# Influences of High-Speed Train Speed on Tunnel Aerodynamic Pressures
## 4 Results  
### Typical Stages of Time History of Aerodynamic Pressures  
To facilitate the illustration, the process of a single high-speed train travelling through a railway tunnel is divided into three stages (Figure 10). Stage I: before the train nose enters the entrance; Stage II: while the train body runs inside the tunnel; Stage III: after the train tail leaves the exit. Noted, the length of tunnel is longer than that of train [8].  
In the case of a single high-speed train travels through a 1000 m long railway tunnel with a speed of 350 km/h (97.22 m/s), the development of aerodynamic pressures with time at some specific monitoring points are shown in Figure 11. It takes 0.5 s from starting for the HSR train nose to arrive at the tunnel entrance. It takes 12.9 s from starting for the train tail to leave the exit. After the train tail leaves the exit, the tunnel aerodynamic pressures last for 67.1 s until the peak pressure value reduces to about 10 % of the maximum peak pressure value of Stage III. It takes 0.15 s (50 m / 340 m/s = 0.15 s) for the initial pressure wave produced by the running of a train to reach the entrance in our designed scenario. Thus, the duration of aerodynamic pressures of Stage I is 0.35 s (0.5 s \(-\) 0.15 s = 0.35 s), and the duration of Stage II is 12.4 s (12.9 s \(-\) 0.5 s = 12.4 s). The duration of Stage II is about 35.4 times that of Stage I, and the duration of Stage III is about 197.1 times that of Stage I. The maximum positive peaks of monitoring point 2-V in Stages I, II, and III are 0.18 kPa, 1.54 kPa, and 0.95 kPa, respectively. The maximum positive peak in Stage II is about 8.6 times that in Stage I. The maximum positive peak in Stage III is about 5.3 times that in Stage I.  
Figure 10: Spatial relationship between train and tunnel.  
Figure 9: Aerodynamic pressures obtained by numerical simulation and field test.  
The peak pressures and the duration of Stage I are negligible in comparison to those of Stage II and Stage III. Therefore, the previous studies did not pay attention to the aerodynamic pressures of Stage I. However, considering the entire tunnel life cycle, the total duration of aerodynamic pressures and the total number of peak pressures of Stage I cannot be ignored. For example, a total of 195 pairs of high-speed trains travel on the Guangzhou-Shenzhen HSR line every day in China. The design life of an HSR tunnel is 100 years [8]. The total duration of aerodynamic pressures and the total amount of peak pressures of Stage I are 1384 h and 1.42 \(\times\) 10\({}^{7}\), respectively.  
The maximum peak pressure of Stage I is much lower than the fracture strength of tunnel lining, and the total number of peak pressures is much higher than 10\({}^{6}\). Thus, the fatigue damage of the tunnel lining produced by the aerodynamic pressures of Stage I can be analyzed by the method of high-cycle fatigue [37]. To comprehensively investigate the long-term influences of aerodynamic effects on tunnel lining, the aerodynamic pressures of Stage I should be considered, especially near tunnel portals.  
Figure 11: Aerodynamic pressures time histories for typical monitoring points (\(v\) = 350 km/h). (**a**) Monitoring point 2-V; (**b**) Monitoring point 10-V; (**c**) Monitoring point 17-V.