## 3 Size Optimization of Coal Pillar in Double-Roadway Excavation
### Coal Pillar Optimization Design Simulation Calculation
#### 3.2.2 Computational Simulation  
The study modeled the plastic zone state and stress distribution in the surrounding rock for varying coal pillar widths of 12, 14, 16, and 18 m after coal seam mining. During the simulation, unloading the mining coal seam at the working face released the surrounding rock's stress field, leading to significant variations in the stress field adjacent to the coal pillar. The medium-high stress zones from mining faces 119 and 111 were interconnected, resulting in stress superposition in the high-stress area. When the coal pillar was 12 m tall, it occupied the medium-high stress core area, with stress exceeding 40 MPa. Therefore, a coal pillar width of less than 12 m negatively impacted its stability. This may lead to the edge of the coal pillar peeling off and the interior being crushed, which in turn may cause the overlying rock layer to collapse, seriously affecting the safe production of the working  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Lithology** & **Density/(kg/m\({}^{3}\))** & **Elastic** & **Tensile** & **Cohesion/(MPa)** & **Internal Friction** \\  & **Modulus/(GPa)** & **Strength/(MPa)** & **Cohesion/(MPa)** & **Angle/(\({}^{\circ}\))** \\ \hline Medium sandstone & 2653 & 12.5 & 4.6 & 2.5 & 31 \\ Mudstone & 2589 & 8.67 & 2.55 & 1.7 & 25 \\ Coarse sandstone & 2813 & 12.35 & 6.5 & 2.7 & 20 \\ Silstone & 2680 & 16.5 & 6.97 & 1.3 & 21 \\ Coal & 1390 & 1.68 & 1.1 & 1.2 & 19 \\ Thickness & 2531 & 14.6 & 6.58 & 2.0 & 32 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical parameters of rocks.  
Figure 3: Diagram of the FLAC\({}^{\rm 3D}\) model.  
face. As the dimensions of the coal pillar expanded from 12 m to 14 m, the stress peak area transitioned from a singular zone to two clearly distinguishable zones. As the stress peak decreased and the coal pillar's stability improved, a 2-8 m stress slow-drop zone developed at the pillar's center. When the coal pillar size ranged from 14 to 16 m, the mutual influence of the two stress peak areas gradually became weak, and a low-stress area appeared in the middle, with a large elastic range, as shown in Figure 4.  
The distribution of the plastic zone indicated that as the coal pillar size exceeded 16 m, both the stability and the elastic zone range increased. In comparison, the 16 m coal pillar not only ensured the long-term stability of the surrounding rock by forming a stable low-stress elastic zone but also kept coal resource losses within a reasonable range, achieving the optimal balance between safe mining and efficient resource utilization. As shown in Figure 5, coal resources would be wasted. As a result, keeping the coal pillar's size around 16 m is preferable.  
A station was installed in that section to monitor the lateral abutment pressure of the coal pillar. The collected data were sorted and fitted to derive the stress distribution curve for coal pillars of varying sizes, as illustrated in Figure 6.  
Figure 4: Coal pillar stress nephogram: (**a**) 12 m coal pillar stress cloud diagram; (**b**) 14 m coal pillar stress cloud diagram; (**c**) 16 m coal pillar stress cloud diagram; (**d**) 18 m coal pillar stress cloud diagram.  
The stress curve indicated that a 12 m section coal pillar reached its vertical stress peak approximately 5 m inward from the edge. With a slight increase in distance, the vertical stress in the coal pillar remained nearly constant. This suggests that in a 12 m section coal pillar, most plastic deformation occurs within the pillar, while the elastic core area is minimal. As the section of the coal pillar expanded to 14 m, there was an obvious elastic core area; the sustaining pressure inside the coal pillar dropped significantly when the size of the section coal pillar approached 16 m, giving rise to an elastic core area of approximately 6 m. An 18 m coal pillar size enhancec the stability of the section by expanding the elastic core area, though it also led to increased resource wastage. This did not facilitate the enhancement of coal resource recovery rates.