Abstracts
Résumé
La construction d'un modèle numérique destiné à prédire la formation et l'évolution de dépôts de sédiments à l'amont d'un barrage est présentée. A partir d'informations sur les apports en eau et en sédiments en provenance du bassin versant consolidées par une analyse hydrologique en QdF, un modèle hydraulique bidimensionnel horizontal couplant équations de Saint Venant et une équation de convection-diffusion est mis en œuvre. L'application de ce modèle sur la retenue de Zardezas de la région de Skikda (Algérie) montre, à la fois, les difficultés pratiques rencontrées dans la mise en œuvre et l'apport possible d'une telle méthode pour la gestion des retenues algériennes.
Mots-clés:
- Modèle numérique,
- hydrogramme de crue,
- débit-durée-fréquence QdF,
- sédiments,
- barrage,
- Algérie
Abstract
Sedimentation rates are often very high in Algeria, reaching about 1% of the reservoir volume per year in most cases. The management of existing reservoirs and the choice of location of new reservoirs may be improved by using a numerical model that simulates sediment deposition. The proposed method was developed on a selected case for which a convenient set of data had been gathered.
Initially, the Zardezas reservoir had a capacity of 34 million m3, but presently, the capacity is only 17 million m3. Due to the levelling of two topographies in 1975 and 1986 and discharge data available from 1968 to 1993, the numerical model could be calibrated for the period 1975-1986.
As the cross-distribution of sediments is thought to be a main factor for the reservoir deposition rate, a 2-D horizontal hydrodynamic model was selected. Sediments were modelled by a concentration that was calculated using an advection-diffusion equation. A source term determining the exchange rate between the flow and the bottom as proportional to an equilibrium concentration was used. Calculation of this source term followed a simplified version of the method developed by VAN RIJN (1984). The set of 4 equations ((8) + (9) + (10) + (11)) was solved by a second-order explicit finite volume scheme of the Godunov type, which allows the modelling of very unsteady flows (PAQUIER, 1998). The bottom elevation was modified at every time step by distributing the calculated deposits inside one cell among the neighbouring vertices.
Globally, the proposed method should be carried out in two steps. The first step involved model calibration including a hydrological analysis in order to determine the inputs (water and sediments) during the calibration period and calculation of the features of the hydrological regime for the extrapolation periods. The second step involved use if the model to define management strategies. The hydrological scenarios are built from the hydrological regime and the 2-D model is used to calculate the sediment deposits for every scenario. This second step is not described in the present paper.
The hydrological analysis involved building QdF (flood-duration-frequency) curves (JAVELLE et al., 2000) from the daily discharges and from the maximum discharges of the rarest floods. Some flood discharge hydrographs were considered and were used to determine the duration of typical floods. Results from this hydrological analysis are summarised by curves in V(d,T) (Table 2) (maximum mean stream flows during the duration d for a return period T) and Q(d,T) (Table 3) (maximum over-threshold during stream flows for T) which were built from the converging QdF model developed by JAVELLE et al. (1999). The main catchment parameters D (characteristic flood duration) and the instantaneous peak discharge over a return period of 10 years were respectively equal to 4 hours and 362 m3 /s. For the estimate of the curves over a return period of 10 years, the gradex of maximum 24 hour rainfalls (estimated to be 24.7 mm) was used. From Table 3 of Q(d,T), mono frequency synthetic discharge hydrographs (HSMF) can be built (e.g. Figure 4) using a rising time equal to D. These hydrographs can be used to define hydrological scenarios by fixing the successive return periods (of the HSMF).
For the calibration period 1975 to 1986, the observed or reconstituted discharge hydrographs were used to be closer to real events (Table 4). Because concentrations were not registered precisely enough, simplified assumptions were used for the calibration period and should be kept for future scenarios (peak concentration was fixed to 100 kg/m3 and a linear relation between discharge and concentration was assumed during the flood (see Figure 5)). Only one class of sediment with a mean diameter of 0.1 mm was considered. The 2-D calculations were performed on a grid of 1005 cells (Figure 6) with a space step between 10 and 80 metres. Model calibration consisted of selecting a suitable coefficient a (in equation (12)), which is equivalent to the average distance required to reach the equilibrium concentration. For the period 1975-1986, the calculation provides 4 m thick deposits through the entire reservoir bottom (Figure 8). The discrepancies with measurements were mainly too few deposits near the dam and too much sediment accumulated on the banks of the reservoir (Figures 7 to 9).
It can be concluded that the proposed method provides useful results although some improvements are required such as: sediment exchange relations between the flow and the bottom; refining the calculation grid and reducing the uncertainty about the inputs by accurately and regularly measuring both discharge and sediment concentrations. The method should be further validated on other existing reservoirs in the same hydroclimatic context.
Keywords:
- Numerical model,
- Flood hydrograph,
- Discharge-duration-frequency QdF,
- Sediments,
- Dam,
- Algeria