U.S. Army Corps of Engineers Detroit District December 2001 December 2001
This report has been prepared for USACE, Detroit District by: W.F. BAIRD & ASSOCIATES LTD. 2981 YARMOUTH GREENWAY MADISON, WISCONSIN 53711 For further information please contact James Selegean, (313) 226-6791, Dr. Rob Nairn, (905) 845-5385 USACE
TABLE OF CONTENTS 1. INTRODUCTION...1 2. INCOMING SEDIMENT...2 3. SEDIMENT TRAP SITES AND SIZES...3 3.1 Sediment Trap Sites...3 3.2 Trap Dimensions...3 4. THEORETICAL ANALYSIS...4 5. HEC-6 MODELLING...8 6. CONCLUSIONS...11 REFERENCES...13 USACE Table of Contents
1. INTRODUCTION This report describes the assessment of sediment traps along the Saginaw River, MI, using existing numerical models and theoretical analysis. Two models were developed in previous studies: HEC-6 was used to model the Saginaw River (Baird 1999); and Mike 21 was used for modeling Saginaw Bay (Baird 2000). The studies indicated that most of the clay and silt from upstream passes through the federal channel and settles in Saginaw Bay, while most of sand settles in the river over the entire length of the channel. The construction of a sediment trap is suggested to catch a considerable fraction of the transported sand. A theoretical analysis of sediment dynamics was developed to evaluate the trap locations and sizes and to roughly assess trap efficiencies. A previously developed HEC-6 model was used to further evaluate the efficiency of the sediment traps. The study results are presented in five parts: incoming sediment analysis; sediment trap sites and sizes; theoretical analysis; HEC-6 modeling; and conclusions. USACE 1
2. INCOMING SEDIMENT The previous HEC-6 model studies provided useful sediment data, such as total sediment load, grain size distribution of suspended sediment and flow discharge. These data as well as the HEC-6 modeling results were used to choose sediment trap sites and dimensions. The relationship of total sediment load (TSL) and discharge was established in the previous studies for discharges varying from 50 cfs to 15,000 cfs. The USGS data indicate the recorded discharge varies from 500 cfs to 35,000 cfs. Therefore, it was necessary to extend this relationship using extrapolation. Figure 1 shows the relationship of sediment load and discharge extending up to 35,000 cfs. The corresponding grain size distribution is shown in Figure 2. It clearly shows that there is a higher percentage of clay for both high and low flows. It should be noted that there is no grain size data available for the flow discharges larger than 15,000 cfs. Based on the HEC-6 model results that were calibrated by dredging records, a constant grain size distribution was assumed for all discharges larger than 15,000 cfs. The extrapolation for TSL and grain size distribution was verified with the incoming TSL results of HEC-6 model. Table 1 lists incoming TSL calculated using the extrapolation and from HEC-6 model results. Table 1. Comparison of the Calculated TSL and GSD with HEC-6 Model Results Calculated HEC-6 Incoming TSL and Grain Size Distribution Total Clay Silt Sand (ton/yr) 280525 156108 93730 30687 (%) 100% 56% 33% 11% (ton/yr) 238099 134759 79645 23695 (%) 100% 57% 33% 10% The calculated TSL using this approach is slightly larger than the HEC-6 model results but the gain size distribution is the same. This is because the HEC-6 model uses input discharges that were developed from daily discharges and doesn t account for sediment load at peak flow. In order to understand the distribution of incoming sediment loads with discharge, a frequency analysis of flow discharge was performed using the 9-year discharge data at the USGS gage, as shown in Figure 3. The sediment load for each flow was calculated using the relationship of sediment load and discharge and is shown in Figure 4. Using the grain size distribution corresponding to that flow, the total sediment loads can be divided into the loads of clay, silt and sand, as shown in Figures 5a, 5b and 5c. It was found that the maximum sediment loads occur at flow discharges from 5,500 to 7,000 cfs for clay and silt and about 14,500 cfs for sand though the latter has no obvious peak load. The absence USACE 2
