This paper uses experimental data derived from surface permeability tests conducted on a bench-scale 508 mm cuboidal sample of Indiana Limestone. These results are used in combination with ...computational modelling to test the hypothesis that the geometric mean is a good proxy to represent permeability when the spatial distribution of the permeability for the heterogeneous rock, with no evidence of hydraulic anisotropy or fractures, is log-normal. The predictive capabilities of the geometric mean as a measure of the effective permeability are further assessed by examining specific examples where three-dimensional flows are initiated in the heterogeneous domain and where the equivalent homogeneous problem gives rise to purely circular flows that have exact solutions. The approach is also applied to examine a hypothetical hydraulic pulse test that is conducted on a cuboidal region with sealed lateral boundaries, consisting of the experimentally measured heterogeneous distribution of permeability and an equivalent homogeneous region where the permeability corresponds to the geometric mean.
Interfaces possess complex mechanical responses that are governed by several factors including the type of material, the local topography of the interacting surfaces, the stress state and the mode of ...deformation. This paper examines the mechanics of a mated smooth interface that is subjected to a normal stress and where the contact is perturbed by a circular patch that can experience dilatancy under shear. The analysis of the static stress drop occurring during shear at the interface is examined using a contact mechanics approach that accounts for the separation at the pre-compressed geological interface induced by the development of dilatancy of the patch during relative shear. This paper presents an elementary model of the mechanics that takes into consideration the normal stress evolution during dilatant shearing of the interface. The problem is of particular interest to the modelling of local phenomena that can occur at material interfaces and geological faults that are subjected to steady movement.
Abstract
Fluid-saturated rocks are multi-phasic materials and the mechanics of partitioning the externally applied stresses between the porous skeleton of the rock and the interstitial fluids has to ...take into consideration the mechanical behaviour of the phases. In these studies the porosity of the multi-phasic material is important for estimating the multi-phasic properties and most studies treat the porosity as a scalar measure without addressing the influence of pore shape and pore geometry. This paper shows that both the overall bulk modulus of a porous medium and the Biot coefficient depend on the shape of the pores. Pores with shapes resembling either thin oblate spheroids or spheres are considered. The Mori–Tanaka and the self-consistent methods are used to estimate the overall properties and the results are compared with experimental data. The pore density and the aspect ratio of the spheroidal pores influence the porosity of the geomaterials. For partially saturated rocks, the equivalent bulk modulus of the fluid–gas mixture occupying the pore space can also be obtained. The paper also examines the influence of the pore shape in estimating the Biot coefficient that controls the stress partitioning in fluid-saturated poroelastic materials.
Abstract
The paper develops theoretical estimates for the parameters that describe the classical theory of poroelasticity for a fluid-saturated porous medium, with a porous elastic skeleton that can ...exhibit imperfect grain contacts. The results for the poroelastic properties predicted from the modelling are compared with experimental results available in the literature.
Fluid-saturated materials are encountered in several areas of engineering and biological applications. Geologic media saturated with water, oil and gas and biological materials such as bone saturated ...with synovial fluid, soft tissues containing blood and plasma and synthetic materials impregnated with energy absorbing fluids are some examples. In many instances such materials can be examined quite successfully by appeal to classical theories of poroelasticity where the skeletal deformations can be modelled as linear elastic. In the case of soft biological tissues and even highly compressible organic geological materials, the porous skeleton can experience large strains and, unlike rubberlike materials, the fluid plays an important role in maintaining the large strain capability of the material. In some instances, the removal of the fluid can render the geological or biological material void of any hyperelastic effects. While the fluid component can be present at various scales and forms, a useful first approximation would be to treat the material as hyperelastic where the fabric can experience large strains consistent with a hyperelastic material and an independent scalar pressure describes the pore fluid response. The flow of fluid within the porous skeleton is defined by Darcy's law for an isotropic material, which is formulated in terms of the relative velocity between the pore fluid and the porous skeleton. It is assumed that the form of Darcy's law remains unchanged during the large strain behaviour. This approach basically extends Biot's theory of classical poroelasticity to include finite deformations. The developments are used to examine the poro-hyperelastic behaviour of certain one-dimensional problems.
