## 2 Rock Mass Characteristics
### Rock Mass Classification  
Due to the large scale and discontinuous nature of in situ rock masses, which is incomparable to conventional engineering materials such as steel or concrete, the estimation \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Lithology** & **Depth** & \(\sigma_{c,i}\) & \(\sigma_{t,i}\) & \(E_{i}\) & **RQD** \\  & **(m)** & **(MPa)** & **(MPa)** & **(MPa)** & **(\%)** \\ \hline Medium-grained sandstone & 957.00–983.50 & 35.6 & 3.8 & 7903 & 100 \\ Mixed-grained sandstone & 983.50–988.50 & 55.2 & 5.8 & 12,254 & 80 \\ Mixed-grained sandstone & 988.50–993.20 & 64.9 & 6.8 & 14,408 & 80 \\ Claystone & 993.20–995.70 & 32.6 & 4.0 & 8932 & 65 \\ Mudstone & 995.70–999.20 & 73.9 & 8.9 & 17,145 & 70 \\ Fine-grained sandstone & 999.20–1012.20 & 67.3 & 6.9 & 14,941 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic mechanical parameters of intact rock, along with RQD values for different lithological units in the area of Shaft II. of rock mass parameters has traditionally been based on empirical classification systems, such as the Rock Mass Rating (RMR) [8], the Geological Strength Index (GSI) [9; 10; 11], or the Q-system [12]. These classification systems take into account factors such as the spacing, condition, and orientation of discontinuities, as well as intact rock strength and groundwater conditions, providing a useful tool for the initial assessment of rock mass quality and potential support solutions. In the present study, the RMR system was adopted for the initial assessment of rock mass quality, while the GSI system was used to obtain the mechanical parameters of the rock mass. The GSI values for different lithological units were calculated using previously estimated RMR index values, based on the equation proposed by [PERSON] and [PERSON] [13]:  
\[GSI=RMR-5. \tag{2}\]  
The estimation of GSI based on the RMR index is a widely adopted approach in numerous studies on the stability of tunnels and mine workings [14; 15; 16; 17; 18; 19]. In other cases, GSI was determined through visual observations of the rock mass appearance and the use of GSI charts for jointed rock masses [20; 21; 22]. The GSI value calculated using Equation (2) was employed to estimate the peak rock mass properties. On the other hand, the Residual Geological Strength Index (GSI\({}_{r}\)) was applied to determine the residual (post-peak) rock mass properties. [PERSON] et al. proposed a method for estimating the GSI\({}_{r}\) value based on in situ block shear test data and the back-analysis of rock slopes [23]. According to [PERSON] et al., the GSI\({}_{r}\) value can be calculated using the following equation:  
\[GSI_{r}=GSI\cdot e^{0.0134\cdot GSI}. \tag{3}\]  
A different approach was proposed by [PERSON] and [PERSON], who analyzed a combined database comprising [PERSON] et al. 's field data and [PERSON] et al. 's laboratory data [24]. They introduced an empirical relationship to calculate the GSI\({}_{r}\) value based on the peak GSI and the Hoek-Brown material constant for intact rock, \(m_{i}\)[25]:  
\[\frac{GSI_{r}}{GSI}=\left(1+\left(\frac{m_{i}}{33}\right)^{1.5}\right)\cdot GSI ^{\frac{m_{i}}{100}}. \tag{4}\]  
The method proposed by [PERSON] et al. most likely represents a lower bound for residual rock mass strength [26]. Therefore, it was ultimately adopted for further analysis, providing an additional safety factor for the designed support structures. The estimated RMR values, along with the peak and post-peak GSI values for different lithological units in the area of Shaft II within a depth range of 957.00-1012.20 m, are summarized in Table 2.