Table Of ContentCISM COURSES AND LECTURES
Se ries Editors:
The Rectors of CISM
Sandor Kaliszky - Budapest
Mahir Sayir - Zurich
Wilhelm Schneider - Wien
The Secretary General of CISM
Giovanni Bianchi - Milan
Executive Editor
Carlo Tasso - Udine
The series presents lecture notes, monographs, edited works and
proceedings in the field of Mechanics, Engineering, Computer Science
and Applied Mathematics.
Purpose of the series is to make known in the international scientific
and technical community results obtained in some of the activities
organized by CISM, the International Centre for Mechanical Sciences.
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES
COURSES AND LECTURES - No. 357
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MODERN ISSUES
IN NON-SATURATED SOlLS
EDlTEDBY
A. GENS
TECHNICAL UNIVERSITY OF CATALUNYA
P.JOUANNA
UNIVERSITY OF MONTPELLIER II
B.A. SCHREFLER
UNIVERSITY OF PADUA
SPRINGER-VERLAG WIEN GMBH
Le spese di stampa di questo volume sono in parte coperte da
contributi deI Consiglio Nazionale delle Ricerche.
This volume contains 118 illustrations
This work is subject to copyright.
All rights are reserved,
whether the whole or part of the material is concemed
specifically those of translation, reprinting, re-use of illustrations,
broadcasting, reproduction by photocopying machine
or similar means, and storage in data banks.
© 1995 by Springer-Verlag Wien
Original1y published by Springer-Verlag Wien New York in 1995
In order to make this volume available as economically and as
rapidly as possible the authors' typescripts have been
reproduced in their original forms. This method unfortunately
has its typographical limitations but it is hoped that they in no
way distract the reader.
ISBN 978-3-211-82783-3 ISBN 978-3-7091-2692-9 (eBook)
DOI 10.1007/978-3-7091-2692-9
PREFACE
This monograph is a revised version oJthe notesJor the Advanced School
lectures given at the International Centre Jor Mechanical Sciences in Udine,
September 19-23, 1994. The aim oJthe course was to provide a review oJ some
oJ the most significant achievements in research on non-saturated soUs, a
material oJ apre-eminent importance in civU engineering, agriculture and
environmental engineering.
A phenomenological point oJ view based on Jictitious continuity oJ the
different constituents is adopted throughout this work, even if reJerences to
lower scale considerations may be made in different parts oJ the text. The
different steps oJ the modelling oJ non-saturated soUs are reviewed in Chapters
1 to 4. Chapters 5 to 11 are devoted to the analysis oJ a number oJ case studies.
In the introductory Chapter 1, non-saturated soUs are considered in the
broader context oJ heterogeneous media. Balance, equilibrium and non-
equilibrium equations are presented using a generalized approach and in the
light oJ the most recent achievements in irreversible thermodynamics. This
approach covers all possible coupled phenomena in a single coherent model but
leads to a complex set oJ equations. In conclusion, an automatic procedure is
proposed Jor overcoming this complexity.
The behaviour laws proposed in Chapter 2 are based on the concept oJ
yield surJaces as classically used in saturated soUs. These laws are Jirst
extended to the case oJ non-saturated soUs and then to non-isothermal
conditions. The effects oJ non-saturation and temperature are incorporated in a
generalized Cam-clay model, the simplest member oJ the Jamily oJ critical state
Jormulations. Some selected comparisons between model predictions and
experimental results are presented.
Examples oJ experimental studies in the laboratory Jor studying coupled
phenomena are presented in Chapter 3.
Numerical methods Jor solving complex thermo-hydro-mechanical
coupling equations are presented in Chapter 4. Basic concepts and different
strategies Jor discretization are examined and different numerical techniques
are described. Fundamental problems oJ consistency, stability and convergence
in linear and non-linear situations are discussed at length using a particular set
oJ governing equations and a finite element method with estimation oJ numerical
errors.
Finally, a broad review of applications covers domains such as water
resources, road engineering, heat storage and consolidation, embankment
dams, seismic behaviour and strain localisation in partially saturated soil,
radioactive disposal and natural thermal reservoir.
Acknowledgements
The presentation of this edited series of lectures is the fruit of team work
by the various authors, first within G.R.E. C. O. "Geomateriaux europeen" and
then in the European network A.L.E.R.T., research institutions founded and
managed at the instigation of Professor Darve, aided efficiently by his advisers
Messrs Hicher and Reynouard and with the institutional backing from the
C.N.R.S.
It would not have been possible to complete this joint research work
without the facilities provided by the International Centre for Mechanical
Sciences in Udinefor both the organisation ofthe lectures and the publication of
the monograph. The editors warmly thank all the organisers of the Centre, and
especially the Rector, Professor Kaliszky, for their competence and hospitality.
Finally the constant help of M-A. Abellan has been deeply appreciated
throughout the course and during preparation of the final manuscript.
