Rocking vibrations of a rigid embedded foundation in a poroelastic half‐space

This paper presents an analysis of the rocking vibrations of a rigid cylindrical foundation embedded in poroelastic soil. The foundation is subjected to time‐harmonic rocking excitation and is perfectly bonded to the surrounding soil. The soil underlying the foundation base is represented by a homogeneous poroelastic half‐space, whereas the soil along the side of the foundation is modeled as an independent poroelastic stratum composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory. The contact surface between the foundation base and the poroelastic soil is assumed to be smooth and either fully permeable or impermeable. The dynamic interaction problem is solved by employing a simplified analytical method. Some numerical results for the nondimensional rocking dynamic impedance and nondimensional angular displacement amplitude of the foundation are presented to show the effect of nondimensional frequency of excitation, poroelastic material parameters, hydraulic boundary condition, depth ratio and mass ratio of the foundation. Copyright © 2009 John Wiley & Sons, Ltd.     

Anisotropic dual-continuum representations for multiscale poroelastic materials: Development and numerical modelling

Dual-continuum (DC) models can be tractable alternatives to explicit approaches for the numerical modelling of multiscale materials with multiphysics behaviours. This work concerns the conceptual and numerical modelling of poroelastically coupled dual-scale materials such as naturally fractured rock. Apart from a few exceptions, previous poroelastic DC models have assumed isotropy of the constituents and the dual-material. Additionally, it is common to assume that only one continuum has intrinsic stiffness properties. Finally, little has been done into validating whether the DC paradigm can capture the global poroelastic behaviours of explicit numerical representations at the DC modelling scale. We address the aforementioned knowledge gaps in two steps. First, we utilise a homogenisation approach based on Levin's theorem to develop a previously derived anisotropic poroelastic constitutive model. Our development incorporates anisotropic intrinsic stiffness properties of both continua. This addition is in analogy to anisotropic fractured rock masses with stiff fractures. Second, we perform numerical modelling to test the DC model against fine-scale explicit equivalents. In doing, we present our hybrid numerical framework, as well as the conditions required for interpretation of the numerical results. The tests themselves progress from materials with isotropic to anisotropic mechanical and flow properties. The fine-scale simulations show that anisotropy can have noticeable effects on deformation and flow behaviour. However, our numerical experiments show that the DC approach can capture the global poroelastic behaviours of both isotropic and anisotropic fine-scale representations.     

Coupled consolidation of a porous medium with a cylindrical or a spherical cavity

This paper presents a theoretical approach to analyse coupled, linear thermoporoelastic fields in a saturated porous medium under radial and spherical symmetry. The governing equations account for compressibility and thermal expansion of constituents, heat sink due to thermal dilatation of water and thermal expansion of the medium, and thermodynamically coupled heat–water flow. It has been reported in the literature that thermodynamically coupled heat–water flows known as thermo-osmosis and thermal filtration have the potential to significantly alter the flow fields in clay-rich barriers in the near field of a underground waste containment scheme. This study presents a mathematical model and examines the effects of thermo-osmosis and thermal-filtration on coupled consolidation fields in a porous medium with a cavity. Analytical solutions of the governing equations are presented in the Laplace transform space. A numerical inversion scheme is used to obtain the time-domain solutions for a cylindrical cavity in a homogeneous or a non-homogeneous medium. A closed form time-domain solution is presented for a spherical cavity in a homogeneous medium. Selected numerical solutions for homogeneous and non-homogeneous media show a significant increase in pore pressure and displacements due to the presence of thermodynamically coupled flows and a negligible influence on temperature. © 1998 John Wiley & Sons, Ltd.     

Coupled wellbore erosion and stability analysis

This paper extends earlier work on sand erosion and presents an attempt to couple sand erosion to mechanical damage of rock around a wellbore. Porosity which evolves in time and space as surface erosion progresses, is chosen as the coupling parameter. Both rock elasticity and strength (cohesion) are assumed to depend on porosity in such a way that the material becomes weaker with increasing porosity. The mathematical model, consists of erosion equations, mixture flow equations and stress equilibrium equations, is solved numerically by Galerkin finite element method. Numerical results suggest that erosion, resulting in sand production, is high close to the free surface. Erosion is accompained by changes in porosity and a significant permeability increase. Erosion in the vicinity of the wellbore induces alterations in the mechanical behaviour of the medium. Weakening of rock stiffness leads to severe alteration of both effective stresses and pore pressure near the cavity. Since cohesion decreases with increasing porosity, one can also identify the time instant at which rock mechanical failure starts. © 1998 John Wiley & Sons, Ltd.     

