UFL/COEL99/017
FINAL REPORT
LOCAL PIER SCOUR MODEL TESTS FOR
JENSEN BEACH BRIDGE
by
D. M. Sheppard
September, 1999
Submitted to:
Morales and Shumer
and
Florida Department of Transportation
District IV
FINAL REPORT
LOCAL PIER SCOUR MODEL TESTS
FOR
JENSEN BEACH BRIDGE
SUBMITTED TO:
MORALES AND SHUMER
AND
FLORIDA DEPARTMENT OF TRANSPORTATION
DISTRICT IV
BY:
D.M.SHEPPARD
COASTAL AND OCEANOGRAPHIC ENGINEERING DEPARTMENT
UNIVERSITY OF FLORIDA
SEPTEMBER 1999
LOCAL PIER SCOUR MODEL TESTS
FOR
JENSEN BEACH BOULEVARD BRIDGE
INTRODUCTION:
The Bridge at the State Road 732 (42nd Street) crossing of the Intracoastal Waterway, in Palm
Beach County Florida, is being replaced. This bridge is referred to here as the Jensen Beach
Boulevard Bridge and its location is shown in Figures 1 and 2. The main piers for this Bascule
bridge, are composed of a pile cap and multiple square piles. Present techniques for predicting
design scour depths for large complex piers are known to be quite conservative and values
obtained from physical model experiments are believed to be more accurate. This report
describes laboratory tests performed on scale models of the proposed piers for the Jensen Beach
Boulevard Bridge and gives recommended design scour depths based on the results of these
tests.
OBJECTIVE:
The objective of this study was to determine the local scour depths that will occur at the
specified 500 year return interval, water depths and flow velocities. This was accomplished by
performing model tests at transition between clearwater and live bed scour conditions and
extending the results to design velocities.
Figure 1. Map showing location of Jensen Beach in Florida.
Figure 2. Map showing location of Jensen Beach Boulevard Bridge.
EXPERIMENTAL PLAN AND PROCEDURES:
Geometric scaling was used to size the model and water depth. Selection of the scaling for the
model was determined by the size of the flume used for the test, and was chosen to be as large as
possible without causing significant contraction scour. The model to prototype scale used was
1:20.
All tests were conducted in the 100 ft long x 8ft wide x 2.5 ft deep flume in the Hydraulics
Laboratory in the Civil Engineering Department at the University of Florida in Gainesville,
Florida. The flume has a 100 hp pump with a discharge capacity (with the existing weir) of 38.8
ft3/sec (1100 1/sec).
In general, the local scour depth increases with increased water depth (for water depths
up to about three times the width of the pier). However, for near waterline pile caps, the
component of scour due to the cap decreases with increasing distance from the bed. For these
piers it was not certain which effect would dominate and produce the greater scour. To answer
this question two initial tests were performed, one with the greater water depth (and greater pile
cap distance to the bed) and one with the lesser water depth (and correspondingly shorter
distance from the pile cap to the bed). For this particular pier shape, the lower water depth (and
reduced distance between pile cap and bed) produced the greater scour depth, although the
difference was small. To insure conservative scour estimations, the lower water depth was used
for the remaining tests. Figure 3 shows a drawing and Figure 4 shows an isometric view of the
model pier used in the scour tests. As the model with the smaller water depth produced the
larger scour, the deeper water depth results are not included in this report in order to avoid
confusion.
The design flow skew angle for the various piers on this bridge varies from 2 to 26 degrees. The
model tests were performed at skew angles that would allow interpolation to the design skew
angles for the prototype piers.
1 17,166 834
1,84 so4,t[O
ISo
14,174 r r i
Figure 3. Drawing of the 1: 20 model of the Jensen Beach Causeway used in the local scour
tests. All dimensions are made in inches.
I
Figure 4. Isometric view of the model of the Jensen Beach Boulevard pier used in the local
scour tests.
The following tasks were performed:
Task 1.
A. A 1:20 model of the proposed pier structure was designed and constructed (see Figures
3 and 4). This included a platform on which the model sits to raise the pile cap above
Bed
the sand bed for comparison.
