Granular Geomaterials Dissipative Mechanics: Theory and Applications in Civil Engineering

By Etienne Frossard

This book develops a new vision in geomechanics which will be of interest to researchers and engineers. It begins with the key theoretical features of dissipative structures induced by elementary contact friction within geomaterials in slow motion, their multi-scale expression in key tensor relations and associated features including strain localization and shear banding.

• Language: English
• Publisher: Wiley
• Release date: Oct 22, 2018
• ISBN: 9781119563556

Book preview

Table of Contents

Cover

Preface

Introduction

I.1. Background

I.2. Main assumptions

I.3. Key of the multi-scale approach: the internal actions, a new tensor concept

1 Fundamentals: The Tensor Structures Induced by Contact Friction

1.1. Microscopic scale: the elementary inter-granular contact

1.2. Mesoscopic scale: the discontinuous granular mass

1.3. Macroscopic scale: the equivalent pseudo-continuum

2 Natural Compatibility With Mechanical Heterogeneity

2.1. Compatibility with the heterogeneity of internal actions

2.2. Compatibility with the heterogeneity of internal forces and internal movement distributions (stress and strain rates)

3 Strain Localization and Shear Banding: The Genesis of Failure Lines

3.1. Background and framework of the analysis

3.2. Shear bands orientation

3.3. Shear bands internal structure

3.4. Localization criterion

3.5. Shear band evolution: the formation of failure lines

4 Failure Criterion: The Micromechanical Basis of Coulomb Criterion

4.1. Background and framework of the analysis

4.2. Failure criterion at a critical state: the Coulomb Criterion

5 Coupling Between Shear Strength and Volume Changes: Generalized 3D Stress–Dilatancy Relations

5.1. Framework of the analysis

5.2. Definition of a general 3D dilatancy rate

5.3. Generalized stress–dilatancy relationships for relevant strain modes

5.4. Simplification into Rowe’s relations for particular conditions

5.5. Failure criterion at peak strength with dilation

5.6. Incidence of strain reversals on volume change rates

5.7. 3D Characteristic state

5.8. Nature of the six allowed strain modes regarding volume changes and motion sustainability

5.9. A direct link with fluid mechanics

5.10. Conclusions

6 Experimental Validations

6.1. Validations from classical triaxial test results

6.2. Validations from simple shear experimental results

6.3. Validations from true 3D compression apparatus results

6.4. Validation from cyclic torsional shear tests data

6.5. Validations from detailed numerical simulations with realistic discrete particles

6.6. Measurement of apparent inter-granular friction – typical values of the parameters

7 Cyclic Compaction Under Alternate Shear Motion

7.1. Background and framework of the analysis

7.2. Key results

7.3. The cyclic compaction ratio versus the principal stress ratio

7.4. Energy efficiency of compaction

7.5. Limit of cyclic compaction when apparent inter-granular friction vanishes

8 Geostatic Equilibrium: the K0 Effect

8.1. Background and framework of the analysis

8.2. The micromechanical process of geostatic stress-building in the soil mass

8.3. The solutions provided by the multi-scale approach

8.4. The resulting K0 formula based on micromechanics

8.5. Comparison with empirical Jaky formula

8.6. The two limits of geostatic equilibrium

8.7. Limit of geostatic equilibriums when apparent inter-granular friction vanishes

9 Scale Effects in Macroscopic Behavior Due to Grain Breakage

9.1. Introduction to grain breakage phenomenon: a framework of the analysis

9.2. Scale effects in shear strength

10 Practical Applications of Scale Effects to Design and Construction

10.1. A new method for rational assessment of rockfill shear strength envelope

10.2. Incidence of scale effects on rockfill slopes stability

10.3. Scale effects on deformation features and settlements

11 Concluding Remarks

11.1. Concluding remarks on features resulting from energy dissipation by friction

11.2. Concluding remarks on features resulting from grain breakage

11.3. Final conclusions

Appendices

A.I. Appendix to Introduction

A.1. Appendix to Chapter 1 – tensor structures induced by friction

A.2. Appendix to Chapter 2 – compatibility with mechanical heterogeneity

