How to Design Bendway Weirs...Project Background • Physical Hydraulic Model Study – Determine...
Transcript of How to Design Bendway Weirs...Project Background • Physical Hydraulic Model Study – Determine...
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
Characteristic Prototype Model Scale FactorManning's' Roughness, n 0.027 0.018 LR
(1/6)
Design Flow (ft3/sec) 6000 12 LR(5/2)
Bend Type 1 Bottom Width (ft) 122 10.17 LR
Bend Type 1 Radius of Curvature (ft) 465 38.75 LR
Bend Type 3 Bottom Width (ft) 72 6 LR
Bend Type 3 Radius of Curvature (ft) 790 65.8 LR
Bed Slope (ft/ft) 0.000863 0.000863 1
Physical Model
Model Construction
Model Construction
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 = WSEX – WSED
• 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 16cfsLeft Bank
-0.020-0.015-0.010-0.0050.0000.0050.0100.0150.020
0 2 4 6 8 10 12 14 16 18Cross Section
∆Ζ
(ft)
Piezo A Piezo B Piezo C
Upstream Bend
Downstream Bend
Super Elevation 16cfsRight Bank
-0.020-0.015-0.010-0.0050.0000.0050.0100.0150.020
0 2 4 6 8 10 12 14 16 18
Cross Section
∆Ζ
(ft)
Piezo E Piezo F Piezo G
Upstream Bend
Downstream Bend
0.911.11.21.31.41.51.61.71.81.922.12.22.32.4
Vel
ocity
(ft/s
)16cfs Downstream Bend
Flow
Cross Section 16
Cross Section 17
Cross Section 18
00.040.080.120.160.20.240.28
Lateral Velocity (ft/s)
16
17
18
Bou
ndar
y Sh
ear S
tress
(psf
)
Flow Direction
0
0.004
0.008
0.012
0.016
0.02
0.024
0.028
0.032
0.036
0.04
Boundary Shear Stress DistributionXSEC 6, 16cfs
0.000
0.004
0.008
0.012
0.016
0.020
0.024
0.028
0.032
0.036
0.0400 4 8 12 16 20
το
-0.100
-0.090
-0.080
-0.070
-0.060
-0.050
-0.040
-0.030
-0.020
-0.010
0.000
Station (ft)
Outer Bank
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
Flow Direction
Boundary Shear Stress DistributionXSEC 10, 16cfs
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.070 3 6 9 12 15
τ ο (p
sf)
- 0.1000
- 0.0900
- 0.0800
- 0.0700
- 0.0600
- 0.0500
- 0.0400
- 0.0300
- 0.0200
- 0.0100
0.0000
Station (ft)
Outer Bank
Bendway Weirs
• Height
• Length
• Orientation Angle
• Spacing Ratio
Literature 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)
• Lagasse (1997)
• Lagrone (1998)
• Smith (1998)
• Heintz (2002)
Literature Review: Weir Spacing
Larc
Flow
Lproj,w
Weir Crest
Larc
Author Recommended Spacing Ratio
Type of Bank Remarks
1 Concave General Practice2-2.5 Convex General Practice4.29 Straight~5 Curves
Joglekar (1971) 2-2.5 Upstream GroynesUS Army (1984a) 2 Mississippi RiverMathes (1956) 1.5Strom (1962) 3-5
Acheson (1968) 3-4 Varies depending on curvature and stream slope
2-6 For bank protection
3-4 T-head groynes for navigation channels
Mamak (1956) 1.5-2 Deep channel for navigationBlench et al. (1976) 3.5Copeland (1983) >3 ConcaveKovacs el al. (1983) 1-2 Danube River
Mohan and Agraval (1979) 5 Submerged groynes of height one-third the depth
5.1-6.3 Straight
2.5-4 Curves
United Nations (1953)
Sloping crested weirs for bank protectionMaza Alvarez (1989)
Richardson et al. (1975)
Ahmad (1951)
Flow
Lproj,cw
Channel Top Width
Weir Crest
Literature Review: Weir LengthAuthor Suggested Length