This paper examines the axisymmetric problem of a penny-shaped crack located in a poroelastic halfspace that is modelled by Biot poroelasticity. The paper first examines the axisymmetric problem of ...the mechanics of fluid injection over a circular area within a halfspace that would create the skeletal stress state necessary to initiate fracture. The triggering of the fracture is assumed to create an axisymmetric penny-shaped crack whose surfaces will be subjected to fluid pressure. The mechanics of the penny-shaped crack in terms of its potential to extend in an axisymmetric fashion is examined by formulating the poroelastic mixed boundary value problem and solving the coupled Fredholm integral equations of the second-kind obtained through successive applications of integral transform techniques. The analysis of the poroelasticity problem of fluid-injection into the crack gives rise to time-dependent skeletal stress intensity factors (SIFs) at the crack tip; these are combined with a mixed-mode brittle skeletal fracture criterion to establish the injection pressures that can lead to the extension of the penny-shaped crack in a self-similar fashion.
Granitic rock from the western part of the Canadian Shield is considered as a potential host rock for the siting of a deep geological repository for the storage of heat-emitting high-level nuclear ...fuel waste. The research program focused on the use of surface permeability measurements conducted at 54 locations on a 300 mm cuboid of granite, obtained from the Lac du Bonnet region in Manitoba, to obtain an estimate for the effective permeability of the cuboid. Companion experiments are conducted on a 280 mm cuboid of granite obtained from Stanstead, Quebec, located in the eastern part of the Canadian Shield. The surface permeabilities for the cuboids of granite are developed from theoretical relationships applicable to experimental situations where steady flow is initiated at a sealed annular surface region with a pressurized central domain. The experimental values for the surface permeability are used with a kriging procedure to estimate the permeability variations within the cuboidal region. The spatial variations of permeability are implemented in computational models of the cuboidal regions to determine the one-dimensional permeabilities in three orthogonal directions. The effective permeability of the granite cuboids is estimated by appeal to the geometric mean. The research provides a non-destructive methodology for estimating the effective permeability of large specimens of rock and the experiments performed give estimates for the effective permeability of the two types of granitic rock obtained from the western and eastern flanks of the Canadian Shield.
On the inflation of poro-hyperelastic annuli Selvadurai, A.P.S.; Suvorov, A.P.
Journal of the mechanics and physics of solids,
October 2017, 2017-10-00, 20171001, Letnik:
107
Journal Article
Recenzirano
The paper presents the radially and spherically symmetric problems associated with the inflation of poro-hyperelastic regions. The theory of poro-hyperelasticity is a convenient framework for ...modelling the mechanical behaviour of highly deformable materials in which the pore space is saturated with fluids. Including the coupled mechanical responses of both the hyperelastic porous skeleton and the fluid is regarded as an important consideration for the application of the results, particularly to soft tissues encountered in biomechanical applications. The analytical solutions for radially and spherically symmetric problems involving annular domains are used to benchmark the accuracy of a standard computational approach. The paper also generates results applicable to the hyperelastic solutions when coupling is eliminated through the presence of a highly permeable pore structure.
The permeability of intact geologic media features prominently in many geo-environmental endeavours. The laboratory estimation of permeability is an important adjunct to the field estimation of bulk ...permeability values, which involves a great deal of supplementary in situ investigations to correctly interpret field data. Laboratory permeability estimation is also a viable method if core samples are recovered from in situ geological mapping of the region under study. The basic methodologies for permeability estimation rely on either steady-state or transient tests of the geologic material depending on the anticipated permeability value. This paper presents a steady flow test conducted on a partially drilled cavity located on the axis of a cylindrical specimen. Certain compact theoretical relationships are proposed for the estimation of steady flow from a cavity of finite dimensions located along the axis of a cylindrical specimen. The relationships are used to estimate the permeability of a cylinder of Lac du Bonnet granite obtained from the western flank of the Canadian Shield. The results from the cavity flow permeability experiments are compared with other estimates for the permeability of granitic rocks reported in the literature.
This paper investigates the influence of the development of elasto-plastic failure on the evolution of the Biot coefficient for a fluid-saturated geomaterial. Attention is restricted to the study of ...an elasto-plastic porous skeleton that has a solid phase with failure characteristics corresponding to an isotropic medium with a von-Mises-type failure criterion and an associated flow rule. The evolution of the Biot coefficient with the development of failure is illustrated through specific examples. The assumptions implicit in standard computational approaches for examining poroelastic behavior in the light of these developments are also discussed.
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