## 4 Results and Discussion
### Aerodynamic Pressure Caused by the Single Train
At the speed of 385 km/h and 495 km/h, values of \(P_{tr-max}^{*}\) obtained from the given cross-section, i.e., PA*-1 to PA*-7, first increases and then decreases as the longitudinal distance \(x_{itin}\) increases. The peak value of \(P_{tr-max}^{*}\) appears at roughly the middle of the tunnel, i.e., \(L_{tu}^{*}=0.5\), which is consistent with [PERSON]'s research [21], and is also consistent with results from the present field measurements (pressure variation in the tunnel center is higher than those detected at remoted locations). Figure 7:2 Dimensionless pressure load \(P_{tu}^{*}\) at tunnel sidewall regarding different longitudinal locations and typical train velocities. Besides, it is very interesting to find out that values of \(P_{tr}^{*}\) (1) coming from sidewall at right hand (PA*-1 to PA*-3) are generally higher than that of the ceiling point PA*-4 and the measuring points from sidewall at left hand (PA*-5 to PA*-7); (2) decreases as the measuring height increases when the dimensionless tunnel length \(L_{tu}^{*}<0.5\); (3) is not sensitive to the change of measuring height once value of \(L_{tu}^{*}\) is beyond 0.5. This is reasonable as pressure spreads radiantly within the tunnel so that sidewall closer to HST suffers higher pressure load. Due to the pressure reflection and superimposed effect, variation of pressure amplitude is likely to be non-monotonic in the tunnel. Illustration by utilizing the pressure contour is then given in Figure 12 to help support the above discussion. For the typical train velocity used in Figure 12 for data analysis (\(v_{tr}=385\) km/h, 390 km/h, 400 km/h, and 460 km/h), pressure contour of the transverse cross-section at \(x_{tin}=120\) m provides a good example of the uneven distribution of pressure waves. Correspond to the data shown in Figure 11, pressures in the contour are also normalized as \(P_{tr}^{*}\). To be clarified, pressure contours regarding different train velocities are measured at different time so that the maximum and minimum value of the color bar are different in the sub-figures. Due to the velocity difference, it is technically hard to capture the pressure contours at the same time. However, this will not challenge the readability of Figure 12 as the overall pressure distribution is not significantly affected by such time delays. Figure 7:3 Dimensionless maximum pressure load \(P_{tw-max}^{*}\) at tunnel sidewall. Figure 7:4 Dimensionless maximum pressure load \(P_{tw}^{*}\) at tunnel sidewall. Despite of the peak pressure, the peak-to-peak pressure, representing the maximum transient pressure variation, is attached with a lot of concern when conducting engineering-oriented safety evaluations associated with tunnel linings and internal facilities. Thus, the maximum, minimum, and peak-to-peak values of pressures at \(x_{itin}=200\) m and \(x_{itin}=314\) m in the field tests are then plotted in Figure 7:5 For a given location, \(x_{itin}=200\) m for example, measurements from Figure 13a denote a linear-like tendency for the maximum, minimum, and peak-to-peak values of pressure. In general, the absolute value of \(P_{tr-max}\), \(P_{tr-min}\), and \(\Delta P_{transient}\) increases with train speed. The maximum pressure difference \(\Delta P_{transient}\) occurs when the train speed is about 370 km/h, where \(\Delta P_{transient}\) at \(x_{itin}=200\) m and \(x_{itin}=314\) m respectively equals to 4.29 and 5.63 kPa. Different from \(P_{tr-max}\), \(\Delta P_{transient}\) at \(x_{itin}=314\) m is approximately 1.34 kPa higher than the value measured at \(x_{itin}=200\) m. Such pressure difference is consistent with the simulation results from Figure 11 and are also observed in some other studies. Measurements from field tests carried out by [PERSON] et al. (2018) show that the pressure peak roughly occurs at tunnel center at the speed of 330 km/h. Research of [PERSON] et al.