Modeling earthquake cycles and wear on rough faults with the mortar finite element method

This paper presents a mortar-based finite element formulation for modelling earthquake cycles and wear on rough faults governed by rate and state friction. The method allows large sliding on the fault and accounts for all stages in the earthquake cycle, using a variable time step size with a transition between quasi-static and fully dynamic time discretizations. Wear laws with linear and power law forms are discretized and implemented into the mortar method, as well as a minimum level of normal traction constraint to treat fault opening. We examine the effect of wear laws on the slip behaviour and near-fault stresses during simulations of earthquake cycles on rough faults. The simulations demonstrate that the implementation of wear allows more realistic modelling of the earthquake cycle without the development of unrealistically large stresses and with less reduction of earthquake magnitude with total fault slip. Moreover, the method enables to study the effects of roughness and fault slip on the gouge zone thickness.