Effect of Surface Topography on Fracture Permeability

Fracture permeability is usually estimated by a cubic law that is based on the theory of hydrodynamics for the laminar flow between flat plates. However, the cubic law is too simple to estimate the fracture permeability correctly, because the surface of real fracture is much more complicated and rougher than the surface of flat plate. In this study, therefore, the discrepancy between the cubic law and actual fracture permeability was investigated experimentally and theoretically to develop a correction factor for the cubic law based on real fracture. A fractal model was applied to describe the topography of real fracture surface, because fractal can describe a complicated geometry such as the topography of fracture surface by a simple power law which is determined by fractal dimension and steepness. Consequently, the discrepancy could be written by a the fractal dimension and the steepness, and the following results were obtained. First, the contact condition of the fracture surfaces is most influential on the discrepancy but fractal dimension does not affect much to the discrepancy. Second, steepness is also influential on the discrepancy but it does not affect as strong as the contact condition.