1D modelling of fine sediments dynamics in a dam reservoir during a flushing event
2 STUDY SITE AND THE 01 FLUSHING EVENT
The Rhône river is a major river in Europe and flows in its upper part in Switzerland and then through France to Mediterranean sea. Downstream Lake Geneva, two dams are built on the Swiss Rhône river: the Verbois and Chancy-Pougny dams. These reservoirs trap a
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large quantity of sediment provided by the Arve River. The 70 m high Génissiat dam is located downstream on the French Upper Rhône River (Fig. 1).
Since the construction of the Verbois dam in the 40s, sediment flushing operations are regularly conducted on the Rhône River to prevent flood hazards in the lowest parts of Geneva city, as the reservoir bed aggradation leads to the rise of water levels (Peteuil et al. 2013). Downstream of the Swiss-French border, and more particularly at the Génissiat res- ervoir, supporting operations are carried out by the CNR to limit the impact of the high SSC released from the Swiss dams. The main challenge for CNR is to maintain an average concentration downstream of Génissiat below 5 g L throughout the operation. Meeting the maximum concentration limits set by the French authorities is based on the dilution capac- ity of the Génissiat dam, thanks tothree hydraulic outlets located at different levels (a bot- tom gate, a half depth gate and a surface spillway). During flushing operations, an extensive measurement network is deployed by CNR on the French Upper Rhône River to monitor the operation progress. In particular, discharges and SSC chronicles are measured at Pougny and at the Génissiat dam outlets (Fig. 1).
Feedbacks from the numerous flushing operations have permitted to improve the manage- ment protocol of the Génissiat reservoir during flushes. The reservoir water level is first low- ered to flush a volume of sediments and then raised again while Swiss reservoirs are flushed. Therefore, a part the sediments removed from the Swiss reservoirs are eventually trapped in the Génissiat reservoir. Suspended load and bedload sampling have shown that solid inflow and outflow during flushing events are mainly composed of fine sediments (clay, silt and fine sand). Those fine sediments have the largest contribution in the Génissiat reservoir volumet- ric budget (Guertault et al. 2014).
3 HYDRO-SEDIMENTARY MODEL
3.1 1D streamwise sediment transport model
The hydro-sedimentary model used in this study is Mage-AdisTS. The hydrodynamic module Mage solves 1D shallow water equations with Manning-Strickler formulation for roughness. An implicit numerical scheme is used to solve the equations, so that the model is not recom- mended for supercritical flows. The Adis-TS module solves advection-dispersion equations in conservative formulation (Equation 1) for several sediment grain sizes (Camenen et al. 2013). Those equations are coupled using source terms that allow to model erosion and deposition. The separation of main channel and medium zone dynamics is possible. Adis-TS is loosely coupled with Mage that provides the evolution of hydrodynamic parameters.
Figure 1. Location of the Upper Rhône river.
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149 ∂ ∂ + ∂ ∂ − ∂ ∂ ∂ ∂ ⎛ ⎝⎜ ⎛⎛ ⎝⎝ ⎞⎠⎟⎞⎞⎠⎠= SC t QC x ∂x D S C x W i+∂ i C C QCC f D CCi i iWWz (EEi−DDi) (1)
where CCC is the concentration for grain size i, Ci
Σ
iCCCi is the total concentration, Q is the discharge, S is the wet section, DD is the diffusion coefficient, E and D are erosion and depo-fsition fluxes, WWW is the river width.z
The source term combines (Partheniades 1965) formula for erosion and (Krone 1962) formula for deposition:
( ) a (( )w h i i PD i(( q i s i = ) ,i( eq , (2)
where CCeq,i is the equilibrium concentration for the grain size i , aPD i, is a calibration param- eter, ws i, is the settling velocity for the grain size i calculated using the Camenen formula (2007), h is the water depth.
The equilibrium concentration depends on the bed shear stress:
Ceq C C i i cr i cr i , , , , , = − ⎛ ⎝⎜ ⎛⎛ ⎝⎝ ⎞ ⎠⎠⎠ cr i ⎧ ⎨ ⎪ ⎧⎧ ⎨⎨ ⎩ ⎪ ⎨⎨ ⎩⎩ 0 C C 1⎞ / cr i>1 ⎠⎟ ⎞⎞ ⎠⎠ 0 / ≤1 τ τ τ τ// τ τ// if if cr i (3)
where CCC0,i is a calibration parameter, τ is the bed shear stress, ττcr,i is the critical shear stress for initiation if movement for the grain size i , estimated using (Soulsby and Whitehouse 1997) formula.
