Failure in Geomaterials: A Contemporary Treatise

By Richard Wan, Francois Nicot and Felix Darve

Failure in Geomaterials offers a unified view of material failure as an instability of deformation modes framed within the theory of bifurcation.

Using mathematical rigor, logic, physical reasoning and basic principles of mechanics, the authors develop the fundamentals of failure in geomaterials based on the second-order work criterion. Various forms of rupture modes and material instabilities in granular materials are explored both analytically and numerically with lab experimental observations on sand as a backdrop. The authors provide a clear picture of inelastic deformations and failure of geomaterials under various loading conditions.

A unique feature of the book is the systematic application of the developed theory to the failure analysis of some selected engineering problems such as soil nailing, landslides, energy resource extraction, and internal erosion in soils.

• Provides the fundamentals of the mechanics of geomaterials for a detailed background on the subject
• Integrates a rigorous mathematical description of failure with mechanisms based on microstructure
• Helps users apply mathematical models of solid mechanics to engineering practice
• Contains a systematic development of the fundamentals of failure in heterogeneous multiphasic materials

• Language: English
• Publisher: Elsevier Science
• Release date: Jul 26, 2017
• ISBN: 9780081010563

Richard Wan

Richard Wan is Professor with the Department of Civil Engineering at the University of Calgary, Canada. He sits on the Editorial Board of several international journals and was the Vice-Chair of the TC103 (Numerical Methods) of the ISSMGE from 2009-2017.

Book preview

Failure in Geomaterials

A Contemporary Treatise

Richard Wan

François Nicot

Félix Darve

Table of Contents

Cover

Title page

Copyright

Foreword

Preface

Acknowledgments

List of Symbols

Part 1: Fundamentals

1: Characteristics of Failure in Geomaterials

Abstract

1.1 Description of failure

1.2 A definition for failure

1.3 Failure as an unstable bifurcation with loss of uniqueness

1.4 Failure patterns

2: Failure in Continuum Geomechanics

Abstract

2.1 Some generalities in continuum mechanics for material systems

2.2 The link between the kinetic energy and the second-order work

2.3 The second-order work in Eulerian formalism

2.4 The second-order work at the material point scale

2.5 The case of homogeneous material specimens

3: The Second-Order Work Criterion

Abstract

3.1 Second-order work and associated quadratic form

3.2 Control parameters and generalized constitutive matrix

3.3 The fundamental role of Ks

3.4 Conclusions

3.5 Appendices

4: Numerical and Experimental Investigations of Bifurcations

Abstract

4.1 Essentials of second-order work criterion

4.2 Discrete computations of failure

4.3 Topology of instability cones

4.4 Experimental support for bifurcation

5: Hierarchy of Failure Modes

Abstract

5.1 Introduction

5.2 Diffuse and localized failure indicators

5.3 Rice localization criterion

5.4 Rice’s localization criterion and second-order work vanishing

5.5 Localized and diffuse failures via discrete element approach

5.6 Localized and diffuse failures via continuous approaches

Part 2: Applications

6: Second-Order Work in Boundary Value Problems

Abstract

6.1 Global second-order work

6.2 Spectral analysis of global tangent stiffness matrix

6.3 Shallow foundation as a benchmark problem

7: Engineering Applications

Abstract

7.1 Stability analysis of a soil-nailed wall

7.2 Stability analysis of Petacciato (Italy) landslide

7.3 Thermo-hydro-mechanical failure analysis of oil sand reservoirs

8: Soil Erosion as an Instability Problem

Abstract

8.1 Introduction

8.2 Modeling the erosion process

8.3 Closing remarks

Bibliography

Index

Copyright

First published 2017 in Great Britain and the United States by ISTE Press Ltd and Elsevier Ltd

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:

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Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

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© ISTE Press Ltd 2017

The rights of Richard Wan, François Nicot and Félix Darve to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

