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330 Pages·1999·10.124 MB·English
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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.

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