3.2 1D Vertical stratification model
For fine granulometric fractions such as clay and silt, the vertical profile of concentration is almost uniform, but for coarser sediment, the buoyancy force inhibits the vertical mixing by tur- bulence and leads to a vertical gradient in SSC (Wright and Parker 2004). Since the 1D transport model only estimates an average concentration for each cross section, a module is implemented to reproduce that vertical stratification and calculate the SSC at dam outlet positioned at differ- ent water depths.
The vertical concentration profile can be derived from the mass conservation equation and assuming a steady state vertical diffusion equation. Different formulations are obtained depending on the model used for the sediment diffusivity. Preliminary calculation have shown that the concentration at the dam half bottom gate can be estimated from the concentration at the dam bottom with an exponential profile:
Ci Ci w z z C C CC i v ( )zz = C(z( )z expz exp) ⎡ wsi( ) ⎣⎣⎣ ⎤ ⎦ ⎥ ⎤⎤ ⎦⎦ 0 z z ( 0)exp)exp ⎣⎣⎣ ∈ (4)
where z0 is the reference elevation, ∈∈v= EEκuuuu h is the sediment diffusivity, σσ is Schmidt E number (σσ = 1 as a first approximation), κ = .E 0 4. 1 is Von Kàrmàn parameter, u ∗ is the shear velocity, h is thewater depth, RRRi wwwssii/κuu is Rouse number for grain size i.u∗
Preliminary calculation have shown that the concentration passing through the dam half bottom gate can be estimated with an exponential profile applied to the concentration pass- ing through the dam bottom gate.
Some assumptions were formulated to apply a stratification model to this study:
• section-averaged hydraulic parameters computed by the 1D model are assumed represent- ative of the real local values,
• the average concentration passing through a gate can be approximated by the concentra- tion calculated at the elevation of the center of gravity of the gate.
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The stratification model implemented is described hereinafter. For each calculation time the shear velocity u∗ is calculated at the outlets location using the results from the hydrodynamic model, and the Rouse number Ri is then calculated for each grain size. An average concen-
tration in the cross-section for each grain size is provided thanks to the Adis-TS model. By definition, the average concentration is:
C h C dz m i C C z z h i C C , =
∫
z 1 0 0 ( )z (5)Using Equations 4 and 5, an expression for the bottom concentration for each grain size i may be written such as:
Ci C C C CCm i R h i R R E Ri R R E ( )z exp ( h z ) 0 1 0 = − ⎡ ⎣ ⎢ ⎡⎡ ⎣⎣ ⎤ ⎦ ⎥ ⎤⎤ ⎦⎦ , h σE σEE (6)
Equation 4 is then applied at the outlet elevations to estimate the concentration for each grain size i in the different gates. For each gate, the total concentration is the sum of concen- trations for all the grain sizes modelled.
4 2012 FLUSHING EVENT MODELLING 4.1 Calibration of the hydraulic model
The computational domain focused on the 24 km long reach from Pougny to the Génissiat dam (Fig. 1). The reservoir geometry was described with about 130 cross sections surveyed in December 2011. From that bathymetry, a 100 m regular mesh was built. Concerning the hydro- dynamic model, upstream and downstream boundary conditions were respectively described by the flush hydrograph measured at Pougny and the water level measured at the Génissiat dam. Strickler coefficients are calibrated to adjust friction to fit waterlines measured during interflush periods and the 2012 flushing event (Fig. 2b). In upper gravel-bed reaches of the res- ervoir, the skin friction coefficient based on the grain size measured in the main channel with the Strickler formula (1923) seems to be representative of the coefficient used in the model (Fig. 2a). Friction is reduced in the downstream part of the reservoir. Approaching the dam, bed substrate is finer and the total Strickler coefficient is lower than the skin friction coef- ficient. The total coefficient takes into account other factors of flow resistance (such as bed forms or the river morphology), that become significant compared to the skin roughness. 4.2 Sediment input
Sediment diameters to be used in the model have been determined. During the 2012 flush, a few samples of suspended sediments have been collected at the water surface at Pougny and at the
Figure 2. Calibrated Strickler coefficients (a) and computed waterlines for the 2012 flush (b).
