## 2 Theoretical Approach
### Initial and Boundary Conditions  
In this paper, we take the proposed 400 km/h high-speed train's head type and the 350 km/h railway tunnel cross-section parameters in China as the background for the research of initial compression wave propagation characteristics. The aerodynamic geometric model of the train is depicted in Figure 1. The train model adopts the full-scale model of a certain type of China 400 km/h high-speed train. The train model reproduces (as much as possible) the real original body structure, including the bogie and windshield, and ignores devices such as pantographs, etc. The train cross-section area is 11.8 m\({}^{2}\), the length of the train's nose is 12 m, the tunnel cross-section area \(F\) is 100 m\({}^{2}\), and the tunnel hydraulic diameter (\(D\)) is 10.64 m. The initial compression waves have three-dimensional characteristics within the near tunnel portal and become significantly one-dimensional characteristics after propagating a shorter distance. In this paper, the complete compression waveform at the measuring point 7D away from the tunnel portal is selected to research the evolution process. This paper researches the propagation characteristics of the initial compression waves generated when a 400 km/h high-speed train enters a tunnel without installing the entrance hood (no hood), an oblique enlarged entrance hood (type A) tunnel, and an expanded equal section non-uniform opening hole entrance hood (type B) tunnel. Figure 2 represents the schematic diagrams of the type of tunnel entrance hoods. The length of the oblique enlarged tunnel entrance hood is 26.8 m, and the maximum cross-sectional area is two times the tunnel area. The maximum open hole area of the tunnel entrance hood is 2.89 m\({}^{2}\). The expanded equal section non-uniform opening hole tunnel entrance hood cross-sectional area is two times the tunnel cross-section area, and the tunnel entrance hood length is 80.0 m. Along the length of the tunnel entrance hood, the ventilation ratio gradually decreases; the area of each small hole in the tunnel entrance hood is 0.25 m\({}^{2}\), the area of each large hole is 1.25 m\({}^{2}\), and the ventilation ratio is 3.75%-0.25%. Figure 1: Schematic diagram of high-speed train’s head type: (**a**) side view; (**b**) front view. Figure 3 presents the initial compression wave pressure and pressure gradient time history curves for the train entering the tunnel with no tunnel entrance hood and two different tunnel entrance hoods. Point a indicates that the pressure at the measuring point inside the tunnel begins to rise prior to the train entering the tunnel. The compression waves generated from the train's nose and shoulder propagate to the measurement points, denoted as points a and c, respectively. Curves a,b, and c are defined as the initial compression waves. Without a tunnel entrance hood, the pressure of the initial compression waves increases rapidly, with a maximum pressure gradient of 18.50 kPa/s and a maximum pressure amplitude of 2.18 kPa. For the type A tunnel entrance hoods, the rate of pressure increase for the initial compression waves is slower compared to with no tunnel entrance hood. The maximum pressure gradient is 12.51 kPa/s, and the maximum pressure amplitude is 2.17 kPa. For the type B tunnel entrance hoods, the initial compression waves transition from a single pressure increase to two stepped increases, resulting in a pressure gradient waveform with two peaks. The maximum pressure gradient is 5.90 kPa/s, and the maximum pressure amplitude is 2.09 kPa. When using type A and type B tunnel entrance hoods, compared to no tunnel entrance hoods, their pressure gradient reduction rates are 32.38% and 68.11%, respectively. Therefore, installing a tunnel entrance hood can prolong the duration of pressure rise, consequently reducing the pressure gradient of the initial compression waves. Figure 3: Comparison of different initial compression waves’ pressure histories and pressure gradient histories.