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1999 | Buch

On the Role of the Interface Mechanical Interaction in a Gravity-Driven Shear Flow of an Ice-Till Mixture Kapitel lesen Erstes Kapitel lesen

Porous Media: Theory and Experiments

herausgegeben von: R. De Boer

Verlag: Springer Netherlands

Enthalten in: Professional Book Archive

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
On the Role of the Interface Mechanical Interaction in a Gravity-Driven Shear Flow of an Ice-Till Mixture
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.
T. Wu, K. Hutter
Finite Deformation Models and Field Performance
Abstract
This paper reports about the derivation of a fully nonlinear model characterized by finite deformations without smallness assumptions. The soil is assumed to be saturated, and no restrictions are introduced on the constitutive laws. Initial boundary value problems are formulated with reference to geotechnical problems, such as consolidation under own weight or sedimentation of solid particles in a quiescent fluid, and back-analyses of field performance of an embankment resting on a soft clay deposit.
S. Arnod, M. Battaglio, N. Bellomo, D. Costanzo, R. Lancellotta, L. Preziosi
The Peculiarities of Linear Wave Propagation in Double Porous Media
Abstract
The features of propagation of longitudinal and transverse waves (LW and TW) in fractured porous medium (FPM) saturated with liquid are investigated by methods of multiphase mechanics. The mathematical model of FPM accounting for inequality of velocities and pressures of liquid in pores and fractures, liquid mass exchange and nonstationary interaction forces is developed. Processes of monochromatic wave propagation are studied. The dispersion relation is obtained and the effect of model parameters on wave propagation is analysed. It is established that one transverse and three longitudinal waves propagate in FPM saturated with liquid. The fastest LW is a deformational wave and the two others are filtrational. Filtrational waves attenuate much stronger than deformational and transverse waves. Distinction of velocities and pressures in liquid in various pore systems provides an explanation for the existence of the two filtrational waves in porous medium with two different characteristic sizes of pores.
A. A. Gubaidullin, O. Yu. Kuchugurina
A Micromechanics-Based Approach to the Failure of Saturated Porous Media
Abstract
This contribution is devoted to the implementation of a homogenization method for deriving the strength or failure properties of a fluid-saturated porous medium, from those exhibited by its individual constituents at the microscopic level. Within this context, a specific attention is paid to the possibility of adopting an effective stress formulation. While the case of a purely cohesive solid matrix provides the first illustrative example where the ‘effective stress principle’ as originally stated by Terzaghi is fully applicable, the analysis is then particularly focused on porous sandstones, modelled as periodic packings of cemented rigid grains. A closed-form analytical expression is thus obtained for the strength criterion of such rock materials, which proves to be a function of a generalized effective stress formed as a linear combination of the total stress and the pore pressure, as in the case of poroelasticity. It is shown in particular that the key microstructural parameter involved in this formulation is the ratio between the intergranular contact area and the grain cross-section area. A possible extension of the homogenization procedure in order to account for a still more realistic description of the sandstone microstructure is finally outlined.
P. De Buhan, L. Dormieux
Contributions to Theoretical/Experimental Developments in Shock Waves Propagation in Porous Media
Abstract
Macroscopic balance equations of mass, momentum and energy for compressible Newtonian fluids within a thermoelastic solid matrix are developed as the theoretical basis for wave motion in multiphase deformable porous media. This leads to the rigorous development of the extended Forchheimer terms accounting for the momentum exchange between the phases through the solid-fluid interfaces. An additional relation presenting the deviation (assumed of a lower order of magnitude) from the macroscopic momentum balance equation, is also presented. Nondimensional investigation of the phases’ macroscopic balance equations, yield four evolution periods associated with different dominant balance equations which are obtained following an abrupt change in fluid’s pressure and temperature. During the second evolution period, the inertial terms are dominant. As a result the momentum balance equations reduce to nonlinear wave equations. Various analytical solutions of these equations are described for the 1-D case. Comparison with literature and verification with shock tube experiments, serve as validation of the developed theory and the computer code.
