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Modélisation 2D discrète du mouvement des piétons : application à l'évacuation des structures du génie civil et à l'interaction foule-passerelle

Abstract : The development of a model for crowd movement simulating the evacuation of public spaces becomes useful and necessary to determine the effectiveness of transportation infrastructures. The effects of pedestrians on civil engineering structures, such as crowd-structure dynamic interaction, must also be considered and modeled. In this thesis, a 2D crowd model is proposed in which the movement of each pedestrian is represented both in time and space. This model is able to take into account the dynamical pedestrians' action on a moving floor. Three steps are needed to assemble the proposed model. The first concerns the management of pedestrian-pedestrian and pedestrian-obstacle interactions. The non-smooth granular model proposed by Frémond to manage collisions between rigid particles is studied and implemented in a MATLAB environment. This discrete approach applies a rigorous thermodynamic framework in which the local interactions between particles are managed using pseudo-potentials of dissipation. A comparison between this model and two others, already adapted to the crowd, is performed. The second step concerns the management of pedestrians' behavior. A displacement strategy has to be defined for each pedestrian. The strategy of the shortest path to get from one point to another is implemented through a Fast Marching algorithm and is used to obtain the instantaneous desired direction of each pedestrian. Social forces are also introduced in order to manage the interaction between each pedestrian and his nearest environment. An original approach allowing us to create and control subgroups, using pseudo-potentials of dissipation, is implemented. The last step deals with the crowd-footbridge coupling for lateral and vertical oscillations of the structure. An alternating (sinusoidal) sideways force is used in order to take into account the pedestrian's oscillations around his trajectory. This force, due to his walking and his action on the bridge, allows one to define the acceleration of each pedestrian's oscillations around his trajectory. The synchronization of the walking frequency of each pedestrian with the oscillations frequency of the system "crowd-footbridge" is managed via a Kuramoto type differential equation which allows one to govern the evolution of the total phase of the walking force generated by each pedestrian on the bridge. An analytical study is also developed to determine the key parameters of the synchronization phenomenon. Numerical simulations using the proposed model dealing with crowd evacuation of civil engineering structures and pedestrians-footbridge interaction are finally presented
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Submitted on : Tuesday, February 28, 2012 - 10:53:20 AM
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Philippe Pecol. Modélisation 2D discrète du mouvement des piétons : application à l'évacuation des structures du génie civil et à l'interaction foule-passerelle. Modélisation et simulation. Université Paris-Est, 2011. Français. ⟨NNT : 2011PEST1109⟩. ⟨pastel-00674774⟩



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