Deformable porous media with double porosity, quasi-statics. II: Memory effects

Abstract

International audienceAs in our previous paper, we investigate the macroscopic quasi-static description of a porous medium with a double porosity constituted by pores and fractures. For this purpose, we use a homogenization technique. As expected, the macroscopic description is sensitive to the ratios between the different scales,l/l′ andl/l′ wherel, l′, l″ are characteristic lengths of the pores, the fractures, and the macroscopic medium, respectively. In the first paper, we investigated the case l′/l″=O(l^2/l′^2)≪1 (case 1) which exhibits a coupling between the flows through the pores and the fractures. In the present paper, we deal with the other homogenizable cases. The case 3 where l/l′=O(l′^2/l″^2)≪1 gives a macroscopic description similar to that of a single porosity medium. The main result, however, is the case 2, where l/l′=O(l′/l″)≪1, which exhibits memory effects. These are due to the seepage through the micropores