Frequency Spectra Analysis of Vertical Stress in Ballasted Track Foundations: Influence of Train Configuration and Subgrade Depth

Railway tracks experience stress during train passage. Understanding these subgrade stresses is essential for the design of track foundations and assessing their serviceability. However, few studies have explored the theoretical aspects of stress response in relation to train configuration. Therefore, this paper introduces a subgrade stress model for ballasted tracks, aiming to analyze the stress fields in track foundations under train loading. The model employs a unit impulse approach to represent the periodic axle sequence of a train moving at constant speed. It characterizes vertical stress transmission within geotechnical media using stochastic diffusion theory. With train configuration, track structure, and soil properties as inputs, the model can reconstruct the quasi-static time history and frequency spectrum of vertical subgrade stress at various depths. Frequency analysis indicates that as the number of axles increases, the dominant stress frequencies first align with integer multiples of the “bogie-passage frequency” and subsequently with integer multiples of the “vehicle-passage frequency.” Zero magnitudes may appear at dominant frequencies, depending on a vehicle's length and wheelbase. Peak stress magnitudes rapidly diminish at higher frequencies, with this attenuation becoming more pronounced as subgrade depth increases. The proposed model accounts for the structural features of trains and tracks, as well as the material properties of subgrade fills. It elucidates the mechanisms driving the quasi-static response of the subgrade when subjected to passing trains.