# Train-Induced Vibration Analysis and Isolation Trench Measures in Metro Depot Structures
## 5 Conclusions  
In this study, numerical simulation analysis was conducted for a metro depot by establishing a train-track and track-soil-building substructure model. The vibration response and propagation characteristics of the slabs in the over-track building of the depot were investigated. Based on this analysis, vibration isolation trench measures for the metro depot were studied. The main conclusions are as follows:  
1. The vibration response of slabs is significantly influenced by stiffness. When the slab thickness is the same, larger slab areas result in lower vertical natural frequencies. This leads to a wider frequency range under train load excitation, making resonance more likely to occur in the slabs. The dominant frequency range of slab vibration in the over-track building is between 25 and 50 Hz. The maximum vibration level in the 1/3 octave band occurs at 31.5-40 Hz. High-frequency vibration in the range of 63-80 Hz shows a decreasing trend with increasing floor height. In contrast, vibration at certain frequency points within the range of 5-31.5 Hz exhibits amplification as the floor height increases. 2. Within the main frequency range of slab vibration, open trenches exhibit the best vibration isolation performance. Numerical analysis indicates that depth is the primary factor affecting the isolation performance of open trenches. As the depth of the trench increases, the vibration isolation effect improves. When the trench depth reaches one Rayleigh wavelength of the surface soil, the Z-vibration levels of the slabs can be reduced by more than 10 dB. The influence of the position and width of open trenches on their vibration isolation performance is weaker than that of their depth. For the position of open trenches, the vibration isolation performance decreases when the trench is located closer to the track structure. It is recommended that the distance between the trench and the track structure should be greater than 0.4 times the Rayleigh wavelength of the surface soil. Regarding the width of open trenches, due to the limited space in the depot area, the trench width cannot be set too large. Therefore, within the width range of 0.5-1.5 m considered in this study, changes in trench width have a relatively minor influence on the vibration isolation performance. 3. Within the dominant frequency range of slab vibration, flexible infilled trenches exhibit better overall vibration isolation performance than rigid infilled trenches. The gravel infilled trench shows almost no vibration isolation effect within the 1-80 Hz frequency range of slab vibration, and the Z-vibration levels of the slabs are amplified by 0.3-1.6 dB. The foam infilled trench achieves the best vibration isolation performance. When a foam infilled trench is used, the Z-vibration levels of the slabs can be reduced by 8.6-13.9 dB. The impedance ratio between the filling material and the surrounding soil is an important factor affecting the vibration isolation performance of infilled trenches. When the impedance ratio deviates further from 1, the vibration isolation performance improves. However, when the impedance ratio approaches 1, the vibration isolation effect decreases and may even disappear. For rigid infilled trenches, when the impedance ratio between the filling material and the surface soil reaches 8.7, further increasing the stiffness of the filling material does not significantly enhance the vibration isolation performance. Methodology, S.Z. and M.Z. ; software, C.L. ; validation, S.Z. ; formal analysis, S.Z. and J.S. ; investigation, S.Z. and J.S. ; resources, M.Z. ; data curation, S.Z. ; writing--original draft preparation, S.Z. ; writing--review and editing, S.Z., J.S. and C.L. ; visualization, S.Z. ; supervision, M.Z. ; project administration, M.Z. and J.S. ; funding acquisition, M.Z. and J.S. All authors have read and agreed to the published version of the manuscript. The work described in this paper was supported by the National Natural Science Foundation of China (52338001 of [PERSON] and 52308475 of [PERSON]).