United Nations (1953) "Start with a shorter length and extend the groynes after space between them has been silted up"
ICBIP (1971): No rules apply, build models to determine appropriated length
Richardson (1975) 50 feet or less
USACE (1980) Should be set at the desired constriction width of channel for navigation purposes
Brown (1985) Less Than 15% of bankfull channel width for impermeable structures
Maza Alvarez (1989) Less than 25% of bankfull channel width
Lagasse (1997) Less than 33% of bankfull channel width
Derrick (1998) Site-Specific Basis, engineering judgment
LaGrone (1998) 16.67%, not a design guideline but a site specific design
Literature Review: Orientation Angle
Flow
θ Weir Crest
Line Tangent to Bank
Author Range of Angles Suggested AngleBrown (1985) 30-150 150 decreasing to 90
Copeland (1983) 60-120 90Derrick (1994) 45-80 60
Indian Central Board of Irrigation and Power (1965): 60-80
Lagasse (1997) 50-85 60Mamak (1964): (Copeland
Literature Review) 70-80
Maza Alvarez (1989) 110 Richardson (1975) 60-150 70-80
Smith (1998) 60-75United Nations (1953) 60-80
USACE (1980) 100-105
Literature 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 Length– 15 – 30% of the top width – Length 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 Matrix
Test Variable Number of Variations Variation Values
Discharge (cfs) 3 8, 12, 16
Spacing Ratio 4 3.4, 4.1, 5.9, 7.6
Weir Length 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 Collection
Data Analysis
• MVR Regression Analysis
• Dimensional Analysis
• MVRout, MVRin, and MVRcenter Prediction Methods
CenterBase
aa MaxV
MaxVMVR =
Preliminary MVR AnalysisOuter Bank Maximum Total Velocity Ratio
0.00.10.20.30.40.50.60.70.80.91.0
0 2 4 6 8 10
Spacing Ratio
MVR
out
16cfs
12cfs
8cfs Upstream
8cfs Downstream
CenterBase
aa MaxV
MaxVMVR =
Preliminary MVR AnalysisOuter Bank Maximum Velocity Ratio vs. Spacing Ratio,
12cfs
0
0.3
0.6
0.9
1.2
1.5
0 2 4 6 8 10
Spacing Ratio
MVR
out 28%
22%15%
• Distinct trends were observed for weirs having varying weir characteristics
Dimensional AnalysisSymbol Definition Dimensions
ρw Density of Water M/L3
νw Kinematic Viscosity of Water L2/Tυw Dynamic Viscosity of Water MT/L2
Symbol Definition DimensionsSo Bed Slope L/L
TWtestflow Top Width at Test Flow Lb Base Width LSs Side Slope L/Ln Mannings' Roughness T/L(1/3)
y Flow Depth Lr radius of curvature Lk Conveyance L3/TAc Area of the Channel at Test Flow L2
Symbol Definition DimensionsLproj,cw Projected Length of Weir Crest L
Lcw Weir Crest Length LLproj,w Projected Length of Weir L
Lw Weir Length Lhw Weir Height LLarc Arc Length Between Weirs Lθw Angle of weir with Respect to Perpendicular Transect L/L
Lperp Distance from Weir Tip Perpendicular to XS through Centerline LAw Area of weir projected on Perpendicular Transect L2
Symbol Definition DimensionsQ Discharge L3/Tg Gravity L/T2
Material Properties
Channel Properties
Weir Properties
External Properties
( )cwcwcwprojtestflowwwprojarc AALLTWhyLLfMVR ,,,,,,,, ,,=
Dimensional AnalysisBuckingham’s Pi theorem (Dimensional Analysis):
Identified the following dimensionless parameters
wproj
arc
LL
,1 =π
weirhy
=2πcwproj
testflow
LTW
