## 2 Geological Conditions and Numerical Modeling  
Shoushan No. 1 Coal Mine is located in Xuchang City, Henan Province, China, and the geographical location is shown in Figure 1. There are two primary mineable seams in the mine area, namely the No. 2 and No. 4 coal seams. This study selected an underground area of 700 m in depth in the mining area as the research object, and the geological profile is shown in Figure 2.  
In order to explore the failure mechanism of deep-turning roadways, four models were developed using 3 DEC to investigate the influences of ground stress and turning radius on roadway stability. This software is a three-dimensional numerical program based on the distinct element method, which represents discontinuous medium as an assemblage  
Figure 1: Location of Shoushan No. 1 Coal Mine. of discrete blocks and allows large displacements along discontinuities and rotations of blocks. Therefore, 3 DEC can capture the failure and deformation behavior of surrounding rocks in underground engineering. The established model's parameters are listed in Table 1. The excavation depths in Cases 1 and 2 were varied, and changes in the turning radius of the roadway were studied in Cases 2 and 3. Cable bolt support was applied in Case 4 to examine differences in support effects. The excavation of the roadways was simulated using the four models, and the rock mass parameters are listed in Table 2. In addition, a strain-softening model was established to describe the failure behavior of the rock mass, with the parameters provided in Table 3. A schematic diagram of the model is shown in Figure 3 (the model of Case 3). Stress boundary conditions were applied to each model's top boundary, reflecting the average weight of the overlying strata, which was 2550 kg/m\({}^{3}\). Roller boundary conditions (no vertical or lateral displacement) were applied at the bottom. For lateral boundaries, stress boundary conditions considering the gravity gradient were applied on corresponding sides in both the x- and y-directions. The gravity gradient was also applied to the model to simulate real in situ stress. The horizontal stress was calculated based on the lateral stress ratio of \(K_{x}=1.10(\sigma_{x}/\sigma_{z})\) and \(K_{y}=1.30(\sigma_{y}/\sigma_{z})\). This study obtained the initial stress field by equilibrating the in situ stress with the applied boundary conditions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case No.**} & \multirow{2}{*}{**Model Size (m)**} & **Tunnel** & **Tunnel** & **Turning** & **Cable** \\  & & **Radius (m)** & **Depth (m)** & **Radius (m)** & **Support** \\ \hline
1 & \(56\times 180\times 30\) & 2.15 & 700 & 101.85 & No \\
2 & \(56\times 180\times 30\) & 2.15 & 1200 & 101.85 & No \\
3 & \(77\times 153\times 30\) & 2.15 & 1200 & 50.93 & No \\
4 & \(56\times 180\times 30\) & 2.15 & 1200 & 101.85 & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of the numerical model’s parameters. Figure 2: Geological profile of the study area. During TBM tunneling, support is carried out synchronously with advancement; therefore, it is necessary to consider the deformation of the surrounding rocks under the action of support. The applied support scheme for Case 4 is illustrated in Figure 4, and the parameters of the cable bolts are detailed in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Young’s Modulus of** & **Cross-Sectional Area** & **Tensile Yield Strength** & **Bond Shear Stiffness** & \\
**Bolt (MPa)** & **of Bolt (m2)** & **of Bolt (MN)** & **(MN/m/m)** & **Bond Strength (MN/m)** \\ \hline \(200\times 10^{3}\) & \(3.14\times 10^{-4}\) & \(153.9\times 10^{-3}\) & 5602 & 2.199 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Material property values of rock cable bolts. Figure 3: Schematic diagram of the numerical model.