# Seismic Response Analysis of Concrete Box-Type Subgrade in High-Speed Railways
## 4 Seismic Response of Box-Type Subgrade  
### System Dynamic Response Characteristics Under Multi-Dimensional Seismic Coupling  
#### 4.1.1 Vibration and Response Analysis of Box Foundation Based on the Time-Frequency Domain Method  
To explore the vibration characteristics of box-type subgrades under the coupling action of multi-dimensional earthquakes, this paper analyzes the acceleration time-history changes at the top slab, the bottom slab, and the side slab of the box-type subgrade under the seismic action with a maximum design basic acceleration of 0.4 g (see Table 1) in Figure 9. Compared with Figure 8b, the acceleration curve of the box-type subgrade is  
Figure 8: Model input seismic waves. (**a**) The directions of seismic wave input. (**b**) Seismic wave acceleration curve. basically consistent with the waveform of the input seismic wave. In addition, the vibration amplification factors of each component of the box-type subgrade are statistically analyzed, that is, the ratio of the output to the input acceleration peak value, as shown in Table 7. It can be observed that the vibration peak value of the bottom slab of the box-type subgrade is consistent with the input acceleration peak value [35], while the vertical acceleration amplification effect of the side slab of the box-type subgrade is the most significant, with an amplification factor reaching a value of 1.44. According to the research results of [PERSON] et al. [36], the horizontal acceleration amplification factor of the single-bridge model of traditional simply supported beams under the Wenchuan earthquake with a magnitude of 0.1 g has already reached a value as high as 2.1. The seismic amplification factor of the box-type subgrade is relatively small, indicating that the seismic performance of the box-type subgrade is better than that of commonly used bridges in strong earthquakes. To further investigate the vibration characteristics of the box-type subgrade structure, the vertical acceleration of the side panel of the box-type subgrade with the largest amplification factor was extracted, and its Fourier transform was performed to obtain a spectral diagram, as shown in Figure 10. The peak of the vibration is at 22.36 Hz, which is close to the vertical natural frequency of the box-type subgrade of 23.10 Hz in 6 of Section 3 mentioned earlier, indicating that the box-type subgrade has resonated with the input vertical seismic wave [37]. However, compared with traditional simply supported beams, the amplification factor is relatively small, indicating good seismic performance of the box-type subgrade. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Vibration Amplification Factors** & **Longitudinal** & **Transverse** & **Vertical** \\ \hline Peak Value of Input Seismic Wave & 3.714 & 3.987 & 1.413 \\ Bottom Slab (Peak Acceleration/Amplification Factor) & 3.714/1 & 3.987/1 & 1.413/1 \\ Side Slab (Peak Acceleration/Amplification Factor) & 4.235/1.14 & 2.673/0.67 & 2.039/1.44 \\ Top Slab (Peak Acceleration/Amplification Factor) & 5.151/1.39 & 1.559/0.39 & 1.945/1.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Vibration amplification factor of each component of box-type subgrade. Figure 9: Time–history acceleration curve for each component of box-type subgrade. China has established an earthquake emergency response system for railway transportation to prevent or mitigate the hazards of earthquakes to the safety of railway transportation. Currently, the alarm method in China adopts a threshold-triggered approach based on ground motion parameters (early warming system) [38]. The acceleration of the box-type subgrade's side panel differs significantly from the original ground motion response spectrum values, but the structural period corresponding to the peak of the curve is essentially consistent, both being 0.034 s in Figure 11. This indicates that with the input of the original ground motion, the frequency characteristics corresponding to the acceleration response time-history of the beam surface have not changed.