A.3. Appendices to Chapter 3 – strain localization and shear banding

A.4. Appendix to Chapter 4 – micromechanical basis of the Coulomb Criterion

A.5. Appendix to Chapter 5 – coupling shear strength and volume changes

A.6. Appendix to Chapter 6 – experimental validations

A.7. Appendix to Chapter 7 – cyclic compaction

A.8. Appendix to Chapter 8 – geostatic equilibrium: the K0 effect

A.9. Appendix to Chapter 9 – scale effects due to grain breakage

A.10. Appendix to Chapter 10 – applications of scale effects to design and construction

A.11. Appendix to Chapter 11 – concluding remarks

References

Index

End User License Agreement

List of Tables

1 Fundamentals: The Tensor Structures Induced by Contact Friction

Table 1.1. The six allowed strain mode situations

4 Failure Criterion: The Micromechanical Basis of Coulomb Criterion

Table 4.1. Strain mode situations to be analyzed

Table 4.2. Strain mode situations allowed

5 Coupling Between Shear Strength and Volume Changes: Generalized 3D Stress–Dilatancy Relations

Table 5.1. Basic dilatancy relations for the six allowed strain modes

Table 5.2. Generalized stress–dilatancy relationships resulting from the dissipation equation

Table 5.3. Characteristics of volume change around motion reversal, under axisymmetric stress conditions or plane strain ( = 0)

Table 5.4. The six strain mode characteristics, regarding volume changes and critical state motion

6 Experimental Validations

Table 6.1. Apparent inter-granular friction for mono-mineral granular media under low confining stresses, for narrow gradations

Appendices

Table A.1. The six strain mode features, regarding volume changes transition

Table A.2. Main features of components of composite motion

Table A.3. Correspondence between stress states and volume change conditions

List of Illustrations

Preface

Figure 1. Large earth and rockfill infrastructures in civil engineering. (a) High-speed railway infrastructures. (b) Marine works. (c) Rockfill dams (Grand-Maison Dam – photo EDF). For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Introduction

Figure I.1. Typical rockfill (basalt) used in civil engineering. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

1 Fundamentals: The Tensor Structures Induced by Contact Friction

Figure 1.1. Synopsis of multiscale tensor structures induced by contact friction. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 1.2. Elementary contact tensor p(c) – physical interpretation and representation by Mohr circles. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 1.3. The granular mass in motion, represented by a set of moving contacts with their internal actions. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 1.4. Example of internal feedback configuration in the granular mass in motion. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 1.5. Theoretical minimal dissipation solutions

Figure 1.6. Geometrical representation of the set of tensor solutions of general dissipation equation

Figure 1.7. Mapping of Table 1.1 strain modes in the octahedral plane. (a) Layout in the octahedral plane. (b) Layout in the angular positioning diagram, with corresponding micro-scale polarization characteristics (contact motion hodographs)

2 Natural Compatibility With Mechanical Heterogeneity

Figure 2.1. Distributions of elementary contact actions (2D medium)

Figure 2.2. Sample of solutions f(θ), as triangular distributions function of parameter R. (a) Direct representation. (b) Polar representation on normal to contacts. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 2.3. Distribution f(θ) and its fluctuating component

Figure 2.4. Strain localization under homogeneous stress

Figure 2.5. Compatible mixed heterogeneity with shear bands and stress concentrations

3 Strain Localization and Shear Banding: The Genesis of Failure Lines

Figure 3.1. Localization process: from local heterogeneity to developed failure lines. (A) Localization criterion. (B) Evolution of shear bands toward failure lines (a) strain mechanisms with failure lines, at different scales (b) corresponding kinds of strain heterogeneities. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 3.2. The overall layout of shear bands orientation. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 3.3. Orientations in motions with stationary-specific volume