B. The model was placed in the flume, the sediment in the test area compacted and
leveled, and the instrumentation calibrated (see Figure 6).
C. The scour test was run for such a period until no more scour was recorded over a 24
hour period. The scour tests were all run with flows near the critical depth averaged
velocity as computed using Shield's Parameter (U/Uc = 0.9).
D. The flume was drained and the post experiment measurements were made.
E. The data collected was reduced and analyzed.
F. Tasks 1A to 1E were repeated for the second pier design (with a lower water depth),
from which it was determined that the lower water depth resulted in a larger scour
depth.
G. Tasks 1A to 1E were repeated using the second pier design for 2 different skew
angles.
Task 2. A preliminary letter report that included summaries of the model conditions and
measured maximum scour depths, as well as prototype conditions and predicted scour
depths was submitted to FDOT District 4 on March 23, 1999.
Task 3. A preliminary final report was completed and submitted on August 27, 1999.
Steps were taken in this test to produce a conservative value of design pier local scour depths.
These include:
1. The tests were conducted near the transition from clear water to live bed scour conditions
(with the results extrapolated to the transition, U/Uc = 1). Flow velocities greater or less
than critical will produce smaller equilibrium scour depths.
2. The sediment grain size distribution used in the test area of the flume is very narrow with
a relatively small standard deviation, c = 1.38. Researchers have shown that with all
other conditions being the same, local scour depth increases with increasing uniformity of
grain size.
3. The duration of the tests was sufficiently long to minimize errors in extrapolating the
results to equilibrium conditions.
4. Predicted 1 in 500 year storm events were used to determine the water depth for the test
even though peak velocities occur at elevations less than the maximum value. In general,
equilibrium scour depths increase with depth up to a water depth to structure diameter
ratio of about three. Beyond this point the scour depth does not change with increasing
depth.
5. The scour producing event is assumed to be of sufficient duration that equilibrium scour
depths are achieved. It is the author's opinion that the duration of most storm events in
Florida is not sufficient to create equilibrium scour depths, even on the leading edge of a
pier structure but certainly not in the interior or near the downstream end of these
complex multiple pile piers.
6. For large, complex, multiple pile structures the spatial variation in the equilibrium scour
depth near the structure can be significant. However, until this phenomenon is better
understood and able to be predicted with more confidence, it is recommend that the
maximum scour depth be used throughout the structure. This, along with the above
items, results in a conservative estimate of the design local pier scour depth.
RESULTS:
The following tables and figures show the results of both the model tests and the
estimated prototype scour depths, for 100 and 500 year storm conditions. Two different methods
are used to compute the prototype scour depths from the model results. One is called the
CONVENTIAL METHOD and the other is called the UNIVERSITY OF FLORIDA (or UF)
method. The conventional method simply multiplies the model scour depth by the model
geometric scale factor to arrive at the prototype scour depth at the flow conditions of the model.
If the design flow velocity is in the live bed scour range (which is usually the case) then the
scaled clearwater scour depth is extrapolated to the design velocity. The slope of the
Uc
and FHWA for use until fthe live bed scour range available). The UF method upon by FDOTp
and FHWA for use until further information became available). The UF method was developed
by the author of this report and is more involved. It attempts to account for the fact that the
sediment (or more specifically the ratio of pier size to sediment size) is not properly scaled in the
model studies. A model to prototype scale factor is developed that depends on both the model
and prototype structure and sediment parameters. Details of this method are presented in
Appendices A and B.
The model conditions and results are given in Table 1 and a plot of model scour depth at
= 1 versus flow skew angle is presented in Figure 5. The UF method utilizes the concept of
UC
an equivalent diameter, D for the pier. That is, the pier will experience the same local scour
depth as a single solid pile with a diameter, D under the same flow and sediment conditions. In
general the reference single pile will not be circular in shape and will have a shape factor of K1.
As pointed out in the appendices, due to the lack of data for large values of it is
D
recommended that when D > 104 it is set equal 104 in the scour prediction equations. This
D50
will result in a conservative estimate of the scour depth. A plot of the equivalent diameter,D ,
versus flow skew angle using a shape factor of 1.73 for the Jensen piers is shown in Figure 6.
