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

Abstract

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.

A study of earthquake recurrence based on a one-body spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity

“…However, the main factors in influencing earthquake occurrences commonly are spatially heterogeneous and also vary with time. Thus, the recurrence times of earthquakes, especially large events, are not constant inferred either from observations (Ando, 1975;Sieh, 1981;Kanamori and Allen, 1986;Wang and Kuo, 1998;Wang, 2005;Sieh et al, 2008) or from modeling (Wang, 1995(Wang, , 1996Ward, 1996Ward, , 2000Wang and Hwang, 2001). Kanamori and Allen (1986) observed that faults with longer T R are stronger than those with shorter T R .…”

“…The one-, two-, three-, and few-body models with various friction laws have also been applied to approach fault dynamics (see Turcotte, 1992). The studies for various friction laws based on spring-slider models are briefly described below: (1) for rate-and state-dependent friction (e.g., Rice and Tse, 1986;Ryabov and Ito, 2001;Erickson et al, 2008Erickson et al, , 2011He et al, 2003;Mitsui and Hirahara, 2009;Bizzarri, 2012a;Abe and Kato, 2013;Kostić et al, 2013a;Bizzarri and Crupi, 2014;Franović et al, 2016); (2) for velocity-weakening friction (e.g., Carlson and Langer, 1989;Huang and Turcotte, 1992;Brun and Gomez, 1994;Wang and Hwang, 2001;Wang, 2003;Kostić et al, 2013b); (3) for simple static-dynamic friction (e.g., Abaimov et al, 2007;Hasumi, 2007).…”

“…Erickson et al (2008) suggested that aperiodicity in earthquake dynamics is due to either the nonlinear friction law (Huang and Turcotte, 1990) or the heterogeneous stress distribution (Lapusta and Rice, 2003). Wang and Hwang (2001) emphasized the importance of heterogeneous frictional strengths. Mitsui and Hirahara (2009) pointed out the effect of thermal pressurization.…”

A Study of Earthquake Recurrence based on a One-body Spring-slider Model in the Presence of Thermal-pressurized Slip-weakening Friction and Viscosity

“…The frictional force F (u, v) is controlled by several factors (see Wang, 2016, and cited references therein). An effect combined from temperature and fluids in a fault zone can result in thermal pressurization (abbreviated as TP hereafter) which would yield a shear stress (resistance) on the fault plane (Sibson, 1973;Lachenbruch, 1980;Rice, 2006;Wang, 2009Wang, , 2011Wang, , 2016Wang, , 2017aBizzarri, 2009). Rice (2006) proposed two end-member models of TP, i.e., the adiabatic undrained deformation (AUD) model and slip-on-aplane (SOP) model.…”

“…One-body spring-slider model. In the figure, t, m, K, η, V p , σ n , F , u, and u o denote, respectively, the time, the mass of the slider, the spring constant, the damping coefficient, the driving velocity, the normal stress, the frictional force, displacement of the slider, and the equilibrium location of the slider (after Wang, 2016). SOP model cannot be associated with the wear process, the SOP model is not used in this study.…”