## 3 Results and Discussion
### Mechanical Properties
#### 3.3.4 Shear Strength Parameters
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Crack Dip Angle** &
\begin{tabular}{c} **Freeze–thaw** \\ **Cycles** \\ \end{tabular} & **Fitting Equation** & **R\({}^{2}\)** & **C/MPa** & \(\varphi f^{2}\) \\ \hline \multirow{8}{*}{0\({}^{\circ}\)} & 0 & \(\sigma_{1f}=67.29+6.58\sigma_{3}\) & 0.984 & 13.12 & 47.40 \\  & 5 & \(\sigma_{1f}=62.26+51\sigma_{7}\) & 0.969 & 13.69 & 42.52 \\  & 10 & \(\sigma_{1f}=99.75+4.53\sigma_{3}\) & 0.961 & 14.04 & 39.67 \\  & 15 & \(\sigma_{1f}=52.19+51\sigma_{6}\) & 0.965 & 11.49 & 42.48 \\  & 20 & \(\sigma_{1f}=46.09+4.95\sigma_{3}\) & 0.967 & 10.36 & 41.60 \\  & 25 & \(\sigma_{1f}=40.97+4.82\sigma_{3}\) & 0.943 & 9.33 & 41.02 \\  & 30 & \(\sigma_{1f}=34.90+5.04\sigma_{3}\) & 0.910 & 7.77 & 41.98 \\ \hline \multirow{8}{*}{30\({}^{\circ}\)} & 0 & \(\sigma_{1f}=59.12+6.92\sigma_{3}\) & 0.992 & 11.24 & 48.37 \\  & 5 & \(\sigma_{1f}=51.70+5.51\sigma_{3}\) & 0.947 & 11.01 & 43.85 \\  & 10 & \(\sigma_{1f}=47.80+5.53\sigma_{3}\) & 0.909 & 10.32 & 43.28 \\  & 15 & \(\sigma_{1f}=41.45+50.90\sigma_{3}\) & 0.953 & 9.19 & 42.19 \\  & 20 & \(\sigma_{1f}=35.09+4.59\sigma_{3}\) & 0.927 & 8.19 & 39.96 \\  & 25 & \(\sigma_{1f}=29.85+4.93\sigma_{3}\) & 0.895 & 6.72 & 41.51 \\  & 30 & \(\sigma_{1f}=26.15+4.27\sigma_{3}\) & 0.876 & 6.33 & 38.35 \\ \hline \multirow{8}{*}{45\({}^{\circ}\)} & 0 & \(\sigma_{1f}=38.64+8.51\sigma_{3}\) & 0.940 & 6.62 & 52.16 \\  & 5 & \(\sigma_{1f}=35.21+6.02\sigma_{3}\) & 0.978 & 7.18 & 45.65 \\ \cline{1-1}  & 10 & \(\sigma_{1f}=33.48+5.63\sigma_{3}\) & 0.964 & 7.06 & 44.29 \\ \cline{1-1}  & 15 & \(\sigma_{1f}=26.10+5.74\sigma_{3}\) & 0.958 & 5.45 & 44.69 \\ \cline{1-1}  & 20 & \(\sigma_{1f}=18.58+5.92\sigma_{3}\) & 0.988 & 3.82 & 45.31 \\ \cline{1-1}  & 25 & \(\sigma_{1f}=21.69+5.67\sigma_{3}\) & 0.988 & 2.66 & 44.44 \\ \cline{1-1}  & 30 & \(\sigma_{1f}=8.51+5.01\sigma_{3}\) & 0.944 & 1.90 & 41.85 \\ \hline \multirow{8}{*}{30\({}^{\circ}\)} & 0 & \(\sigma_{1f}=31.05+4.47\sigma_{3}\) & 0.890 & 7.34 & 39.37 \\  & 5 & \(\sigma_{1f}=27.06+4.31\sigma_{3}\) & 0.840 & 6.52 & 38.56 \\ \cline{1-1}  & 10 & \(\sigma_{1f}=24.55+4.17\sigma_{3}\) & 0.854 & 6.01 & 37.82 \\ \cline{1-1}  & 15 & \(\sigma_{1f}=19.90+3.67\sigma_{3}\) & 0.806 & 5.19 & 34.87 \\ \cline{1-1}  & 20 & \(\sigma_{1f}=15.59+3.65\sigma_{3}\) & 0.881 & 4.08 & 34.74 \\ \cline{1-1}  & 25 & \(\sigma_{1f}=11.97+3.07\sigma_{3}\) & 0.853 & 3.42 & 30.57 \\ \cline{1-1}  & 30 & \(\sigma_{1f}=6.23+2.34\sigma_{3}\) & 0.897 & 2.04 & 23.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Shear parameters of grouting reinforcement body. Figure 23: Effect of freeze–thaw cycle on shear strength parameters of sample (**a**) cohesion; (**b**) angle of internal friction. The data reveal that the extreme value ratio of cohesion in the grouting reinforcement body is significantly greater than that of the internal friction angle, suggesting that the effect of freeze-thaw cycles primarily induces damage related to the weakening of the cementation between rock particles. Under low-temperature conditions, the internal pore water within the grouting reinforcement body freezes, generating frost heave forces that lead to an increase in the internal pore volume. With repeated freeze-thaw cycles, internal damage within the grouting reinforcement body progressively accumulates. As the internal pore water increases, the frost heave forces generated during freezing intensify, gradually reducing the cohesion of the grouting reinforcement body after multiple freeze-thaw cycles, thereby directly affecting its macroscopic physical and mechanical properties. In the initial stages of the freeze-thaw cycle, the cement damage within the rock is minimal, resulting in only a slight decrease in cohesion. However, after repeated freeze-thaw cycles, severe damage to the cementation within the rock leads to a sharp decline in the cohesion of the grouting reinforcement body.