Theory of Porous Media: Highlights in Historical Development and Current State

625 Pages·2000·17.172 MB·English

by  Professor Dr.-Ing. Reint de Boer (auth.)

Reint de Boer
Theory of Porous Media
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Reint de Boer
Theory of Porous Media
Highlights in Historical
Development and Current State
With 176 Figures
Springer
Professor Dr.-Ing. Reint de Boer
o. Professor fUr Mechanik
an der Universitat Essen
Institut fur Mechanik
Fachbereich 10 - Bauwesen
D-45117 Essen
URL: http://mechanik.bauwesen.uni-essen.de/pup.htrnl
EMAIL: [email protected]
ISBN-I3: 978-3-642-64062-9 Springer Verlag Berlin Heidelberg New York
Library of Congress Cataloging-in-Publication Data
Boer, Reint de:
Theory of porous media: Highlights in Historical Development and
Current State I Reint de Boer. - Berlin ; Heidelberg; New York;
Barcelona; Hong Kong; London; Milano; Paris; Singapore; Tokyo;
Springer, 2000
ISBN-I 39:78-3-642-64062-9 cISBN-13:978-3-642-59637-7
DO!: I 0.10 07/978-3-642-59637-7
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Preface
Porous media theories play an important role in many branches of engineering,
including material science, the petroleum industry, chemical engineering, and
soil mechanics, as well as in biomechanics. When, in the early 1980s, investi
gations into these theories were begun at the University of Essen, it was soon
recognized that some known theories were incomplete, unclear, and even parti
ally incorrect. The original plan to write a book on the theory of porous media
was quickly abandoned. The chief reason for this was the completely insufficient
constitutive theory of granular and brittle materials (of which most porous so
lids consist) within the framework of the geometrically-linear and non-linear
theory. Therefore, a program was embarked upon in order to develop a consi
stent theory for the complex field of liquid and/or gas saturated porous solids.
This program initially included two strategies.
The first strategy involved the creation of clearly defined mechanical and
thermodynamic terms for saturated porous bodies, and the description of the
material-independent fundamental equations of these media (i.e., the kinema
tics of deformations, the balance equations, and the entropy inequality), avoi
ding any contradictions. It was revealed that, for this purpose, only elements of
the mixture theory, restricted by the concept of volume fractions, were suitable,
because they proceeded from the axioms of mechanics and thermodynamics
and applied them to the individual constituents, under consideration of all cou
pling mechanisms as well as the bulk body. Existing classical models - for
example, the models of K. von Terzaghi and M.A. Biot - seem to have been
developed more intuitively. They are not derived from the basic equations of
mechanics, contain partially unclear definitions, neglect important mechanical
quantities in certain parts, and sometimes introduce the coupling terms bet
ween the constituents in an obscure way. These models do not admit further
scientific developments; indeed, they hinder them.
The second strategy involved the development of consistent constitutive
equations, in particular for the porous solid in the plastic range. In this range,
immense difficulties arose in describing material behavior. "Natural" porous bo
dies, such as rock and soil, as well as artificially created ones, such as concrete
and sinter metals, consist of granular and brittle materials. In comparison to
ductile materials, these materials, known as frictional materials, show a distinct
VIII Preface
dependence of the material behavior on the hydrostatic pressure in the plastic
range. The influence of hydrostatic pressure causes new and different effects,
which are unknown in the plasticity theory of ductile materials and which make
the creation of a consistent plasticity theory difficult. It is true that, in the early
1980s, extensive investigations were already being made into the material beha
vior of frictional materials, in particular in experimental work. However, these
investigations were mainly restricted to the development of failure functions
and flow rules within the framework of the geometrically-linear theory for one
component materials. Publications on the hardening of plastically-deformed
granular and brittle materials referred almost entirely to isotropic hardening.
The effect of kinematic hardening, in experiments confirmed and supported by
thermodynamic investigations, was dealt with in only a few papers. Thus, it was
recognized that, in the constitutive theory of frictional materials, a long-awaited
demand existed, in particular a demand for the embedding of existing results
into the general porous media theory.
