Discrete element method-finite difference method coupled analysis of dynamic response in reinforced ballast-subgrade systems under moving train loads

In existing studies on reinforced ballast beds, dynamic loads are predominantly applied as fixed-point excitation. This approach fails to replicate the stress deflection effect generated in substructure elements by actual moving train loads. Moreover, the subgrade structure is frequently omitted in such studies, resulting in an unclear understanding of how reinforced ballast beds influence the dynamic response of the subgrade. Therefore, this study employs a coupled discrete element method–finite difference method (DEM–FDM) to establish a ballast–subgrade coupled numerical model. The model is used to comparatively investigate the effects of ballast reinforcement on the responses of both ballast particles and the subgrade under moving train loads. The results indicate that ballast reinforcement increases the diffusion angle α beneath the sleeper by approximately 7°, thereby promoting the extension of force chains further into the inter-sleeper zone. This effectively mitigates stress concentration within the ballast bed. The increase in the total energy dissipation of the system after reinforcement is primarily supplied by damping energy, while the reduction in frictional energy helps alleviate wear among ballast particles. Since reinforcement enhances the overall energy dissipation capacity of the ballast bed, the dynamic stress at various depths within the subgrade is reduced. Specifically, the peak dynamic stress at the subgrade surface and the bottom of the subgrade bed is decreased by 13.4% and 2.2%, respectively. Compared with an unreinforced ballast bed, the variation in the rotation angle of the principal stress axis within the subgrade is reduced after reinforcement. This reduction helps alleviate subgrade settlement issues induced by the rotation of the principal stress axis.