A Constitutive Criterion for the Fault: Modified Velocity-Weakening Law

Abstract

Expanding on a previous article, constitutive laws for solid friction are examined jointly with available experimental results. The models are evaluated by means of numerical dynamic analysis of two sliding blocks simulating adjacent fault sections. Effective constitutive laws are determined as relations between mean values of the relevant variables on a selected area of the sliding surfaces. The material is initially assumed elastic and homogeneous and the influence of nonhomogeneity evaluated next by modeling mass density, Young’s modulus, and friction coefficient as correlated random fields. The effect of fractures in rock close to the fault is also numerically assessed. Finally, the influence of rupture of protrusions (microasperities) between the sliding surfaces is analyzed. The influence of size of the averaging interface area on the parameters of the effective constitutive law is then obtained by means of Monte Carlo simulation. When the rock regions adjacent to the fault are assumed to be linearly elastic and homogeneous or nonhomogeneous no size effect is observed. On the other hand, when the friction coefficient is characterized by a random field, a size effect is detected. Fracture occurrence in the region surrounding the fault does not cause significant alteration of the macroconstitutive law, producing only minor perturbations of the mean law determined without fracture, but it should also introduce high-frequency slave vibrations. Finally, a macroconstitutive law that takes into account the shear rupture of microasperities on the sliding surfaces is suggested. The proposed modified velocity-weakening law, constitutes a more general and flexible constitutive law.