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The dynamic transverse response of beam type bridges under railway traffic is addressed in this contribution. In particular, how soil-structure interaction may affect the critical or resonant speeds and the associated vibratory amplitudes is evaluated in detail. Resonance in beams, due to the circulation of equidistant loads, is highly influenced by the free vibration response that every single load leaves after traversing the structure. On this basis a numerical investigation is carried out analysing the effects of the wave propagation problem on the free vibration response of simply-supported beams in a wide range of travelling speeds. To this end a coupled three-dimensional boundary element-finite element model formulated in the time domain is used to reproduce the soil and structural behaviour, respectively. A catalogue of bridge deck typologies is defined, covering lengths, associated linear masses and fundamental frequencies that may experience high levels of transverse accelerations under resonant conditions, for nowadays existing trains and design speeds. Lengths ranging from 12.5 to 25 m are evaluated, along with fundamental frequencies covering most common typologies. A homogeneous soil is considered with shear wave speeds in the interval 150 to 365 m/s. From the single load free vibration parametric analysis conclusions are derived regarding the conditions of maximum free vibration and cancellation of the deck response. These conclusions are used afterwards to justify how resonant amplitudes of the bridge under the circulation of railway convoys may be affected by the soil properties, leading to substantially amplified responses or to almost imperceptible ones, and a numerical example is included to show the aforementioned situations.

Constant moving load models are widely adopted in the dynamic analysis of railway bridges under moving trains. However, the use of this simple model may overestimate the resonant response of simply supported bridges if the vehicle-bridge interaction (VBI) effects are neglected, particularly for short spans. To account for the VBI effects, Eurocode 1 allows engineers to consider an additional amount of structural damping which depends on the bridge span. This method is the so-called Additional Damping Method (ADM), and was formulated in order to provide a conservative prediction of the interaction benefit. Nevertheless, the Additional damping method may sometimes yield to an unsafe prediction of the bridge peak response. Considering the interaction benefits, an alternative analytical approach based on an equivalent VBI model under resonant excitations is presented in this investigation. The key parameters dominating the additional damping problem are subsequently identified. According to the numerical demonstrations supplied, the presented approach provides insights that enable an accurate prediction of the additional amount of damping needed in order to account for VBI effects on short simply-supported railway bridges.

Railway induced vibrations on short-to-medium span simply-supported (SS) bridges is addressed in this contribution. Such structures may experience high levels of vertical acceleration at the platform, leading to adverse consequences such as a premature degradation of the ballast layer and passenger discomfort. In the present study, the evolution of the bridge dynamic response when soil-structure interaction (SSI) is taken into account is investigated. To this end a coupled three-dimensional (3D) Boundary Element-Finite Element model (BEM-FEM) formulated in the time domain is implemented to reproduce the soil and structural behaviour, respectively. First, a set of soil-bridge systems of interest is defined, covering a wide range of lengths and natural frequencies for the structures, and an interval of expectable elastic properties and damping levels for the soil. Then, different types of analyses are performed on the soil-bridge systems extracting conclusions regarding the effect of including SSI in numerical models for predicting the bridge behaviour under railway traffic. In particular natural frequencies and modal damping levels are identified, and the structure amplification after the passage of a moving load in free vibration is investigated. Conclusions regarding how resonance and cancellation conditions may be affected by soil properties are extracted. Finally, the dynamic response of a real bridge, belonging to the Spanish railway network, is evaluated under the circulation of trains that induce second and third resonances of the bridge fundamental mode. The effect of the soil flexibility, soil material damping and the bridge resonance order are evaluated. Conclusions regarding the appropriateness of the results provided by common models which do not include SSI effects are extracted.

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