## 5 Numerical Simulation Analysis
### Analysis of Numerical Simulation Results  
The cloud diagram of the surrounding rock displacement before and after the optimization of the roadway support is shown in Figure 6 (Figure 7), and the amount of surrounding rock displacement is shown in Figure 8.  
From Figures 6 and 7, it can be seen that before the optimization of the tunnel support, the horizontal displacement of the two gangs is 37 mm, the maximum subsidence of the top plate is 49 mm, and the maximum deformation of the bottom plate is 55 mm, which results in larger deformation of the bottom plate and easily occurs due to the broken peripheral rock of the roadway; the anchor rods and anchor ropes are weak when controlling the peripheral rock, which leads to the occurrence of the bottom bulge of the roadway. After the optimization of the tunnel support, the maximum horizontal displacement of the two gangs is 12 mm, the top plate sinking is 11 mm, and the maximum deformation of the bottom plate is 13 mm; compared with the pre-optimization conditions, the horizontal displacement of the two gangs is reduced by 70%, the top plate sinking is reduced by 77.5%,  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Rock Statum**} & \multicolumn{2}{c}{**Uniaxial**} & \multirow{2}{*}{**Capacity**} & \multicolumn{2}{c}{**The Angle of**} & \multirow{2}{*}{**Poisson**} & \multicolumn{2}{c}{**Uniaxial**} & \multirow{2}{*}{**Cohesion**} & \multicolumn{2}{c}{**Elastic**} \\  & **Compressive Strength** & & & & & **Ratio** & **Tensile Stress** & **Modulus** \\  & **/MPa** & \(\mathbf{/g\cdot cm^{-3}}\) & \(f^{c}\) & & & **/MPa** & **/MPa** & **/GPa** \\ \hline Sandy & \multirow{2}{*}{14} & \multirow{2}{*}{2.32} & \multirow{2}{*}{30} & \multirow{2}{*}{0.32} & \multirow{2}{*}{1.12} & \multirow{2}{*}{0.52} & \multirow{2}{*}{4.38} \\ Mudstone & & & & & & & \\ \hline Silstone & 53.18 & 2.64 & 37 & 0.28 & 4.67 & 4.25 & 11.65 \\ \hline Argillaceous & \multirow{2}{*}{22} & \multirow{2}{*}{2.50} & \multirow{2}{*}{31} & \multirow{2}{*}{0.28} & \multirow{2}{*}{1.80} & \multirow{2}{*}{4.25} & \multirow{2}{*}{11.65} \\ Silstone & & & & & & & \\ \hline Coal Area & 12 & 1.6 & 18 & 0.42 & 1.43 & 1.50 & 0.45 \\ \hline Argillaceous & \multirow{2}{*}{22} & \multirow{2}{*}{2.50} & \multirow{2}{*}{31} & \multirow{2}{*}{0.21} & \multirow{2}{*}{1.80} & \multirow{2}{*}{4.25} & \multirow{2}{*}{11.65} \\ Silstone & & & & & & & \\ \hline Medium & \multirow{2}{*}{40} & \multirow{2}{*}{2.64} & \multirow{2}{*}{37} & \multirow{2}{*}{0.21} & \multirow{2}{*}{1.80} & \multirow{2}{*}{4.25} & \multirow{2}{*}{11.65} \\ Grained & & & & & & & \\ \hline Quartz & \multirow{2}{*}{40} & \multirow{2}{*}{2.64} & \multirow{2}{*}{37} & \multirow{2}{*}{0.21} & \multirow{2}{*}{1.80} & \multirow{2}{*}{4.25} & \multirow{2}{*}{11.65} \\ Sandstone & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical parameters of rock formation.  
Figure 5: Numerical analysis model diagram of FLAC3D: (**a**) numerical analysis model of rock formation; (**b**) numerical analysis model of support.  
and the deformation of the bottom plate is reduced by 76.4%. Through the optimization of the tunnel support, the deformation of the surrounding rock tends to be uniformly distributed, and the stability of the broken surrounding rock is effectively controlled.  
Figure 6: Surrounding rock displacement nephogram: (**a**) horizontal displacement nephogram before optimization. (**b**) Horizontal displacement nephogram after optimization. (**c**) Vertical displacement nephogram before optimization. (**d**) Vertical displacement nephogram after optimization.