## 2 Experimental Scheme  
Figure 2 illustrates the primary operational process steps involved in the experimental section. In accordance with the geological investigation report associated with the tunnel of a hydropower project, as well as the \"Code for Rock Tests in Water and Hydropower Projects\", cylindrical specimens were fabricated. The fundamental physical parameters, including mass, height, and diameter, were measured, along with the longitudinal wave velocity. Following this, samples exhibiting low dispersion were selected, categorized, and assigned identification numbers. The samples employed in the testing process are depicted in Figure 3. The statistical data pertaining to various fundamental physical indicators of the samples are presented in Table 1. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multirow{2}{*}{**Diameter**} & \multirow{2}{*}{**Altitude**} & \multicolumn{3}{c}{**Dry Condition**} & \multicolumn{3}{c}{**Saturated Condition**} & \multirow{2}{*}{**Saturated**} \\  & & & **Wave** & & **Weight** & & **Density** & **Wave** & **Weight** & **Density** & **Moisture** \\  & & & **(km/s)** & & **(g)** & & **(g/cm\({}^{3}\))** & & **(km/s)** & & **(g/cm\({}^{3}\))** & **Content** & \\ \hline S1 & 49.72 & 99.97 & 1.558 & 423.86 & 2.185 & 1.414 & 453.98 & 2.340 & 7.106\% & 15.526\% \\ S2 & 50.43 & 100.09 & 1.525 & 424.25 & 2.123 & 1.478 & 454.76 & 2.276 & 7.192\% & 15.269\% \\ S3 & 49.71 & 100.09 & 1.619 & 426.86 & 2.199 & 1.464 & 455.48 & 2.346 & 6.705\% & 14.741\% \\ S4 & 49.64 & 100.05 & 1.484 & 423.94 & 2.191 & 1.413 & 453.63 & 2.344 & 7.003\% & 15.341\% \\ S5 & 50.20 & 100.07 & 1.522 & 423.11 & 2.137 & 1.395 & 454.60 & 2.296 & 7.443\% & 15.907\% \\ S6 & 50.00 & 99.82 & 1.486 & 421.34 & 2.151 & 1.441 & 452.12 & 2.308 & 7.305\% & 15.712\% \\ S7 & 49.57 & 99.86 & 1.542 & 421.69 & 2.189 & 1.419 & 451.08 & 2.342 & 6.970\% & 15.258\% \\ S8 & 49.57 & 99.82 & 1.486 & 420.78 & 2.185 & 1.387 & 451.73 & 2.346 & 7.355\% & 16.074\% \\ S9 & 49.58 & 99.84 & 1.541 & 420.68 & 2.184 & 1.416 & 451.73 & 2.345 & 7.381\% & 16.117\% \\ Mean value & 49.82 & 99.96 & 1.529 & 422.95 & 2.172 & 1.425 & 453.23 & 2.327 & 7.162\% & 15.549\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical analysis of fundamental physical parameters under both dry and saturated rock conditions. Figure 1: Schematic diagram of the combined effects of excavation unloading and freeze–thaw erosion on the tunnel excavation face. (**a**) Unloading disturbance effect; (**b**) freeze–thaw erosion effect; and (**c**) combined effects of unloading disturbance and freeze–thaw erosion. The samples utilized in this experiment were obtained through core drilling from the original geological formation at the engineering site and subsequently underwent secondary processing to conform to the sample size specifications outlined in the relevant standards. The diameter should range from 48 mm to 54 mm, while the height-to-diameter ratio should be maintained between 2.0 and 2.5. During the sample selection process, macro cracks and defects were subjected to visual inspection, and the longitudinal wave velocity was measured using a wave velocity instrument to assess the presence of internal fractures and defects within the rock. Samples exhibiting natural defects were systematically excluded from consideration. The statistical data pertaining to various fundamental physical indicators of the samples are presented in Table 1.  
To evaluate the degree of variability for each indicator, the coefficient of variation (defined as the ratio of the standard deviation to the mean) was employed, as illustrated in Equation (1). The results of these calculations are detailed in Table 2, which demonstrates  
Figure 3: Sandstone sample. Figure 2: Main steps of the test. that the variation for each indicator of the rock samples did not exceed 3.50%. Consequently, it is concluded that the dispersion of the rock samples satisfies the experimental criteria.