An extended finite element algorithm for cracks with rate- and state-dependent coefficient of friction

The coefficient of friction between two contacting rough surfaces sliding past each other is known to vary with slip speed and a state variable reflecting the maturity of contact. For rocks this rate- and state-dependence of the coefficient of friction commences as soon as a crack forms during the period of slip weakening. In this work we report the performance of a recently developed numerical algorithm based on the extended finite element method for simulating the process of slip weakening and frictional sliding at different speeds on rocks with a well-defined frictional interface. Rate-dependence of the coefficient of friction leads to a first-order ordinary differential equation for balance of momentum, which we integrate numerically with the generalized trapezoidal method. We use the extended finite element algorithm to simulate some of the laboratory experiments performed by Dieterich and co-workers, as well as investigate the feasibility of using the rate-dependence of the coefficient of friction as a regularization to the problem of frictional crack propagation.