Stability analyses and numerical simulations of the single degree of freedom spring-slider system obeying the revised rate- and state-dependent friction law

Abstract

The linear and nonlinear stabilities of the single degree of freedom spring-slider system which accords to the revised rate- and state-dependent friction law (RSF) (Nagata et al. J Geophys Res 117 (B2):B2314, 2012) are analyzed. The revised ageing law obtained by Nagata et al. (J Geophys Res 117 (B2):B2314, 2012) incorporates the effects of changes in shear stress. Numerical simulations on the cyclic stick–slip motions of the system are developed and compared with the results of the systems according to the original ageing law or the slip law. From the insight of the stability analyses and numerical simulations, it is found that the revised ageing law integrates the “healing effect” feature of the original ageing law and the dynamic slip features of the slip law. In the stick–slip cycles, the velocity decreases with non-constant states during the dynamic overshoot for the revised ageing law, which is different from both the original ageing law and the slip law. Although the revised ageing law concluded from the low velocity friction experiments cannot account for the earthquake-like high velocity friction experiments, it can be used in earthquake nucleation with low velocity. The stability analyses and the results of numerical simulations are helpful to understanding the implications of the revised ageing law.