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 simu lations to occur by two basic modes, the expanding crack and self-healing m odes. In the expanding crack mode, as the rupture zone on a fault keeps exp anding, slip continues growing everywhere within the rupture. In the self-h ealing mode, rupture occurs as a slip pulse propagating along the fault, wi th 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 elast ic half-spaces that are uniformly prestressed at background loading level t au(0)(b) outside a perturbed zone where rupture is nucleated. The interface follows a rate and state law such that strength tau(strength) approaches a velocity-dependent steady-state value tau(ss)(V) for sustained slip at vel ocity V, where d tau(ss)(V)/dV less than or equal to 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 rang e of parameters within each, we develop explanations of when one or the oth er mode of rupture will result. The explanation is given in terms of a crit ical stress level tau(pulse) and a dimensionless velocity-weakening paramet er T that is defined when tau(0)(b) greater than or equal to tau(pulse). He re tau(pulse) is the largest value of tau(0)(b) satisfying tau(0)(b) - (mu/ 2c)V less than or equal to tau(ss)(V) for all V > 0, where mu is the shear modulus and c is the shear wave speed. Also, T = [- d tau(ss)(V)/dV]/(mu/2c ) evaluated at V = V-dyna, which is the largest root of tau(0)(b) - (mu/2c) V = tau(ss)(V); T = 1 at tau(0)(b) = tau(pulse), and T diminishes toward 0 as tau(0)(b) is increased above tau(pulse). We thus show that the rupture mode is of the self-healing pulse type in the low-stress range, when tau(0)(b) < tau(pulse) or when tau(0)(b) is only sl ightly greater than tau(pulse), 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 tau(0)(b) abo ve a certain threshold tau(arrest), with tau(arrest) < tau(pulse) in the ca ses examined. When tau(0)(b) is sufficiently higher than tau(pulse) that T is near zero (e.g., T < 0.4 in our 2D antiplane simulations), the rupture m ode is that of an enlarging shear crack. Thus rupture under low stress is in the self-healing mode and under high st ress in the cracklike mode, where our present work shows how to quantify lo w and high. The results therefore suggest the possibility that the self-hea ling mode is common for large natural ruptures because the stresses on faul ts are simply too low to allow the cracklike mode.