## 4 Numerical Analysis of Active Bearing of the FSP
### Analysis of Active Bearing Effect of the FSP
Taking the 50 mm diameter FSP as an example, when the end of the steel pipe is preloaded by 10 cm, and the load release rate of the surrounding rock is 5%, the settlement of the vault is reduced by 24.57%. When the load release rate is 20%, the settlement reduction of the vault is 0.83%, and the FSP's active bearing effect is not apparent. The main reason is that when the deformation pressure of the surrounding rock is slight, the FSP can provide sufficient bearing capacity in preloading. Sufficient bearing capacity can effectively reduce the release of surrounding rock pressure, thereby controlling the settlement of the vault. By comparing the control effects of different FSPs on the vault settlement after preloading, it can be seen that increasing the number of FSPs and the amount of preloading at the ends can reduce the vault settlement. Taking the 89 mm diameter of FSP as an example, when the load release rate is 5%, the preloading of the FSP increases from 5 cm to 10 cm, and the reduction of the vault settlement increases from 30.79% to 41.84%. After the FSP number is increased from 2 to 4, the vault settlement is reduced from 12.92 mm to 5.40 mm, and the reduction rate is doubled. Therefore, when the preload is constant, if the overall bearing stiffness of the FSP is more considerable, the active bearing effect will be more obvious. (3) Variation of active bearing effect with the excavation time  
After the tunnel is excavated, the surrounding rock stress is gradually released with the development of time. According to the on-site monitoring and calculation results, the change of the surrounding rock pressure with time is calculated. The surrounding rock pressure at the corresponding time is brought into the simulation calculation, and the variation law of the vault settlement with time under the active action of the FSP with or without the foot lock is obtained. This method can more realistically simulate the effect of the active bearing of the FSP on the settlement of the vault after the tunnel is excavated on the upper benches. Figure 10 is a detailed comparison of the tunnel support effect of 42 \(\times\) 4 mm FSP with or without active bearing based on the known controlling effect of 50 \(\times\) 5 mm FSP. As can be seen from Figure 16, with the steel pipe with small stiffness, that is, under the steel pipe diameter of 42 mm and the steel pipe diameter of 50 mm without active bearing, it can be seen that the settlement curve of the steel pipe with the diameter of 50 mm is located above the diameter of 42 mm, and when the steel pipe with the diameter of 42 mm is actively bearing, obviously the curve of the steel pipe with the diameter of 42 mm under the active bearing is located above the steel pipe with the diameter of 50 mm without active bearing. This shows that even the steel pipe with small stiffness can play a better supporting effect by preloading, which is feasible. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Load Release Rate**} & \multirow{2}{*}{**The Normal State**} & \multicolumn{2}{c}{**Preload a Displacement of 5 cm**} & \multicolumn{2}{c}{**Preload a Displacement of 10 cm**} \\  & & \multicolumn{2}{c}{**at the End of the Steel Pipe**} & \multicolumn{2}{c}{**at the End of the Steel Pipe**} \\ \cline{2-6}  & **Settlement of the** & **Settlement of the** & **Damping/\%** & **Settlement of the** & **Damping/\%** \\  & **Vault/mm** & **Vault/mm** & **Damping/\%** & **Vault/mm** & **Damping/\%** \\ \hline
5\% & 18.6706 & 12.9227 & 30.79 & 10.8579 & 41.84 \\
10\% & 42.695 & 37.9235 & 11.18 & 36.5386 & 14.42 \\
15\% & 72.1146 & 68.9974 & 4.32 & 68.0879 & 5.58 \\
20\% & 105.973 & 104.522 & 1.37 & 104.124 & 1.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The influence of two active bearing FSPs of 89 \(\times\) 8 mm on settlement of the arch vault. Figures 17 and 18 compare the support effect of 89 mm steel pipe preloading displacement of 50 mm. At the end of the third day, the steel pipe was prepressed, and the active load was applied.