Simple mathematical model of a rough fracture

A simple mathematical model of rough-walled fractures in rock is described which requires the specification of only three main parameters: the fractal dimension, the rms roughness at a reference length scale, and a length scale describing the degree of mismatch between the two fracture surfaces. Fractured samples, collected from natural joints and laboratory specimens, have been profiled to determine the range of these three parameters in nature. It is shown how this surface roughness model can be implemented on a computer, allowing future detailed study of the mechanical and transport properties of single fractures and the scale dependence of these properties.

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