## 2 Current Status of Support Instability in the Working Face of SDCS
### Establishment of Numerical Model
#### 3.2.2 Numerical Simulation Parameters and Experimental Process  
The numerical simulation employs the Mohr-Coulomb constitutive model. For FLAC3D implementation, the failure criterion can be graphically represented in the (\(\sigma_{1}\), \(\sigma_{3}\)) principal stress plane coordinate system, as shown in Figure 10. The failure envelope segment between points A and B is governed by the Mohr-Coulomb failure criterion, which is defined when \(\hat{f}=0\). \[f^{\rm s}=\sigma_{1}-\sigma_{3}N_{\phi}+2c\sqrt{N_{\phi}} \tag{1}\]  
Figure 10: FLAC3D Mohr–Coulomb failure criterion. Figure 9: Filling range of the numerical model. All critical parameters of the coal and rock strata were determined through field sampling and laboratory testing. The specific parameters are presented in Table 1. In FLAC3D numerical simulations, directly applying laboratory-measured rock mechanical parameters (e.g., strength and elastic modulus) may lead to deviations between computational results and actual engineering responses. This discrepancy arises because laboratory parameters typically represent small-scale intact rock properties, whereas FLAC3D models must account for rock mass behavior at the engineering scale. To address this, the GSI-based Hoek-Brown criterion can be employed to convert laboratory-derived intact rock parameters into equivalent rock mass parameters [28; 29; 30], which are then used as inputs for FLAC3D simulations. The rock mass characteristic parameters are shown in Table 2.  
The numerical simulation experiment process is as follows:  
1. Roadway Excavation Stage: The return airway and haulage gateway are excavated separately, with a cross-sectional dimension of 5 m in width and 3 m in height. Each roadway extends 400 m in length, adopting a full-face single-pass excavation method to simulate the initial stress release of the surrounding rock during roadway driving. 2. Working Face Mining Process: When the working face advances 10 m, the caving operation is initiated with the caving position dynamically trailing 5 m behind the working face. After each caving operation, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{**Rock Layers**} & \multirow{2}{*}{\begin{tabular}{c} **Volume Weight** \\ **(kg/m3)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Modulus of** \\ **Elasticity** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Uniaxial** \\ **Compressive** \\ **Strength (MPa)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Cohesion** \\ **(MPa)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Internal Friction** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} } \\ \hline
1 & Silstone & 2350 & 5000 & 36.0 & 2.8 & 28 \\
2 & Coal & 1350 & 3900 & 10.0 & 2.7 & 23 \\
3 & Carbon mudstone & 2500 & 5500 & 18.0 & 4.0 & 23 \\
4 & Mudstone & 2470 & 3800 & 20.0 & 2.9 & 30 \\
5 & Fine sandstone & 2710 & 5600 & 34.0 & 3.9 & 25 \\
6 & Coarse sandstone & 2570 & 4800 & 28.0 & 5.0 & 32 \\
7 & Sandstone & 2520 & 4900 & 36.0 & 2.9 & 35 \\
8 & Fine sandstone & 2710 & 5600 & 35.0 & 3.7 & 25 \\
9 & Conglomente & 2520 & 4900 & 29.0 & 3.0 & 33 \\
10 & Coarse sandstone & 2570 & 4800 & 28.0 & 4.6 & 32 \\
11 & Backfill & 1900 & 2900 & / & 0.1 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Coal and rock physical and mechanical parameters.