Double porousity theory in geomechanics and multiscale homogenization analysis

The double porosity theory was first given by Bareblatt, Zheltov and Kochina, which considers the effect of fissures and matrix porosity in the rock-mass seepage problem, and they introduced an assumption that the mass flow between the two porosity systems is determined by the pressure gap of the two systems. It was extended to deformable porous media (i.e., consolidation theory). These conventional double porosity theory is based on a local-averaged mixture theory. The modern homogenization theory was developed for the materials with periodic micro-structures. Starting with Navier-Stokes and mass-conservation equations and applying the homogenization procedure to a porous media flow yield Darcy's law and the seepage equation. It is important that the flow field in porous media is determined on a balance of the pressure field and the velocity field, and that we can identify the local pressure/velocity field by the homogenization theory. We here present a new double porosity theory applying on a multiscale homogenization analysis method for porous materials with two-scale porosity systems.