Estimates of slip weakening distance for different dynamic rupture models

We model the dynamic propagation of a 2-D in-plane crack obeying to either slip weakening (SW) or rate- and state-dependent friction laws (R&S). We compare the value of slip weakening distance (Dc), adopted or estimated from the traction versus slip curves, with the critical slip distance measured as the slip at the time of peak slip velocity (D'c). The adopted friction law and the constitutive parameters control the slip acceleration as well as the timing and the amplitude of peak slip velocity. Our simulations with R&S show that the direct effect of friction and the friction behavior at high slip rates affect the timing of peak slip velocity and thus control the ratio D'c/Dc. The difference observed in this study between the Dc values and the inferred D'c can range between few percent up to 50%.