of a peak in the distribution for sand (Figure 5c) may be attributed to the fact that sand transport rates are highest at high flows and these high flows occur infrequently. The total sediment load delivered by the Saginaw River is estimated to be 280,525 tons each year, consisting of 56% clay, 34% silt, and 10% sand. The accumulated frequencies of sediment loads for clay, silt and sand are shown in Figure 6. 3. SEDIMENT TRAP SITES AND SIZES 3.1 Sediment Trap Sites Four sediment trap sites were selected based on previous HEC-6 model results. Figure 7 shows the sediment deposition distribution along the river. Four locations were proposed based on heavy sediment deposition and where dredging is not prohibited (e.g., by the presence of underground cables). Figure 8 shows the locations of the proposed sediment traps. The corresponding river miles for these traps are listed in Table 2. Trap D is expected to capture sand while the others are expected to capture coarse silt as well as sand. Table 2. Locations of the Proposed Sediment Traps Sediment Trap River Miles from Mouth Description A 1 Between Buoy 4 and Buoy 8 B 3 Upstream Buoy 20, Rupp Oil Co. C 4.8 Around Buoy 27, Bay City Marina D 12.5 Between Buoy 70 and Buoy 72 3.2 Trap Dimensions Flow velocity and shear stress are key parameters to determine the deposition of sediments. For a given discharge, the flow velocity is inversely proportional to crosssectional area. Sediment starts settling when flow velocity is less than the critical flow velocity. In other words, by increasing the cross-sectional area, the flow velocity decreases allowing more sediment to settle to the riverbed. It is assumed that the local maximum river width can be used in the analysis for each of the four traps. Drege depths of 5, 10 and 15ft below the existing depth were selected and used for both the analysis and the model investigation. The required length can be determined by the ratio of flow velocity and sediment settling velocity and water depth. Capturing small particles requires a longer trap because their USACE 3
settling velocities are small. In this assessment, three trap lengths of 300, 600 and 1200 ft were used for the HEC-6 modeling and the theoretical analysis. 4. THEORETICAL ANALYSIS Bottom shear stress is usually used to describe the hydrodynamic force acting on the sediment bed. Sediment deposition and erosion is determined by the relative states of bottom shear stress and critical shear stress. Bed sediments are resuspended when the bottom shear stress is larger than the critical shear stress. Otherwise, the suspended sediments are deposited. Therefore, the relationship between flow discharge and bottom shear stress should be established to determine the states of sediment deposition and erosion. Bottom shear stress can be determined by the following formula: 2 2 2 2 2 U n U n Q τ b = ρg = ρg = ρg (1) 2 1 3 2 7 3 C h B h where τ b --- bottom shear stress (N/m 2 ) ρ --- water density (kg/m 3 ), g --- gravity acceleration (m/s 2 ), U --- averaged velocity (m/s), Q --- flow discharge (m 3 /s), h --- water depth (m), B --- river width (m), 1 6 C --- Chezy s coefficient h 1 C =, n n --- Manning s coefficient. By replacing the bottom shear stress with critical shear stress, the critical discharge can be calculated as follows: 7 6 τ cr Bh Qcr = (2) ρg n where τ cr is the critical shear stress and Q cr is the critical discharge. Sediment starts settling when discharge is less than the critical discharge. The critical shear stress can be calculated according to van Rijn s formulae which was developed based on Shield s curve: USACE 4
θ where cr cr ( s ) 50 1 3 ( s 1) g 1 0.24D* for 1 < D* 4 0.64 0.14D* for 4 < D* 10 0.1 θ cr = 0.04D* for 10 < D* 20 (3) 0.29 0.013D 20 < 150 * for D* 0.055 for D* > 150 = τ ρ ρ gd, is the critical Shields parameter; D* = d 2 50 ν d 50 is the median grain size (m); ρ s is the sediment density (kg/m 3 ); ρ is the water density (kg/m 3 ); ν is the kinematic viscosity (m 2 /s); g is the gravity acceleration (m/s 2 ); s = ρ s /ρ., particle parameter; Then total incoming sediment load under the critical discharge can be calculated from Section 2. The amount of sediment that will settle in the trap depends on the flow velocity, trap length and original water depth. If the trap is shorter, more of the sediment passes through the trap and cannot settle down to the bed. As the depth