Moreover, in the 1980s, attention was almost exclusively focused on incom
pressible porous media. It took a long time to also develop a theory for porous
media with individual compressible constituents.
During the processing of both strategies, it became evident that a third stra
tegy was necessary, namely the investigation of the historical development of the
porous media theory. Such investigations are not only interesting from a purely
historical point of view, they also clarify issues and complicated relations that
exist in a theory as complex as that of porous media, and intensify the search for
the recognition of specific and important mechanical and thermodynamic ef
fects which can occur in saturated porous bodies. Finally, historical studies give
us access to several published contributions which have been almost completely
ignored and forgotten.
The consistent treatment of the material-independent fundamental equati
ons of the theory of porous media, the development of constitutive equations
for frictional materials in the elastic and plastic range, and the task of tracing
the historical development of porous media theory all involved a large amount
of effort during the 1980s through the first half of the 1990s on the part of
the mechanics group of the University of Essen, Germany. The results of these
intensive investigations are included in this book. Thus, for the first time, a
unique treatment of fluid-saturated porous solids is presented containing the
historical development of the corresponding theory, almost from its inception,
as well as the current state of the theory of porous media.
Many persons have supported me to enable me to write this book. I would
like to thank Dr. techno A. Lechner and Dipl.-Ing. E. Jiresch from the Archive of
the Technical University of Vienna for their cooperation. Mrs. Enerson and the
staff from the Norwegian Geotechnical Institute (N.G.I.) supported my work in
the Terzaghi Library in every respect.
Several colleagues have given me valuable hints concerning the theory of
porous media and its historical development. In particular, I would like to
Contents
1 Introduction 1
2 The Early Era 5
2.1 The Development of the Principles of Mechanics 6
2.2 The Dynamics of Rigid Bodies . . . . 12
2.3 The Theory of Ideal Fluids ..... . 16
2.4 Euler's Description of a Porous Body. 23
2.5 Coulomb's Earth Pressure Theory .. 25
2.6 Woltman's Contribution to the Porous Media Theory:
The Introduction of the Angle of Internal Friction
and the Volume Fraction Concept 31
2.7 Concluding Remarks. 45
2.8 Biographical Notes . 46
3 The Classical Era 69
3.1 Cauchy's Formulation of the Stress Concept . 70
3.1.1 Cauchy's Predecessors. 70
3.1.2 The Final Step ............ . 72
3.1.3 Biographical notes .......... . 75
3.2 The Development of the Linear Elasticity Theory . 78
3.2.1 Theoretical Molecular Formulations. 79
3.2.2 Continuum Mechanics Approach ..... 85
3.2.3 Completion of the Theory . . . . . . . . . 86
3.2.4 Some Solutions of the Fundamental Equations 89
3.2.5 Final Remarks . . . . . . . . . . . . . . . . . . 91
3.2.6 Biographical Notes .............. . 93
3.3 Discovery of Fundamental Laws (Delesse, Fick, Darcy) . 95
3.3.1 The Delessian Law. 96
3.3.2 Fick's Law ..... 97
3.3.3 Darcy's Law .. . . 99
3.3.4 Biographical Notes 101
XII Contents
3.4 The Development of the Theory of Viscous Fluids 102
3.4.1 Introduction: The Navier-Stokes Equations 102
3.4.2 .T he Historical Development of the Theory 103
3.4.3 Biographical Notes ............. 110
3.5 The Mohr-Coulomb Failure Condition and other Plasticity