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Génissiat dam gates outputs (Lerch and Thizy 2013; Launay 2013). Assuming each granulo- metric mode can be represented by a normal distribution, a classification into 5 granulometric modes with median diameters from 4 μm to 400 μm allows to reproduce the total distribution of the samples. The upstream boundary condition has been described for each population. It is deduced from the total SSC measured at Pougny and weighted by the proportion of each population found in the samples. The reservoir bed substrate was described according to river- bed samples collected along the main channel of the reservoir before the flushing event (Fig. 3). A sublayer of fine sediment that could be eroded has been defined along the reservoir. Their thickness is the maximum thickness of the deposits in the subreach during the previous inter- flush period. Between 15 km and 10 km upstream of the dam, the sediment layer is composed by medium sand with a diameter of 400 μm (Fig. 3a). Closer to the dam, the sediment layer is a sediment mixture of fine sand, silt and clay. Thickness of the sediment layer increases approaching the dam (Fig. 3b).
Parameters related to the physical properties of the sediment were determined from field data or literature. Table 1 includes the properties of the sediment used in the model. Con- solidation processes were not taken into account. A porosity was estimated for each grain size, however since the bottom layer consists of a mixture of several classes of sediment, a constant value p = 0.45 was considered for fine sediments.
4.3 Adis-TS model calibration
C0i C
C, and aPD i, parameters have been calibrated for each grain size. An analysis of the asymp- totic behaviour of the sediment transport law has been done:
• when CCeq,i= 0, D a CDi aaPPD iD i,iCwss is i,/H, which means that aPD i, is the most significant parameter to
calibrate deposition rate,
• when C = 0 and τ τττ τ/ττcr,i≥1, EEi aaaPPD iD i,iC (CCC0,ii crccr ii,i 1)ws is is,/H, which means that both aPD i, and
C0i C
C, have an effect on erosion process calibration.
aPD i, was considered as a non-equilibrium adaptation coefficient as suggested by (Armanini
and Di Silvio 1988) related to the fact that under unsteady flow conditions, the solid flow does not immediately reach the equilibrium, so that erosion and deposition mechanisms present an inertia. This coefficient represents the responsiveness of the evolution of the solid load compared with
Figure 3. Median diameter (a) and thickness (b) of the sediment layer in the main channel of the reservoir in the model.
Table 1. Physical properties of the model sediment sizes.
Name Clay Fine silt Coarse silt Fine sand Medium sand
d50 (m) 4 20 40 100 400
Settling velocity (m/s) 9.0 10−6 2.3 10−4 9.0 10−4 5.3 10−3 3.6 10−2
Critical shear stress (Pa) 0.15 0.15 0.15 0.16 0.22
Porosity 0.45 0.45 0.45 0.45 0.4
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the variations of the hydraulic conditions. CCC0,i was considered as a surface erosion rate constant, with the dimension of aconcentration, representative of the bottom sediment mobility.
According to surveys, the sediment load in the half depth gate is almost exclusively com- posed of clay and silt, when the sediment load in the bottom gate is also composed of sand. The first step is to calibrate aPD i, and CCC0,i for clay and silt for which the SSC vertical profile is homogeneous, to reproduce measured SSC and proportion of each fraction in the half depth gate. aPD i, and CCC0,i are then calibrated for sand to reproduce measured SSC and proportion of each fraction in the bottom gate.
4.4 Results
Calibration parameters used to model the 2012 flush are presented Table 2.
For fine sediments (d<0.1 mm), aPD i, decreases when grain size increases, until it reaches a constant value for sands. An interpretation for the quite high value used for clay is that this parameter counterbalances the settling velocity calculated for a single clay particle whereas flocculation may occur. CCC0,i also decreases when grain size increases.
From the average concentration (Fig. 4d) computed by the model Adis-TS, the stratifica- tion model estimates the concentration in the dam outlets. Erosion of the Génissiat reservoir during the first week of the flush is well reproduced in terms of SSC transport dynamics. It is not well reproduced in terms of values, as the model is not able to reproduce SSC peaks measured in the bottom gate. During the second week of the flush, when the Swiss reservoirs are drawn down, the model seems less efficient. The first SSC peak coming from Swiss reser- voirs 8 days after the beginning of the operation is overestimated by the model. (Fig. 4a.b.c). An interpretation is that the 1D model is not able to reproduce the propagation and diffusion ofthe concentration that should delay and attenuate the concentration signal. Concentration is also underestimated in the bottom gate (Fig. 4a). It may be due to the fact that the upstream sediment inflow in the model is estimated from surfacesamples and may be unrepresentative of the real inflow because it underestimates a part of sand load which is not measured at the Table 2. Calibration of C0 and aPD parameters.
