DEFORMABLE POROUS-MEDIA WITH DOUBLE POROSITY - QUASI-STATICS .1. COUPLING EFFECTS

We investigate the macroscopic quasi-static description of a deformable porous medium with a double porosity constituted by pores and fractures. For this purpose, we use an homogenization technique which gives the macroscopic modelling from the description at the pore and fracture levels. It appears that the macroscopic description is sensitive to the ratios between the different scales, l/l' and l'/l", where l,l',l" are characteristic lengths of the pores, the fractures and the macroscopic medium, respectively. In the first paper we investigate the case l'/l" = (l/l')2, which exhibits a coupling between the flows through the pores and the fractures. The macroscopic description is shown to depend on a single pressure field and exhibits a broken symmetry. Other situations will be examined in a subsequent paper. Large spectra of pore and fracture sizes are also evoked.