Figure 3.4. Shear motion with dilatancy by grains separation. (a) Basic mechanism. (b) Global motion within shear band

Figure 3.5. Shear motion with dilatancy by grain rocking. (a) Basic mechanism. (b) Global motion within shear band

Figure 3.6. Motion referential in the shear band

Figure 3.7. Overall features of shear band steady solutions. (a) Simple shear motion. (b) Biaxial compression motion

Figure 3.8. Shear profile inside a shear band (experimental data from Nemat-Nasser and Okada [NEM 01])

Figure 3.9. Micro-mechanism within the stationary shear band structure – terms of energy dissipation balance

Figure 3.10. Dissipative structure in the stationary shear band

Figure 3.11. Limit to the concentration of shear into stationary shear bands. (a) Quasi-homogeneous motion. (b) Intermediate configuration. (c) Maximal concentration

Figure 3.12. The system of parallel shear bands – an example of a shear profile

Figure 3.13. Experimental data [see Figure 6.1(a)] transcribed into space . (a) Evolution of specific dissipation rate with a specific volume. (b) Evolution of specific dissipation rate with specific deformation. (c) Evolution of specific volume with specific deformation. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 3.14. Evolution of a set of parallel shear bands

4 Failure Criterion: The Micromechanical Basis of Coulomb Criterion

Figure 4.1. Coulomb Failure Criterion and key geomechanical issues in Civil Engineering. (a) Coulomb Failure Criterion. (b) Stability of slopes. (c) Thrusts on retaining structures. (d) Bearing capacity of foundations

Figure 4.2. Mapping of Table 4.1 strain modes in the deviatoric plane {b, c}. (a) Ordered coaxiality domain. (b) Limitations resulting from the dissipation relation

Figure 4.3. Critical state least shear resistance solution and failure criterion (with associated micro-scale polarization features). (a) In the {b,c,z} coordinates space. (b) On the plane {b,c}: minimum solution deviatoric relation. (c) Resulting failure criterion (octahedral plane section): the Coulomb Criterion pyramid

Figure 4.4. Investigated boundary conditions A and B

Figure 4.5. Least dissipation criterion for boundary conditions A. (a) In the {b,c,z} coordinates space. (b) On the {b,c} diagram: minimum solution deviatoric relation. (c) Resulting failure criterion (octahedral plane section): the Coulomb Criterion pyramid

Figure 4.6. The link between least shear strength and least dissipation criteria (with their respective deviatoric relations)

Figure 4.7. Relative arrangement of tensors σ, , and π, for critical state failure criterion. (a) Projections on an octahedral plane. (b) On the unit ball (octahedron) of tensorial norm N

Figure 4.8. Critical state failure criterion – incidence of small deviations from minimal solution. (a) Assumed deviatoric relation. (b) Resulting failure criterion. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

5 Coupling Between Shear Strength and Volume Changes: Generalized 3D Stress–Dilatancy Relations

Figure 5.1. Peak shear strength failure criterion (with dilatancy dmax = 2). Incidences of moderate deviations from the minimum solution. (a) Assumed deviatoric relation. (b) Resulting failure criterion. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 5.2. Characteristic state: any motion associated with a stress-path remaining inside the pyramid generates a contraction of specific volume

Figure 5.3. Precis of global characteristics resulting from the dissipation relation, regarding coupling between shear strength and volume changes. (a) Features on stress–strain curves and volume changes for Mode I (b = 0): coupling between shear strength and volume changes in the dilatancy diagram. (b) Features on an octahedral stress plane: shear strength criteria and b = cst. Stress-paths. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

