Porous Media: Theory and Experiments

330 Pages·1999·10.124 MB·English

by  T. Wu, K. Hutter (auth.), R. De Boer (eds.)

POROUS MEDIA: THEORY AND EXPERIMENTS
POROUS MEDIA:
THEORY AND
EXPERIMENTS
Edited by
R.DEBOER
University of Essen, Germany
Reprinted from Transport in Porous Media
Volume 34, Nos. 1-3 (1999)
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-5939-8 ISBN 978-94-011-4579-4 (eBook)
DOI 10.1007/978-94-011-4579-4
Printed on acid-free paper.
All Rights Reserved
© 1999 by Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1999
Softcover reprint of the hardcover Ist edition 1999
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
Table of Contents
Preface 1-2
T. WU and K. HUTTER I On the Role of the Interface Mechanical Interaction
in a Gravity-Driven Shear Flow of an Ice-Till Mixture 3-15
S. ARNOD, M. BATTAGLIO, N. BELLOMO, D. COSTANZO, R.
LANCELLOTTA and L. PREZIOSI I Finite Deformation Models and
Field Performance 17-27
A. A. GUBAIDULLIN and O. YU. KUCHUGURINA I The Peculiarities of
Linear Wave Propagation in Double Porous Media 29-45
P. DE BUHAN and L. DORMIEUX I A Micromechanics-Based Approach to
the Failure of Saturated Porous Media 47-62
S. SOREK, A. LEVY, G. BEN-DOR and D. SMEULDERS I Contributions to
Theoretical/Experimental Developments in Shock Waves Propagation
in Porous Media 63-100
ANJANI KUMAR DlDWANIA and REINT DE BOER I Saturated Compress
ible and Incompressible Porous Solids: Macro-and Micromechanical
Approaches 101-115
INNA YA. EDELMAN I Wave Dynamics of Saturated Porous Media and
Evolutionary Equations 117-128
J. M. HUYGHE and J. D. JANSSEN I Thermo-Chemo-Electro-Mechanical
Formulation of Saturated Charged Porous Solids 129-141
W. Y. GU, W. M. LAI and V. C. MOW I Transport of Multi-Electrolytes in
Charged Hydrated Biological Soft Tissues 143-157
W. EHLERS and W. VOLK I Localization Phenomena in Liquid-Saturated and
Empty Porous Solids 159-177
W. EHLERS and G. EIPPER I Finite Elastic Deformations in Liquid-Saturated
and Empty Porous Solids 179-191
S. DIEBELS I A Micropolar Theory of Porous Media: Constitutive Modelling 193-208
ZHANFANG LIU and REINT DE BOER I Propagation and Evolution of Wave
Fronts in Two-Phase Porous Media 209-225
S. J. KOWALSKI and A. RYBICKI I Computer Simulation of Drying Optimal
Control 227-238
vi TABLE OF CONTENTS
S. J. KOWALSKI and G. MUSIELAK I Deformations and Stresses in Dried
Wood 239-248
REINT DE BOER and JOACHIM BLUHM I Phase Transitions in Gas- and
Liquid-Saturated Porous Solids 249-267
UDO DUNGER, HERBERT WEBER and HANS BUGGISCH I A Simple
Model for a Fluid-Filled Open-Cell Foam 269-284
STEFAN BREUER I Quasi-Static and Dynamic Behavior of Saturated Porous
Media with Incompressible Constituents 285-303
PASQUALE GIOVINE I A Linear Theory of Porous Elastic Solids 305-318
M. CIESZKO and J. KUBIK I Derivation of Matching Conditions at the Contact
Surface Between Fluid-Saturated Porous Solid and Bulk Fluid 319-336
1
Preface
The EUROMECH Colloquium 366, 'Porous Media - Theory and Experiments'
was held at the Bildungszentrum fiir die Entsorgungs-und Wasserwirtschaft GmbH
B·E·W, Essen, Germany, from 23 to 27 June 1997.
The goal of EUROMECH 366 was the presentation of recent findings in the
macroscopic porous media theory (mixture theory restricted by the volume fraction
concept) concerning general concepts and special investigations in the theoretical
as well as the experimental field. Herein, numerical results requiring new solution
strategies were also to be included. Moreover, foundations of fundamental state
ments in the macroscopic porous media theory (e.g. the effective stress principle
for incompressible and compressible constituents by micromechanic investigations)
were welcome.
