## 3 Friction Experiments of Granitoid Fault
### Slide-Hold-Slide Experiment  
Laboratory slide-hold-slide (SHS) experiments serve as a fundamental analog for studying the seismic cycle and are widely employed to measure strength recovery in simulated fault systems. SHS tests consist of alternating periods of induced stick-slip and quasi-static holds during which time-dependent strength recovery occurs. The strength changes according to secant friction \(\mu=\tau/(\sigma_{\rm n}-P_{\rm f})\), \(\tau\) and \(\sigma_{n}\) are shear and normal stress measured on the fault surface, and \(P_{\rm f}\) is pore pressure. The magnitude of restrengthening (\(\Delta\mu\)) is calculated by the difference between the peak failure strength upon the resumption of the slip and the steady-state sliding strength preceding the hold (Figure 4). With subsequent shearing, the shear stress gradually declines to its original steady-state value (\(\tau_{\rm ss}\)). Seismic observations reveal that the drop in earthquake stress rises logarithmically over time, while studies on rock friction demonstrate that restrengthening increases with the log of hold time, an equation that can be characterized by the logarithmic relation defined in previous studies [49; 64; 66].  
Previous studies under room temperature (\(T\)) indicate that the frictional healing rate is sensitive to time and the slip rate. [PERSON] [27] conducted an SHS test under constant normal stress of 25 MPa using quartz sand sheared between rough westerly granite surfaces. The results indicate that the friction decreased during hold periods, reaching a peak value (the steady-state friction coefficient) when reloaded. Additionally, friction increased almost linearly and logarithmically with the hold time. This trend is consistent with many other earth materials [87; 88; 89; 90]. However, when the T increases to levels corresponding to the  
Figure 3: Compilation of published experimental data for steady-state friction coefficient as function of temperature. Velocity (\(V\)) is expressed in \(\mu\)m/s [9; 36; 37; 41].  
shallow crust, the friction coefficient of westerly granite linearly increases with \(T\), but \(T\) has little effect on the rate of change in static friction with hold time. It is cautioned that extrapolating laboratory results to natural faults should be undertaken carefully. Neglecting the effect of \(T\) could lead to an underestimation of the fault strength under dry conditions by up to 10% [45]. Recent studies show that frictional weakening was observed in hydrothermal SHS tests at _Ts_\(\geq\) 200 \({}^{\circ}\)C, indicating that SHS tests are more effective in promoting weakening than VS tests [37]. The simulation of long-duration holds at 250 \({}^{\circ}\)C further suggests that hydrothermal alterations occur at this \(T\) because the negative state variable is not required to simulate shorter hold periods or lower _Ts_. Although the precise mechanisms controlling frictional behavior remain unclear, the data imply that the processes involved are water-assisted, temperature-dependent, and chemically complex with a characteristic time delay in the order of 1000 s [69]. [PERSON] et al. [91] measured the restrengthening of wet quartzite samples under a broader range of effective normal stress of 20-200 MPa. The restrengthening (\(\Delta\mu\)) increases with the log of hold duration, the 200 \({}^{\circ}\)C healing rate, and the 0.014 per e-fold increase in time, which is comparable to that determined from seismological observations along the Calaveras Fault. Overall, they indicate that cohesive healing is negligible at _Ts_\(<\) 200 \({}^{\circ}\)C, and strength recovery is predominantly due to frictional healing processes.