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