## 3 Results
### Pressurized Water Injection into the Fault Plane
Like the shear stress, the sliding rate of granite and limestone faults decreased like an exponential curve as a whole (Figure 4a,c) and showed oscillatory behavior during the decreasing process (Figure 4(a2,c2)); but in the sandstone faults, the sliding rate varied with the fluctuation in the pore pressure and changed nearly linearly at the decreasing and increasing stages (Figure 4b). When the fault reached a new steady state, the sudden decrease in loading velocity in the velocity stepping test produced an observed decrease in sliding rate in the three faults. To investigate how water injection affects the frictional strength, we calculated the apparent friction coefficient (\(\mu_{a}\)) by taking the ratio of shear stress to effective normal stress (\(\tau/\sigma_{\textit{eff}}\)) (Figure 5, Table 3). The differences in apparent friction coefficient (\(\mu_{a}\)) between dry and wet samples with 1 MPa pressurized water were less than 0.01 in three faults, suggesting that the injection hardly affected the fault friction coefficients. However, when the 15 MPa pressurized water injection started, the apparent friction coefficients increased sharply, in contrast to the 1 MPa pressurized water injection. Furthermore, when the fault reached the steady state, the apparent friction coefficients of the granite and sandstone faults were larger than that in 1 MPa pressurized water injection, and the differences were 0.06 and 0.03. However, the apparent friction coefficient of the limestone fault was smaller than that in 1 MPa pressurized water injection, and the difference was \(-\)0.04 (Figure 5). In summary, when 15 MPa pressurized water was injected, three faults exhibited noticeable differences in shear stress reduction, stress drop, and variation in apparent friction coefficient, suggesting that the actual pore pressure on the faults may not be equal to the injection pressure and show differences in three samples. To evaluate this difference, we took the apparent friction coefficient in 1 MPa pressurized water as the friction coefficient of the fault and then put it into the effective stress law to calculate the actual pore pressure on the fault. The actual pore pressure on the granite fault was 8.5 MPa, significantly lower than the injection pressure. It was about 11.5 MPa on the sandstone fault, close to the injection pressure. The actual pore pressure on the limestone fault was about 19.1 MPa, much higher than the injection pressure (Figure 6, Table 3). The stress reduction caused by water injection was proportional to the actual pore pressure on the faults. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Fault**} & \multicolumn{3}{c}{**Dry**} & \multicolumn{3}{c}{**Injection of 1 MPa**} & \multicolumn{3}{c}{**Injection of 15 MPa Pressurized Water**} \\ \cline{2-11}  & \(\mu_{a}\) & \(a-b\) & \(\mu_{a}\) & \(a-b\) & \(\mu_{a}\) & \(a-b\) & \(\Delta\tau\) & _Dis_ & \(t_{\textit{slide}}\) & \(P_{\textit{actual}}\) \\ \hline Granite & 0.52\(\sim\)0.53 & 0.0009 & 0.54\(\sim\)0.56 & 0.022 & 0.61\(\sim\)0.62 & 0.034 & 6.9 & 0.28 & 290 & 8.5 \\ Sandstone & 0.56 & 0.034 & 0.56 & 0.022 & 0.59 & 0.026 & 10.4 & 0.19 & 145 & 11.5 \\ Limestone & 0.58\(\sim\)0.59 & 0.026 & 0.60 & 0.034 & 0.56 & 0.069 & 18 & 0.57 & 490 & 19.1 \\ \hline \hline \end{tabular} Note: \(\mu_{a}\) = Apparent friction coefficient \(\Delta\tau\) (MPa) = stress drop; _Dis_ (mm) = sliding displacement; \(t_{\textit{slide}}\) (s) = sliding time; \(P_{\textit{actual}}\) (MPa) = actual pore pressure.  
\end{table} 
Table 3: Parameters of the fault slip caused by water injection. Figure 5: The apparent friction coefficient changes with time in (**a**) granite, (**b**) sandstone, and (**c**) limestone faults as the water is injected into the fault plane. (**a1–c1**) are enlarged views of the time window denoting the injection of 1 MPa pressurized water. The black dotted lines denote the locations of enlarged views. The blue dotted lines denote the processes of pressurized water injection.