Prediction of ground vibration from trains using the wavenumber finite and boundary element methods

Ground vibration is an important aspect of the environmental impact of rail traffic. Vibration from about 2–200 Hz is caused by trains moving on the ground surface or in tunnels. The wave field thus created must be modelled in three dimensions because of the excitation under each axle and the movement of the train. For arbitrary geometry of structures and ground surface to be allowed in the analysis, numerical models are required. In most practical situations, the ground and built structures, such as tunnels and tracks, can be considered to be homogeneous in the track direction and may be modelled using the wavenumber finite/boundary element method which is formulated in terms of the wavenumber in that direction. Compared with a conventional, three-dimensional finite/boundary element model, this model is more computationally efficient and requires far less memory since discretization is only made over the vertical–transverse section of the ground and/or built structures. With this model it is possible to predict complete vibration spectra. In this paper, the wavenumber-based modelling approach is outlined and then the applicability of the method to surface vibration and tunnel vibration analyses is demonstrated.