A 1-D TVD-based numerical study of shock wave propagation in saturated porous media, is presented. A parametric investigation using the developed computer code is also given.
S. Sorek, A. Levy, G. Ben-Dor, D. Smeulders
Saturated Compressible and Incompressible Porous Solids: Macro- and Micromechanical Approaches
Abstract
In this paper two complementary approaches are used to describe the mechanical behavior of saturated compressible and incompressible porous solids. The macroscopic investigation is based on the mixture theory, restricted by the volume fraction concept. In the micromechanical approach, a hierarchy of conditionally ensemble averaged fluid and solid phase momentum balance equations are derived for a simple model of quasi-static liquid saturated porous media. The ensemble averaged equations for both the phases agree remarkably well with the macroscopic results. A micromechanical basis for Terzhagiés effective stress concept is presented. In addition, an expression for additional partial solid stress modifying the effective stress principle, to account for deformability of solid materials, is also derived.
Anjani Kumar Didwania, Reint De Boer
Wave Dynamics of Saturated Porous Media and Evolutionary Equations
Abstract
Nonlinear wave dynamics of an elastically deformed saturated porous media is investigated following the Biot approach. Mathematical models under research are the Biot model and its generalization by consideration of viscous stresses inside liquids. Using two-scales and linear WKB methods, the classical Biot system is transformed to a first-order wave equation. To construct the solution of the other system, an asymptotic modified two-scales method is developed. Initial system of equations is transformed to a nonlinear generalized Korteweg-de Vries-Burgers equation for quick elastic wave. Distinctions of wave propagation in the context of the Biot model and its generalization are shown.
Inna Ya. Edelman
Thermo-Chemo-Electro-Mechanical Formulation of Saturated Charged Porous Solids
Abstract
A thermo-chemo-electro-mechanical formulation of quasi-static finite deformation of swelling incompressible porous media is derived from a mixture theory including the volume fraction concept. The model consists of an electrically charged porous solid saturated with an ionic solution. Incompressible deformation is assumed. The mixture as a whole is assumed locally electroneutral. Different constituents following different kinematic paths are defined: solid, fluid, anions, cations and neutral solutes. Balance laws are derived for each constituent and for the mixture as a whole. A Lagrangian form of the second law of thermodynamics for incompressible porous media is used to derive the constitutive restrictions of the medium. The material properties are shown to be contained in one strain energy function and a matrix of frictional tensors. A principle of reversibility results from the constitutive restrictions. Existing theories of swelling media should be evaluated with respect to this principle.
J. M. Huyghe, J. D. Janssen
Transport of Multi-Electrolytes in Charged Hydrated Biological Soft Tissues
Abstract
A mechano-electrochemical theory for charged hydrated soft tissues with multielectrolytes was developed based on the continuum mixture theory. The momentum equations for water and ions were derived in terms of a mechanochemical force (gradient of water chemical potential), electrochemical forces (gradient of Nernst potentials) and an electrical force (gradient of electrical potential). The theory was shown to be consistent with all existing specialized theories. Using this theory, some mechano-electrokinetic properties of charged isotropic tissues were studied. The well-known Hodgkin-Huxley equation for resting cell membrane potential was derived and the phenomenon of electro-osmotic flow in charged hydrated soft tissues was investigated. Analyses show that the tissue fixed charge density plays an important role in controlling the transport of water and ions in charged hydrated soft tissues.
W. Y. Gu, W. M. Lai, V. C. Mow
Localization Phenomena in Liquid-Saturated and Empty Porous Solids
Abstract
Localization phenomena occur as a result of local concentrations of plastic deformations in small bands of finite width (shear bands). Porous materials, as, for instance, soil, rock, concrete and sinter materials as well as polymeric and metallic foams exhibit a strong tendency towards shear banding caused by plastic dilatation in the brittle deformation range. This kind of behaviour is of great practical importance in engineering design, for example in the study and computation of failure mechanisms in soil mechanics (base failure, slope failure, etc.). From the mathematical point of view, the computation of localization phenomena, for example within the framework of the finite element method (FEM), yields an ill-posed problem, since each mesh refinement leads to smaller shear bands until one obtains (ideally) a singular surface. Following this, regularization mechanisms should be introduced to obtain reliable and robust results.
