Solving the dynamic rupture problem with different numerical approaches and constitutive laws

We study the dynamic initiation, propagation and arrest of a 2-D in-plane s hear rupture by solving the elastodynamic equation by using both a boundary integral equation method and a finite difference approach. For both method s we adopt different constitutive laws: a slip-weakening (SW) law, with con stant weakening rate, and rate- and state-dependent friction laws (Dieteric h-Ruina). Our numerical procedures allow the use of heterogeneous distribut ions of constitutive parameters along the fault for both formulations. We f irst compare the two solution methods with an SW law, emphasizing the requi red stability conditions to achieve a good resolution of the cohesive zone and to avoid artificial complexity in the solutions. Our modelling results show that the two methods provide very similar time histories of dynamic so urce parameters. We paint out that, if a careful control of resolution and stability is performed, the two methods yield identical solutions. We have also compared the rupture evolution resulting from an SW and a rate- and st ate-dependent friction law. This comparison shows that despite the differen t constitutive formulations, a similar behaviour is simulated during the ru pture propagation and arrest. We also observe a crack tip bifurcation and a jump in rupture velocity (approaching the P-wave speed) with the Dieterich -Ruina (DR) law. The rupture arrest at a barrier thigh strength zone) and t he barrier-healing mechanism are also reproduced by this law. However, this constitutive formulation allows the simulation of a more general and compl ex variety of rupture behaviours. By assuming different heterogeneous distr ibutions of the initial constitutive parameters, we are able to model a bar rier-healing as well as a self-healing process. This result suggests that i f the heterogeneity of the constitutive parameters is taken into account, t he different healing mechanisms can be simulated. We also study the nucleat ion phase duration T-n, defined as the time necessary for the crack to reac h the half-length l(c). We compare the T-n values resulting from distinct s imulations calculated using different constitutive laws and different sets of constitutive parameters. Our results confirm that the DR law provides a different description of the nucleation process than the SW law adopted in this study. We emphasize that the DR law yields a complete description of t he rupture process, which includes the most prominent features of SW.