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
Field Conditions
Turbulent flow Armored streambed
Scour is the result of work
Sf = stream force (kg m/s2);
D84 = grain size >84 % of armor layer (mm).
84D
SffScour
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
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
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)
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).
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
)
_
_
_
_
| | | | |
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
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
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
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
EstimatedScour
vsMeasured
Scour
Summary ofEstimated and Measured Scour
New Hampshire StudyField measurements
New Hampshire StudyGPR & fixed instruments
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
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