Multistable slip of a one-degree-of-freedom spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity

Abstract

This study is focused on multistable slip of earthquakes based on a one-degree-of-freedom spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity by using the normalized equation of motion of the model. The major model parameters are the normalized characteristic displacement, Uc, of the friction law and the normalized viscosity coefficient, η, between the slider and background plate. Analytic results at small slip suggest that there is a solution regime for η and γ ( = 1∕Uc) to make the slider slip steadily. Numerical simulations exhibit that the time variation in normalized velocity, V∕Vmax (Vmax is the maximum velocity), obviously depends on Uc and η. The effect on the amplitude is stronger due to η than due to Uc. In the phase portrait of V∕Vmax versus the normalized displacement, U∕Umax (Umax is the maximum displacement), there are two fixed points. The one at large V∕Vmax and large U∕Umax is not an attractor, while that at small V∕Vmax and small U∕Umax can be an attractor for some values of η and Uc. When Uc<0. 55, unstable slip does not exist. When Uc ≥ 0. 55, Uc and η divide the solution domain into three regimes: stable, intermittent, and unstable (or chaotic) regimes. For a certain Uc, the three regimes are controlled by a lower bound, ηl, and an upper bound, ηu, of η. The values of ηl, ηu, and ηu − ηl all decrease with increasing Uc, thus suggesting that it is easier to yield unstable slip for larger Uc than for smaller Uc or for larger η than for smaller η. When Uc<1, the Fourier spectra calculated from simulation velocity waveforms exhibit several peaks, thus suggesting the existence of nonlinear behavior of the system. When Uc>1, the related Fourier spectra show only one peak, thus suggesting linear behavior of the system.