## 3 Results and Discussion
### The Identification of One-Dimensional Waveform of the Entire Initial Compression Wave  
The one-dimensional and three-dimensional characteristics of the initial compression wave have been elucidated in Section 3.2. To provide boundary conditions for the propagation of the initial compression wave, the initial compression wave at measurement points needs to meet two conditions: firstly, it must exhibit the entire waveform of the initial compression wave, and secondly, it must have already evolved into a one-dimensional feature. Therefore, this section will determine the waveform that provides boundary conditions for the propagation of the initial compression wave. As shown in Figure 15, measurement points are located at sections 3_Di_-6_Di_ from the tunnel entrance, with five measurement points arranged at each section. Two measurement points are set at a height of 1.8 m above the ground, located on the left and right tunnel walls, labeled as points 1 and 5. Points 1 and 5 form point T with the centerline of the tunnel. Taking point T as the origin, draw rays at a 45\({}^{\circ}\) angle to the centerline of the tunnel. The intersection points of these rays with the tunnel wall are designated as points 2 and 4. The point at the top of the tunnel is designated as point 3. Previous studies have shown that the intensity of micro-pressure waves is closely related to the pressure gradient of the initial compression wave. Given this, Figures 16-19 compare the waveforms and the pressure gradients of the initial compression waves at five measurement points from 3_Di_ to 6_Di_ cross-sections. According to Figure 16, the waveforms of initial compression waves captured by the 5 points on the 3_Di_ cross-section exhibit consistency in the AB segment, but there are significant differences in the BC segment. This indicates that the disturbances generated by the train during open-air operation have already transitioned into one-dimensional characteristics at the 3_Di_ cross-section, whereas the pressure disturbances generated when the train enters the tunnel still exhibit three-dimensional characteristics at the 3_Di_ cross-section. Among them, point 1 has the highest pressure (i.e., the maximum amplitude of the initial compression wave) at C, followed by point 2, and the lowest is at point 5. This indicates that under three-dimensional effects, the amplitude of the compression wave is closely related to the distance of the measuring point from the train. Point 1 has a pressure amplitude 10.21% greater than that of point 5. Additionally, the amplitude of pressure gradients is also closely related to the distance of the measurement point from the train. Compared to point 1, the amplitude of pressure gradients at point 5 has decreased by 2.31%. Figure 15: The layout of pressure measurement points inside the tunnel: (**a**) front view; (**b**) top view. As shown in Figure 17, the waveforms of initial compression waves at various points in the 4_Di_ section are similar to those in the 3_Di_ section. The BC segment is still affected by the three-dimensional effect of the train's nose, but compared to the 3_Di_ section, this effect is weakened. Although the maximum pressure gradient differences of the initial compression waves at the five measurement points are negligible (0.21%), there is a considerable variance in pressure gradient near point C. As illustrated in Figures 18 and 19, the waveforms of the initial compression wave captured by five measurement points at the 5_Di_ and 6_Di_ cross-sections are consistent, exhibiting one-dimensional characteristics. Comparing the waveform and pressure gradient distribution of the initial compression wave between the 5_Di_ and 6_Di_ cross-sections, both the pressure amplitude and the maximum pressure gradient amplitude are less than 1%, indicating that the initial compression wave captured at the 5_Di_ cross-section is complete.