Longitudinal stability and state evolution analysis of ballasted track in steep-slope rack railway

To address ballast bed sliding and structural instability in rack railways operating on steep gradients, this study developed a coupled Multi-Flexible-Body Dynamics–Discrete Element Method (MFBD-DEM) model to investigate the mechanism by which an enhanced steel sleeper improves the longitudinal stability of ballasted track. Cyclic train loading was further applied to the DEM ballast bed model to simulate the evolution of track condition over the service period. The results show that increasing gradient weakens the longitudinal load-carrying capacity of the ballast bed, whereas the enhanced sleeper improves both longitudinal and lateral track stability by strengthening the sleeper–ballast interface constraint. Further analysis indicates that ballast particles undergo continuous migration under the combined action of downslope gravity and dynamic loading, leading to thinning of the upper ballast bed and an increased risk of local track deformation. Increasing the initial compactness level of the ballast bed effectively reduces particle mobility, thereby mitigating structural settlement and enhancing overall stability. Based on the analysis, the ballast bed density prior to commissioning of lines with a 480‰ gradient should not be lower than 1.67 g/cm 3 , and it is recommended to maintain a density of 1.70 g/cm 3 or above. This recommended value is also expected to satisfy the operational requirements of rack railway lines with lower gradients.