# Aerodynamic Characteristics When Trains Pass Each Other in High-Speed Railway Shield Tunnel
## 4 Results and Discussion
### Pressure Wave Characteristics in Tunnels
When a pressure wave reaches the tunnel exit, part of the wave is released to the outside in the form of micro-pressure waves. The resulting expansion/compression wave is always weaker than the previous expansion/compression wave. Furthermore, since the propagation speed of the wave was 340 m/s greater than the speed of the high-speed train (97.22 m/s), the wave propagation line was steeper than the displacement line between the head and tail of the train. Figure 8b shows the pressure changes with time at a height of 1.5 m from the track surface at the center of the tunnel. As shown in Figure 8b, under the three different tunnel lining structures, the pressure change trends of the tunnel wall were similar. Due to the differences of the lining structures, the peak pressures at the tunnel wall were different. The peak pressure of the molded lining structure overall was greater than the wall pressure of the shield tunnel. The reason was that there were a large number of bolt holes in the shield tunnel. At this time, the pressure wave was reflected more, and the non-linear effect caused a greater reduction in the peak value. A more specific analysis is presented in Section 4.2. Figure 7: Pressure–time history curve at the central point of measurement of the shield tunnel. Figure 8b also shows that since the two trains entered the tunnel at the same time, the compression wave generated by the nose of the train propagated into the tunnel, and the compression waves C\({}_{\text{AH}}\) and C\({}_{\text{BH}}\) generated by trains A and B were superimposed in the center of the tunnel, as shown in Figure 8b-(1). At t = 2.76 s, the pressure was slightly reduced due to the low-pressure area of the train shoulder. Between t = 2.95 and 3.88 s, as the train moved further into the tunnel, the frictional force between the train and the wall of the tunnel on the air in the annular space gradually increased, causing the pressure to rise slowly. When the two trains moved by each other, the space between the two trains gradually decreased, and finally, the first pressure peak reached 4017 Pa. As the expansion waves E\({}_{\text{AT}}\) and E\({}_{\text{BT}}\) generated when the train's rear entered the tunnel were also superimposed at the central measurement point of the tunnel, the pressure at the measurement point decreased, as shown in Figure 8b-(2). The compression waves (C\({}_{\text{AH}}\) and C\({}_{\text{BH}}\)) propagated to the exit of the tunnel and were reflected back. When expansion waves (E\({}_{\text{AH}}\) and E\({}_{\text{BH}}\)) propagated to the central measurement point of the tunnel again, the pressure at the measurement point at this time dropped again, as shown in Figure 8b-(3). When the nose tip of the train passed the measurement point, the pressure of the wall measurement point dropped sharply, as shown in Figure 8b-(4). When the two trains met, the compression wave reflected by the expansion wave was superimposed at the center of the tunnel. At this time, the pressure at the point of measurement in the center of the tunnel first decreased and then increased. For example, when the tails of the two trains met, the aerodynamic pressure on the tunnel wall increased sharply, as shown in Figure 8b-(5). After this, the pressure at the point of measurement in the center of the tunnel fluctuated with the propagation and reflection of the compression wave and the expansion wave. Figure 8b-(6,7) show that the compression or expansion wave caused by the head or tail of the train exiting the tunnel met at the central measurement point of the tunnel, causing the wall pressure to rise or fall, respectively. To more clearly display the change in pressure in the tunnel and on the surface of the train as the train passed through, Figure 9 shows the pressure distributions at different times for high-speed trains meeting at constant speed. The tunnel ground pressure changed drastically with the progress of the train crossing.