## 3 Numerical Simulation and Analysis of Support Pressure on Tunnel Face
### Simulation Conditions and Implementation Steps  
Numerical simulations were directed at analyzing the river-bottom cross-section. In order to investigate the effect of the overburden thickness on the support pressure, the river-bottom section conditions were categorized into three conditions: an overburden thickness of 3 m was considered in Case I, an overburden thickness of 2 m was considered in Case II, and an overburden thickness of 1 m was considered in Case III. The theoretical values of the tunnel-face support pressures were applied, as shown in Table 3.  
To explore the variation characteristics of the support pressure in the tunnel face, the support pressure ratio coefficient \(\lambda\) of the tunnel face was adopted, as demonstrated in Equation (10).  
\[\lambda=\frac{\sigma_{\mathrm{s}}}{\sigma_{0}} \tag{10}\]  
Here, \(\lambda\) is the support pressure ratio at the pipe-jacking tunnel face; \(\sigma_{\mathrm{s}}\) is the support pressure at the center point of the pipe-jacking tunnel face, kPa; and \(\sigma_{0}\) is the soil and water pressure at the center point of the pipe-jacking tunnel face, kPa.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **I** & **II** & **III** \\ \hline Thickness of overburden (m) & 3.00 & 2.00 & 1.00 \\ Theoretical value of support pressure (kPa) & 88.5 & 74.3 & 60.0 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Calculation cases.  
Displacement monitoring points were arranged on the center vertical line of the tunnel face and on the ground surface along lateral and vertical lines, as depicted in Figure 6.  
Mud-water-balancing pipe construction is a step-by-step process. To simulate dynamic construction that matches reality, step-by-step excavation was used. The effect of the jacking force on the disturbance of the soil in front of the tunnel face was considered. The numerical simulation calculation process was as follows:  
1. The basic numerical model was established. Material properties were assigned, and corresponding displacement boundary conditions were imposed. Ground stress equilibrium calculations were performed under initial stress conditions that were designed to simulate the initial ground stress state.
2. Support pressure equal to the resistance applied in front of the tunnel face was set. The next step was to simulate the disturbance caused by the jacking to the strata ahead until a steady state was reached.
3. In actual construction, pipe jacking excavates to the bottom of the river channel. The soil is removed, and the pipe support structure is activated. At the same time, an excavation process can be completed by setting up a support pressure applied to the tunnel face.
4. The overall deformation of the tunnel face and the displacement changes at the corresponding monitoring points were observed and recorded.
5. According to the support pressure ratio \(\lambda\), the magnitude of the mud-water pressure applied at the center point of the tunnel face was altered. Re-excavation calculations were carried out, and the overall deformation of the tunnel face, as well as the displacement changes at the corresponding monitoring points, were observed and recorded.