Dimitrios Kolymbas (Editor) Constitutive Modelling of Granular Materials
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Dimitrios Kolymbas (Editor)
Constitutive Modelling of Granular Materials
Springer-Verlag Berlin Heidelberg GmbH
Engineering ONLINE LIBRARY
http://www.springer.de/ engine/
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
Cataloging-in-Publication Data applied for
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
This work is subject to copyright. A l l rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution act under German Copyright Law.
© Springer-Verlag Berlin Heidelberg 2000
Softcover reprint of the hardcover 1st edition 2000
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Typesetting: camera ready copy from author Cover-Design: MEDIO Innovative Medien Service GmbH Berlin Cover-Illustration: Gerd Gudehus Printed on acid-free paper SPIN 10754041 62/3020 5 4 3 2 1 0
Preface
Granular materials such as soils often undergo large deformations. Their mechanical behaviour is pronouncedly anelastic. Mathematical models describing 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 hypoplasticity is better than elastoplasticity, I wish to point to the fact that the involved problems are very complex and there are still many open questions 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 Euroconferences 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 Euroconference. 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 contributed to the success of the conference and the preparation of this volume: Mrs. Christine Neuwirt who brilliantly managed the intricate economic administration of the conference, and Mr. Josef Wopfner who persistently and skilfully re-formated and processed the papers.
Innsbruck, September 1999
Dimitrios J(olymbas
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
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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
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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
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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
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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
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3 An application to the weathering of granite ..................... 401 4 Conclusions ................................................. 409 Reference ...................................................... 411
A plasticity-based constitutive model for natural soils: a hier-archical approach . ............................................ 413 A. AMOROSI, M. J. KA VVADAS 1 Introduction ................................................. 413 2 Some aspects of the mechanical behaviour of natural soils ......... 414 3 The proposed model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 4 Conclusions ................................................. 436 References ..................................................... 436
Experimental bases for a new incremental non-linear consti-tutive relation with 5 parameters ............................. 439 F. DARVE, X. ROGUIEZ 1 Introduction ................................................. 439 2 Non linear incremental formalism .............................. 439 3 Generalized triaxial apparatus ................................. 441 4 Sand characteristics .......................................... 442 5 Initial Experiments ........................................... 443 6 Analysis of the tangent characteristics of a curve ................. 445 7 Classical oedometric test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 8 Oedometric test of class C2 •.•..••.•....••..•••.....•..••....•• 450 9 Oedometric test of class C3 ....•.....•..•..•.••....•..•..•..•.. 453 10 Conclusion .................................................. 454 11 Acknowledgements ........................................... 455 References ..................................................... 456
Numerical applications
Implicit integration of hypoplastic models .................... 457 O. M. HEERES, R. de BORST 1 Introduction ................................................. 457 2 Introduction to hypoplasticity ................................. 458 3 A hypoplastic model for granular materials with a predefined limit
state ....................................................... 463 4 Finite element simulations of the direct shear box test ............ 466 5 Concluding remarks .......................................... 469 References ..................................................... 470
Soil-water coupling analysis of progressive failure in cuts with a strain softening model ...................................... 471 T. ADACHI, F. OKA, H. OSAKI, F. ZHANG 1 Introduction ................................................. 471
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2 Elasto-plastic model with strain softening ....................... 472 3 Finite element analysis of progressive failure in cuts of ideal model
