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

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