# Train-Induced Vibration Analysis and Isolation Trench Measures in Metro Depot Structures
## 1 Introduction  
In recent years, urban rail transit has developed rapidly in major cities around the world due to its high transportation efficiency, convenience, safety, and environmental friendliness. The metro depot, as an important component of the urban rail transit system, primarily provides necessary logistical services for the daily operation of metro trains. However, the large area of metro depots occupies significant land resources. Therefore, many cities both domestically and internationally have begun to implement Transit-Oriented Development (TOD) models. These models involve constructing large platforms on plannedrail transit parking lots (stations) and developing residential real estate on these platforms [1; 2]. While metro depots are extensively developed, vibrations caused by the frequent operation of trains are transmitted through the tracks, soil, and structural columns to the buildings above. This transmission leads to floor vibrations and radiated noise, as shown in Figure 1, which severely impacts people's normal lives [3; 4; 5]. Therefore, it is of great significance to effectively reduce the train-induced vibrations of the floors. Based on the vibration transmission chain, the problem of train-induced vibrations in metro systems can be divided into three subsystems: \"vibration source, transmission path, and sensitive target\". Accordingly, train vibration control can be categorized into three parts: active vibration reduction at the source, vibration isolation along the transmission path, and passive vibration isolation of building structures. Vibration control at the source is typically divided into train-based measures and track-based measures. For train-based measures, researchers [6; 7; 8] have noted that train characteristics, such as train weight, operating speed, and the conditions of wheels and rails, are key factors influencing vibrations. Reducing train weight, lowering operating speed, and maintaining the smoothness of wheels and rails can effectively reduce train-induced vibrations. For track-based measures, methods such as vibration reduction at fasteners [9; 10], sleepers [11], and ballast beds [12; 13; 14] have been proposed. These measures have demonstrated good vibration reduction effects when applied in engineering practices. For passive vibration isolation of building structures, many researchers have suggested laying flexible vibration isolation pads at building foundations [15] or installing steel spring supports and rubber bearings [16; 17; 18] to isolate vibrations. Others have proposed using floating floor systems [19; 20] to reduce floor vibrations. Although these two methods can effectively reduce vibrations in building structures, their application to existing rail lines and nearby buildings often requires secondary modifications to tracks and structures, which increases construction difficulty. In contrast, vibration isolation along the transmission path can avoid these challenges. Furthermore, selecting appropriate vibration isolation measures along the transmission path can simultaneously reduce vibrations for multiple sensitive targets, providing higher efficiency. Currently, many studies focus on vibration isolation measures along the transmission path. In terms of isolation trenches, [PERSON] [21] and [PERSON] [22] investigated the vibration isolation performance of open trenches using the boundary element method. [PERSON] [23] and [PERSON] [24] conducted full-scale experiments on foam infilled trenches and explored their vibration isolation effects. [PERSON] et al. [25] conducted large-scale experiments to study the isolation effects of open trenches and gravel  
Figure 1: Train vibration propagation. infilled trenches under single-frequency load excitation. Numerous practical applications of infilled trenches have been reported worldwide, achieving favorable results. For example, in 1984, air-cushion-filled trench was first used in Stockholm, Sweden [26], reducing floor vibration in buildings by more than 70%.