Flushing of coarse and graded sediments—a case study using reduced scale model
3 REDUCED SCALE MODEL STUDIES
The tests to evaluate bottom outlet efficiency in removing accumulated sediments were per- formed in the reduced scale model with a geometric scale of 1:70 and operated according to the Froude similarity criterion.
3.1 Reproduction of alluvial material
Many studies of sediment transport in reduced scale models are performed with special solid material with a greater diameter and smaller density, as cited in Novak and Cabelka (1981). The CEHPAR has performed sedimentation and entrainment studies in reduced scale mod- els reproducing the alluvial material using treated imbuia wood sawdust (Chella, 2002), with a density of 1150 kg/m3 to simulate sand particles (density 2650 kg/m3 with a fine diameter
and homogeneous). However, the alluvial material in the area of this enterprise, indicated in Figure 1, is well graded and has significant percentage of large grains (up to 0.8 m in diameter). For cases like this, it is not appropriate to use imbuia sawdust. Due to its uniform- ity, it is impossible to reproduce in the model the occurrence of segregation of fine and coarse fractions of the material, a process known as armoring.
Therefore it was decided to use a non-cohesive granular material, composed by sand and gravel, with a grain size distribution selected appropriately. The grain size of the material used was determined in such a way as to allow similarity in the critical shear stresses that provoke its entrainment. Thus, the material was specific so that each grain size range would be entrained when the grains that composed it were submitted, in the model, to shear stresses similar to those that would be observed in the prototype if these particles were moved.
In order to determine this similarity, the simple application of the Froude criterion was not adopted. This would reduce the grain size curve of the prototype geometrically on the scale of 1:70. The methodology used was as follows: with the diameter of each range of the material, in the prototype, sedimentation velocity ω and critical shear velocity v*
cr were determined.
Figure 1. Grain size analysis to determine the material to be used in the tests.
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The scale of velocities (Froude similarity) was applied to these values to obtain the velocities ω and v*
cr in the model. Based on these values, the diameters of the particles in the model
were obtained, which would be similar from the point of view of entrainment capacity. The settling velocity (ω) was determined using the classical figure that presents settling velocity according to the diameter and the shape factor at different temperatures—U.S. Inter-Agency Committee on Water Resources, Subcommittee on Sedimentation (1957). A shape factor equal to 0.7 was used, and a temperature of 20º C. For the critical shear velocity (v*
cr) the
well known Shields criterion was used. The grain size resulting from the material used in the model is represented in Figure 1. To make the comparison easier, all grain size curves are in prototype magnitudes. It is observed that the results to adopt similarity of settling velocity and shear velocity were practically the same, slightly larger for the smaller diameter range compared to simple geometric transformation of the material.
This criterion used to determine the grain size of the material is certainly more effective than the simple geometrical transformation, since it reproduces the physical mechanisms that rule sediment transport in canals most correctly. It enabled utilizing a coarser material that is less influenced by the reduced scale, since it is not easily transported by suspension in water— a less important process for flushing material from the Yaque del Sur river which contains coarse material subjected to entrainment movements.
3.2 Tests performed
In order to evaluate the efficiency of the bottom outlet to remove sediment accumulated in the reservoir, 6 tests were carried out, with a duration equivalent to 12 hours and 30 minutes, simulating the reservoir purging operation for two different initial sedimentation levels: 784.0 m and 790.0 m (total silting up until the spillway crest) and three inflows, as indicated in Table 1. The purging operations were performed with complete opening of the bottom outlet tainter gate.
In these tests outflowing water was collected from the bottom outlet every 15 minutes to determine the concentration of solid material present in the jet (Cs). With this information
it was possible to obtain the volume of reservoir recovered over time, by Equations 1 and 2, and thus evaluate the efficiency of the purging operation. Topo bathymetric surveys of the mobile bed upstream from the dam were also performed after 4 hours of test duration and at the end of test in cross sections with a 40 m spacing.
QS CS Q Q C Q CCCS⋅ (1) Vre Q dt V V c S S Q Q ∫QQS⋅ ρS ρ (2)
where: Qs= solid discharge of sediments; Cs= volume concentration of sediments in the jet discharged from the bottom outlet; Q = outflow from the bottom outlet adopted as being equal to the inflow into the reservoir; Vrec= reservoir volume recovered by the purging opera- tion; ρs= density of solids; and ρ = density of water.
