## 4 Calculation and Verification of a Shield Tunnel in Changsha
### Analysis of Calculation Results  
The shield tunnel segments with a buried depth of 6 m were calculated using the two modules by the software, respectively. The hydrogeological input parameters were selected according to the detailed survey parameters. The calculation results of the outer diameter of 4.1 m with a segment thickness of 0.25 m, the outer diameter of 8.2 m with a segment thickness of 0.4 m with the specific rotational stiffness, and the elastic modulus of 34.5 GPa are shown in Figure 10.  
Under the same hydrogeological conditions, there is a certain difference between the calculation result of the modified routine method and the beam-spring method module. The normal pressure acting on the segment, the axial force of the segment, the bending moment, and the formation deformation was monitored to verify the rationality of the developed software module. Additionally, the data obtained from the shield tunneling test section and on-site measurements were used for inversion correction calculation of the pressure load, as the comparison reference for the continuous correction of the software input parameters, and the built-in calculation framework. The field segment data measurement is shown in Figure 11.  
Table 2 shows the calculation results of the shield tunnel with an outer diameter of 4.1 m and segment thickness of 0.25 m. Compared with the measured data, it is certain that the beam-spring discontinuity model and the modified routine method model after inversion and correction of the parameters improved the accuracy of the results accordingly. By combining the above calculations and relying on the development software to calculate the segment structure of shield tunnels with different outer diameters, the calculation program uses the bending moment and displacement values of different tunnel segments on the same section as the basis for the inversion, and different tunnel segments are calculated. The bending stiffness reduction coefficient \(\eta\) of the lining ring can improve the similarity between the change rule of the bending moment of the lining ring at different positions and the change rule of the measured value at different positions. Based on the principle of reducing the relative error with the actual measured value and compared with \begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Parameter** \\ \hline Diameter & Out D \(\varphi\)4100 mm, Inner D \(\varphi\)3600 mm \\ \hline Lining ring block & 6 (17\({}^{\circ}\)\(\times\) 1 + 63.5\({}^{\circ}\)\(\times\) 2 + 72\({}^{\circ}\)\(\times\) 3) \\ \hline Lining thickness & 250 mm \\ \hline Lining ring width & 1000 mm (150 m \(\leq\) R \(<\) 300 m) \\  & 1200 mm (R \(\geq\) 300 m and Straight) \\ \hline \multirow{2}{*}{Wedge} & 36 mm (150 m \(\leq\) R \(<\) 300 m) \\  & 40 mm (R \(\geq\) 300 m and Straight) \\ \hline Interface & Nitrile Cork Rubber with 2 mm thickness \\ \hline Material & C50, Impermeability grade P12 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main design parameters of shield segment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **On-Site** & \begin{tabular}{c} **Modified Routine** \\ **Method** \\ \end{tabular} & \
\begin{tabular}{c} **Beam–Spring** \\ **(Discontinuous)** \\ \end{tabular} &
\begin{tabular}{c} **Beam–Spring** \\ **(Continuous)** \\ \end{tabular} \\ \hline Max bending moment (kN m) & 34.7 & 32.7 & 39.9 & 45.2 \\ \hline Axial Force (kN) & 367 & 319 & 389 & 412 \\ \hline Error of bending moment & \(-6.12\%\) & +15.0\% & +30.3\% \\ \hline Error of Axial Force & \(-15.0\%\) & +6.05\% & +12.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The relationship between measured value of internal segment force and calculation value of software.