## 4 Results and Discussion  
### Flight Characteristics of Falling Debris  
#### 4.1.1 Falling Debris Translation  
Figure 8 provides a comparison of the three-dimensional flight trajectories of falling debris under single-train and trains-crossing conditions at speeds ranging from 250 to 350 km/h. The origin in the figure represents the center of gravity at the initial moment of falling debris. Observations based on Figure 8 are as follows. The flight trajectory of falling debris exhibits noticeable three-dimensional features under both single-train and trains-crossing scenarios. In the \(X\)Z plane, the trajectory opposes the direction of train operation, while in the \(Y\)Z plane, falling debris moves in the -\(Z\) direction. Specifically, under the single-train conditions, debris diverges from the train, whereas under trains-crossing conditions, debris consistently moves in the direction of the train. Different operating conditions lead to significant variations in the impact of train speed on falling debris trajectories. In the case of a single train, the shape of the falling debris trajectory in both the \(X\)Z and \(Y\)Z planes, under various train speeds, resembles a parabola. The flight distance of falling debris in the \(X\) and \(Z\) directions increases with higher train speeds. Relevant research suggested that aerodynamic effects (such as aerodynamic pressure and piston wind speed) generated by train operation typically follow a power function relationship with train speed [40]. Figure 9 employs a power function to model the relationship between flight distance and train speed under the single-train conditions. The analysis reveals that the flight distance of falling debris in the \(X\) and \(Z\) directions is approximately proportional to the square of the train speed. The corresponding determination coefficient (\(R^{2}\)), exceeds 0.97, indicating a strong correlation. Under the condition of trains crossing, the flight trajectory of falling debris deviates from the previously observed law. In the \(X\)Z plane, the trajectory becomes increasingly intricate as the train speed rises. At a speed of 250 km/h, the flight trajectory resembles that under single-train conditions, consistently moving in the negative direction along the \(X\) axis, forming a shape akin to a parabola. At 300 km/h, when the falling debris reaches half of the vertical height of the tunnel, a notable maximum negative displacement in the \(X\) direction occurs (\(-\)0.00313). Subsequently, the flight direction changes, moving in the positive \(X\) direction, yet the final landing position remains in the negative direction of the initial position. Upon reaching a speed of 350 km/h, the flight direction of falling debris undergoes multiple reversals, but as it approaches the ground, the flight direction becomes negative along the \(X\) axis. Figure 8: Flight trajectory of falling debris: (**a**) single train; (**b**) trains crossing. Comparing the conditions of trains crossing with that of a single train, the flight distance of the falling debris is greater in the single-train scenario. Specifically, when the train speed is in the range of 250-350 km/h, the average flight distance of falling debris in the \(X\) and \(Z\) directions under the single-train conditions is 10.3 times and 5.5 times that under the trains crossing condition, respectively. This observation underscores the significant impact of the crossing-trains scenario on the trajectory and ultimate landing positions of falling debris, indicating more intricate and variable behavior compared with the single-train conditions. Figure 10 provides a detailed comparison of the flight velocity of falling debris under two scenarios: a single train and trains crossing, with speeds ranging from 250 to 350 km/h. In the case of a single train, the trajectory of falling debris in the \(X\) and \(Z\) directions exhibits an accelerated motion in the negative direction. Notably, the flight velocity in the \(X\) direction is considerably higher than that in the \(Z\) direction.