Parameter Clay Fine silt Coarse silt Fine sand Medium sand
aPD,i 15 2 0.5 0.5 0.5
C0,i 1.7 1 0.8 0.3 0.3
Figure 4. Measured and calculated concentration at Génissiat dam during the 2012 Flush at the: bot- tom gate (a), half depth gate (b), surface spillway (c) and average modelled concentration (d).
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surface. The signal at the spillway (Fig. 4c) is not well reproduced may be due to the fact that it is located on the right bank section average parameters are likely to represent it poorly.
Fluxes presented Table 3 illustrate former comments on Figure 4. The agreement between calculated and measured fluxes is good for the first phase, but the model overestimates the flux during the second phase for the three outlets.
5 DISCUSSION
The contribution of the stratification model is quite significant. It can be highlighted by com- paring the total sediment mass passing through the dam outlets calculated with either SSC measured during the flush (1667 103 T), average SSC computed from Adis-TS model (4000
103 T), or SSC computed from the stratification model (2446 103 T). Even if the model over-
estimates fluxes at the Génissiat dam, the stratification model gives a better estimate of those fluxes than the only section averaged model. Several causes can explain differences between measured and calculated SSC. First, a finer sediment description of initial and boundary conditions thanks to additional data such as the quantification of the sand input at Pougny and a better reservoir bed substrate description could be useful. The calibration of param- eters aPD i, and CCC0,i could also be improved.
Some improvement of the model may be done. For example, the calculation of local instead of section averaged shear stress could be implemented. Mud consolidation could be taken into account with the use of a different ττ for erosion for consolidated or fresh deposits. It may cr be worth to take into account fine particles aggregation because the settling velocity of flocs is higher than the one for single particles and should promote deposition. Several suggestions might help to reproduce SSC peaks, as for example the implementation of a bank failure module. Cores sampled close to the dam (Tissot and Merketa 1994) have shown that the bed substrate is composed of alternate layers of fine sediments and sands that can not be described by the model in which the bed substrate is homogeneous in the vertical. Occurrence of sandy layers should promote coarse sediment transport close to the dam and thus SSC peaks.
The 1D model may also be not accurate enough to reproduce correctly the main processes involved in fine sediments dynamics. Indeed, the presence of a large alluvial reach with a secondary channel at the upper part of the reservoir should lead to 2D hydro-sedimentary processes, inducing transversal diffusion, particularly during the second phase of the flush. Moreover, the configuration close to the dam is three dimensional, with a particular system of dam gates. The bottom gate is located 200 m upstream from the dam in the right side, the half depth gate is located 50 m upstream from the dam in the left bank and the surface spill- way is located in the right bank of the dam. The 1D model is thus limited by its unidimen- sional description of hydraulic parameters, even if the stratification model takes into account the vertical dimension close to the dam.
6 CONCLUSION
A 1D hydro-sedimentary model is used to reproduce the fine sediment dynamics of the Génis- siat reservoir during the 2012 flush. To address the dimensional limitation of the 1D model, especially in the vertical dimension in case of high water levels and low velocities close to
Table 3. Scores characterizing the calibration accuracy. Fluxes first
phase (103 T)
Fluxes second phase (103 T)
Model Measure Model Measure
Bottom gate 891 732 ± 220 648 421 ± 127
Half depth gate 477 466 ± 134 219 124 ± 37
Surface spillway 0 0 211 129 ± 39
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the dam, a stratification model is proposed. The SSC vertical profile is calculated and allows to estimate the SSC at the dam outlets. The model accuracy is estimated by comparing the results to field measurements showing a significant contribution of the stratification model. Sediment fluxes at the dam are better reproduced.
As a validation, the model will be used to reproduce other flushes such as the 2003 flush. The sensibility to calibration parameters and the hydro-sedimentary description of the event for both the 1D and stratification model will also be evaluated. 1D model assumptions will be verified with 2D and 3D models close to the dam, particularly the currentology depending on the gates open- ing, and the shear stresses distribution within a cross section. Those results should help choosing further developments to improve the model among the solutions cited in the discussion. ACKNOWLEDGEMENTS
Authors want to thank J.B. Faure from Irstea Lyon for developing the Mage Adis-TS model and field measurement teams of Irstea and CNR for collecting the data used to build the model. REFERENCES
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