## 3 Mechanical Parameters of Rock Mass Under the Influence of Freeze-Thaw Cycles
### Determination of Mechanical Parameters of Rock Mass Considering Freezing and Thawing Effects
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Lithology** & **Number of Freeze-Thaw Cycles** & **P-Wave Velocity Vp m/s** & **GSI** \\ \hline \multirow{4}{*}{Dacite} & 0 & 5682 & 72 \\  & 30 & 5530 & 70 \\  & 60 & 5450 & 69 \\  & 90 & 5384 & 68 \\ \hline \multirow{4}{*}{Magnetic} & 0 & 6799 & 86 \\  & 30 & 6309 & 80 \\  & 60 & 6049 & 76 \\  & 90 & 5778 & 73 \\ \hline \multirow{4}{*}{Skarn} & 0 & 5814 & 74 \\  & 30 & 5682 & 72 \\ \cline{1-1}  & 60 & 5586 & 71 \\ \cline{1-1}  & 90 & 5492 & 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: GSI values of the three types of rocks at different freeze-thaw times. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(J_{v}\)(strips/m\({}^{3}\)) & \textgreater{}35 & 35–20 & 20–10 & 10–3 & \textless{}3 \\ \hline \(K_{v}\) & \textless{}0.15 & 0.15–0.35 & 0.35–0.55 & 0.55–0.75 & \textgreater{}0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relationship between \(J_{v}\) and \(K_{v}\). For undisturbed rock masses, the disturbance coefficient D is assigned a value of 0. However, severely disturbed or damaged rock masses (e.g., those affected by large-scale blasting or F-T cycling in this open-pit mine) were assigned D = 1.0. According to the Technical Specification for Slope Engineering in Non-Coal Surface Mines (GB 51016-2014) [33], the mechanical parameters of the rock mass can be calculated using the following formula. Rock compression can be calculated by the following formula:  
\[\sigma_{cm}=\sigma_{c}\frac{[m_{b}+4s-a(m_{b}-8s)](m_{b}/4+s)^{a-1}}{2(1+a)(2+ a)} \tag{5}\]  
where \(\sigma_{cm}\) is the rock compressive strength. The tensile strength of the rock can be calculated by the following formula:  
\[\sigma_{\text{tm}}=\frac{-\sigma_{c}s}{m_{b}} \tag{6}\]  
where \(\sigma_{tm}\) is the tensile strength of the rock mass. The deformation modulus of the rock mass can be calculated by the following Equation:  
\[E_{\text{rm}}=E_{\text{i}}\left\{0.02+\frac{1-D/2}{1+\text{e}^{[(60+15D-GST)/ 11]}}\right\} \tag{7}\]  
where \(E_{rm}\) is the deformation modulus of the rock mass and \(E_{i}\) is the deformation modulus of the intact rock. Meanwhile, Hoek-Brown-derived Expressions (6) and (7) for the shear strength indexes, internal friction angle \(\varphi\) and cohesion \(c\), by establishing a quantitative relationship between the Mohr-Coulomb and Hoek-Brown criteria [34], as follows:  
\[\varphi=sin^{-1}\left[\frac{6 am_{b}(s+m_{b}\sigma_{3n})^{\alpha-1}}{2(1+a)(2+a )+6 am_{b}(s+m_{b}\sigma_{3n})^{\alpha-1}}\right] \tag{8}\]  
\[c=\frac{\sigma_{c}[(1+2a)s+(1-a)m_{b}\sigma_{3n}](s+m_{b}\sigma_{3n})^{\alpha -1}}{(1+a)(2+a)\sqrt{1+\left[6 am_{b}(s+m_{b}\sigma_{3n})^{\alpha-1}\right]/ \left[(1+a)(2+a)\right]}} \tag{9}\]  
\[\frac{\sigma_{3 max}}{\sigma_{cm}}=0.72\left(\frac{1000\sigma_{cm}}{\gamma H} \right)^{-0.91} \tag{10}\]  
\[\sigma_{3n}=\frac{\sigma_{3 max}}{\sigma_{c}} \tag{11}\]  
where \(\sigma_{3n}\) is the ratio of maximum confining pressure to uniaxial compressive strength, \(\sigma_{3 max}\) is the maximum confining pressure, H is the slope height, and \(\gamma\) is the rock mass weight. According to Equations (3)-(11), the mechanical parameters of rock masses under varying F-T cycles were calculated and summarized in Table 5. After 90 F-T cycles, significant degradation was observed: uniaxial compressive strength (UCS) decreased by 29.7-45.8%, elastic modulus (EM) by 42.7-63.3%, Poisson's ratio by 16.0-42.1%, cohesion by 71.7-77.1%, internal friction angle by approximately 52.0%, and tensile strength by 79.3-83.6%.