Domain decomposition method for dynamic faulting under slip-dependent friction

Badea, Lori; Ionescu, Ioan R.; Wolf, Sylvie

doi:10.1016/j.jcp.2004.06.003

Cited by 4 publications

(15 citation statements)

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“…Dynamic simulations were performed on the above conÿguration, using a Newmark ÿnite di erence scheme and a domain decomposition method (see Reference [22] for a detailed description). Such simulations can be used to check the validity of the computed value of ÿ 0 (found with 2 = 0).…”

Section: Spectral Analysis Vs Time Evolution On Two Parallel Faultsmentioning

confidence: 99%

Interaction of faults under slip‐dependent friction. Non‐linear eigenvalue analysis

Ionescu

Wolf

2004

Math Methods in App Sciences

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SUMMARYWe analyse the evolution of a system of ÿnite faults by considering the non-linear eigenvalue problems associated to static and dynamic solutions on unbounded domains. We restrict our investigation to the ÿrst eigenvalue (Rayleigh quotient). We point out its physical signiÿcance through a stability analysis and we give an e cient numerical algorithm able to compute it together with the corresponding eigenfunction.We consider the anti-plane shearing on a system of ÿnite faults under a slip-dependent friction in a linear elastic domain, not necessarily bounded. The static problem is formulated in terms of local minima of the energy functional. We introduce the non-linear (static) eigenvalue problem and we prove the existence of a ÿrst eigenvalue=eigenfunction characterizing the isolated local minima. For the dynamic problem, we discuss the existence of solutions with an exponential growth, to deduce a (dynamic) non-linear eigenvalue problem. We prove the existence of a ÿrst dynamic eigenvalue and we analyse its behaviour with respect to the friction parameter. We deduce a mixed ÿnite element discretization of the non-linear spectral problem and we give a numerical algorithm to approach the ÿrst eigenvalue=eigenfunction. Finally we give some numerical results which include convergence tests, on a single fault and a two-faults system, and a comparison between the non-linear spectral results and the time evolution results.

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Section: Spectral Analysis Vs Time Evolution On Two Parallel Faultsmentioning

confidence: 99%

Interaction of faults under slip‐dependent friction. Non‐linear eigenvalue analysis

Ionescu

Wolf

2004

Math Methods in App Sciences

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“…For instance, a finite difference scheme was proposed in [29], for the anti-plane (2D, mode III) problem, and developed thereafter in [18,19] for the in-plane (2D, mode II) and 3D problems, but the use of a finite difference method restricts the applications on planar fault geometries. Further references on earthquake simulations can be bound for instance in [6]. We shall mention here a few recent works that constitute effective efforts to model realistic fault geometries.…”

Section: Introductionmentioning

confidence: 99%

“…There are much fewer finite element models [1,5,6,36] in the field of earthquake rupture simulation, because they are more difficult to implement than finite differences, and because low order schemes can lead to undesirable numerical dissipation. However, finite element methods have numerous advantages compared with finite differences.…”

Section: Introductionmentioning

confidence: 99%

“…However, finite element methods have numerous advantages compared with finite differences. They can handle strong heterogeneities as well as complex geometries [6,[37][38][39]. Besides, in dynamic contact mechanics, related friction laws are currently modeled using finite elements and there is a large number of papers and books on this topic (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…This article is a sequel to [6], which presented the first domain decomposition method to model dynamic faulting under slip-dependent friction in the anti-plane shearing configuration. Even if important features of the physical phenomenon (like stress interactions) are active in this configuration, only a limited number of geophysical faults are satisfactorily described by the anti-plane geometry.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Schwarz method for earthquake source dynamics

Badea

Ionescu

Wolf

2008

Journal of Computational Physics

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Mechanics of normal fault networks subject to slip-weakening friction

Wolf

Manighetti

Campillo

et al. 2006

Geophysical Journal International

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International audienceWe seek to understand how the stress interactions and the slip-weakening process combine within a non-coplanar, normal fault network to allow a slip instability to develop, and shape the final slip distribution on the system. In a first part, we perform a non-linear spectral analysis to investigate the conditions of stability and the process of slip initiation in an antiplane non-coplanar fault system subject to a slip-dependent friction law. That numerical model allows determining the zones that are able to slip within a fault network, as well as the location of the stress singularities. The resulting slip profiles on the faults show only a few different shapes, some of them with long, linear sections. This leads to formulate a general classification of slip profiles that can be used to infer the degree of fault interaction within any non-coplanar system. In a second part of work, we use our modelling to try reproducing the cumulative slip profiles measured on three real normal interacting faults forming a large-scale en echelon system. For that, we assume that cumulative slip profiles can be compared to the first static modal solution of our conceptual model. We succeed reproducing the profiles quite well using a variable weakening along the faults. Overall, the weakening rate decreases in the direction of propagation of the fault system. Yet, modelling the slip along the propagating, isolated termination segment of the system requires an unlikely distribution of weakening. This suggests that factors not considered in our analysis may contribute to slip profile shaping on isolated, propagating faults

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Domain decomposition method for dynamic faulting under slip-dependent friction

Cited by 4 publications

References 46 publications

Interaction of faults under slip‐dependent friction. Non‐linear eigenvalue analysis

Interaction of faults under slip‐dependent friction. Non‐linear eigenvalue analysis

Schwarz method for earthquake source dynamics

Mechanics of normal fault networks subject to slip-weakening friction

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