Modelling track and ground vibrations for a slab ballastless track as an infinitely long periodic structure subject to a moving harmonic load

Abstract

This paper presents a model for predicting ground vibration generated from a slab ballastless track, subject to a moving harmonic load. The track consists of four layers: two rails, track slabs, bed plates and a track base resting on the ground. Different from existing models for slab tracks, the one developed in this paper takes into account both the discrete supports to the rail and the discontinuity of the slabs and bed plates, and treats the track/ground system as an infinitely long periodic structure. The rail and the base are represented as, respectively, an infinitely long Timoshenko beam and an infinitely long Euler-Bernoulli beam. The slabs and bed plates are modelled as Euler-Bernoulli beams of finite length, of which the responses are formulated using the mode superposition method. By using square window functions, the differential equations of motion of each track slab and bed plate are defined for the entire track length. The ground is idealised to be a horizontally layered structure. The steady-state response of the track/ground system is sought and formulated in the frequency-wavenumber domain. By using the periodic condition of a periodic structure, it is shown that the steady-state response of the track/ground system can be determined by the modal coefficients of the slabs and plates in the 0th unit cell (the 0th bay). Formulae are derived for these modal coefficients. Results including receptances of the rail, displacement spectra of the ground and critical speeds of an axle load are produced for two sets of track/ground parameters and compared with those when the slab and bed plates are assumed to be continuous beams, demonstrating when the later treatment works. The role of veering in dispersion curves of a periodic track in critical speed is identified. Formulations in this paper can be directly applied to the Chinese CRTS II and III tracks on a layered ground. They provide a basis for developing a complete ground vibration prediction model that incorporates a moving train, an infinitely long periodic track and a homogeneous or horizontally layered ground. They can also be used to assess if a periodic track/ground system can be simplified to be invariant in the track direction.