# Train-Induced Vibration Analysis and Isolation Trench Measures in Metro Depot Structures
## 3 Propagation Law of Train-Induced Vibration in Metro Depot
### Vibration Response Analysis of the Floor in the Over-Track Building
The Z-vibration level reflects the overall vertical vibration level of the floor slab, while the vibration level in the 1/3 octave band represents the vibration levels within different frequency ranges of the floor slab. Different weighting correction methods were applied in this study for the analysis of Z-vibration levels and vibration levels in the 1/3 octave band of the floor slab. The Z-vibration levels were determined using the W\({}_{\text{k}}\) weighting curve provided in ISO 2631-1:1997 [36], while the vibration levels in the 1/3 octave band were calculated using the weighting method specified in the Chinese standard \"Limits and Measurement Methods for Building Vibration and Secondary Noise Induced by Urban Rail Transit\". Figure 14 shows the variation trends of Z-vibration levels for slabs 1 and 3 across the 1 st to 9 th floors. For slab 1, the minimum Z-vibration level is 62.8 dB, occurring on the 5 th floor, while the maximum Z-vibration level is 68.6 dB, occurring on the top floor. The overall Z-vibration level of slab 1 decreases initially, fluctuates slightly in the middle floors, and then gradually increases toward the top floors. For slab 3, the minimum Z-vibration level is 65.6 dB, occurring on the 3 rd floor, while the maximum Z-vibration level is 74.6 dB, also occurring on the top floor. The overall Z-vibration level of slab 3 decreases initially and then gradually increases toward the top floors. Both slabs 1 and 3 exhibit a significant amplification  
Figure 13: Acceleration amplification factor in the 1/3 octave band for the floor slab: (**a**) 2 nd floor; (**b**) 4 th floor. of Z-vibration levels near the top floors. This is similar to the conclusions drawn in reference [37]. After the vibrations propagate from the ground floor to the top floor, the upper part no longer contains structures that can absorb energy. Therefore, the floors near the top experience a significant amplification of vibrations due to the superposition of incident and reflected waves. Figure 15 shows the vibration levels in the 1/3 octave band for slabs 1 and 3. As shown in Figure 15, the dominant vibration frequencies of slabs 1 and 3 are mainly concentrated in the range of 25 to 50 Hz. Vibrations above 100 Hz become weaker due to attenuation through the soil. The maximum vibration level of slab 1 is 67.1 dB, occurring at 40 Hz on the 9 th floor of the building. For slab 3, the maximum vibration level is 73.7 dB, occurring at 31.5 Hz on the ground floor of the building. The reason for the maximum vibration levels in the 1/3 octave band of floor slabs 1 and 3 occurring at different frequency points is mainly related to the first-order vertical natural frequency of the slabs. Figure 16 shows the first-order mode shape diagram of the slabs. As shown in Figure 16, the first-order frequency of floor slab 1 is 45.7 Hz, while that of floor slab 3 is 29.4 Hz. The frequency points corresponding to the maximum vibration levels in the 1/3 octave band are close to the fundamental frequency of each slab. Figure 14: Floor Z-vibration level. Figure 15: Heatmap of floor slab vibration levels of 1/3 octave band: (**a**) floor slab 1; (**b**) floor slab 3.