## 4 Refined Numerical Simulation of Shield Tunneling  
### Numerical Model and Calculation Parameters  
FLAC3D 6.0 software was used to develop a revised numerical model that can carry out the fluid-structure interaction analysis, as illustrated in Figure 6, to further examine the influence law of shield tunneling parameters on ground deformation in water-rich soft stratum. The numerical calculation model was set as length \(\times\) height \(\times\) width = 80 \(\times\) 60 \(\times\) 35 m, which was large enough to avoid the influence of boundary effects. The numerical model contained approximately 54,325 nodes and 50,560 three-dimensional elements. The tunnel's diameter was 6.2 m, with an overburden thickness of 10 m, and the groundwater level was located on the surface. The boundary conditions of the numerical model included two types: displacement boundary conditions and pore boundary conditions. Displacement boundary condition: normal displacement constraints were imposed on the side and bottom of the model. Pore boundary condition: hydrostatic pressure with a gradient of 10 kPa/m was imposed below the groundwater table on the side of the model, while the pore water pressure above the groundwater table was simplified to 0. The shield shell, lining, and tunnel face were set as impermeable boundaries. The support pressure of the excavation face was simulated by applying the surface load distributed along with the depth trapezoid on the excavation face. The jacking pressure on the segments was simulated by applying the element node force on the shield tail segment, and the ground deformation caused by the overcut was simulated by constructing a conical shield shell [20]. To approximate shield advancement, the stiffness transfer method was used [27]. The model advanced the length of one segment ring in each calculation cycle, with each cycle lasting for 4 h. The blue line and red dots in Figure 6 indicate the layout of the monitoring points. Measuring points A, B, C, and D were located on the surface, tunnel vault, bottom, and hance, respectively. The soil constitutive model was the Mohr-Coulomb model, and the equivalent zone constitutive model was the isotropic elastic model. The necessary parameters of the soil for the simulation calculation included the modulus of elasticity, Poisson's ratio, cohesion, internal friction angle, bulk density, void ratio, and permeability coefficient. The soil bulk density was obtained from geological exploration reports. The remaining parameters were obtained from the laboratory test. Table 2 shows the soil and equivalent zone calculation parameters. The equivalent zone was a treatment for the shield tail gap and the slurry filling in the gap that is equivalent.  
Figure 6: \(Cont.\)The shield shell and segment were simulated by lining structural elements, and the constitutive model was the isotropic elastic model. Considering the segments as the homogeneous ring, the bending stiffness rate was introduced to simulate the influence of the joint on the segment stiffness. In the model, the bending stiffness rate of the segment was taken as 0.75 [28]. According to research results [20], the sliding friction coefficient between the shield skin and soil \(\mu\) was 0.15-0.30 when the shield moved. The static friction coefficient between the shield skin and soil \(\mu\) was 0.25-0.45, and the static friction coefficient between segment and grouting body \(\mu\) was 0.30-0.40 as the shield started up. Therefore, the shield shell's shear coupling spring friction angle in the model was set to \(7^{\circ}\) (corresponding to \(\mu\) = 0.17), while the segment's shear coupling spring friction angle was set to \(17^{\circ}\) (corresponding to \(\mu\) = 0.31). The calculation parameters of the structural element are shown in Table 3.