Modeling the effect of roughness on the nucleation and propagation of shear rupture

Yuval Tal, & Bradford H. Hager

Published July 22, 2016, SCEC Contribution #6350, 2016 SCEC Annual Meeting Poster #051

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 at the scale of small earthquakes, in which realistic geometry and friction law parameters can be incorporated in the model. We choose the minimum roughness wavelength to be at the size of lab samples (10 – 20 cm) and thus use the observed lab-scale slip or rate based friction laws without modifying the constitutive parameters, assuming that the experimental data already include the effects of smaller wavelengths of roughness.

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. In this method, Lagrange multipliers are used to enforce the continuity of stress, the non-penetration condition, and Coulomb friction on the fault in a weak integral sense. 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.

Simulations of 20-meter rough faults governed by velocity-weakening rate-and state- friction show the significant effect of roughness on: (1) Seismic moment; (2) Stress drop; (3) Slip rate; and (4) Nucleation and propagation properties such as nucleation length, rupture velocity, and breakdown zone. Generally, under the same range of external loads, rougher faults experience more events with smaller magnitudes and slip rates, where the roughest faults experience only slow-slip aseismic events. As the roughness amplitude increases, local barriers of large normal stresses complicate the nucleation process and result in asymmetric expansion of the rupture and larger nucleation length. In the propagation phase of the seismic events, the roughness results in larger breakdown zones.

Key Words
Roughness; rupture nucleation; Mortar method

Citation
Tal, Y., & Hager, B. H. (2016, 07). Modeling the effect of roughness on the nucleation and propagation of shear rupture. Poster Presentation at 2016 SCEC Annual Meeting.

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)