Probabilistic assessment of the dynamic interaction between multiple pedestrians and vertical vibrations of footbridges

The effect of human-structure interaction in the vertical direction for footbridges is studied based on a probabilistic approach. The bridge is modeled as a continuous dynamic system, while pedestrians are schematized as moving single-degree-of-freedom systems with random dynamic properties. The non-dimensional form of the equations of motion allows us to obtain results that can be applied in a very wide set of cases. An extensive Monte Carlo simulation campaign is performed, varying the main non-dimensional parameters identified, and the mean values and coefficients of variation of the damping ratio and of the non-dimensional natural frequency of the coupled system are reported. The results obtained can be interpreted from two different points of view. If the characterization of pedestrians' equivalent dynamic parameters is assumed as uncertain, as revealed from a current literature review, then the paper provides a range of possible variations of the coupled system damping ratio and natural frequency as a function of pedestrians' parameters. Assuming that a reliable characterization of pedestrians' dynamic parameters is available (which is not the case at present, but could be in the future), the results presented can be adopted to estimate the damping ratio and natural frequency of the coupled footbridge-pedestrian system for a very wide range of real structures.