# Influences of High-Speed Train Speed on Tunnel Aerodynamic Pressures
## 4 Results
### Aerodynamic Pressures in Stage II  
Most previous studies in the field of the aerodynamic pressure waves inside tunnel focused on the behaviours in Stage II. The reflection of pressure waves from tunnel portals was widely investigated [38]. However, the reflection and transmission of pressure waves associated with the running train inside the tunnel have not been substantially explored, which have notable influences on the tunnel lining pressure. To cater to this issue, we systematically analyze the development of the pressure waves associated with the train body in this research. The schematic diagram of propagation and reflection of a pressure wave between tunnel wall and train body is shown in Figure 15. When a compression wave \(P_{a}\) arrives at train tail, the effective sectional area of the airspace inside the tunnel is suddenly contracted due to the train. Then, most of the pressure wave \(P_{a}\) continues to transmit as a compression wave, and the magnitude of transmitted wave \(P_{tu}\) is larger than \(P_{a}\). The pressure wave \(P_{a}\) is partially reflected back as a compression wave, and the magnitude of the reflected wave \(P_{m}\) is smaller than \(P_{a}\). When the compression wave \(P_{tu}\) arrives at train nose, the effective sectional area of the airspace is suddenly enlarged, and the magnitude of transmitted wave \(P_{tu}\) is decreased. The reflected wave \(P_{rta}\) turn into a rarefaction wave. Noted, the reflected wave is inverted (turning upside down) if the incident pressure wave disturbs a more massive medium, and the reflection is upright if the incident wave disturbs a less massive medium. The transmission of a pressure wave from the train nose to tail is similar to that from tail to nose. In fact, a pressure wave is partially reflected and partially transmitted at the boundary between media (i.e., tunnel portals, trains inside the tunnel). Therefore, numerous pressure waves are generated and propagate inside the tunnel, of which the superposition results in a complex pressure field on tunnel lining. Because of the friction effects of tunnel wall and train body, the intensity of pressure waves gradually decreases and ultimately disappears. \begin{table}
\begin{tabular}{c c c c c c c} \hline Train speed (km/h) & 275 & 300 & 325 & 350 & 375 & 400 \\ \hline Propagation distance (m) & 222.55 & 204.00 & 188.31 & 174.86 & 163.20 & 153.00 \\ \hline \end{tabular}
\end{table} 
Table 1: Propagation distances of initial pressure waves at different train speeds in Stage I.  
Figure 14: Peak pressure versus train speed of monitoring point 1-V in Stage I. The relationship between the wave diagram and the pressure variations of monitoring point 10-V in Stage II is shown in Figure 16. The train speed is 350 km/h. In Figure 16a, the solid lines (with letters C and c) and dotted lines (with letters R and r) denote compression and rarefaction waves, respectively. The letters N and T denote the running paths of train nose and tail inside the tunnel, respectively. The paths C1 and R1 denote the initial pressure waves produced by the entering of train nose and tail, respectively. Except for C1 and R1, the uppercase letters (C and R) denote the reflected waves from tunnel portals. The lowercase letters (c and r) denote the reflected waves from the train nose and tail. The Arabic numerals denote the sequence of the reflected waves from a boundary (portal or train body) in the form of compression or rarefaction waves. As the intensity of the reflected wave from the train body is smaller than that of the incident wave, the subsequent reflections of this reflected wave are ignored. As a result, multiple pressure waves move between the tunnel portals during a train travelling in the tunnel. The recorded aerodynamic pressures of monitoring point 10-V, 500 m from both tunnel portals, are shown in Figure 16b. The vertical lines represent the moments at which the train nose, train tail, and pressure waves arriving at the monitoring section.