## 1 Introduction  
The urban rail transit system possesses numerous advantages, including its high transport capacity, ability to alleviate traffic congestion and pollution, speed and efficiency, reliability, as well as comfort and safety. These attributes render it an indispensable component of contemporary urban transportation planning. The development of urban rail transit has been progressing rapidly and plays a pivotal role in contributing to the socio-economic landscape. To address the issue of urban land scarcity and provide financial support for metro operations, an increasing number of over-track buildings are being constructed above metro lines. However, train operations can result in noticeable vibrations for individuals residing or working in buildings located above the tracks, leading to discomfort and potential adverse effects on human health [1, 2]. Therefore, comprehending and assessing the impact of train-induced vibrations on these buildings is crucial for implementing necessary mitigation measures. Two highly accurate methods for assessing the impact of train-induced vibrations on buildings are available: on-site measurements and numerical modeling. Regarding on-site measurements, previous studies have been conducted to investigate the characteristics of indoor vibrations in buildings located along rail transit lines [3; 4; 5; 6]. Additionally, scholars have performed on-site vibration measurements at metro depots with over-track buildings to examine the effects of train-induced vibrations and conduct comprehensive analyses regarding the internal transmission laws within these structures [7; 8; 9; 10]. Furthermore, some researchers have also carried out on-site vibration measurements focusing on soil-structure interaction in adjacent or over-track buildings [11]. Numerical modeling has been employed by scholars to accurately predict the vibration effects of rail traffic on adjacent or over-track buildings, with some establishing a train track-soil-building model [12; 13; 14], while others have conducted dynamic interaction studies of vehicle-track-bridge-soil [15; 16; 17; 18; 19; 20] to investigate the behavior of rail bridges and soil-structure effects. Some scholars have taken into account the soil-structure interaction effect to investigate the dynamic interplay between soil inclusion and soil properties [21; 22]. Some scholars have also taken into account the soil-structure interaction effect to investigate the impact of the vibration induced by train operation on adjacent or over-track buildings [23; 24; 25; 26]. There are relatively few studies on the propagation of vibrations in buildings above tracks caused by train operation in different construction stages [27; 28; 29; 30]. By investigating the impact of the surface foundation on ground vibration during the construction phase, [PERSON] et al. [27] examined the response of flexible plates made of homogeneous or layered soil to horizontal propagation waves in terms of distance and frequency. [PERSON] et al. [28] analyzed the lateral and vertical pile loading effects, as well as the influence of the pile length, to study the dynamic source-receiver interaction between an underground railway tunnel and a pile foundation during the construction stage. [PERSON] et al. [29] investigated the impact of construction activities on the vibration characteristics of building foundations during the construction phase and proposed a simplified model for analyzing the influence of additional structures. [PERSON] et al. [30] studied the variation in ground vibration levels during the construction phase, with the progress of construction, and analyzed the effects of additional foundations and additional buildings on the attenuation or amplification of ground vibration levels caused by buildings through coupling loss. In summary, a plethora of field measurements are available on the vibration caused by train operation on adjacent or over-track buildings and related soil-structure interaction.