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Numerical simulation of sediment mixture deposition part 1 ... - LTHE

Numerical simulation of sediment mixture deposition part 1 ... - LTHE

Fig. 9. Bed surface

Fig. 9. Bed surface material related to subsurface material. Fig. 7. a. Grain size distribution of bed load and surface material at equilibrium. b. Sieve curves of bed-load and surface material at equilibrium. 5 Evolution of grain size distribution Bed deposition can be related to grain size distribution at the bed surface. This is done in Figure 8 for two different points of the model. The history of deposition is also visible in a vertical section of bed material at the end of the simulation (Figure 10 ). Comparison of this vertical profile with mean diameter and elevation of the highest substrata during the deposition process (Figure 9) gives some clues for interpreting its characteristics. Front deposition is recorded as an accumulation of fine sediment (d = 5-10 mm). Further aggradation is progressively coarser and coarser. Surface layer material is even coarser than subsurface material. For the comparison, mean diameter of sediment input is also reported in Figure 10 . Fig. 10. Mean diameter of sediment deposit (x = 25m) Fig. 8. Bed surface material related to bed aggradation. The different stages are reflected by the mean diameter of the bed surface. The initial coarse bottom is first covered with a thin layer of very fine sediment. As outlined by Seal et al. (1997) the front deposit is made of relatively fine sediment and the wedge deposit (upstream front) is made of coarser gravel. The mean diameters of the surface (mixing layer) and the immediate substratum (upper stratum) are plotted in Figure 9. The similarity of the surface layer at time 84 hr with the subsurface at time 96 hr downstream x = 30 m is a direct consequence of the rules which were adopted for the calculation. The upper stratum is fed with material coming from the mixing layer. At a certain time, subsurface sediment is similar to surface sediment at the moment this material was deposited. We need to acknowledge the simplicity of our model in comparison with hypotheses given in the literature. With the rules programmed in SEDICOUP, the bed deposit is made of direct storage of material that has settled at previous times. Sorting equation (4), which was first written by Rahuel et al. (1989), is nothing else than a continuity equation written for a given control volume (the mixing layer). As bed-load transport is directly connected to its grain distribution (equation 1), subsurface grain distribution is only indirectly linked to bed-load transport through sediment exchange between surface and subsurface. During aggradation with a mixing layer whose thickness is unchanged, bed-load transport is not dependent on subsurface grain distribution. Parker (1991) made a suggestion that part of the deposited material is directly transferred to the subsurface. Toro-Escobar et al. (1996) follow the same idea in their interpretation of SAFL experiments. Size distribution of the surface layer is still 422 JOURNAL DE RECHERCHES HYDRAULIQUES, VOL. 38, 2000, NO. 6

the reference for bed load calculation and therefore elimination of material that results from subsurface transfer modifies the amount of bed-load transport. Di Silvio (1991) agreed with Parker's ideas and made an attempt to discuss the physical processes involved in fluxes between transport load, pavement (equivalent to our mixing layer) and subpavement (equivalent to our upper stratum). Note that "experimental evidence that the pavement remains coarser than the subpavement even during intense deposition" (Di Silvio 1991) is not reproduced by our calculation downstream and in the lower part of the front deposit (see plot of mean diameter at time 96 hr in Figure 11, downstream of x = 28 m). Di Silvio (1991) and Sieben (1997), among others, have developed refined models. In Di Silvio’s, four different layers are considered and separate formulations describe horizontal and vertical fluxes of sediment, respectively in and among these layers. These authors acknowledge the difficulty of acquiring pertinent data for real validation and the calibration of these detailed models should be re-considered in every case. The merit of such models is in any case their contribution to a better understanding of existing processes. However, most existing models (e.g. Cui et al. 1996) rely on a sharing of vertical fluxes between surface and subsurface and some modification of the basic transport formula for single sized sediment. There is no real difference from our basic rules because coupling exists between size fractions within the mixing layer (used for calculation of transport rate) and subsurface material. These basic rules can be refined by a more clever definition of the mixing layer thickness on the one hand, and by accounting for hiding effects in the sediment transport formula on the other hand. 6 Bedload discharge Back-calculation from bed profile measurements allowed Toro- Escobar et al. (1996) some quantification of total bedload transport rate. Similar results can be directly plotted from the simulation (Figure 11). The same linear decrease as for SAFL experiments is observed, with only very slow variations of transport rate after passage of the front. This particularity corresponds to the quite constant aggradation rate that is observed in Figure 6 before the front reaches the downstream end of the flume. As flow conditions become uniform (with the full "hydraulic" meaning of the word), the solid transport rate tends to a uniform value, which is the upstream feed rate. Fig. 11. Bed load transport rate versus x, comparison with transport capacity at time 96 hr. Grain size distribution of bedload The profile of bed load transport rate can be plotted with distinction of the different sediment size classes (time 84 hr in Figure 12). Fine sediment (d < 1 mm) is deposited in the lower part of the front (x = 22-35 m) and eventually downstream for the very fine class 1, thus reproducing the "basal sand" deposit which is described by Seal et al. (1997). There is no deposition of this fine sediment upstream of the front where its presence within the mixing layer has adjusted at a low level, corresponding to its transit downstream. Medium sizes (d = 1-15 mm) fall after a short distance (a few meters, x = 16-20 m), thus building what was named by Seal et al. (1997) the 'gravel front'. The coarsest sediment (sediment classes 9, 8, and 7 partially), are dropped in the upstream part of the deposit. The mean diameter of the wedge will tend progressively to its equilibrium value d m = 27.8 mm. Fig. 12. Bedload transport profiles for each sediment size class at time 84 hr. Mechanism of transport Longitudinal profiles of dimensionless shear stress θ j (equation 2), computed from flow parameters at time 84 hr, are plotted in Figure 13 . Shield’s critical shear (θ c = 0.06) is exceeded within Fig. 13. Longitudinal profile of shear stress (t = 84 hr). the whole length for the finest sediment (d

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