Instabilities Modeling in Geomechanics. Jean Sulem
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SCIENCES
Mechanics, Field Director – Gilles Pijaudier-Cabot
Geomechanics, Subject Head – Cino Viggiani
Instabilities Modeling in Geomechanics
Coordinated by
Ioannis Stefanou
Jean Sulem
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
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John Wiley & Sons, Inc.
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© 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
Introduction
Ioannis STEFANOU1 and Jean SULEM2
1GeM, Ecole Centrale de Nantes, France
2Navier, Ecole des Ponts ParisTech, Université Paris-Est, Marne-la-Vallée, France
Nuclear waste disposal, petroleum engineering, CO2 sequestration, geothermal energy, tunneling, slope stability, geotechnics, borehole stability, drying cracking and earthquake nucleation are important applications of geomechanics with short- and long-term environmental and societal impacts. Geomechanical systems involve various multiphysical and non-linear processes at several length and time scales. These complex mechanisms are described by non-linear differential equations that express the evolution of the various state variables of a system (e.g. displacements, temperature, pore pressure etc.). In order to study the evolution of the system and the possible occurrence of instabilities, it is necessary to explore the mathematical properties of the governing equations. Therefore, questions about the existence, uniqueness and stability of solutions arise naturally. Bifurcation theory and stability analysis are robust and rigorous tools for qualitatively and quantitatively investigating various instabilities such as strain localization, thermal runaway and unstable pressure increase, without explicitly determining the solutions of the governing non-linear equations of a geomechanical system.
The purpose of this book is to present the basic ideas of bifurcation theory and its application to classical problems of geomechanics. The book is organized into nine chapters.
The first chapter, “Multiphysics Role in Instabilities in Geomaterials: A Review”, provides in situ and laboratory evidence of instabilities in geomechanical applications, mostly induced by multiphysical phenomena at various scales, such as heat generated during pre-cursor creep in the development of landslides, geochemical reactions, the effect of heat on inducing possible failure through pressurization of pore water, the effect of evaporation-induced suction and air entry during drying and subsequent cracking of soils.
The second chapter, “Fundamentals of Bifurcation Theory and Stability Analysis”, aims to provide the basic ideas of bifurcation theory and stability analysis. It focuses on giving the necessary vocabulary for the classification of common bifurcations that are often met in applications and, finally, it presents the application of the theory for studying strain localization in