Homogenization of a cracked saturated porous medium: Theoretical aspects and numerical implementation

The purpose of this paper is to determine, via a homogenization technique and in the framework of small strains, the macroscopic poroelastic properties of a saturated, deformable, cracked porous medium. The poroelastic matrix is assumed to be homogeneous and the cracks to be connected discontinuities, infilled with a poroelastic material. They are periodically distributed, with the size of the period being small compared to the size of the sample. The considered up-scaling method (based on asymptotic expansions) will provide two uncoupled mechanical and hydraulic problems describing the overall behavior of the material. The degradation of the mechanical properties due to damage is then introduced. Damage depends on cracks’ opening, thus making the problem non-linear. A numerical solution of the problem is provided using finite elements. Any stress-strain loading path can be reproduced. The numerical solution of an oedometric test and a biaxial test allows the exploration of the non-linear anisotropic behavior along with the bifurcation phenomenon.