## 4 Results and Discussion  
### Aerodynamic Pressure Caused by the Single Train  
Figure 8 plots the spread of pressure wave inside the test tunnel and the evolution of pressure load recorded by the measuring point at sidewall surface (\(x_{lin}=200\) m, \(v_{tr}=369\) km/h). Assisted by the pressure spreading lines in Figure 8, typical pressure increase or pressure drop can be well illustrated. The first pressure peak appears at \(t=a\), corresponding to the moment when the pressure wave approaches the measuring point. The subsequent pressure increase respectively occurs at \(t=e\), g, and \(h\) are all caused by reflected compression pressure waves. Similarly, pressure drops emerged at \(t=f\) is induced by the expansion wave. When the expansion pressure wave approaches the measuring \begin{table}
\begin{tabular}{c c c c} \hline
**Test No.** & **Train A/km\(\cdot\)h\({}^{-1}\)** & **Train B/km\(\cdot\)h\({}^{-1}\)** & **Test Scenario** \\ \hline
1 & 350 & / & \\
2 & 385 & / & \\
3 & 390 & / & \\
4 & 400 & / & \\
5 & 420 & / & Single train \\
6 & 440 & / & \\
7 & 460 & / & \\
8 & 480 & / & \\
9 & 490 & / & \\
10 & 495 & / & \\ \hline
11 & 400 & 400 & \\
12 & 450 & 450 & \\
13 & 495 & 495 & Intersection \\
14 & 495 & 450 & \\
15 & 495 & 400 & \\
16 & 450 & 400 & \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation plans. Figure 7: Validation of simulated data: (**a**) mesh sensitivity analysis; (**b**) comparison with field measurements. point at \(t=c\), the pressure evolution curve shows a shortly increase instead of decreasing due to the expansion wave effect. However, this is rational to occur in the full-scale test as it is technically hard to maintain the train velocity being unchanged. Such velocity fluctuation is likely to result in the dislocation of time point corresponding to the wave diagram. Besides, pressure drop and increase appearing at \(t=b\) and \(d\) are respectively resulted by the passage of train head and train tail [32]. In the following, dimensionless pressure \(p^{*}\) and velocity \(v_{tr}^{*}\) will be used for the further discussion associated with the aerodynamic pressure and the relationship between pressure and train velocity. The normalized pressure \(p^{*}\) is the ratio of measured pressure \(p\) to the pressure amplitude of the first compression wave for reference [33], i.e.,  
\[p^{*}=p//_{1} \tag{1}\]  
with  
\[J_{1}=\frac{\rho_{0}(v_{s}M_{tr})^{2}\phi_{tr}(1+\phi_{tr})}{\left(1-{M_{tr}}^{ 2}\right)} \tag{2}\]  
with Mach number of HST being generated as  
\[M_{tr}=\frac{v_{tr}}{v_{s}} \tag{3}\]  
blockage ratio \(\phi_{tr}\) being calculated as  
\[\phi_{tr}=\frac{A_{tr}}{A_{tu}} \tag{4}\]  
where \(\rho_{0}\) is the ambient air density, \(v_{s}\) indicates the velocity of sound, \(A_{tr}\) and \(A_{tu}\) respectively denotes the area of HST and tunnel. To be clarified, as displayed in Figure 8, pressure peak periodically repeats due to the reflection of pressure waves. The maximum value of TPL and MPW is likely to occur at the later peaks due to the pressure superposition. To simplify the calculation, values of \(p\) in Equation (1) represents the first pressure peak  
Figure 8: Pressure spread and its evolution curve (\(x_{itin}\) = 200 m). are utilized for the data analysis in the present study. In the similar way, dimensionless velocity of HST \(v_{tr}^{\star}\) is calculated as  
\[v_{tr}^{\star}=v_{tr}/\sqrt{gR_{tu}} \tag{5}\]  
with  
\[R_{tu}=\frac{4A_{tu}}{S_{tu}} \tag{6}\]  
where \(R_{tu}\) represents equivalent tunnel diameter, \(S_{tu}\) is the perimeter of tunnel, and \(g\) is gravity. Histories of the initial pressure waves derived from field tests, considering different train speeds at \(x_{tin}\) = 200 m and tunnel center \(x_{tin}\) = 314 m are exhibited in Figure 9. Similar varying trend can be found in the plotted lines. As the train speed increases from 250 km/h to 376 km/h, the maximum value of TPL at tunnel surface gradually increases.