## 4 Numerical Analysis of Active Bearing of the FSP
### Analysis of Active Bearing Effect of the FSP  
(1) The influence of steel pipe length  
To study the influence of the length to FSP's bearing capacity, we explored the efficient use of the steel pipe length in practical engineering applications on the premise of not changing the parameters of rock and steel pipe materials, only gradually shortening the modeling of the steel pipe length, exerting the same displacement at the end of the steel \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Density** & **Elastic Modulus** & **Poisson’s** & **Cohesive** & **The Angle of** & **Constitutive** \\  & **(kN/m\({}^{3}\))** & **(MPa)** & **Ratio** & **Forces (kPa)** & **Internal Friction (\({}^{\circ}\))** & **Model** \\ \hline
15\% water content of loess 20\% water content of loess 16 & 10 & 0.3 & 40 & 22 & M-C \\
20\% water content of loess 20\% steel pipe (HPB235) & 16 & 8 & 0.3 & 16 & 22 & M-C \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameter table. Figure 11: Numerical calculation model. Figure 12: Details of nonlinear spring setting. pipe, through the bearing and deformation behavior of the steel pipe and contact stress analysis of the influence degree of the length of steel pipe bearing. Figure 13 shows the bearing deformation curves of the 42 \(\times\) 4 mm steel pipe with different pipe lengths in loess stratum with 15% water content. It can be seen from the comparison that when the length of the steel pipe is 1.0 m or above, the bearing curves basically coincide and have no influence on the bearing deformation characteristics. When the length of the steel pipe is in the range of 0.75 m\(\sim\)1.0 m, the pipe length only affects the shape and slope of the bearing curve of the steel pipe but does not affect the ultimate bearing capacity of the steel pipe. When the pipe length is less than 0.75 m, the pipe length has a great influence on the bearing curve and ultimate bearing capacity of the steel pipe. Figure 14 compares the bending deformation patterns of steel tubes with different lengths under a transverse load. According to the bending form of the steel pipe, when the length of the steel pipe is less than 0.75 m, the steel pipe has no obvious bending phenomenon, and the soil cannot restrain the penetrating failure of the bottom of the steel pipe, and the bottom deformation can reach 0.02 m. When the length of the steel pipe is 0.75 m\(\sim\)1.0 m, with the increasing contact area between the soil and the upper part of the steel pipe, the steel pipe will gradually bend at a certain point, and the ultimate bearing capacity of the steel pipe is gradually independent of the length. When the length of steel pipe is greater than 1.0 m, the bearing characteristic curve of steel pipe is directly unrelated to the length of steel pipe, so the length of steel pipe commonly used in the tunnel has almost no influence on the bearing capacity. Figure 14: Deformation of steel pipe with different lengths in soil (m). (a) Steel pipe of 50 cm in length. (b) Steel pipe of 75 cm in length. (c) Steel pipe of 100 cm in length. Figure 13: Relationship between pipe length and bearing deformation curve of steel pipe. By comparing the vault settlement with and without active bearing under various supporting conditions, it can be found that the active bearing of the steel pipe has a certain control effect on the vault deformation. By comparing the active bearing effect of the FSP under different load release rates, it is found that the lower the load release coefficient of the surrounding rock, the smaller the vault settlement after preloading the FSP and the greater the reduction of the vault settlement. After excavation, the FSP was installed as soon as possible, and the active bearing scheme was adopted, which significantly reduced the deformation of the support in the early stage.