For all the authors,
A. Gens
P.Jouanna
B. A. Schrefler
CONTENTS
Page
Preface
Chapter 1
Generalized Approach to Heterogeneous Media
by P. Jouanna and M-A. Abellan ................................................................... 1
Chapter2
Constitutive Laws
by A. Gens .................................................................................................. 129
Chapter 3
Experimental Studies
by D. Bovet, P. Jouanna, E. Recordon and C. Saix ................................... 159
Chapter4
Numerical Solutions of Thermo-Hydro-Mechanical Problems
by B.A. Schrefler and L. Simoni ................................................................. 213
Chapter 5
Forced and Natural Convection
by D. Bovet and E. Recordon .................................................................... 277
Chapter 6
Large Scale Road Test
by E. Recordon .......................................................................................... 283
Chapter7
Non Saturated Consolidation Under Thermo-Hydro-Mechanical Actions.
An in Situ Heat Storage Facility in a Clayey Silt
by M-A. Abellan, P. Jouanna and C. Saix ................................................. .301
Chapter 8
Construction and Impoundement of an Earthdam.
Application ofthe Coupled Flow-Deformation Analysis
of Unsaturated Soils
by E. Alonso and F. Batlle ......................................................................... 357
Chapter 9
Large Strain Static and Dynamic Hydro-Mechanical Analysis of
Porous Media
by E.A. Meroi and B.A. Schrefler ............................................................... 397
Chapter 10
Importance of Boundary Conditions. A Radioactive Storage Case
by L. Simoni ............................................................................................... 449
Chapter 11
Regional Problems:
Vertically Averaged Modelling. Abano Thermal Problem
by L. Simoni ............................................................................... ................. 461
Annex
Some Phenomenological Models of Polyphasic Soils
by D. Bovet ................................................................................................. 475
Chapter 1
GENERALIZED APPROACH TO HETEROGENEOUS MEDIA
P. Jouanna and M·A. Abellan
University of Montpellier 11, Montpellier, France
ABSTRACT
This first chapter is devoted to the description of a coherent and synthetic generalized
phenomenological approach to heterogeneous media, which overcomes former difficulties
and incoherences. Generalized balance equations are written following an arbitrary virtual
movement, independent of the movement of the matter. Classical state relations are extended
to pseudo-state relations to take hysteretic phenomena into account. Non-equilibrium
relations deduced from the analysis of the entropy source include physico-chemical reactions
and are revised according to the generalized approach. Linking phenomenological variables
and physical variables is performed by complementary balance relations. Finally a
systematic guide is presented for handling such a complex modelling, with a rationallisting
of variables and associated relations. It covers all couplings between complex thermo-hydro-
mechanical and physico-chemical phenomena as encountered in modern engineering
practice.
2 P. Jouanna and M-A. Abellan
1.0 INTRODUCTION
Situation of Chapter 1
This first chapter is a guide for modelling complex situations as encountered in modem
engineering practice.
_The physics of complex media covers different chemical species within a given material
domain submitted to coupled stresses related to physico-chemical, mechanical and heat
exchanges. For instance, rock, water, air, and various other chemical species like oxides,
~1ts, etc. exist in a soil. These chemical species can occur in different phases. The most
common example is water which can exist as ice, liquid or vapour. A constituent will be
defined as a chemical species in a given phase. For example, liquid water and-water vapour
are considered as two different constituents.
The study of ilcterogeneous media can be envisaged at different scales from atomic to
macroscopic. Distinctions can be made between three levels of modelling:
• the first level consists of describing phenomena as they appear under a microscope. Up to
now, this description is essentially visual and modelling at this scale is not a common
practice. This level is beyond the scope of the present study;
• a second point of view consists of awarding average physical properties to each
constituent, such as average specific mass, partial press ure, etc. within the volume occupied
by each constituent in an elementary representative volume element. Such average physical
{>roperties will be assumed to be known through the use of techniques such as
homogenization, averaging, ete.;
• finaIly, the phenomenological point of view assumes the matter of each constituent to be
extended to the total volume occupied by the heterogeneous medium, leading to a fictitious
continuum where cIassic mathematical tools can be used. The phenomenological approach,
discussed in the present chapter, is used in most engineering applications, as shown in
Chapters 5 to 12.
State of art and questions
(i) The first comprehensive study of heterogeneous media was performed by Truesdell &
Toupin [1960] as an extension of the cIassical field theory developed for homogeneous
media. In this study, the kinematics of heterogeneous media was based on the barycentrie
velocity used as a referenee and thus was essentially adapted to mixtures where different
eonstituents have velocities of the same order of magnitude. When the baryeentrie velocity
looses its physical meaning, for example in the presence of fluids and one porous solid, the
movement of the fluids can be referred to the solid. However, new difficulties arise when
different solids are present or when the solid chosen as a reference disappears due to some
physico-chemical reaction, etc.
(ii) Moreover, incoherences appear in the definition of total stresses or fluxes, when
constituents have different velocities. These incoherences can be hidden by different
misleading procedures, such as working on the total medium only or defining the so-called
"inner" parts of stresses or fluxes ignoring diffusion terms.
