How to Design Bendway Weirs

Project Background U.S. Bureau of Reclamation: Middle Rio Grande Channel Maintenance Program 29-Mile Study Reach: Cochiti Dam to Bernalillo Geomorphic Changes Due to Dam Construction Meandering Threatening Critical Riverside Facilities Two Endangered Species and Degrading Habitat Employ Native Material and Rock Weir Techniques

Project Background

Project Background Physical Hydraulic Model Study Determine Design Criteria for Native Material and Rock Weir Structures Bendway Weirs W-Weir, V-Weirs J-Hooks Root Wads

Study Objectives Collect Empirical Data to Describe the Flow in Bends Collect Empirical Data in an Effort to Quantify the Performance of Bendway Weirs While Varying Geometric Parameters Determine an Optimal Spacing for Bendway Weir Design Develop Design Criteria Applicable to Bends of Varying Geometry

Physical Model Characteristic Prototype Model Scale Factor Manning's' Roughness, n 0.027 0.018 (1/6) R Design Flow (ft 3 /sec) 6000 12 (5/2) R Bend Type 1 Bottom Width (ft) 122 10.17 R Bend Type 1 Radius of Curvature (ft) 465 38.75 R Bend Type 3 Bottom Width (ft) 72 6 R Bend Type 3 Radius of Curvature (ft) 790 65.8 R Bed Slope (ft/ft) 0.000863 0.000863 1

Model Construction

Instrumentation Mobile Instrumentation Cart w/ Standard Point Gage 122 Piezometer Taps and Stilling Wells 3-D ADV Meter Preston Tube

Baseline Data Collection Model Flows 8, 12, 16, and 20 cfs Measurements Collected Over Each Piezometer Tap WSE Using Piezometer Taps 60.001 ft 3-D Velocity Profiles at 10% Depths Preston Tube Shear

Baseline Data Analysis Water Surface Super Elevation DZ = WSE X WSE D Velocity Vector Mapping of 3-D Velocities Plan View Cross Section: Helical Flow Shear Stress Contour Mapping Cross Section Distribution vs 1-D Model Output Turbulence Stresses

Super Elevation 16cfs eft Bank Piezo A Piezo B Piezo C Ζ (ft) 0.020 0.015 0.010 0.005 0.000-0.005-0.010-0.015-0.020 Upstream Bend 0 2 4 6 8 10 12 14 16 18 Cross Section Downstream Bend Piezo E Piezo F Piezo G Super Elevation 16cfs Right Bank Ζ (ft) 0.020 0.015 0.010 0.005 0.000-0.005-0.010-0.015-0.020 Upstream Bend Downstream Bend 0 2 4 6 8 10 12 14 16 18 Cross Section

18 16cfs Downstream Bend 17 2.4 16 Cross Section 18 2.3 2.2 2.1 Velocity (ft/s) 2 1.9 1.8 1.7 1.6 1.5 1.4 Cross Section 17 1.3 1.2 1.1 1 0.9 Cross Section 16 0.28 0.24 0.2 0.16 0.12 0.08 0.04 0 Flow ateral Velocity (ft/s)

Flow Direction Boundary Shear Stress Distribution XSEC 6, 16cfs 0.000 0.000 0.004 Outer Bank -0.010 0 0.008-0.020 0.004 0.012-0.030 0.008 0.016-0.040 0.012 0.016 0.02 0.024 0.028 Boundary Shear Stress (psf) τ ο 0.020 0.024 0.028 0.032 0.036-0.050-0.060-0.070-0.080-0.090 0.032 0.036 0.040-0.100 0 4 8 12 16 20 0.04 Station (ft)

Flow Direction Boundary Shear Stress Distribution XSEC 10, 16cfs 0.00 0.01 0.02 Outer Bank 0.0000-0.0100-0.0200-0.0300 το (psf) 0.03 0.04-0.0400-0.0500-0.0600 0.05-0.0700-0.0800 0.06-0.0900 0.07-0.1000 0 3 6 9 12 15 Station (ft) 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065

Bendway Weirs Height ength Orientation Angle Spacing Ratio

iterature Review United Nations (1953) Indian Central Board of Irrigation and Power (1971) Richardson (1975) USACE (1980) Copeland (1983) Brown (1985) Maza Alvarez (1989) Derrick (1994 & 1998) Przedwojski (1995) agasse (1997) agrone (1998) Smith (1998) Heintz (2002)

