Computational homogenization of fully coupled hydro-mechanical analysis of micro-fractured porous media

Abstract

In this paper, a computational homogenization technique is developed for fluid flow through the deformable micro-fractured porous media. The coupled hydro-mechanical analysis is performed using an efficient multiscale procedure. Micro-fractures are defined within the microscopic domain, which is associated with each macro-scale quadrature point. According to the first-order homogenization approach, proper form of virtual power relations is defined by applying the Hill-Mandel principle of macro-homogeneity to achieve a consistent multiscale formulation. Moreover, the transient behavior of micro-structures is taken into account by employing transient governing equations for the micro-scale problem. In order to transfer the transient effects of micro-structures, an additional domain integral constraint is augmented to the conventional periodic boundary conditions in the micro-scale analysis. The fractures in micro-scale domain are modeled using the X-FEM technique with appropriate enrichment functions for the displacement and pressure fields. In order to study the accuracy of the proposed computational approach, several numerical examples with different boundary conditions and crack configurations, such as mechanical and hydro-mechanical analyzes are solved and the results are compared with those obtained from the direct numerical simulation. It has been shown that the proposed computational multiscale algorithm on the basis of domain integral constraint, which is augmented to periodic boundary conditions can be used efficiently to achieve accurate results in comparison with the direct numerical simulations, while the linear boundary conditions fails to produce acceptable results in some complex cases.