Slip of a Two-degree-of-freedom Spring-slider Model in the Presence of Slip-dependent Friction and Viscosity

Jeen-Hwa Wang

doi:10.4401/ag-7295

Abstract

In this study, we study the slip of a two-degree-of-freedom spring-slider model, consisting of two sliders, in the presence of slip-dependent friction and viscosity. Simulation results show that the coupling between the sliders is weak when the stiffness ratio, s , of the model is smaller than 5 and/or either U c1 or U c2 , which are the characteristic displacements of slip-dependent friction law at the two sliders, is smaller than 0.5. The patterns of motions of two sliders yielded by large U c1 and small U c2 are opposite to those by small U c1 and large U c2 . The ratio of static friction force at slider 2 to that at slider 1 is a factor in influencing the motions of two sliders. A higher static friction force at slider 2 leads to a longer delay time to trigger its motion. Slider 2 cannot move when the static friction force at it is higher than a critical value which will depend on other model parameters. The presence of viscosity between the slider and moving plate results in increases in duration times and predominant periods of motions of sliders and depresses the generation of nonlinear behavior. Viscosity results in small amplitudes and low velocities of motions of sliders.

Highlights

IntroductionThe rupture processes of an earthquake essentially consist of three steps: nucleation (or initiation), dynamical propagation, and arrest
The rupture processes of an earthquake essentially consist of three steps: nucleation, dynamical propagation, and arrest
4.1 Effect due to seismic coupling The lower-bound value of s for yielding strong coupling between the two sliders can be seen from Figures 4 and 5, which are the simulation results for s=5 and s=1, respectively, when the values of other model parameters are equal

Summary

Introduction

The rupture processes of an earthquake essentially consist of three steps: nucleation (or initiation), dynamical propagation, and arrest. When fluids are present in faults, thermal pressurization can play a significant role on earthquake rupture and result in resistance on the fault plane [Sibson, 1973; Fialko, 2004; Bizzari and Cocco, 2006a,b,c; Rice, 2006; Wang, 2009, 2011, 2013, 2016a; Bizzarri, 2010; Bizzarri, 2011a,b]. Wang [2016a] studied frictional and viscous effects on slip of a one-degree-of-freedom spring-slider model associated to a fault. I will explore the effects of slip-weakening friction due to thermal pressurization and viscosity on earthquake ruptures based on a two-degree-offreedom spring-slider model, which is generally used to approach an earthquake fault, because numerous earthquakes consist of few segments [Galvanetto, 2002; Turcotte, 1992; Dragoni and Santini, 2010, 2011, 2012, 2014; and cited references ]. Results will be significant on the understanding of earthquake ruptures

Two-degree-of-freedom Spring-slider Model

Discussion

Conclusions