6 Experimental Validations

Figure 6.1. Experimental validation of the energy dissipation relation based on friction through triaxial compression tests. (a) Stress–strain data. (b) Stress–dilatancy diagram. (c) Peak data. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 6.2. Shear strength envelope for reduced-basalt rockfill. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 6.3. Theoretical envelopes on dilatancy diagrams of cyclic triaxial tests (adapted after Pradhan et al. [PRA 89]). (a) Cyclic motion and stress-path in the octahedral plane. (b) Stress–strain trajectories. (c) Specific dilatancy diagram. For a color version of this figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 6.4. Theoretical envelopes on dilatancy diagrams of simple shear tests (adapted after Oda [ODA 75], on data from Cole [COL 67]). (a) Motion, stresses, and micro-scale polarization pattern. (b) Specific dilatancy diagrams. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 6.5. Validation of features set by the energy dissipation relation: large amplitude cycling testing on 3D apparatus (adapted from [LAN 84]). (a) Scheme of apparatus, stress-path, and micro-scale polarization patterns. (b) Untreated stress–strain and volume change recordings. (c) Energy diagram results. (d) Detailed interpretation of stress–strain and volume change records. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 6.6. Theoretical envelopes on dilatancy diagrams of cyclic torsional shear tests (adapted after Pradhan et al. [PRA 89]). (a) Cyclic motion, stresses, and micro-scale polarization patterns. (b) Stress–strain diagram. (c) Specific dilatancy diagram. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 6.7. Rotations in biaxial tests numerical simulations with discrete particles of different shapes (from [NOU 05a]). (a) Typical randomly-shaped irregular convex polygons with various elongation ratios Ra. (b) Mean rotations developing with strains during monotonic biaxial compression. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 6.8. Dilatancy diagrams for cyclic biaxial numerical simulations with realistic discrete particles (from [NOU 05a]). For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 6.9. Typical particle morphology of tested granular materials

7 Cyclic Compaction Under Alternate Shear Motion

Figure 7.1. Alternate shear motion. (a) Common experience. (b) Usual compaction practice in civil works. (c) Simple shear schematic representation

Figure 7.2. Small alternate shear motions analyzed. (a) Position on monotonic stress–strain curves. (b) Position on specific dilatancy diagram, with micro-scale polarization patterns. (c) Resulting volume changes versus shear strains. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 7.3. Effect of repeated cycles of small alternate simple shear motion. (a) Void ratio evolution displaying the typical ratchet effect. (b) Cyclic compaction ratio versus principal stress ratio. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

8 Geostatic Equilibrium: the K0 Effect

Figure 8.1. Principles of design thrusts for underground works in soft ground. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 8.2. Normal geostatic equilibrium – stress adjustment process. (a) Stress adjustment process and associated elementary shear movements. (b) Resultant granular mass tensor P and micro-scale polarization patterns

Figure 8.3. Earth pressure coefficient at rest. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 8.4. The other limit of the geostatic equilibrium

Figure 8.5. Geostatic coefficients and hydrostatic equilibrium

9 Scale Effects in Macroscopic Behavior Due to Grain Breakage

Figure 9.1. Main features of grain breakage – (a) and (b) basic failure patterns and (c) typical experimental results from [MAR 72]. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 9.2. Charles and Watts’ compilation of rockfill shear strength envelopes. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 9.3. Shear strength envelopes for homothetic groups of granular materials – (a) original compilation by Barton [BAR 81] and (b) schematic of scale effects. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 9.4. Evidence of scale effects in Charles and Watts’ compilation. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 9.5. Geometric correspondence between shear strength envelopes of materials A and B, set by scale effect rule

10 Practical Applications of Scale Effects to Design and Construction

Figure 10.1. Typical rockfill used in dam construction. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 10.2. A new method for rockfill shear strength assessment. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 10.3. Combined impacts on rockfill embankment safety factors of size effects and other key parameters: rockfill gradation size, embankment height and slopes. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 10.4. Stability coefficient Γ for rockfill slopes (source: [CHA 84]). For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 10.5. Compensation of scale effects related to dam height, rockfill size, and slopes. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 10.6. The main section of Ghrib rockfill dam (Algeria)