The 100 and 500year prototype design scour depths using these two methods are given in
Tables 2 and 3 along with Taylor Engineering's predicted values (using HEC18 equations and
methods). Before and after photographs for one of the tests are shown in Figures 7, 8, 9 and 10.
It should be pointed out that none of these methods take duration of the storm event into
consideration. All of the methods predict equilibrium scour depths. Design flow conditions
produced by hurricane storm surge are, in general, of short duration so that equilibrium scour
depths are reached. In addition, there have been no adjustments to the scour depth due to the
distribution of sediment grain sizes in the prototype situation. The model tests were performed
in near uniform grain size sand, which produces a larger scour depth for a given flow. For these
reasons the scour depths predicted by the UF method are conservative. It is recommended that
the values obtained by the UF method be used for design.
0.32
0.28
0.26
0.24 
0.22
4 8 12 16 20 24 28
Flow Skew Angle (degrees)
Figure 5. Plot of model scour depth at U/U =1 versus flow skew angle.
0.3
. 0.2
0.1
%j
0 10 20
Flow Skew Angle (degrees)
Figure 6. Plot of D* versus flow skew angle.
8
*
U.4
Table 1. 1:20 model test conditions and measured maximum scour depths.
Flow Median Upstream Depth Critical Average
Skew Sediment Water Averaged Depth Water D* Test Maximum Scour at
Test Angle Diameter Depth Velocity Averaged U Temp. Model Duration Measured U 1
(deg) Dso (mm) yo(m) U (m/s) Velocity Uc T (deg C) (m) (hr) Scour (m) Uc
Uc (m/s) (m)
1 16 0.172 0.402 0.238 0.263 0.9 29.6 0.124 112.5 0.210 0.222
2 16 0.172 0.372 0.255 0.294 0.87 28.5 0.206 90.5 0.247 0.268
3 6 0.172 0.371 0.256 0.296 0.86 27 0.176 113.7 0.231 0.253
4 26 0.172 0.371 0.257 0.296 0.87 27 0.376 91.6 0.278 0.301
Table 2. Prototype 100 year return interval flow conditions and predicted local scour depths.
Conventional UF HEC18
Flow Ulive bed peak Assumed D* Method Method Prediction
Pier Skew D5o yo U Uc U U1p T Prototype Scour Depth Scour (Taylor
(deg) (mm) (m) (m/s) (m/s) Uc (m/s) (deg C) () (m) Depth Engineering
(m) (m)
7 17 0.2 6.47 0.853 0.346 2.47 5.862 15.5 5.25 6.05 3.76 6.81
8 16 0.2 7.08 0.853 0.349 2.45 6.124 15.5 5.05 6.01 3.73 6.34
9 7 0.2 7.08 0.853 0.349 2.45 6.124 15.5 3.25 5.56 2.77 5.07
10 2.2 0.2 7.08 0.853 0.349 2.45 6.124 15.5 2.29 5.32 2.17 4.65
11 13.9 0.2 7.11 0.701 0.349 2.01 6.137 15.5 4.63 5.74 3.12 5.44
12 25.7 0.2 6.50 0.549 0.346 1.59 5.875 15.5 6.99 6.16 3.40 6.34
Table 3. Prototype 500 year return interval conditions and predicted local scour depths.
Conventional UF HEC18
Flow Ulive bed pek Assumed D* Method Method Prediction
Pier Skew Dso yo U Uc U UIp T Prototype Scour Depth Scour (Taylor
(deg) (mm) (m) (m/s) (m/s) Uc (m/s) (deg C) (m) (m) Depth Engineering
(m) (m)
7 17 0.2 7.02 1.036 0.348 2.97 6.098 15.5 5.25 6.23 4.34 7.39
8 16 0.2 7.63 1.036 0.351 2.95 6.350 15.5 5.05 6.19 4.26 6.88
9 6.9 0.2 7.63 1.036 0.351 2.95 6.350 15.5 3.23 5.72 3.08 5.51
10 6.3 0.2 7.63 1.036 0.351 2.95 6.350 15.5 3.11 5.70 2.99 5.05
11 14 0.2 7.66 0.853 0.351 2.43 5.945 15.5 4.65 5.91 3.64 5.91
12 25.7 0.2 7.11 0.640 0.349 1.83 6.137 15.5 6.99 6.25 3.84 6.75
Figure 7. Photograph of Model Test #2 prior to start of experiment.
