## 3 Dynamic Response under the Moving Train Loads
### Dynamic Response Laws of Different Types of Foundations  
For the numerical calculation, a train speed of 350 km/h is taken. Referring to the results of [PERSON] et al. [26] and [PERSON] et al. [28], the peak vibration acceleration, peak \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Name**} & **Dynamic Modulus of** & \multirow{2}{*}{**Density/(g\(\cdot\)cm\({}^{-3}\))**} & **Dynamic Poisson’s** \\  & **Elasticity/MPa** & & **Ratio** \\ \hline Miscellaneous fill & \(168\) & \(1.8\) & \(0.341\) \\ Silty sand & \(199\) & \(1.68\) & \(0.31\) \\ Medium sand & \(281.9\) & \(1.73\) & \(0.293\) \\ Silty clay & \(368.7\) & \(1.93\) & \(0.303\) \\ Medium sand & \(563.5\) & \(1.97\) & \(0.290\) \\ Silty clay & \(358.5\) & \(1.91\) & \(0.303\) \\ Medium sand & \(610.7\) & \(2.06\) & \(0.287\) \\ Train track & \(210,000\) & \(7.835\) & \(0.3\) \\ Concrete & \(34,020\) & \(2.5\) & \(0.2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Stratigraphy and main structural parameters. Figure 8: Numerical calculation models. (**a**) Pile-soil composite foundation. (**b**) Pile-soil composite foundation with adjacent tunnels. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Numerical Calculation Model**} & **Period of the First Mode** & **Period of the Second Mode** \\ \hline Pile-soil composite foundation & \(1.62\) & \(1.13\) \\ Pile-soil composite foundation & \(1.57\) & \(1.12\) \\ with adjacent tunnels & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Period of the main vibration. vibration velocity, and peak vibration displacement were used as the indexes to evaluate the dynamic response. The results of the vertical monitoring points between the pile foundation and the tunnel and the horizontal monitoring points at the burial depth of the tunnel axis were extracted to analyze the dynamic response of the foundation. The dynamic response indexes of the monitoring points for the two numerical models are shown in Figures 9 and 10. Figure 9: Vertical dynamic response characteristics of the foundation. (**a**) Peak vibration acceleration. (**b**) Peak vibration velocity. (**c**) Peak vibration displacement. Figure 9 shows that, when there is an adjacent tunnel, the dynamic response indexes of the foundation under the moving train loads are similar to the results of the model test. All the dynamic response indexes are at maximum at the ground surface, and the peak vibration acceleration, peak vibration velocity, and peak vibration displacement are 286.4 mm.s\({}^{-2}\), 9.2 mm.s\({}^{-1}\), and 1.1 mm, respectively, which meet the corresponding control thresholds. With the increase in the distance from the surface, the dynamic response indexes of both models decrease, especially at the burial depth of the adjacent tunnel. The vibration  
Figure 10: Horizontal dynamic response characteristics of the foundation. (**a**) Peak vibration acceleration. (**b**) Peak vibration velocity. (**c**) Peak vibration displacement. acceleration, vibration velocity, and vibration displacement peaks of the pile-soil composite foundation as a whole increase significantly in the presence of the adjacent tunnel, with the greatest increase at the burial depth of the tunnel roof, increasing by 142%, 58%, and 41%, respectively. The above analysis illustrates the strong effect of the adjacent tunnel on the dynamic response of the pile-soil foundation. Therefore, when there is an adjacent tunnel, the dynamic response of the pile-soil foundation caused by the moving train loads needs immediate attention. Figure 10 indicates that, when there is an adjacent tunnel, the horizontal dynamic response of the foundation is still significantly greater than that of the ordinary pile-ground foundation, and, at the tunnel burial depth between the tunnel and the pile, each dynamic response index is monotonically varying, all increasing and decreasing with the distance from the pile.