UFL/COEL94/006
PREDICTION OF SCOUR NEAR SINGLE PILES IN
STEADY CURRENTS
by
Budianto Ontowirjo
Thesis
1994
PREDICTION OF SCOUR NEAR SINGLE PILES IN STEADY CURRENTS
By
BUDIANTO ONTOWIRJO
A Report submitted to the Department of Coastal and Oceanographic Engineering
University of Florida
In Partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
1994
Prediction of Scour Near Single Piles In Steady Currents
ACKNOWLEDGEMENTS
I would like to express my deepest gratitude to my advisor and supervisory committee
chairman, Dr. Donald M. Sheppard, without whose guidance and continuous support this report
would not have been completed.
My sincere gratitude is also due to Dr. Robert G. Dean and Dr. Michael K. Ochi for
serving as members on my supervisory committee.
Two colleagues deserve special mention: Mark Gosselin provided considerable assistance
in experimental work and many enlightening discussions regarding the completion of the report,
and Tom Copps provided assistance in experimental work. I hope I have been able to reciprocate
in some small way.
Thanks are also due to Kailash Khrisnamurti, Ben Yang, Ashley and Ashraf Assaly for
the help during the hydrodynamic and scour experiments.
Financial support from Coastal Engineering Department at the University of Florida is
greatfully acknowledged.
There are not enough words to express my feeling to my parents and my sisters for their
persistent love, patience and support during the busiest years in the school. This paper is as
much yours as mine.
Prediction of Scour Near Single Piles In Steady Currents
SYMBOLS
H Water Depth
d5o Mean Sediment Size
D Pier Diameter
d, Local Scour Depth
dse Equilibrium Scour Depth
Fr Froude Number
H1, H2 Pump Head
g Gravitational Acceleration
N, Sediment Number, Uo / ((S, 1) g do)12
Re Reynolds Number
So Energy Slope
t Time
T Temperature
U, Uo Mean Velocity
u. Shear velocity, (g H So)/2
uc Critical Shear Velocity for Particle Entrainment
Uoc Critical Mean Velocity for Particle Entrainment
w Fall Velocity
a Static Angle of Repose
Y Specific Weight of Water
7s Specific Weight of Sediment
oa Standard Deviation
Prediction of Scour Near Single Piles In Steady Currents
TABLE OF CONTENTS
ABSTRACT: ...................................
CHAPTER I INTRODUCTION .......................
CHAPTER II LITERATURE SURVEY ...................
II.1 Mechanism of Local Scour ...............
11.2 Factors Affecting Local Sediment Scour Near Single
11.2.1 Flow Velocity Ratio (U/Uc) .........
11.2.2 Aspect Ratio (H/D) ..............
11.2.3 Sediment Grain Size to Structure Diameter
CHAPTER III DATA ANALYSIS METHODS ..............
III.1 Method of Fitting the Data ...............
CHAPTER IV DATA ANALYSIS RESULTS ..............
CHAPTER V SUMMARY AND CONCLUSION ............
APPENDIX A DATA ............................
APPENDIX B CLEAR WATER EXPERIMENTS ............
BIBLIOGRAPHY ................................
Pile Piers
Ratio (ds0/D)
Prediction of Scour Near Single Piles In Steady Currents
List of Figures
Figure I.1 Schematic drawing of a vortex near a Cylinder . . . . .
Figure 11.2.1 Schematic drawing of force balance on a submerged particle . . .
Figure III.1 Plot
Figure III.2 Plot
Figure III.3 Plot
Figure IV. 1 Plot
Figure IV.2 Plot
Figure IV.3 Plot
Figure IV.4 Plot
Figure IV.5 Plot
Figure IV.6 Plot
Figure IV.7 Plot
Figure IV.8 Plot
Figure IV.9 Plot
of dse/D versus U/Uc for constant d5o/D and H/D .............
of dse/D versus H/D for constant d5o/D and U/Uc ................
of dse/D versus d5o/D for constant U/Uc and H/D ............
of de/D versus H/D for constant d5o/D and U/Uc .................
of dse/D versus H/D for constant d5o/D and U/Uc ..............
of dse/D versus H/D for constant d5o/D and U/Uc ................
of dse/D versus H/D for constant d5o/D and U/Uc .................
of dse/D versus U/Uc for d5o/D = 0.00104 and H/D = 5 ........
of de/D versus U/Uc for d5s/D = 0.00165 and H/D = 5 ........
of dse/D versus U/Uc for d5s/D = 0.00547 and H/D = 5 ........
of de/D versus U/UC for d50/D = 0.00876 and H/D = 5 ........
of d, D versus log d50/D for U/Uc= 0.85 and H/D = 5 ........
