Hierarchical homogenization of fluid saturated porous solid with multiple porosity scales

Abstract In this Note, we investigate the macroscopic response of an elastic porous skeleton subjected to a mechanical loading. The pores of two different sizes are filled with a compressible fluid which can redistribute at both the microscopic and mesoscopic scales since the pores form one system of connected network. We apply the asymptotic homogenization method to upscale a microscopic fluid–structure interaction problem. The obtained poroelastic model describes the matrix behavior at the mesoscopic level. The homogenization procedure is repeated to give rise a double-porosity model relevant to the macroscopic scale. We discuss relationships obtained with the standard Biot poroelasticity theory. As an advantage, the approach reported here provides a direct procedure to calculate the effective properties for any 3D microstructure without any restrictions concerning the shape or topology of the pore network. Note that for the particular case of disconnected networks, i.e. with occluded pores, the model can be adapted easily.