On the slip-weakening behavior of rate- and state-dependent constitutive laws

We study the dynamic traction behavior within the cohesive zone during the propagation of earthquake ruptures adopting rate and state dependent constitutive relations. The resulting slip weakening curve displays an equivalent slip weakening distance (D0_eq), which is different from the parameter L controlling the state variable evolution. The adopted constitutive parameters (a, b, L) control the slip weakening behavior and the absorbed fracture energy. The dimension of the nucleation patch scales with L and not with D0_eq. We propose a scaling relation between these two lengthscale parameters which prescribes that D0_eq/L ~ 15.