of the syste...Figure 10.14. Effect of THM couplings on the evolution of the shear band thickne...Figure 10.15. Effect of shear rate on the stress–strain diagram for a perfectly ...Figure 10.16. Comparison of the evolution of the shear band thickness obtained b...Figure 10.17. a) Observation of the principal shear zone (PSZ) for the punchbowl...

1 Cover

2 Table of Contents

3 Title Page SCIENCES Mechanics, Field Director – Gilles Pijaudier-Cabot Geomechanics, Subject Head – Cino Viggiani

4 Copyright First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK www.iste.co.uk John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA www.wiley.com © ISTE Ltd 2020 The rights of Ioannis Stefanou and Jean Sulem to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2019955403 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78945-000-2 ERC code: PE1 Mathematics PE1_7 Topology PE10 Earth System Science PE10_5 Geology, tectonics, volcanology

5 Introduction

6 Begin Reading

7 List of Authors

8 Index

9 End User License Agreement

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