## 2 Methodology
### Description of Finite Element Model  
In the proposed research, to simulate the real operation of underground metro trains, the influence of variable load and variable speed moving load on the damage identification results of tunnel structures was analyzed through the 30-m soil-tunnel structure model. The metro tunnel was taken at full scale in the finite element model of the soil tunnel, as shown in Figure 5. The finite element model of a metro tunnel structure was built with ABAQUS software, and the parameters and dimensions were taken from the Wuhan metro tunnel office, China [33; 34]. The finite element program ABAQUS was employed with suitable elements to model the used metro tunnel structure. The size and material properties of the metro tunnel, concrete, and soil are given in Table 4 for the proposed metro tunnel structure investigation. Shell63 elements were used in the study.  
In this proposed research analysis, the entire structural framework follows the linear assumption; the linear connection is assumed to be minor structural damage that can only cause a small change in the structure. The soil and tunnel boundaries are simulated using full-circle ground springs. The complete mechanical model system with the parameters taken from past studies conducted by different researchers [33;35] is shown in Table 5.  
The established finite element model to simulate the training constraint given by the contiguous sections was not modeled at the end of the tunnel for boundary conditions controlled with springs.  
In the built finite element model, in order to simulate the training constraints given by the contiguous sections, they were not modeled at the end of the tunnel boundary conditions controlled with springs. The rotational spring's stiffness was known to be (1 \(\times\) 1011 N\(\cdot\)m/rad). Therefore, when the soil dimension is more than ten times the metro tunnel dimension, the boundary outcome may be overlooked. The soil dimension was assumed to be beyond the 10-fold tunnel diameter range. The finite element segment model and the tunnel's finite element models are shown in Figures 6 and 7, respectively.  
By splitting the entire tunnel into portions, the metro tunnel was assembled using a lumped mass in the mechanical model used in this analysis. Every element mass was located in the middle of the entire tunnel model. Consequently, both the excitation of the moving load and the tunnel were represented as point masses. Concrete and soil densities were both 2500 kg/m\({}^{3}\) and 1800 kg/m\({}^{3}\), respectively. This proposed study analysis for metro tunnel structure and soil simulation used the design of the Wuhan metro.  
\begin{table}
\begin{tabular}{c c c} \hline
**Properties** & **Value** & **Units** \\ \hline Metro Tunnel: & & \\ Diameter outside (D1) & 5.85 & m \\ Diameter inside (D2) & 5.05 & m \\ Length of the Metro (L) & 30 & m \\ Concrete: & & \\ Density (gc) & 2500 & kg/m\({}^{3}\) \\ Young’s Modulus (Ec) & \(3.1\times 104\) & MPa \\ Passion ratio (\(\mu\)c) & 0.2 & \\ Soil: & & \\ Width (Lw) & 58.5 & m \\ Depth (Ld) & 58.5 & m \\ Length (Ll) & 30 & m \\ Density (gs) & 1800 & kg/m\({}^{3}\) \\ Young’s Modulus (Es) & 18 & Mpa \\ Poisson ratio (\(\mu\)s) & 0.36 & \\ \hline \end{tabular}
\end{table}
Table 4: Material properties and unit values.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Label No** & **Damage Scenarios** & **Segment** & **Damage Locations** & **Damage Severity \%** \\ \hline
0 & UDG & null & null \\
1 & DMG1 & S100 & x = 100 m & 4\% \\
2 & DMG2 & S100 & x = 100 m & 8\% \\
3 & DMG3 & S100 & x = 100 m & 10\% \\
4 & DMG4 & S100, S180 & x = 100, 180 m & 4\% \\
5 & DMG5 & S100, S180 & x = 100, 180 m & 8\% \\
6 & DMG6 & S100, S180 & x = 100, 180 m & 10\% \\
7 & DMG7 & S100, S180, S200 & x = 100 m, 180 m, 200 m & 4\% \\
8 & DMG8 & S100, S180, S200 & x = 100 m, 180 m, 200 m & 8\% \\
9 & DMG9 & S100, S180, S200 & x = 100 m, 180 m, 200 m & 10\% \\ \hline \end{tabular}
\end{table}
Table 5: Damage cases to carry out numerical simulation.