Wrinkle-like Pulse Research Articles

Distributions of strong ground motion due to dynamic ruptures across a bimaterial fault: Implications for seismic hazard analyses

We perform 2-D finite element calculations of mode II rupture along a bimaterial interface governed by regularized rate- and state-dependent friction law, with the goal of understanding how the bimaterial interface influences the strong ground motion. By comparison with properties of rupture in a homogeneous solid, we found that bimaterial mechanism is important for earthquake ruptures and influences the strong ground motion significantly. The simulated results show that mode II rupture evolves with propagation distance along a bimaterial interface to a unilateral wrinkle-like pulse in the direction of slip on the compliant side of the fault, namely in the positive direction. Strong ground motion caused by seismic waves emanated from the rupture propagation is asymmetrically distributed in space. The computed peak ground acceleration (PGA) is high in the near-fault region. Particularly, PGA is much larger in the region on the side in the positive direction. In addition, it is greater in the more compliant area of the model than that in the stiffer area with corresponding locations. Moreover, the differential PGA due to bimaterial effect increases with increasing degree of material contrast across the fault. It is hoped that the results obtained in this investigation will provide some implications for seismic hazard assessment and fault rupture mechanics.

Examining tendencies of in-plane rupture to migrate to material interfaces

SUMMARY We perform a numerical parameter-space study of 2-D in-plane ruptures in a model consisting of two different half-spaces separated by a low-velocity layer and possible simultaneous slip along multiple faults. Ruptures are nucleated by a bilateral expanding stress drop in a limited source region, and may continue to propagate spontaneously (or not) along one or several faults. Most calculations are done for purely elastic media and faults governed by Coulomb friction, but some simulations employ Prakash‐Clifton friction and Kelvin-Voigt viscosity. The faults, two of which are material interfaces, are situated equidistant and parallel to each other. Using different nucleation locations, different initial stress, different velocity contrasts, different frictional fault separations, different widths of a low-velocity zone, and different number of faults, we examine the range of conditions for which ruptures migrate to other faults and continue to propagate in a self-sustaining manner. The model produces diverse migration and propagation phenomena represented by several phase diagrams. However, a general result of the study is that ruptures tend to migrate to the material interfaces and become self-sustained wrinkle-like pulses for wide ranges of conditions. The wrinkle-like pulses propagate along each material interface unilaterally in the direction of motion on the more compliant side of the interface (referred to as the ‘positive’ direction). The existence of a large number of faults produces, like viscosity, distributed deformation that reduces the divergent behaviour of the wrinkle-like pulses. In many cases, ruptures migrate to the interface with the stronger contrast and propagate unilaterally in the positive direction associated with that interface and the overall contrast across the fault zone. In smaller number of cases, ruptures migrate to the interface with the weaker contrast and propagate unilaterally in the opposite positive direction associated with that interface. For various parameter combinations, self-sustained unilateral pulses travel simultaneously, in the two opposite positive directions, along the interfaces on the opposite sides of the low-velocity layer. A low-resolution imaging of these ruptures would lead to an inference on bilateral propagation. The M6, 2004 September, Parkfield California earthquake may provide a natural example of such a case.

Particle Velocimetry and Photoelasticity Applied to the Study of Dynamic Sliding Along Frictionally-Held Bimaterial Interfaces: Techniques and Feasibility

A laser interferometry-based technique was developed to locally measure the in-plane components of particle velocity in dynamic experiments. This technique was applied in the experimental investigation of dynamic sliding along the incoherent (frictional) interface of a Homalite–steel bimaterial structure. The bimaterial specimen was subjected to uniform compressive stress and impact-induced shear loading. The evolution of the dynamic stress field was recorded by high-speed photography in conjunction with dynamic photoelasticity. The combination of the full-field technique of photoelasticity with the local technique of velocimetry was proven to be a very powerful tool in the investigation of dynamic sliding. A relatively broad loading wave with an eye-like structure emanated from the interface. The particle velocity measurements established that sliding started behind the eye-like fringe pattern. It propagated with supershear speed with respect to Homalite. A shear Mach line originating from the sliding tip is visible in the photoelastic images. A vertical particle velocity measurement revealed the existence of a wrinkle-like pulse traveling along the bimaterial interface. The wrinkle-like pulse followed the initial shear rupture tip and propagated at a specific subshear speed.

Dynamic rupture on a bimaterial interface governed by slip-weakening friction

We perform 2-D finite-difference calculations of mode II rupture along a bimaterial interface governed by slip-weakening friction, with the goal of clarifying rupture properties and the conditions leading to the development of unilateral wrinkle-like pulses. The simulations begin with an imposed bilateral rupture in a limited source region. Rupture properties outside the imposed source are examined for ranges of values of the degree of material contrast γ across the fault, the difference between static fs and dynamic fd coefficients of friction, and the difference between static friction and initial shear stress. The results show that mode II rupture evolves with propagation distance along a bimaterial interface, for broad ranges of realistic conditions, to a unilateral wrinkle-like pulse in the direction of slip on the compliant side of the fault. These conditions span in our calculations the ranges fs−fd < 0.4 and γ > 2–5 per cent. When the difference between the static friction and initial shear stress is smaller, the evolution to unilateral wrinkle-like pulses occurs for smaller values of γ. The amount of slip increases with propagation distance, due to the incorporation of slip-weakening friction, in contrast to earlier results based on Coulomb and Prakash–Clifton friction laws with slip-independent coefficient. In all cases leading to wrinkle-like pulses, the rupture velocity in the preferred (+) propagation direction is V+r≈CGR, where CGR is the generalized Rayleigh wave speed. Simulations with imposed rupture speed in the source region close to the slower P wave speed P− can excite, in addition to the primary wrinkle-like pulse in the preferred direction with V+r≈CGR, a weak pulse in the opposite (−) direction with V−r≈P−. In some cases leading to bilateral crack-like propagation (e.g. fs−fd= 0.7), the rupture velocities in the opposite directions are V+r≈P+ (the faster P wave speed) and V−r≈P−, with the initial supershear crack front in the + direction followed by a pulse with V+r≈CGR.

