# Aerodynamic Characteristics When Trains Pass Each Other in High-Speed Railway Shield Tunnel
## 4 Results and Discussion
### Aerodynamic Effects of Different Tunnel Lining Structures
Therefore, for the pressure curve at each measurement point, only the micro-pressure part formed by the divergence of the compression wave pulse should be analyzed. Figure 12 shows the micro-pressure wave curve when the constant-velocity trains crossed in the middle of the tunnel and the single train was 20 m outside the tunnel exit. From the moment when the peak appeared in Figure 12, the micro-pressure waves were all  
Figure 10: Comparison of aerodynamic pressures at the midpoints of the tunnels with different lining structures. formed by the initial compression wave generated by the train entering the tunnel and the radiation diverging from the tunnel exit. Figure 12 and Table 2 show that when the high-speed trains crossed in the center of the molded lining tunnel, the micro-pressure waves (positive and negative peaks) generated were the largest. Compared with the micro-pressure waves generated by the trains passing through the integrally molded lining tunnel, the micro-pressure waves of the shield tunnel were reduced by 10.78%. In contrast, when the high-speed trains traveled in one-way and two-way directions in the shield tunnel, the micro-pressure wave when the two trains met in the center of the tunnel increased by 2.6%. Figure 13 shows the pressure decay rate at the central measurement point of the tunnel at a height of 1.5 m from the track surface after the train exited the tunnel. The black solid line and the dashed line in Figure 13 represent the pressure attenuation rates of the positive and negative peaks of the same attenuation period under different tunnel lining structures, respectively, which were calculated by the formulae \((p_{l_{i}-\max}-p_{S_{i}-\max})/p_{l_{i}-\max}\) and \((p_{l_{i}-\min}-p_{S_{i}-\min})/p_{l_{i}-\min}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Lining Structure Type** & \begin{tabular}{c} **Integral Lining** \\ **Tunnel–100 m2** \\ \end{tabular} & \multicolumn{2}{c}{**Shield Tunnel–100 m2**} & \multicolumn{2}{c}{**MPW Variation Rate**} \\ \hline Situation & Intersection at the midpoint & Single train & \begin{tabular}{c} Intersection at \\ the midpoint \\ \end{tabular} & \
\begin{tabular}{c} Comparison of \\ different lining tunnels \\ \end{tabular} &
\begin{tabular}{c} Single train \\ and intersection \\ \end{tabular} \\ \hline MPW maximum (Pa) & 45.54 & 39.6 & 40.63 & 10.78\% & 2.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the peak values of the micro-pressure wave 20 m from the exit of the tunnel. Figure 11: Pressure–time history curves from each measurement point when the trains met in the center of the tunnel. Figure 12: Micro-pressure wave curves 20 m from the exit of the tunnel. The positive and negative peak pressures of the shield tunnel at different cycle numbers are represented by \(p_{S_{i}-\max}\) and \(p_{S_{i}-\min}\), respectively, and those of the molded lining tunnel are represented by \(p_{I_{i}-\max}\) and \(p_{I_{i}-\min}\), where \(i\) is the cycle number (1, 2, 3,..., 10), \"S\" represents the shield tunnel, and \"I\" stands for molded lining tunnel. Similarly, the blue solid line and the dashed line represent the positive and negative peak pressure decay rates of different cycle periods under the shield tunnel, respectively, which were calculated by the formulae \((p_{S_{i}-\max}-p_{S_{i+1}-\max})/p_{S_{i}-\max}\) and \((p_{S_{i}-\min}-p_{S_{i+1}-\min})/p_{S_{i}-\min}\). The red solid line and the dashed line represent the positive and negative peak pressure attenuation rates of different cycle periods under the molded lining tunnel, respectively, which were calculated by the formulae \((p_{I_{i}-\max}-p_{I_{i+1}-\max})/p_{I_{i}-\max}\) and \((p_{I_{i}-\min}-p_{I_{i+1}-\min})/p_{I_{i}-\min}\). As shown in Figure 13, after the train left the tunnel, as the fluctuation period increased, the peak pressure of the tunnel lining structure at the point of measurement gradually attenuated. The positive and negative peak attenuation rates of the shield tunnel were higher than those of the molded lining tunnel.