,3 =π
cw
cwproj
LL ,
4 =πTotalAreaWeirArea
=5π
⎟⎟⎠
⎞⎜⎜⎝
⎛=
c
w
cw
cwproj
cwproj
testflow
wwproj
arc
AA
LL
LTW
hy
LL
fMVR ,,,, ,
,,
Data Analysis: Linear Regression
Necessary Analysis included:
• Multiple Linear Regression
• Natural Log Transformation of Intrinsically Linear data
• Best Subsets method to determine the most suitable regression model
• Analysis of Variance (ANOVA), contribution of independent variables, and determination of possible outliers
( )54321 ,,,, πππππfMVR =
Data Analysis: Multivariate Linear Regression (MVR Out)
Trial # Vars R-Sq Adj. R-Sq C-p s π1 π2 π3 π4 π51 1 38.6 37.4 62.9 0.413 X2 1 35.0 33.7 69.5 0.425 X3 1 28.5 27.1 81.4 0.446 X4 1 1.3 0.0 131.5 0.524 X5 1 1.0 0.0 132.0 0.524 X6 2 68.0 66.8 10.8 0.301 X X7 2 66.4 65.1 13.7 0.308 X X8 2 45.6 43.4 52.1 0.393 X X9 2 43.6 41.4 55.7 0.400 X X
10 2 39.0 36.6 64.3 0.416 X X11 3 73.3 71.7 3.2 0.278 X X X12 3 70.2 68.4 8.8 0.294 X X X13 3 68.6 66.8 11.7 0.301 X X X14 3 68.0 66.1 12.8 0.304 X X X15 3 66.4 64.4 15.7 0.311 X X X16 4 73.7 71.6 4.4 0.278 X X X X17 4 73.3 71.1 5.2 0.281 X X X X18 4 70.2 67.8 10.8 0.296 X X X X19 4 68.7 66.2 13.5 0.304 X X X X20 4 54.7 51.0 39.3 0.365 X X X X21 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 = Larc/Lw
• Spacing Ratio: 3.4 - 8.4
Larc
Flow
Lproj,w
Weir Crest
Larc
Weir Variables: Orientation Angle
Flow
Lproj,cw
Channel Top Width
Weir Crest
Flow
θ Weir Crest
Line Tangent to Bank
Data Analysis: Multivariate Linear Regression
109.0
,
153.0700.0,
153.2
⎟⎟⎠
⎞⎜⎜⎝
⎛
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⎛
=
wproj
arc
c
w
cw
cwproj
in
LL
AA
LL
MVR
859.0
35.2,
899.0
,019.0
⎟⎟⎠
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⎛
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c
w
cw
cwproj
wproj
arc
out
AA
LL
LL
MVR
160.0567.0,
160.0
,
350.1 ⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
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⎛=
c
w
cw
cwproj
wproj
arccenter A
AL
LLL
MVR
Data Analysis: Multivariate Linear Regression (MVR Out)
MVRout:: Observed vs. Predicted
0.0
0.4
0.8
1.2
0.0 0.4 0.8 1.2
Predicted MVRout
Obs
erve
d M
VRou
t
Test DataIdeal Fit
Error = Observed MVR – Predicted MVR
Average Error = 0.01
Average Absolute Error = 0.07
859.0
35.2,
899.0
,019.0
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c
w
cw
cwproj
wproj
arc
out
AA
LL
LL
MVR
Data Analysis: MultivariateLinear Regression (MVR Center)
MVRcenter: Observed vs. Predicted
1.0
1.2
1.4
1.6
1.8
1.0 1.2 1.4 1.6 1.8
Predicted MVRcenter
Obs
erve
d M
VRce
nter
Test DataIdeal Fit
Average Error = 0.00
Average Absolute Error = 0.07
160.0567.0,
160.0
,
350.1 ⎟⎟⎠
⎞⎜⎜⎝
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⎛=
c
w
cw
cwproj
wproj
arccenter A
AL
LLL
MVR
Data Analysis: Multivariate Linear Regression (MVR In)
MVRin: Observed vs. Predicted
0.8
1.0
1.2
1.4
1.6
1.8
0.8 1.0 1.2 1.4 1.6 1.8
Predicted MVRin
Obs
erve
d M
VRin
Test DataIdeal Fit
Average Error = 0.00
Average Absolute Error = 0.05109.0
,
153.0700.0,
153.2
⎟⎟⎠
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=
wproj
arc
c
w
cw
cwproj
in
LL
AA
LL
MVR
Data Analysis: Multivariate Linear Regression (Summary)