Figure 10.7. Scale effects on strains required to achieve equilibrium. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 10.8. Campos-Novos rockfill dam in Brazil (height 202 m, volume 13 hm3 of rockfill). (a) General view at end of construction. (b) View of upstream watertight concrete facing damaged at impounding. (c) Details of damages (failure of the reinforced concrete facing slab in compression). For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 10.9. Scale effects in rockfill rigidity modulus at the end of construction – correlation with grain size (reworked from Hunter and Fell [HUN 03]). For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 10.10. Scale effects in rockfill rigidity modulus at end of construction – correlation with a layer thickness (reworked from Johannesson [JOH 07]). For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 10.11. Settlement micro-mechanisms in concrete-faced rockfill dam body. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure 10.12. Scale effects in horizontal strains in CFRD under concrete face. (a) Simplified analytical assessment of strains at mid-height. (b) Corresponding diagram of risks for concrete facing failure. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Appendices

Figure A.1. Sketch of referential

Figure A.2. Granular materials A and B in perfect similarity. For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Figure A.3. Gradations of similar materials A and B

Figure A.4. Simplified three-dimensional analysis of settlements in dam body at impounding. (a) Dam section. (b) Vertical cross-valley section. (c) Simplified methods for rockfill moduli determination (reworked after Hunter et al. [HUN 03]). For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

Granular Geomaterials Dissipative Mechanics

Theory and Applications in Civil Engineering

Etienne Frossard

First published 2018 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:

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© ISTE Ltd 2018

The rights of Etienne Frossard to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2018952755

British Library Cataloguing-in-Publication Data

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

ISBN 978-1-78630-264-9

Preface

Granular materials are present in numerous sectors of economic activity outside civil engineering, from agriculture and agro-industry to pharmaceutical and chemical industries, mining industry, etc. It is estimated that more than two-thirds of raw materials used by world industries are in the form of granular materials, involving gigantic quantities, about 10 billion tons each year, of which processing and transport represent about 10% of energy consumption worldwide [DUR 96]. However, most often, the methods for their process remain rather traditional and lack optimization.

Regarding geomaterials, sand for the construction industry is the second most consumed natural resource after water [LEH 018], and its extraction represents serious environmental issues in certain areas, (including the disappearance of beaches and retreat of shoreline).

Construction of large civil engineering infrastructures commonly involves large volumes of earthfills and rockfills, constituted by sand, gravel, and rock blocks, sometimes up to tens of millions of cubic meters or even more, as in highways or railway platforms, marine infrastructures or large rockfill dams (see Figure 1). Examples of these include the Grand-Maison Dam in France (height 160 m, volume 14 hm³) with a central compacted clay core, or the Campos Novos Dam in Brazil (202 m, 13 hm³) with an impervious concrete slab on the upstream face, which will be discussed in Chapter 10.

For this last type of dams, which has become dominant in dam construction today, a major part of the design methods is based on the empirical extrapolation of the standard ones used (in the past) for lower dams. This empirical approach, based on experience, has led to serious technical accidents during commissioning on very high dams in the mid-2000s. As a consequence, concern in the profession has arisen, prompting a return to more rational approaches in design, and particularly Granular Geomaterials Dissipative Mechanics engineering approaches, through structural analysis and relevant material testing as should be the case for any large civil engineering structure. This highlights the need to improve our knowledge of the behavior of the granular geomaterials constituting these infrastructures, as well as of the behavior of these large structures. A way for such improvement may be sought in the integration of physical local phenomena within the materials, up to the scale of the engineering structures.

Figure 1. Large earth and rockfill infrastructures in civil engineering. (a) High-speed railway infrastructures. (b) Marine works. (c) Rockfill dams (Grand-Maison Dam – photo EDF). For a color version of the figure, please see www.iste.co.uk/frossard/geomaterials.zip

This book, resulting from a long-term work into the physics of granular materials as well as engineering of large civil works, is an attempt to relevantly move forward proposing a new vision of mechanical behavior