Author iterature Review: Weir Spacing Recommended Spacing Ratio Type of Bank Remarks United Nations (1953) Ahmad (1951) 1 4.29 Concave Straight General Practice 2-2.5 ~5 Convex Curves General Practice Joglekar (1971) 2-2.5 Upstream Groynes US Army (1984a) 2 Mississippi River Mathes (1956) 1.5 Strom (1962) 3-5 Varies depending on curvature 3-4 Acheson (1968) and stream slope 2-6 For bank protection Richardson et al. (1975) T-head groynes for navigation 3-4 channels Mamak (1956) 1.5-2 Deep channel for navigation Blench et al. (1976) 3.5 Copeland (1983) >3 Concave Kovacs el al. (1983) 1-2 Danube River Mohan and Agraval (1979) 5 Submerged groynes of height onethird the depth Maza Alvarez (1989) 5.1-6.3 Straight 2.5-4 Curves Sloping crested weirs for bank protection Flow Weir Crest proj,w arc arc

iterature Review: Weir ength Author United Nations (1953) ICBIP (1971): Richardson (1975) USACE (1980) Brown (1985) Maza Alvarez (1989) agasse (1997) Derrick (1998) agrone (1998) Suggested ength "Start with a shorter length and extend the groynes after space between them has been silted up" No rules apply, build models to determine appropriated length 50 feet or less Should be set at the desired constriction width of channel for navigation purposes ess Than 15% of bankfull channel width for impermeable structures ess than 25% of bankfull channel width ess than 33% of bankfull channel width Site-Specific Basis, engineering judgment 16.67%, not a design guideline but a site specific design Channel Top Width Flow proj,cw Weir Crest

iterature Review: Orientation Angle Author Range of Angles Suggested Angle Brown (1985) 30-150 150 decreasing to 90 Copeland (1983) 60-120 90 Derrick (1994) 45-80 60 Indian Central Board of Irrigation and Power (1965): 60-80 agasse (1997) 50-85 60 Mamak (1964): (Copeland iterature Review) 70-80 Maza Alvarez (1989) 110 Richardson (1975) 60-150 70-80 Smith (1998) 60-75 United Nations (1953) 60-80 USACE (1980) 100-105 Flow θ Weir Crest ine Tangent to Bank

iterature Review: Conclusions Design criteria are largely based upon engineering judgment and field experiences Typically, design criteria do not quantitatively explain changes in flow conditions due to bendway weir installations Cumulative effects of changing weir spacing, length, and angle are uncertain

Bendway Weirs: Design Review Weir Height At or just below the bankfull or channel forming flow depth Weir ength 15 30% of the top width ength perpendicular to the bank Weir Orientation Angle Pointing upstream or perpendicular to the bank: 60 90 degree angle Spacing Ratio between spacing and length, spacing ratio = 1 6.3

Test Variable Test Matrix Number of Variations Variation Values Discharge (cfs) 3 8, 12, 16 Spacing Ratio 4 3.4, 4.1, 5.9, 7.6 Weir ength 3 15%, 22%, 28% Orientation Angle 2 90, 60 72 tests examining weir length, angle, and spacing 18 (and counting) supplemental tests, examining weir spacing Over 90 tests in all

Data Collection

Data Analysis MVR Regression Analysis Dimensional Analysis MVR out, MVR in, and MVR center Prediction Methods MVR = a MaxV MaxV a CenterBase

Preliminary MVR Analysis Outer Bank Maximum Total Velocity Ratio MVRout 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 16cfs 12cfs 8cfs Upstream 8cfs Downstream 0 2 4 6 8 10 Spacing Ratio MVR = a MaxV MaxV a CenterBase

Preliminary MVR Analysis Outer Bank Maximum Velocity Ratio vs. Spacing Ratio, 12cfs MVRout 1.5 1.2 0.9 0.6 0.3 28% 22% 15% 0 0 2 4 6 8 10 Spacing Ratio Distinct trends were observed for weirs having varying weir characteristics

Dimensional Analysis Material Properties Symbol Definition Dimensions ρ w Density of Water M/ 3 ν w Kinematic Viscosity of Water 2 /T υ w Dynamic Viscosity of Water MT/ 2 Channel Properties Symbol Definition Dimensions S o Bed Slope / TW testflow Top Width at Test Flow b Base Width S s Side Slope / n Mannings' Roughness T/ (1/3) y Flow Depth r radius of curvature k Conveyance 3 /T A c Area of the Channel at Test Flow 2 Weir Properties Symbol Definition Dimensions proj,cw Projected ength of Weir Crest cw Weir Crest ength proj,w Projected ength of Weir w Weir ength h w Weir Height arc Arc ength Between Weirs θ w Angle of weir with Respect to Perpendicular Transect / perp Distance from Weir Tip Perpendicular to XS through Centerline Aw Area of weir projected on Perpendicular Transect 2 MVR = f External Properties Symbol Definition Dimensions Q Discharge 3 /T g Gravity /T 2 (, y, h, TW,,, A, A ) arc, proj, w w testflow proj, cw cw w c

