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

Abstract : As 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.
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J.L. Auriault, C. Boutin. Deformable porous media with double porosity, quasi-statics. II: Memory effects. Transport in Porous Media, Springer Verlag, 1993, 10 (2), pp.153-169. ⟨hal-00936353⟩

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