Emphasis was placed upon the need to bring together scientists from various
branches where porous media theories playa dominant role, namely from theoretical
mechanics, agriculture, biomechanics, chemical engineering, geophysics and soil
mechanics as well as from petroleum energy and environmental engineering.
More than 80 people from 12 different countries expressed their interest in the
Colloquium, and finally, 58 took part in the meeting presenting 42 papers. Among
the talks were seven principal lectures given by leading scientists in the a.m. fields
invited by the organizers.
As Chairman of EUROMECH 366, I would like to thank the co-chairmen and all
of my co-workers from the Institute of Mechanics, FB 10, University of Essen, for
their help in organizing the Colloquium, in particular, Dr.-Ing. W. Walther, Priv.-Doz.
Dr.-Ing. J. Bluhm and Dipl.-Ing. S. Breuer. Moreover, I would like to express my
gratitude to the sponsors who financially supported the meeting - Fordervereinigung
fiir die Stadt Essen e.V., A. Sutter GmbH, Essen, Robert-Bosch-Stiftung, Stuttgart,
Bildungszentrum fUr die Entsorgungs- und Wasserwirtschaft GmbH B·E·W, Essen,
Universitat Essen.
The Editor of Transport in Porous Media kindly offered to publish a special issue
of the Journal with selected new papers reflecting the contents of the talks at the
conference. Originally, more than 30 authors intended to contribute to the special
issue. After the peer-reviewing process, 20 articles were approved for publication. It
is my wish to thank the reviewers for their careful examination of the manuscripts.
The large number of accepted papers is a testament to the high quality of all those
submitted.
This special issue of Transport in Porous Media with its 20 articles will provide,
without any doubt, a valuable overview of recent developments in the field of porous
2 PREFACE
media, on the theoretical as well as the experimental level, and it will be helpful in
the realization of a consistent macroscopic porous media theory.
R.DEBOER
Chairman
3
On the Role of the Interface Mechanical Interaction in a
Gravity-Driven Shear Flow of an Ice-Till Mixture
T. WU and K. HUTTER
Department ofM echanics, Technische Universitat Darmstadt, Hochschulstraj3e 1, D-64289
Darmstadt, Germany
(Received: 18 December 1996; in final form: 8 October 1997)
Abstract. The ice-till mixtures at the base of glaciers and ice sheets play a very important role
in the movement of the glaciers and ice sheets. This mixture is modelled as an isothermal flow
which is overlain by a layer of pure ice. In this model, ice is treated as usual as a very viscous fluid
with a constant true density, while till, which is assumed to consist of sediment and bound (that is,
moving with the sediment) interstitial water and/or ice, is also assumed in a first approximation to
behave such as a fluid. For an isothermal flow below the melting point the water component can be
neglected. Therefore, only the mass and momentum balances for till and ice are needed. To complete
the model, no-slip and stress-free boundary conditions are assumed at the base and free-surface,
respectively. The transition from the till-ice mixture layer to the overlying pure ice layer is idealized
in the model as a moving interface representing in the simplest case the till material boundary, at
which jump balance relations for till and ice apply. The mechanical interactions are considered in the
mixture basel layer, as well as at the interface via the surface production. The interface mechanical
interaction is supposed to be only a function of the volume fraction jump across the interface. In the
context of the thin-layer approximation, numerical solutions of the lowest-order form of the model
show a till distribution which is reminiscent to the ice-till layer in geophysical environment.
Key words: ice-till mixture, thermodynamic consistent formulation, gravity shear flow, interface
interaction, numerical solutions.
1. Introduction
Observations in bore-hOles drilled into glaciers till the base (Engelhardt et al., 1978)
have shown that, close to the rock bed, the glacier ice is increasingly contaminated
by sediment. In the extreme case, a basal layer consisting predominantly of sediment
and bound (that is, moving with the sediment) water forms a so-called till, with up
to approximately 85% till possible (Wu et al., 1996), the remainder consisting of
ice, free water and/or possibly cavities. The sediment part of this till is likely eroded
from the basal rock surface by the moving ice and incorporated into the near-bottom
ice as the glacier or ice sheet moves. Assuming, on the scale of the entire base of a
glacier or ice sheet, that the free water constituent is negligible, a glacier or ice sheet
can be idealized as consisting of a relatively thick pure ice layer riding on top of a
relatively thin ice-till mixture layer at the base.
