Résumé
We investigate the macroscopic quasi-static description of a porous rigid medium witha double porosity constituted by pores and fractures. We use an homogenization method whichallows the macroscopic modelling from the description at the pore and the fracture scales. Themacroscopic description is strongly dependent upon the ratios between the different scales l/l' andl'/l" where l, l', l" are characteristic lengths for the pores, the fractures and the macroscopicmedium, respectively. We investigate here the case: l'/f' =0((l/l')² ). The macroscopic descriptionwhlch is obtained is a mass balance equation with a classical Darcy's law. The interest of theinvestigation lies in the source term that highlights the role of a compressible fluid reservoir playedby the microporous medium.