## 3 Experimental Results and Analysis
### Strain Rate Effects on Characteristic Stresses
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**CP (MPa)**} & \multicolumn{2}{c}{\(\sigma_{\rm ci}\)} & \multicolumn{2}{c}{\(\sigma_{\rm cd}\)} & \multicolumn{2}{c}{\(\sigma_{\rm p}\)} \\ \cline{2-6}  & **Fitting Equation** & \(\mathbf{R^{2}}\) & **Fitting Equation** & \(\mathbf{R^{2}}\) & **Fitting Equation** & \(\mathbf{R^{2}}\) \\ \hline
10 & \(\sigma_{\rm ci}=5.54\lg\dot{\varepsilon}\,+140.80\) & 0.38 & \(\sigma_{\rm cd}=8.29\lg\dot{\varepsilon}+221.54\) & 0.69 & \(\sigma_{\rm p}=11.57\lg\dot{\varepsilon}\,+287.11\) & 0.64 \\
20 & \(\sigma_{\rm ci}=8.25\lg\dot{\varepsilon}+199.27\) & 0.55 & \(\sigma_{\rm cd}=15.39\lg\dot{\varepsilon}\,+308.42\) & 0.94 & \(\sigma_{\rm p}=15.59\lg\dot{\varepsilon}\,+380.65\) & 0.99 \\
30 & \(\sigma_{\rm ci}=6.73\lg\dot{\varepsilon}+223.54\) & 0.65 & \(\sigma_{\rm cd}=11.29\lg\dot{\varepsilon}\,+350.98\) & 0.87 & \(\sigma_{\rm p}=11.86\lg\dot{\varepsilon}\,+425.93\) & 0.81 \\
40 & \(\sigma_{\rm ci}=9.32\lg\dot{\varepsilon}+270.74\) & 0.77 & \(\sigma_{\rm cd}=18.03\lg\dot{\varepsilon}\,+421.20\) & 0.99 & \(\sigma_{\rm p}=18.08\lg\dot{\varepsilon}\,+206.39\) & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The fitted equations related to the relationship between characteristic stresses and strain rate under triaxial loading (CP—confining pressure). Figure 9: The relationship between the ratios of characteristic stresses and the logarithm of strain rate under triaxial loading (**(a)** scatter plot; **(b)** statistical graph). factors for characteristic stresses (CSDIF), enabling quantitative comparison of rate effects across varying confining pressures through normalization methodology. \[\text{CSDIF}=\frac{\sigma_{\text{min}}}{\sigma_{\text{max}}} \tag{2}\]  
where \(\sigma_{\text{min}}\) and \(\sigma_{\text{max}}\) represent characteristic stresses at strain rates of \(10^{-6}\) s\({}^{-1}\) and \(10^{-2}\) s\({}^{-1}\), respectively. The CSDIF values for granite under different confining pressures are systematically presented in Table 4 and Figure 10, and the result demonstrates that (1) under unconfined conditions (0 MPa), \(\sigma_{\text{p}}\) exhibits the highest CSDIF (1.41), followed by \(\sigma_{\text{cd}}\) (1.30), with \(\sigma_{\text{ci}}\) demonstrating the lowest amplification (1.15); (2) at a 10 MPa confining pressure, the CSDIF for \(\sigma_{\text{cd}}\) and \(\sigma_{\text{p}}\) decrease to 1.14 and 1.13, respectively, while the value of \(\sigma_{\text{ci}}\) remains stable at 1.14. Comparative analysis reveals that under triaxial loading conditions (\(\sigma_{3}\) = 10 MPa), the values of CSDIF corresponding to three characteristic stresses exhibit a significant reduction trend compared with those under uniaxial loading. Existing studies [35] have confirmed a pronounced positive correlation between the heterogeneity degree of rock materials and their strain rate sensitivity characteristics. The confining pressure effectively attenuates the rate sensitivity of characteristic strains in triaxial conditions through facilitating microcrack closure and compaction effects, which significantly reduces structural heterogeneity in rock; (3) beyond a 10 MPa confining pressure, all three factors display oscillatory convergence with diminishing inter-parameter differences, ultimately approaching the same value. Comparative analysis in Figure 10b reveals that the CSDIF of \(\sigma_{\text{cd}}\) and \(\sigma_{\text{p}}\) demonstrate significant pressure-dependent attenuation, whereas the crack initiation factor maintains remarkable stability across the full confining pressure range. In addition, Figure 10b reveals that the CSDIF of \(\sigma_{\text{cd}}\) and \(\sigma_{\text{p}}\) exhibit significant confining pressure-dependent reductions with increasing confining pressure (0-40 MPa), while the CSDIF of \(\sigma_{\text{ci}}\) maintains exceptional stability throughout the pressure loading spectrum.