A Time-continuous Compartment Model for Building Evacuation

Modèle à compartiments continu en temps de l'évacuation d'un bâtiment

Bertrand Antti Maury (1, 2, 3) , Sylvain Faure (2, 3) , Jacques Angelé (3) , Rémi Bachimont (3)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 Signactif

We propose here a general framework to estimate global evacuation times of complex buildings, and to dynamically investigate the dependence of this evacuation time upon various factors. This model relies on a network, which is in some way the skeleton of the building, the nodes of which are the bottlenecks or exit doors. Those nodes are connected by edges which correspond to portions of egress paths located within a given room. Such models have been proposed in a discrete setting. The model we propose takes the form of a continuous evolution equation of the differential type. It relies on a limited number of variables, namely the number of people gathered upstream each node, together with the number of people on their way from a node to the next one. The basic parameters of the model are the capacities of doors, and the time needed to walk from one node to the next one. In spite of its macroscopic character (the motions of pedestrians are not described individually), this approach allows to account for complex and nonlinear effects such as capacity drop at bottlenecks, congestion induced speed reduction, and possibly some dispersion in evacuees behaviors. We present here the basic version of the model, together with the numerical methodology which is used to solve the equations, and we illustrate the behavior of the algorithm by a comparison with experimental data.

Mots clés: modeling; human behavior; risk assessment; evacuation times; exit capacities

Domaines: Modélisation et simulation

Bertrand Antti Maury, Sylvain Faure, Jacques Angelé, Rémi Bachimont. A Time-continuous Compartment Model for Building Evacuation. third European symposium on fire safety sciences (ESFSS2018) , Sep 2018, Nancy, France. ⟨hal-01813639⟩