Conditions under which velocity-weakening friction allows a self-healing versus a cracklike mode of rupture

Slip rupture processes on velocity-weakening faults have been found in simulations to occur by two basic modes, the expanding crack and self-healing modes. In the expanding crack mode, as the rupture zone on a fault keeps expanding, slip continues growing everywhere within the rupture. In the self-healing mode, rupture occurs as a slip pulse propagating along the fault, with cessation of slip behind the pulse, so that the slipping region occupies only a small width at the front of the expanding rupture zone. We discuss the determination of rupture mode for dynamic slip between elastic half-spaces that are uniformly prestressed at background loading level τb0 outside a perturbed zone where rupture is nucleated. The interface follows a rate and state law such that strength τstrength approaches a velocity-dependent steady-state value τss(V) for sustained slip at velocity V, where dτss(V)/dV ≦ 0 (velocity weakening). By proving a theorem on when a certain type of cracklike solution cannot exist, and by analyzing the results of 2D antiplane simulations of rupture propagation for different classes of constitutive laws, and for a wide range of parameters within each, we develop explanations of when one or the other mode of rupture will result. The explanation is given in terms of a critical stress level τpulse and a dimensionless velocity-weakening parameter T that is defined when τb0 ≥ τpulse. Here τpulse is the largest value of τb0 satisfying τb0 − (μ/2c)V ≤ τss(V) for all V > 0, where μ is the shear modulus and c is the shear wave speed. Also, T = [−dτss(V)/dV]/(μ/2c) evaluated at V = Vdyna, which is the largest root of τb0 − (μ/2c)V = τss(V); T = 1 at τb0 = τpulse, and T diminishes toward 0 as τb0 is increased above τpulse. We thus show that the rupture mode is of the self-healing pulse type in the low-stress range, when τb0 < τpulse or when τb0 is only slightly greater than τpulse, such that T is near unity (e.g., T > 0.6). The amplitude of slip in the pulse diminishes with propagation distance at the lowest stress levels, whereas the amplitude increases for τb0 above a certain threshold τarrest, with τarrest < τpulse in the cases examined. When τb0 is sufficiently higher than τpulse that T is near zero (e.g., T < 0.4 in our 2D antiplane simulations), the rupture mode is that of an enlarging shear crack. Thus rupture under low stress is in the self-healing mode and under high stress in the cracklike mode, where our present work shows how to quantify low and high. The results therefore suggest the possibility that the self-healing mode is common for large natural ruptures because the stresses on faults are simply too low to allow the cracklike mode.