Theory Studies . . . . . . . . . . . . . . . . . . . . . . . 112
3.5.1 w.J. Macquorn Rankine's Fundamental Failure
Condition for Granular Material. . . . . . . . . . . .. 113
3.5.2 O. Mohr's Contributions to the Determination
of the Elasticity and Failure Limits 118
3.5.3 Extension of the Plasticity Theory . 122
3.5.4 Biographical Notes . ....... . 132
3.6 Motion of Liquids in Rigid Porous Solids . 135
3.6.1 Motion of Liquids Through Narrow Tubes 136
3.6.2 Flow of a Liquid Through Porous Bodies
with Statistically-Distributed Pores 138
3.6.3 Application..... . ... 139
3.7 Foundation of the Mixture Theory. . . . . 140
3.7.1 Introduction............. 140
3.7.2 Stefan's Development of the Mixture Theory 141
3.7.3 Biographical notes. . . . . . . . 145
3.8 The Foundation of Thermodynamics. . . . . . . . . 146
3.8.1 Development in the Early Days ....... 147
3.8.2 The Achievements of Carnot (1796-1832) and
Clapeyron (1799-1864) . . . . . . . . . . . . . 149
3.8.3 Robert Mayer, the Discoverer of the Mechanical
Equivalent of Heat. . . . . . . . . . . . . . . . . 154
3.8.4 The Contributions of Mohr, Seguin, Colding, Holtzmann,
and Helmholtz. . . . . . . . . . . . . . . . . . . . 159
3.8.5 The Decisive Investigations of Joule . . . . . . . . 163
3.8.6 The Foundation of Thermodynamics by Clausius,
Rankine and Thomson . . . . . . . . . . . . . . . 164
3.8.7 Discussions on the Correct Form of the Mechanical
Theory of Heat and Further Developments 176
3.8.8 Biographical Notes ............. 178
4 The Modern Era 187
4.1 Discovery of Fundamental Effects of Liquid-Saturated
Rigid Porous Solids ........................ 188
4.2 The Treatment of the Liquid-Saturated Deformable Porous Solid
by von Terzaghi ....................... . .. 201
4.3 The Foundation of Modern Porous Media Theory by Fillunger 209
Contents XIII
4.4 The Tragic Controversy Between the Viennese
Professors Fillunger and von Terzaghi in 1936/37 213
4.5 The Further Development of the Viennese Affair
and in Soil Mechanics . . . . . . . . . . . . . 246
4.6 Biographical Notes . . . . . . . . . . . . . . . 260
4.7 The Followers of von Terzaghi and Fillunger:
Biot, Heinrich and Frenkel 284
4.7.1 Biot's Theory ............ . 285
4.7.2 Heinrich's Theory ......... . 297
4.7.3 Frenkel's Description of Moist Soil . 301
4.7.4 Further Developments ...... . 303
4.7.5 Biographical Notes ........ . 305
4.8 Further Development of the Elasticity and Plasticity Theories . 307
4.8.1 Elasticity Theory .............. . 307
4.8.2 Plasticity Theory .............. . 311
4.9 Modern Continuum Mechanics and Mixture Theory 318
4.10 Theories of Immiscible Mixtures . 321
5 Current State of Porous Media Theory 331
5.1 Introductory Remarks to Porous Media Theory . 331
5.2 The Volume Fraction Concept 332
5.3 Kinematics....... 336
5.4 Balance Equations . . . . . . . 345
5.4.1 Balance of Mass .... 345
5.4.2 Balance of Momentum and Moment of Momentum 347
5.4.3 Balance of Energy . . . . . . . . . . . . . . . 349
5.5 Entropy Inequality . . . . . . . . . . . . . . . . . . . 351
5.6 The Closure Problem and the Saturation Constraint 353
5.7 Principle of Virtual Work . . . . . . . . . 356
5.8 Constitutive Theory . . . . . . . . . . . . . . . . . . 358
5.8.1 Principle of Material Objectivity ...... . 359
5.8.2 The Introduction and Evaluation of the Entropy
Inequality for a General Binary Porous Medium Model 362
a) The Introduction and Evaluation of the Entropy
Inequality for a Binary Porous Medium Model with
Incompressible Constituents ........... 365
b) The Introduction and Evaluation of the Entropy
Inequality for a Binary Porous Model with
Compressible Constituents ............ 367