Rupture propagation with finite stress in antiplane strain

Andrews, D. J.

doi:10.1029/jb081i020p03575

Cited by 430 publications

(344 citation statements)

References 18 publications

Supporting

Mentioning

330

Contrasting

Order By: Relevance

“…Note also that the cohesive zone size is inversely proportional to the crack half-length L. For L ) L o , the crack half-length L would be approximately equal to the propagation distance. The functional form (37) is identical to Andrews' [1976Andrews' [ , 2004Andrews' [ , 2005 estimate obtained by somewhat different considerations.…”

Section: Cohesive Zone and Constraints On Discretizationsupporting

confidence: 61%

“…This is identical to the scaling that Andrews [1976Andrews [ , 2004 derived from a somewhat different (but essentially equivalent) line of reasoning. The stress drop Dt used in our test calculation, 7 MPa, is about twice the average stress drop for shallow crustal earthquakes, making the test case modestly conservative in this respect (that is, had we used a more typical stress drop value of 3 MPa, the cohesive zone sizes and hence N c would have been larger).…”

Section: Scale Collapsementioning

confidence: 55%

“…[11] Several different finite difference methods have been used to solve the spontaneous rupture problem [e.g., Andrews, 1976;Miyatake, 1980;Day, 1982b;Madariaga et al, 1998]. These have been limited for the most part to faults consisting of planar segments, although a few recent solutions are for nonplanar faults [e.g., Cruz-Atienza and Virieux, 2004; Kase and Day, 2004;Zhang et al, 2004].…”

Section: Finite Difference Methodsmentioning

confidence: 99%

“…This simple model provides an adequate basis for testing the numerical methods, though it may have significant shortcomings as a model for earthquakes, in which interface frictional properties may be better represented by more complicated relationships that account for rate and state effects [e.g., Dieterich, 1979;Ruina, 1983] and thermal phenomena such as flash heating and pore pressure evolution [e.g., Lachenbruch, 1980;Smith, 1985, 1987;Rice, 1999]. Moreover, the energy dissipation may not be confined mostly to the fracture surface, but rather distributed in a damage zone of finite thickness around the surface [e.g., Andrews, 1976Andrews, , 2005Dalguer et al, 2003aDalguer et al, , 2003b.…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…where m s and m d are coefficients of static and dynamic friction, respectively, and d 0 is the critical slip-weakening distance [e.g., Ida, 1972;Andrews, 1976;Day, 1982b, Madariaga et al, 1998, Dalguer et al, 2001. In the event that the normal stress and frictional parameters are constant over the entire fault, as will be the case in the test problem considered here, this idealized model results in constant fracture energy G with G = js n j(m s À m d )d 0 /2.…”

Section: Theoretical Formulationmentioning

confidence: 99%

See 4 more Smart Citations

Comparison of finite difference and boundary integral solutions to three‐dimensional spontaneous rupture

et al. 2005

View full text Add to dashboard Cite

[1] The spontaneously propagating shear crack on a frictional interface has proven to be a useful idealization of a natural earthquake. The corresponding boundary value problems are nonlinear and usually require computationally intensive numerical methods for their solution. Assessing the convergence and accuracy of the numerical methods is challenging, as we lack appropriate analytical solutions for comparison. As a complement to other methods of assessment, we compare solutions obtained by two independent numerical methods, a finite difference method and a boundary integral (BI) method. The finite difference implementation, called DFM, uses a traction-at-split-node formulation of the fault discontinuity. The BI implementation employs spectral representation of the stress transfer functional. The three-dimensional (3-D) test problem involves spontaneous rupture spreading on a planar interface governed by linear slip-weakening friction that essentially defines a cohesive law. To get a priori understanding of the spatial resolution that would be required in this and similar problems, we review and combine some simple estimates of the cohesive zone sizes which correspond quite well to the sizes observed in simulations. We have assessed agreement between the methods in terms of the RMS differences in rupture time, final slip, and peak slip rate and related these to median and minimum measures of the cohesive zone resolution observed in the numerical solutions. The BI and DFM methods give virtually indistinguishable solutions to the 3-D spontaneous rupture test problem when their grid spacing Dx is small enough so that the solutions adequately resolve the cohesive zone, with at least three points for BI and at least five node points for DFM. Furthermore, grid-dependent differences in the results, for each of the two methods taken separately, decay as a power law in Dx, with the same convergence rate for each method, the calculations apparently converging to a common, grid interval invariant solution. This result provides strong evidence for the accuracy of both methods. In addition, the specific solution presented here, by virtue of being demonstrably grid-independent and consistent between two very different numerical methods, may prove useful for testing new numerical methods for spontaneous rupture problems.Citation: Day, S. M., L. A. Dalguer, N. Lapusta, and Y. Liu (2005), Comparison of finite difference and boundary integral solutions to three-dimensional spontaneous rupture,

