## 3 Numerical Calculation Model  
According to the geological conditions of the underpass section, a three-dimensional numerical calculation model was established using the finite element software Midas-GTS to analyze the deformation law of the existing Maglev viaduct pier and rail row. The overburden soil of the double-line tunnel is 16 m. According to the positional relationship between the old and new structures, the length is 200 m, the width is 100 m, and the thickness of the model is 50 m from the surface.  
The D-P criterion was selected for soil constitution. [PERSON] and [PERSON] proposed the generalized Mises yield and failure criterion considering the influence of hydrostatic pressure in 1952, abbreviated as the Drucker Prager (D-P) yield criterion. Its function can be expressed as:  
\[F=\sqrt{J_{2}}-\alpha I_{1}-\kappa=0 \tag{1}\]  
in which \(I_{1}=\) the first invariant of stress tensor; \(J_{2}=\) the second invariant of deviator stress tensor; \(\alpha\), \(\kappa=\) material parameters.  
Solid element simulation is used for soil and bridges to avoid stress concentration [31]. The initial support of the new tunnel is simulated by the shell element, the pile foundation is simulated by the beam element, the F rail and rail sleeper in the Maglev track are simulated by the beam element, and the connection is elastic. Grouting reinforcement is simulated by the solid element, and grouting reinforcement construction is simulated by endowing the model grouting reinforcement area with the original soil layer grouting properties. The ground surface (the upper surface of the model) is taken as the free boundary, and normal constraints are taken around and at the bottom of the model. The calculation model is shown in Figure 8 and the calculation parameters are shown in Table 3.  
The first step of calculation is the derivation of the equilibrium of the initial ground stress, and then the excavation of subsurface tunnel is simulated. The excavation steps are properly simplified; the left and right lines are divided into eight sections, each about 8 m, and the right line is ahead of the left line by 16 m in the synchronous construction. The specific construction process is shown in Table 4 and Figure 9.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Steps No.** & **Specification** \\ \hline
1 & Right line step excavation 8 m, apply upper primary lining and middle partition plate. \\ \hline
2 & Right line step excavation 8 m, apply upper primary lining and middle partition plate; \\  & Right line lower bench excavation 8 m, Apply lower primary lining. \\ \hline
3 & Right line step excavation 8 m, apply upper primary lining and middle partition plate; \\  & Right line lower bench excavation 8 m, apply lower primary lining; \\  & Left line step excavation 8 m, apply upper primary lining and middle partition plate. \\ \hline
4–10 & Left and right line synchronous excavation according to the upper and lower steps. \\ \hline
11 & Complete all middle partition middle partition removal, complete all secondary lining. \\ \hline \hline \end{tabular}
\end{table}
Table 4: Construction process.  
Figure 8: Numerical calculation model. (**a**) Overall model; (**b**) viaduct details; (**c**) cross-section details.  
Figure 9: _Cont._