Table 1. Initial conditions of the tests performed. Nr. of test Total inflow (m3/s) Level of sediments in the reservoir (m) 1 50.0 784.0 2 75.0 784.0 3 150.0 784.0 4 50.0 790.0 5 75.0 790.0 6 150.0 790.0 PFISTER-Book.indb 141 PFISTER-Book.indb 141 7/15/2014 3:57:48 PM7/15/2014 3:57:48 PM
142 3.3 Results obtained
The material was entrained through canals that formed in the mobile material bed initially imposed in the reservoir. It was observed that these canals generally had trapezoidal sections, and over time the geometry varied greatly, which is evident that the sediment transport process is not continuous. However, common to all the tests was that at some moment armoring occurred in the more distant regions of the dam, as indicated in Figure 2, which limited the recovery of the reservoir volume due to the diminished entrainment of sediment in these regions.
According to White (2001), the embankment slopes in the trapezoidal section (i.e. of the banks) resulting from the purging operation are steeper, and may even be almost vertical, the more consolidated are the deposits in the reservoir. In reduced scale model tests, the consolidation of the sediment deposit cannot be reproduced. However, it was observed that, in certain cases, the slopes of the canal embankments were practically vertical due to the cohesive force among the wet sand particles, which in a way makes the model results slightly conservative. But this process provokes the collapse of the bank that is in a non regular form, thus, the sediment concentration may suddenly increase after a bank slumping.
Figure 3 presents the results obtained in the readings of the concentration under the two extreme conditions tested: Test 1—smaller discharge and less sedimentation. Test 6—greater discharge and greater sedimentation. Since the sediment transport process is not continu- ous and permanent, there is a great variation of the amount of solid material concentration present in the jet discharged from the bottom outlet throughout the test. In order to improve
Figure 2. Armoring in the regions that are further away from the dam—Test 6.
Figure 3. Concentration of solid material in the bottom outlet jet—Tests 1 and 6.
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understanding of the evolution of purging operation efficiency, based on the derivation of a polynomial equation that reproduces the volume recovery of the reservoir, a curve of the concentration tendency of solid material present in the jet discharged from the bottom outlet was adjusted. Figures 4 and 5 show, for instance, the adjustment performed for Test 6.
Figure 6 shows the concentrations of solid material in the bottom outlet jet for all tests. This allows evaluating the efficiency of the process without taking into account the
Figure 4. Test 6—Adjustment for the recovered reservoir volume.
Figure 5. Test 6—Adjustment for the evolution of the concentration of solid material in the bottom outlet jet.
Figure 6. Concentration of solid material present in the bottom outlet outflow jet.
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instantaneous values of Cs which are highly influenced by the changes in the conditions of
material entrainments and collapse of the banks. It is observed that, in all situations, the value of Cs tends to stabilize at around 5% after 5 hours of purging operations. Figure 7 shows the
reservoir volume recovery curves throughout the tests.
The evaluation of the reservoir volume recovered based on the information about concentrations of solid material in the bottom outlet jet is adequate since, as indicated in Table 2, the comparison of the final volume calculation was similar to that obtained from the topo bathymetric surveys.
Table 2. Comparison of the reservoir volume recovered. Nr. of
test
Volume based on the data of Cs (m
3/s)
Volume based on topo bathymetry (m3/s) 1 276,646 285,964 2 256,827 320,488 3 302,240 372,611 4 278,280 398,719 5 460,532 531,905 6 604,677 732,490
Figure 7. Relation of reservoir recovery x time of operation and purging.
Figure 8. Longitudinal profile of canals formed—Tests 4, 5 and 6.
