Scaling of Stress Drop with Rate-and-State Frictional Parameters in Spring-Block Models

Numerical simulations of earthquake cycles provide essential insights into fault mechanics and the physical interpretation of frictional parameters. Here, we utilize a spring-block system governed by rate-and-state friction to systematically compare earthquake cycle behaviors under quasi-dynamic and fully dynamic conditions. Our simulations demonstrate that for both approaches, the static stress drop, dynamic stress drop, and peak stress scale linearly with the logarithm of the loading rate [ln(Vpl/V0)]; however, the scaling coefficients are distinct and are modulated by both frictional parameters and the system stiffness. Specifically, we observe stress overshoot during the coseismic phase in dynamic models, contrasting with the undershoot observed in quasi-dynamic simulations. Additionally, parameter sweeps reveal that stress drops decrease as the stiffness ratio kc/k increases. This study highlights the importance of the inertial term effect in interpreting earthquake cycle behaviors.