## 5 Evolution of Rock Mass Mechanical Parameters Under Freeze-Thaw Cycles
### Quantification of Rock Mass Mechanical Parameters Under Freeze-Thaw Cycles  
The \(m_{i}\) of the rock can be calculated according to the following equation [23]:  
\[m_{i}=\frac{16\sigma_{t}}{\sigma_{c}}-\frac{\sigma_{c}}{\sigma_{t}} \tag{5}\]  
By substituting the uniaxial compressive strength and indirect tensile strength of the rock after freeze-thaw cycles into Equation (5), the variation in the hardness-softness degree of the rock with burial depth and freeze-thaw cycles can be obtained (Figure 8). Its variation pattern can still be fitted by the following exponential function (fitting coefficient: 0.70):  
\[m_{i}=12.80e^{(0.00181Y-0.0184)N} \tag{6}\]  
Figure 7: Identification of step\(-\)like structural features at a depth of 645 m (bench height). The green areas represent transverse cracks, while the red areas correspond to longitudinal cracks. The values of \(m_{b}\), \(s\), \(a\), the rock mass strength \(\sigma_{cm}\), and the ratio of the maximum confining pressure to the uniaxial compressive strength of the rock block (\(\sigma_{3 nt}\)) are determined by the following equations:  
\[m_{b}=m_{i}\exp\biggl{(}\frac{GSI-100}{28-14D}\biggr{)} \tag{7}\]  
\[\mathrm{s}=\exp\biggl{(}\frac{GSI-100}{9-3D}\biggr{)} \tag{8}\]  
\[\alpha=\frac{1}{2}+\frac{1}{6}\Bigl{(}\mathrm{e}^{\frac{-GSI}{15}}-\mathrm{e} ^{\frac{-20}{3}}\Bigr{)} \tag{9}\]  
\[\sigma_{cm}=\sigma_{c}\frac{[m_{b}+4s-a(m_{b}-8s)]\bigl{(}\frac{m_{b}}{4}+s \bigr{)}^{a-1}}{2(1+a)(2+a)} \tag{10}\]  
\[\sigma_{3 nt}=\frac{\sigma_{3 max}}{\sigma_{c}} \tag{11}\]  
where \(D\) is the coefficient representing the disturbance to the rock mass caused by blasting or stress release, taken as 1.0 in this study. The \(\sigma_{3 nt}\) term denotes the ratio of the maximum confining pressure to the uniaxial compressive strength of the rock block. The \(\sigma_{3 max}\) term represents the upper limit of the constrained stress under the relationship between the Hoek-Brown criterion and the Mohr-Coulomb criterion, determined by the following equation:  
\[\frac{\sigma_{3 max}}{\sigma_{cm}}=0.72\biggl{(}\frac{\sigma_{cm}}{\rho gH} \biggr{)}^{-0.91} \tag{12}\]  
Figure 8: The variation in rock hardness and softness with the number of freeze–thaw cycles (mi—a key parameter in the Hoek–Brown strength criterion). where \(\rho\) is the density of the rock mass (kg/m\({}^{3}\)), \(g\) is the gravitational acceleration, taken as 9.8 m/s\({}^{2}\), and \(H\) is the slope height (m). By inserting \(\sigma_{3n}\) into Equations (13) and (14), the internal friction angle and cohesion value of the rock mass can be calculated:  
\[m_{i}=12.80e^{(0.00181Y-0.0184)N} \tag{6}\]0  
\[m_{i}=12.80e^{(0.00181Y-0.0184)N} \tag{6}\]1  
As shown in Figures 9 and 10, the internal friction angle (\(\varphi\)) and cohesion (\(c\)) of granite at different burial depths in the 645 m bench of the northern slope of the Wushan Open\(-\)pit Mine showed significant decreases with the increase in the number of freeze-thaw cycles and the decrease in burial depth. The decrease in cohesion was more pronounced than that in the internal friction angle. The internal friction angle and cohesion of the rock mass without freeze-thaw cycles were 40.73\({}^{\circ}\) and 223.89 kPa, respectively. At a burial depth of 5.27 m, after 20 freeze-thaw cycles, the internal friction angle decreased to 33.25\({}^{\circ}\), and the cohesion decreased to 147.95 kPa, corresponding to reductions of 18.36% and 33.92%, respectively. In contrast, at a burial depth of 0.10 m, after 20 freeze-thaw cycles, the internal friction angle and cohesion reached only 27.77\({}^{\circ}\) and 111.64 kPa, with reduction percentages as high as 31.81% and 50.14%, respectively. The degradation patterns of both the internal friction angle and cohesion still followed exponential functions, with a goodness\(-\)of\(-\)fit R\({}^{2}\) of 0.94 and 0.92, respectively (For other rock strength degradation curves with the number of freeze-thaw cycles, please refer to Appendix B).