A Constitutive Scaling Law for Shear Rupture that is Inherently Scale-dependent, and Physical Scaling of Nucleation Time to Critical Point

It is shown that the rupture nucleation length increases up to the critical length with time according to a power law, and that the accelerating phase of nucleation leading up to the critical point is scaled in the framework of fracture mechanics based on slip-dependent constitutive formulation. Geometric irregularity of the rupturing surfaces plays a fundamental role in scaling the accelerating phase of nucleation up to the critical point. A power-law scaling relation between the rupture growth length and the nucleation time to the critical point is derived from theoretical consideration based on laboratory data. This power-law scaling relation has no singularity, and hence it may be useful for the predictive purpose of an imminent, large earthquake.