## 4 Case Study and Analysis of Vibration Control Effect
### Analysis of Ground Vibration-Reduction Effect  
Figure 15 shows a comparison of the ground vertical acceleration at the detection point calculated using the model under the SFST conditions before and after the periodic row piles were installed in the time domain. Figure 16 shows a comparison of the one-third octave curves of the calculated ground vertical vibration acceleration under the normal track, SFST and comprehensive vibration reduction and isolation conditions.  
Figure 14: 3D track bed–tunnel–soil row pile FE model.  
Figure 12: Bandgap calculation results.  
Figure 13: The ground vibration acceleration corresponds to different pile lengths.  
After using the local resonant periodic row piles, the ground vibration acceleration in the time domain decreased compared with that before using the row piles, with a peak vibration acceleration decrease of approximately 10% and RMS value decrease of 0.2 \(\times\) 10\({}^{-4}\) m/s\({}^{2}\) (Figures 15 and 16). In the frequency domain, the vibration waves in the 7-9 Hz frequency range were effectively blocked by the periodic row piles, resulting in a decrease of approximately 3-5 dB for the ground vibration acceleration near the natural vibration frequency of the SFST (6-12 Hz) compared with when row piles were not used. Furthermore, the ground vibration acceleration was significantly lower than the acceleration under ordinary track conditions at the natural vibration frequency of the SFST. The use of periodic row piles eliminated the adverse effect of the FST on the increase in ground vibration in the frequency range near its natural frequency. The combined control method proposed in this study controls ground vibrations induced by metro train operations in the full-frequency range.  
Furthermore, the material composition of the row piles was varied to determine the low-frequency vibration control effect on the ground based on the vibration control collaborative method. Local resonance row piles were replaced with hollow row pipe piles. Specifically, the rubber was replaced with concrete, and the original concrete pile position was designed to be hollow. The ground vibration accelerations at the detection point under the conditions of the SFST only, SFST with local resonance row piles and SFST with rows of hollow pipe piles were calculated using the model (Figure 17).  
The method with hollow row pipe piles could further reduce the ground vibration in the time domain, with an RMS value decrease of 0.12 \(\times\) 10\({}^{-4}\) m/s\({}^{2}\) (Figure 17). Furthermore, from a frequency-domain perspective, the vibration in the 7 Hz low-frequency range significantly decreased by 4-10 dB, and the ground vibration of other frequency bands did not change compared to the condition comprising the local resonance row piles. At the natural  
Figure 16: One-third octave spectrum curves of ground vibration acceleration under three working conditions.  
Figure 15: Time histories of ground vibration acceleration with and without periodic row piles.  
frequency of the SFST, the ground vibration level was still lower than that of the ordinary track condition when the combined control method of the SFST and hollow row pipe piles were used, although it was slightly higher than that of the control method combined with local resonance row piles. Overall, the comprehensive vibration control method of the FST with hollow row pipe piles can control ground vibration in the full-frequency range, and it is more effective than other methods in low-frequency vibration control.