Dimensional Analysis Buckingham s Pi theorem (Dimensional Analysis): Identified the following dimensionless parameters π = 1 arc proj, w π 2 = y hweir π 3 = TW testflow proj, cw π 4 = proj, cw cw π 5 = WeirArea TotalArea arc y TWtestflow proj, cw MVR = f,,,, proj, w hw proj, cw cw A A w c

Data Analysis: inear Regression MVR = f ( π, π, π, π π ) 1 2 3 4, 5 Necessary Analysis included: Multiple inear Regression Natural og Transformation of Intrinsically inear data Best Subsets method to determine the most suitable regression model Analysis of Variance (ANOVA), contribution of independent variables, and determination of possible outliers

Data Analysis: Multivariate inear Regression (MVR Out) Trial # Vars R-Sq Adj. R-Sq C-p s π 1 π 2 π 3 π 4 π 5 1 1 38.6 37.4 62.9 0.413 X 2 1 35.0 33.7 69.5 0.425 X 3 1 28.5 27.1 81.4 0.446 X 4 1 1.3 0.0 131.5 0.524 X 5 1 1.0 0.0 132.0 0.524 X 6 2 68.0 66.8 10.8 0.301 X X 7 2 66.4 65.1 13.7 0.308 X X 8 2 45.6 43.4 52.1 0.393 X X 9 2 43.6 41.4 55.7 0.400 X X 10 2 39.0 36.6 64.3 0.416 X X 11 3 73.3 71.7 3.2 0.278 X X X 12 3 70.2 68.4 8.8 0.294 X X X 13 3 68.6 66.8 11.7 0.301 X X X 14 3 68.0 66.1 12.8 0.304 X X X 15 3 66.4 64.4 15.7 0.311 X X X 16 4 73.7 71.6 4.4 0.278 X X X X 17 4 73.3 71.1 5.2 0.281 X X X X 18 4 70.2 67.8 10.8 0.296 X X X X 19 4 68.7 66.2 13.5 0.304 X X X X 20 4 54.7 51.0 39.3 0.365 X X X X 21 5 73.9 71.2 6.0 0.280 X X X X X

Weir Variables Weir Height Design Flow 12cfs Height of Weirs Equal to 12cfs Measured Depth Orientation Angle Varying angle to bank Crest Width Set at 1ft

Weir Variables: Spacing Spacing Ratio Measurement S = arc/w Spacing Ratio: 3.4-8.4 Flow Weir Crest proj,w arc arc

Weir Variables: Orientation Angle Flow θ Weir Crest ine Tangent to Bank Channel Top Width Flow proj,cw Weir Crest

Data Analysis: Multivariate inear Regression 0.109, 0.153 0.700, 2.153 = w proj arc c w cw cw proj in A A MVR 0.859 2.35, 0.899, 0.019 = c w cw cw proj w proj arc out A A MVR 0.160 0.567, 0.160, 1.350 = c w cw cw proj w proj arc center A A MVR

Data Analysis: Multivariate inear Regression (MVR Out) MVR out: : Observed vs. Predicted 1.2 Observed MVR out 0.8 0.4 Test Data Ideal Fit 0.0 0.0 0.4 0.8 1.2 Predicted MVR out MVR out = 0.019 arc proj, w 0.899 A A w c 0.859 proj, cw cw 2.35 Error = Observed MVR Predicted MVR Average Error = 0.01 Average Absolute Error = 0.07

Data Analysis: Multivariate inear Regression (MVR Center) 1.8 MVR center : Observed vs. Predicted 1.6 Observed MVR center 1.4 1.2 Test Data Ideal Fit 1.0 1.0 1.2 1.4 1.6 1.8 Predicted MVR center MVR center = 1.350 arc proj, w 0.160 proj, cw cw 0.567 A A w c 0.160 Average Error = 0.00 Average Absolute Error = 0.07

Data Analysis: Multivariate inear Regression (MVR In) MVR in: Observed vs. Predicted 1.8 1.6 Observed MVR in 1.4 1.2 1.0 Test Data Ideal Fit MVR in = cw 2.153 0.8 0.8 1.0 1.2 1.4 1.6 1.8 0.700 0.153 Predicted MVR in proj, cw Aw arc proj, w A c 0.109 Average Error = 0.00 Average Absolute Error = 0.05

