The effect of roughness on the nucleation and propagation of shear rupture on small faults

Faults are rough at all scales and can be described as self-affine fractals. This deviation from planarity results in geometric asperities and a locally heterogeneous stress field, which affect the nucleation and propagation of shear rupture. We study this effect numerically and aim to understand the relative effects of different fault geometries, remote stresses, and medium and fault properties, focusing on small earthquakes, in which realistic geometry and friction law parameters can be incorporated in the model. Our numerical approach includes three main features. First, to enable slip that is large relative to the size of the elements near the fault, as well as the variation of normal stress during slip, we implement slip-weakening and rate-and state-friction laws into the Mortar Finite Element Method, in which non-matching meshes are allowed across the fault and the contacts are continuously updated. Second, we refine the mesh near the fault using hanging nodes, thereby enabling accurate representation of the fault geometry. Finally, using a variable time step size, we gradually increase the remote stress and let the rupture nucleate spontaneously. This procedure involves a quasi-static backward Euler scheme for the inter-seismic stages and a dynamic implicit Newmark scheme for the co-seismic stages. In general, under the same range of external loads, rougher faults experience more events but with smaller slips, stress drops, and slip rates, where the roughest faults experience only slow-slip aseismic events. Moreover, the roughness complicates the nucleation process, with asymmetric expansion of the rupture and larger nucleation length. In the propagation phase of the seismic events, the roughness results in larger breakdown zones.