Uncertainty quantification and propagation of crowd behaviour effects on pedestrian-induced vibrations of footbridges

The reliable prediction of pedestrian-induced vibration is essential for vibration serviceability assessment and further vibration mitigation design of footbridges. The response of the footbridge is governed by not only the structure dynamic model but also the crowd-induced load, which naturally involves randomness and uncertainty. It is consequently significant to appropriately characterize the uncertainties during the numerical modelling of the crowd behaviour effects on crowd-induced load. This work proposes a comprehensive approach to quantify the uncertainty from both the structure dynamic model and the crowd behaviour, and subsequently, to propagate the multiple sources of uncertainties from the input parameters to the response of the footbridge. The crowd behaviour is simulated using the social force model and translated to the crowdinduced load by combining with a single pedestrian induced walking force model. By decoupling the continuous model into several single degrees of freedom systems according to relevant modes in the vibration serviceability evaluation, the structure dynamic model of the footbridge is developed where the structural responses are calculated. In this paper, all the uncertain parameters are investigated together in a double-loop framework to perform uncertainty quantification and propagation in the form of probability-box (shortly termed as P-box). The uncertainty space of the peak structural responses is finally obtained by the Monte Carlo sampling and optimization in the outer loop and inner loop, respectively. Feasibility and performance of the overall approach are demonstrated by considering a real scale footbridge, and the failure probability of each comfort class regarding the peak acceleration response is also evaluated. Results show that, special attention should be paid on both the epistemic and aleatory uncertainties from the crowd behaviour in the vibration serviceability assessments of footbridges. The proposed uncertainty quantification framework may provide significant insights and improve the reliability for future vibration serviceability evaluations of footbridges by incorporating the crowd behaviour effects.