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Viability and Applicability of Simplified Models for the Dynamic Analysis of Ballasted Railway Tracks
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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.
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Palavras-chave
High speed rail Structural vibrations Finite element method Simplified models