3D discrete-continuum simulation of differential settlement in ballasted railway transition zones

The Discrete Element Method (DEM) is a powerful computational approach for analyzing granular materials, such as those found in railway embankments. While DEM offers high-resolution insights into particle-scale interactions by solving force-displacement equations based on Newtonian mechanics, its computational intensity and limitations in representing continuous structural components remain challenges. This study addresses two core issues in the DEM modeling of granular materials for high-speed railway applications. Firstly, the study investigates the impact of particle scaling techniques on the shear behavior and computational efficiency of granular materials with fine angular particles. By examining variations in particle size distribution and angularity, it is demonstrated that appropriate scaling can substantially reduce simulation time without compromising accuracy. Secondly, to address DEM's limitations in modeling continuous components such as rails and subgrade, a novel hybrid modeling approach is developed. This integrates a 3D DEM model for ballast and sub-ballast layers with a continuum-based Finite Difference Method (FDM) for rail beams and subgrade layers, and a nonlinear 2D Finite Element Method (FEM) to model vehicle–track dynamic interaction. The hybrid DEM–FDM–FEM framework enables the simulation of both short-term dynamic responses and long-term differential settlements in railway transition zones. A specialized Periodic Cell Replication Method is used to create large-scale DEM models, enhancing realism and computational efficiency. Validation against full-scale physical experiments and benchmark FEM models confirms the framework’s ability to capture critical mechanisms such as gap formation beneath sleepers, stiffness gradients, and vertical misalignment induced by repeated axle loads. Results reveal how abrupt stiffness transitions amplify dynamic loads, leading to progressive settlement and degradation of track geometry. The study highlights the importance of combining granular and continuum modeling techniques to more accurately predict and mitigate long-term degradation in ballasted railway transition zones. The study shows that a stiffness gradient at railway transition zones amplifies dynamic wheel–rail forces, leading to voided sleepers and a peak in ballast settlement a few meters into the softer track, highlighting the need for a gradual stiffness change to limit long-term differential settlement.