The Effects of Plasticity and the Evolution of Damage Zones in Earthquake Cycle Simulations

Abstract:

How does plastic response during the earthquake cycle affect nucleation and propagation during individual events and the recurrence intervals between events? How do damage zones evolve with increasing cumulative slip and how do they affect subsequent rupture? To explore these questions we are developing a robust, physics-based earthquake cycle model accounting for off-fault yielding over multiple event sequences. The method is developed for the anti-plane framework where interseismic loading is imposed at the remote boundary. Spontaneous, quasi-dynamic events nucleate at the fault governed by rate-and-state friction.

The off-fault volume is discretized with finite difference methods and time-dependent boundary conditions impose the free surface, remote loading and friction law at the fault. Stresses in the domain are limited by a Drucker-Prager yield condition, with depth-dependent normal stresses that remain constant in time during antiplane shear deformation. The constitutive theory furnishes a nonlinear equilibrium equation that makes use of an elastoplastic tangent stiffness tensor. One of the difficulties arising in our application problems is that plasticity reduces the effective shear modulus to values approaching zero and the equilibrium equations undergo a loss of solvability. One possible solution to this is through the incorporation of hardening which can provide a lower bound (away from zero) of the shear modulus.

We assume zero initial plastic strain prior to the first event which nucleates down dip near a locking depth of 12 km. Plastic flow ensues when stresses exceed the yield condition. The event ruptures up dip with reduced rupture speed and slip velocity compared to its elastic counterpart, generating a flowerlike plastic strain distribution corresponding to greater damage near Earth's free surface. Our preliminary exploration of parameter space show that once the first event terminates, an interseismic loading period follows during which no further plastic strain occurs. The incorporation of hardening causes the yield surface to expand during plastic response, thus subsequent ruptures generate a decreasing amount of additional plastic strain. It is likely that this behavior will change if the off-fault material softens, instead of hardens, during plastic straining.