## 1 Introduction
[44] conducted a detailed study on the blocking effect of periodic in-filled pipes on low-frequency (1-10 Hz) vibration. [PERSON] et al. [10; 45] investigated the vibration reduction effect of periodic pile barriers with specially designed bandgaps. They found that vibration waves of specific frequencies could be prevented from propagating in the formation by designing the bandgaps of the periodic piles. The successful application of periodic row piles for specific frequency-band vibration isolation in the field of engineering vibration isolation provides a novel idea for the comprehensive vibration isolation design of metro train-induced vibrations by adjusting the bandgap design of periodic row piles. Overall, with the improvement of precision instruments and other equipment, their requirements for environmental vibration have significantly increased in recent years. Many universities and research institutions have been equipped with high-precision instruments with vibration requirements of VC-D or VC-E levels [46]. The phenomenon that the application section of FST amplifies the ground vibration at its natural frequency is unacceptable for such instruments. In the past two years, multiple universities and scientific research institutions in Tianjin, such as Nankai University, have complained about the adverse effects of ground vibration below 10 Hz on instruments in the FST section, resulting in economic losses and legal consequences for the metro operator. Meanwhile, the legal consequences of train-induced structure-borne noise and vibration are also very noteworthy [47]. Taking China as an example, the Law of the People's Republic of China on the Prevention and Control of Noise Pollution [48] was issued in 2022, which strictly regulates noise pollution from the national level, including the issue of train-induced structural secondary noise. If this issue is not properly addressed, it will inevitably lead to subsequent legal issues. A full-frequency control method for train-induced environmental vibration needs to be proposed urgently. According to previous studies, the control of environmental vibrations caused by metro trains is often conducted using a single approach. A vibration control method that combines vibration source reduction and propagation path isolation may be extremely effective in minimizing the impact of train operations on the surrounding sensitive buildings and precision instruments and achieving vibration reduction and iso lation within the full-frequency range. In this study, an environmental vibration control method that combines FST with periodic row piles was developed, which is based on the bandgap theory and considers frequency matching. First, a novel 3D train-FST coupling analytical model in the frequency domain and a 3D tunnel-soil finite element (FE) model were established to predict ground vibration (Section 2). Second, field measurements were performed to determine the ground vibration responses of an existing metro line in Tianjin to calibrate the model calculation results (Section 3). Subsequently, the parameters of the FSTs and periodic row piles were designed, which was based on the bandgap theory, and the ground vertical acceleration levels were calculated to compare and analyse the vibration control effect for the different cases (Section 4). The conclusions of this study are presented in Section 5. Notably, the 3D train-FST coupled analytical model in the frequency domain is proposed for the first time, and the idea of comprehensively using floating slab tracks and row piles, considering bandgap theory, to control train-induced ground vibration is also novel.