Unstable Slip Pulses and Earthquake Nucleation as a Nonequilibrium First-Order Phase Transition

Brener, Efim A.; Aldam, Michael; Barras, Fabian; Molinari, Jean‐François; Bouchbinder, Eran

doi:10.1103/physrevlett.121.234302

Cited by 37 publications

(56 citation statements)

References 60 publications

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“…Therefore, the solution to the steady state pulse problem associated with a particular constitutive behavior provides a tool to determine the exact conditions (notably in terms of background stress) leading to the existence of sustained ruptures. Our analysis on the role of unstable slip pulses in controlling the growth of large scale ruptures is consistent with recent theoretical results from Brener et al (), who analyzed numerically the stability of slip pulses driven by a nonlinear rate‐dependent friction law. Numerical simulations indicate that such slip pulses are also unstable to small perturbations, and Brener et al () argue that such instabilities can be viewed as the nucleation process of large ruptures.…”

Section: Discussionsupporting

confidence: 90%

Stability of Pulse‐Like Earthquake Ruptures

2019

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Pulse‐like ruptures arise spontaneously in many elastodynamic rupture simulations and seem to be the dominant rupture mode along crustal faults. Pulse‐like ruptures propagating under steady state conditions can be efficiently analyzed theoretically, but it remains unclear how they can arise and how they evolve if perturbed. Using thermal pressurization as a representative constitutive law, we conduct elastodynamic simulations of pulse‐like ruptures and determine the spatiotemporal evolution of slip, slip rate, and pulse width perturbations induced by infinitesimal perturbations in background stress. These simulations indicate that steady state pulses driven by thermal pressurization are unstable. If the initial stress perturbation is negative, ruptures stop; conversely, if the perturbation is positive, ruptures grow and transition to either self‐similar pulses (at low background stress) or expanding cracks (at elevated background stress). Based on a dynamic dislocation model, we develop an elastodynamic equation of motion for slip pulses and demonstrate that steady state slip pulses are unstable if their accrued slip b is a decreasing function of the uniform background stress τb. This condition is satisfied by slip pulses driven by thermal pressurization. The equation of motion also predicts quantitatively the growth rate of perturbations and provides a generic tool to analyze the propagation of slip pulses. The unstable character of steady state slip pulses implies that this rupture mode is a key one determining the minimum stress conditions for sustainable ruptures along faults, that is, their “strength.” Furthermore, slip pulse instabilities can produce a remarkable complexity of rupture dynamics, even under uniform background stress conditions and material properties.

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Section: Discussionsupporting

confidence: 90%

Stability of Pulse‐Like Earthquake Ruptures

2019

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“…The major difference compared to the results presented in Fig. 7b, where c(τ 0 ) for rupture fronts is shown to be an increasing function of τ 0 , is that for healing fronts c(τ 0 ) is a decreasing function of τ 0 [101,102]. This implies that the two propagation speed spectra intersect at some loading level, say τ * .…”

Section: Propagating Frictional Modesmentioning

confidence: 57%

“…The figure presents a slip pulse that appears to propagate over long distances without appreciably changing its shape and propagation speed. Such pulses are sometimes termed sustained pulses [102], though determining whether they are truly steady-state objects or not is difficult based on dynamic simulations. The quite pronounced differences in the shape of the slip pulses presented in Figs.…”

Section: Propagating Frictional Modesmentioning

confidence: 99%

“…It turns out that small-H steady-state pulse solutions, an example of which is presented in Fig. 8a, are actually unstable [102]. In particular, it has been shown that small-H steady-state pulse solutions can be used to sort out perturbations based on their spatial extent; suppose that a homogeneous state corresponding to the stick fixed-point of the steady-state friction curve at a given τ 0 > τ * is introduced with a slip velocity perturbation.…”

Section: Propagating Frictional Modesmentioning

confidence: 99%

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Spatiotemporal Dynamics of Frictional Systems: The Interplay of Interfacial Friction and Bulk Elasticity

et al. 2019

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Frictional interfaces are abundant in natural and engineering systems, and predicting their behavior still poses challenges of prime scientific and technological importance. At the heart of these challenges lies the inherent coupling between the interfacial constitutive relation -the macroscopic friction law -and the bulk elasticity of the bodies that form the frictional interface. In this feature paper, we discuss the generic properties of the macroscopic friction law and the many ways in which its coupling to bulk elasticity gives rise to rich spatiotemporal frictional dynamics. We first present the widely used rate-and-state friction constitutive framework, discuss its power and limitations, and propose extensions that are supported by experimental data. We then discuss how bulk elasticity couples different parts of the interface, and how the range and nature of this interaction are affected by the system's geometry. Finally, in light of the coupling between interfacial and bulk physics, we discuss basic phenomena in spatially-extended frictional systems, including the stability of homogeneous sliding, the onset of sliding motion and a wide variety of propagating frictional modes (e.g. rupture fronts, healing fronts and slip pulses). Overall, the results presented and discussed in this feature paper highlight the inseparable roles played by interfacial and bulk physics in spatially-extended frictional systems. * eran.bouchbinder@weizmann.ac.il arXiv:1908.02820v1 [cond-mat.soft]

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“…At a larger scale, rate and state friction has been extensively used to analyze and explain different aspects of earthquake scenarios [5,6,7]. Instability of rate and state friction and the corresponding critical nucleation length have been the topic of several recent works [8,9,10,11].…”

Section: Introductionmentioning

confidence: 99%

Finite element modeling of dynamic frictional rupture with rate and state friction

Rezakhani

Barras

Brun

et al. 2020

Journal of the Mechanics and Physics of Solids

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Numerous laboratory experiments have demonstrated the dependence of the friction coefficient on the interfacial slip rate and the contact history, a behavior generically called rate and state friction. Although numerical models have been widely used for analyzing rate and state friction, in general they consider infinite elastic domains surrounding the sliding interface and rely on boundary integral formulations. Much less work has been dedicated to modeling finite size systems to account for interactions with boundaries. This paper investigates rate and state frictional interfaces in the context of finite size systems with the finite element method in explicit dynamics. It is shown that due to the highly non-linear nature of rate and state friction and its sensitivity to numerical noise, the time integration step to achieve an accurate steady state solution is orders of magnitude smaller compared to the stable time step required in boundary integral formulations. We provide evidence that the noise, which is source of instability in the finite element solution, originates from internal discretization nodes. We then investigate the long term behavior of the sliding interface for two different friction laws: a velocity weakening law, for which the friction monotonously decreases with increasing sliding velocity, and a velocity weakening-strengthening law, for which the friction coefficient first decreases but then increases above a critical velocity. We show that for both friction laws at finite times, that is before wave reflections from the boundaries come back to the sliding interface, a temporary steady state sliding is reached, with a well-defined stress drop at the interface. This stress drop gives rise to a stress concentration and leads to an analogy between friction and fracture. However, at longer times, that is after multiple wave reflections, the stress drop is essentially zero, resulting in losing the analogy with fracture mechanics. Finally, the simulations reveal that velocity weakening is unstable at long time scales, as it results in an acceleration of the sliding blocks. On the other hand, velocity weakening-strengthening reaches a steady state sliding configuration.

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Unstable Slip Pulses and Earthquake Nucleation as a Nonequilibrium First-Order Phase Transition

Cited by 37 publications

References 60 publications

Stability of Pulse‐Like Earthquake Ruptures

Stability of Pulse‐Like Earthquake Ruptures

Spatiotemporal Dynamics of Frictional Systems: The Interplay of Interfacial Friction and Bulk Elasticity

Finite element modeling of dynamic frictional rupture with rate and state friction

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