Estimation des niveaux d'inondation pour une crue éclair en milieu urbain : comparaison de deux modèles hydrodynamiques sur la crue de Nîmes d'octobre 1988 Estimation of the flood levels for a flash flood in urban area : comparison of two hydrodynamic models on the 1988's Nîmes flood

Résumé

Lors des crues extrêmes en ville, une forte part des écoulements reste en surface. Pour simuler ces inondations, deux modèles sont présentés : le logiciel REM² U unidimensionnel a pour objectif de simuler la propagation des débits de crue dans l'ensemble d'un réseau de rues alors que le logiciel Rubar 20 bidimensionnel vise à fournir plus d'information sur ces écoulements. Des calculs avec ces deux logiciels ont été menés sur la crue d'octobre 1988 dans un quartier de Nîmes. Lors de cet événement, les hauteurs d'eau maximales ont dépassé deux mètres en certains points et les vitesses 2 m/s ce qui entraînait des passages en régime torrentiel. A partir des données rassemblées sur les sections en travers des rues, des maillages de calcul limités au réseau de rues ont été construits pour les deux logiciels afin de permettre un calcul détaillé. La comparaison des résultats avec les laisses de crue montre des situations très contrastées d'un point à un autre pour une hauteur d'eau maximale moyenne sur l'ensemble de la zone inondée correctement simulée. L'écart sur cette hauteur est, en moyenne, de 1 m ce qui provient des incertitudes sur les observations, sur la topographie et sur les conditions aux limites, des approximations lors de la modélisation et de particularités locales non décrites. Entre les deux logiciels, l'évolution des hauteurs et des vitesses est généralement très proche bien que, comme pour la comparaison avec les laisses de crue, des différences locales importantes sont observées.

Abstract

The hydraulic models that are used to simulate floods in rural areas are not adapted to model floods through urban areas, because of details that may deviate flows and create strong discontinuities in the water levels, and because of the possible water flow running in the sewage network. However, such modelling is strongly required because damage is often concentrated in urban areas. Thus, it is necessary to develop models specifically dedicated to such floods. In the southern part of France, rains may have a high intensity but floods generally last a few hours. During extreme events such as the October 1988 flood in the city of Nîmes, most of the flow remained on the ground with high water depths and high velocities, and the role of sewage network can be neglected. A 1-D model and a 2-D model were used to calculate such flows, which may become supercritical. On the catchments of the streams which cross the city of Nîmes, the rainfall was estimated as 80 mm in one hour and 250 mm in six hours in October 1988, although some uncertainties remain. The return period can be estimated between 150 and 250 years. The zone selected to test the models was an area 1.2 km long and less than 1 km wide in the north-eastern part of the city. It includes a southern part with a high density of houses. The slope from the North (upstream) to the South (downstream) was more than 1 % on average and was decreasing from North to South. Various topographical and hydrological data were obtained from the local Authorities. The basic data were composed of 258 cross sections of 69 streets with 11 to 19 points for each cross section. Observations of the limits of the flooded areas and of the peak water levels at more than 80 points can be used to validate the calculation results. The inputs consisted of two discharge hydrographs, estimated from a rainfall-discharge model from rains with a return period of 100 years, which may result in an underestimate of these inputs. These two hydrographs correspond to the two main structures that cross the railway embankment, which constitutes an impervious upstream boundary of the modelled area. Whereas the western and eastern boundaries are well delimitated by hills above maximum water levels, the downstream southern boundary is somewhat more questionable because of possibilities of backwater and inflows from neighbouring areas.

The 1-D software REM²U solved the Saint Venant equations on a meshed network. At crossroads, continuities of discharge and of water heads were set. The hydraulic jump was modelled by a numerical diffusion applied wherever high water levels were found. The Lax Wendroff numerical scheme was implemented. It included a prediction step and a correction step, which implied precise solving of these very unsteady and hyperbolic problems. The software was validated on numerous test cases (Al Mikdad, 2000) which proved the adaptation to problems of calculations in a network of streets.

The 2-D software Rubar 20 solves 2-D shallow water equations by an explicit second-order Van Leer type finite volume scheme on a computational grid made from triangles and quadrilaterals (Paquier, 1998). The discontinuities (hydraulic jumps for instance) are treated as ordinary points through the solving of Riemann problems. For the Nîmes case, the grid was built from the cross sections of the streets. Four grids were built with respectively 4, 5, 7 or 11 points for every cross section and these points correspond to the main characteristics of the cross section: the walls of the buildings, the sidewalks, the gutters and the middle point. The simplest crossroads were described from the crossings of the lines corresponding to these points, which provide respectively 16, 25, 49 or 121 computational cells. The space step was about 25 metres along the streets but went as low as 0.1 m in the crossroads; due to the explicit scheme, which implies that the Courant number was limited to 1, the time step was very small and a long computational time was required.

The computations were performed with a uniform Strickler coefficient of 40 m^1/3/s. Both 1-D and 2-D models provided results that agreed well with observed water levels. The limits of the flooded area were also quite well simulated. However, locally, the differences between calculated and observed maximum water depths were high, resulting in an average deviation of about 1 metre. The reasons for such deviations could come from three main causes. First, the uncertainty of topographical data is relatively high, because of the interpolation between measured cross sections without a detailed complementary DEM (digital elevation model). Second, the observed levels were also uncertain and reveal local situations that are not reconstructed by the hydraulic models which provided maximum water levels averaged on one cell which may not coincide with the exact location of the observations. Finally, modelling means a simplification of the processes, which implies cancelling the level variations due to some obstacles, such as cars, which are not simple to identify.

In conclusion, both software packages can model a flood, even a flash flood, in an urbanised area. Research is still necessary to develop methods to fully use urban databases in order to define details more precisely. The improvements to the 1-D software should include a better modelling of storage and of crossroads with an integration of adapted relations for the head losses. 2-D software has a greater potential but the difficulty to build an optimal computational grid means a long computational time, which limits the use of such software to small areas. For both software packages, methods still need to be developed in order to represent exchanges with the sewage network, storage inside buildings and inputs directly coming from rainfall.

Keywords:

• Flash floods,
• urban risk,
• hydrodynamic modelling,
• de Saint Venant equations,
• october 1988 Nîmes flood,
• 1-D software,
• 2-D software,
• hydraulic jump