Vol.:(0123456789) 1 3 Journal of Vibration Engineering & Technologies https://doi.org/10.1007/s42417-022-00741-3 ORIGINAL PAPER Analysis of Dynamic Response of Ballasted Rail Track Under a Moving Load to Determine the Critical Speed of Motion Pranjal Mandhaniya 1  · J. T. Shahu 1  · Sarvesh Chandra 2 Received: 18 May 2022 / Revised: 25 September 2022 / Accepted: 7 October 2022 © Krishtel eMaging Solutions Private Limited 2022 Abstract Purpose The critical speed of a railway track is the speed at which the vibration occurs at the largest magnitude. Thus, its identifcation is necessary to prevent derailments and damage to the rail tracks. The present study attempted a three- dimensional fnite element analysis of a typical ballasted rail track under a single moving wheel load at diferent 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 (infnite layers). Track response was recorded in the form of stress, displacement, velocity, and acceleration responses to identify the critical speed of the rail track. Diferent parameters were analyzed to fnd the critical speed, such as the method of applying moving load, the material model of the primary load-carrying layer (bal- last), the efect of boundaries, and the type of data extracted from the output databases. Parametric studies were performed on material damping and stifness of track substructure layers to see their efect on the track’s dynamic response. The efect of shear strength parameters (cohesion and friction) of the subgrade was also analyzed to examine their efect 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 efect 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 fnite element analysis shows a good agreement with the shear and Rayleigh wave velocities calculated from empirical approximations. Keywords Ballasted track · Finite element analysis · Critical speed · Moving load · Infnite layers · Elastoplastic · Wheel motion Introduction High-speed rail transportation requires a careful design of a rail track. The frst step of design is to analyze the capac- ity of existing infrastructure and improve it based on the requirements. The capacity of a transportation system (e.g., rail track or highway) can be accessed in the form of feasible speed of motion and load-bearing capacity. These quantities can be manipulated to control the trafc on the transport infrastructure, thus, allowing its application at its fullest without damage. The speed of motion that can cause sig- nifcant damage to a rail track is generally termed the critical speed of motion. The critical speed, similar to the resonant frequency for a structure, causes the vibrations to magnify at their peak [1, * Pranjal Mandhaniya pranjalmandhaniya@gmail.com J. T. Shahu shahu@civil.iitd.ac.in Sarvesh Chandra sarviitk@gmail.com 1 Department of Civil Engineering, Indian Institute of Technology Delhi, Delhi 110016, India 2 Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India