4g'~
Figure 8. Photograph of Model Test #2 on completion of experiment.
SII
.ir . .. .
','~ '.u "..
,.. i'~ 4
Figure 9. Photograph of Model Test #2 on completion of experiment.
B~se~x~l "U~LJ~s
"C=.
.a...
~i~t~i
,.
Sr
:e
Figure 10. Photograph of Model Test #2 on completion of experiment.
Figure 2. Definition sketch of circular pile showing flow, sediment and structure parameters.
The critical depth averaged velocity, Uc, must be obtained first. Tables 1 4 have Uc as a
function of median sediment size, D50, water depth, yo, and relative roughness of the bed, RR
for quartz sand. Knowing the design and critical velocities the scour regime can be determined
(i.e. is the design velocity in the clearwater scour or the live bed scour regime).
Clearwater Scour (0.4 < 1.0):
Uc
dse = c cl 1
I=co iL I.0 ()
To simplify the algebra define
k tanh 0.31+0.051 exp logi b + 0.75
b D( 50b
The coefficients co and cl can then be computed as follows:
2
co =I k and
3
A2
*PIENDIX*
CollY~tio of Lar~ b~ ~*~ (sr CiM~ ~i*
Computation of Local Scour at a Single Circular Pile
D. Max Sheppard
September 1999
The equilibrium local scour depth at a single circular pile can be computed as
follows. Refer to the definition sketch in Figure 1. For design purposes the scour
depth is computed by one of three straightline equations depending on the value of
U If the velocity where the scour depth is desired is in the clearwater scour
Uc
range (i.e. 0.4 < u <1.0) the scour is computed using the equation for the line
Uc
between points 1 and 2 in the sketch. For velocities in the live bed scour range
1.0 < __ < Up, (where Ulp is the velocity at the live bed peak scour depth) the
Uc Uc
equation for the line between points 2 and 3 is used. For > P the
U
dimensionless scour depth is constant at the value at point 3.
dse/b
00.4 1.0
Ud/Uc Up/Uc
U/Uc
Figure 1. Definition sketch. Nondimensional equilibrium, local scour depth versus
nondimensional depth averaged velocity.
A1
Page A2
is missing
from original
5
cl 
Note: It is recommended that if b > 104, that b be set equal to 104 in the above equations.
D50 D50
If the design velocity is in the live bed regime then the velocity where the maximum scour depth
in the live bed range occurs (Ulp) must be determined. For quartz sand this value can be
obtained from Table 5. This requires knowledge of the median sediment size and the water
depth. The equilibrium (live bed) local scour depth can then be computed using the following
equations.
Live Bed Scour 1.0< Ui < UI
Uc Uc )
where
k 2.4 tanhY
C2= fp and
I U t
C3= 2.4 tanh([jQ
If L > ,then
Uc Uc
A guide for the proper relative roughness is given below:
Bed Condition RR
Laboratory flume, smooth bed ripple forming sand (Dso < 0.6 mm) 5.0
Laboratory flume, smooth bed nonripple forming sand (Dso > 0.6 mm) 2.5
Laboratory flume, smooth bed live bed test with dunes 10
Field smooth bed 10
Field moderate bed roughness 15
Field rough bed 20
A 3
       
Definition of symbols
dse = equilibrium local scour depth,
b = circular pile diameter,
D50 = median diameter of sediment,
yo water depth upstream of the pile,
U = depth averaged velocity upstream of the pile,
Uc = critical depth averaged velocity upstream of the pile
= velocity of impending motion of the sediment,
Ulp a velocity at the maximum (or peak) scour depth in the live bed scour range
A4
Table 1. Critical velocity Uc (m/s) as a function of median grain diameter Dso (mm),
and water depth yo (m). Bed relative roughness, RR = 2.5.