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White (2001) suggests, for the prior evaluation of the reservoir volume recovered by the purging operation, that the canal geometry be simplified by a trapezoidal cross section and constant slope, similar to the natural slope of the river. Figure 8 shows the profiles of the canals formed by purging operations for tests on initial sedimentation level at El. 790.0 m. The mean slopes observed were 5.7% for Test 4, 3.1% for Test 5 and 2.6% for Test 6. Figure 9 shows the final configuration of the sediment deposit after the end of Test 6. It is noted that for the case studied, the simplification was confirmed only for cases of purging operations with the 75.0 and 150.0 m3/s flows. It is interesting to compare these slopes with
Equation 3, obtained by Pinto (1977) for cofferdam (diversion sill) built in flowing water by normal dump river closure. This equation assumes Shields critical condition for relatively large sediments and Manning equation with Strickler coefficient for a flume in equilibrium with uniform flow with specific discharge q.
i D q s = ⋅⎛ ⎝⎜ ⎛⎛ ⎝⎝ ⎞ ⎠⎟ ⎞⎞ ⎠⎠ ⋅ ⎛ ⎝ ⎜ ⎛⎛ ⎝⎝ ⎞ ⎠ ⎟ ⎞⎞ ⎠⎠ 0 245 10 7 9 7 6 7 , ρ ρs− ρ (3)
where: ρs= specific density of solid grains (equal to 2650 kg/m3 for the tested material); ρ = spe-
cific density of water (equal to 1000 kg/m3); D = representative diameter of the material used in
the model (having adopted D75); q = specific flow of model over mobile bed.
As has already been discussed, the geometry of the canals is very variable during the test. For this reason it is difficult to know precisely the value of the specific flow. For this study, based on observations made during the tests, a mean width was adopted equal to approxi- mately 23.0 m. It should be emphasized that the discharge used for this calculation is equal half the test discharge, since the reservoir is formed in two rivers, and the condition tested is distribution of 50% in each of them.
Figure 9. Configuration of sediment deposit at the end of Test 6. Table 3. Theoretical (Eq. 3) and experimental slopes for tests 4, 5 and 6.
Nr. of test Theoretical slope (%) Experimental slope (%) 4 5.5 5.7 5 3.1 3.1 6 2.2 2.6 PFISTER-Book.indb 145 PFISTER-Book.indb 145 7/15/2014 3:57:50 PM7/15/2014 3:57:50 PM
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The diameter used for calculations was D75. This choice is justified because the coarse
particles are more important in forming the armor that protects the bed, since the fines are easily removed.
Table 3 summarizes the calculations (Equation 3) made for the previously described tests. It also highlights the deviations found among the experimental and theoretical slopes.
4 CONCLUSION
Traditionally, sedimentation and entrainment tests in reduced scale models are carried out reproducing the alluvial material with special materials, such as sawdust, bakelite, coal, etc. For the Palomino Project study, however, a non-cohesive granular material was used, with a grain size distribution selected so that there would be similar critical shear stresses that pro- voke its entrainment. The material selected proved adequate, since it was possible to repro- duce the physical mechanisms, including the onset of armoring, which rule the transport of coarser sediments, such as those that exist in the region of the project.
Similarly, the volume transported in movable bed tests on reduced scale models is usually defined only by topo bathymetric surveys in well defined step of the test. However, the stud- ies performed sought to characterize the sediment purging operation over time by measuring the sediment concentration of the flow from the bottom outlet. This methodology proved adequate, since the volumes obtained from the information about solid material concentra- tion in the jet of the bottom outlet were similar to those obtained from the topo bathymetric surveys.
The tests adopted a few simplifications such as constant flow, homogeneous sedimentation material throughout the reservoir and initial sedimentation defined by a plane on a specific level. But certainly, the physical modeling is able to supply important information taking into account the different particularities of the reservoir configuration, the layout of the structures and the bottom outlet. The identification of the reservoir region where volume was recovered was very useful to confirm that the flushing process enables the recovery of a large part of the useful storage volume of the reservoir.
REFERENCES
Chella, M.R. 2002. Physical Simulation of Sediment Transport and Sedimentation in Reservoirs—a Case Study for Melissa Hydroelectric Development. Master Thesis. Curitiba: Parana Federal University. (in Portuguese).
Pinto, N.L.S. 1977. Contribution to the Study of Rockfill Dams Constructed in Flowing Water. Curitiba: Parana Federal University (in Portuguese).
Straub, L.G. 1963. Caroni River Hydroelectric Development. Report on Gury Project River Diversion Scheme. St. Anthony Falls Hydraulic Laboratory.
White, R. 2001. Evacuation of Sediments from Reservoirs. Bristol, UK. HR Wallingford: Ed. Thomas Telford Publishing.
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