Validating theoretical dynamic amplification factors using in-situ measurements for a wide range of train speeds

The vertical displacement of the whole railway infrastructure, including the natural ground underneath, depends on the train speed. This phenomenon is usually known as dynamic amplification. In the most extreme situation, trains may attain a “critical speed” at which the vertical displacement of the railway system would increase infinitely if no damping were present. Since the current trend worldwide is to increase the operational train speed, the question arises about what vertical displacements can be expected in the track for these new train speeds. The beam on elastic foundation model has been successfully applied to railways at relatively low train speeds for many decades. In this article, the power of this model to predict track vertical displacements at very high train speeds, including values close to the site's critical speed, is empirically proven for the first time. To this end, results predicted by this model are compared herein to direct measurements of track vertical displacement for a broad range of train speeds, including (i) in situ field measurements taken in four different sites (France, United Kingdom, The Netherlands and Sweden), and (ii) data from several tests performed in the CEDEX Track Box facility (CTB, Spain). The match between theoretical results and direct measurements confirms the applicability of the beam on elastic foundation model for predicting dynamic track deflections under future increases in maximum commercial train speeds, providing essential insights for the safe design and maintenance of high-speed railway lines.