Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-25T12:16:37.247Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling crowd-structure interaction

Published online by Cambridge University Press:  09 December 2010

Philippe Pécol ,
Stefano Dal Pont ,
Silvano Erlicher  and
Pierre Argoul
Philippe Pécol*
Affiliation:
Université Paris-Est, Laboratoire Navier, École des Ponts-ParisTech, LCPC, CNRS, 6–8 Av. Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne la Vallée Cedex 2, France
Stefano Dal Pont
Affiliation:
Université Paris-Est, Laboratoire Central des Ponts et Chaussées, LCPC-BCC, 58 boulevard Lefebvre, 75732 Paris, France
Silvano Erlicher
Affiliation:
IOSIS Industries, 35 rue du Val de Marne, 75013 Paris, France
Pierre Argoul
Affiliation:
Université Paris-Est, Laboratoire Navier, École des Ponts-ParisTech, LCPC, CNRS, 6–8 Av. Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne la Vallée Cedex 2, France
*
a Corresponding author: philippe.pecol@enpc.fr
Get access

Abstract

An emerging research topic in civil engineering is the dynamic interaction between crowds and structures. Structures such as footbridges, which oscillate due to the crossing of a group of pedestrians, or stands within stadia or concert halls, which vibrate due to the rythmic movement of the audience are of particular interest. The objective of this study is twofold: modelling the movement of pedestrians with consideration of pedestrian-pedestrian, and pedestrian-obstacle interactions, and the incorporation of a pedestrian-structure coupling in the previous model. Frémond’s model, which allows us to simulate the movement of an assembly of particles and accounts for collisions among considered rigid particles, is presented and adapted to the crowd by giving a willingness to the circular particles, which allows each pedestrian to move according to a given target. To handle the crowd-structure interaction in the case of lateral oscillations of footbridges, the Kuramoto differential equation governing the time evolution of the lateral motion of each pedestrian is implemented in the previous model. Preliminary results obtained from numerical simulations are presented and discussed.

Keywords

Granular assemblycrowdcontactcrowd-structure interactionsynchronizationfootbridgeAssemblée de grainsfoulecontactinteraction foule-structuresynchronisationpasserelle
Type
Research Article
Information
Mechanics & Industry , Volume 11 , Issue 6: VCB (Vibrations, Chocs et Bruits) , November 2010 , pp. 495 - 504
Copyright
© AFM, EDP Sciences 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