π = 1 arc proj, w Data Analysis: Multivariate inear Regression (Summary) π = 4 proj, cw cw π 5 = WeirArea TotalArea MVR out = π 0.019 π 0.899 2.35 1 4 0.859 π 5 MVR center = 1.350π π π 0.160 1 0.567 4 0.160 5 MVR in = π 2.153 π 0.700 0.153 4 5 0.109 π1

Design Example: Site Selection Middle Rio Grande: 10 miles downstream of Cochiti Dam 0 2000 Southwestern Willow Flycatcher

Design Example: Site Selection 2001 Aerial Photograph Bend Properties: r c = 578 r c Channel Top Width = 188.5 Channel ength = 1090 r c /TW = 3.07 0 2000

Design Example: Site Selection Bend Properties: r c = 578 Channel Top Width = 188.5 Channel ength = 1090 r c /TW = 3.07 Bend Type Top Width Radius of Curvature Relative Curvature Rc (ft) (ft) dimensionless 1 230.4 465 2.02 3 180 789.96 4.39

Design Example: Design Channel Design Channel Properties: Base Width = 80 Design Top Width = 134.2 Side Slope = 3:1 (H:V) Design Flow = 6000 cfs n = 0.027 Bed Slope = 0.000863 Q = 1.486 n AR 2 3 S 1 2 Flow depth = 9.24 ft Q = VA Velocity = 6.0 ft/sec

Design Example: Baseline Conditions Estimated Centerline Maximum baseline velocity = 6.0 ft/sec Estimated Outer Bank Maximum baseline velocity = (1.1)*(6.0 ft/s) = 6.62 ft/sec From Sediment Transport Analysis a 60 % reduction of baseline conditions is desired Desired Outer Bank Velocity = 2.65 ft/sec MVR out = MaxV MaxV out CenterBase = 2.65 6.00 =.40

Design Example: Preliminary Weir Design Weir Design depends upon design Top Width Start with 3 primary weir variables: Weir ength, Angle, and Spacing Keep two variables constant, change the third to achieve desired MVR results

Design Example: Preliminary Weir Design π 1 = Weir Crest ength = 20% Orientation Angle = 75 o Spacing =? Calculate known weir variables arc proj, w π = 4 proj, cw Projected ength of Weir Crest (ft) 26.84 ength of Weir Crest (ft) 27.79 ength of Weir (ft) 37.03 Projected ength of Weir (ft) 35.77 Area of Channel (ft) 995.33 Projected area of Weir (ft) 161.19 cw π 5 = WeirArea TotalArea

Design Example: Preliminary Weir Design MVR out = 0.019 arc proj, w 0.899 A A w c 0.859 proj, cw cw 2.35 Solving for arc length yields a value of 203.8 ft A Spacing Ratio of 5.7 results (within tested limits)

Design Example: Preliminary Weir Design 0 500

Design Example: Velocities along Other Axes MVR in = 2.153 proj, cw cw 0.700 arc proj, w A A w c 0.109 0.153 MVR = In MaxV MaxV In CenterBase Solving results in MVR in = 1.32 Solving results in a Maximum predicted inner bank velocity of 7.89 ft/sec Is this acceptable?

Design Example: Velocities along Other Axes MVR center = 1.350 arc proj, w 0.160 proj, cw cw 0.567 A A w c 0.160 MVR = Center MaxV MaxV Center CenterBase Solving results in MVR center = 1.31 Solving results in a Maximum predicted center channel velocity of 7.84 = ft/sec Is this acceptable?

Design Example: Examination of Sensitivity Sensitivity of Angle Trial # % Top Theta MaxV Spacing MVR out Width out (degrees) (ft/sec) 1 20 75 5.7 0.400 2.40 2 20 90 5.7 0.430 2.58 Sensitivity of Spacing Trial # % Top Theta MaxV Spacing MVR out Width out (degrees) (ft/sec) 1 20 75 5.7 0.400 2.40 3 20 75 4.6 0.329 1.97 Trial #1: arc = 203.86 Trial #3: arc = 164.52 Sensitivity of ength Trial # % Top Theta MaxV Spacing MVR out Width out (degrees) (ft/sec) 1 20 75 5.7 0.400 2.40 4 25 75 5.7 0.326 1.96 Trial #1: proj,w = 26.84 Trial #4: proj,w = 33.55

Conclusions Regression analysis permits the prediction of MVR s as a function of weir characteristics. Solutions may be optimized for specific project constraints/objectives. Design procedure is still evolving!

Questions?