Numerical investigation on mesoscopic and macroscopic behaviours of ballasted track in steep-gradient rack railways under gear-rack traction using coupled MFBD-DEM

Rack railway represents a distinctive solution for mountain rail transportation due to its superior adaptability to steep gradients, but the gear-rack traction mechanism introduces complex longitudinal forces that may challenge track stability. This study employs a coupled Multi-Flexible-Body Dynamics-Discrete Element Method (MFBD-DEM) framework to develop a rack train-ballasted track interaction model. The proposed model enables closed-loop force-displacement transmission among the train, track, and discrete ballast bed, and its reliability is validated through field dynamic tests. Based on this model, both mesoscopic ballast behaviour and macroscopic track responses were examined under straight-line operation on a 360‰ gradient. The results reveal that, compared with the conventional wheel-rail driving method, the gear-rack driven system promotes enhanced longitudinal migration of ballast particles. As train speed increases, the dominant particle velocity direction expands from 255°–270° to 210°–270°, indicating a more pronounced downslope flow tendency. Furthermore, the sleepers experience approximately 0.1–0.2 mm permanent longitudinal displacement and 0.3°–0.5° of cumulative rotation during operation, suggesting the risk of irreversible longitudinal deformation within the track structure.