Mechanics of pressurized planar hyperelastic membranes.

The paper examines the mechanics of inflation of incompressible planar hyperelastic membranes that are rigidly fixed at their boundary and subjected to a uniform pressure. Strain energy functions characterized by the neo-Hookean, Mooney-Rivlin and the Ogden forms are used. Fixity is provided along either circular or elliptical boundaries. The computational results indicate that the strain energy function has a significant influence on the pressure versus inflated volume response of the deformed membrane. When the strain energy function corresponds to a Mooney-Rivlin form, the circular membrane displays no tendency to develop any instability. The equivalent circular membranes composed of both the neo-Hookean and Ogden-type strain energy functions developed an initial 'Wrinkling Instability'. For planar membranes with an elliptical planform, the wrinkling instability is more pronounced; membranes composed of hyperelastic materials with a Mooney-Rivlin form of the strain energy function continue to deform without the development of an initial instability point, whereas membranes composed of both the neo-Hookean and Ogden materials exhibit wrinkling behaviour at critical locations at the interior of the fixed boundary region. The dependency of the strain energy function on the second invariant of the Cauchy-Green strain tensor has an influence in the suppression of hyperelastic effects. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Poroelastic properties of rocks with a comparison of theoretical estimates and typical experimental results.

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.

The influence of the pore shape on the bulk modulus and the Biot coefficient of fluid-saturated porous rocks.

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.

A Multi-Phasic Perspective of the Intact Permeability of the Heterogeneous Argillaceous Cobourg Limestone.

The Cobourg limestone is a heterogeneous argillaceous rock consisting of lighter nodular regions of calcite and dolomite, interspersed with darker regions composed of calcite, dolomite, quartz and a clay fraction. The intact permeability of the Cobourg limestone is estimated to be in the range of K ∈ (10-23, 10-19) m2. This paper discusses the factors influencing the measurement of the intact permeability of the Cobourg limestone and presents an upscaling approach for estimating this parameter. The procedure first involves the dissection of a cuboidal sample of the rock measuring, 80 mm × 120 mm × 300 mm, into ten 8 mm-thick slabs. Digital imaging and mapping of the larger surfaces of these sections are used to create, from both surface image extrusion and surface image interpolation techniques, the fabric within the dissected regions. The estimated permeabilities of the lighter and darker regions are used in the computational models of the computer-generated fabric to estimate the effective permeability of the rock. These results are complemented by estimates derived from mathematical theories for estimating permeabilities of multiphasic composites.

Indentation of a surface-stiffened elastic substrate.

The paper deals with the problem of the indentation of a substrate in the form of an isotropic elastic halfspace that is reinforced at the surface by a bonded layer, which has flexibility characteristic of a Poisson-Kirchhoff-Germain thin plate. The presence of the reinforcing layer changes the characteristics of the indentation problem, in that the techniques that are applicable for the solution of the direct indentation of the halfspace cannot be applied to develop a load-displacement relationship for the indenter. The integro-differential equation governing the indentation of the surface reinforced halfspace is solved using a discretization approach and numerical results are presented to demonstrate the influence of the stiffness of the reinforcing layer on the Boussinesq indention problem.

Poromechanical behaviour of a surficial geological barrier during fluid injection into an underlying poroelastic storage formation.

A competent low permeability and chemically inert geological barrier is an essential component of any strategy for the deep geological disposal of fluidized hazardous material and greenhouse gases. While the processes of injection are important to the assessment of the sequestration potential of the storage formation, the performance of the caprock is important to the containment potential, which can be compromised by the development of cracks and other defects that might be activated during and after injection. This paper presents a mathematical modelling approach that can be used to assess the state of stress in a surficial caprock during injection of a fluid to the interior of a poroelastic storage formation. Important information related to time-dependent evolution of the stress state and displacements of the surficial caprock with injection rates, and the stress state in the storage formation can be obtained from the theoretical developments. Most importantly, numerical results illustrate the influence of poromechanics on the development of adverse stress states in the geological barrier. The results obtained from the mathematical analysis illustrate that the surface heave increases as the hydraulic conductivity of the caprock decreases, whereas the surface heave decreases as the shear modulus of the caprock increases. The results also illustrate the influence of poromechanics on the development of adverse stress states in the caprock.

Radial flow permeability testing of an argillaceous limestone.

Argillaceous Lindsay limestone is the geologic storage formation that will be encountered at the site for the construction of a deep ground repository in Ontario, Canada, for the storage of low to intermediate level nuclear waste. The permeability of the Lindsay limestone is a key parameter that will influence the long-term movement of radionuclides from the repository to the geosphere. This paper describes the use of both steady-state and transient radial flow laboratory tests to determine the permeability of this argillaceous limestone. The interpretation of the tests is carried out using both analytical results and computational models of flow problems that exhibit radial symmetry. The results obtained from this research investigation are compared with the data available in the literature for similar argillaceous limestones mainly found in the Lindsay (Cobourg) formation. The experiments give permeabilities in the range of 1.0 × 10(-22) to 1.68 × 10(-19) m(2) for radial flows that are oriented along bedding planes under zero axial stress. The factors influencing transient pulse tests in particular and the interpretation of the results are discussed.

Permeability hysterisis of limestone during isotropic compression.

The evolution of permeability hysterisis in Indiana Limestone during application of isotropic confining pressures up to 60 MPa was measured by conducting one-dimensional constant flow rate tests. These tests were carried out either during monotonic application of the confining pressure or during loading-partial unloading cycles. Irreversible permeability changes occurred during both monotonic and repeated incremental compression of the limestone. Mathematical relationships are developed for describing the evolution of path-dependent permeability during isotropic compression.

On cavity flow permeability testing of a sandstone.

This paper describes a laboratory experiment designed to measure the bulk permeability of a cuboidal sample of sandstone measuring approximately 450 mm(2) in plan area and 508 mm in height. The relatively large dimensions of the sandstone specimen allow the determination of the permeability of the material by creating a central cavity that can be pressurized to maintain a constant flow rate. The paper describes the experimental details and the test procedure, and discusses the computational and analytic approaches that have been used to interpret the test results.