Transition of Mode-II Cracks From Sub-Rayleigh to Supershear Speeds in the Presence of Favorable Heterogeneity

Understanding sub-Rayleigh-to-supershear transition of mode II cracks is a fundamental problem with important practical implications for earthquake dynamics and seismic radiation. In the Burridge-Andrews mechanism of supershear transition on interfaces with homogeneous friction properties and constant prestress, a daughter crack nucleates, for sufficiently high prestress, at a shear stress peak traveling with the shear wave speed in front of the main crack. The daughter crack is supershear from its very beginning. This transition mechanism requires high enough prestress and has transition distances that depend on the prestress level and friction properties of the interface through two nondimensional parameters. We perform detailed numerical simulations of spontaneous mode II rupture on an interface governed by a linear slip-weakening friction and find that sub-Rayleigh-to-supershear transition of mode II cracks occurs in a number of models that subject cracks to supershear loading fields. We consider a spontaneously expanding sub- Rayleigh crack (or main crack) which advances, along a planar interface with linear slip-weakening friction, towards a place of favorable heterogeneity, such as a preexisting subcritical crack, a small patch of higher prestress, or a small patch of lower static strength. For a range of model parameters, a secondary dynamic crack nucleates at the heterogeneity and acquires supershear speeds due to the supershear stress field propagating in front of the main crack. Transition to supershear speeds occurs directly at the tip of the secondary crack, with the tip accelerating rapidly to values numerically equal to the Rayleigh wave speed and then abruptly jumping to a supershear speed. Models with favorable heterogeneity achieve supershear transition and propagation for much lower prestress levels than the ones implied by the Burridge-Andrews mechanism and have transition distances that depend on the position of heterogeneity. Inferences of supershear earthquake propagation are sometimes interpreted using the Burridge-Andrews mechanism to constrain prestress or parameters of fault friction. If supershear transition is governed by presence of heterogeneity as considered here, such inferences may be misleading. We investigate the dependence of supershear transition and subsequent crack propagation on model parameters using the case with a patch of higher prestress. The dependence on patch size and prestress is far from trivial. For example, under certain conditions, a smaller patch results in sustained supershear propagation far beyond the patch location, while a larger patch causes only a short supershear burst, with the speeds returning to sub-Rayleigh beyond the patch. We will present the parameter study and our explanation for this and other phenomena. We also find that the procedure of initiating the main crack significantly affects subsequent crack propagation and hence the loading provided by the main crack to the location of favorable heterogeneity. That, in turn, affects the nucleation of the secondary crack and crack tip speed beyond the location of heterogeneity. This study indicates that a small preexisting crack or higher-stressed patch can completely change the failure process on the interface, perturbing a sub-Rayleigh crack into becoming supershear. Our preliminary 3D results suggest qualitatively similar but quantitatively different behavior.