Abstract
<span style="font-family: 新細明體;">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 <span style="font-family: 新細明體;">[eta]</span> and <span style="font-family: 新細明體;">[gamma]</span> to make the slider slip steadily without strong attenuation. The viscous effect is stronger than the frictional effect. Meanwhile, a change of <span style="font-family: 新細明體;">[eta]</span> results in a larger effect on the slip of the slider than a change of <span style="font-family: 新細明體;">[gamma]</span>. 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.</span>
Highlights
The rupture processes of an earthquake consist of three steps: nucleation, dynamical propagation, and arrest
This leads to the marginal analyses of slip of one-body spring-slider model in the presence of friction, and the results could work for slow earthquakes
In order to study the effects on earthquake ruptures caused by slip-weakening friction and viscosity, the slip of a one-body dynamical slider-slider model is theoretically analyzed and numerically simulated when the two factors are present
Summary
The rupture processes of an earthquake consist of three steps: nucleation (or initiation), dynamical propagation, and arrest. In order to perform the analytical study of the frictional effect on earthquake ruptures based on the onebody spring-slider model, a simplified linearly slipweakening friction law in the form of F(u) = Fo−cu [Wang 2016], where c is the weakening rate, is considered hereafter. This leads to the marginal analyses of slip of one-body spring-slider model in the presence of friction, and the results could work for slow earthquakes. The TP friction law leads to a faster drop of friction and a higher stress drop than the other two
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