## 3 Dynamic Response under the Moving Train Loads
### Dynamic Response Laws of Different Types of Foundations
The dynamic response of the ordinary pile-soil foundation has a small variation, and each dynamic response index decreases and then increases with the increase in distance from the pile and has a \"wavy\" variation. This characteristic is due to the superimposed effect of the train vibration generated inside the foundation, which is conducted by the piles on both sides, respectively. When there is an adjacent tunnel, the tunnel prevents the vibration from propagating in the stratum, and the soil between the neighboring piles and the tunnel is less affected by the vibration of other piles, resulting in a monotonic variation in the dynamic response indexes of the foundation between the pile and the tunnel. The peak vibration velocity is often used to evaluate damage to building structures. For the safety control threshold of the dynamic response of underground structures under moving train loads, as shown in Table 4, [PERSON] et al. [28] graded and supplemented the control threshold of the vibration velocity. The pile-soil foundation at the burial depth of the tunnel was divided into three affected zones according to the graded control thresholds, as shown in Figure 11.  
Figure 11 indicates that, when the pile-soil foundation has an adjacent tunnel under moving train loads, the foundation between the pile and tunnel is affected by the moving \begin{table}
\begin{tabular}{c c c} \hline
**Peak Vibration** & **Evaluation of** & **Measures** \\
**Velocity** & **Vibration Effects** & **No** \\ \hline \(\leq\)2.5 mm\(\cdot\)s\({}^{-1}\) & No effect & No \\
2.5-5 mm\(\cdot\)s\({}^{-1}\) & Weak & Deciding on whether to take measures depends on the importance of the structure. \\
5-10 mm\(\cdot\)s\({}^{-1}\) & Strong & Corresponding vibration damping measures recommend to be used. \\ \(\geq\)10 mm\(\cdot\)s\({-1}\) & Dangerous & Corresponding vibration damping measures must be used. \\ \hline \end{tabular}
\end{table} 
Table 4: Graded control thresholds for the dynamic response of underground structures. Figure 11: Evaluation of dynamic response under moving train loads. train loads and the ratio of dangerously affected zone: strongly affected zone: weakly affected zone is about 1:2:1. The peak vibration velocity of the foundation at the burial depth of the tunnel within 3.6 m from the pile (red zone) exceeds 10 mm\(\cdot\)s\({}^{-1}\). The foundations in this zone account for approximately 24.8% of the foundations between the piles and the tunnel. The underground structure within this zone of high-speed train operation has a large safety risk, which must be paid attention to, and corresponding damping measures must be adopted. The foundation in the range of 3.6-11.4 m near the pile (yellow zone) is the strongly affected zone, and it represents approximately 53.8% of the foundation between the piles and the tunnel. Although the vibration will not cause serious damage to the underground structure within this zone, it is still recommended to use the corresponding vibration damping measures. The foundation outside 11.4 m from the pile to the tunnel (green zone) are in the weakly affected zone, and the impact of the moving train loads on the underground structure in this area is low. This part of the foundation accounts for approximately 21.4% of the foundations between the piles and the tunnel. The importance and deterioration of the underground structure are taken into account to determine whether damping measures need to be taken. Taking this project as a case, the tunnel structure of the underpass section is in the weakly affected zone. If the tunnel is used with low requirements, such as ordinary hydraulic tunnels, the impact of moving train loads can be ignored. If the tunnel is used with high requirements, such as traffic tunnels, especially those with rails, then partial vibration damping measures can be considered. Moreover, if the adjacent tunnel has been in service, this needs to be considered in combination with the service time of the tunnel.