An extended finite element framework for slow‐rate frictional faulting with bulk plasticity and variable friction

We present an extended finite element (FE) approach for the simulation of slow‐rate frictional faulting in geologic media incorporating bulk plasticity and variable friction. The method allows the fault to pass through the interior of FEs without remeshing. The extended FE algorithm for frictional faulting, advocated in two recent articles, emanates from a variational equation formulated in terms of the relative displacement on the fault. In the present paper we consider the combined effects of bulk plasticity and variable friction in a two‐dimensional plane strain setting. Bulk plasticity is localized to the fault tip and could potentially be used as a predictor for the initiation and propagation of new faults. We utilize a variable velocity‐ and state‐dependent friction, known as the Dieterich–Ruina or ‘slowness’ law, formulated in a slip‐weakening format. The slip‐weakening/variable friction model is then time‐integrated according to the generalized trapezoidal rule. We present numerical examples demonstrating the convergence properties of a global Newton‐based iterative scheme, as well as illustrate some interesting properties of the variable friction model. Copyright © 2009 John Wiley & Sons, Ltd.