Mathematical Modeling of the Rail Track Superstructure–Subgrade System

The “rail track superstructure–subgrade” system is a sophisticated engineering structure critical in ensuring safe and efficient train operations. Its analysis and design rely on mathematical modeling to capture the interactions between system components and the effects of both static and dynamic loads. This paper offers a detailed review of contemporary modeling approaches, including discrete, continuous, and hybrid models. The research’s key contribution is a thorough comparison of five primary methodologies: (i) quasi-static analytical calculations, (ii) multibody dynamics (MBD) models, (iii and iv) static and dynamic finite element method (FEM) models, and (v) wave propagation-based models. Future research directions could focus on developing hybrid models that integrate MBD and FEM to enhance moving load predictions, leveraging machine learning for parameter calibration using experimental data, investigating the nonlinear and rheological behavior of ballast and subgrade in long-term deformation, and applying wave propagation techniques to model vibration transmission and evaluate its impact on infrastructure.