## 4 Results and Discussion
### Aerodynamic Pressure Caused by the Single Train
Peak values of the transient pressure, namely \(P_{tr-max}\), at \(x_{tin}\) = 200 m and \(x_{tin}\) = 314 m (tunnel center), are 1.72 kPa and 1.37 kPa, respectively. Such pressure difference indicates that aerodynamic pressure acting at tunnel lining is unevenly distributed along the longitudinal direction. To be noticed, for a certain varying range of train speed, i.e., 328 km/h to 376 km/h exhibited in Figure 9, the increase of the peak pressure \(P_{tr-max}\) at \(x_{tin}\) = 314 m is generally higher than the value recorded at \(x_{tin}\) = 200 m while the pressure trough \(P_{tr-min}\) shows opposite varying trend. This is due to the non-uniform distribution of pressure wave induced by the wave superposition during its reciprocation within the tunnel, which will be discussed later. By utilizing the numerical method, spread of pressure waves can be well illustrated. The plotted curves drawn in Figure 10 are pressure histories from different velocities recorded at 20 m and 100 m away from tunnel portals. Pressure curves show different varying tendencies when the measuring position changes. For the pressure waves recorded nearby the tunnel portals, i.e., \(x_{tin}\) = 20 m and 602 m, even though the peak value of \(P_{tw}^{\star}\) presents significant difference, both these two curves show a sharp pressure jump (see the dotted lines in Figure 10) where the pressure peak occurs. On the contrary, pressure variation at \(x_{tin}\) = 100 m and 500 m are more moderate within its peak region. The total increase of pressure at \(x_{tin}\)= 100 m is decomposed into two parts (marked as \(\Delta P_{1}\) and \(\Delta P_{2}\)), wherein the time cost to approach its maximum value is much longer. Pressure variation at \(x_{tin}\) = 500 m also behave similarly with what observed at \(x_{tin}\) = 100 m, indicating the transient pressure loads acting at the tunnel sidewall being influenced by the longitudinal locations. Figure 7:0 Pressure histories at tunnel sidewall: (**a**) \(x_{tin}\) = 200 m (**b**) \(x_{tin}\) = 314 m.  
Investigation associated with the pressure distribution has been addressed by some previous studies wherein different opinions are observed. Based on the research addressing the wave spread of compressed gas conducted by [PERSON] et al. [34], an earlier study from [PERSON] et al. [35] through field measurements and CFD simulation declare that the compression wave exponentially attenuates with the distance \(x_{itin}\) inside both the slab track and ballast track tunnels, i.e.,  
Figure 7:1  
where \(x_{0}\) represents the reference point at tunnel entrance, \(\Delta P_{x_{itin}}\) and \(\Delta P_{x_{0}}\) are respectively the pressure rises at \(x_{itin}\) and \(x_{0}\), \(\kappa\) is the attenuation factor determined by experiments, \(D_{t}\) is the equivalent diameter of the tunnel. According to the field measurements from Shinkansen tunnels, values of \(\kappa\) for the tunnel utilizing slab and ballast track are adopted as 4.5 \(\times\) 10\({}^{-4}\) and 6.5 \(\times\) 10\({}^{-4}\) for the condition that the train speed reaches 215 km/h. The later researches conducted by [PERSON] et al. [21] and [PERSON] et al. [36] declare different findings. In their research, filed measurements derived from Xiyema Tunnel located at Chinese Beijing-Shanghai line indicate that the pressure amplitude recorded at sidewall surface first increases and then decrease as the longitudinal distance \(x_{itin}\) increases from 20 m to 680 m. Both the growing and decreasing lines show linear-like tendency instead of the exponential trend. Further investigation is thus conducted by plotting the maximum pressure load \(P_{tr-max}^{*}\) derived from different transverse and longitudinal locations in Figure 11 as below. Dimensionless tunnel length \(L_{tu}^{*}\), generated as \(L_{tu}^{*}=\frac{x_{itin}-x_{0}}{D_{tu}}\), is obtained to represent the relative position of measuring points.