A mixed space-time and wavenumber domain model for predicting ground vibration from railway tracks

Abstract

In this paper, a mixed model for studying ground vibration generated from surface railway tracks is presented. A ballasted track with nonlinear resilient components is modelled in the time domain using the Finite Element method. The ground is modelled as a linear homogeneous half-space in the wavenumber domain for faster computation. The interaction between the track and the ground is incorporated into the track model through a lumped parameter model representing the vertical dynamic stiffness of the ground. The coefficients of the components of the lumped parameter model are obtained by curve fitting of the transfer function of the half-space for a load applied at its origin. The coupled equation of motion for the track/ground system is formulated with excitation from a stationary point load-consisting of static and dynamic partsacting at the centre of the rail. The coupled equation is solved by numerical integration. The calculated interaction forces at the ballast/ground interface from the space-time domain track model are Fourier transformed to the wavenumber domain and used as excitation to the ground model in order to calculate free-field surface vibration of the ground. Results are presented for the vertical dynamic stiffness for the ground, and for the track and ground displacement in the vicinity of the track and in the free-field. A comparative study between the mixed formulation with the lumped parameter model for the ground, and a fully coupled wavenumber domain model is conducted for linear parameters. Using the fully coupled model as a benchmark, it is observed that the inclusion of the lumped parameter ground model in the track model gives good estimation of the transmitted forces, and hence ground vibration, both in the near and far fields. Finally, the effect of nonlinear track components is briefly investigated for different levels of static preload.