Simulation of the spontaneous growth of a dynamic crack without constraints on the crack tip path

Kame, Nobuki; Yamashita, Teruo

doi:10.1046/j.1365-246x.1999.00940.x

Cited by 80 publications

(88 citation statements)

References 23 publications

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“…In contrast, dynamic rupture growth in a poroelastic medium is generally independent of n. The preliminary conclusion is that we may be able to get some constraints on the values of poroelastic constants of fault zone material from observation of the directions of coseismic and postseismic fault tip extensions. However, it is still premature to make such estimate in this paper because of the assumptions G 1 = G 2 and c 1 = c 2 and of simple model geometry; in a more realistic treatment we may have to take account of fault zone structure around a fault [e.g., Chester et al, 1993] and/or bending and branching of fault [Kame and Yamashita, 1999;Ando et al, 2004].…”

Section: Discussionmentioning

confidence: 99%

Postseismic quasi‐static fault slip due to pore pressure change on a bimaterial interface

Yamashita

2007

J. Geophys. Res.

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[1] We theoretically study the mechanism of afterslip, generally observed after the occurrence of large shallow earthquakes, taking account of poroelastic effects including fluid flow. A two-dimensional in-plane shear fault is assumed on a bimaterial interface that separates mechanically different poroelastic media. We first derive analytical expressions for the stress tensor components and fluid pressure as integrals of fault slip; the rigidity and diffusivity of the two media separated by the fault are assumed to be equal in value to derive the solution analytically. We then numerically solve these integral equations assuming stress boundary condition on the fault and obtain the spatiotemporal evolution of fault slip. The Coulomb failure criterion is assumed for the quasi-static growth of fault. We find that the positive feedback between the fluid pressure raised at the extending fault tip and evolving fault slip promotes the quasi-static fault tip extension; the amount of afterslip is found to be larger for smaller value of the Biot-Willis coefficient. It is also found that the poroelastic bimaterial effect favors unilateral extension of fault. Our calculations show that the patch of postseismic fault slip does not overlap that of coseismic slip significantly. We also observe a rapid decrease in postseismic moment release rate with time. These are in harmony with geodetic observation related to afterslips. We will have to resort to purely numerical analysis if we remove the assumptions about the rigidity and diffusivity; however, our present study can provide a reference point for such analysis.Citation: Yamashita, T. (2007), Postseismic quasi-static fault slip due to pore pressure change on a bimaterial interface, J. Geophys.

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Section: Discussionmentioning

confidence: 99%

Postseismic quasi‐static fault slip due to pore pressure change on a bimaterial interface

Yamashita

2007

J. Geophys. Res.

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“…The boundary integral equation method (BIEM) has been quite popular for crack and rupture propagation problems (Das, 1980;Andrews, 1985;Das and Kostrov, 1988;Perrin et al, 1995;Geubelle and Rice, 1995;Kame and Yamashita, 1999;Aochi et al, 2000;Lapusta et al, 2000;Day et al, 2005;Noda et al, 2009). BIEM reduces the problem to solving only for the solution along the fault, with the material response entering through convolutions over the past history of slip or tractions on the fault.…”

Section: Related Work On Seismic Wave Propagation and Dynamic Rupturementioning

confidence: 99%

Simulation of Dynamic Earthquake Ruptures in Complex Geometries Using High-Order Finite Difference Methods

2012

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We develop a stable and high-order accurate finite difference method for problems in earthquake rupture dynamics capable of handling complex geometries and multiple faults. The bulk material is an isotropic elastic solid cut by preexisting fault interfaces. The fields across the interfaces are related through friction laws which depend on the sliding velocity, tractions acting on the interface, and state variables which evolve according to ordinary differential equations involving local fields.The method is based on summation-by-parts finite difference operators with irregular geometries handled through coordinate transforms and multi-block meshes. Boundary conditions as well as block interface conditions (whether frictional or otherwise) are enforced weakly through the simultaneous approximation term method, resulting in a provably stable discretization.The theoretical accuracy and stability results are confirmed with the method of manufactured solutions. The practical benefits of the new methodology are illustrated in a simulation of a subduction zone megathrust earthquake, a challenging application problem involving complex free-surface topography, nonplanar faults, and varying material properties.

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“…Thus, it can be difficult to develop well-conditioned multi-block decompositions of geometries that arise in realistic fault systems. Boundary integral equation methods (e.g., [3,4,28,59]) have also been developed. Though these methods are extremely efficient for simple geometries, they are currently unable to account for heterogeneity in the material as well as topography, and some suffer from numerical instabilities.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

OReilly

Nordström

Kozdon

et al. 2015

Commun. Comput. Phys.

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Abstract.A numerical method suitable for wave propagation problems in complex geometries is developed for simulating dynamic earthquake ruptures with realistic friction laws. The numerical method couples an unstructured, node-centered finite volume method to a structured, high order finite difference method. In this work we our focus attention on 2-D antiplane shear problems. The finite volume method is used on unstructured triangular meshes to resolve earthquake ruptures propagating along a nonplanar fault. Outside the small region containing the geometrically complex fault, a high order finite difference method, having superior numerical accuracy, is used on a structured grid. The finite difference method is coupled weakly to the finite volume method along interfaces of collocated grid points. Both methods are on summation-by-parts form. The simultaneous approximation term method is used to weakly enforce the interface conditions. At fault interfaces, fault strength is expressed as a nonlinear function of sliding velocity (the jump in particle velocity across the fault) and a state variable capturing the history dependence of frictional resistance. Energy estimates are used to prove that both types of interface conditions are imposed in a stable manner. Stability and accuracy of the numerical implementation are verified through numerical experiments, and efficiency of the hybrid approach is confirmed through grid coarsening tests. Finally, the method is used to study earthquake rupture propagation along the margins of a volcanic plug. AMS subject classifications: 35L05,35L65,35Q35,65M06,65M08,65M12,65Z05

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Simulation of the spontaneous growth of a dynamic crack without constraints on the crack tip path

Cited by 80 publications

References 23 publications

Postseismic quasi‐static fault slip due to pore pressure change on a bimaterial interface

Postseismic quasi‐static fault slip due to pore pressure change on a bimaterial interface

Simulation of Dynamic Earthquake Ruptures in Complex Geometries Using High-Order Finite Difference Methods

Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

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