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

•This work investigates the crowd behaviour which is uncertain by nature.•Social force model translates the crowd behaviour into the crowd-induced load.•A double-loop uncertainty quantification and propagation framework is formulated.•The uncertainty is quantified and propagated in the form of P-boxes.•The obtained response P-box is significant for serviceability design of footbridges.