A 2D discrete model for crowd-structure interaction
Résumé
An emerging problem for civil engineering in the field of dynamics is the modelling of dynamic effects due to crowd-structure interaction. We are particularly concerned with structures such as footbridges, which oscillate due to the crossing of a group of pedestrians. The objective of this study is double: to model the movement of pedestrians with consideration of pedestrian-pedestrian and pedestrian-obstacle interactions and to include a pedestrian-structure coupling in the proposed model. This 2D discrete model would be able to study the problem of synchronization between pedestrians and structure on footbridges. Our idea is to extend the modelling of particles movements to study the movements of a crowd. The non-smooth discrete model of Frémond initially proposed to simulate a granular assembly, is chosen. It applies a rigorous thermodynamic framework in which the local interactions between particles are managed by the use of dissipation pseudo-potentials. Social forces as well as a desired direction/ velocity are introduced in order to simulate the behaviour of pedestrians. Concerning the pedestrian-structure coupling, a differential equation of Kuramoto allows one to manage the evolution of the pedestrians' phase. Two cases are studied depending on the sensitivity of pedestrians to the footbridge's oscillations. Numerical simulations on the Millenium Bridge are performed and discussed.
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