Jean Sulem - Instabilities Modeling in Geomechanics

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SCIENCES

Mechanics, Field Director – Gilles Pijaudier-Cabot

Geomechanics, Subject Head – Cino Viggiani

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

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

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, CO 2sequestration, 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 solids. Some aspects related to shear band thickness, mesh dependency and higher order continua are also briefly discussed.

The third chapter, “Material Instability and Strain Localization Analysis”, covers the principles of strain localization analysis as applied to geomaterials. The conditions for the formation of different types of deformation bands are given and an extension of the analysis to fluid-saturated porous media is presented.

The fourth chapter, “Experimental Investigation of the Emergence of Strain Localization in Geomaterials”, focuses on strain field measurements of strain localization. Full field methods, imaging tools and experimental loading apparatus have evolved considerably over the past 15 years. This chapter presents recent developments on the characterization of the strain localization process and introduces the methods that are most frequently used.

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