## 3 Analysis of Compound Strata and Surface Settlement
### Numerical Model Establishment  
Due to the stress-strain caused by the excavation of underground tunnels, actual effects only exist within a space 3-5 times the diameter of the tunnel excavation around the center of the tunnel. Therefore, the length of the model was set to 150 m along the \(X\)-axis, the width along the \(Y\)-axis (driving direction) was set to 200 m, and the height along the \(Z\)-axis was set to 80 m. Normal displacement constraints were added around the model, full constraints were added at the bottom, and no constraints were added at the top. The shield excavation diameter was set to 16.03 m, the outer diameter of the pipe was set to 15.4 m, the inner diameter was 14.2 m, and the grouting strata thickness was 0.63 m, with a shell thickness of 0.2 m. The three-dimensional numerical model is shown in Figure 8.  
Based on the shield tunnelling parameters collected on site, the synchronous grouting pressure was set to 0.3 MPa, and the face pressure was set to 0.2-0.4 MPa. As shown in Figure 9, the shield tunnelling process was simulated using the model-change function, activating the face pressure and killing excavation soil elements to generate shield shell elements while generating lining and grouting elements at the shield tail and activating  
Figure 8: Numerical model diagram. Figure 7: Comparison between fitted and monitored ground settlement values for stratum 7.  
synchronous grouting pressure. This process was repeated for each excavation step, with a length of 2 m per step and a total of 100 excavation steps. Figure 9 presents a schematic diagram illustrating the parameter settings for shield tunneling in the numerical model, with the mesh division utilizing C3d8r eight-node linear hexahedral elements. The Mohr-Coulomb constitutive model was selected for all soil layers due to its straightforward physical concept, limited parameter set, and its ability to capture the yielding and failure characteristics of geotechnical materials. To account for the specific geological conditions of the project, the physical property parameters for each soil stratum are provided in Table 1. The shield shell, lining segments, and grouting material were modeled using the elastic-plastic constitutive model. As the lining segments were connected by bolts to form a circular structure, the elastic modulus of the segments needed to be multiplied by a rigid reduction factor of 0.8. The hardening process of the grouting material was achieved by controlling the temperature field to vary the elastic modulus and Poisson's ratio. The elastic modulus and Poisson's ratio of the grouting material were 0.9 MPa and 0.4, respectively, when the shield was removed, and increased to 4 MPa and 0.35 after one excavation step and to 800 MPa and 0.25 after two steps. The physical property parameter values for each component are listed in Table 5, respectively. Figure 10 illustrates a cloud map of the vertical displacement of the formation after shield tunneling. The results confirm that there is a substantial difference between the surface settlement in stratum 6 in comparison to stratum 7. Near the composite surface of the two formations along the tunneling direction, non-uniform settlements were observed. Considering a numerical model for the analysis, 50 monitoring sections were selected at a 2 m interval (\(L=2\) m) for each formation interval. The Peck formula regression analysis method (discussed in Section 3.2) was utilized to determine the \(S_{\text{max}}\) and \(i\) values of each monitoring section based on the simulation results. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Name**} & \(\gamma\)/ & \multirow{2}{*}{**E/MPa**} & \multirow{2}{*}{**v**} \\  & (\(\text{kN}\cdot\text{m}^{-3}\)) & & \\ \hline Segment lining & 25 & 34,500 & 0.2 \\ \multicolumn{4}{c}{Grout material} & 25 & 0.9, 4, 800 & 0.4, 0.35, 0.25 \\ \hline \hline \end{tabular}  
* The table includes the following parameters: \(\gamma\) for unit weight, E for elastic modulus, and v for Poisson’s ratio.  
\end{table}