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, U_c, 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∕U_c) to make the slider slip steadily. Numerical simulations exhibit that the time variation in normalized velocity, V∕V_max (V_max is the maximum velocity), obviously depends on U_c and η. The effect on the amplitude is stronger due to η than due to U_c. In the phase portrait of V∕V_max versus the normalized displacement, U∕U_max (U_max is the maximum displacement), there are two fixed points. The one at large V∕V_max and large U∕U_max is not an attractor, while that at small V∕V_max and small U∕U_max can be an attractor for some values of η and U_c. When U_c<0. 55, unstable slip does not exist. When U_c ≥ 0. 55, U_c and η divide the solution domain into three regimes: stable, intermittent, and unstable (or chaotic) regimes. For a certain U_c, the three regimes are controlled by a lower bound, η_l, and an upper bound, η_u, of η. The values of η_l, η_u, and η_u − η_l all decrease with increasing U_c, thus suggesting that it is easier to yield unstable slip for larger U_c than for smaller U_c or for larger η than for smaller η. When U_c<1, the Fourier spectra calculated from simulation velocity waveforms exhibit several peaks, thus suggesting the existence of nonlinear behavior of the system. When U_c>1, the related Fourier spectra show only one peak, thus suggesting linear behavior of the system.