Hydraulic Evaluation of Discharge Over Rock Closing Dams on the Upper Mississippi River

Jon Hendrickson, P.E.
Senior Hydraulic Engineer, St Paul District

Introduction

Prototype data was used for calibrating a weir equation to improve predictions of discharge over closing dams on the Upper Mississippi River (UMR). Closing dams are weir-like rock structures constructed across secondary channels to reduce flow break-outs from the main channel to backwater areas. Most of the closing dams in the St. Paul District reach of the UMR were constructed over 100 years ago as part of inland navigation system improvements. Originally constructed as emerged structures, they were permanently submerged when the locks and dams were constructed in the mid 1930's. In the last decade, some of the original closing dams have been modified, and new ones have been constructed, both for navigation channel improvement and for habitat rehabilitation. Being able to accurately predict the discharge over closing dams, will result in better management decisions and project designs.

Variable List

Available Prototype Data

Hydrodynamic and geometric data for several closing dams (or rock weirs) are listed in Table 1. This information was obtained through the St. Paul Districts', River Monitoring Program.
Table 1. Hydrodynamic and geometric data at closing dams.
Benover Slough Rock Weir, Pool 8, UMR River Mile 686.7
L/D 8
Flow (CFS)		 Site
Flow (CFS)		 hl
(ft)		 A
(ft2)		 L
(ft)		 W
(ft)		 H
(ft)		 h
(ft)		 Date of Measurements
115650 2565 0.28 640 150 20 4.53 4.25 04/21/93
81850 1804 0.23 575 148 20 4.11 3.88 05/04/93
77625 1517 0.20 480 148 20 3.45 3.25 06/02/93
Wisconsin Channel Closing Dam, Pool 4, UMR River Mile 793.1
L/D 3
Flow (CFS)		 Site
Flow (CFS)		 hl
(ft)		 A
(ft2)		 L
(ft)		 W
(ft)		 H
(ft)		 h
(ft)		 Date of Measurement
16000 3580 .021 2870 640 50 4.5 4.48 10/21/92
Belvidere Slough, Closing Dam 2, Pool 5, UMR River Mile 747.5
L/D 5
Flow (CFS)		 Site
Flow (CFS)		 hl
(ft)		 A
(ft2)		 L
(ft)		 W
(ft)		 H
(ft)		 h
(ft)		 Date of Measurement
30350 3282 0.06 1775 584 50 3.1 3.04 10/22/92
Peterson Lake Rock Weir, Site 8, Pool 4, UMR River Mile 754.4
L/D 4
Flow (CFS)		 Site
Flow (CFS)		 hl
(ft)		 A
(ft2)		 L
(ft)		 W
(ft)		 H
(ft)		 h
(ft)		 Date of Measurement
97600 3473 0.36 881 190 5 5 4.64 04/17/96
Sommers Chute Rock Weir, Pool 7, UMR River Mile 706.4
L/D 7
Flow (CFS)		 Site
Flow (CFS)		 hl
(ft)		 A
(ft2)		 L
(ft)		 W
(ft)		 H
(ft)		 h
(ft)		 Date of Measurements
68300 15800 0.44 2770 410 15 7.2 6.76 03/21/95
77500 20200 0.57 2890 410 15 7.6 7.03 03/27/95
53700 11800 0.27 2675 410 15 6.8 6.53 06/06/95
33650 5890 0.09 2580 410 15 6.4 6.31 07/08/95
27200 5000 0.04 2560 410 15 6.3 6.26 09/18/95

Review of Weir Equations and Coefficients

Closing dams are essentially broad crested weirs, and if a weir coefficient can be determined, and other physical characteristics calculated or measured, discharge over the structure can be predicted. The discharge characteristics at weirs are satisfied by the following two equations:

Free Flow: Q = Cf * L * H 3/2
Submerged Flow: Q = Cs * L * h * (2g*hl)1/2
The criteria for free versus submerged flow is based on the relationship between tailwater and headwater depth (Reference 3, Arkansas River Study). A plot of this is shown on Figure 1,
Figure 1 - Prototype data from St Paul District Closing Dams Plotted on Plate 40 of Waterways Experiment Sation Technical Report 2-650 (reference 3)
along with the prototype data measured at closing dams in the St. Paul District. In all cases, flow was submerged. Because of this, the focus of this study will be on determining representative values of Cs for use in the submerged flow equation.

