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 r0 b outside a perturbed zone where rupture is nucleated. The interface follows a rate and state law such that strength z-strength approaches a velocity-dependent steady-state value z-s,(V) for sustained slip at velocity V, where dz-ss(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 z-pulse and a dimensionless velocity-weakening parameter T that is defined when ro b --> z-pulse. Here Z'puls e is the largest value of z0 b satisfying z-o b (,u/2c)V 0, where ,u is the shear modulus and c is the shear wave speed. Also, T = [-dz-~(V)/dV]/(,u/2c) evaluated at V = Vdyna , which is the largest root of z-o b (,u/2c)V = rs~(V); T = 1 at z-b = Z-pulse, and T diminishes toward 0 as z-o b is increased above z-pulseWe thus show that the rupture mode is of the self-healing pulse type in the lowstress range, when z-o b < z-pulse o r when Zo b is only slightly greater than zpulse, 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 z-o b above a certain threshold z-west, with z-arrest < z-pulse in the cases examined. When z-o b is sufficiently higher than z-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. Introduction: Self-healing Pulse versus Cracklike Slip Rupture Mode Computational simulations (Cochard and Madariaga, 1994, 1996; Perrin et aL, 1995; Beeler and Tullis, 1996) have shown that dynamic slip on homogeneous velocityweakening faults may occur by either an enlarging crack mode or a self-healing slip pulse mode. Our goal here is to establish conditions, in terms of applied loading and features of the constitutive response, under which one or the other mode occurs. The study is for slip on the interfacial fault, on the plane y = 0, between two identical elastic halfspaces. In the most general 3D circumstances, the slip c~ varies with both coordinates in the fault plane, fi = 3(x, z, t). We develop some general results for that 3D context, but