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From individual behaviour to an evaluation of the collective evolution of crowds along footbridges

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Abstract

This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real-world problems is tested by considering the pedestrian traffic along footbridges, of interest for Structural and Transportation Engineering. The genuinely macroscopic quantitative description of the crowd flow directly matches the engineering need of bulk results. However, three issues beyond the sole modelling are of primary importance: the pedestrian inflow conditions, the numerical approximation of the equations for non trivial footbridge geometries and the calibration of the free parameters of the model on the basis of in situ measurements currently available. These issues are discussed, and a solution strategy is proposed.

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Notes

  1. Throughout the paper, the subscript t is used to denote a dependence on time (hence, in particular, not a time derivative).

  2. Notice that intersections of rectangles taken from orthogonal grids, instead, give rise just to rectangular intersections.

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Acknowledgments

The work of A. Corbetta was supported by a Lagrange Foundation PhD scholarship.

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Authors and Affiliations

  1. Department of Architecture and Design, Politecnico di Torino, Viale Mattioli 39, 10125, Turin, Italy

    Luca Bruno

  2. Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy

    Alessandro Corbetta

  3. Department of Mathematics and Computer Science, CASA - Centre for Analysis, Scientific Computing and Applications, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Alessandro Corbetta

  4. Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185, Rome, Italy

    Andrea Tosin

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  1. Luca Bruno
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  2. Alessandro Corbetta
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Correspondence to Andrea Tosin.

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Bruno, L., Corbetta, A. & Tosin, A. From individual behaviour to an evaluation of the collective evolution of crowds along footbridges. J Eng Math 101, 153–173 (2016). https://doi.org/10.1007/s10665-016-9852-z

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