In the present article, two natural regularization mechanisms for liquid-saturated and empty granular porous materials are discussed. These mechanisms are (1) the inclusion of additional independent degrees of freedom in the sense of the Cosserat brothers for the granular porous solid and (2) the inclusion of pore-fluid viscosity in the saturated case.
W. Ehlers, W. Volk
Finite Elastic Deformations in Liquid-Saturated and Empty Porous Solids
Abstract
Based on the Theory of Porous Media (TPM), a formulation of a fluid-saturated porous solid is presented where both constituents, the solid and the fluid, are assumed to be materially incompressible. Therefore, the so-called point of compaction exists. This deformation state is reached when all pores are closed and any further volume compression is impossible due to the incompressibility constraint of the solid skeleton material. To describe this effect, a new finite elasticity law is developed on the basis of a hyperelastic strain energy function, thus governing the constraint of material incompressibility for the solid material. Furthermore, a power function to describe deformation dependent permeability effects is introduced.
After the spatial discretization of the governing field equations within the finite element method, a differential algebraic system in time arises due to the incompressibility constraint of both constituents. For the efficient numerical treatment of the strongly coupled nonlinear solid-fluid problem, a consistent linearization of the weak forms of the governing equations with respect to the unknowns must be used.
W. Ehlers, G. Eipper
A Micropolar Theory of Porous Media: Constitutive Modelling
Abstract
The extension of the classical mixture theory by the concept of volume fractions leads to the theory of porous media. In this article, the theory of porous media is generalised to micropolar constituents. The kinematic relations and the balance equations for a porous medium are developed without restricting the number of constituents. Based on the entropy inequality, the general form of the constitutive equations are derived for a binary medium consisting of a porous elastic skeleton saturated by a viscous pore-fluid. Both constituents are assumed to be compressible. Handling the saturation constraint by a Lagrangian multiplier leads to a compatibility of the proposed model to so-called hybrid and incompressible models.
S. Diebels
Propagation and Evolution of Wave Fronts in Two-Phase Porous Media
Abstract
An investigation is made into the propagation and evolution of wave fronts in a porous medium which is intended to contain two phases: the porous solid, referred to as the skeleton, and the fluid within the interconnected pores formed by the skeleton. In particular, the microscopic density of each real material is assumed to be unchangeable, while the macroscopic density of each phase may change, associated with the volume fractions. A two-phase porous medium model is concisely introduced based on the work by de Boer. Propagation conditions and amplitude evolution of the discontinuity waves are presented by use of the idea of surfaces of discontinuity, where the wave front is treated as a surface of discontinuity. It is demonstrated that the saturation condition entails certain restrictions between the amplitudes of the longitudinal waves in the solid and fluid phases. Two propagation velocities are attained upon examining the existence of the discontinuity waves. It is found that a completely coupled longitudinal wave and a pure transverse wave are realizable in the two-phase porous medium. The discontinuity strength of the pore-pressure may be determined by the amplitude of the coupled longitudinal wave. In the case of homogeneous weak discontinuities, explicit evolution equations of the amplitudes for two types of discontinuity waves are derived.
Zhanfang Liu, Reint De Boer
Computer Simulation of Drying Optimal Control
Abstract
The subject of this paper is the control of computer-simulated drying processes for the purpose of their optimization. The simulated processes are carried out in such a way that the drying-induced stresses never exceed the stress limit. This paper presents results of a mechanically admissible drying process on the example of a prismatic bar dried convectively, using the theory for drying of capillary-porous materials. The procedure of designing the safe drying processes, in which the destruction of dried materials no longer proceeds, is presented.
S. J. Kowalski, A. Rybicki
Deformations and Stresses in Dried Wood
Abstract
The deformations and the evolution of drying-induced stresses in wood are studied based on a model which takes into account the alteration of mechanical properties of wood in the course of drying. A two-dimensional initial-boundary value problem is solved with the help of the finite element method. An influence of wood anisotropy on the deformation and the stress distributions and evolution of maximal stresses is analysed.
