Une approche pour la comparaison, du point de vue fonctionnement hydraulique, de propositions d'extension d'un réseau d'assainissement An approach to compare, from the hydraulic operation viewpoint, propositions of extension of an urban storm drainage network

Résumé

Les outils informatiques développés dans le cadre de la conception des réseaux d'assainissement permettent de concevoir plusieurs solutions de réseaux pour un même problème. Il revient ensuite au décideur de choisir quelle solution retenir. Le problème qui se pose alors est la comparaison des propositions selon des critères économiques, écologiques, de fonctionnement, de maintenance, .... La difficulté vient du fait que certains de ces critères sont difficiles à évaluer. Nous présentons dans cet article une méthode permettant d'évaluer l'un de ces critères : le fonctionnement global d'un réseau d'assainissement suite à l'extension de ce dernier. Cette méthode est basée sur des simulations hydrauliques. Or ces simulations donnent des informations en chaque noeud du réseau (histogrammes de vitesses, débits ou hauteurs de charge) et non une indication sur la qualité de fonctionnement du réseau dans son ensemble. Il nous a donc fallu élaborer une technique d'agrégation permettant de passer de l'élément isolé (le tronçon) à l'ensemble organisé (le réseau). Cette technique d'agrégation utilise les notions de "période d'insuffisance" d'un tronçon qui est la période de retour d'une pluie pour laquelle ce tronçon dépasse un certain seuil de dysfonctionnement (dans notre cas, le débordement) et de sensibilité du tissu urbain à un dysfonctionnement hydraulique du réseau. Cette dernière notion est nécessaire car certains tronçons peuvent très bien déborder sans induire de désordres apparents s'ils ont, par exemple, une capacité d'écoulement faible et/ou s'ils se trouvent dans une zone non bâtie. Les informations nécessaires à l'utilisation de cette méthode étant souvent de qualité inégale en termes de précision, nous avons pris le parti de raisonner non sur des valeurs déterminées ais sur des classes d'appartenance modélisées sous forme de sous-ensembles flous.

Mots-clés:

• Assainissement pluvial,
• fonctionnement hydraulique,
• inférences floues,
• évaluation

Mots-clés:

• Urban storm drainage,
• hydraulic operation,
• fuzzy inferences,
• evaluation

Abstract

Software packages developed for the design of urban storm drainage networks allow several solutions to be proposed for the same problem. It then falls to the designer to choose which solution to use, the main problem being the evaluation of the efficiency (quality) of each solution. A multi-criteria approach represents one theoretical solution to the problem. This necessitates the determination of which criteria to use and how to evaluate them. In this paper, we present a method of evaluation of the criteria related directly to the functioning of an urban storm drainage network after its extension. This method is developed on the basis of hydraulic simulations of the network. These simulations produce results (histograms of discharge, water levels, rates of filling, hydraulic head, ...) for each pipe. Given these results, the designer must be able to assess whether the proposed solution is satisfactory, and then compare it with other solutions. The problem is therefore to be able to evaluate a complete network, whereas the results of conventional simulations present a fragmented and partial view of its functioning (pipe by pipe). A solution to this problem is proposed in the form of a tool, able to calculate a single combined value from the simulation results. The following calculation steps are proposed:

1. First we model the effectiveness of each pipe. To do that, we determine the "return period of failure" of a pipe which is the return period of a rainfall for which the pipe passes a certain level of failure (in this paper, we take the level of failure as the state of overflow). The rainfall model used is the same one used for the design of the network. Then we attribute a numerical value (S) for the operation of a pipe according to its return period of failure by way of a satisfaction function.

2. Secondly we model the weighting given to each pipe. This weighting is constructed from the discharge capacity of the pipe and the sensitivity of the urban fabric (in proximity to the pipe) to system failure. The discharge capacity is calculated using Manning's formula on the basis of diameter, slope and internal roughness. The value of the coefficient (R), which indicates the sensitivity, necessitates a good knowledge of the urban fabric. Among the important variables related to this factor, we can identify the population density, the traffic density and the density of land use -DLU- (this variable is identified by the density of residential land use, the density of commercial land use, ...). We can then write R=f(density of population, density of traffic, DLU,...). Considering the difficulty of the identification of (f), we preferred to explore an expert approach. The rules have been identified from a bibliographical analysis and limited expertise. An example of theses rules is presented here : IF density of population is high and density of commercial land use is average THEN the degree of sensibility is average. The examination of the identified rules shows the use of words like low, average and high. To model this linguistic qualifying information, we have chosen fuzzy sets. Also the inferences of fuzzy information are treated by using operations of fuzzy logic.

3. Finally, we aggregate the results with the following equation:

    n

C=∑Q_aixR_ix∆S_i

  i=1

where DS_i=S_i - S_i' represents a measure of the effect of network modification upon the operation of the pipe i (S_i and S_i' are the effectiveness of the pipe respectively before and after the proposed modification), Q_ai is the discharge capacity of the pipe i, R_i is the coefficient of sensitivity of the area to failure associated with pipe i and C is a factor which quantifies the effect on the general operation of the network.

With the coefficient C, the designer is now able to classify the different solutions of extension of an existing urban drainage network according to their impacts on its functioning and to introduce this classification order in a multi-criteria method.