Constitutive Modelling of Granular Materials

556 Pages·2000·22.251 MB·English

by  D. Kolymbas (auth.), Professor Dr. techn. Dimitrios Kolymbas (eds.)

Dimitrios Kolymbas (Editor)
Constitutive Modelling of Granular Materials
Springer-Verlag
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Engineering
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Dimitrios Kolymbas (Editor)
Constitutive Modelling
of Granular Materials
With 259 Figures
Springer
Professor Dr. techn. Dimitrios Kolymbas
Universität Innsbruck, Austria
Institut für Geotechnik und Tunnelbau
Techniker Straße 13
6020 Innsbruck
Austria
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Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Kolymbas, Dimitrios (Hrsg.)
ISBN 978-3-642-63115-3 ISBN 978-3-642-57018-6 (eBook)
DOI 10.1007/978-3-642-57018-6
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Preface
Granular materials such as soils often undergo large deformations. Their me
chanical behaviour is pronouncedly anelastic. Mathematical models describ
ing this anelastic behaviour are indispensable to understand it and to carry
out numerical calculations. Most of these mathematical models are assembled
within the framework of the so-called elasto-plasticity. The younger theory
of hypoplasticity is a new paradigma, i.e. a completely different approach
to mathematical modelling of anelastic behaviour. Far from stating that hy
poplasticity is better than elastoplasticity, I wish to point to the fact that
the involved problems are very complex and there are still many open ques
tions in constitutive modelling. With the support of the European Union,
which is kindly acknowledged, a series of three Euroconferences were devoted
to Developments and Perspectives of Hypoplasticity. The last of these Euro
conferences took place in the small Greek village of Horton and was given a
larger scope in order to compare also approaches different from hypoplastic
ones and provide, thus, a State of the Art in the constitutive modelling of
granular materials. The present volume contains the papers of this Eurocon
ference. These papers refer to the general situation of constitutive modelling,
to alternatives of hypoplasticity, to micromechanical and thermodynamical
approaches, to numerical applications and, last but not least, to the present
developments and also the perspectives of hypoplasticity.
In concluding I wish to cordially thank two persons who greatly con
tributed to the success of the conference and the preparation of this volume:
Mrs. Christine Neuwirt who brilliantly managed the intricate economic ad
ministration of the conference, and Mr. Josef Wopfner who persistently and
skilfully re-formated and processed the papers.
Innsbruck, Dimitrios J(olymbas
September 1999
Contents
AUTHORS.................................................... 1
Introductory considerations
The misery of constitutive modelling . . . . . . . . . . . . . . . . . . . . . . . .. 11
D.KOLYMBAS
1 Introduction................................................. 11
2 Meaning of material constants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12
3 A review of the present situation in constitutive modelling ........ 13
4 Validation of constitutive models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15
5 On the physical foundation of constitutive models. . . . . . . . . . . . . . .. 15
6 Requirements on constitutive models . . . . . . . . . . . . . . . . . . . . . . . . . .. 16
7 How simple should a model be? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
8 Numerical implementations ................................... 20
9 Cooperation................................................. 22
10 The future of research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23
References ..................................................... 23
Does engineering need science? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25
C. VIGGIANI
1 Foreword................................................... 25
2 Definition of engineering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25
3 Definition of science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25
4 Relations between engineering and sciences. . . . . . . . . . . . . . . . . . . . .. 27
5 Some examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31
6 The forthcoming Middle Ages? ................................ 33
References ..................................................... 35
The role of models in civil engineering. . . . . . . . . . . . . . . . . . . . . . .. 37
D. MUIR WOOD
1 Introduction................................................. 37
2 Models..................................................... 38
3 Children's models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39
4 Students' models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42
5 Engineers' models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 46
6 Philosophers' models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50
7 Conclusion.................................................. 52
References ..................................................... 55
VIII
Overview of hypoplasticity
Hypoplasticity then and now ....... . . . . . . . . . . . . . . . . . . . . . . . . .. 57
W. WU, D. KOLYMBAS
1 Introduction................................................. 57
2 A heuristic example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58
3 Some historical remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
4 Framework of hypoplasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 65
5 Response envelope: a useful tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 72
6 Extensions: a tale of two terms ................................ 82
7 Simple boundary value problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92
8 Miscellaneous................................................ 96
9 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99
References ..................................................... 101
A review of two different approaches to hypoplasticity ........ 107
C. TAMAGNINI, G. VIGGIANI, R. CHAMBON
1 Introduction ................................................. 107
2 Mathematical structure ....................................... 109
3 Invertibility, consistency and limit states ........................ 118
4 Strain localization and bifurcation analysis ...................... 126
5 Conclusions ................................................. 137
References ..................................................... 138
A Gudehus/Bauer K-hypoplastic model. .......................... 144
B von Wolffersdorff K-hypoplastic model ......................... 144
Uniqueness, second order work and bifurcation in hypoplasticity147
R. CHAMBON
1 Introduction ................................................. 147
2 Existence and uniqueness of boundary value problems involving hy-
poplastic constitutive equations ................................ 148
3 Rice analysis with hypoplastic constitutive equations ............. 155
4 Invertibility and controlability seen as boundary value problems ... 161
5 Conclusion .................................................. 163
References ..................................................... 164
Stationary states in hypoplasticity ............................ 167
E. BA UER, l. HERLE
1 Introduction ................................................. 167
2 Historical development of hypoplastic models of the Kolymbas type 169
3 Stationary states and modeling of the critical stress state surface ... 179
4 Determination of the material parameters ....................... 183
