# Train-Induced Vibration Analysis and Isolation Trench Measures in Metro Depot Structures
## 4 Study on Vibration Isolation Trench Measures for Depot
### The Effect of Open Trench Depth on Vibration Isolation  
Open isolation trenches are typically placed on both sides of the track. By excavating soil to a certain depth and width, a barrier is formed, which alters the propagation path of train-induced vibrations. This helps to reduce the vibrations caused by the train. Most  
Figure 17: Vibration levels in the 1/3 octave band of floor slabs: (**a**) floor slab 1; (**b**) floor slab 2; (**c**) floor slab 14; (**d**) floor slab 15.  
of the vibration energy in the soil propagates outward in the form of Rayleigh waves [38]. The calculation formula for the Rayleigh wave velocity is shown as follows. \[V_{R}=\frac{0.87+1.12v}{1+v}V_{S} \tag{5}\]  
where \(V_{R}\) represents the Rayleigh wave velocity, \(v\) is the Poisson's ratio, and \(V_{S}\) is the shear wave velocity. In this study, the shear wave velocity of the first-layer soil in the metro depot is 203 m/s, and the Poisson's ratio is 0.31. Through calculation, the Rayleigh wave velocity of the first-layer soil is determined to be 188 m/s. As shown in Figure 15, the frequency range corresponding to the maximum vibration levels in the 1/3 octave band of the floor slabs in the over-track building is 31.5-40 Hz. Therefore, the Rayleigh wavelength of the first-layer soil at 31.5 Hz is denoted as \(\lambda_{R}=5.98\) m \(\approx\) 6 m. In the section investigating the effect of trench depth on vibration isolation performance, four working conditions are set: 1.5 m, 3 m, 4.5 m, and 6 m. The maximum trench depth corresponds to the Rayleigh wavelength of the first-layer soil at 31.5 Hz. For all four conditions, the trench width is set to 0.5 m, and the trench is located 2.4 m from the track centerline. The specific layout of the open trench is shown in Figure 18.  
Figure 19 presents the acceleration attenuation coefficients of slab 1 on the 1 st, 4 th, 6 th, and 9 th floors under different trench depths. It can be observed that, for all four conditions, the acceleration attenuation coefficients of the slabs are concentrated in the range of 0.1 to 1, showing an overall attenuation trend. Additionally, as the trench depth increases, the acceleration attenuation coefficients of the slabs decrease, and the vibration isolation effect of the trench is gradually enhanced. From the acceleration attenuation curves of slab 1 on the 1 st, 4 th, 6 th, and 9 th floors, it can be seen that the isolation effect of the trench on low-frequency vibrations below 8 Hz is weaker than its effect on mid- to high-frequency vibrations in the range of 8-200 Hz. For trench depths of 4.5 m and 6.0 m, the minimum acceleration attenuation coefficients within the main vibration frequency range of 1-80 Hz are both less than 0.3, and the attenuation coefficients for high-frequency vibrations in the range of 160-200 Hz are even below 0.1. This indicates that the slab vibrations are effectively reduced. However, for the trench depth of 1.5 m, the acceleration attenuation coefficients for vibrations in the range of 1-200 Hz are generally higher than those of the other three conditions, with more frequency points showing vibration amplification. This indicates that the vibration isolation effect is relatively weaker. Figure 18: Layout of open trench. Figure 20 shows the Z-vibration levels of slab 1 on each floor under different trench depths. When the trench depth is 1.5 m, the Z-vibration levels of the slabs on floors 1-9 are reduced by 3.3-5.9 dB. When the trench depth is 3 m, the Z-vibration levels are reduced by 4.8-10.2 dB. For a trench depth of 4.5 m, the Z-vibration levels are reduced by 8.9-13.2 dB. When the trench depth reaches 6 m, the Z-vibration levels are reduced by 11.0-17.2 dB. It can be observed that as the trench depth increases, the vibration isolation effect becomes stronger, and the Z-vibration levels of the slabs decrease continuously. When the trench depth reaches one Rayleigh wavelength of the surface soil, the Z-vibration levels of the over-track building slabs can be reduced by more than 10 dB.