gets larger, the flow velocity decreases, thereby increasing the amount of sediment deposited in the trap. The percentage of sediment that settles down to the trap is calculated by β = αlω s /UH (4) where β is percentage of sediment captured by the trap, L is the trap length, H is the water depth before dredging, U is the flow velocity, ω s is the settling velocity, and α is a coefficient adjusted for non-uniform distribution of concentration in the vertical, which depends on the suspension parameter or the ratio of settling velocity and shear velocity. If sediment concentration is uniformly distributed vertically, α should be one. In most cases, α should be larger than one, which means that sediment concentration at the river bottom is larger than that at the surface. In this assessment, based on averaged grain size and averaged velocity, α was set as two. The 9-year discharge data recorded at the USGS gage and the sediment loads developed in Section 2 were used for the theoretical calculation. The following steps were carried out: 1. Calculate critical shear stress for each sediment class using Eq. (3); 2. Calculate critical discharge using Eq. (2) based on trap dimensions. The Manning s coefficient is 0.025, which was used in the HEC-6 model; USACE 5
3. Calculate total sediment load when flow discharge is below the critical discharge for each class. This amount of sediment may settle down to the river bed; 4. Calculate the percentage of sediment which is captured by the trap using Eq. (4); 5. Calculate total sediment settling in the trap as the product of the total sediment load calculated in step 3 and the percentage of captured sediment calculated in step 4. All sediment loads and sediment volume deposited in the traps were converted to annually averaged values for comparison. Table 3 lists annually averaged incoming sediment, sediment volume deposited in the traps, and trap efficiency for clay, silt and sand. The dredging depth is the additional depth to be dredged for the sediment trap (i.e. below the existing river bed). The percentage of sediment presents the percentage of the total captured sediments in relation to the total incoming sediment load. The percentages of the three classes represent the percentages of the captured clay, silt and sand relating to total incoming clay, silt and sand loads, respectively. It was found that almost all of the incoming clay passes through the traps. It is hard to capture clay because of its small settling velocity and ease of suspension. Conversely, it is easy to capture sand due to its large settling velocity. Almost all sands carried by flows which are less than the critical discharge are successfully captured. In other words, increasing the dredging depth, hence decreasing flow velocity, can more efficiently capture sands rather than increasing the trap length. For example, 31% of sand is captured by Trap A with a dredged depth of 5ft for all trap lengths, 48% of sand is captured with a dredged depth of 10 ft and 62% of incoming sand is captured for a dredged depth of 15ft. However, the trap performance for silt is quite different. Since silt has a smaller settling velocity, it requires more time to settle to the riverbed. Trap length has a significant effect on the settling of silt. Increasing the trap length can improve the trap efficiency for silt. Trap A can capture about 10% of incoming silt with a 300 ft long trap and up to 22% with a 1200 ft long trap. River width has significant effects on trap efficiency as well. Increasing the trap width can increase the amount of captured sediment. Note that the impacts of decreasing trap depth due to deposition on the flow are not considered in the calculation. In other words, it was assumed that all sediment deposited in the trap was removed frequently to keep the trap of depth the same. Trap design will require an assessment of trap capacity and required frequency of maintenance dredging. An analysis tool using Microsoft Excel was developed. It allows users to adjust trap depth, trap length and location to evaluate trap efficiency quickly and easily. USACE 6
