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This study is focused on analytic study at small displacements and numerical simulations of slip of a one-body dynamical slider-slider model in the presence of slip-weakening friction and viscosity. Analytic results with numerical computations show that the displacement of the slider is controlled by the decreasing rate, [gamma], of friction force with slip and viscosity, [eta], of fault-zone material. The natural period of the system with slip-weakening friction and viscosity is longer than that of the system without the two factors. There is a solution regime for [eta] and [gamma] to make the slider slip steadily without strong attenuation. The viscous effect is stronger than the frictional effect. Meanwhile, a change of [eta] results in a larger effect on the slip of the slider than a change of [gamma]. Numerical simulations are made for a one-body dynamical slider-slider model in the presence of three slip-weakening friction laws, i.e., the thermal-pressurization (TP) friction law, the softening-hardening (SH) friction law, and a simple slip-weakening (SW) friction law, and viscosity. Results show that slip-weakening friction and viscosity remarkably affect slip of the slider. The TP and SW friction laws cause very similar results. The results caused by the SH friction law are quite different from those by the other two. For the cases in study, the fixed points are not an attractor

Slip of a one-body dynamical spring-slider model in the presence of slip-weakening friction and viscosity