D50
(mm)_
0.1 0.2 0.3 0.4 0.5 0.75 1 2 4 6 10
0.5 0.30 0.32 0.33 0.34 0.36 0.41 0.46 0.65 0.94 1.11 1.33
1 0.33 0.34 0.36 0.37 0.39 0.45 0.50 0.72 1.04 1.24 1.50
1.5 0.34 0.36 0.37 0.39 0.41 0.47 0.53 0.76 1.10 1.32 1.60
2 0.35 0.37 0.38 0.40 0.42 0.48 0.54 0.78 1.14 1.37 1.67
y0(m) 2.5 0.35 0.37 0.39 0.40 0.43 0.50 0.56 0.81 1.18 1.41 1.73
3 0.36 0.38 0.40 0.41 0.44 0.51 0.57 0.82 1.20 1.45 1.77
3.5 0.36 0.38 0.40 0.42 0.44 0.51 0.58 0.84 1.23 1.48 1.81
4 0.37 0.39 0.41 0.42 0.45 0.52 0.59 0.85 1.25 1.50 1.84
4.5 0.37 0.39 0.41 0.43 0.45 0.53 0.59 0.86 1.26 1.52 1.87
5 0.37 0.40 0.41 0.43 0.46 0.53 0.60 0.87 1.28 1.54 1.90
Table 2. Critical velocity Uc (m/s) as a function of median grain diameter Dso (mm), and water
depth yo (m). Bed relative roughness, RR = 5.0.
RR=5 D50
(mm)
0.1 0.2 0.3 0.4 0.5 0.75 1 2 4 6 10
0.5 0.30 0.30 0.30 0.31 0.32 0.37 0.42 0.59 0.83 0.98 1.16
1 0.32 0.32 0.33 0.34 0.35 0.41 0.46 0.65 0.94 1.11 1.33
1.5 0.33 0.34 0.34 0.35 0.37 0.43 0.48 0.69 1.00 1.19 1.43
2 0.34 0.35 0.35 0.36 0.38 0.44 0.50 0.72 1.04 1.24 1.50
yO (m) 2.5 0.35 0.35 0.36 0.37 0.39 0.45 0.51 0.74 1.07 1.28 1.56
3 0.35 0.36 0.37 0.38 0.40 0.46 0.52 0.76 1.10 1.32 1.60
3.5 0.36 0.36 0.37 0.38 0.41 0.47 0.53 0.77 1.12 1.35 1.64
4 0.36 0.37 0.38 0.39 0.41 0.48 0.54 0.78 1.14 1.37 1.67
4.5 0.36 0.37 0.38 0.39 0.42 0.48 0.55 0.80 1.16 1.39 1.70
5 0.37 0.38 0.38 0.40 0.42 0.49 0.55 0.81 1.18 1.41 1.73
A5
Table 3. Critical velocity Uc (m/s) as a function of median grain diameter Dso (mm), and water
depth yo (m) for quartz sand. Bed relative roughness, RR = 10.0.
D50
(mm)
0.1 0.2 0.3 0.4 0.5 0.75 1 2 4 6 10
1 0.30 0.29 0.29 0.30 0.32 0.37 0.42 0.59 0.83 0.98 1.16
2 0.32 0.32 0.32 0.33 0.35 0.41 0.46 0.65 0.94 1.11 1.33
3 0.33 0.33 0.33 0.34 0.36 0.43 0.48 0.69 1.00 1.19 1.43
4 0.34 0.34 0.34 0.35 0.38 0.44 0.50 0.72 1.04 1.24 1.50
yO(m) 5 0.35 0.35 0.35 0.36 0.39 0.45 0.51 0.74 1.07 1.28 1.56
6 0.36 0.35 0.36 0.37 0.39 0.46 0.52 0.76 1.10 1.32 1.60
8 0.36 0.36 0.37 0.38 0.41 0.48 0.54 0.78 1.14 1.37 1.67
10 0.37 0.37 0.38 0.39 0.41 0.49 0.55 0.81 1.18 1.41 1.73
15 0.38 0.38 0.39 0.40 0.43 0.51 0.58 0.84 1.24 1.49 1.83
20 0.39 0.39 0.40 0.42 0.44 0.52 0.59 0.87 1.28 1.54 1.90
Table 4. Critical velocity Uc (m/s) as a function of median grain diameter Dso (mm), and water
depth yo (m) for quartz sand. Bed relative roughness, RR = 20.
