Nucleation process of unstable rupture in the brittle regime: A theoretical approach based on experimentally inferred relations

Abstract

Ohnaka and Kuwahara investigated the nucleation process of unstable rupture in their elaborate laboratory experiment with a very high resolution, using a rock sample with a simulated fault. They found, among other things, that the crack growth resistance such as the stress σp — σi (σp being the peak stress at the crack tip and σi being the shear stress at the propagating tip on the verge of slip) and the breakdown stress drop increase with crack growth in the nucleation zone. They also found that the critical slip displacement is inhomogeneously distributed on the fault in the nucleation zone. We investigate whether inhomogeneous distribution of the crack growth resistance can necessarily cause the stable and quasi‐static nucleation process in the brittle regime. The slip‐dependent breakdown zone model has been assumed in the present theoretical analysis of crack. It has theoretically been shown that an increase in the critical slip displacement with the distance is required for the occurrence of stable crack growth. Its increase rate must be larger than a certain threshold value. The transition to unstable rupture growth occurs at a location where the increase rate falls short of the threshold value. The inhomogeneous distribution of the critical slip displacement may physically be attributed to that of fault surface roughness, as shown in laboratory experiments. The stress distributions on the crack plane prescribe the rate of stable crack growth. The stable rupture growth process observed by Ohnaka and Kuwahara can be explained quantitatively assuming inhomogeneously distributed stresses and critical slip displacement, which have also been observed in their experiments. The present theoretical study shows that both the distribution of the crack growth resistance, particularly that of the critical slip displacement, and the size of preexisting initial crack play important roles in creating stable and quasi‐static nucleation in the brittle regime. We show that diverse rupture phenomena can be caused by the differences in the distribution of critical slip displacement and in the size of preexisting initial crack.