Uncertainties in crowd dynamic loading of footbridges: A novel multi-scale model of pedestrian traffic

•Sources of uncertainty in crowd loads are reviewed.•A new multi-scale framework is proposed to model uncertainties in pedestrian traffic.•Each component of the framework is specified.•Approach is applied to ideal benchmarks, in the current lack of in situ measurements.•Variability of traffic random variables is larger than structural properties ones. The study of the probabilistic response of pedestrian-excited structures as well as their reliability analysis need to take into account the influence of a large number of uncertain parameters ascribed to structural characteristics, single pedestrian walking features and pedestrian traffic phenomena. Although pedestrian traffic is characterized by an intrinsic high variability and plays a key role in determining the pedestrian load, its probabilistic description remains scarce in literature. The present work aims at contributing to the probabilistic evaluation of the pedestrian traffic across footbridges. First, a categorized state of the art focused on sources of uncertainty is provided. Second, a new modeling framework for the probabilistic evaluation of pedestrian traffic is introduced in general and conceptual terms. The framework is conceived in analogy to the approach developed in another engineering field, i.e. wind engineering, on the basis of the phenomenological features of the pedestrian traffic. In order to put the framework in practice, each of its main modeling components is specified. We introduce a statistic approach to evaluate the incoming traffic and a microscopic traffic model to simulate the propagation along the footbridge of the uncertain pedestrian entrance. In order to prove its technical feasibility, the proposed framework is finally applied to an ensemble of real world crowd events and to two ideal footbridges with differently shaped walkway. As a final result, the pedestrian density along the footbridge is described as a random field in terms of its joint and unconditioned probability density functions and correlation lengths.