The vertical dynamic actions transmitted by railway vehicles to the ballasted track infrastructure are evaluated taking into account models with different degrees of detail. In particular, this matter has been studied from a two-dimensional finiteelement model to a fully coupled three-dimensional multibody finite-element model. The vehicle and track are coupled via a nonlinear Hertz contact mechanism. The method of Lagrange multipliers is used for the contact constraint enforcement between the wheel and rail. Distributed elevation irregularities are generated based on power spectral density distributions, which are taken into account for the interaction. Due to the contact nonlinearities, the numerical simulations are performed in the time domain, using a direct integration method for the transient problem. The results obtained include contact forces, forces transmitted to the infrastructure (sleeper) by railpads, and envelopes of relevant results for several track irregularities and speed ranges. The main contribution of this work is to identify and discuss coincidences and differences between discrete two-dimensional models and continuum three-dimensional models, as well to assess the validity of evaluating the dynamic loading on the track with simplified two-dimensional models.

Verification of the serviceability limit state of vibrations due to traffic live loads can be neglected in conventional types of concrete road bridges but becomes critical in the design of slender structures like Under-Deck CableStayed bridges. The novelty of the work presented in this article is that an innovative vehicle-bridge interaction model is employed, in which realistic wheel dimensions of heavy trucks, road roughness profiles and the cross slope of the road are considered in nonlinear dynamic analyses of detailed three-dimensional finite element models. An extensive parametric study is conducted to explore the influence of the bridge parameters such as the longitudinal and transverse cable arrangement and the support conditions, in addition to the load modelling, road quality, the wheel size, the transverse road slope and the vehicle position and speed on the response of under-deck cable-stayed bridges. It has been observed that the vibrations perceived by pedestrians can be effectively reduced by concentrating the cable-system below the deck at the bridge centreline. The Fourier amplitude spectrum of the acceleration at critical positions along the deck proved that the response of Under-Deck Cable-Stayed bridges is not dominated only by contributions at the fundamental mode and, consequently, the conventional deflection-based methods are not valid to assess the users comfort. Instead, Vehicle-Bridge Interaction analyses are recommended for detailed design, considering the wheel dimensions if the pavement quality is bad and/or if the wheel radius is large. Finally, we verify through multiple approaches that the comfort of pedestrian users is more critical than that of vehicle users. However, the comfort of vehicle users is shown to be significantly affected when the road quality is poor.

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