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

Abstract

S U M M A R YWe 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 (motherdaughter) 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.

Stress heterogeneities in earthquake rupture experiments with material contrasts

“…Here we mainly compare our experimental setups in a qualitative way, so we abstain from using a pressure-dependent D c , although it has been shown to be pressure dependent by Lu et al (2009 -56 47 41 37 36 ---51 42 ---53 24.0 32 30 28 26 23 17 9 7 27 22 15 9 7 7 6 6 38 31 19 12 8 7 6 6 62 49 36 17 9 7 6 6 22 19 17 14 8 7 6 6 16 11 8 7 6 6 6 6 16 11 7 6 6 6 6 6 14 9 7 6 6 6 6 5 24.5 27 23 18 16 10 7 7 6 16 11 8 7 6 6 6 6 19 14 9 7 6 6 6 6 26 16 11 8 7 6 6 6 18 16 10 7 7 6 6 6 11 7 7 6 6 6 5 5 10 7 6 6 6 6 5 5 9 7 6 6 6 5 5 5 25.0 18 16 11 8 7 6 6 6 10 8 7 6 6 5 5 5 11 8 7 6 6 6 6 5 13 9 7 6 6 6 6 5 15 9 7 7 6 6 6 5 8 6 6 5 5 5 5 5 7 6 6 6 5 5 5 5 7 6 6 6 5 5 5 5 µs = 0.63, µ d = 0.23 20.0 Table A.3: Here we show the sensitivity of supershear transition length to a change in static and dynamic friction. The numerical nucleation method and D c = 5 µm are used.…”

“…This would relax peak stresses and prevent supershear transitions in the positive direction. Relaxation of a fault by µm-scale slipping could partially contribute to the findings of Lu et al (2009), that their numerical models with a homogeneous material had 30 to 40 percent shorter supershear transition lengths than the laboratory experiments by Xia et al (2004).…”

“…Studies of rupture along homogeneous interfaces (Andrews, 1976;Harris and Day, 1993;Coker et al, 2005;Liu and Lapusta, 2008;Lu et al, 2009) are not affected by the stress-distortions described in this paper, as long as they do not employ horizontally confined boundaries (which practically introduce a material interface at the edge of the model). Likewise simulations with bimaterials are not affected, if the fault separates two semi-infinite half-spaces as in Cochard and Rice (2000).…”

“…We choose our nucleation patch size of 7 mm in accordance with previous work (Lu et al, 2009), and we set the nucleation patch centered about the midpoint of the fault. When choosing larger values for the nucleation patch size, rupture occurs more readily and is more likely to be crack-like than pulse-like, as shown by Ampuero and Ben-Zion (2008).…”

“…The rupture nucleation mechanism is known to influence rupture propagation and supershear transition behavior (Festa and Vilotte, 2006;Shi et al, 2008;Lu et al, 2009). We therefore consider two different nucleation methods: In the first method (called the numerical nucleation method), we lower the static friction in the nucleation patch, so that the rupture is just initiated.…”