A regularized continuum model for fault zones with rate and state friction

Accurate representation of fault zones is important in many applications in Earth sciences, including natural and induced seismicity. The framework developed here can efficiently model fault zone localization, evolution, and spontaneous fully dynamic earthquake sequences in a continuum plasticity framework. The geometrical features of the faults are incorporated into a regularized continuum framework, while the response of the fault zone is governed by a rate and state-dependent friction. Although a continuum plasticity model is advantageous to discrete approaches in representing evolving, unknown, or arbitrarily positioned faults, it is known that either non-associated plasticity or strain-softening can lead to mesh sensitivity of the numerical results in absence of an internal length scale. A common way to regularize the numerical model and introduce an internal length scale is by the adoption of a Kelvin-type visco-plasticity element. The visco-plastic rheological behavior for the bulk material is implemented along with a return-mapping algorithm for accurate stress and strain evolution. High slip rates (in the order of 1 m/s) are captured through numerical examples of a predefined strike-slip fault zone, where a detailed comparison with a reference discrete fault model is presented. Additionally, the regularization effect of the Kelvin viscosity parameter is studied on the fault slip velocity for a growing fault zone due to an initial material imperfection.  The model is consistently linearized leading to quadratic convergence of the Newton solver. Although the proposed framework is a step towards the modeling of earthquake sequences for induced seismicity applications, the numerical model is general and can be applied to all tectonic settings including subduction zones.