Constraints from Fault Roughness on the Scale-Dependent Strength of Rocks

Abstract:

Principal slip surfaces in faults have measurable roughness generated during slip. The roughness both records previous events and poses the boundary conditions for future rupture. Digital, high precision roughness data is now available at the field scale (10’s of centimeters to 10’s of meters) for at least 22 faults and at the lab scale (millimeters to 10’s of centimeters) for a subset of these. We quantify the slip surface roughness by measuring the aspect ratio, which is the average asperity height divided by the profile length. Higher aspect ratios indicate rougher surfaces. From the field studies two major trends have emerged: (1) fault surfaces roughness falls in a restricted range with aspect ratios in the slip parallel direction of 0.07-0.5% for profiles of 1 m length, and (2) faults surfaces are rougher at small scales than large ones. These features can both be interpreted as fingerprints of scale-dependent strength, which sets a limit to the aspect ratio of the surface. The measurements imply that shear strength scales with the observation scale L as L^-0.4. The new understanding of the physical controls on roughness allows generalization of the extant measurements to a wide array of faults.