## 4 Numerical Simulation of Repeated Supportability of Roadway Roof
### The Influence of Varying Buried Depths of Different Roadways on the Repeatability of Roof Support  
Following the excavation and formation of the roadway, the depth at which it is buried becomes crucial as it directly influences the level of original rock stress exerted on the roadway after excavation, thereby significantly impacting its stability. To examine the reproducibility of roof support in roadways with varying buried depths, we selected roadway buried depths of 200 m, 500 m, and 800 m to represent shallow, medium, and deep burial conditions, respectively. Through the application of various load sizes on the geological simulation model of the roadway, we simulated stress conditions corresponding to different buried depths. The relationship between the buried depth of the roadway and the applied load size is presented in Table 3.  
This section presents the results of numerical simulations conducted at a roadway depth of 500 m. Additionally, numerical simulation results for roadway depths of 200 m and 800 m are provided to further supplement the findings. Each roadway depth was examined considering various lithologies for the direct roof, including sandstone, sandy mudstone, and mudstone. Moreover, direct roof thicknesses of 0.8 m, 1.6 m, and 2.4 m were considered for each lithology. By varying the applied load and simulating changes in roadway depth and ground stress, important parameters such as the fragmentation  
Figure 25: Basic roof and direct roof monitoring line displacement and relative displacement change results. (**a**) Direct roof thickness 0.8 m, (**b**) Direct roof thickness 1.6 m, (**c**) Direct roof thickness 2.4 m.  
range of the direct roof after twin-link stepping temporary support (X1), the maximum displacement of the direct roof (X2), and the relative displacement between the direct roof and the basic roof (X3) were obtained. These parameters play a vital role in evaluating the repeatability of roof support. Detailed numerical simulation results for roadway depths of 200, 500, and 800 m are presented in Tables 4-6, respectively. Based on the numerical simulation results presented in Tables 4-6 for various depths at which roadways are buried, it is observed that by employing temporary and permanent support measures, the maximum displacement of the direct roof surface can be effectively limited to 50 mm across different roadway conditions, thus mitigating the occurrence of roof accidents. Based on the numerical simulation results presented in Table 4 for a roadway buried at a depth of 200 m, it is observed that in the presence of a sandstone direct roof, various thicknesses of the direct roof can meet the requirements for repeatability of roof support. When the direct roof consists of sandy mudstone, the range of direct roof fracturing is between 0.5-0.6 m, indicating the repeatability of the roadway roof for different roof thicknesses. However, with a mudstone direct roof, the range of direct roof fracturing \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Buried Depths (m)**} & \multirow{2}{*}{**Vertical Stress**} & \multicolumn{2}{c}{**Minimum**} & **Maximum** \\  & & **(Pa)** & **Horizontal Principal** & **Horizontal Principal** \\  & & **Stress (Pa)** & **Stress (Pa)** \\ \hline
200 & \(-5\times 10^{6}\) & \(-6\times 10^{6}\) & \(-8\times 10^{6}\) \\
500 & \(-10\times 10^{6}\) & \(-12\times 10^{6}\) & \(-15\times 10^{6}\) \\
800 & \(-18\times 10^{6}\) & \(-20\times 10^{6}\) & \(-22\times 10^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The effects of different load sizes on the buried depths of roadways.