4652 - MODES OF DYNAMIC RUPTURE ON INTERFACES WITH NONLINEAR RATE AND STATE FRICTION LAWS

Dynamic ruptures on frictional interfaces propagate as dynamic frictional shear cracks with well-defined rupture fronts and rupture velocities comparable to the wave speeds of the surrounding elastic media. On a frictional interface, the faces of the shear crack behind the rupture front are not traction-free and, in general, slide past each other as prescribed by the imposed friction law. In this study, laboratory-derived nonlinear rate and state friction laws are considered in which the frictional strength (or resistance) of the interface depends on the local sliding rate (or relative particle velocity) V and a state variable. The state variable incorporates dependence on the history of slip and describes the evolving properties of the microscopic contacts on the interface. Zheng and Rice [1] showed that if an interface between two identical elastic half-spaces is described by these laws of steady-state rate-weakening type, the dynamic rupture can proceed in two ways: as the so-called crack-like mode or pulse-like mode. In the crack-like mode, the slip duration at the points on the interface is comparable to the duration of the dynamic rupture itself. In the pulse-like mode, the points slip for a much shorter time and then dynamically heal, so that the resulting mode resembles a wrinkle (in a shear sense) propagating along the interface. The rupture mode is determined by two factors: How high the interface shear stress is before the dynamic rupture and how strong the rate weakening is (Zheng and Rice [1]). We find that there is another possibility, the multi-pulse mode, in which there are several pulses of slip propagating along the interface (Lapusta and Rice [2]). These multiple pulses occur in our simulations of dynamic ruptures in a two-dimensional anti-plane problem. The rupture starts in the crack-like mode but then the sliding behind the rupture front destabilizes with a wave-like pattern which grows into separated pulses of slip. The multiple pulses and their nucleation are well-resolved numerically, both in time and in space, and are reproducible in simulations with higher resolution. They are present only when the rate and state formulation incorporates sufficiently strong rate weakening so that the steady-state frictional resistance varies approximately as 1/V at high sliding rates V. For the logarithmic rate dependence of the traditional DieterichRuina laws, only the crack-like mode results. The new multi-pulse mode is consistent with the classification of Zheng and Rice [1] and fits in the transitional regime between the crack-like and pulse-like modes. The origin of these multiple pulses and their spacing can be explained by the linearized stability analysis of the steady elastodynamic sliding to Fourier mode perturbation. The analysis shows that there is the critical wavelength such that perturbations with shorter wavelengths decay and perturbations with longer wavelengths grow (Rice et al. [3]). We study the behavior of the growing wavelengths and find that there is a wavelength with the maximum growth rate (i.e., the perturbation with that wavelength grows the fastest). This is exactly the wavelength that we see during the nucleation of the multiple pulses behind the rupture front. The growth rate of that wavelength strongly depends on the amount of rate weakening in the friction law. The multiple pulses appear during the life-time of the dynamic rupture only if this growth rate is high enough. That is why we see multiple pulses only in the cases with strong rate weakening.