Conditions governing the occurrence of supershear ruptures under slip‐weakening friction

Abstract

A general theory for transitions between sub‐Rayleigh and intersonic rupture speeds is developed for faults governed by slip‐weakening friction. The transition occurs when stresses moving at intersonic speeds ahead of expanding or accelerating sub‐Rayleigh ruptures exceed the peak strength of the fault, initiating slip within a daughter crack. Upon reaching a critical nucleation length, the daughter crack becomes dynamically unstable, expanding into a self‐sustaining intersonic rupture. This mechanism holds in both two and three dimensions. On faults with uniform properties, the seismic S ratio [S = (τp − τ0)/(τ0 − τr)], a measure of the initial loading stress, τ0, relative to the peak and residual strengths, τp and τr, respectively, must be smaller than some critical value for the transition to occur. The maximum S value for unbounded faults in three dimensions is 1.19, smaller than the value of 1.77 that Andrews (1985) has shown to govern the transition in two dimensions. The supershear transition length (i.e., how far the rupture propagates before reaching intersonic speeds) is proportional to a length scale arising from the friction law governing the nucleation and stability of the daughter crack. A sufficiently narrow fault width suppresses the transition; the critical width is approximately 0.8 times the transition length on an unbounded fault. The transition length is highly sensitive to the form of the slip‐weakening law even when the associated fracture energies are identical. Heterogeneous propagation, in the form of abrupt accelerations or increases in stress‐release rate, induces stress‐wave radiation that can trigger transient bursts of intersonic propagation.