5 Extension to a polar continuum ................................ 185
Acknowledgements .............................................. 188
References ..................................................... 189
IX
Generalized continua and microscopic approach
Microscopic approach contributions to constitutive modelling. 193
C. THORNTON
1 Introduction ................................................. 193
2 Macroscopic ensemble behaviour ............................... 194
3 Induced structural anisotropy ................................. 194
4 Physics at the grain scale ..................................... 198
5 Conclusions ................................................. 207
6 Acknowledgements ........................................... 207
References ..................................................... 207
Discrete and continuum modelling of granular materials ...... 209
H.-B. MUHLHAUS, L. MORESI, H. SAKAGUCHI
1 Introduction ................................................. 209
2 Formulation ................................................. 211
3 Lagrangian Particle Method ................................... 217
4 Examples ................................................... 220
5 Concluding Remarks ......................................... 223
References ..................................................... 224
2nd Gradient constitutive models ............................. 225
1. VARDOULAKIS
1 The continuum assumption .................................... 225
2 A veraging and the meaning of 2nd gradients ..................... 226
3 A simple 2nd gradient structural model ......................... 229
4 A Mindlin-type 2nd gradient linear elasticity ..................... 231
5 A 2nd gradient plasticity model for granular materials ............ 239
6 Acknowledgments ............................................ 247
References ..................................................... 247
Micro-mechanically based higher-order continuum models for
granular materials ............................................ 249
A.S.l. SUIKER, R. de BORST, C.S. CHANG
1 Introduction ................................................. 249
2 Micro-level particle interaction ................................. 250
3 From micro-level to macro-level ................................ 254
4 Macroscopic constitutive formulation ........................... 256
5 Continuum models versus discrete lattice model .................. 259
6 Higher-order continuum model that includes particle rotation ...... 266
7 Conclusions ................................................. 272
References ..................................................... 272
x
Relevant local variables for the change of scale in granular
materials ... ................................................... 275
B. CAMBOU, F. DEDECKER, M. CHAZE
1 Introduction ................................................. 275
2 Definition of the material and considered scales ................. 275
3 Analysis of the change of scale when the local level is defined at the
contact between particles ..................................... 278
4 Analysis of the change of scale when the local level is defined for a
local array of particles ........................................ 285
5 Conclusion .................................................. 287
References ..................................................... 289
Physical aspects
On the physical background of soil strength .................. 291
G. GUDEHUS
1 Introduction ................................................. 291
2 Steady states . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
3 Dilatant soils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
4 Contractant soils. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
5 Miscellaneous................................................ 299
References ..................................................... 300
The influence of time derivative terms on the mechanical be-
haviour of loose sands ........................................ 303
C. di PRISCO, S. IMPOSIMATO
1 Introduction ................................................. 303
2 Experimental observations .................................... 304
3 Mathematical Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
4 Concluding remarks .......................................... 315
5 Acknowledgements ........................................... 317
References ..................................................... 317
Appendix A .................................................... 318
An approach to plasticity based on generalised thermody-
namics ........................................................ 319
G. T. HOULSBY, A.M. PUZRIN
1 Introduction ................................................. 319
2 Thermomechanical formulation ............. . . . . . . . . . . . . . . . . . . . 320
3 Computational Examples ..................................... 326
4 Classification of plasticity models .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
5 Conclusions ................................................. 330
6 Acknowledgment ............................................. 331
References ..................................................... 331
XI
Comparison of different approaches
Comparison of hypoplastic and elastoplastic modelling of
undrained triaxial tests on loose sand ......................... 333
I. HERLE, T. lJOANH, W. WU
1 Introduction................................................. 333
2 Experimental observations .................................... 333
3 Constitutive models .......................................... 337
4 Comparison of experiments with calculations .................... 338
5 Instability surface ............................................ 342
6 Modification of the hypoplastic model .......................... 344
7 Conclusions................................................. 348
Acknowledgement ............. " ............... " ............... 349
References ..................................................... 349
Hypoplastic and elastoplastic modelling - a comparison with
test data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
Th. MARCHER, P.A VERMEER, P.-A. von WOLFFERSDORFF
1 Introduction ................................................. 353
2 Experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
3 Hypoplastic calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
4 Elastoplastic calculations ..................................... 360
5 Comparison................................................. 365
6 Conclusions ................................................. 370
7 Acknowledgements ........................................... 371
References ..................................................... 371
Strain response envelope: a complementary tool for evaluating
hypoplastic constitutive equations ............................ 375
T. DOANH
1 Introduction ................................................ 375
2 Experimentalobservations .................................... 376
3 Hypoplastic analysis ......................................... 380
4 Predictive capability of hypoplasticity .......................... 390
5 Conclusions ................................................ 394
References ........................................ . . . . . . . . . . . . . 394
Special models
Modelling weathering effects on the mechanical behaviour of
granite ....................................................... 397
R. NOVA
1 Introduction ................................................. 397
2 Conceptual model for weathering effects on rock behaviour ....... 398