EVALUATING SELECTED SCOUR EQUATIONS FOR BRIDGE PIERS IN COARSE STREAMBEDS IN NEW YORK
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EVALUATING SELECTED SCOUR EQUATIONS FOR BRIDGE PIERS IN
COARSE STREAMBEDS IN NEW YORK
L.J. Welch, Jr. and G.K. Butch
In cooperation with
New York State
Department of Transportation
by
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Field Conditions
Turbulent flow Armored streambed
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Scour is the result of work
Sf = stream force (kg m/s2);
D84 = grain size >84 % of armor layer (mm).
84D
SffScour
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Stream Force
Sf = stream force (kg m/s2);
= water density (103 kg/m3);
y1 = water depth (m);
w = flow width (1 m);
V0= flow velocity (m/s).
201wVρySf
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Database Statistics
Variable Min. Max. Mean
Historical (55 measurements, 1943-89)
Flow velocity (m/s) 0.2 4.6 2.5
Water depth (m) 1.4 7.7 3.6
D50 armor layer (m) 22 68 39
D84 armor layer (m) 38 134 80
Scour depth (m) 0.0 1.0 0.4
Discrete (61 measurements, 1972-96)
Flow velocity (m/s) 0.2 4.2 2.7
Water depth (m) 1.4 9.7 4.6
D50 armor layer (m) 27 57 35
D84 armor layer (m) 53 127 71
Scour depth (m) 0.0 1.9 0.3
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Model Calibration
Calculated 19 scour depths measured in 1996 (10 = 0.0 m)
1996 MEAN ERROR
0
0.1
0.2
0.3
0.4
0.5
1996 data zeroscour
excluded
Historical &Discrete data(1943-95)
Discrete data(1972-95)
MEAN ERROR
(m)
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New York Equation (1972-96)
.
84D
Sf Scour 4106.210.07
Sf = stream force (kg m/s2);
D84 = grain size >84 % of armor layer (mm).
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Relation of Scour Depth to Stream Force and Bed Material
-0.5
0.0
0.5
1.0
1.5
2.0
0 500 1000 1500 2000 2500 3000
STREAM FORCE / D 84 , (kg x m/s2) / mm
SC
OU
R D
EP
TH
(m
)
_
_
_
_
| | | | |
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Sensitivity Analysis
-60
-40
-20
0
20
40
60
80
100
-50 -30 -10 10 30 50
% CHANGE IN SELECTED PARAMETER
% C
HA
NG
E IN
SC
OU
R
flow velocity
water depth
grain size,
D 84
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FHWA Equation
ys = scour depth; K1 = pier-nose shape;
a = pier width; K2 = pier shape & flow alignment;
y1 = water depth; K3 = streambed condition;
Fr1 = Froude number; K4 = armoring by bed-material size.
,
y 2.0 a K K K K
y
a Fr
s 1 2 3 4 1
0.35
1 0.43
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K4 (modified by Mueller)
If D50 > 2 mm and D95 > 20 mm and f(V) > 0, otherwise K4 = 1
D50 = median grain size; D95 = grain size >95 percent of armor
layer;
V0 = approach flow velocity;
V /
cD50
= approach velocity corresponding to critical velocity at pier for D50 ;
V /
cD95
= approach velocity corresponding to critical velocity at pier for D95 ;
V cD50
= critical velocity for incipient motion for D50 .
,
0.15
04
9550
500.4Κ
cD'
cD
cD'
VV
VV
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Froehlich Equation
ys = scour depth; = pier shape;
g = gravity; V0 = flow velocity;
y0 = water depth; b = pier width;
D50 = median grain size.
y 0.32 g V y b D s
0.1 0 0.2
0 0.36 0.62
50 0.08
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EstimatedScour
vsMeasured
Scour
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Summary ofEstimated and Measured Scour
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New Hampshire StudyField measurements
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New Hampshire StudyGPR & fixed instruments
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SUMMARY
• New York equation:- scour a function of stream force and bed material- derived from field measurements
- alternative for coarse streambeds- estimates associated with specific peak discharges
• Mueller modified-K4 and Froehlich equations:- less error than FHWA equation in New York
study