Analytical extension of double-porosity solutions under three-dimensional axisymmetric loadings

Abstract

Fractures in geologic formation can interconnect to form additional flow channels in the matrix. Pore pressures in the matrix and fractures dissipate at different rates, which drives the inter-porosity communication of fluid mass. Such a phenomenon had been widely analyzed by the double-porosity model, but most of the analytical solutions were limited to plane-strain problems. In this paper, we extended the double-porosity model to account for the three-dimensional cases under axisymmetric loadings. The matrix and fractures jointly sustaining the external loading and the exchange of pore fluid within two porosity networks were considered in the conservation of momentum and fluid mass. The governing equations were then decoupled by the Laplace-Hankel transform to obtain analytical solutions. The results of a double-porosity finite layer showed that the local compression caused a non-uniform distribution of double Mandel-Cryer buildups of pore pressures in the matrix. The vertical deformation stretched a horizontal displacement near the surface toward the center of loading, and a concentration of shear stress occurred under the edge of the loading. A parametric study was carried out to analyze the effects of the additional flow channel introduced by the fractures, which presented the potential application of this model in geotechnical engineering.