ground .................................. , .................. 475 4 Conclusions ................................................. 487 References ..................................................... 490
Advances in modelling soil anisotropy ........................ 491 L. ZDRA VKOVIC, D.M. POTTS 1 Introduction ................................................. 491 2 Experiments on silt .......................................... 492 3 Modelling anisotropic soil behaviour. . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 4 Examples ................................................... 498 5 Conclusions ................................................. 513 Appendix ...................................................... 515 References ..................................................... 519
Examples of finite element calculations with the hypoplastic law ........................................................... 523 K.NUBEL,R. CUDMANI 1 Settlement of earth embankment on a landfill material. . . . . . . . . . . . 523 2 Cyclic twisting of a tube in sand ............................... 528 References ..................................................... 538
Hypoplastic simulation of complex loading paths ............. 539 S. V LAVRIKO~A. Ph. REVUZHENKO 1 Introduction................................................. 539 2 Realization of experiments .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540 3 Hypoplastic homogeneous simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 542 4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 5 Hypoplastic simulation of the boundary value problem. . . . . . . . . . . . 548 6 Incremental solution .......................................... 550 7 Calculation of results ......................................... 551 References ..................................................... 553
Authors
Adachi T. Kyoto University, Dept. of Civil Engineering Construction Engineering Lab. Sakyo, Kyoto, 606-8501, Japan Tel.: +81-75-753-5106 Fax: +81-75-753-5104 e-mail: [email protected]
Amorosi A. Universita degli Studi di Roma "La Sapienza" Dip. di Ingegneria Strutturale e Geotecnica Via Monte d'Oro 28 1-00186 Roma, Italy Tel.: +39/06/49919611 Fax: +39/06/6878923 e-mail: [email protected]
Bauer E. TU Graz Institut fi.ir Mechanik Kopernikusgasse 24 A-801O Graz, Austria Tel.: +43/316/873-7148 Fax: +43/316/873-7641 e-mail: [email protected]
de Borst R. Delft University of Technology Faculty of Aerospace Engineering NL-2600 NL-GA Delft, The Netherlands P.O. Box 5048 Tel.: +3115 2785464 Fax: +31 15 2611465 e-mail: [email protected]
Cambou B. Ecole, Centrale de Lyon Departement de Mecanique des Soli des UMR C5513 36 avenue Guy de CoIlongue, B.P. 163 F-69131 EcuIly Cedex, France Tel.: +33/472186000 Fax: +33/472189144 e-mail: [email protected]
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Chambon R Institut National Poly technique de Grenoble Laboratoire 3S - CNRS B.P.53 F-38041 Grenoble Cedex 9, France Tel.: +33/476825 169 Fax: +33/476827000 e-mail: [email protected]
Chang Ching S. University of Massachusetts Amherst College of Engineering Department of Civil and Environmental Engineering Box 5205, Marston Hall 30 Amherst, Massachusetts 01003-5205 Tel: (413) 545-5401' Fax: (413) 545-2840
Chaze M. Ecole, Centrale de Lyon Departement de Mecanique des Solides UMR C5513 36 avenue Guy de Collongue, B.P. 163 F-69131 Ecully Cedex, France e-mail: [email protected]
Cudmani R Universitat Karlsruhe Institut fUr Boden- und Felsmechanik Postfach 6980 D-76128 Karlsruhe, Germany Tel.: +49/721/608-3279 Fax: +49/721/696096 e-mail: [email protected]
Darve F. Institut National Poly technique de Grenoble Laboratoire 3S - CNRS B.P.53 F-38041 Grenoble Cedex 9, France Tel.: +33/476825276 Fax: +33/476827000 e-mail: [email protected]
Dedecker F. Ecole, Centrale de Lyon Departement de Mecanique des Solides UMR C5513 36 avenue Guy de Collongue, B.P. 163 F -69131 Ecully Cedex, France e-mail: [email protected]
Doanh T. Ecole Nationale des Travaux Publics de l'Etat Dept. Genie Civil et Batiment Rue Maurice Audin F-69518 Vaulx-en-Velin, France Tel.: +33/472 047 072 Fax: +33/472 047 156 e-mail: [email protected]
di Prisco C. Politecnico di Milano Dipartimento 1ngeneria Strutturale Piazza L. Da Vinci 32 1-20133 Milano, Italy Tel.: +39/02/2399-4298 Fax: +49/02/2399-4220 e-mail: [email protected]
Gudehus G. U ni versi tiit Karlsruhe Institut fur Boden- und Felsmechanik Postfach 6980 D-76128 Karlsruhe, Germany Tel.: +49/721/608-2221 Fax: +49/721/696096 e-mai1:[email protected]
Heeres O. Delft University of Technology Faculty of Civil Engineering P.O.Box 5048 NL-2600 Delft, The Netherlands Tel.: +31/15/2784856 Fax: +31/15/2611465 e-mail: [email protected]
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Herle I. Academy of Sciences of the Czech Republic Institute of Theoretical and Applied Mechanics Prosecka 74 19000 Praha 9, Czech Republic Tel.: +42/02/882334 Fax: +42/02/884634 e-mail: [email protected]
Houlsby G.T. University of Oxford Department of Engineering Science Parks Road Oxford OX1 3PJ, UK Tel: +44 1865 2 73138 Fax: +44 1865 2 83301 e-mail:[email protected]
