## 4 Parametric Analysis
### Effect of Reinforcement Range  
Based on the numerical simulation of the above typical cross-sections, under the premise of keeping other parameters of the model unchanged, only the reinforcement range of the steel channel is changed. The equivalent spring stiffness in different cases is shown in Table 3.  
Figure 12 shows that increasing the reinforcement range can effectively reduce the maximum longitudinal displacement of the segment lining. With the increase in the reinforcement range, the maximum longitudinal displacement decreases sharply at first, and then increases linearly with a slow increase rate. When the reinforcement range is eight rings, the maximum longitudinal displacement is the smallest, which is 10.01 mm. The effect is most obvious when the front four-ring segment is reinforced, and the maximum longitudinal displacement is greatly reduced. When the reinforcement range is greater than eight rings, the maximum longitudinal displacement increases slowly as the reinforcement range further increases. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Reinforcement Range** & **Reinforcement Length** & **Equivalent Spring Stiffness** \\  & **(m)** & **(N/m)** \\ \hline
4 & 8 & \(1.34\times 10^{9}\) \\
8 & 16 & \(6.71\times 10^{8}\) \\
12 & 24 & \(4.48\times 10^{8}\) \\
16 & 32 & \(3.36\times 10^{8}\) \\
20 & 40 & \(2.69\times 10^{8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Equivalent spring stiffness of steel channel under different reinforcement ranges. It can be seen from Figure 13 that under the same reinforcement range, the farther the segment ring is from the shield tail, the smaller the opening of circumferential joints \(x_{i}\). When the reinforcement range is less than five rings, since the first four-ring segments are not affected by the formation friction, they will be completely separated. With the increase in the reinforcement range, the equivalent spring stiffness K gradually decreases, and the reinforcement effect is weakened. When the reinforcement range is 20 rings, the maximum opening of the circumferential joints \(x_{i}\) is 5.97 mm. As shown in Figure 14, the variation trend of the opening of circumferential joints \(x_{i}\) and the longitudinal maximum displacement is similar. The difference is that when the reinforcement range just reaches the ring, the opening of circumferential joints  
Figure 12: Maximum longitudinal displacement under different reinforcement ranges. Figure 13: The relationship curve between the opening of circumferential joints and the number of rings under different reinforcement ranges. suddenly changes to the minimum. The first four-ring segment has the best reinforcement effect, which is the position with the largest opening of circumferential joints. When the reinforcement reaches 20 rings, the opening of the circumferential joints is 5.97 mm, which is less than the critical opening of circumferential joints. Due to the existence of formation friction, the maximum opening of subsequent circumferential joints is only 3.94 mm. Steel channel reinforcement will change the opening of subsequent circumferential joints slightly, but the reinforcement effect is not obvious. From the above analysis, it can be seen that the closer to the shield tail, the more significant the reinforcement effect is, and the change of the reinforcement range has no effect on the opening of circumferential joints after 18 rings. The reason for this phenomenon is that friction force between the segment lining and the soil leads to the limited influence range and the effect of thrust unloading on the segment lining. The method of adding a steel channel is equivalent to transferring the internal force of the segment lining, and no external force is applied, so the change of the segment reinforcement range will not affect the opening of circumferential joints after 18 rings.