D50
(mm)
0.1 0.2 0.3 0.4 0.5 0.75 1 2 4 6 10
1 0.27 0.26 0.27 0.27 0.29 0.34 0.38 0.53 0.73 0.85 0.99
2 0.30 0.29 0.29 0.30 0.32 0.37 0.42 0.59 0.83 0.98 1.16
3 0.31 0.30 0.30 0.32 0.34 0.39 0.44 0.63 0.89 1.06 1.26
4 0.32 0.31 0.31 0.33 0.35 0.41 0.46 0.65 0.94 1.11 1.33
y0(m) 5 0.32 0.32 0.32 0.33 0.36 0.42 0.47 0.68 0.97 1.15 1.39
6 0.33 0.32 0.33 0.34 0.36 0.43 0.48 0.69 1.00 1.19 1.43
8 0.34 0.33 0.34 0.35 0.38 0.44 0.50 0.72 1.04 1.24 1.50
10 0.34 0.34 0.35 0.36 0.39 0.45 0.51 0.74 1.07 1.28 1.56
15 0.36 0.35 0.36 0.38 0.40 0.47 0.54 0.78 1.13 1.36 1.66
20 0.37 0.36 0.37 0.39 0.41 0.49 0.55 0.81 1.18 1.41 1.73
A 6
Table 5. Velocity at live bed peak, U p (in m/s), as a function of median grain diameter
Dso (mm), and water depth yo (m) for quartz sand.
D50
(mm)
0.1 0.2 0.3 0.4 0.5 0.75 1 2 4 6 10
0.5 1.65 1.80 1.92 2.03 2.10 2.32 2.45 2.70 2.90 3.04 3.24
1 2.30 2.44 2.59 2.89 2.82 3.04 3.19 3.47 3.81 3.99 4.18
1.5 2.80 2.95 3.07 3.22 3.33 3.59 3.73 4.03 4.32 4.67 4.93
2 3.22 3.38 3.48 3.64 3.76 4.05 4.18 4.52 4.91 5.20 5.53
2.5 3.58 3.75 3.85 4.00 4.15 4.45 4.61 4.93 5.30 5.64 6.03
3 3.91 4.09 4.19 4.31 4.49 4.80 4.98 5.28 5.70 6.01 6.46
3.5 4.21 4.39 4.51 4.62 4.79 5.10 5.31 5.59 6.06 6.34 6.83
y0(m) 4 4.48 4.67 4.81 4.91 5.07 5.39 5.61 5.91 6.39 6.65 7.17
4.5 4.74 4.93 5.08 5.17 5.32 5.67 5.89 6.22 6.69 6.98 7.48
5 4.99 5.18 5.34 5.43 5.56 5.94 6.15 6.51 6.97 7.28 7.76
6 5.45 5.66 5.82 5.92 6.04 6.43 6.62 7.04 7.47 7.83 8.26
8 6.25 6.51 6.65 6.78 6.87 7.28 7.50 7.94 8.36 8.75 9.24
10 6.95 7.26 7.37 7.54 7.64 7.99 8.26 8.70 9.21 9.51 10.10
15 8.41 8.82 8.95 9.11 9.25 9.54 9.82 10.31 10.93 11.28 11.81
20 9.63 10.13 10.29 10.40 10.59 10.85 11.09 11.69 12.30 12.74 13.22
A7
APPENDIX B
Method for Computing Prototype Scour Depth
from
Measured Model Scour Depth
Prototype Local Scour Depths from Physical Model Tests
D. Max Sheppard
September 1999
Most model tests are performed at flow velocities just below critical velocity (the depth averaged
velocity that will produce the critical bed shear stress on the flat bed in front of the structure) for
the sediment and flow conditions in the flume. Most prototype design velocities are, however, in
the live bed scour range. In order to estimate the prototype scour depth at the (live bed) design
velocity from the measured model (clearwater) scour depth the following procedure can be used.
