Scaling of the shear rupture process from nucleation to dynamic propagation: Implications of geometric irregularity of the rupturing surfaces

Abstract

Abstract. A series of systematic, high-resolution laboratory experiments have been performed on the nucleation of propagating slip failure on preexisting faults having different surface roughnesses to demonstrate how the size scale and duration of shear rupture nucleation are affected by geometric irregularity of the rupturing surfaces. On the basis of the experimental results it has been discussed theoretically how consistently scaledependent physical quantities inherent in shear rupture are scaled. The experiments led to conclusive results that the nucleation process consists of two phases (phase I, an initial, quasi-static phase, and phase II, a subsequent accelerating phase) and that the nucleation process is greatly affected by geometric irregularities on the rupturing surfaces. In phase I the rupture grows at a slow, steady speed which is independent of the rupture growth length L. In contrast, during phase II the rupture develops at accelerating speeds V, which increase with an increase in L, obeying a power law V/Vs = c•(L/Xc) n, where Vs is the shear wave velocity, X c is the characteristic length representing the geometric irregularity of the fault surfaces, and c• and n are constants (c• = 8.87 x 10 -29 and n = 7.31). Scale dependency of scale-dependent physical quantities, including the nucleation zone size and its duration, is commonly ascribed to scale dependency of the slipdependent constitutive law parameter Dc, which is in turn governed by X c. It has been discussed that a unified comprehension can be provided for shear rupture of any size scale if the constitutive law for shear rupture is formulated as a slip-dependent law. IntroductionOnce shear rupture instability occurs in the brittle regime, the rupture propagates dynamically at a high speed close to sonic velocities. This is often referred to as brittle rupture, and a typical large-scale example is the earthquake rupture instability that takes place in the brittle layer in the Earth's crust. From a physical viewpoint, however, shear rupture cannot begin to propagate abruptly at speeds close to sonic velocities immediately after the instability is attained when the constitutive property of the fault is inhomogeneous. cleation process consists of two phases: phase I is an initial, quasi-static phase, and phase II is the subsequent accelerating phase, which eventually leads to dynamic high-speed propagation of the rupture. However, understanding the nucleation process of shear rupture quantitatively in terms of the underlying physics is still far from complete. It has widely been recognized that some physical quantities inherent ifi shear rupture are scale-dependent. For instance, recent studies [Ohnaka, 1996[Ohnaka, , 1998] suggest that the size of shear rupture nucleation and its duration are scale-dependent; that is, the

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“…However, such variations do not allow the breakdown stress drop to scale with the eventual seismic moment. Our results of scale-dependent l 0 can be interpreted as scale-dependent D C , where D C is the critical slip displacement, because the size of the nucleation region is proportional to D C in the slip-dependent constitutive law (Ohnaka and Shen, 1999). This interpretation and scale-independent breakdown stress drop are consistent with conclusions of previous theoretical works (Shibazaki and -16 -Matsu'ura, 1998;Ohnaka, 2000). )…”

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“…Systematic high-resolution laboratory experiments have been performed by Ohnaka and Shen (1999) on the nucleation of propagating slip failure on pre-existing faults having different surface roughness to demonstrate how the size scale and duration on shear rupture nucleation are affected by geometric irregularity of the rupturing surfaces. The authors conclude that the rougher the rupturing surfaces, the greater the timescales of rupture nucleation are.…”