Imposimato S. Politecnico di Milano Dipartimento Ingeneria Strutturale Piazza Leonardo da Vinci 32 1-20133 Milano, Italy Tel.: +39/02/2399-4274 Fax: +39/02/2399-4220 e-mail: [email protected]
Kavvadas M. Department of Civil Engineering National Technical University of Athens 42 Patission St., Athens GR-10682, Greece Tel: +30-1-7723412 Fax: +30-1-7723428 e-mail: [email protected]
Kolymbas D. Universitiit Innsbruck Institut fUr Geotechnik und Tunnelbau Techniker Str. 13 A-6020 Innsbruck, Austria Tel.: +43/512/507-6670 Fax: +43/512/507-2996 e-mail: [email protected]
Lavrikov S. Independent Siberian University ul. Sibirjakov-Gvardeitsew 27-69 630048 Novosibirsk, Russia Tel.: +7/3832/903531 Fax: +7/3832/903531 e-mail: [email protected]
Marcher Th. Universitat Stuttgart Institut fUr Geotechnik Postfach 801140 D-70511 Stuttgart, Germany Tel.: +49/711/685-3776 Fax: +49/711/685-2439 e-mail: [email protected]
Miihlhaus H.-B. Centre for Rock Mechanics CSIRO Division of Exploration and Mining PO BOX 437, Nedlands, WA 6009, Australia Tel.: +61/8/93898421 Fax: +61/8/9389 1906 e-mail: [email protected]
Muir-Wood D. University of Bristol Dpt. of Civil Engineering Queens Building, University Walk GB- Bristol BS8 1 TR, United Kingdom Tel.: +44/117/928-7706 Fax: +44/117/928-7783 e-mail: [email protected]
Nova R. Politechnico di Milano Dipartimento Ingeneria Strutturale Piazza L. Da Vinci 32 1-20133 Milano, Italy Tel.: +39/02/2399-4232 Fax: +39/02/2399-4220 e-mail: [email protected]
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Nubel K. Universitat Karlsruhe Institut fur Boden- und Felsmechanik Postfach 6980 D-76128 Karlsruhe, Germany Tel.: +49/721/608-3275 Fax: +49/721/696096 e-mail:[email protected]
OkaFo Department of Civil Engineering, Division of Soil Mechanics Graduate school of Engineering Kyoto University Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan Tel.: 81+75+753+5084 Fax.: 81+75+753+5086 e-mail: [email protected]
Potts D.M. Imperial College Dpt. of Civil and Environmental Eng. Soil Mechanics Section GB- London SW7 2BU, United Kingdom Tel.: +44/171/594-6084 Fax: +44/171/594-6150 e-mail: [email protected]
Puzrin A. Technion - Israel Institute of Technology Faculty of Civil Engineering Geotechnical Department Haifa 32000, Israel Tel.: +972/4/8292269 Fax: +972/4/8237149 e-mail: [email protected]
Roguiez X. Institut National Poly technique de Grenoble Laboratoire 3S - CNRS B.P.53 F-38041 Grenoble Cedex 9, France Tel.: +33/476827 045 Fax: +33/476827 000 e-mail: Xavier [email protected]
Revuzhenko A. Independent Siberian University ul. Sibirjakov-Gvardeitsew 27-69 630048 Novosibirsk, Russia Tel.: +7/3832/903531 Fax: +7/3832/903531 e-mail: [email protected]
Sakaguchi H. CSIRO Division Exploration and Mining 39 Fairway (PO BOX 437) Nedlands, WA 6009, Australia Tel.: +61/8/9389-8421 Fax: +61/8/9389-1906 e-mail: [email protected]
Suiker A.S.J. Delft University of Technology Faculty of Civil Engineering PO Box 5048 NL-2600 NL-GA Delft, The Netherlands Tel.: +31/15/2782731 Fax: +31/15/2611465 e-mail: [email protected]
Tamagnini C. Universita degli studi di Perugia Istituto di Ingegneria Ambientale Strada S. Lucia, loco Canetola 1/ A-6 1-06125 Perugia, Italy Tel.: +39/075/5852763 Fax: +39/075/5852756 e-mail: [email protected]
Thornton C. Aston University; School of Engineering & Applied Science Civil & Mechanical Engn. Division Aston Triangle GB- Birmingham B4 7ET, United Kingdom Tel.: +44/121/3593611 ext. 4364 Fax: +44/121/333 3389 e-mail: [email protected]
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Vardoulakis 1. National Technical University of Athens Dept. of Eng. Science; Sect. of Mechanics 5 Heroes of Poly technion A venue GR-157 00 Athen, Greece Tel.: +30/1/772-1217 Fax: +30/1/772-1302 e-mail: [email protected]
Vermeer P. A. Universitiit Stuttgart Institut fur Geotechnik Pfaffenwaldring 35 D-70569 Stuttgart, Germany Tel.: +49/711/685-2436 Fax: +49/711/685-2439 e-mail: [email protected]
Viggiani C. Universita di Napoli Federico II Istituto di Geotecnica, Facolta di Ingegneria Via Claudio, 21 I - 80125 Napoli, Italy Tel.: +39/81/7693468 e-mail: [email protected]
Viggiani G. Laboratoire Sols Solides Structures B.P.53 F-38041 Grenoble Cedex 9, France Tel.: +33/476827038 Fax: +33/476827000 e-mail: [email protected]
von Wolffersdorff P.-A. (Address valid from November 1999) Baugrund Dresden Ingenieurgesellschaft mbH Paul-Schwarze-Strasse 2 D-01097 Dresden, Germany Tel.: +49/351/78241350 Fax: +49/351/8030786 e-mail:[email protected]
WuW. Lahmeyer Int. Friedberger Str. 173 D-61118 Bad Vilbel, Germany Tel.: +49/6101/55-1177 e-mail: [email protected]
Zdravkovic L. Imperial College Dpt. of Civil and Environmental Eng. Soil Mechanics Section GB- London SW7 2BU, United Kingdom Tel.: +44/171/594-6076 Fax: +44/171/594-6150 e-mail: [email protected]
Zhang F. Dept. of Civil Engineering Faculty of Engineering Gifu University Yanagido 1-1, Gifu, 501-1193, Japan Tel. : +81-58-2932465 Fax:+81-58-2301891 e-mail: [email protected]
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