Constraints from fault roughness on the scale-dependent strength of rocks

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 are now available at the field scale (tens of centimeters to tens of meters) for at least 22 faults, and at the laboratory scale (millimeters to tens 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 surface roughness lies 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) fault 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 of a wide array of faults.