## 3 A Simulation Model and Verification of Its Rationality
### A Simulation Model of the Over-Track Platform of a Metro Depot  
A three-dimensional finite element model composed of the track, soil, and over-track platform is shown in Figure 3 (excluding over-track buildings). The size of the soil model was 140 m \(\times\) 140 m \(\times\) 45 m. It was simplified from top to bottom as an artificial fill layer (5 m thick), a pulverized clay layer (25 m thick), and a fine sand layer (15 m thick). The viscoelastic artificial boundary was set at the bottom and around the soil, with a thickness of 1 m. The distance between two rails of a metro line is 1.435 m, while the sleeper spacing was 0.6 m. The thickness of the track-bed and the width at the bottom of the track-bed were 0.35 m and 4 m, respectively. The height of the over-track platform was 7.5 m, the platform thickness was 0.25 m, and the cross-sectional dimensions of columns under platform were 1.0 m \(\times\) 1.0 m. If the side length of mesh size takes a value of 1/12 \(\lambda_{\text{min}}\) in the model, the total number of grid elements in the simulation model and the calculation cost will be too large. Therefore, the mesh size in the area near the rail takes a value of 1/12 \(\lambda_{\text{min}}\) and the mesh size in the area far away from the rail is enlarged appropriately. The material parameters for each component of over-track platform were listed in Table 1[19]. The mesh size of the simulation model was taken as 0.2-2 m. The integration step in time domain was taken as 0.002 s in the simulating calculation. The range of vibration frequencies perceived by human bodies is 0 Hz-80 Hz. The vertical Z-weighted vibration acceleration level, \(VL_{\text{Z}}\), is the indicator evaluating the influence of vibration on humans. As shown in Figure 4, verification points Z1 and Z2 were set on the ground floor and the sides of columns on the over-track platform on the throat area, respectively. The field vibration test photos are shown in Figure 5. The maximal vertical Z-weighted vibration acceleration level, \(VL_{\text{Zmax}}\), from the measured results and simulated results at each verification point are shown in Table 2. The comparison of the measured and simulated 1/3 octave spectrum of the vertical vibration acceleration level, \(VAL\), is shown in Figure 6. The error between the simulated value and measured value at each verification point given in Table 2 is 2.2-2.6 dB, and the relative error was less than 4.00%. In summary, the simulated results for the over-track platform of metro depots were close to the measured results, which indicated that the simulation method and parameter settings were reasonable. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Materials**} & \multirow{2}{*}{**Density (kg/m\({}^{3}\))**} & **Elastic Modulus (MPa)** & \multirow{2}{*}{**Poisson’s Ratio**} \\ \hline Rail & 7850 & 210,000 & 0.25 \\ Sleeper & 2500 & 30,000 & 0.20 \\ Track-bed & 2500 & 420,000 & 0.30 \\ Artificial fill layer & 1980 & 205 & 0.31 \\ Pulverized clay layer & 1530 & 120 & 0.35 \\ Fine sand layer & 1940 & 175 & 0.44 \\ C40 concrete & 2500 & 32,500 & 0.20 \\ Standard brick & 1600 & 2000 & 0.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The material parameters of each component. Figure 3: The geometric model of track, soil, and over-track platform and building. Figure 4: Layouts of verification points in the measured metro depot. Figure 5: Layouts of vibration acceleration sensors at each sampling point: (**a**) ground; (**b**) column of the over-track platform. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Verification Point**} & \multirow{2}{*}{**Position**} & \multicolumn{5}{c}{**\(\boldsymbol{V_{\text{Zmax}}}\) (dB)**} \\ \cline{3-6}  & & **Measured Results** & **Simulated Results** & **Error** & **Relative Error** \\ \hline Z1 & Ground floor & 84.2 & 86.8 & 2.6 & 3.08\% \\ Z2 & Platform columns & 77.6 & 78.3 & 1.3 & 1.67\% \\ \hline \hline \end{tabular}
\end{table}