11. Model for Vertical Dynamic Analysis of the Vehicle–Track–Subgrade–Ground Coupling System

Chapters 6, 7, 8, 9, and 10 detailed several models and their algorithms for vertical dynamic analysis of the vehicle-track coupling system. These analyses excluded subgrade and ground effects, instead simplifying the subgrade as viscoelastic damping elements. However, an accurate assessment of the vehicle-induced dynamic actions on track structures must account for interactions among the vehicle, track, subgrade, and ground. In this chapter, both the slab track-embankment-ground system model and the ballast track-embankment-ground system model under moving loads are established, and the flexibility matrices for the moving vehicle at the wheelset and for the track structure at the wheel–rail contact point are derived respectively. By incorporating moving axle loads and track irregularity, an numerical algorithm for the coupled vibration analysis of the moving vehicle-track-subgrade-ground system is presented. As an application case, dynamic response analysis of a high-speed train-track-subgrade-ground coupling system is carried out.