## 3 Results and Discussion
### Long-Term Strength Analysis of the Unloaded Sample  
Long-term strength is an important safety indicator reflecting the stability of rock engineering. Under normal conditions, the long-term strength value of a rock is 60% to 90% of the instantaneous strength value. For unloaded rock, considering the excavation unloading effect, the stress state of the rock is changed. Additionally, its structural damage is intensified after freeze-thaw action, so it is very important to determine the long-term strength of this type of rock. Currently, the most widely used method for determining long-term strength is the isochronous curve cluster method. The isochronous curve cluster method is based on the Boltzmann superposition principle to superimpose the graded loading creep stress time curves and obtain the stress-strain isochronous curve cluster, with time as the parameter, and it is generally believed that the isochronous curve cluster will have a visible inflection point when the stress increases to a certain stage; the stress corresponding to this point is considered to be the long-term strength [26].  
With the isochronous curve cluster method, isochronous curves were drawn. Figure 7 shows that the overall isochronous curve drawn at each time node consists of linear and nonlinear segments. At low stress levels, the rock deformation is mainly elastic deformation, which is reflected by the curves clustering together; with an increase in stress level, plastic deformation gradually dominates, which is reflected by the curve clustering changing from dense to loose. Using this method, the long-term strength of the unloaded sample under different conditions was determined, as shown in Table 3.  
The above analysis shows that the long-term strength decay of unloaded samples at room temperature is mainly controlled by the unloading damage effect, and the long-term strength decay degree does not change significantly after the initial confining pressure increases, although the unloading confining pressure value increases. This also reflects the high confining pressure on the damage deterioration, and crack expansion of the unloaded sample has a suppressive effect. In addition, the slope excavation process is the main reason for the rapid release of stress and the deterioration of the rock structure. During the excavation and unloading process, the rock particle misalignment and fracture derivation provide a channel for the water body to intervene and provide conditions for the water-ice phase change caused by freezing and thawing. As shown in Table 3, the long-term strength decay of sandstone samples degraded by unloading damage superimposed on freeze-thaw periods has a certain correlation with the freezing time. Comparing the long-term strength results of unloaded sandstone samples under different freezing periods, it was found that the effect of freezing period on the long-term strength of unloaded samples of the same lithology has a certain threshold value.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Sample Number**} & **Long-Term Strength/MPa** & **Triaxial Peak Strength/MPa** & **Long-Term Strength/Triaxial Peak Strength** \\ \hline R15-0 & 87.52 & & 54.4\% \\ R15-7 & 85.53 & 160.8 & 53.2\% \\ R15-14 & 83.22 & & 51.7\% \\ \hline R21-0 & 110.14 & & 54.7\% \\ R21-7 & 106.64 & 201.0 & 53.0\% \\ R21-14 & 90.12 & & 44.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Isochronous curve method to determine long-term strength under different conditions.