## 5 Engineering Verification
### Analysis of Simulated Result  
Numerical simulations were conducted using the HSS model, HS model, and M\(-\)C model for the shield tunnel passing beneath the Heihe River phase 2 water-supply pipeline. For the simulation using the HSS model, calculations were performed based on the improved Formulas (4), (7) and (8), as well as on results with \(1.5E_{\rm{ur}}^{\rm{ref}}\), \(2E_{\rm{ur}}^{\rm{ref}}\), and \(3E_{\rm{ur}}^{\rm{ref}}\) multipliers. The simulation results were compared and verified against on-site monitoring data, as shown in Figure 12a. The comparison between the calculation results of the M\(-\)C and HS models and the field monitoring data is presented in Figure 12b.  
As the shield tunnel advances, the settlement at the center of the bottom of the Heihe River water-supply pipeline gradually increases. The maximum value monitored on-site is 2.5 mm. The maximum settlement value simulated by the M\(-\)C model is 13.6 mm, while the maximum settlement simulated by the HSS model when \(G_{0}^{\rm{ref}}=1.5E_{\rm{ur}}^{\rm{ref}}\) is 4.1 mm. It can be seen that the HSS model fits the on-site monitoring data better than the M\(-\)C and HS models. The engineering requirement is that the cumulative settlement of the Heihe River water pipeline must not exceed 8 mm. It is evident that the calculation results of the M\(-\)C and HS models are overly conservative, and the accuracy of these results no longer meets the needs of this project.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Soil Layer Name** & \(\mathbf{E_{ood}^{ref}}\)/**MPa** & \(\mathbf{E_{50}^{ref}}\)/**MPa** & \(\mathbf{E_{ur}^{ref}}\)/**MPa** & \(\mathbf{K_{0}}\) \\ \hline II 3-1 New Loess & 9.7 & 12.6 & 62.6 & 0.40 \\ III 3-2 Paleosol & 10.8 & 14 & 69.4 & 0.39 \\ IV 4-1-1 Old Loess & 9.3 & 12.1 & 60.1 & 0.43 \\ V 4-1-2 Old Loess & 6.3 & 8.3 & 40.9 & 0.43 \\ VI 4-2-2 Old Loess & 7.2 & 9.4 & 46.5 & 0.47 \\ \hline \end{tabular}
\end{table}
Table 6: Partial parameters of HSS model.  
Figure 11: Model structure diagram.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Structure** & **Thickness** & **Unit Weight** & \begin{tabular}{c} **Elastic** \\ **Modulus** \\ **GPa** \\ \end{tabular} & \
\begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ - \\ \end{tabular} \\ \hline
\begin{tabular}{c} Lining of tunnel \\ Ling of Heihe Water Pipeline \\ \end{tabular} & 0.35 & 24.1 & 34.5 & 0.2 \\ \hline \end{tabular}
\end{table}
Table 7: The table of concrete lining.  
Among the various methods of determining the value of \(G_{0}^{\text{ref}}\), the simulation results from the three empirical formulas are similar, but all are lower than the on-site monitoring data. When \(G_{0}^{\text{ref}}\) is set to \(2E_{\text{ur}}^{\text{ref}}\), the simulation results from the HSS model are the closest to the on-site monitoring data, and the settlement values obtained from the simulation are slightly greater than the monitoring data, which could be more conducive to construction safety.  
Figure 12: Variations in the bottom centerline settlement of the Heihe water pipeline due to shield tunneling. (**a**) The settlement prediction results of the HSS model under different values of \(G_{0}\). (**b**) The prediction results of the HS model and M-C model.