S. J. Kowalski, G. Musielak
Phase Transitions in Gas- and Liquid-Saturated Porous Solids
Abstract
Phase transitions in porous media consisting of a porous solid filled with liquid and gas constituents can occur, for example, due to freezing and drying processes. Although these phenomena are of certain relevance in soil mechanics and material sciences, a general thermodynamical theory is still awaited. Based on recent findings in the porous media theory, this paper is concerned with the development of thermodynamic restrictions for the constitutive relations of an elastic, incompressible porous solid, filled with an incompressible liquid and a compressible gas. The investigations show that mass conversions are related to the differences of the chemical potentials and energy transitions to the differences of temperatures. Thus, they confirm well-known results in classical thermodynamics of gases.
Reint De Boer, Joachim Bluhm
A Simple Model for a Fluid-Filled Open-Cell Foam
Abstract
A simple microstructure model is used to describe a fluid-filled open-cell foam. In the simplest case it consists of parallel elastic plates with gaps between them, which are filled with a Newtonian fluid. We assume that the load applied to this model material is uniaxial. The constitutive equation is formulated with the pressure of the fluid as an inner variable. The model yields an evolutional equation for the fluid pressure which itself is a field equation, that is a partial differential equation in time and space coordinates. This differential equation is solved for an instantaneously applied constant load and for a harmonically oscillating load. The solution of the differential equation, in combination with the constitutive equation leads to a relation between mean applied load and global strain of the test specimen. Finally, we obtain the creep compliance and the complex modulus of the foam material, respectively. The influence of different geometries of the foam and of different material behaviour of the matrix and fluid on the creep compliance and the complex modulus is discussed.
Udo Dünger, Herbert Weber, Hans Buggisch
Quasi-Static and Dynamic Behavior of Saturated Porous Media with Incompressible Constituents
Abstract
In this paper the field equations governing the dynamic response of a fluid-saturated elastic porous medium are analyzed and built up for the study of quasi-static and dynamical problems like the consolidation problem and wave propagation. The two constituents are assumed to be incompressible. A numerical solution is derived by means of the standard Galerkin procedure and the finite element method.
Stefan Breuer
A Linear Theory of Porous Elastic Solids
Abstract
The theory of porous elastic solids with large vacuous interstices, considered by Giovine like materials with ellipsoidal structure, includes, as a particular case, the nonlinear theory of Nunziato and Cowin of elastic materials with small spherical voids finely dispersed in the matrix.
In this paper we propose appropriate constitutive relations and then specialize the basic balance equations of Giovine to the linear theory. Also, generalizing the developments of Cowin and Nunziato, we formulate boundary-initial-value problems and examine classical applications as responses to homogeneous deformations and small-amplitude acoustic waves.
Pasquale Giovine
Derivation of Matching Conditions at the Contact Surface Between Fluid-Saturated Porous Solid and Bulk Fluid
Abstract
The compatibility conditions matching macroscopic mechanical fields at the contact surface between fluid-saturated porous solid and adjacent bulk fluid are considered. Special attention is paid to the derivation of conditions for tangential components of the fluid flow velocities and to the verification of validity of the condition postulated by Beavers and Joseph. It has been shown that at the contact surface between two media, a dissipation of mechanical energy due to the fluid viscosity does exist and thus the form of a dissipation function has been proposed. It has been proven that this relation determines the form of two linear compatibility conditions derived for the tangential components of the relative fluid velocities and that these conditions describe the experimental results more precisely than the condition postulated by Beavers and Joseph.
M. Cieszko, J. Kubik
Metadaten
Titel
Porous Media: Theory and Experiments
herausgegeben von
R. De Boer
Copyright-Jahr
1999
Verlag
Springer Netherlands
Electronic ISBN
978-94-011-4579-4
Print ISBN
978-94-010-5939-8
DOI
https://doi.org/10.1007/978-94-011-4579-4