Study of Flow in a Staircase at Subway Station

The flooding service of the Regie Autonome des Transports Parisiens (RATP) initiated hydrodynamic modeling of flows in its metro network in order to improve its Plan of Flood Risk Prevention. The modeling was performed using the software mike urban (MU), software developed by the Danish Hydraulic Institute (DHI) for open channel flows normally dedicated to the modeling of sewage network. The selected event to check this model is the exceptional flood in 1910. Modeling the RATP network in MU requires to introduce boundary conditions as time series of flows for each water inlet (staircase, ventilation grille, trap, etc.). The estimated flow represents a major element of the modeling process, and its quality can significantly influence the calibrated parameters and therefore the model output. This document details and discusses the assumptions that determine the flow rate Q entering in a staircase at subway station as a function of water level taking into account the presence of a facing wall on three of the four sides of the entrance to the metro. Three approaches will be discussed for this problem: theoretical, numerical, and experimental. The objective here is to present the results of the first two approaches and their limitations and to clarify the contributions of the experimental approach. The numerical approach has been able to model stationary flow through a staircase although some geometric shapes such as stairs are not fully represented. Tests by this software showed that the flow discharge through a staircase corresponds to the theoretical values.