Mfm Hussein

Modelling of floating-slab track with discontinuous slab part 1: response to oscillating moving loads

This paper presents three different methods for modelling a track with discontinuous slab under oscillating moving loads. These are the Fourier-Repeating-unit method, the Periodic-Fourier method and the Modified-phase method. The first two methods, borrowed from the literature of periodic infinite structures, are accurate if careful consideration is taken when performing numerical integrations. The third method, not presented elsewhere before, is faster and simpler; it is only valid for velocities of moving loads lower than the critical velocity of the track, but this “velocity effect” is of no consequence for underground railways. Discontinuity of slab provides a parametric excitation for moving loads over floating-slab tracks. It is shown that in the frequency range of ground-borne vibration, more vibration propagates form such tracks at resonance frequencies of the slabs, compared with tracks with continuous slabs. It is found that the velocity effect is insignificant when calculating displacements of a typical floating-slab track under oscillating moving loads with velocities less than 100km/hr. However, a correction has to be made to account for the right phase between the input force and the output displacement.

Modelling of floating-slab track with discontinuous slab part 2: response to moving trains

A floating-slab track with discontinuous slab provides a spatially-varying stiffness under a constant moving load. When a train moves on such a track, even with the absence of rail roughness, a parametric excitation develops as wheels move up and down applying dynamic forces at the wheel-rail interface. The dynamic force is magnified if one of its principal frequencies matches with any of the train or the track resonance frequencies. In this paper, a new method based on a Fourier series representation is developed to couple a moving train to a track with discontinuous slab. A two-degree-of-freedom system is used to model a quarter of a train with four axles and two bogies moving on a track with constant velocity. The purpose of this work is to investigate the dynamic effect of slab discontinuity on trains running in underground railway tunnels, where the velocity is less than 100km/hr. For typical parameters of a train and a track, it is found that the force at the wheel-rail interface is only increased by 1% of its static value due to slab discontinuity. However, the dynamic effect may be more important in circumstances where high-speed or heavy-axled trains are used in underground tunnels.

A coupled periodic FE-BE model for ground-borne vibrations from underground railways

An efficient and modular numerical prediction model is presented to predict vibrations in the free field due to metro trains in the tunnel. The three-dimensional dynamic tunnel-soil interaction problem is solved with a subdomain formulation, using a finite element formulation for the tunnel and a boundary element method for the soil. The periodicity of the tunnel and the soil in the longitudinal direction is exploited using the Floquet transform, limiting the discretization effort to a single bounded reference cell. The Craig-Bampton substructuring technique is used to efficiently incorporate a track in the tunnel. The track-tunnel-soil interaction problem is solved in the frequency-wavenumber domain and the wave field radiated into the soil is computed.