Numerical upscaling of the permeability of a randomly cracked porous   medium
  The equivalent permeability of a randomly cracked porous material is studied using a finite element program in which a four-nodes zero-thickness element is implemented for modelling the cracks. The numerical simulations are performed for geometries with different cracks densities and for different values of matrix permeability and cracks conductivity, but the cracks length are taken equal to one. The method used for determination of the equivalent permeability resulted in a perfectly symmetric equivalent permeability tensor for each case. Based on the obtained results a simple relation is presented for the equivalent permeability of a randomly cracked porous material as a function of the matrix permeability and the cracks density and conductivity. This relation is then generalized for the cracks of any length using a linear transformation. 
Siavash Ghabezloo (ENPC-Cermes), Ahmad Pouya (LCPC)