Stability of quasi-static slip in a single degree of freedom elastic system with rate and state dependent friction

Ranjith, K.; Rice, James R.

doi:10.1016/s0022-5096(98)00113-6

Cited by 79 publications

(87 citation statements)

References 9 publications

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“…Because the sliding behaviour and the condition for the occurrence of unstable slip are different for the two types of state evolution law (MARONE 1998;RANJITH and RICE 1999), the simulation results in the present study cannot be directly compared with those using the slip type of the state evolution law.…”

Section: Modelmentioning

confidence: 98%

Complex Earthquake Cycle Simulations Using a Two-Degree-of-Freedom Spring-Block Model with a Rate- and State-Friction Law

Abe

Kato

2012

Pure Appl. Geophys.

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Abstract-Numerical simulations of complex earthquake cycles are conducted using a two-degree-of-freedom spring-block model with a rate-and state-friction law, which has been supported by laboratory experiments. The model consisted of two blocks coupled to each other and connected by elastic springs to a constant-velocity, moving driver. By widely and systematically varying the model parameters, various slip patterns were obtained, including the periodic recurrence of seismic and aseismic slip events, and several types of chaotic behaviour. The transition in the slip pattern from periodic to chaotic is examined using bifurcation diagrams. The model system exhibits typical period-doubling sequences for some parameter ranges, and attains chaotic motion. Simple relationships are found in iteration maps of the recurrence intervals of simulated earthquakes, suggesting that the simulated slip behaviour is deterministic chaos. Time evolutions of the cumulative slip distance in chaotic slip patterns are well approximated by a time-predictable model. In some cases, both seismic and aseismic slip events occur at a block, and aseismic slip events complicate the earthquake recurrence patterns.

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Section: Modelmentioning

confidence: 98%

Complex Earthquake Cycle Simulations Using a Two-Degree-of-Freedom Spring-Block Model with a Rate- and State-Friction Law

Abe

Kato

2012

Pure Appl. Geophys.

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“…Furthermore we have used the nondimensional forms (a and b) of the frictional constitutive parameters and denoted the characteristic length by D c . In a number of previous studies [e.g., Gu et al, 1984;Rice and Tse, 1986;Gu and Wong, 1991;Boatwright and Cocco, 1996;Ranjith and Rice, 1999], the characteristic length is denoted by L, and the constitutive parameters (A = sa and B = sb) have dimensions of stress.…”

Section: Friction Constitutive Equationsmentioning

confidence: 99%

“…Likewise investigations of the dynamics under variable normal stress [He et al, 1998] have been conducted for the slip law only. While linear stability analyses [Ruina, 1983] have shown that the slip and slowness laws give identical responses under small perturbations, Ranjith and Rice [1999] recently showed that nonlinear stability behavior for the slowness law can be very different from that for the slip law [Gu et al, 1984]. Therefore, it is likely that the inertia-controlled motion in a stick-slip cycle will also have different dynamic attributes for the two classes of friction law.…”

Section: Introductionmentioning

confidence: 99%

Scaling of stress drop with recurrence interval and loading velocity for laboratory‐derived fault strength relations

Wong

Beeler

2003

J. Geophys. Res.

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[1] The dynamics of a spring-slider system with a single degree of freedom was investigated, focusing on two different rate-and state-dependent friction laws. While the inertia-controlled behavior and stick-slip cycles for a system that obeys the slip law have been extensively simulated, this study presents a comparative study of a system that obeys the slowness law. A key conclusion is that for both friction laws the overall stress drops are linearly related to the logarithm of the loading velocity (and the recurrence time) through the velocity-weakening parameter b À a and normal stress. Relatively higher peak stresses, larger quasi-static stress drop, and larger effective fracture energy are associated with a system that obeys the slowness law. Consequently, the partitioning of stress drop between quasi-static and dynamic slips, as well as dynamic overshoot and strength recovery, varies according to whether the slowness or slip law has been adopted. Analytic approximations were derived that elucidate the interplay of dynamics, energetics, and frictional constitutive behavior in controlling the scaling of stress drops with loading velocity and recurrence time. Seismological implications of the scaling behavior are also discussed.

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“…With the decrease of the average slip rate 0 δ  , the stability period of the fault increases. The change of compressive stress 0 Ω has little effect on the stability of the fault (sequence number 7,8), but the peak value of sliding rate increases with the increase of the normal stress.…”

Section: B Characteristic Earthquakes On the Fault Segmentmentioning

confidence: 99%

Analysis on the Critical Condition of Active Fault Instability and the Parameters of the Interface Model

Liu¹,

Liu²,

Zhao³

et al. 2017

Proceedings of the 3rd International Conference on Wireless Communication and Sensor Networks (WCSN 2016)

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Abstract-In this paper, earthquake triggering is described as the process of local instability of system in mathematical and physical way. And critical instability conditions of the fault in analysis domain are given. Based on elastic-plastic theory general constitutive relationship of the fault plane is derived. And its stability state is discussed by the example of rate and state related friction law corresponding to the characteristic earthquake. The relationship between seismic precursors and fault stability is analyzed in the three conditions of the rock stiffness, the fault interface stiffness and the stress and state of the fault. And the relationship between the parameters of the rate and state related friction law and the repeated interval of characteristic earthquakes is enumerated.

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Stability of quasi-static slip in a single degree of freedom elastic system with rate and state dependent friction

Cited by 79 publications

References 9 publications

Complex Earthquake Cycle Simulations Using a Two-Degree-of-Freedom Spring-Block Model with a Rate- and State-Friction Law

Complex Earthquake Cycle Simulations Using a Two-Degree-of-Freedom Spring-Block Model with a Rate- and State-Friction Law

Scaling of stress drop with recurrence interval and loading velocity for laboratory‐derived fault strength relations

Analysis on the Critical Condition of Active Fault Instability and the Parameters of the Interface Model

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