## 3 Mechanical Model of Overburden Rock Structure
### Top Coal Subsidence Model and Numerical Simulation
#### 3.2.2 Numerical Simulation  
Based on the actual geological conditions of the 8310 working face and the mechanical parameters of coal-rock strata (Table 1), this study established a numerical analysis model measuring 180 m \(\times\) 53 m (length \(\times\) width) using UDEC 7.0 software (see Figure 9), aiming to simulate the stress evolution law and overburden structure characteristics under different fracture positions of the main roof. The left, right, and lower boundaries of the model limit the speed and displacement. The upper boundary applies a 12.0 Pa uniform load and increases according to the buried depth gradient. The lateral pressure coefficient is set to 1.2.  
As the coal mining face progresses, the rock strata above lose their support from the coal seam, resulting in phenomena such as cracking, tilting, and settlement. This process results in the significant deformation of the roof, forming a drastic deformation zone. Since the MRFL sits directly over the roadway, any shifts in its position directly affect the stability of the roadway's ceiling. Through simulations and actual measurements, we observed that block B fractures along the MRFL, causing a certain degree of compression on the underlying coal body, and stress concentration develops in the roadway roof, resulting in the localized failure of the roof structure, as shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Lithology** & **Density** & **Bulk Modulus** & **Shear Modulus** & **Friction Angle** & **Cohesion** & **Tensile Strength** \\  & **(kg/m\({}^{3}\))** & **(GPa)** & **(GPa)** & **(\({}^{\circ}\))** & **(MPa)** & **(MPa)** \\ \hline Silstone & 2650 & 10.2 & 7.8 & 39 & 3.3 & 2.4 \\ Carbon mudstone & 2298 & 6.4 & 5.5 & 25 & 1.9 & 1.6 \\ Coal & 1450 & 2.6 & 1.6 & 19 & 0.9 & 0.5 \\ Silty mudstone & 2446 & 6.0 & 5.3 & 29 & 2.2 & 1.8 \\ Fine sandstone & 2611 & 9.3 & 7.3 & 37 & 3.1 & 2.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Numerical simulation of formation parameters.  
Figure 9: Model modeling.  
Figure 11 displays the vertical stress distribution in the roadway's surrounding rock, derived from UDEC7.0 numerical simulations, for various distances between the MRFL and the coal pillar side. The conclusions are as follows:  
1. The numerical results demonstrate that the roadway roof experiences tensile stresses of approximately 2 MPa under both operational conditions, significantly exceeding the tensile strength 0.5 MPa for coal seams. This substantial stress-strength imbalance indicates a high risk of roof failure.
2. The compressive stress value at the junction of the coal seam and the immediate roof fluctuates in the range of 2 to 5 MPa. Notably, shear failure has already taken place within the coal mass at this location and the shear position is located directly below the fracture line.
3. When the MRFL is arranged at 1.5 m from the side of the coal pillar, the solid coal side of the roadway is closer to the vertical stress peak area. In contrast, when the distance is 2.5 m, the vertical stress peak covers a wider range on the solid coal side. The vertical stress peak of the former is 19.5 MPa, and the vertical stress peak of the latter is 21.6 MPa.  
Figure 11: Vertical stress distribution cloud diagram. (**a**) The MRFL is 1.5 m away from the coal pillar side. (**b**) The MRFL is 2.5 m away from the coal pillar side.  
Figure 10: UDEC numerical simulation of block structure.