Table 3. Annual Captured Sediment and Trap Efficiency Through Theoretical Incoming Sediment (ton) Analysis Total Clay Silt Sand 280525 156108 93730 30687 Trap Efficiency (%) River Trap Dimensions (ft) Mile Width Dredged Length Depth Captured Sediment (ton) Total Clay Silt Sand 300 19668 427 9653 9589 7% 0% 10% 31% 5 600 24504 853 14062 9589 9% 1% 15% 31% 1200 32142 1706 20847 9589 11% 1% 22% 31% A 787 300 27329 519 12169 14641 10% 0% 13% 48% 10 600 33200 1038 17521 14641 12% 1% 19% 48% 15 300 33461 586 13830 19045 12% 0% 15% 62% 600 39966 1172 19749 19045 14% 1% 21% 62% 5 300 17688 363 8718 8606 6% 0% 9% 28% 600 21837 727 12504 8606 8% 0% 13% 28% B 690 10 300 24639 445 10950 13244 9% 0% 12% 43% 600 29667 889 15534 13244 11% 1% 17% 43% 15 300 30273 506 12547 17220 11% 0% 13% 56% 600 35972 1012 17740 17220 13% 1% 19% 56% 5 300 14825 311 7589 6925 5% 0% 8% 23% 600 18459 622 10912 6925 7% 0% 12% 23% C 620 10 300 21202 403 9861 10938 8% 0% 11% 36% 600 25767 806 14023 10938 9% 1% 15% 36% 15 300 27108 468 11661 14979 10% 0% 12% 49% 600 32431 935 16516 14979 12% 1% 18% 49% 5 300 8669 183 4920 3566 3% 0% 5% 12% 600 11173 365 7241 3566 4% 0% 8% 12% D 490 10 300 13389 301 7109 5979 5% 0% 8% 19% 600 16929 602 10349 5979 6% 0% 11% 19% 15 300 18593 386 9129 9078 7% 0% 10% 30% 600 23013 771 13163 9078 8% 0% 14% 30% USACE 7
5. HEC-6 MODELLING Based on the analysis described above, eleven proposed sediment traps were simulated using the HEC-6 model (see Table 4). The HEC-6 model of the Saginaw River developed in the previous studies was used for this assessment. In order to eliminate the effect of lake level fluctuation on the assessment, a 10 year simulation was carried at for each trap. Cross-sections around the traps were modified based on the trap dimensions as described in Table 4. All other conditions, such as incoming sediment, discharge, and lake level were kept the same. Table 5 lists the amount of captured sediment and trap efficiency. Because there is no function for outputting trap efficiency of a reach in the HEC-6 model, the trap efficiency was calculated by Qs, in Qs, out p = 100% (5) Q s, in where Q s,in is the total sediment passing through the upstream edge of a trap; Q s,out is the total sediment passing through the downstream edge of a trap, and p is the percentage of captured sediment. Note that incoming sediment load at the upstream boundary was not used to calculate the trap efficiency because sediment erosion occurred in the upstream reaches of the river. Table 4. HEC-6 Model Run Parameters HEC-6 Model Trap Site Dredged Depth (ft) Length (ft) Run1 A 5 300 Run2 A 5 600 Run3 A 5 1200 Run4 A 10 600 Run5 A 15 600 Run6 B 5 600 Run7 B 10 600 Run8 B 15 600 Run9 D 5 600 Run10 D 10 600 Run11 D 15 600 Table 5 lists sediment deposition in the traps and trap efficiency estimated by the HEC-6 modeling. It is seen that almost all of the clay passes through the traps. Most of the USACE 8
sediment captured by the traps was sand. The modeling results showed that 47% to 87% of sand and about 10% of silt was captured by Trap A. The total sediment captured by Trap A was from 15% to 26%, depending on the trap dimensions. It was also found that increasing the trap depth significantly increases the trap efficiency for sand but extending the trap length may not increase trap efficiency. This finding is consistent with the theoretical analysis as described in the previous section. The modeling results indicate that increasing both trap depth and length can improve trap efficiency for silt as well. It is noted that these findings regarding the role of trap depth and length apply to the range of depths and lengths considered. For example, there will be a critical trap length (less than 300 ft) where further reductions in trap length begin to reduce the efficiency of the trap. Comparing the model results with the theoretical analysis, it was found that the trap efficiency estimated using the theoretical analysis (called theoretical efficiency below) was generally close to that estimated using the HEC-6 model (called modeling efficiency below). However, the theoretical efficiency of total sediment is less than modeling efficiency. This probably results from different incoming sediment data used in the theoretical analysis and the HEC-6 modeling. The theoretical analysis was based on the total incoming sediment load at the upstream boundary of the HEC-6 model, which is significantly less than the sediment load passing through the