wproj
arc
LL
,1 =π
cw
cwproj
LL ,
4 =πTotalAreaWeirArea
=5π
859.05
35.24
899.01019.0π
ππ•=outMVR
109.01
153.05
700.04153.2π
ππ=inMVR
160.05
567.04
160.01350.1 πππ=centerMVR
Design Example: Site Selection
0 2000’
Middle Rio Grande:
• 10 miles downstream of Cochiti Dam
Southwestern Willow Flycatcher
Design Example: Site Selection
• 2001 Aerial Photograph
• Bend Properties:
• rc = 578’
• Channel Top Width = 188.5’
• Channel Length = 1090’
• rc/TW = 3.07
0 2000’
rc
Bend Properties:
rc = 578’
Channel Top Width = 188.5’
Channel Length = 1090’
rc/TW = 3.07
Design Example: Site Selection
Top WidthRadius of Curvature
Relative Curvature Rc
(ft) (ft) dimensionless1 230.4 465 2.023 180 789.96 4.39
Bend Type
Design Example: Design ChannelDesign 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
VAQ =
21
32486.1 SAR
nQ = Flow depth = 9.24 ft
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
40.00.665.2
===CenterBase
outout MaxV
MaxVMVR
Design Example: Preliminary Weir Design
• Weir Design depends upon design Top Width
• Start with 3 primary weir variables:
• Weir Length, Angle, and Spacing
• Keep two variables constant, change the third to achieve desired MVR results
Design Example: Preliminary Weir Design
• Weir Crest Length = 20%
• Orientation Angle = 75o
• Spacing = ?
• Calculate known weir variables
Projected Length of Weir Crest (ft) 26.84Length of Weir Crest (ft) 27.79Length of Weir (ft) 37.03Projected Length of Weir (ft) 35.77Area of Channel (ft) 995.33Projected area of Weir (ft) 161.19
wproj
arc
LL
,1 =π
cw
cwproj
LL ,
4 =πTotalAreaWeirArea
=5π
859.0
35.2,
899.0
,019.0
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cw
cwproj
wproj
arc
out
AA
LL
LL
MVR
Design Example: Preliminary Weir Design
• 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 5000 5000 500
CenterBase
InIn MaxV
MaxVMVR =
109.0
,
153.0700.0,
153.2
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c
w
cw
cwproj
in
LL
AA
LL
MVR
Design Example: Velocities along Other Axes
• Solving results in MVRin = 1.32
• Solving results in a Maximum predicted inner bank velocity of 7.89 ft/sec
• Is this acceptable?
160.0567.0,
160.0
,
350.1 ⎟⎟⎠
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w
cw
cwproj
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arccenter A
AL
LLL
MVR
Design Example: Velocities along Other Axes
CenterBase
CenterCenter MaxV
MaxVMVR =
• Solving results in MVRcenter = 1.31
• Solving results in a Maximum predicted center channel velocity of 7.84 = ft/sec
• Is this acceptable?
Design Example: Examination of Sensitivity
Theta MaxVout
(degrees) (ft/sec)1 20 75 5.7 0.400 2.402 20 90 5.7 0.430 2.58
% Top WidthTrial # Spacing MVRout
Sensitivity of Spacing
Sensitivity of Angle
Sensitivity of Length
Trial #1: Lproj,w = 26.84’
Trial #4: Lproj,w = 33.55’
Theta MaxVout
(degrees) (ft/sec)1 20 75 5.7 0.400 2.403 20 75 4.6 0.329 1.97
Trial # Spacing MVRout% Top Width
Theta MaxVout
(degrees) (ft/sec)1 20 75 5.7 0.400 2.404 25 75 5.7 0.326 1.96
Spacing MVRout% Top WidthTrial #
Trial #1: Larc = 203.86’
Trial #3: Larc = 164.52’
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?