J. Bodgi, Synchronisation piétons-structure: Application aux vibrations des passerelles souples, Ph.D. thesis, École Nationale des Ponts et Chaussées, 2008
Strogatz, S., Abrams, D., McRobie, A., Eckhardt, B., Ott, E., Theoretical mechanics: Crowd synchrony on the Millenium bridge, Nature 438 (2005) 43–44 CrossRefGoogle Scholar
Zivanovic, S., Pavic, A., Reynolds, P., Vibration serviceability of footbridges under human-induced excitation: a litterature review, J. Sound Vib. 279 (2005) 1–74 CrossRefGoogle Scholar
S. Zivanovic, V. Ravic, I. El-Bahnasy, A. Pavic, Statistical characterisation of parameters defining human walking as observed on an indoor passerelle, in Experimental Vibration Analysis for Civil Engineering Structures, EVACES’07, Porto, Portugal, 219-225 (2007)
D.M. Abrams, Two coupled oscillator models: the Millenium bridge and the chimera state, Ph.D. thesis, Cornell University, 2006
Bodgi, J., Erlicher, S., Argoul, P., Lateral vibration of footbridges under crowd-loading: continuous crowd modelling approach, Key Engineering Materials 347 (2007) 685–690 CrossRefGoogle Scholar
P. Charles, C. Delavaud, A. Hekimian, J. Renault, T. Saez, Dispositif d’essais sur un modèle de passerelle, rapport d’essais SETRA, 2005
Hankin, B.D., Wright, R.A., Passenger flow in subways, Oper. Res. 9 (1958) 81–88 CrossRefGoogle Scholar
Helbing, D., Traffic and related self-driven many-particle systems, Rev. Mod. Phys. 73 (2002) 1067–1141 CrossRefGoogle Scholar
Henderson, L.F., The statistics of crowd fluids, Nature 229 (1971) 381–383 CrossRefGoogle ScholarPubMed
J. Venel, Modélisation mathématique des mouvements de foule, Ph.D. thesis, Laboratoire de Mathématiques, Université Paris XI, Orsay, France, 2008
Blue, V., Adler, J., Cellular automata microsimulation of bi-directional pedestrian flows, J. Transp. Res. Board 1678 (2000) 135–141 CrossRefGoogle Scholar
Teknomo, K., Application of microscopic pedestrian simulation model, Transp. Res. Part F 9 (2006) 15–27 CrossRefGoogle Scholar
S.P. Hoogendoorn, P.H.L. Bovy, W. Daamen, Microscopic pedestrian wayfinding and dynamics modelling, Pedestrian and Evacuation Dynamics (2001) 123–154
Helbing, D., Molnar, P., Social force model for pedestrian dynamics, Phys. Rev. E 51 (1995) 4282–4286 CrossRefGoogle ScholarPubMed
Reynolds, C., Flocks, herds, and schools: A distributed behavioral model, Comput. Graph. 21 (1987) 25–34 CrossRefGoogle Scholar
Paris, S., Pettré, J., Donikian, S., Pedestrian reactive navigation for crowd simulation: a predictive approach, Comput. Graph. Forum 26 (2007) 665–674 CrossRefGoogle Scholar
S. Paris, Caractérisation des niveaux de services et modélisation des circulations de personnes dans les lieux d’échanges, Ph.D. thesis, Université de Rennes 1, 2007
M.S. Garcia, Stability, scaling and chaos in passive-dynamic gait models, Ph.D. thesis, Cornell University, 1999
S. Erlicher, A. Trovato, P. Argoul, Modeling the lateral pedestrian force on a rigid floor by a self-sustained oscillator, Mech. Syst. Signal Process 2010 doi:10.1016/j.ymssp.2009.11.006
P.A. Cundall, A computer model for simulating progressive large scale movements of blocky rock systems, in Proc. Symp. Int. Soc. Rock Mech., 1971, Vol. 1
Cundall, P.A., Strack, O.D.L., A discrete numerical model for granular assemblies, Geotechnique 29 (1979) 47–65 CrossRefGoogle Scholar
Y. Kishino, Disk model analysis of granular media, Micromechanics of Granular Materials (1988) 143–152
M.P. Allen, D.J. Tildesley, Computer simulation of liquids, Oxford University Press, 1987
M. Jean, J.J. Moreau, Unilaterality and dry friction in the dynamics of rigid bodies collection, Contact Mechanics Int. Symp. (1992) 31–48
Frémond, M., Rigid bodies collisions, Phys. Lett. A 204 (1995) 33–41 CrossRefGoogle Scholar
Radjai, F., Jean, M., Moreau, J.J., Roux, S., Force distributions in dense two-dimensional granular systems, Phys. Rev. Lett. 77 (1996) 264–277 CrossRefGoogle ScholarPubMed
Jean, M., The non smooth contact dynamics method, Compt. Methods Appl. Math. Eng. 177 (1999) 235–257 CrossRefGoogle Scholar
Paoli, L., Time discretization of vibro-impact, Phil. Trans. R. Soc. A 359 (2001) 2405–2428 CrossRefGoogle Scholar
M. Renouf, Optimisation numérique et calcul parallèle pour l’étude des milieux divisés bi- et tridimensionnels, Ph.D. thesis, Université Montpellier II, Sciences et Techniques du Languedoc, 2004
Saussine, G., Cholet, C., Gautier, P.E., Dubois, F., Bohatier, C., Moreau, J.J., Modelling ballast behaviour under dynamic loading, Part 1: a 2d polygonal discrete element method approach, Comput. Meth. Appl. Mech. Eng. 195 (2006) 2841–2859 CrossRefGoogle Scholar
M. Frémond, Collisions, Edizioni del Dipartimento di Ingegneria Civile dell’Università di Roma Tor Vergata, ISBN 978-88-6296-000-7, 2007
J.J. Moreau, Unilateral contact and dry friction in finite freedom dynamics, in J.J. Moreau, P.-D. Panagiotopoulos (ed.) Non Smooth Mechanics and Applications, CISM Courses and Lectures, Vol. 302, Springer-Verlag, Wien, New York, 1988, pp. 1–82
J.J. Moreau, Some numerical methods in multibody dynamics: Application to granular materials, Eur. J. Mech. A/Solids (1994) 93–114
C. Ericson, Real Time Collision Detection, Morgan Haufmann Publishers, 2004
Dal Pont, S., Dimnet, E., A theory for multiple collisions of rigid solids and numerical simulation of granular flow, Int. J. Solids Struct. 43/20 (2006) 6100–6114 CrossRefGoogle Scholar
Dal Pont, S., Dimnet, E., Theoretical approach to instantaneous collisions and numerical simulation of granular media using the A-CD2 method, Communications in Applied Mathematics and Computational Science, Berkeley 3/1 (2008) 1–24 Google Scholar
Moreau, J.J., Sur les lois du frottement, de la viscosité et de la plasticité, C. R. Acad. Sci. Paris 271 (1970) 608–611 Google Scholar
R. Kimmel, J.A. Sethian, Fast marching methods for computing distance maps and shortest paths, Technical Report 669, CPAM, University of California, Berkeley, 1996
Helbing, D., Farkas, I., Vicsek, T., Simulating dynamic features of escape panic, Nature 407 (2000) 487–490 CrossRefGoogle Scholar
D. Helbing, I. Farkas, P. Molnár, T. Vicsek, Simulation of pedestrians crowds in normal and evacuation situations, M. Schreckenberg and S. Deo Sarma (Ed.), Pedestrian and evacuation dynamics, 2002, pp. 21–58
Zivanovic, S., Pavic, A., Reynolds, P., Probability-based prediction of multi-mode vibration response to walking excitation, Eng. Struct. 29 (2007) 942–954 CrossRefGoogle Scholar
Andriacchi, T.P., Ogle, J.A., Galante, J.O., Walking speed as a basis for normal and abnormal gait measurements, J. Biomech. 10 (1977) 261–268 CrossRefGoogle ScholarPubMed
Dallard, P., Fitzpatrick, A.J., Flint, A., Low, A., Ridsdill-Smith, R.M., The Millenium bridge London – problems and solutions, The Structural Engineer 79 (2001a) 15–17 Google Scholar
Dallard, P., Fitzpatrick, A.J., Flint, A., Low, A., Ridsdill-Smith, R.M., The Millenium bridge London, The Structural Engineer 79 (2001b) 17–33 Google Scholar