Analysis of Dynamic Response of Ballasted Rail Track Under a Moving Load to Determine the Critical Speed of Motion

Purpose The critical speed of a railway track is the speed at which the vibration occurs at the largest magnitude. Thus, its identification is necessary to prevent derailments and damage to the rail tracks. The present study attempted a three-dimensional finite element analysis of a typical ballasted rail track under a single moving wheel load at different speeds to evaluate the critical speed. Methods The track’s ballast, subballast, and subgrade layers (substructure) were modeled as elastoplastic material with material damping and radiation damping (infinite layers). Track response was recorded in the form of stress, displacement, velocity, and acceleration responses to identify the critical speed of the rail track. Different parameters were analyzed to find the critical speed, such as the method of applying moving load, the material model of the primary load-carrying layer (ballast), the effect of boundaries, and the type of data extracted from the output databases. Parametric studies were performed on material damping and stiffness of track substructure layers to see their effect on the track’s dynamic response. The effect of shear strength parameters (cohesion and friction) of the subgrade was also analyzed to examine their effect on the critical speed of the rail track. Results and Conclusions The study shows that the combination of vertical velocity, stress, and acceleration trends can be used to identify the critical speed of the rail track. Young’s moduli of substructure do not show direct proportionality with the critical speed. The damping ratio has a small but noticeable effect on the critical speed, while the increase in shear strength of the subgrade increases the critical speed. A phase-lag was observed as the speed transitions from subcritical to supercritical. The critical speed from the finite element analysis shows a good agreement with the shear and Rayleigh wave velocities calculated from empirical approximations.