Library of Congress Cataloging in Publication Data

A catalog record for this book is available from the Library of Congress

ISBN 978-1-78548-009-6

Printed and bound in the UK and US

Foreword

The subject of geomechanics is a recent development in the field of soil mechanics that attempts to provide a wider perspective of the applications of mathematical multi-physics to problems in the earth sciences. In this regard, the clear identification of the processes and laws that can describe failure in geomaterials is central to the successful practice of geomechanics. The notion of failure can take different interpretations depending on the type of the geomaterial and its current state as characterized by the stress state and stress history. The classical experiments conducted by Theodore von Karman, where a rock such as marble that can exhibit brittle fracture under unconfined conditions can be made to experience plastic flow at high confining stress states, clearly exemplifies the challenge of the description of both deformation and failure of geomaterials. The importance of a sound theoretical basis for describing failure is of fundamental mathematical interest and has an impact on a variety of modern geomechanics problems, including the analysis of stability and deformation of earth masses, movement of earth materials and particulates relevant to debris flows, the role of fluids in influencing failure in geomaterials including saturated and unsaturated regions, energy resources geomechanics and conventional examples of interest to geotechnical engineering practice.

The theories of classical plasticity, enriched by advanced failure and flow concepts, are now widely used in geotechnical engineering practice. Nonetheless, the opportunity exists to revisit the definitions implicit in these classical theories to identify the issues that still need attention and clarification. The scope of this book is primarily focused on advanced issues related to the description of failure interpreted as either a bifurcation phenomenon, or the development of instability or the loss of uniqueness. The major tool that has a unifying role is Hill’s criterion or the concept of second-order work. The authors of the volume have made important contributions to this topic and are in a unique position to present the interpretation of failure in geomaterials through the various formulations. The book is written in an easily readable style and the authors devote a great effort to complement the mathematical framework of the developments with clear descriptions of the processes and, where relevant, experimental evidence. The volume also addresses the hierarchical nature of failure modes in terms of diffused or localized failure and relates the second-order work to Rice’s localization criterion. The use of discrete element approaches for the study of localized and diffused failure is also examined.

The authors have made a commendable effort to place the theoretical development in a practical context. To this end, the second part of the volume deals with the application of the second-order work concept to commonly occurring boundary value problems in geomechanics related to either specimen testing or classical benchmark problems such as shallow footings. The volume culminates in examining the classical stability problems associated with soil-nailed walls, mechanics of landslides that incorporate unsaturation effects and thermo-hydro-mechanical processes in resource extraction where developments related to localization phenomena will add value to the modelling, understanding and interpretation of failure. Most importantly, the material presented will also serve as exercises for benchmarking the capabilities of current and new advances in computational modelling of failure in geomaterials.

In summary, the volume is an informative exposition of the current advances in the formulation of geomechanical problems where failure in all its manifestations, localized, diffused and combinations thereof, is important to characterizing the mechanical properties of complex geomaterials. Geomaterials are diverse enough that nearly all interpretations of failure will be of benefits to the researcher and practitioner alike. The volume is also a re-affirmation of the adage there is nothing more practical than a good theory. It is also a reminder to new researchers in geomechanics that theories that are deep-rooted in fundamental concepts of a mathematical or mechanics origin deserve as much consideration as do computational advances or sophisticated experimental techniques. Since the volume addresses fundamental issues related to the identification and description of failure in geomaterials, it is bound to serve as a standard reference for researchers in geomechanics and geosciences in general.

Patrick Selvadurai, Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada

Preface

Richard Wan

François Nicot

Félix Darve May 2017

This book introduces the reader to a modern school of thought on the topic of failure in geomaterials. The chapters are a collection of ideas and principles that have matured over the past several decades to give way to contemporary approaches that tackle, in a generalized framework, the multifaceted characteristics of geomaterials and the subtle way they fail. With recent advances in modern computer techniques and progresses in mechanics, the field of geomechanics has evolved with new approaches such as the discrete element method offering new insights, while also complementing mainstream continuum geomechanics.

The precise definition of failure becomes somewhat elusive when it comes to geomaterials due to their particulate and multiphasic nature. Conventionally, the analysis of failure takes as its starting point the restriction of stress states to lie within the Mohr-Coulomb limit, defining a plastic limit surface on which unlimited strains can occur under constant stress through a plasticity flow rule. However, we can evoke instances of failure occurring well inside the plastic limit surface under some special loading conditions such as stress-controlled undrained shearing of saturated loose sands or isochoric deformations in the dry state. The response of the material is a characteristic peak in the deviatoric stress that is well below the Mohr-Coulomb plastic limit, after which the material succumbs spontaneously to failure without any apparent failure plane or discontinuity surface of finite thickness. In distinct contrast, dense sands when sheared reveal shear bands associated with zones of finite thickness within which intense deformations are localized. Hence, the hallmark of failure in geomaterials seems to be directly related to the two principal modes by which it is manifested: one with localized slips and another variant where deformations are diffused without any localization phenomena.

