MS11.3- Footbridge Vibrations

The further development and improvement of prediction models for crowd-induced vibrations of footbridges requires detailed information on representative operational loading data. This paper uses an inverse method to estimate the parameters that govern human-structure interaction from the resulting structural response. The parameters of interest concern the dynamic characteristics of a mass-spring-damper (MSD) system, applied to describe the mechanical interaction between the pedestrian and the structure. The dynamic characteristics of the MSD interaction model are estimated by minimizing the discrepancy between the observed and the simulated power spectral density of the structural response. The parameter estimation procedure assumes that the dynamic behavior of the empty structure, the average weight and the distribution of step frequencies in the crowd are known. The proposed approach is verified using numerical simulations and the influence of modeling errors is investigated. The results show that as footbridges and the human body are by nature lowly (≤2\%) and highly (≈30\%) damped, respectively, the structural response is most sensitive to small variations in the natural frequency of the MSD interaction model. The results furthermore show that the parameter estimation problem is mostly sensitive to errors related to the mean value of the distribution of step frequencies and the structural modes' natural frequency and modal mass. The impact of the structural modeling errors is found to decrease as the impact of human-structure interaction increases. Next, the approach is applied to two real footbridges where the walking behavior and the structural response induced by high pedestrian densities are observed. The results show that an estimate of the natural frequency (≈3.0Hz) and damping ratio (≈34%) of the MSD interaction model is obtained that is in line with recent findings in the literature. These estimates are, however, for the first time ever based on full-scale observations involving high pedestrian densities.

Despite extensive research in the last twenty years, there is still lack of reliable models for human-induced excitation, especially with reference to crowded conditions. Guidelines provide equivalent resonant uniformly-distributed loading with an increased loading amplitude for high density in order to account for the possible synchronization among pedestrians in very dense traffic conditions. This very simple loading condition does not take into account the variation of the walking velocity and step frequency with pedestrian density and may lead to unreliable predictions of the vibration level. A reliable human-induced loading model on footbridges taking into account pedestrian interaction requires experimental tests on full scale structures, that are scarce in the literature and limited to low pedestrian densities [1]. In the literature, experimental tests in straight corridors have been carried out, both in the case of unidirectional (e.g. [2]) and bidirectional traffic (e.g. [3]), providing fundamental diagrams of the mean walking speed as a function of pedestrian density. As an alternative to experimental characterization , numerical simulations based on suitable crowd dynamics models can be carried out (see, e.g. [4], limited to unidirectional pedestrian flow). The authors of the present paper carried out a wide campaign of numerical simulations of unidirectional and bidirectional pedestrian traffic through an agent-based model, considering variable pedestrian densities and deck widths [5]. The present paper has two distinct objectives: 1) to validate the results of numerical simulations carried out by the authors against the experimental measurements available in the literature, 2) to adopt the results of numerical simulations of pedestrian traffic in order to assess the reliability of guidelines’ predictions. Two structure case studies are considered, pedestrian-induced forces are derived from numerical simulations of pedestrian traffic and the footbridges’ dynamic response is calculated for different levels of pedestrian density. Then, the dynamic response obtained from numerical simulations is compared with guidelines’ predictions in order to assess their reliability in vibration serviceability assessment of footbridges. REFERENCES [1] K. Van Nimmen, J. Hauwermeiren and P. Van den Broeck, “Eeklo Footbridge: benchmark dataset on pedestrian-induced vibrations”, Journal of Bridge Engineering ASCE: 05021007 (2021). [2] J. Zhang, W. Klingsch, A. Schadschneider and A. Seyfried, “Transitions in pedestrian fundamental diagrams of straight corridors and T-junctions”, Journal of Statistical Mechanics: Theory and Experiment: P06004 (2011). [3] T. Kretz, A. Grunebohm, M. Kaufman, F. Mazur, M. Shreckenberg, “Experimental study of pedestrian counterflow in a corridor”, Journal of Statistical Mechanics Theory and Experiment: P10001 (2006). [4] E. Bassoli, L. Vincenzi, “Parameter calibration of a Social Force Model for the crowd-induced vibrations of footbridges”, Frontiers in Built Environment, doi: 10.3389/fbuil.2021.656799 (2021). [5] F. Venuti and F. Tubino, “Human-induced loading of footbridges due to restricted pedestrian traffic: probabilistic characterization and equivalent spectral model”, Structure and Infrastructure Engineering, doi: 10.1080/15732479.2021.1897630 (2021).

Following a previous work [1], the paper describes the serviceability assessment of a footbridge over the Lambro River near Milano (Italy), based on the comparative analysis of on-field tests and of the outcome of the Hyvoss guidelines. The 3-span footbridge, for a bicycle-pedestrian mixed use, is 107 m long, 4.4 m wide and roughly symmetric about both mid-span and the longitudinal axis. A reinforced concrete (RC) deck is supported by a steel structure: two longitudinal welded I-profiles, braced in their lower part, support the transverse beams that, in turn, support the RC deck. Ambient vibration tests identified the footbridge modal properties, detecting the fundamental bending mode, with the maximum amplitude recorded at mid-span, at 1.75 Hz, well within the critical range of excitation from walking pedestrians. For this reason, a series of forced vibration tests was subsequently performed, involving single pedestrians or groups of up to 12 people. Sensors, located as in AVTs, recorded footbridge acceleration, both horizontal and vertical. In all the tests, pedestrians walked in resonance conditions with the first mode frequency along straight trajectories. To excite further the first mode, their spatial configurations were symmetric about the longitudinal axis of the bridge. Difference among tests concerns not only the number of test subjects (TSs), but also their spatial configuration and/or the TSs involved in each test. The comparison among tests sharing similar spatial configurations, with TSs either in a row or in a column, allows a serviceability assessment directly from the experimental footbridge response. The numerical analyses are based on a FE model previously developed [1], showing an excellent reproduction of the first bending mode frequency, but a poor simulation of the second torsional mode. The outcome of the analyses performed according to HiVoSS guideline is in good agreement with the experimental results, in spite of the very low crowd density of the on-field tests and the unsatisfactory reproduction of the torsional mode within the FE model. [1] A. Cigada, C. Gentile, G. Lastrico and M. G. Mulas. Measuring the dynamic response of a lively footbridge to ambient and walking excitation. Proceedings of Eurodyn 2020, XI International Conference on Structural Dynamics, M. Papadrakakis, M. Fragiadakis, C. Papadimitriou (eds.) Athens, Greece, 22–24 June 2020. Keywords: Lively footbridge; ambient vibration tests; forced vibration tests; serviceability assessment; walking pedestrians; resonance conditions.