Self-healing solitonic slip pulses in frictional systems

A prominent spatiotemporal failure mode of frictional systems is self-healing slip pulses, which are propagating solitonic structures that feature a characteristic length. Here, we numerically derive a family of steady state slip pulse solutions along generic and realistic rate-and-state dependent frictional interfaces, separating large deformable bodies in contact. Such nonlinear interfaces feature a nonmonotonic frictional strength as a function of the slip velocity, with a local minimum. The solutions exhibit a diverging length and strongly inertial propagation velocities, when the driving stress approaches the frictional strength characterizing the local minimum from above, and change their character when it is away from it. An approximate scaling theory quantitatively explains these observations. The derived pulse solutions also exhibit significant spatially-extended dissipation in excess of the edge-localized dissipation (the effective fracture energy) and an unconventional edge singularity. The relevance of our findings for available observations is discussed.

Unstable Slip Pulses and Earthquake Nucleation as a Nonequilibrium First-Order Phase Transition

The onset of rapid slip along initially quiescent frictional interfaces, the process of "earthquake nucleation," and dissipative spatiotemporal slippage dynamics play important roles in a broad range of physical systems. Here we first show that interfaces described by generic friction laws feature stress-dependent steady-state slip pulse solutions, which are unstable in the quasi-1D approximation of thin elastic bodies. We propose that such unstable slip pulses of linear size L^{*} and characteristic amplitude are "critical nuclei" for rapid slip in a nonequilibrium analogy to equilibrium first-order phase transitions and quantitatively support this idea by dynamical calculations. We then perform 2D numerical calculations that indicate that the nucleation length L^{*} exists also in 2D and that the existence of a fracture mechanics Griffith-like length L_{G}<L^{*} gives rise to a richer phase diagram that features also sustained slip pulses.

Dynamical model of faulting in two dimensions and self-healing of large fractures

We describe a model for the simulation of extended two-dimensional in-plane dynamical ruptures and for the rapid calculation of statistical properties of repeated model-seismicity events. The discretization involves first- and second-nearest neighbors and is isotropic in both compression and shear properties. All rupture events obey a fracture criterion in the appropriate coordinate frame and numerical oscillations in slip velocity at crack tips due to discretization are minimized. The rupture velocities of fractures, in cases of homogeneous stress drop equal to the strength, are the supershear P-wave velocity in the direction of the prestress and the S-wave velocity in the perpendicular direction. We use the model to study the growth and healing of individual faults to understand the formation of propagating slip pulses. We confirm two mechanisms for the generation of isolated rupture pulses that have been proposed, namely, (1) a decrease in the dynamical friction with accelerating slip and (2) the encounter of the growing crack with extended regions of large difference between the threshold fracture stress and the prestress. We describe a third mechanism which is that of a velocity-dependent friction that operates equally on both the phases of increasing and decreasing slip velocities and has a characteristic length scale. It is a proxy for energy loss by radiation in a three-dimensional medium. In the case of an elongated rectangular model fault with an upper free surface and lower rigid boundary, pulses develop due to the influence of stress waves reflected from the rigid bottom boundary. In general, the excess of strength over stress drop controls crack fracture speeds; if it is too large, the crack stops. Under homogeneous stress conditions, isolated slip pulses are controlled by the spatial distribution of heterogeneities and by the velocity-dependent friction parametrization.

Pulse-like and crack-like ruptures in experiments mimicking crustal earthquakes

Theoretical studies have shown that the issue of rupture modes has important implications for fault constitutive laws, stress conditions on faults, energy partition and heat generation during earthquakes, scaling laws, and spatiotemporal complexity of fault slip. Early theoretical models treated earthquakes as crack-like ruptures, but seismic inversions indicate that earthquake ruptures may propagate in a self-healing pulse-like mode. A number of explanations for the existence of slip pulses have been proposed and continue to be vigorously debated. This study presents experimental observations of spontaneous pulse-like ruptures in a homogeneous linear-elastic setting that mimics crustal earthquakes; reveals how different rupture modes are selected based on the level of fault prestress; demonstrates that both rupture modes can transition to supershear speeds; and advocates, based on comparison with theoretical studies, the importance of velocity-weakening friction for earthquake dynamics.

Self-Healing Pulse-Like Shear Ruptures in the Laboratory

Models predict that dynamic shear ruptures during earthquake faulting occur as either sliding cracks, where a large section of the interface slides behind a fast-moving rupture front, or self-healing slip pulses, where the fault relocks shortly behind the rupture front. We report experimental visualizations of crack-like, pulse-like, and mixed rupture modes propagating along frictionally held, "incoherent" interfaces separating identical solids, and we describe the conditions under which those modes develop. A combination of simultaneously performed measurements via dynamic photoelasticity and laser interferometry reveals the rupture mode type, the exact point of rupture initiation, the sliding velocity history, and the rupture propagation speed.