Analysis of slip‐weakening frictional laws with static restrengthening and their implications on the scaling, asymmetry, and mode of dynamic rupture on homogeneous and bimaterial interfaces

Olsen-Kettle, Louise; Weatherley, Dion; Saez, E.; Gross, Lutz; Mühlhaus, H. B.; Xing, Huilin

doi:10.1029/2007jb005454

Cited by 21 publications

(45 citation statements)

References 65 publications

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“…A fractal distribution for μ s along the fault was employed to investigate the effect of heterogeneities along the fault (Olsen-Kettle et al 2008;Olsen-Kettle & Mühlhaus in press). The dynamic coefficient of friction was proportional to μ s , where μ d = α μ μ s and α μ ranged from 0.6 to 0.75.…”

Section: Numerical Results For Earthquake Modelmentioning

confidence: 99%

“…F n and F τ are normal and tangential restoring forces at the fault interface given by the penalty method to prevent slip from occurring. The elastic wave equation was solved using the finite-element method (Olsen-Kettle et al 2008).…”

Section: Numerical Results For Earthquake Modelmentioning

confidence: 99%

“…The central difference approximation for the spatial derivatives is only accurate to second order in the mesh spacing. This is typically used in finite-difference and finite-element codes (Olsen-Kettle et al 2008). We can analyse the error solving the nonlinear shock-wave equation using the central-difference method.…”

Section: Mesh Dependence In Nonlinear Wave Equationsmentioning

confidence: 99%

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A study of localization limiters and mesh dependency in earthquake rupture

Olsen-Kettle

Mühlhaus

Baillard

2010

Phil. Trans. R. Soc. A.

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No complete physically consistent model of earthquake rupture exists that can fully describe the rich hierarchy of scale dependencies and nonlinearities associated with earthquakes. We study mesh sensitivity in numerical models of earthquake rupture and demonstrate that this mesh sensitivity may provide hidden clues to the underlying physics generating the rich dynamics associated with earthquake rupture. We focus on unstable slip events that occur in earthquakes when rupture is associated with frictional weakening of the fault. Attempts to simulate these phenomena directly by introducing the relevant constitutive behaviour leads to mesh-dependent results, where the deformation localizes in one element, irrespective of size. Interestingly, earthquake models with oversized mesh elements that are ill-posed in the continuum limit display more complex and realistic physics. Until now, the mesh-dependency problem has been regarded as a red herringbut have we overlooked an important clue arising from the mesh sensitivity? We analyse spatial discretization errors introduced into models with oversized meshes to show how the governing equations may change because of these error terms and give rise to more interesting physics.

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Section: Numerical Results For Earthquake Modelmentioning

confidence: 99%

Section: Numerical Results For Earthquake Modelmentioning

confidence: 99%

Section: Mesh Dependence In Nonlinear Wave Equationsmentioning

confidence: 99%

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A study of localization limiters and mesh dependency in earthquake rupture

Olsen-Kettle

Mühlhaus

Baillard

2010

Phil. Trans. R. Soc. A.

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“…MESH DEPENDENCE AND SLIP COMPLEXITY 1663 modified slip-weakening model when a point on the fault is no longer slipping inelastically [12]. Both pulse-like and crack-like rupture can be produced since the fault can re-strengthen to its initial static value of friction after rupture.…”

Section: Mesh Dependence and Slip Complexitymentioning

confidence: 98%

Mesh dependence and slip complexity in earthquake fault models

Olsen-Kettle

Mühlhaus

2010

Concurrency and Computation

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SUMMARYWe study the origins of mesh dependence in earthquake dynamics and show that mesh sensitivity in numerical models of earthquake rupture can unearth new, exciting physical phenomena, and provide hidden clues to discovering the physics underlying earthquake complexity. We show (in agreement with previous numerical studies of dynamic rupture at faults) that coarse meshes or discrete models produce more interesting physics because these numerical simulations produce richer spatio-temporal complexity at faults over multiple earthquake cycles. These discrete models are desirable as they reproduce the observed Gutenberg-Richter power-law frequency magnitude distribution of earthquakes more accurately. However, this complexity is lost as the mesh size is refined, which is undersirable from a physical point of view. We investigate this mesh sensitivity by analysing the higher-order perturbative terms introduced into numerical models with coarse meshes. The introduction of these higher-order, nonlinear terms into standard continuum models generally used to describe earthquake dynamics may provide a key to reproducing earthquake complexity while partially removing the associated mesh dependence without the need to modify the underlying mesh. This is a first step towards deriving a physical law capable of reproducing the scale-invariant behaviour in earthquake sizes and reconciling continuum and discrete models of earthquake rupture.

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“…Olsen-Kettle et al (2008) showed that this greatly reduces the mesh-dependency associated with the ill-posedness in the sense of Renardy (1992).…”

Section: Friction Lawmentioning

confidence: 99%

Stress heterogeneities in earthquake rupture experiments with material contrasts

Langer¹,

Weatherley²,

Olsen-Kettle³

et al. 2013

Journal of the Mechanics and Physics of Solids

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We investigate significant heterogeneous stresses along bimaterial interfaces in laboratory and numerical experiments. These stresses, partially induced by model or experimental configuration, affect the supershear transition length and rupture speed, mode and directivity in uniaxial compression tests and dynamic rupture experiments with bimaterial interfaces. Using numerical simulations we show that normal and tangential stresses at the fault are distorted by the different stress-strain relationships of the materials. This distortion leads to altered supershear transition lengths, higher rupture potencies and amplifies the preference for rupture in the direction of slip of the slower and more compliant material. We demonstrate how this stress-distortion can be decreased in laboratory experiments by using larger specimen samples and in numerical models by using periodic boundary conditions.

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Analysis of slip‐weakening frictional laws with static restrengthening and their implications on the scaling, asymmetry, and mode of dynamic rupture on homogeneous and bimaterial interfaces

Cited by 21 publications

References 65 publications

A study of localization limiters and mesh dependency in earthquake rupture

A study of localization limiters and mesh dependency in earthquake rupture

Mesh dependence and slip complexity in earthquake fault models

Stress heterogeneities in earthquake rupture experiments with material contrasts

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