## 4 Parametric Analysis
### Effect of Quantity of Steel Channels  
Given the numerical simulation of the above typical cross-sections, under the premise of keeping other parameters of the model unchanged, only the quantity of the steel channels is changed. The equivalent spring stiffness in different cases is shown in Table 4.  
Figure 15 shows that increasing the quantity of channels can effectively reduce the longitudinal displacement of the segment lining. With the increase in the quantity of steel channels, the maximum longitudinal displacement gradually decreases, and the reduction rate also decreases.  
Figure 14: The relation curve between reinforcement range and the opening of circumferential joints for different rings.  
As shown in Figures 16 and 17, the variation trend of the opening of circumferential joints is roughly the same under the different quantities of steel channels. With the increase in the quantity of steel channels, the opening of circumferential joints becomes smaller and smaller, and with the increase in the quantity of steel channels, the opening of circumferential joints decreases gradually, and the reduction rate also decreases. The reinforcement effect of the front four rings is more significant, which reduced the openings from 9.99 mm to 5.13 mm. The openings of subsequent circumferential joints was also slightly reduced, but the reinforcement effect is relatively weak. The openings of the first four rings are the largest. When the quantity of steel channels is 24, the maximum opening size is 5.97 mm. If the quantity of steel channels is less than 24, the opening of circumferential joints will exceed the critical value of 6 mm, which does not meet the specification requirements.  
Through the above analysis, adding a steel channel is equivalent to several springs in parallel that resist the longitudinal tension of the segment lining. With the increase in the quantity of steel channels, the tensile stiffness of the reinforcement area becomes larger and larger; meanwhile, the ability to resist longitudinal tension becomes stronger and stronger. However, due to the large size of compressive stiffness of rubber gasket, the reinforcement effect on the segment ring far from the shield tail is weak. It can be seen from the simulation results that the engineering requirements can be met when the quantity of steel channels is greater than 24. Given the above analysis, and considering various factors such as the layout space, the degree of difficulty, and the cost-effectiveness of construction, when using No. 14 steel channel to reinforce the 20-ring segment ring, it is more appropriate to make sure that the quantity of steel channels is not less than 24.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**The Quantity of Steel** & **The Total Area** & **Equivalent Spring Stiffness** \\
**Channels** & **(m\({}^{2}\))** & **(N/m)** \\ \hline
8 & \(1.71\times 10^{-2}\) & \(8.95\times 10^{7}\) \\
16 & \(3.41\times 10^{-2}\) & \(1.79\times 10^{8}\) \\
24 & \(5.16\times 10^{-2}\) & \(2.69\times 10^{8}\) \\
32 & \(6.82\times 10^{-2}\) & \(3.58\times 10^{8}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Equivalent spring stiffness of steel channels under different quantities.  
Figure 15: Maximum longitudinal displacement under different quantities.