Fracture morphology and viscous transport

International audienceThe morphology of a fracture in a granite block is sampled using a high resolution profiler providing a 3999×4000 pixel image of the roughness. We checked that a self-affine model is an accurate geometrical model of the fracture morphology on the basis of a spectral analysis. We also estimated the topothesy of the experimental surface to be l r ≈ 2 10 −7 mm and the roughness exponent to be ζ ≈ 0.78. A finite difference scheme of the Stokes equation was used to model the viscous flow through a fracture aperture that included the experimental fracture surface. It consists of a semi-fracture between a flat Plexiglas plate and the rough fracture surface. We finally compare our numerical results to experimental measurements of the fluid flux through the fracture using a glycerol/water mixture (to be at sufficiently low Reynolds number where Stokes equations holds). The comparison is successful despite a limited resolution of the experimental measurements. We finally show that only long wavelengths of the fracture control its hydraulic conductivity