Abstract

The numerical models of the railway track are fundamental tools for the study of their dynamic behaviour, with implications for the safety and comfort of rail transport and the degradation and need for maintenance of the track. The importance of these models has increased alongside the speed and capacity of the railway vehicles over the last decades. Although the use of three-dimensional finite element models is becoming common practice, simplified models are still relevant, due to their simplicity of implementation and results interpretation, and low computational cost. However, the general validity of these models has not yet been demonstrated in the relevant literature. The present thesis aims to establish the applicability and viability of such simplified models in the analysis of the dynamic behaviour of the ballasted railway track. The following questions are considered: 1. Are these models able to approximate the real rail displacement due to the passage of rail vehicles, despite their simplicity? 2. If yes, for which situations (i.e., track properties and loading conditions) can they be used reliably? 3. In these situations, is it possible to define adequate parameters for the simplified models based on the track’s geometry and mechanical properties? To that end, three linear elastic models are implemented: a detailed three-dimensional finite element model, a one-dimensional beam in discrete supports model, and a one-dimensional beam on elastic foundation model. Transient and steady-state dynamic solutions for a load moving at moderate and high speed are obtained. The vertical displacement of the rail is chosen as the reference to measure the equivalence between the models, since it is a common element between all models and is the interface between the load and the track. The three-dimensional model is validated by comparison with published experimental measurements. Its results cover a representative range of the properties of the ballast and subgrade, and are used as a reference to calibrate the simplified models using genetic algorithms and non-linear programming. It is concluded that a good approximation to the reference solution can be achieved, particularly when the load moves slower than the velocity of propagation of the elastic waves in the soil. For high velocities and/or soft soils, the wave propagation becomes more relevant to the dynamic behaviour of the track, and the simplified models become less reliable. Following a review of the existing literature, theoretical expressions for the determination of the parameters of the simplified models are proposed. It is concluded that these are suitable for the beam on discrete supports model, but not for the beam on elastic foundation model, whose optimum parameters are less consistent across the different properties of the track and load speeds.