Quasi-static deformation of a poroelastic half-space with anisotropic permeability by two-dimensional surface loads

Abstract

SUMMARY An analytical solution is obtained of the fully coupled diffusion–deformation system of equations governing the quasi‐static plane strain deformation of a poroelastic half‐space with anisotropic permeability and compressible constituents. The stresses and the pore pressure are taken as the basic state variables. Displacements are obtained by integrating the coupled constitutive relations. The problem of surface loads is discussed in detail. Explicit analytical solutions are derived for normal line loading, shear line loading and normal strip loading. The permeability anisotropy is found to have a significant effect on the quasi‐static deformation of the half‐space. However, in the drained and undrained limits, the anisotropy has no effect. The stresses in the drained and undrained states are independent of the poroelastic parameters. Numerical computation of the pore pressure indicates that ignoring permeability anisotropy may lead to an overestimation of the pore pressure at points vertically below the point of normal loading. Further, anisotropy in permeability may lead to a dilution in the theoretical prediction of the Mandel–Cryer Effect.

Consolidation of a poroelastic half-space with anisotropic permeability and compressible constituents by axisymmetric surface loading

“…Since, in general, χ r > χ z , the theoretical prediction of the Mandel-Cryer effect may get diluted in materials with anisotropic permeability. A similar conclusion was drawn in the two-dimensional plane strain analysis (Singh et al 2007). Figure 5 shows the influence of the compressibility of the solid constituents of the poroelastic medium on the diffusion of the pore pressure with time.…”

“…Both the permeability and the poroelasticity of the medium were assumed to be transversely isotropic, but its fluid and solid constituents were assumed to be incompressible. In a recent study, Singh et al (2007) discussed the quasi-static plane strain deformation of a poroelastic half-space with anisotropic permeability and compressible constituents by twodimensional surface loads. An analytical solution was obtained by using a pure compliance formulation in which the stresses and the pore pressure are taken as the basic state variables.…”

Uncoupled state space solution to layered poroelastic medium with anisotropic permeability and compressible pore fluid

“…Assembling Eqs. (7), (8), (11), (12), (13), (14), (15), and (16), we can obtain two sets of equations of six and two state vectors in the Laplace-Fourier transform domain, which can be expressed in matrix form as follows:…”

“…In the actual engineering situations, the soils and rocks are formed through a sedimentation process which produces the horizontal stratification. Consequently, the horizontal permeability often differs from that of the vertical [13][14][15]. Some experimental results have shown that horizontal permeability of the soil may be an order of magnitude, or even more greater than vertical permeability.…”

Non-axisymmetric Biot consolidation analysis of multi-layered saturated poroelastic materials with anisotropic permeability

“…A finite layer numerical method was used by Mei et al (2004) to examine the consolidation analysis of cross-anisotropic homogeneous poroelastic materials. Singh et al (2007Singh et al ( , 2009) took advantage of the fully coupled Biot quasi-static theory to study plane strain deformation under two-dimensional surface loads and axisymmetric consolidation under axisymmetric surface loads of a poroelastic half-space with anisotropic permeability. Another analytical technique was proposed by Ai and Wu (2009b) to study the plane strain consolidation of multi-layered poroelastic materials considering the anisotropy of permeability.…”