# Train-Induced Vibration Analysis and Isolation Trench Measures in Metro Depot Structures
## 4 Study on Vibration Isolation Trench Measures for Depot
### The Effect of Trench Filling Materials on Vibration Isolation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Filling Material** & **Density (kg/m3)** & **Elastic Modulus (MPa)** & **Poisson’s Ratio** & **Impedance Ratio** \\ \hline Gravel & 2100 & 500 & 0.24 & 1.511 \\ LAC & 1800 & 14,000 & 0.2 & 8.712 \\ C30 concrete & 2500 & 30,000 & 0.2 & 13.935 \\ Fly ash & 500 & 25 & 0.35 & 0.174 \\ Rubber & 1480 & 4.5 & 0.48 & 0.123 \\ Foam & 50 & 5 & 0.4 & 0.024 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Filling material parameters. trench performs relatively weaker. In the high-frequency range of 160-200 Hz, the rubber infilled trench demonstrates superior vibration isolation performance. According to the analysis in Section 3, the dominant vibration frequency range of the slabs in the over-track building is 25-50 Hz. A comparison of Figures 26 and 27 shows that the effective vibration isolation frequency range of flexible infilled trenches is broader than that of rigid infilled trenches. Additionally, in the 25-50 Hz frequency range, flexible infilled trenches achieve better overall vibration isolation performance than rigid infilled trenches. Therefore, it can be concluded that flexible infilled trenches are more suitable for vibration isolation in metro depots. Figure 28 presents the Z-vibration levels of slab 1 under six different filling materials. It can be observed that when flexible materials are used to fill the trench, the Z-vibration levels of the slabs on floors 1-9 are generally lower than those with rigid infilled trenches. For rigid infilled trenches, the vibration isolation performance of the C30 concrete infilled trench is the best, with Z-vibration levels of the slabs reduced by 1.5-6.4 dB. The LAC infilled trench performs slightly worse than C30 concrete infilled trench, with Z-vibration levels reduced by 1.5-5.1 dB. The gravel infilled trench amplifies the vibration in the dominant frequency range of the slabs, resulting in the worst vibration isolation performance, with Z-vibration levels increased by 0.3-1.6 dB for floors 1-9. For flexible infilled trenches, the foam infilled trench achieves the best vibration isolation performance, with Z-vibration levels of the slabs reduced by 8.6-13.9 dB. The vibration isolation effect of the foam infilled trench is closest to that of the open trench with the same dimensions. The fly ash infilled trench performs relatively weaker, with Z-vibration levels reduced by 2.2-7.0 dB. The rubber infilled trench achieves intermediate performance between the foam infilled and fly ash infilled trenches, with Z-vibration levels reduced by 4.5-9.1 dB. Based on the comparative analysis of the impedance ratio of filling materials and the attenuation effects of slab acceleration and Z-vibration levels, it can be concluded that the impedance ratio is a key factor influencing the vibration isolation performance of infilled trench. The farther the impedance ratio deviates from 1, the better the vibration isolation performance of the infilled trench. Conversely, when the impedance ratio approaches 1, the vibration isolation effect decreases and may even disappear. This indicates that the stiffer the rigid material and the softer the flexible material, the better the vibration  
Figure 28: Influence of infilled trench on floor Z-vibration level. Figure 27: Influence of flexible infilled trench on floor acceleration: (**a**) 1 st floor; (**b**) 4 th floor; (**c**) 6 th floor; (**d**) 9 th floor. isolation performance of the infilled trench. For flexible infilled trenches, while they can provide better vibration isolation performance for the over-track building, flexible materials may face long-term stability issues such as compression creep, water absorption-induced swelling, and decomposition. In addition, flexible materials typically exhibit lower overall mechanical strength, and therefore often need to be used in conjunction with structural elements such as secant piles or diaphragm walls. This increases construction complexity and maintenance difficulty.