Mesoscopic Heterogeneous Modeling Method for Polyurethane-Solidified Ballast Bed Based on Virtual Ray Casting Algorithm

This study introduces a mesoscale modeling methodology for polyurethane-solidified ballast beds (PSBBs) that eliminates reliance on X-ray computed tomography (XCT) and addresses constraints in specimen size, capital cost, and post-processing complexity. The approach couples the Discrete Element Method (DEM) with the Finite Element Method (FEM). A high-fidelity discrete-element geometry is reconstructed from three-dimensional laser scans of ballast particles. The virtual-ray casting algorithm is then employed to identify the spatial distribution of ballast and polyurethane and map this information onto the finite-element mesh, enabling heterogeneous material reconstruction at the mesoscale. The accuracy of the model and mesh convergence are validated through comparisons with laboratory uniaxial compression tests, determining the optimal mesh size to be 0.4 times the minimum particle size (0.4 Dmin). Based on this, a parametric study on the effect of sleeper width on ballast bed mechanical responses is conducted, revealing that when the sleeper width is no less than 0.73 times the ballast bed width (0.73 Wb) an optimal balance between stress diffusion and displacement control is achieved. This method demonstrates excellent cross-material applicability and can be extended to mesoscale modeling and performance evaluation of other multiphase particle–binder composite systems.