Parameter Calibration of a Social Force Model for the Crowd-Induced Vibrations of Footbridges

A reliable prediction of the human-induced vibrations of footbridges relies on an accurate representation of the pedestrian excitation for different loading scenario. Particularly, the modeling of crowd-induced dynamic loading is a critical issue for the serviceability assessment of footbridges. At the design stage, the modeling of crowd loading is often derived from single pedestrian models, neglecting the effect of the structural vibrations as well as the interactions among pedestrians. A detailed description of the crowd behavior can be achieved employing a social force model that describes the different influences affecting individual pedestrian motion. These models are widely adopted to describe the crowd behavior especially in the field of evacuation of public buildings, public safety and transport station management while applications in the serviceability assessment of footbridges are less common. To simulate unidirectional pedestrian flows on footbridges, this paper proposes a parameter calibration of the Helbing's social force model performed adopting the response surface methodology. Parameters of the social force model are calibrated so as to represent the fundamental relation between mean walking speed and density of the pedestrian crowd. The crowd-induced vibrations are then simulated by modeling each pedestrian in the crowd as a vertical load that crosses the footbridge with time varying trajectory and velocity estimated from the calibrated social force model. Finally, results are compared to those obtained from a multiplication factor approach proposed in literature. This considers the crowd as a uniform distribution of pedestrians with constant speed and given synchronization level and the footbridge response is evaluated as the response to a single pedestrian scaled by a proper enhancement factor.