R. Boer (ed.), Porous Media: Theory and Experiments
© Kluwer Academic Publishers 1999
4 T. WU AND K. HUTTER
In general, the sediment part of the till consists of various-sized particles (for
example clay, silt, sand, gravel, boulders, and so on) which together constitute a
granular material. In a first approximation treated in this work, we ignore the
(higher-order) effects due to the volume-fraction-gradient dependence of the till
stress tensor, and treat the till constituent as viscous. In other words, the effects of
volume fraction gradients and friction between the sediment grains on the stress
are assumed negligible, something that is perhaps in fact not very realistic for high
sediment concentrations; on the other hand, interstitial water could have a lubricating
effect, such that the effect of intergranular friction is reduced. Note in addition that
the study of creeping flow of soil containing various amounts of water has shown
that the assumption of viscous behaviour can account for observed deformations
both in the laboratory and in the field (Hutter and Vulliet, 1985; Vulliet and Hutter,
1988a, b). On this basis, we follow Hutter et al. (1994), and Svendsen et al. (1996) in
treating the ice-till system as a mixture of two constant true density viscous fluids. In
addition, we assume for simplicity that this mixture is saturated, that is, the mixture
volume is always equal to that of till plus ice in the mixture, that is, no cavities or
voids arise during the flow. Analogous to the constraint of constant density in a fluid,
this constraint is maintained by a pressure, the so-called saturation pressure.
Since the motion of the layer is extremely slow, Stokes flow is assumed. The till
and ice momentum balances reduce then to force balances between the constituent
stresses, gravitation and the momentum exchange forces. The boundary conditions
at the base are assumed to be no-slip for both constituents, while the free surface
is assumed to be stress free. As such, we neglect the process of entrainment of
sediment at the base into the flow, and concentrate on the mechanical aspects of
the basal layer. The interface between the till and overlying pure ice moves with
the till material velocity, and is nonmaterial with respect to the ice. As such, the
jump balance relations for both till and ice apply at this interface. In addition, as
recognized by Hutter et al. (1994), ice and till can interact mechanically with each
other at this interface, just as they do via, for example, drag forces in the bulk. The
interface mechanical interactions were introduced into this model. Using the constant
mechanical interaction Wu et al. (1996) show that it is predominantly the thickness
of the basal (mixture) layer that is influenced by the ice-till momentum interaction. In
the current work the interface mechanical interaction is assumed to be only dependent
on the volume fraction jump at the interface. Using a relatively simple form of this
interaction, we investigate qualitatively the effect of this interface interaction between
ice and till on the mechanical behaviour and thickness of the lower layer, modelled
as a till-ice mixture.
To begin with, the governing field equations, along with boundary and transition
conditions, are formulated in Section 2. Next, the mechanical interactions in the
bulk as well as at the interface are introduced into the model (Section 3). Mter that,
a scaling analysis for gravity-driven shear flow down an inclined curved surface
is carried out and the governing equations are then simplified (Section 4). Lastly,
numerical solutions of the lowest- order form of the resulting model are obtained and
THE ROLE OF THE INTERFACE MECHANICAL INTERACTION 5
their implications for the mechanical behaviour and thickness of the basal layer are
discussed in Section 5.
2. Governing Equations and Boundary Conditions
Consider the isothermal flow of an ice-till mixture overlain by a pure ice layer down
an inclined plane (Figure 1). As discussed above, the lower layer is modelled as a
mixture of two very viscous, constant true density fluids, so that the constituents true
=
density Pa is constant and the partial density Pa Va Pa varies only with the till
volume fraction Va, where the index a is T for till and I for ice. In this case the volume
fraction Va is the independent variable, instead of the partial density. Assuming no
mass exchange between ice and till, the mass and momentum balances for till and
ice in the mixture layer then take the forms
-aVa + .
at d1V(va va) = 0,
(2.1)
div Ta + Pa Va g + rna = O.
Here, Va and T a represent the partial velocity and constituent partial stress for till
and ice with the index T and I, respectively; g is the vector of gravity acceleration.
The mechanical interaction force between till and ice can be simply written as rnT =
-rnI = rn. Since Stokes flow was assumed, the accelaration term in the momentum
balance was neglected. In addition, the lower mixture layer is assumed to be saturated,
i.e.,
VT+VI=1. (2.2)
In other words, we assume that no 'cavities' or 'voids' can arise in this layer
during its flow. Defining V = VT, we then have VI = 1 - v. The relation (2.2) is
a saturation constraint which leads to the loss of an independent variable, one of
the volume fractions. Such a constraint is analogous to the classical constant density
Figure 1. Two-dimensional model geometry. YR, YI, and )IF represent the positions of the
base, interface, and free surface of the system as a function of x and t.