show abstract

Section: Cohesive Zone and Constraints On Discretizationsupporting

confidence: 61%

Section: Scale Collapsementioning

confidence: 55%

Section: Finite Difference Methodsmentioning

confidence: 99%

Section: Theoretical Formulationmentioning

confidence: 99%

Section: Theoretical Formulationmentioning

confidence: 99%

See 3 more Smart Citations

Comparison of finite difference and boundary integral solutions to three‐dimensional spontaneous rupture

et al. 2005

View full text Add to dashboard Cite

show abstract

Predicting fault damage zones by modeling dynamic rupture propagation and comparison with field observations

Johri

Dunham²,

Zoback

et al. 2014

J. Geophys. Res. Solid Earth

View full text Add to dashboard Cite

We use a two-dimensional plane strain dynamic rupture model with strongly rate-weakening friction and off-fault Drucker-Prager plasticity to model damage zones associated with buried second-order thrust faults observed in the SSC reservoir. The modeling of ruptures propagating as self-sustaining pulses is performed in the framework of continuum plasticity where the plasticity formulation includes both deviatoric and volumetric plastic strains. The material deforming inelastically due to stress perturbations generated by the propagating rupture is assumed to be the damage zone associated with the fault. Dilatant plastic strains are converted into a fracture population by assuming that the dilatant plastic strain is manifested in the form of fractures. The cumulative effect of multiple slip events is considered by superposition of the plastic strain field obtained from individual slip events. The relative number of various magnitude slip events is chosen so as to honor the Gutenberg-Richter law. Results show that the decay of fracture density (F) with distance (r) from the fault can be described by a power law F = F 0 r À n . The fault constant F 0 represents the fracture density at unit distance from the fault. The decay rate (n) in fracture density is approximately 0.85 close to the fault and increases to~1.4 at larger distances (>10 m). Modeled damage zones are approximately 60-100 m wide. These attributes are similar to those observed in the SSC reservoir using wellbore image logs and those reported in outcrop studies. Considering fault roughness affects local damage zone characteristics, these characteristics are similar to those modeled around planar faults at a scale (~10 m) that affects bulk fluid-flow properties.

show abstract

Expected seismic shaking in Los Angeles reduced by San Andreas fault zone plasticity

Roten

Olsen

Day

et al. 2014

Geophysical Research Letters

104

View full text Add to dashboard Cite

Computer simulations of large (M≥7.8) earthquakes rupturing the southern San Andreas Fault from SE to NW (e.g., ShakeOut, widely used for earthquake drills) have predicted strong long‐period ground motions in the densely populated Los Angeles Basin due to channeling of waves through a series of interconnected sedimentary basins. Recently, the importance of this waveguide amplification effect for seismic shaking in the Los Angeles Basin has also been confirmed from observations of the ambient seismic field. By simulating the ShakeOut earthquake scenario (based on a kinematic source description) for a medium governed by Drucker‐Prager plasticity, we show that nonlinear material behavior could reduce the earlier predictions of large long‐period ground motions in the Los Angeles Basin by up to 70% as compared to viscoelastic solutions. These reductions are primarily due to yielding near the fault, although yielding may also occur in the shallow low‐velocity deposits of the Los Angeles Basin if cohesions are close to zero. Fault zone plasticity remains important even for conservative values of cohesions, suggesting that current simulations assuming a linear response of rocks are overpredicting ground motions during future large earthquakes on the southern San Andreas Fault.

show abstract

Rupture propagation with finite stress in antiplane strain

Cited by 430 publications

References 18 publications

Comparison of finite difference and boundary integral solutions to three‐dimensional spontaneous rupture

Comparison of finite difference and boundary integral solutions to three‐dimensional spontaneous rupture

Predicting fault damage zones by modeling dynamic rupture propagation and comparison with field observations

Expected seismic shaking in Los Angeles reduced by San Andreas fault zone plasticity

Contact Info

Product

Resources

About