Passing trains generate vibrations in the soil, caused by the train response to track irregularities. This is particularly the case in soft-soil regions, where the surface wavespeed is comparable to the train speed. Interaction between ground vibrations and the train can give rise to di!erent e!ects. On the one hand, the waves generated by an axle can in#uence the vibration of adjacent axles. There is some concern that interaction between axles, through vibrations propagating in the near subsurface, might lead to stronger vibrations or even instabilities. This interaction mechanism is investigated in the present paper. On the other hand, the waves can propagate to nearby structures and cause annoyance to people living or working in these buildings (or even damage the buildings).
The e!ect of a train of vertical loads on a half-space has been discussed by Alabi [1]. Krylov [2] investigates the e!ect of track dynamics on the vibrations due to high-speed trains. The vibrations generated by the bending track are computed with the aid of a Green function formulation and its far"eld asymptotic behavior in an elastic half-space. For trains travelling with a speed less than the Rayleigh-wave speed of the half-space, the presence of sleepers appears to be important for the generation of vibrations. In Krylov's study, the e!ect of dynamically induced loads was not considered. The e!ect of a moving load on a Timoshenko beam-half-plane system has been investigated by Suiker et al. [3]. Sheng et al. [4,5] investigate the vibrations of a harmonic load moving over a layered earth. The track, including rails, rail pads, sleepers and ballast, is modelled by means of a layered beam structure. They "nd that harmonic loads give rise to signi"cant vibrations.
In reference [6], Krylov investigates the e!ect of road humps on the excitation of axle}hop resonances. In this study of dynamically induced loads from a road vehicle, the interaction between di!erent axles is not taken into account. Herman [7] considers the problem of vibrations generated by the presence of heterogeneities near the track. The interaction between a mass}spring system moving along a beam on an elastic half-space is investigated by Metrikine and Popp [8]. They demonstrate that instabilities can arise if the