Relationships between the discharge coefficient and flow characteristics at the structure are available from references 1 through 4. In the Arkansas River Study (Reference 3), Cs varied from 1.2 to 2, depending on the submergence ratio h/H. In a similar Waterways Experiment Station study on channel control structures for the Souris River, Minot, North Dakota (Reference 2) a weir coefficient of 1.25 was used to predict flow over rock weirs. Yarnell (Reference 4), used the free flow equation for all flow conditions and found a wide range of weir coefficients.

In the Arkansas River study, it was concluded that the roughness of the four stone gradations didn't have an appreciable effect on discharge characteristics. Gradations investigated were both coarser and finer than those typically used by the St. Paul District in closing dam construction. However, in the 1964 USGS report "Discharge Characteristics of Embankment Shaped Weirs" it was concluded that boundary roughness affected the coefficient of discharge and that because of this the embankment width was important also.

Calculated Weir Coefficient Based on Field Data

Using the available prototype data, the equation for submerged flow was solved for Cs (Table 2). The average value of Cs of 0.99 (range of 1.22 to 0.82) is less than those found in the literature. For example, Plate 44 of the Arkansas River Report gives values of Cs of 1.3 to 2.0 for the same range of submergence ratios. Plots of Cs versus hydrodynamic and structure characteristics are shown on Figure 2. There appears to be weak trends of increasing weir coefficient value with increasing submergence ratio and hydraulic radius (R2 = 0.14 and 0.53 respectively). Best-fit lines were drawn showing this trend. No trend was apparent between weir coefficient and weir width.

Table 2. Hydrodynamic data, geometric data, and calculated values of Cs at closing dams.
Site Date Cs R
(ft)		 h
(ft)		 h/H W
(ft)
Benover Slough 04/21/93 0.95 3.60 4.12 .936 20
Benover Slough 05/04/93 0.82 3.33 3.77 .942 20
Benover Slough 06/02/93 0.88 2.85 3.15 .940 20
Wisconsin Channel 10/21/92 1.07 4.48 4.48 .996 50
Belvidere Slough 10/22/92 0.95 3.04 3.04 .981 50
Sommers Chute 03/21/95 1.07 6.41 6.76 .939 15
Sommers Chute 03/27/95 1.15 6.65 7.03 .925 15
Sommers Chute 06/06/95 1.06 6.20 6.53 .960 15
Sommers Chute 07/08/95 0.95 6.00 6.31 .986 15
Sommers Chute 09/18/95 1.22 5.96 6.26 .994 15
Peterson Lake, Site 8 04/17/96 0.82 4.21 4.64 .928 5
Averages   0.99        

Figures 2a,2b, and 2c: Submerged Flow Weir Coefficent, Cs, versus Closing Dam Prototype Data

Conclusions

  1. Flow over closing dams on the Upper Mississippi River is usually submerged and the equation for submerged flow should be used with a weir coefficient of 0.99.

    Q = Cs * L * h * (2 g * hl)1/2 Cs = 0.99

  2. The submerged flow weir coefficient increases slightly with increasing submergence ratio and hydraulic radius (Figure 2). No trend was apparent between the weir coefficient and weir width.

References:

  1. U.S Geological Survey Water Supply Paper 1617-A "Discharge Characteristics of Embankment Shaped Weirs" 1964

  2. Waterways Experiment Station Report HL-81-3 "Channel Control Structures for Souris River, Minot,ND" 1981

  3. Waterways Experiment Station Technical Report 2-650, "Stability of Riprap and Discharge Characteristics, Overflow Embankments, Arkansas River, Arkansas". 1964

  4. Yarnell, D.L. and F.A. Nagler (1930) Flow of Flood Water Over Railway and Highway Embankments. Public Roads, Vol 11, Number 2.