The Effects of Off-fault Plasticity in EarthquakeCycle Simulations

Brittany A. Erickson, & Eric M. Dunham

Published December 2012, SCEC Contribution #1883

Field observations of damage zones around faults reveal regions of fractured or pulverized rocks on the order of several hundred meters surrounding a highly damaged fault core. It has been postulated that these damage zones are the result of the fracturing and healing within the fault zone due to many years of seismogenic cycling. In dynamic rupture simulations which account for inelastic deformation, the influence of plasticity has been shown to significantly alter rupture propagation speed and the residual stress field left near the fault. Plastic strain near the Earth's surface has also been shown to account for a fraction of the inferred shallow slip deficit. We are developing an efficient numerical method to simulate full earthquake cycles of multiple events with rate-and-state friction laws and off-fault plasticity. Although the initial stress state prior to an earthquake is not well understood, our method evolves the system through the interseismic period, therefore generating self-consistent initial conditions prior to rupture. Large time steps can be taken during the interseismic period while much smaller time steps are required to fully resolve quasi-dynamic rupture where we use the the radiation damping approximation to the inertial term for computational efficiency. So far our cycle simulations have been done assuming a linear elastic medium. We have concurrently begun developing methods for allowing plastic deformation in our cycle simulations where the stress is constrained by a Drucker-Prager yield criterion. The idea is to simulate multiple events which allow for inelastic response, in order to understand how plasticity alters the rupture process during each event in the cycle. We will use this model to see what fraction of coseismic strain is accommodated by inelastic deformation throughout the entire earthquake cycle from the interseismic period through the mainshock. Modeling earthquake cycles with plasticity will also allow us to study how an initial plastic strain distribution, representing damage left by past earthquakes, affects subsequent rupture. We consider a vertical strike slip fault where constant creep is imposed at the downdip extension of the fault, intended to capture the effect of slow tectonic loading. For the volume discretization required to incorporate the plastic response we use high order summation-by-parts finite difference operators and weak enforcement of boundary conditions. We assume antiplane deformation in 2D and our numerical methods achieve high order convergence for the static elastic problem in the time-stepping method. We are currently integrating plasticity into this routine to allow for inelastic response during each event in the cycle. Incorporating the constitutive relations for plasticity furnishes a nonlinear equilibrium equation for displacement. The equilibrium equation is solved by an iterative solution procedure which makes use of an elastoplastic tangent stiffness tensor and the return mapping theorem to solve for stresses consistent with the constitutive theory. Plastic yielding can occur at the edges of the domain and into the medium by enforcing boundary conditions that push the shear stress to the yield surface. During each iteration the equilibrium equation requires finite difference operators for variable material properties where we show second order convergence.

Citation
Erickson, B. A., & Dunham, E. M. (2012, 12). The Effects of Off-fault Plasticity in EarthquakeCycle Simulations. Poster Presentation at AGU Fall Meeting 2012.