Simulation of dynamic train–track interaction with state-dependent track properties

A previously published numerical method for simulation of vertical dynamic interaction between a train and a railway track is expanded to account for state-dependent track properties. Track properties are separated into linear contributions corresponding to an unloaded track, and non-linear contributions that are dependent on the time-variant state of the different track components due to the dynamic loading from a moving train model. A complex modal superposition is adopted to decouple the equations of motion of the linear track model with a non-proportional spatial distribution of viscous damping. The state-dependent properties are accounted for by applying equivalent transient external forces to the corresponding nodes of the linear finite element model of the track. Simulations are carried out in the time domain with a moving mass model. The need for a state-dependent track model is discussed with respect to reported field and laboratory measurements. The numerical method and the state-dependent track model are validated versus field measurements of wheel–rail contact force and rail bending moment as caused by a 100 mm long and 0.9 mm deep wheel flat.