This book presents a unified treatment of failure in geomaterials as an instability of homogeneous deformations. The observed failure mode is a result of the underlying constitutive equations admitting bifurcations in solutions for the material response. This mathematical view of failure is to be found in Hill’s stability condition or the so-called second-order work criterion. The concept of second-order work, viewed as a fundamental building block to frame the theory of material failure, and its extension to geomaterials are right at the core of this book. The second-order work criterion reflects the fact that stability in material behavior is guaranteed whenever the product of incremental stress and strain remains positive for all kinematically admissible velocity fields. Thus, this can be interpreted as such: whenever the stress-strain involves plastic softening, the second-order work becomes negative, meaning that the material may continue to deform without any input of energy from external agents. At the scale of a geostructure, the loss of positiveness of the second-order work may become pervasive to the extent that failure may be possible in the form of diffuse collapse like in the case of liquefaction in a landslide. The second-order work criterion also encompasses instability of the Mandel-Hadamard type associated with singularities in the acoustic tensor due to the loss of ellipticity (convexity) of the underlying constitutive equations, and thus ill-posedness in a boundary value problem. In the static case, these singularities correspond to surfaces across which jumps in strains are possible, hence strain localization.

In line with the above discussion, this book is a natural outgrowth of venerable work carried over the past decade or so by the Grenoble Geomechanics group on the topic of failure in geomaterials with the second-order work as the central theme. We have endeavored to present the second-order work criterion and its various ramifications in a pedagogical way, while also presenting careful theoretical developments to describe the physics at hand. The analytical developments are amply supported by numerical modeling examples that hinge on both discrete and continuum approaches. Thus, the discrete element modeling (DEM) approach is essentially used to explore subtle facets of failure in granular materials at the particle scale which are related to loss of uniqueness of response, controllability or sustainability of loading, failure modes, and most importantly the dynamics aspects of failure. Continuum approaches based on classical elasto-plasticity and variants of hypoplasticity such as linear and nonlinear incremental laws are also used to verify theoretical findings. It is found that numerical results obtained from discrete and continuum approaches corroborate, and thus lend support to the failure concepts developed in this book. One of the most outstanding results presented in this book is with regard to the notion of effective and non-effective failures. An effective failure is deemed to occur whenever three necessary and sufficient conditions are satisfied: (1) the stress state must be within the bifurcation domain, (2) the direction of loading must be contained in the cone of instability and (3) the proper control parameters should be in place.

The book is divided into two parts: Part 1 delves at length into theoretical developments surrounding the second-order work criterion and the subsequent verification of important concepts put forward via discrete element modeling and continuum approaches based on elasto-plasticity and incremental laws, and Part 2 is dedicated to the extension of the second-order work definition to a boundary value problem setting and its applications in analyzing failure in some selected engineering problems.

In the opening of Chapter 1, the basic concepts of failure in engineering materials are revisited so as to frame a proper theory for geomaterials with bifurcation as the central idea. A definition of failure for geomaterials is thus offered as an unstable bifurcation with loss of uniqueness of the underlying equations describing their constitutive behavior. The notions of material instability and loss of uniqueness vis-à-vis failure are thus clarified. Rich deformational patterns that emerge during failure are then introduced to link them to material instability.

Chapter 2 is devoted to basic elements of continuum mechanics to set the scene for introducing the second-order work and its linkage to kinetic energy using both Eulerian and Lagrangian formalisms. The expression of the second-order work at the material point is thus derived in Chapter 3, highlighting its associated quadratic form. The notion of control and load parameters is thereafter introduced in the context of mixed loading (stress and strain increments). This is to illustrate how failure is a consequence of loss of uniqueness between load and control parameter vectors, which in fact is linked to the second-order work. As stated previously, requirements for an effective failure include the satisfaction of three criteria: (1) bifurcation criterion, (2) second-order work criterion and (3) control-choice criterion that are formally derived in Chapter 3.

Chapter 4 presents both numerical and experimental investigations of various bifurcations covered in the previous chapters.