## 4 Results and Discussion
### Variation Characterization of Pressure Gradient and Amplitude of Compression Waves  
Based on the formation of micro-pressure waves to mitigate the micro-pressure waves at the tunnel exit, a tunnel entrance hood can be installed at the tunnel entrance. This increases the wavelength of the initial compression wave and reduces the maximum pressure gradient of the initial compression wave. From the previous research analysis, it is concluded that during the propagation of the initial compression wave in the tunnel, the amplitude of the tunnel compression wave decreases, but the compression wave waveforms steepen, and the maximum pressure gradient increases. The \"Steepening\" of the compression waves will \"counteract\" the effect of the tunnel entrance hood, instead enhancing the micro-pressure waves. To compare and describe the effect of the waveform on the propagation of the initial compression waves, this paper introduces the following two concepts. The pressure amplitude of the compression waves at the entrance and at a distance \(x\) from the entrance are denoted by \(\Delta p_{0}\) and \(\Delta p_{\mathrm{x}}\), respectively. The attenuation ratio \(\zeta\) is defined as:  
\[\zeta=\frac{\Delta p_{x}}{\Delta p_{0}} \tag{22}\]  
The maximum pressure gradient of the compression waves at the entrance and at a distance \(x\) from the entrance is denoted by \(\frac{\partial p}{\partial t}(\max,0)\) and \(\frac{\partial p}{\partial t}(\max,x)\), respectively. The steepening rate \(\eta\) is defined as:  
\[\eta=\frac{\frac{\partial p}{\partial t}(max,x)}{\frac{\partial p}{\partial t}( max,0)} \tag{23}\]  
Figure 15 depicts the pressure waveforms and pressure gradient curves at measurement points 1 km, 4 km, 7 km, 10 km, 13 km, 16 km, and 19 km; this occurs during the 20 km tunnel propagation of the initial compression waves generated by the train entering different tunnel entrance hoods. When the initial compression waves propagate inside the tunnel, its waveform undergoes a process of initially steepening and then gradually  
Figure 14: The variation pattern of max pressure gradient with wavelength. Figure 13: The variation pattern of wavelength with the propagation distance. flattening. Both type A tunnel entrance hoods and type B tunnel entrance hoods increase the rise time of the compression wave pressure, resulting in a relatively lower pressure gradient during the propagation of the compression waves compared to when no tunnel entrance hood is present. The waveform of the initial compression waves under both no tunnel entrance hood and type A tunnel entrance hoods show a rapid steepening within propagation short distances. Due to the type B tunnel entrance hood, the waveform of the compression waves exhibits two distinct rising steps, resulting in two peaks in the pressure gradient. This significantly reduces the pressure gradient of the compression waves. When propagating to 13 km, the two distinct rising steps on the waveform of the compression waves disappear, and the pressure gradient increases sharply at this point. Figure 16 illustrates the variation patterns of the maximum pressure gradient and steepening rate with a propagation distance for the initial compression waves propagating. Figure 17 illustrates the variation characteristics of the pressure amplitude and attenuation ratio with a propagation distance. In the cases of no tunnel entrance hoods, type A tunnel entrance hoods, and type B tunnel entrance hoods, as the compression waves propagate in the tunnel, their pressure gradient shows a trend of initially increasing and then decreasing. The nonlinear effects of compression waves lead to the phenomenon of steepening during their propagation. During the propagation of the compression waves, the wavefront travels through stationary air, while the wave tail propagates through air moving in the same direction. Additionally, the density and temperature of the air increase, leading to an increase in the speed of sound.