This work was initiated 904 while B.A.E. was supported by the NSF under Award No. EAR-0948304 905 and completed with support from NSF under Award No. EAR-1547603 and 906 by the Southern California Earthquake Center. SCEC is funded by NSF 907 Cooperative Agreement EAR-0529922 and USGS Cooperative Agreement 908 07HQAG0008 (SCEC contribution number 7166).
Journal of the Mechanics and Physics of Solids
Earthquakes -- Mathematical models, Finite differences, Elastoplasticity -- Mathematical models
We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiationdamping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm. Solutions are verified by convergence tests and comparison to a finite element solution. We quantify how viscosity, isotropic hardening, and cohesion affect the magnitude and off-fault extent of plastic strain that develops over many ruptures. If hardening is included, plastic strain saturates after the first event and the response during subsequent ruptures is effectively elastic. For viscoplasticity without hardening, however, successive ruptures continue to generate additional plastic strain. In all cases, coseismic slip in the shallow sub-surface is diminished compared to slip accumulated at depth during interseismic loading. The evolution of this slip deficit with each subsequent event, however, is dictated by the plasticity model. Integration of the off-fault plastic strain from the viscoplastic model reveals that a significant amount of tectonic off-set is accommodated by inelastic deformation (~0.1 m per rupture, or ~10% of the tectonic deformation budget).
Brittany A. Erickson, Eric M. Dunham, Arash Khosravifar, A Finite Difference Method for Off-fault Plasticity throughout the Earthquake Cycle, Journal of the Mechanics and Physics of Solids (2017), doi: 10.1016/j.jmps.2017.08.002