Comment on “The wrinkle-like slip pulse is not important in earthquake dynamics” by D. J. Andrews and R. A. Harris

[1] Andrews and Harris [2005] (hereinafter referred to as AH) found in several numerical simulations that effects associated with prescribed stress heterogeneities and timeweakening friction can suppress those generated dynamically by rupture on a bimaterial interface, and concluded that the wrinkle-like rupture mode is generally not important for earthquake dynamics. Their results are based on selective cases, rather than a systematic parameter-space study, and they do not form the basis for a general conclusion. Moreover, most of their cases are associated with conditions for which the bimaterial effects are weak due to combination of assumed parameter values, mixed rupture modes, relatively small propagation distance, and coarse grid. Considerations of a larger body of theoretical results and observations suggest that the wrinkle-like rupture may be relevant to earthquake dynamics. [2] Weertman [1980] showed analytically that mode II slip pulse on a bimaterial interface governed by Coulomb friction produces dynamic changes of normal stress that depend on the slip function, material properties and direction of rupture propagation. Subsonic propagation in the direction of slip of the compliant solid reduces dynamically the normal stress, whereas propagation in the opposite direction increases the normal stress. Adams [1995] showed analytically that mode II rupture on a bimaterial Coulomb interface has a strong dynamic instability that transfers energy during propagation to shorter wavelengths, leading to pulse sharpening and increasing slip velocity with propagation distance. The discussed effects are pure mode II phenomena on a bimaterial interface, and they do not exist for mode III rupture or in a homogeneous solid. For additional theoretical background, see Ranjith and Rice [2001] and Ben-Zion [2001]. [3] The analytical properties of mode II slip pulse on a bimaterial interface render numerical simulations of such rupture highly challenging. Very fine grid is needed to capture the sharp features associated with the pulse, while large propagation distance is required to reach a dynamic regime that is relatively free of initial transients and reflects the attractor of the evolving dynamic behavior. Andrews and Ben-Zion [1997] simulated mode II ruptures on a bimaterial Coulomb interface with a nucleation consisting of a localized stress drop having a favored propagation direction. They observed wrinkle-like slip pulses with properties compatible to the analytical results of Weertman and Adams. Similar pulses were found in subsequent simulations with increasing refinements and incorporation of additional physical ingredients, including a nucleation mechanism that generalizes the procedure of Andrews and Ben-Zion to a symmetrically expanding source without a preferred direction and slip-weakening friction [Shi and Ben-Zion, 2006]. [4] An assessment of the possible relevance of the wrinkle-like pulse to earthquake dynamics should focus on situations associated with mode II ruptures. Important such cases are large earthquakes on plate-bounding strikeslip faults. These earthquakes (referred to below as the ‘‘target’’ earthquakes) saturate the seismogenic zone, propagate predominately as mode II rupture, and are likely to be affected primarily by the elastic properties of the bounding crustal blocks (rather than the myriad of possible smallscale heterogeneities). As discussed below, the simulations of AH address in a rather limited way the dynamics of the large target earthquakes.

Properties and implications of dynamic rupture along a material interface

AbstractWe perform two-dimensional plane-strain finite-difference calculations of dynamic rupture along an interface separating different elastic media. The calculations extend earlier results of Andrews and Ben-Zion (1997) who found a self-sustaining narrow slip pulse associated with dynamic reduction of normal stress along a material interface governed by constant friction, in agreement with Weertman (1980). The pulse propagates in a wrinklelike mode having remarkable dynamic properties that may be relevant to many geophysical phenomena. Here we examine the range of values of elastic parameters, friction coefficient, and strength heterogeneities allowing for the existence of the wrinklelike pulse. Rupture is initiated in the simulations by imposed slip in a limited space-time domain. Outside the region of the imposed slip, the pulse becomes narrower and higher with propagation distance along the interface. The strength of the wrinklelike pulse increases with S-wave velocity contrast up to a maximum at about 35% contrast. Beyond such a velocity contrast, there is no solution for a generalized Rayleigh wave along a material interface, and the strength of the pulse decreases. However, the wrinklelike pulse can still propagate in a self-sustaining manner for larger velocity contrasts. For a fixed S-wave velocity contrast, the strength has little dependence on density contrast or Poisson's ratio, but the pulse strength increases rapidly with increasing coefficient of friction. Stress and strength heterogeneities with small correlation length have little effect on the pulse, while long wavelength heterogeneities reduce the strength of the pulse. The high mechanical efficiency of the wrinklelike pulse suggests that earthquake ruptures may favor such mode of failure when possible.