## 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  
To obtain the mechanical parameters of rock masses under freeze-thaw cycles, the Hoek-Brown criterion was adopted to degrade the rock mechanical parameters under laboratory test conditions. The generalized Hoek-Brown failure criterion for jointed rock masses is defined as follows:  
\[\sigma_{1}=\sigma_{3}+\sigma_{c}\bigg{(}m_{b}\frac{\sigma_{3}}{\sigma_{c}}+s \bigg{)}^{a} \tag{1}\]  
where \(\sigma_{1}\) is the major principal stress at failure, \(\sigma_{3}\) is the minor principal stress at failure, \(\sigma_{c}\) is the uniaxial compressive strength of intact rock \(m_{b}\), \(s\), and \(\alpha\) are empirical parameters reflecting the structural and quality characteristics of the rock mass. In 2002, the geological strength index (\(GSI\)) was introduced by [PERSON] et al. to comprehensively account for rock mass and structural plane characteristics, with the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Lithology**} & **Triaxial Confining Pressure** & **Axial Stress** & **Cohesive Force** & **Angle of Internal Friction** \\  & \(\sigma_{3}\)/MPa & \(\sigma_{1}\)/MPa & \(c\)/MPa & \(\sigma_{6}\)/\(c\) \\ \hline \multirow{3}{*}{Dacite} & 5 & 222.0 & & \\  & 10 & 247.0 & 41.9 & 43.5 \\ \cline{1-1}  & 15 & 274.1 & & \\ \hline \multirow{3}{*}{Magnetite} & 5 & 197.9 & & \\  & 10 & 216.9 & 39.6 & 42.9 \\ \cline{1-1}  & 15 & 264.0 & & \\ \hline \multirow{3}{*}{Skarn} & 5 & 228.3 & & \\ \cline{1-1}  & 10 & 267.8 & 42.3 & 45.8 \\ \cline{1-1}  & 15 & 298.2 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical parameters of rock triaxial compression under different circumferential pressure conditions. Figure 5: Triaxial compressive stress–strain curves of rocks under different circumferential pressure conditions. (**a**) Dacite; (**b**) magnetite; (**c**) skarn. incorporation of a disturbance parameter D. A methodology for calculating \(m_{b}\), \(s\), and \(\alpha\) using GSI and D was proposed, as formulated in Equation (2):  
\[\left\{ \begin{array}{c}m_{b}=m_{i}exp\Big{(}\frac{GSI-100}{28-14D}\Big{)}\\ s=exp\Big{(}\frac{GSI-100}{9-30}\Big{)}\\ \alpha=\frac{1}{2}+\frac{1}{6}\Big{(}e^{-GSI/15}-e^{-20/3}\Big{)}\end{array} \right. \tag{2}\]  
where \(GSI\) is the geological strength index, \(m_{i}\) is the intact rock material constant, and \(D\) is the engineering disturbance factor. The Standard for Engineering Classification of Rock Mass (GB/T 50218-2014) [29] specifies that when the integrity index (\(K_{v}\)) cannot be obtained through field measurements, it may be determined using the volumetric joint count (\(J_{v}\)) of the rock mass. The empirical relationship between \(K_{v}\) and \(J_{v}\) is provided in Table 3.  
[PERSON] et al. [30] systematically measured and statistically analyzed the rock discontinuities in the mining study area. The volumetric joint count (\(J_{v}\)) of the rock slope was determined as 2.11, resulting in an integrity coefficient (\(K_{v}\)) of 0.83. An empirical relationship between the geological strength index (GSI) and P-wave velocity (Vp) was conducted by [PERSON] et al. [31] based on the statistical analysis of extensive rock engineering data, expressed as follows:  
\[GSI=\big{(}40V_{pm}+10\big{)}/3 \tag{3}\]  
\[V_{pm}=V_{p}\sqrt{K_{v}} \tag{4}\]  
where \(V_{p}\) is the longitudinal wave velocity of rock and \(V_{pm}\) is the longitudinal wave velocity of rock mass. Rock specimens subjected to predetermined F-T cycles were tested by the ZBL-U5200 non-metallic ultrasonic tester for P-wave velocity and the data were averaged to ensure reliability. The P-wave velocities (\(V_{p}\)) and geological strength index (\(GSI\)) values of the three rock types under varying freeze-thaw (F-T) cycles are summarized in Table 4.  
The intact rock material constant m\({}_{i}\) was determined as 22 for dacite, and 26 for both skarn and magnetite [32].