## 3 Results and Discussion
### The One-Dimensional and Three-Dimensional Characteristics of the Initial Compression Wave
In the \(4 Di\) cross-section, the pressure distribution becomes more even, exhibiting one-dimensional characteristics. Based on the above analysis, the compression waves exhibit three-dimensional characteristics near the train, while one-dimensional plane waves always appear at a certain distance in front of the train. To quantify the transition of the compression wave from three-dimensional to one-dimensional characteristics, Figure 14 illustrates the distribution of maximum and minimum pressures inside the tunnel at different times and provides the change ratio of pressure difference to identify the critical transition location. The formula for calculating the pressure difference ratio \(\eta\) is as follows:  
\[\eta=\left\lvert(p_{\max}-p_{\min})/p_{\max}\right\rvert, \tag{2}\]  
where \(p_{\max}\) and \(p_{\min}\) represent the maximum pressure and minimum pressure, respectively. Figure 11: The characteristics of pressure distribution inside the tunnel at 0 s: (**a**) The pressure distribution of the train’s surface and the tunnel wall; (**b**) the three-dimensional distribution of pressure iso-surfaces at 200 Pa, 400 Pa, and 800 Pa; (**c**) the pressure distribution across cross-sections from \(1 Di\) to \(8 Di\) away from the tunnel entrance. Figure 12: The characteristics of pressure distribution inside the tunnel at 0.0675 s: **(a)** The pressure distribution of the train’s surface and the tunnel wall; **(b)** the three-dimensional distribution of pressure iso-surfaces at 400 Pa, 800 Pa, and 1600 Pa; **(c)** the pressure distribution across cross-sections from \(1 Di\) to \(8 Di\) away from the tunnel entrance. Figure 13: The characteristics of pressure distribution inside the tunnel at 0.135 s: **(a)** The pressure distribution of the train’s surface and the tunnel wall; **(b)** the three-dimensional distribution of pressure iso-surfaces at 500 Pa, 1000 Pa, and 2000 Pa; **(c)** the pressure distribution across cross-sections from \(1 Di\) to \(8 Di\) away from the tunnel entrance. Here, we consider that if the pressure difference ratio \(\eta\) of a section is less than 1%, then the pressure distribution on that section is even. At 0 s and 0.0675 s, the train has not yet reached the \(1 Di\) section. From the \(1 Di\) to \(8 Di\) sections, both the pressure amplitude and the pressure differential ratio gradually decrease, becoming one-dimensional characteristics at the \(3 Di\) and \(4 Di\) sections, respectively. At 0.135 s, the \(1 Di\) section is located at the train body, exhibiting significant three-dimensional characteristics. The maximum negative pressure is detected at the bottom of the train, with a pressure differential ratio reaching  
Figure 14: Comparison of maximum and minimum pressures across different cross-sections from the tunnel entrance at (**a**) 0 s; (**b**) 0.0675 s; (**c**) 0.135 s; (**d**) 0.2025 s; (**e**) 0.27 s.  
95.39%. The 2_Di_ section, located in front of the train, shows a substantial increase in both maximum and minimum pressures, with a pressure differential ratio of 11.06%. Following the 4_Di_ section, the pressure differential ratio decreases to below 1%. At 0.2025 s and 0.27 s, one-dimensional plane waves form at positions 4_Di_ and 5_Di_, respectively.