## 3 Friction Experiments of Granitoid Fault  
The standard RSF law, derived from laboratory friction experiments, has been extensively utilized to quantify the frictional properties of rock faults and simulate the various stages of both natural and induced seismic events [27; 56; 57; 58], as well as laboratory earthquakes [37; 59; 60; 61]. This includes the preseismic, nucleation, coseismic, and interseismic healing processes. The RSF framework effectively captures a broad spectrum of fault slip behaviors, ranging from stable sliding to slow-slip events and dynamic ruptures. In this section, we summarize laboratory friction experiments under both dry and hydrothermal conditions for diverse granites and their gauges (Table 1). Friction experiments were conducted using various apparatus, such as saw-cut, direct-shear, double-direct-shear, and rotary-shear configurations. These various experimental setups facilitated the investigation of frictional strength variations under constant-velocity slip, the assessment of velocity dependence parameters (\(a-b\)) during velocity-stepping tests, and the evaluation of fault healing behavior through slide-hold-slide experiments [26].  
As a fundamental basement rock in the continental upper crust, granite and its fault gouges have been extensively investigated in laboratory experiments since the 1950s. We focused on the frictional properties of rocks/gouges under varying temperatures, normal stress, pore pressure, and sliding rate, which are key parameters controlling granite fault mechanical behavior. Given that in situ crustal conditions exhibit linear-like gradients in temperature and pressure with depth (geothermal gradient: 25-30 \({}^{\circ}\)C/km), understanding earthquake nucleation and induced seismic under coupled thermos-hydro-mechanical conditions remains a central scientific challenge. Early friction experiments were primarily conducted on Westerly granite, which is composed predominantly of \(\sim\)28% quartz, \(\sim\)35% plagioclase, \(\sim\)34% K-feldspar, and \(<\)5% biotite [27; 62] but with biotite replaced by chlorite and muscovite. Subsequent studies have incorporated natural fault gouges retrieved from continental drilling projects and fault cores, which are characterized by higher proportions of illite- and chlorite-rich components [7; 9; 40; 41; 63].  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Gauge/Rock** \\ **Sample** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Temperature** \\ **T** \\ **(\({}^{\circ}\)C)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Effective** \\ **Normal Stress** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Pore Fluid** \\ **Pressure** \\ **P\({}_{f}\)** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Slip Rate** \\ **(\({}^{\circ}\)V** \\ **(\({}^{\circ}\)m/s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Shear** \\ **Displacement** \\ **(\({}^{\circ}\)S** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Experiment** \\ **Type** \\ \end{tabular} } \\ \hline \multicolumn{1}{c}{Westerly granite} & ambient & 2-10 & dry & 0.1–10 & \(\sim\)1 & & [64] \\ \hline \multicolumn{1}{c}{Westerly granite} & ambient & 27-84 & dry & 0.01–10 & \(\sim\)70 & \
\begin{tabular}{c} Bare surface, \\ CV/VS \\ \end{tabular} & [65] \\ \hline \multicolumn{1}{c}{Westerly granite} & ambient-845 & CP: 250 & dry &
\begin{tabular}{c} 0.0476–0.476–4.76–4.