Modeling creeping flow through a closed crack with a self-affine geometry and an extension to permeability of cracked media

Abstract : To model a creeping flow through closed cracks in cracked materials we study a normal mechanical contact between two elastic half-spaces with rough surfaces is studied. The roughness is modeled using a filtering technique in Fourier space: the root mean squared roughness, the spectral content and the fractal dimension are prescribed. The non-linear contact problem is solved using a spectral boundary element method. A general transmissivity laws for incompressible fluid linking roughness parameters and applied load are deduced up to the percolation limit. In this analysis it is assumed that hydrostatic pressure is much smaller than contact pressures. It is shown that the transmissivity decreases exponentially with the effective contact area, which in turn grows linearly with the contact pressure. The effective contact area includes both contact clusters and zones of trapped fluid. A strongly coupled problem of trapped fluid in the wavy contact interface is also considered for compressible and incompressible fluid. The influence of the trapped fluid on the friction angle is studied.