# 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  
The effects of trench depth, width, and position on vibration isolation performance were discussed in detail above. It was found that trenches with a certain excavation depth can achieve good vibration isolation performance. However, in practical engineering, the excavation of vibration isolation trenches should also consider factors such as construction convenience, long-term maintenance, and the impact of the trench on the structural stability and safety of the depot. Therefore, compared to open trenches, infilled trenches have greater advantages. The vibration isolation mechanism of infilled trenches involves filling the trench with specific materials (e.g., gravel, concrete, rubber, fly ash, foam, etc.) to create differences in stiffness and shear wave velocity between the trench and the surrounding soil. This causes vibration waves to undergo reflection and refraction at the trench walls, which increases the propagation path and reduces the propagation speed of the waves, thereby achieving the effect of vibration isolation. The concept of impedance was first introduced in the field of acoustics. It is defined as the product of the medium density \(\rho\) and the wave velocity \(v\) within the medium. The impedance ratio refers to the ratio of the impedance \(\rho_{1}v_{1}\) of the first medium to the impedance \(\rho_{2}v_{2}\) of the second medium [39]. The specific formula is shown as follows:  
\[\alpha=\frac{\rho_{1}v_{1}}{\rho_{2}v_{2}} \tag{6}\]  
Figure 24: Influence of open trench position on floor Z-vibration level. For vibration isolation infilled trenches, the impedance ratio is an important factor for evaluating the vibration isolation performance of the medium. In practical engineering, the first medium is typically the filling material, while the second medium is the soil surrounding the infilled trench. Table 8 presents the physical properties of commonly used filling materials and the impedance ratios between the filling materials and the topsoil. Based on the impedance ratio, filling materials can be classified into rigid materials and flexible materials. Materials with an impedance ratio greater than 1 are classified as rigid materials, while those with an impedance ratio between 0 and 1 are classified as flexible materials. In this study, six materials from Table 8 were selected as filling materials. Among them, gravel, lightweight aggregate concrete (LAC), and C30 concrete have impedance ratios greater than 1 compared to the topsoil and are classified as rigid materials. Fly ash, rubber, and foam have impedance ratios less than 1 and are classified as flexible materials. The depth of the infilled trenches was set to 6 m, the width to 0.5 m, and the relative distance to 2.4 m from the track centerline. The specific layout of the infilled trench is shown in Figure 25.  
Figure 26 shows the acceleration attenuation of slab 1 on the 1 st, 4 th, 6 th, and 9 th floors under the filling of three rigid materials. Figure 27 shows the acceleration attenuation of the same slabs under the filling of three flexible materials. It can be observed that different filling materials exhibit varying vibration isolation effects. For rigid infilled trenches, the overall vibration isolation effect of gravel infilled trench is the weakest. The acceleration attenuation coefficients fluctuate slightly around 1 in the 1-80 Hz frequency range, indicating almost no vibration isolation effect. The vibration isolation effects of the LAC infilled trench and C30 concrete infilled trench are better than that of the gravel infilled trench. Certain vibration isolation effects are observed in both types of trenches within the frequency ranges of 8-16 Hz, 31.5-63 Hz, and 160-200 Hz. For flexible infilled trenches, the foam infilled trench exhibits the best overall vibration isolation effect in the 5-125 Hz frequency range, followed by the rubber infilled trench, while the fly ash infilled  
Figure 25: Layout of infilled trench.