upstream edge of the traps in the model because sediment erosion occurs in the upstream reach of the river and more sediment is carried downstream. In addition, bed load was not considered in the theoretical analysis, which may have resulted in an underprediction of the theoretical efficiency. On the other hand, the impacts of trap deposition in turn decreasing trap depth (that are considered in HEC-6) are not considered in the theoretical analysis, which may result in an overprediction of the theoretical efficiency. It was also found that the theoretical efficiency was larger than the modeling efficiency for the silt class but less for the sand class. This may result from the constant coefficient used for α in Eq. (4). The coefficient α presents non-uniform distribution of concentration in the water column. In reality the vertical distribution of concentration depends on grain size. The smaller the grain size, the more uniform the vertical concentration distribution. The coefficient α for sand should be larger than that for silt. Averaged grain size was used to determine the coefficient α, which may be smaller than that for sand and larger than that for silt. Another factor is the bed sediment load which is mostly composed of coarse sand. The bed load is not considered in the theoretical analysis. It should be pointed out that the theoretical analysis disregards the trap locations. This means that the same incoming sediment loads are applied for all traps. However, the HEC-6 model analysis used local sediment load and accounted for the sediment load change along the river. USACE 9
Table 5. Sediment Deposition and Trap Efficiency Estimated Using HEC-6 Modeling Trap Dimensions (ft) Captured Sediment (ton/yr) Trap Efficiency (%) Trap Dredged Total Width Depth Length Clay Silt Sand Total Clay Silt Sand 300 37191 974 5449 30768 15.1% 0.8% 10.3% 47.2% 5 600 38363 1013 5679 31671 15.6% 0.8% 10.7% 48.5% A 787 1200 39908 1089 6074 32745 16.2% 0.9% 11.5% 50.1% 10 600 54405 1022 6154 47229 22.2% 0.8% 11.6% 72.7% 15 600 64909 1018 6493 57398 26.4% 0.8% 12.3% 87.7% 5 600 32494 369 2419 29706 13.0% 0.3% 4.3% 45.5% B 690 10 600 44440 374 2702 41363 17.8% 0.3% 4.9% 63.1% 15 600 51709 371 2776 48562 20.7% 0.3% 5.0% 74.0% 5 600 9510 390 2760 6360 3.5% 0.3% 4.1% 8.7% D 490 10 600 21300 403 3221 17676 7.8% 0.3% 4.8% 24.0% 15 600 35149 406 3500 31243 12.8% 0.3% 5.2% 42.3% USACE 10
6. CONCLUSIONS The trap efficiencies were evaluated using both theoretical analysis and HEC-6 modeling. The key findings of the assessment were as follows: Based on our theoretical analysis: 1. The various sediment trap configurations considered can capture between 3% to 14% of the total incoming sediment, or between 12% to 62% of the total incoming sand, and 5% to 22% of the total incoming silt, depending on the trap location, depth and length. This doesn t take into account the bed load (which would increase the efficiencies); 2. Downstream sediment traps can capture more incoming sediment than upstream traps. Downstream sediment traps are more likely to capture silt; 3. The sediment traps can capture a greater fraction of coarser sediment such as sand and coarse silt. Almost all clay passes through the traps; 4. Increasing the trap depth will result in capturing more sand. But increasing the trap length beyond the maximum deposition length has no significant effect on the trapping of sand. These findings apply to the range of trap lengths and depths considered here; 5. Increasing both trap length and depth can improve the trap efficiency for silt. 6. The developed tool for theoretical analysis which has been calibrated with the HEC-6 model can be used to quickly assess trap efficiency. Based on our HEC-6 modeling analysis: 1. The various sediment trap configurations considered capture between 4% to 26% of total sediment load, or between 9% to 88% of total sand load and 4% to 12% of total silt load passing through the traps, depending on the location and size of the trap. 2. Captured sediments are mostly sand and some silt. Almost all clay passes through and is deposited in Saginaw Bay; USACE 11
