Rate and state dependent friction and the stability of sliding between elastically deformable solids

Rice, James R.; Lapusta, N.; Ranjith, K.

doi:10.1016/s0022-5096(01)00042-4

Cited by 574 publications

(672 citation statements)

References 52 publications

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“…Rice et al [2001] derived a regularized expression based on the friction laws of Dieterich [1979] and Ruina [1983] which overcomes this limitation. Assuming for simplicity that there are no state evolution effects, which may be appropriate for high temperature sliding of granite surfaces [Blanpied et al, 1998], solid plug shear tractions t p are equal to…”

Section: Motion Of the Solid Plugmentioning

confidence: 99%

Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes

Anderson¹,

Segall²

2011

J. Geophys. Res.

115

154

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[1] We present a model of effusive silicic volcanic eruptions which relates magma chamber and conduit physics to time-dependent data sets, including ground deformation and extrusion rate. The model involves a deflating chamber which supplies Newtonian magma through a cylindrical conduit. Solidification is approximated as occurring at fixed depth, producing a solid plug that slips along its margins with rate-dependent friction. Changes in tractions acting on the chamber and conduit walls are used to compute surface deformations. Given appropriate material properties and initial conditions, the model predicts the full evolution of an eruption, allowing us to examine the dependence of observables on initial chamber volume, overpressure, and volatile content. Employing multiple data sets in combination with a physics-based model allows for better constraints on these parameters than is possible using kinematic idealizations. Modeling posteruptive deformation provides an improved constraint on the rate of influx into the magma chamber from deeper sources. We compare numerical results to analytical approximations and to data from the 2004-2008 eruption of Mount St. Helens. For nominal parameters the balance between magma chamber pressure and frictional resistance of the solid plug controls the evolution of the eruption, with little contribution from the fluid magma below the idealized crystallization depth. While rate-dependent plug friction influences the timedependent evolution of the eruption, it has no control on the final chamber pressure or extruded volume.Citation: Anderson, K., and P. Segall (2011), Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes,

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Section: Motion Of the Solid Plugmentioning

confidence: 99%

Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes

Anderson¹,

Segall²

2011

J. Geophys. Res.

115

154

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“…During the following interseismic period, the locked region of patch A shrinks by penetration of creep from the surrounding areas, which occurs due to stress concentration at the boundary between creeping and locked regions (e.g., Tse and Rice, 1986;Lapusta et al, 2000). Earthquake rupture nucleates when the creeping region within patch A becomes comparable to the nucleation size estimates (Rice and Ruina, 1983;Rice et al, 2001;Rubin and …”

mentioning

confidence: 99%

Stable creeping fault segments can become destructive as a result of dynamic weakening

Noda

Lapusta

2013

Nature

Self Cite

463

388

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1 Supplementary Information S1. Model parameters Figure S1 and Table S1 show the model geometry and parameters used in the simulation presented in the main article. S2. Model response that reproduces a range of observationsThe rich model response described in the main text is animated by the two supplementary movies which show the time evolution of slip rate distribution V z (x, z, t) on the fault from 4300 to 4800 years (movie I) and from 3500 to 4000 years (movie II) after the beginning of the numerical simulation. Coseismic slip rates of the order of 0.1 m/s and higher are indicated by white to blue colors. The slower slip rates are shown in progressively darker yellow and orange, with the long-term plate rate of 10 -9 m/s indicated in red. Locked regions which have, by definition, much smaller slip rates than the plate rate are indicated by black patches.The simulated time and the maximum slip rate over the fault at that time are given at upper-right and upper-left corners of the movies, respectively. The movie frames are taken every 30 computational time steps, which vary in the computation, and hence the time intervals between the frames are quite heterogeneous. During coseismic periods, the typical time step is 2/150 s and the typical interframe rate is 0.4 s. In the interseismic periods, the interframe rates reach values of about 1 year.Movie I illustrates the behavior of the model that combines, in the same patch, creep in the interseismic periods and large seismic slip. It starts at a time when the interseismic fault slip rate distribution is as expected for the slow-rate friction properties adopted in the model: patch A is mostly locked and patch B is creeping with the long-term plate rate, like the creeping areas that surround the two patches. During the following interseismic period, the locked region of patch A shrinks by penetration of creep from the surrounding areas, which occurs due to stress concentration at the boundary between creeping and locked regions (e.g., Tse and Rice, 1986;Lapusta et al., 2000). Earthquake rupture nucleates when the creeping region within patch A becomes comparable to the nucleation size estimates (Rice and Ruina, 1983;Rice et al., 2001;Rubin and

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“…(Turcotte and Schubert, 1982), and can yield viscosity on the fault plane (Byerlee, 1968). Rice et al (2001) discussed that rate-and state-dependent friction in thermally activated processes allows creep slippage at asperity contacts on the fault plane. Scholz (1990) suggested that the friction melts would present significant viscous resistance to shear and thus inhibit continued slip.…”

Section: Viscositymentioning

confidence: 99%

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

Wang

2017

Nonlin. Processes Geophys.

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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.

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Rate and state dependent friction and the stability of sliding between elastically deformable solids

Cited by 574 publications

References 52 publications

Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes

Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes

Stable creeping fault segments can become destructive as a result of dynamic weakening

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

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