Roughness and wear during brittle faulting

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Abstract
In many natural fault systems, the thickness of gouge and breccia increases approximately linearly with displacement. In contrast, many experimental faults show non linear thickness/displacement relationships. The linear relationship for natural faults has been explained in the past using engineering models for adhesive or abrasive wear. Non linear relationships for experimental faults have not been explained. A model for wear during brittle faulting which considers the scaling of surface roughness can successfully describe the difference between wear on experimental faults and wear on natural faults. We suggest the linear relationship for natural faults results from the approximately self‐similar roughness of the fault surfaces. Experimental faults do not generally follow linear relationships because the roughness of ground surfaces normally used in experimental studies scales differently than the roughness of natural rock surfaces. A simple model which assumes that the volume of wear material created is proportional to the volume of mismatch between the surfaces can explain the differences between wear on experimental faults and wear on natural faults. For ground surfaces of experimental samples, the volume of mismatch is independent of the total slip because at the largest scales these surfaces are flat. In contrast, for natural, self‐similar surfaces the volume of mismatch increases with slip, because slip isolates larger and larger asperities from their original positions in the opposite surface. Natural and experimental faults evolve differently because of the difference in scaling of their respective surface roughnesses.

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