Analysis of supershear transition regimes in rupture experiments: the effect of nucleation conditions and friction parameters

We consider the effect of the rupture initiation procedure on supershear transition of Mode II ruptures on interfaces governed by linear slip-weakening friction. Our study is motivated by recent experiments, which demonstrated the transition of spontaneous ruptures from sub-Rayleigh to supershear speeds in the laboratory. In these works the experiments were analysed using the Burridge-Andrews model of supershear transition, in which a supershear daughter crack is nucleated in front of the main mother rupture. It was concluded that the critical slip of the linear slip-weakening formulation needs to be pressure-dependent for a good match with experiments. However, the dynamic rupture initiation mechanism in the experiments was conceptually different from the quasi-static one adopted in the numerical work used for comparison. Here, our goal is to determine the effect of the nucleation by numerically modelling the experiments using a rupture initiation procedure that captures the dynamic nature of the wire explosion mechanism used in the experiments. We find parameter regimes that match the experimentally observed transition distances for the entire range of experimental conditions. Our simulations show that the dynamic rupture initiation procedure significantly affects the resulting transition distances, shortening them by about 30-50 per cent compared to those predicted through the quasi-static rupture initiation process. Moreover, for some cases, the dynamic initiation procedure changes the very mode of transition, causing a direct supershear transition at the tip of the main rupture instead of the mother-daughter mechanism. We find reasonable parameter regimes which match experimentally determined transition distances with both direct supershear transition at the rupture tip and the Burridge-Andrews (mother-daughter) mechanism, using both pressure-independent and pressure-dependent critical slip. The results show that there are trade-offs between the parameters of the rupture initiation procedure and the properties of interface friction. This underscores the importance of quantifying experimental parameters for proper interpretation of the experiments and highlights the importance of the rupture initiation procedure, in simulations of both experiments and real-life earthquake events.