## 3 Numerical Simulation and Analysis of Support Pressure on Tunnel Face
### Simulation Model and Basic Assumptions
Therefore, the mechanical behavior related to pipe jacking was appropriately simplified in our numerical \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material Type** & **Elastic Modulus** & **Poisson’s Ratio** & **Volumetric Weight** & **Thickness** \\  & **E (MPa)** & \(\mu\) & \(\gamma\) (kN/m\({}^{3}\)) & **(m)** \\ \hline Reinforced concrete & 28,000 & 0.2 & 23 & 0.3 \\ Digging machine & 206,000 & 0.3 & 78.5 & 0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Pipe-jacking sheet parameters. Figure 5: Numerical model of three-lane parallel pipe jacking. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Parameter** & **Elastic Modulus** & **Poisson’s Ratio** & **Cohesive Force** & **Angle of Internal Friction** & **Volumetric Weight** & **Thickness (m)** \\  & **E (MPa)** & \(\mu\) & **c (kPa)** & **\(\varphi\) (\({}^{\circ}\))** & **\(\gamma\) (kN/m\({}^{3}\))** & **(m)** \\ \hline Filling soil & 8.0 & 0.27 & 10 & 10.0 & 18.00 & 0.5–1.5 \\ Silty chalky & 3.2 & 0.27 & 6.2 & 5.8 & 17.52 & 1.2–2.7 \\ Clay & 12.0 & 0.25 & 70 & 16.9 & 19.22 & 5.9–7.5 \\ Silty clay & 11.3 & 0.25 & 40 & 15.5 & 19.22 & 4.8–6.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Stratigraphic physical and mechanical parameters. simulations. This not only allowed the simulations to meet the requirements of the software for calculation but also led the numerical calculation results to better reflect the construction process and reveal the regularity of the construction's impact. Based on the actual situation of the examined project, the numerical simulation included the following assumptions:  
1. Each stratum was assumed to be ideally elasticoplasticity. The numerical simulation model only considered the soil settlement caused by self-weight and the pipe-jacking process and ignored the effects of underground water, as well as consolidation settlement of the soil. 2. The soil pressure was considered a circular distributed load acting on the tunnel face. It was assumed that the gap grouting units around the perimeter of the pipe were distributed in equal thicknesses along the radial direction of the pipe sheet (the modulus of elasticity was taken as 1/50 of the in situ stratigraphic unit, and the thickness of the grouted iso-surrogate layer was 2 cm). Friction between the pipe and soil was achieved by setting a coefficient of friction on the contact surface (the friction between the pipe and soil was a certain value and was uniformly distributed along the pipe-jacking direction). The model ignored the effect of grouting pressure on the construction process and the pipe joints. The jacking pressure was taken from the lateral static soil pressure at the center point of the pipe's tunnel face, as 88.5 kPa. The friction between the pipe and soil was taken as 3.5 kPa. The previous study [38] by our team used strength reduction and numerical simulation methods. This study analyzed in detail the stability of surrounding strata unloaded by pipe jacking under different water depths, overburden thicknesses, and clearances. The surrounding strata were divided into the mutual-influence non-self-stability zone, the mutual-influence self-stability zone, and the no-mutual-influence self-stability zone. The assumptions for the numerical simulation and the specific simulated construction conditions in this study are consistent with those in [38], so they are not described here in detail.