This paper presents dynamic measurements performed on two pedestrian bridges inSweden subjected to different loading scenarios. Using accelerometers, the natural frequencies,the experimental mode shapes and damping properties were determined for each bridge. Analysiswere performed using the generalized single degree of freedom theory, the finite elementmethod and the coupled system approach taking into account the flying phase of the runningload. Additionaly, a simplified sensitivity analysis is presented in terms of accelerations dueto the pedestrian transient event of a running load case. The results indicate that there is anexcellent agreement between the aforementioned modelling strategies and, that it is possible tohave human structure interaction under running load scenarios.

One approach for upgrading existing high-speed railway bridges which are susceptible to excessive vibrations is to install damping devices. In this article, a model of a simply supported bridge with supplemental fluid viscous dampers installed between the superstructure and the abutments is derived based on an arbitrary mode of vibration. The aim is to ensure the robustness of the proposed vibration mitigation method by conducting Monte Carlo simulations including uncertainties associated with the bridge-damper system. From this statistical screening, it is possible to evaluate the probability of exceedance of a stipulated acceleration level, as well as studying the sensitivity of the ingoing random variables. This probabilistic evaluation highlights the necessity of conducting a statistical assessment to determine an estimate for the distribution of the acceleration limit and model uncertainty for dynamic analyses. The results show that the required damping coefficient could be multiply reduced, as compared to a deterministic analysis.

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.

Mainly because of the infamous incident with excessive vibrations of the London Millennium Bridge, the behavior of lively footbridges has been thoroughly studied lately. The liveliness of such bridges is strongly connected to various interaction effects between the pedestrians and the bridges. One such effect is the variation in the modal properties of the bridge, due to the presence of a crowd. In theoretical models of such systems, this is often accounted for by describing each pedestrian as a spring-mass-damper system, having its own dynamic properties, producing a time-variant system. A major drawback with models of this kind is that the computational time increases rapidly with the size of the system, i.e. for a larger crowd. Therefore, with the objective to reduce the computational time needed, this study focuses on describing vertical human-structure interaction by means of a simplified model. The paper describes a new methodology for taking this effect into consideration when predicting the dynamic response of a footbridge, subjected to human-induced, vertical loads. The method is used to predict the vertical bridge deck accelerations of a simply supported footbridge. The predictions produced by the proposed methodology are compared with existing models and it is shown that for certain bridges, it produces an accurate approximation at a significantly reduced computational cost.

Several bridges along the Bothnia railway line in Sweden do not fulfil the Eurocode requirements regarding the maximum vertical bridge deck acceleration. The aim of this study is to investigate the possibility of reducing the acceleration of one of these bridges to an acceptable level by using post-installed viscous dampers. The bridge-damper system is described by a single-degree-of-freedom model. Assuming that the dampers do not change the mode shapes of the bridge, the model is further generalized to include higher order bending modes. The dampers are connected between the bottom surface of the bridge deck and the abutments.This creates an eccentricity between the connection point of the dampers and the neutral axis of the bridge, which is found to have a significant influence on the efficiency of the dampers. The results of this study also indicate that the proposed retrofit method can reduce the accelerations to an acceptable level.

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.