Pedestrian-induced lateral vibration of footbridges: A comparison study of different loading models

The pedestrian-induced lateral vibration of footbridges has attracted much attention since the London Millennium Bridge incident. Significant investigations were mainly performed by external-excited force models and self-excited force models. The first type models consider pedestrians as harmonic forces and/or spring-mass-damping (SMD) systems. The second type consider the self-excited forces of pedestrians that initialize the instability of footbridges by e.g. applying the inverted pendulum (IP) model. This study compares performance of different models in reproducing the observed results of typical living footbridges: the London Millennium Bridge (UK), T-bridge (Japan) and Pedro e Ines footbridge (Portugal). With varying step frequencies and pedestrian numbers, both the acceleration time history and the discrepancy between the input work and consumed work exhibit a consistent trend for the harmonic force (HF) model and SMD model, yet a notable difference for the IP model. The HF model and SMD model are better suited for assuming synchronization, making them convenient for estimating the serviceability of pedestrian-induced lateral vibration. On the other hand, the IP model is more appropriate for incorporating random step frequencies and can better capture observed instability phenomena realistically. Because the SMD model with (inconsistent) parameters from literature may result in significant differences in predicting the acceleration amplitudes, this paper modifies the SMD model and proposes a pedestrian synchronization ratio formula as an exponential function of the maximum lateral acceleration. It is validated by comparing the analytical and numerical results for the three footbridges. Furthermore, by the modified SMD model, the lateral lock-in phenomenon of footbridges is simulated reliably and conveniently. This work contributes to analyze pedestrian-induced lateral vibration of footbridges.