The influence of dynamic soil-structure interaction (SSI) on simply supported railway bridges is investigated. Impedance functions are calculated considering shallow foundations in soil strata limited by bedrock. The impedance functions are coupled to bridge models, and the assembled soil-bridge systems are investigated addressing the modal properties. A parametric study is performed on a large set of soil-bridge systems. Finally, the response to train loading is analysed. The study shows that the effects of SSI are essentially different depending on whether radiation damping is active or not. Shorter bridges are often affected by radiation damping and the response due to train loading may be significantly reduced when SSI is considered. However, for longer bridges (>15 m) the effect of SSI is often small. Due to the stiffness reduction of the impedance, some bridges may even have a detrimental effect from SSI and a reduction of the traffic speed is obtained.

The effects of model assumptions on the dynamic impedance junctions of shallow foundations are investigated using finite elements. The shallow foundations are considered massless and rigid and are positioned in strata of frictional soil on top of bedrock. Two studies are established. The first investigates the combined effects of model assumptions including the variation of modulus with depth, the embedment of the foundation, and permanent load acting on the foundation. The second study is a parametric analysis investigating the effects of permanent load considering strata with varying soil modulus coefficients and with varying soil depths. Functions describing the small-strain modulus and the modulus reduction of frictional soil are used in an iterative process to update the spatial modulus distribution of the soil due to the permanent load. The results show that model assumptions can have a large effect on the impedance functions. The static stiffness coefficients vary substantially, in some instances by more than 100 %. The impedance functions, normalized with the static stiffness coefficients, match each other well in the frequency range below the fundamental frequency. However, in the frequency range above the fundamental frequency, the normalized impedance functions differ substantially from each other. Further, the results show that the effect of the permanent load is largest in the case of shallow and stiff soil strata, both regarding normalized impedance functions as well as the static stiffness coefficient, which was increased up to 67 %. The variation in fundamental frequency is however small.

The influence of model assumptions on the dynamic impedance functions of shallow foundations is investigated using finite elements in two studies. The first investigates the effects of model assumptions in different combinations including embedment of the foundation, variation of modulus with depth, and permanent load acting on the foundation. The second study is a parametric analysis investigating the effects of permanent load at varying soil depths and with different soil modulus coefficients. Shallow foundations in strata of frictional soil on top of bedrock are considered. Small-strain modulus and modulus reduction relationships are used in an iterative process to update the modulus due to the permanent load. The results show that model assumptions can have a large influence on impedance functions. The static stiffness coefficients differ, in some instances by more than 100%. The impedance functions, normalized with the static stiffness coefficients match each other well in the pre-resonance frequency range. However, in the frequency range above the fundamental frequency, the normalized impedance functions show a large variation. Further, the results show that the influence of the permanent load is largest in the case of shallow and stiff soil strata, both regarding normalized impedance functions as well as the static stiffness coefficient, which can be increased up to 67%. The change in fundamental frequency was however minimal.

This paper presents a full-scale dynamic testing on a simply supported railway bridge with integrated end-shields, by using a hydraulic exciter. Experimental frequency response functions are determined based on load controlled frequency sweeps. Apart from accurate estimates of natural frequencies, damping and mode shapes, the experimental testing also gives valuable information about the dynamic characteristics at resonance and amplitude dependent nonlinearities. Numerical models are used to simulate the dynamic response from passing trains which is compared to experimental testing of similar train passages. The results show that the bridge deck is partially constrained due to the interaction between the end-shields and the wing walls with the surrounding soil. Measurements at the supports also show that the flexibility of the foundation needs to be accounted for. An updated numerical model is able to accurately predict the response from passing trains. The response is lower than that predicted from the initial simulations and the bridge will fulfil the design requirements regarding vertical deck acceleration.

This article presents preliminary theoretical results on the influence of dynamic soil-structure interaction (SSI) of slab foundations. Impedance functions, representing the dynamic SSI, were obtained from FE-models depicting the soil for a few cases of different geotechnical preconditions. The obtained impedance functions were attached to single-span bridges and HSLM-A analyses were performed. The effect of the impedance functions on the bridge response was studied and compared to the ultimate case of a bridge on rigid supports. The influence of SSI seems to have a significant effect on railway bridges. This study shows that by including this effect in bridge design, the damping ratio of the system is largely increased, giving lower acceleration amplitudes in the bridge, while the natural frequencies are less affected.

This report contains a parametric study on the dynamic response of railway bridges on flexible supports. The results are based on simulations using 2D and 3D models. The dynamic stiffness of the supports is described by separate models of the foundation, including relevant stress and strain dependent soil properties from permanent loading that is linearized in a subsequent dynamic analysis. The complex-valued dynamic stiffness constitutes the boundary conditions in a separate analysis of the bridge superstructure that is solved in frequency domain.

Two different foundation types are studied; shallow slab foundation with relatively good ground conditions, and pile group foundations with relatively poor ground conditions. In both cases, the foundation slab and the pile group have fixed geometry. In the parametric study, the corresponding vertical static foundation stiffness range from 2 – 20 GN/m for the slab foundation and 5 – 25 GN/m for the pile group foundation.

For the slab foundations, both the stiffness and damping highly depends on the properties of the soil, foundation depth and geometry of the foundation slab. For the pile group foundations, the stiffness is mainly governed by the pile group and the damping by the soil.

Based on the simulations, the additional damping from the slab foundation is in most cases negligible. Only for relatively soft foundations and short-span bridges significant additional damping is seen. For the pile group foundations, the additional damping is in some cases significant, especially for deeper foundations and short-span bridges. Considering a lower bound of the parametric study does however result in a negligible contribution.

The dynamic response from passing trains show that the assumption of fixed supports in most cases is conservative. However, the flexible supports may result in a lower natural frequency that should be accounted for in order to not underestimate the resonance speed of the train.

If flexible supports are included in a dynamic analysis, both the stiffness and damping component needs to be included. The frequency-domain approach presented in this report is a viable solution technique but is not implemented in most commercial software used in the industry.

Short and stiff bridges are generally quite sensitive to the dynamic effects arising from train-bridge interaction. In the Swedish landscape, such bridges are common and represent 60-70% of the total bridge stock. Recent research has clearly shown that simple structural models may result in highly conservative predictions of the dynamic response of such structures. This has a large impact on the economy of these structures both for existing railway lines on which an increased maximum allowable speed could lead to a more efficient operation and for the design of new bridges on dedicated high-speed railways. This paper describes two promising modelling details that could lead to models that more accurately predict the dynamic response of such bridges; dynamic soilstructure interaction and the influence of rolling and sliding friction in bridge bearings. Currently, several research and development projects are aiming at increasing our understanding of these phenomena and at deriving simplified models that include these details in practical bridge design. Bridges with integrated abutments are common in Sweden as they provide an economic solution for many short bridges. However, simple models, which exclude the interaction between the abutments and the embankments, typically lead to theoretical dynamical responses that exceed the acceleration criteria given by the Eurocode. Recent research indicates that by modelling the interaction with the embankment, a more accurate and less conservative response may be obtained. Research regarding the influence of friction in bridge bearings has shown that a considerable additional damping can exist in bridges resting on either rolling or sliding bearings. An ongoing project attempts to quantify this additional damping and derive phenomenological models to include this effect in dynamic analyses of railway bridges in particular and bridges in general.