3. Increasing the trap depth can significantly improve the trap efficiency for sand. However, increasing trap length more than 300 ft does not improve the trap capacity as much as increasing trap depth; 4. Increasing both the trap depth and length can improve the trap efficiency to some degree. 5. Using a wider river segment for the sediment trap can increase trap efficiency, as demonstrated with Trap A. In summary, the proposed sediment traps capture incoming sediment with varying degrees of success depending on the trap dimensions and incoming grain sizes. These traps are located in the river segment where there is a sediment deposition environment. The developed theoretical analysis and HEC-6 modeling can be used for sediment trap design and assessment of trap efficiency. The theoretical analysis approach was verified by the HEC-6 modeling results and can be used to quickly and roughly assess trap efficiency. The HEC-6 model requires more effort to prepare the input data and process output data and can be used to assess the trap efficiency for final design. In order to capture as much sediment as possible, it is recommended to use Trap A and Trap D together. Trap D is most effective at capturing sand and Trap A is more effective at capturing coarse and medium silt. There is a marsh beside Trap D, which could be used to extend the trap width. This may significantly improve the efficiency of Trap D. There is still large portion of incoming sediment delivered to the lake and deposited in the outer channels and the surrounding area (i.e. passes through the proposed traps). The previous MIKE 21 model study shows that the most of silt and sand is deposited in the outer channel and clay disperses to the surrounding water. This silt and sand could be captured by a sediment trap located at the river mouth. A theoretical analysis and model study could be performed to assess the feasibility of sediment traps in the outer channel in Saginaw Bay. USACE 12
REFERENCES Baird & Associates (1999), on Sheboygan River and Harbor, Wiscosin, Baird & Associates Technical Report; Baird & Associates (2000), Sediment Transport Modelling: Saginaw Bay, Saginaw River Basin, Baird & Associates Technical Report, USACE, HEC-6 User Manual, U.S. Army Corps of Engineers, Hydrologic Engineering Center. Van Rijn, (L.C.) (1989), Handbook for Sediment Transport by Currents and Waves, Delft Hydraulic USACE 13
Total Sediment Load (T/d) 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 0 5000 10000 15000 20000 25000 30000 35000 40000 Discharge (cfs) Figure 1 Relationship of Total Sediment Load and Discharge 70% 60% Clay Sand Silt 50% Percentage (%) 40% 30% 20% 10% 0% 0 5000 10000 15000 20000 25000 30000 35000 40000 Discharge (cfs) Figure 2 Suspended Sediment Grain Size Distribution USACE 14
1.8% 1.6% 1.4% Percentage 1.2% 1.0% 0.8% 0.6% 500 2500 4500 6500 8500 10500 12500 14500 0.4% 0.2% 0.0% 16500 Discharge (cfs) 18500 20500 22500 24500 26500 28500 30500 32500 34500 Figure 3 - Frequency of Flow Discharge Recorded at USGS Gage # 04157000 (interval 100 cfs) 25000 Total Sediment Load (T) 20000 15000 10000 5000 0 500 2500 4500 6500 8500 10500 12500 14500 16500 Discharge (cfs) 18500 20500 22500 24500 26500 28500 30500 32500 34500 Figure 4 - Total Incoming Sediment Load Distribution Over Discharge from 1988 to 1998 (Interval 100 cfs) USACE 15
Clay Sediment Load Silt Sediment Load Sand Sediment Load 1.4E+04 1.2E+04 1.0E+04 8.0E+03 6.0E+03 4.0E+03 2.0E+03 0.0E+00 8.0E+03 7.0E+03 6.0E+03 5.0E+03 4.0E+03 3.0E+03 2.0E+03 1.0E+03 0.0E+00 3.E+03 2.E+03 2.E+03 1.E+03 5.E+02 0.E+00 500 2500 4500 6500 8500 10500 12500 14500 16500 500 2500 4500 6500 8500 10500 12500 14500 16500 18500 Q (cfs) 18500 Q (cfs) 20500 22500 24500 26500 28500 30500 32500 34500 Silt 20500 22500 24500 26500 28500 30500 32500 34500 Clay Sand 500 2500 4500 6500 8500 10500 12500 14500 16500 18500 20500 22500 24500 26500 28500 30500 32500 34500 Q (cfs) Figure 5 Incoming Sediment Load Distribution Over Discharge (note: sediment load scales differ) USACE 16
Percentage (%) 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Clay Silt Sand 0 5000 10000 15000 20000 25000 30000 35000 Q (cfs) Figure 6 Accumulated Incoming Sediment Load 100000 50000 Trap A Trap C Trap D Clay Silt Sand Total Sediment Deposited (cu.yds) 0 0 5 10 15 20 25 Trap B -50000-100000 -150000 River Mile (mi) Figure 7 Sediment Deposition Distribution Along the River USACE 17
A B C D Figure 8 Selected Sediment Trap Sites USACE 18