# Analysis of the Interaction Effects of Shield Structure Oblique Passing under an Existing Tunnel
## 3 Three-Dimensional Numerical Model
### Numerical Simulation Process  
The specific process of numerical simulation can be divided into two stages: (1) excavation of the existing tunnel and (2) the shield tunnel underpassing the existing tunnel. Since this paper focuses on the second stage and does not consider the influence of the existing tunnel excavation process, the soil and structure displacements were removed after the excavation of the existing tunnel, and the application of the second lining was completed. In the second stage, a detailed simulation of the shield excavation process was carried out assuming that the shield was a step-by-step leap forward, and in order to save calculation time, each excavation mileage used two-tube sheet ring widths (the lining ring width was taken as 2.0 m, and a total of 30 excavation steps were used), which can better reflect the non-linear mechanical properties of the soil. Thus, the Mohr-Coulomb constitutive model was selected for the soil and grouting materials, and the lining, shield shell, and existing \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Shield Type**} & \multicolumn{4}{c}{**Physical Diameter**} & \multicolumn{4}{c}{**Dynamical System**} \\ \cline{2-7}  & **Excavation** & **Lining** & **Lining** & **Lining** & **Naneter** & **Shield** & **Lining Width** & **Rated Torque** & **Normal** & **Shield Cutter** \\  & **Diameter (m)** & **Out-Diameter (m)** & **Diameter (m)** & **Thickness (m)** & **(m)** & **(0.8m)** & **(0.8m)** & **(0.8m)** \\ \hline CTE6450 & 6.48 & 6.20 & 5.50 & 0.35 & 1.50 & 6000 & 100 & 38\% \\ \hline M0 Ring Bolts & M30 Longitudinal bolts & & & & & & \\  & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Geometric and technical parameters of the shield. Figure 5: Illustration of lining ring: (**a**) lining divided (mm); (**b**) reinforcement of segment lining (mm). elastic structure models were adopted for the tunnel second lining. The construction steps of the numerical simulation were as follows:  
1. Excavation process: A ring with a large stiffness and high weight shell unit was extracted at the top of the excavation surface to simulate the shield shell bearing the surrounding soil load caused by the shield excavation and the reaction force of the shield shell on the soil. The digging pressure was set to 0.10 MPa according to the actual construction process (as shown in Figure 6a). 2. Lining ring assembly process: The elastic shell element structure was extracted under the use of the shield shell, and the simulated segment was subjected to the extrusion load of the surrounding rock. The lining ring was assembled using the staggered seam assembly method, and the lining ring bolt adopted a rigid connection simulation. By setting the jacking force to simulate the actual lining construction process, the jacking force perpendicular to the uniform pressure on the cross-section of the lining had a value of 0.10 MPa (according to the value of the field monitoring data) (as shown in Figure 6b,d). 3. Synchronized grouting process: The grouting process was simulated by changing the grid boundary conditions and applying the grouting pressure, which is a uniform pressure of 0.20 MPa (taken according to the measured data in the field) perpendicular to the surface of the tube sheet ring and outward (as shown in Figure 6c). Figure 6: Midas GTS simulation shield construction flow chart: (**a**) excavation process; (**b**) lining ring assembly process; (**c**) synchronized grouting process; (**d**) lining ring assembly detail. During the numerical simulation, part of the soil in front of the working face was inactivated to simulate the shield machine segmental excavation process. The shell units extracted at the top of the excavation face were then activated to simulate the supporting action of the shield shell.