## 2 Engineering Background
### Establishment of Numerical Simulation Model
After simplification, the thickness of each stratum was set to 5.0 m for plain filling soil layer, 5.0 m for muddy gravel sand layer, 7.0 m for plastic gravel clay layer, 13.0 m for hard plastic gravel clay layer, and 20.0 m for completely weathered biotite granite layer. The basic physical and mechanical parameters of each stratum are shown in Table 1. The concrete grade of the lining segment structure was defined as C50, the material weight was taken as 25 kN/m, and the elastic modulus was defined as 35 GPa. Considering the influence of the circumferential joint's lining on the stiffness of the lining structure, the stiffness wasreduced by 0.2, and the stiffness reduction coefficient was taken as 0.8. The elastic modulus of the lining structure was defined as 28 GPa, and Poisson's ratio was taken as 0.2. The constitutive model adopted in this study is an isotropic elastic-plastic model that conforms to the Mohr-Coulomb yield criterion. Shield construction mainly includes soil excavation and lining pipe assembly. The shield tunneling, soil excavation, and lining pipe assembly were simulated in ABAQUS using the raw and dead unit method. The total length of the excavated tunnel is 60 m, and each excavation step is 3 m, divided into 20 steps. The simulation steps in the specific construction process were as follows:  
1. The initial ground stress equilibrium was established, the initial ground stress field was obtained, and the initial displacement was returned to zero. 2. ABAQUS birth and death element method was used to kill the 3 m excavation soil element, and the temperature field was used to change the soil elastic modulus and Poisson's ratio, which was used to simulate the stress release in the soil excavation process. 3. The ABAQUS life and death element method activate the 3 m lining segment element in contact with the soil. Shield excavation of 3 m soil, assembling 3 m lining segments as a complete analysis step, the whole process of a total of 20 cycles to simulate the whole process of shield tunneling. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Stata Name** & \
\begin{tabular}{c} **Density** \\ **(kN/m\({}^{3}\))** \\ \end{tabular} &
\begin{tabular}{c} **Deformation** \\ **Modulus** \\ **(MPa)** \\ \end{tabular} & **Poisson’s Ratio** & **Cohesion (kPa)** & **Friction Angle (\({}^{\circ}\))** & **Stata Thickness (m)** \\ \hline Plain fill & 21.0 & 16 & 0.30 & 6 & 12 & 5 \\ Muddy & 19.5 & 18 & 0.31 & 12 & 10 & 5 \\ gravel sand & 18.3 & 15 & 0.34 & 20 & 28 & 7 \\ Clay soil & 19.0 & 30 & 0.32 & 23 & 26 & 13 \\ Hard plastic & 19.5 & 70 & 0.29 & 30 & 22 & 20 \\ gravel sand & & & & & & \\ Plastic gravel & 18.3 & 15 & 0.34 & 20 & 28 & 7 \\ Hard plastic & 19.0 & 30 & 0.32 & 23 & 26 & 13 \\ gravel soil & & & & & & \\ Fully weathered & 19.5 & 70 & 0.29 & 30 & 22 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic mechanical indexes of soil in each stratum. Figure 3: The directions of principle stresses around the tunnel with advancing TBM face. In the process of numerical simulation, the transverse monitoring section X was set up at y = 30 m along the tunneling direction of the shield tunnel, and 21 monitoring points were set up at the surface of the monitoring section. The spacing of each monitoring point is 3 m, symmetrically arranged on both sides of the tunnel axis, and the number is A\({}_{1}\)-A\({}_{21}\) from left to right. Among them, the three monitoring points at the surface above the excavation boundary of the shield tunnel are A\({}_{10}\), A\({}_{11}\), and A\({}_{12}\). Surface monitoring points A\({}_{10}\), A\({}_{11}\), and A\({}_{12}\) from top to bottom, respectively, in the buried depth of 5 m, 10 m, 15 m, 17 m, and 20 m set strata subsidence monitoring points, in turn, numbered B\({}_{10}\)-F\({}_{10}\), B\({}_{11}\)-F\({}_{11}\), and B\({}_{12}\)-F\({}_{12}\), as shown in Figure 4.