# Influences of High-Speed Train Speed on Tunnel Aerodynamic Pressures
## 4 Results
### Aerodynamic Pressures in Stage III  
The wave diagram and the aerodynamic pressure time history of monitoring point 10-V in Stage III are shown in Figure 19. The train speed is 350 km/h. After train tail leaves the exit, the pressure field of tunnel lining is produced by the reflections of pressure waves from tunnel portals. The solid and dotted lines denote compression and rarefaction waves, respectively. The red and magenta lines denote pressure waves produced by the entering of train nose and tail, respectively. The blue and green lines denote pressure waves produced by the leaving of train nose and tail, respectively. As the energy of the pressure waves reflected from the train nose and tail is relatively small and has been reduced by the friction effect in Stage II, these reflected waves are ignored in Stage III. The aerodynamic pressure time history presents a periodic variation due to the periodic reflections of the pressure waves from tunnel portals. The period of the aerodynamic pressures is mainly determined by tunnel length and wave speed. The pressure wave period can be defined as \(T_{ac}=2\,L/c\) (\(L\): tunnel length, \(c\): sonic speed). The energy of pressure waves is gradually reduced by the dissipations at tunnel portals and the frictions on boundary surfaces (e.g., tunnel wall and track). Therefore, the amplitude of the aerodynamic pressures decreases with time. The amplitude of the aerodynamic pressures is increased after two or more pressure waves, with the disturbances along the same line, arriving at the monitoring section. Moreover, the amplitude of the aerodynamic pressures is decreased  
Figure 18: Maximum peak pressures versus train speed of typical monitoring points in Stage II. (**a**) Maximum positive peak; (**b**) Maximum negative peak; (**c**) Maximum peak-to-peak value. after two pressure waves, with the disturbances along the different lines, arriving at the monitoring section. The distributions of the maximum peak pressures along the tunnel vault are shown in Figure 20. The maximum peak pressure values of the points near tunnel middle section are generally larger than those near tunnel portals. The relationships between the maximum peak pressure and the train speed of specific monitoring points in Stage III are shown in Figure 21. The three types of maximum peak pressure values of the points near tunnel portals increase with increasing train speed. The three types of maximum peak pressure of tunnel middle section are more complex than those near tunnel portals. There are one or more turning points of these three types of maximum peak pressure of tunnel middle section. Figure 19: Wave diagram and aerodynamic pressure time history of monitoring point 10-V in Stage III at train speed of 350 km/h. Figure 21: Maximum peak pressure values at different train speeds of typical monitoring points in Stage III. (**a**) Maximum positive peak; (**b**) Maximum negative peak; (**c**) Maximum peak-to-peak value. Figure 20: Distributions of maximum peak pressures along tunnel vault in Stage III. As shown in Figure 19, when the train speed is 350 km/h, the aerodynamic pressure of the point near tunnel middle section achieves the maximum positive peak at 14.1 s. After three consecutive rarefaction waves pass through the monitoring section, the aerodynamic pressure achieves the maximum negative peak at 16.9 s. When the train speed is 375 km/h, the aerodynamic pressure of the point near tunnel middle section achieves the maximum positive peak at 14.2 s (Figure 22). After two rarefaction waves and one compression wave pass through the monitoring section, the aerodynamic pressure achieves the maximum negative peak at 17.0 s. As a result of the superimposed effect of pressure waves, the maximum negative peak pressure value of the point near tunnel middle section decreases after train speed increases from 350 km/h to 375 km/h. The existence of other turning points can also be explained by the superimposed effect of pressure waves.