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## Conditions Under Which Velocity-Weakening Friction Allows a Self-Healing Versus a Cracklike Mode of Rupture

Gutuan Zheng, & James R. Rice

Published December 1998, SCEC Contribution #560

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 {tau}b0 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 velocity V, where d{tau}ss(V)/dV less double equals 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 {tau}pulse and a dimensionless velocity-weakening parameter T that is defined when {tau}b0 ≥ {tau}pulse. Here {tau}pulse is the largest value of {tau}b0 satisfying {tau}b0 – (µ/2c)V ≤ {tau}ss(V) for all V > 0, where µ is the shear modulus and c is the shear wave speed. Also, T = [–d{tau}ss(V)/dV]/(µ/2c) evaluated at V = Vdyna, which is the largest root of {tau}b0 – (µ/2c)V = {tau}ss(V); T = 1 at {tau}b0 = {tau}pulse, and T diminishes toward 0 as {tau}b0 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}b0 < {tau}pulse or when {tau}b0 is only slightly 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}b0 above a certain threshold {tau}arrest, with {tau}arrest < {tau}pulse in the cases examined. When {tau}b0 is sufficiently higher than {tau}pulse 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.

Citation
Zheng, G., & Rice, J. R. (1998). Conditions Under Which Velocity-Weakening Friction Allows a Self-Healing Versus a Cracklike Mode of Rupture. Bulletin of the Seismological Society of America, 88(6), 1466-1483.