Numerical investigation of train-induced ground vibrations in ballastless embankment considering wheel–rail geometric nonlinearity

Predicting train-induced ground vibrations is essential for assessing the environmental impact of high-speed rail systems. However, many existing numerical models rely on simplified wheel–rail interaction formulations, which can lead to unreliable predictions due to inaccurate representation of the excitation source. In this study, a novel three-dimensional (3D) Vehicle–Track–Embankment–Ground (VTEG) finite element (FE) model is developed, explicitly incorporating rail irregularities and fully coupled wheel–rail geometric interaction. The proposed model is validated against field measurements in terms of subgrade dynamic soil stresses and ground surface vibration velocities. A parametric case study identifies two characteristic velocities. Critical Velocity I (CV I) closely corresponds to the Rayleigh wave velocity of the weakest supporting soil layer, whereas Critical Velocity II (CV II), associated with the peak maximum dynamic displacement (MDD) of track, lies between the Rayleigh wave velocities of the softest ground layer and the embankment base. Comparative analyses show that a conventional 2.5D linear FE model provides adequate accuracy under weakly dynamic conditions (V ≤ CV I) but progressively underestimates the track MDD as train speed approaches CV II. At CV II, the peak MDD is underestimated by approximately 14.6% relative to the proposed 3D nonlinear model, with about 54% of this discrepancy attributable to reduced model dimensionality and the remaining 46% to linear wheel–rail contact assumptions. Furthermore, foundation reinforcement markedly increases both CV I and CV II and reduces the peak MDD by approximately 43.5%, thereby effectively mitigating resonance-like behaviour at ultra-high train speeds. In addition, foundation reinforcement significantly suppresses ground-borne vibrations and modifies the characteristics of surface wave propagation, producing more circular wavefronts within the reinforced zone while maintaining Mach-cone-type features outside. These findings provide quantitative guidance for vibration assessment, modelling strategy selection and mitigation design in high-speed railway engineering.