A decoupled numerical procedure for modelling soil interaction in the computation of the dynamic response of a rail track

The problem of vibration transmitted by train traffic to the soil in the case of railway lines in urban areas is gaining increasing attention in environmental impact analysis. An efficient method to consider both the train-track interaction in detail and the vibration transmitted to the soil nearby with an affordable computational cost is desirable. The paper proposes a numerical procedure based on a substructuring approach, in which the system is divided into three main subdomains: the train running on the track, the rail subjected to the loads coming from the train and the reactions from the sleepers and the “ground” sub-system, composed by the sleepers, the ballast with its subgrade and the actual ground. The overall procedure is divided into subsequent steps: first, the finite element modelling of the sleeper-ballast-subgrade combined system, characterized within the linear elastic field by means of frequency response functions at rail-sleeper interfaces. In a second step, moving loads transmitted to the track are computed by numerical time domain integration of the equations of motion of the train running on a model of the track only, in which the subgrade is modelled as a series of spring-damper elements, whose parameters are tuned according to the results of the FE model used in the first step and therefore consistent with it. Non-linear behavior of the rail-wheel interaction can be accounted for by the time-domain procedure. The track dynamics is finally computed via direct frequency domain analysis; the track is again modelled by Finite Elements, loaded by the forces transmitted by the train wheels and by the supporting sleepers. Finally, the vibrations propagated through the soil to a general receiver point are evaluated. The procedure can exploit favorable properties of frequency domain analysis in treating moving loads; in addition, frequency dependent properties of materials can be introduced.