3. Directionality of rupture and rupture velocity in inhomogeneous fault systems
2.1 Introduction
mechanism of subRayleigh to supershear transition of laboratory earthquake ruptures. We also probe the parameter space governing the physics of the subRayleigh to supershear transition of dynamic ruptures along incoherent (frictional) interfaces.
Vallee’s work is the most recent of a series of papers reporting supershear rupture growth occurring during large earthquake events; moreover it presents the first seismological evidence for transition from subRayleigh to supershear. In this respect it will be shown to be highly relevant to the experiments discussed in this chapter.
The question of whether earthquake ruptures propagate at supershear speeds is still a subject of active debate within the seismological community. This is because of the often insufficient field data as well as the limited resolution and non-uniqueness of the inversion process. A widespread view in seismology speaks of crustal earthquake ruptures mainly propagating at subRayleigh speeds between 0.75 and 0.95 CR (Kanamori 1994). However, the multiplicity of independently collected evidence warrants further investigations of the mechanics of supershear rupture propagation. Whether and how supershear rupture occurs during earthquakes has an important implication for seismic hazard because the rupture velocity has a profound influence on the character of near-field ground motions (Aagaard and Heaton 2004).
The main goal of this chapter is to report on highly instrumented experiments that mimic the earthquake rupture process and to examine the physical plausibility and conditions under which supershear ruptures can be generated in a controlled laboratory environment. We study spontaneously nucleated dynamic rupture events in incoherent, frictional interfaces held together by the application of far-field tectonic loads. Thus we depart from the body of experimental work that addresses the dynamic shear fracture of coherent interfaces of some intrinsic strength, which are loaded by the application of dynamic, stress wave induced loading (Lambros and Rosakis 1995; Rosakis, Samudrala, et al. 1999; Coker and
Rosakis 2001; Rosakis 2002). A spontaneous rupture is commonly believed to be the closest physical model of an earthquake rupture.
Classical dynamic fracture theories of growing shear cracks have many similarities to the earthquake rupture processes (Freund 1990; Broberg 1999). Such theories treat the rupture front as a distinct point (sharp tip crack) of stress singularity.
These conditions are close to reality in cases that feature coherent interfaces of finite intrinsic strength and toughness. The singular approach ultimately predicts that dynamic shear fracture is allowed to propagate either at a subRayleigh wave speed or at only one supershear speed, which is 2 times the shear wave speed.
As a result, it excludes the possibility of a smooth transition of a steady-state rupture from subRayleigh to supershear speed for a steady-state rupture.
The introduction of a distributed rupture process zone has allowed fracture mechanics to better approximate the conditions that exist during real earthquake events (Ida 1972; Palmer and Rice 1973). Based on this so-called cohesive zone fracture mode, there is a forbidden speed range between CR, the Rayleigh wave speed, and CS, the shear wave speed (Burridge, Conn, et al. 1979; Samudrala, Huang, et al. 2002; Samudrala, Huang, et al. 2002). In the subRayleigh speed range all speeds are admissible, but only the Rayleigh wave speed is a stable speed; in the supershear speed range all speeds are admissible, but only speeds larger than 2CS are stable. Ruptures with unstable speeds will accelerate to a stable speed as determined by loading conditions. The theoretical results of the cohesive zone rupture model ultimately predict that earthquake ruptures can propagate either at Rayleigh wave speed or supershear speeds larger than 2CS. Early theoretical results by Burridge (Burridge 1973; Burridge, Conn, et al. 1979), along with numerical results by Andrews (Andrews 1976) and Das and Aki (Das
and Aki 1977) have predicted the possibility of supershear rupture and have alluded to a mechanism (Rosakis 2002) for transition from the subRayleigh to the supershear rupture velocity regime. According to the two-dimensional Burridge- Andrews mechanism, a shear rupture accelerates to a speed very close to CR soon after its initiation. A peak in shear stress is found sitting at the shear wave front and is observed to increase its magnitude as the main rupture velocity approaches CR. At that point, the shear stress peak may become strong enough to promote the nucleation of a secondary micro-rupture whose leading edge propagates at a supershear speed. Shortly thereafter, the two ruptures join up and the combination propagates at a speed close to CP. It is interesting that this transition was also clearly visualized by recent two-dimensional, atomistic calculations of shear rupture in the micro-scale, which provided an impressive demonstration of the length scale persistence of this subRayleigh to supershear rupture transition mechanism (Abraham and Gao 2000). The Burridge-Andrews mechanism is also known as the mother-daughter mechanism in mechanics literature.
For mixed-mode (tensile and shear) ruptures, a different transition model has also been suggested (Geubelle and Kubair 2001; Kubair, Geubelle, et al. 2002; Kubair, Geubelle, et al. 2003). Based on numerical simulation, Geubelle and Kubair suggest that a mix-mode rupture can speed up and cross the forbidden speed range between CR and CS continuously. Finally, recent numerical investigations of frictional rupture have identified alternate, asperity based, mechanisms that provide a three-dimensional rationalization of such a transition (Day 1982;
Madariaga and Olsen 2000; Dunham, Favreau, et al. 2003). In this case, 3-D effects play an important role in the transition. The rupture front focusing effect provides extra driving to speed up the spontaneous rupture.
The experimental confirmation of the possibility of supershear (intersonic) fracture followed many years after the first theoretical predictions. Indeed, a long series of experiments summarized by Rosakis (Rosakis 2002) showed that intersonic crack growth in constitutively homogenous systems featuring coherent interfaces (interfaces with inherent strength) is possible and may also occur in various combinations of bimaterial systems. However, in all of the various cases discussed by Rosakis (Rosakis 2002), the cracks were nucleated directly into the intersonic regime and there was no observation of a transition from subRayleigh to supershear speeds. This was due to the nature of the impact induced stress wave loading without pre-existing static loading and the nature of the relatively strong coherence of the interface (provided by glue). The major differences between the conditions during earthquake rupture and those fracture experiments have left questions regarding the plausibility of spontaneously generated intersonic rupture in frictionally held, incoherent interfaces unanswered. In addition, earlier laboratory earthquake experiments (Dieterich 1972; Scholz, Molnar, et al. 1972; Brune 1973; Johnson and Scholz 1976; Okubo and Dieterich 1984) dating back to the ‘70s, which simulated spontaneous rupture in the laboratory, have lacked the spatial and temporal resolution to produce conclusive proof of supershear rupture growth and to investigate the issue of rupture velocity transition.