Hydromechanical behavior of radially multilayered cylinders under time-varying loads

ABSTRACT

Geotechnical strata are often treated as horizontally homogeneous for hydromechanical analysis due to the vertical deposition of geological layers; however, such a treatment becomes no longer valid when vertical drilling or construction causes the localized disturbance of subsurface, which would result in radial heterogeneity of geomaterials. This paper presents a poroelastic solution for the saturated multilayered cylinder where multilayer is used to represent radial heterogeneity. After the application of Laplace transform, the governing equations in cylindrical coordinates are derived to obtain the stiffness matrix between stresses, displacements, and pore water pressure. The global matrix is assembled by the boundary conditions and the compatibility of interfaces between adjacent layers. Under time-dependent horizontal compression loads, a parametric study is performed for a cylinder comprised of two layers with distinct properties, and the results show that the load frequency and radial heterogeneity play a significant role in hydromechanical behavior of geomaterials: (1) the time-varying loading can induce a negative pore pressure, and the influence of cyclic loading with a high frequency is limited near the outer surface; (2) the radial heterogeneity due to permeability and compressibility affects the development of pore pressure.     

Micromechanics approach to poroelastic behavior of a jointed rock

The formulation of macroscopic poroelastic behavior of a jointed rock is investigated within the framework of a micro–macro approach. The joints are modeled as interfaces, and their behavior is modeled by means of generalized poroelastic state equations. Starting from Hill's lemma extended for a jointed medium and extending the concept of strain concentration to relate the joint displacement jump to macroscopic strain, the overall poroelastic constitutive equations for the jointed rock are formulated. The analysis emphasizes the main differences and similarities of the resulting behavior with respect to that characterizing ordinary porous media. It is shown that, unlike ordinary porous media, conditions on the poroelastic parameters of joints are required for the macroscopic drained stiffness to entirely define the poroelastic behavior. This is achieved, for instance, if the joint network is characterized by a unique Biot coefficient. Extension of the analysis to non‐linear poroelasticity is also outlined. Finally, the theoretical formulation is applied to two particular cases of jointed rock for which explicit expressions of the overall poroelastic parameters are derived. Copyright © 2011 John Wiley & Sons, Ltd.     

Sensitivity analysis for parameter identification in quasi‐static poroelasticity

This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi‐static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and tested on two numerical examples for the case of isotropic and homogeneous material. The presented formulations can be extended to more complex behaviour in poromechanics. Copyright © 2004 John Wiley & Sons, Ltd.     

Porothermoelastic analyses of anisotropic hollow cylinders with applications

It has been known that material anisotropy and thermal stresses affect borehole stability significantly. Aiming at the experimental studies associated with borehole stability in anisotropic (transversely isotropic) poroelastic materials subject to non‐isothermal conditions, this paper details and applies an anisotropic porothermoelastic solution to an unjacketed hollow cylinder in a triaxial set‐up. Numerical analyses are presented to demonstrate thermal and material anisotropy effects on the pore pressure and the stress concentrations in and around the geometry of a hollow cylinder subjected to thermal and stress perturbations. Copyright © 2004 John Wiley & Sons, Ltd.     

Revisiting the constitutive equations of unsaturated porous solids using a Lagrangian saturation concept

This paper aims at revisiting the constitutive equations of unsaturated porous solids at the light of a Lagrangian saturation concept. By referring the currently wetted porous volume to the reference configuration, the Lagrangian saturation is the state variable associated with the interfacial energy changes only, irrespective of the elastic energy required for deforming the solid matrix. The Lagrangian saturation concept provides the basis of a generic approach to the theory of poroelastoplasticity in unsaturated conditions. We successively examine the case where the saturating fluids occupy disconnected networks and the case where the networks are connected so that the saturating fluids can invade the porous solid or recede from it. The analysis provides the restricted situations where the averaged pore pressure may play the role of an effective pore pressure. Copyright © 2007 John Wiley & Sons, Ltd.