A scale factor that transforms the model scour depth at a velocity near the critical velocity for the
model sediment and flow conditions to that for the prototype pile at the critical velocity for the
prototype sediment and flow conditions can be obtained as follows. The assumption is made that
the scour at a complex pier behaves like that for a single pile with an effective diameter, D*.
The single pile need not be circular in crosssection. In fact in many cases there is no circular
pile diameter that will produce the measured scour depth for the flow and sediment conditions of
the experiment. When this occurs, the scour for the complex pier must be related to that for a
noncircular pile (one with a shape factor coefficient, K1, other than one). It is assumed that the
model and prototype sediment properties (mass density, D50(m), Ds0(p)) are known:
The scale factor is defined as:
dse(prototype) evaluated at = 1
SF = (1)
dse(model) evaluated at t
Therefore the prototype scour depth at = 1 is simply
UC
dse(prototype) = (SF) dse(model) evaluated at Utest  (2)
The expression for computing (clearwater, 0.4 I 51.0) equilibrium scour depth is
Uc
dse = D *K, co cU 1.0 .
where
co 2k,
c = and
2
k tanhY 0.31+0.051exp log1o D+ 0.75o
(D D50 Dj
logD50.
(Note: It is recommended that if > 104, that b be set equil tol04 in the above
D50 D50
equations.)
Note that the effective diameter, D for both model and prototype are needed in the evaluation
of the scale factor, SF. The model effective diameter can be determined by solving the following
equation for Dm:
dse (measured)= Dm K1 co c U 1.0, (4)
where
co =k,
5
c1 = and
11
k_ tanh o) 0.31+0.051 exp loglo Dm 075
Dm D50(m) 1 Dmo
D50(m)
K1 should be the minimum value that will allow a real root (Dm) to the above equation.
The prototype effective diameter, Dp, is then
D= G D  (5)
where
G geometric scale of the model (20, 30, etc.).
Knowing Dm and Dp the scale factor SF and the prototype scour depth at 1 can be
Uc
computed. Next the prototype scour depth at the desired live bed scour velocity will be
computed using the prototype scour depth at transition (i.e. = 1). To do this the following
Uc
live bed scour equation is used. In order to use this equation the velocity at which the scour
R 3
depth peaks in the live bed scour range, Ulp, must be determined. Ulp can be obtained from
Table 5 in the previous section.
If (1.0 < U l
then the prototype pier scour depth at the desired velocity can be computed from
then the prototype pier scour depth at the desired velocity can be computed from
I
where
dse at U = 1 2.4 K tanh
D Uc D
U >
If >
Uc
c3 = 2.4 K1 tanh  and
Dp)
UD desired (design) velocity.
Ulp
Uc
then the following equation is used
= 2.4 Kltanh LY.
Dp Dp
(7)
The scale factor was introduced to illustrate the differences in this approach and the currently
used method for obtaining prototype scour depths from model scour depths. There is a more
direct procedure, without computing SF, that can be used to obtain the same result. This is
outlined below.
R4
1. Construct model of prototype pier to some geometric scale, G (e.g. 1:50). Scale all pier
dimensions and the water depth according to the geometric scale. Select a convenient sand
size for the flume with near uniform grain size (small ).
2. Obtain information about the prototype sediment properties and the design flow velocity.
3. Obtain the critical velocities for the model and the prototype (see Tables 14).
4. Perform flume test with model test at a velocity just below the critical velocity for the flume
U
sediment (e.g. = .9) and obtain the equilibrium scour depth for the model.
5. Substitute the measured scour depth into Equation 4 and solve for K1 and Dm.
6. Compute Dp using Equation 5.
7. Obtain the velocity at the live bed peak scour, Ulp, (see Tables 5).
8. Compute the prototype pier scour depth at the desired (live bed) velocity using the following
equation.
If 1.0 < UD < Ulp
e, Uc Uc
= K1 c2 U J + (8)
D Uc
where
k 2.4 tanh
2 = and
Uc Uc
d, = 2.4 K tanh (9)
Dp Dp
B5