Figure IV. 10 Plot of dJD versus log d5o/D for U/Uc= 0.9 and H/D = 5 . .
Figure IV. 11 Plot of djD versus log d5o/D for U/Uc= 0.95 and H/D= 5 ........
Figure IV. 12 Plot of d,,/D versus log d5o/D for U/Uc = 1.0 and H/D = 5 ........
Figure A. 1 Surface Plots d,,/D versus d5o/D and U/U, .........................
Prediction of Scour Near Single Piles In Steady Currents
ABSTRACT
Single piles have received the most attention by researchers over the years. Unfortunately
much of the data obtained is of limited value due to one or more of the important parameters
not being measured or reported. Also, the duration of many of the experiments was not
sufficient to be able to accurately determine the equilibrium scour depths. In addition, there is
still disagreement among researchers as to the most important parameters and the manner in
which the scour equations should be formulated.
This study involved the compilation of local sediment scour data from a number of
researchers, the formulation of a predictive equation and regression analyses to fit the equation
to the data. In addition, two laboratory experiments were performed to extend the data set into
areas not previously covered. The independent parameters used in the predictive equation are
velocity ratio, U/Uc aspect ratio, H/D, and sediment size to structure diameter ratio, d5o /D.
Prediction of Scour Near Single Piles In Steady Currents
CHAPTER I
INTRODUCTION
A number of papers have been written that describe the complexity of the flow and
sediment transport processes associated with structureinduced scour near single pile structures
(e.g. Melville (1975), Ettema (1980), Chabert and Engeldinger (1956) and Chiew (1984)). Many
papers have formulated scour prediction equations for the equilibrium local scour depth. Most
have differed on which of the many parameters that characterize these processes are most
important and the form of the empirical predictive equations. Unfortunately, much of the data
are of limited value due to one or more of the important quantities not being measured or
reported. Also the duration of many of the experiments was not sufficient to be able to
accurately determine the equilibrium depths.
When water flows in an open channel a shear stress is exerted on the bottom. As the
velocity increases the bottom shear stress increases. The depth average velocity that produces
the shear stress needed to initiate movement of the surface sediment is referred to as the critical
velocity, Uc. Consider an experiment where a vertical cylinder is imbedded in a cohesionless
sediment (sand) bottom in an open channel and the velocity upstream of the cylinder is slowly
increased from rest (Figure I.1). When the upstream depth average velocity, U, reaches about
one half Uc sediment starts to scour near the cylinder. Thus one may conclude that the cylinder
has modified the flow near the cylinder in such a way as to increase the bottom shear stress.
Since the bottom shear stress varies as the velocity squared this would indicate that the shear
stress near the unscoured cylinder is roughly proportional to four times the upstream velocity
squared. An examination of the flow near the cylinder reveals the existence of secondary flows
in the form of both horizontal and vertical vortices and of course an accelerated time mean
flow. The horizontal vortex which occurs at the base of the cylinder wraps around the cylinder
and extends down stream as shown in Figure I.1.
Figure I.1 Schematic drawing of a vortex near the cylinder
As viewed from above the vortex has a horseshoe appearance and is referred to as a
horseshoe vortex The flow around the cylinder separates and a wake region is formed. Vertical
vortices are formed on both sides of the cylinder in the wake region and depending on the
magnitude of Reynolds Number (based on the cylinder diameters) either remain attached or are
shed and swept down stream. The flow in the core of these vortices has a vertically upward
component which appears to have some impact on the scour process.
The horseshoe vortex clearly plays a major role in the scour process. It produces both
bed load and suspended sediment transport in the near vicinity of the cylinder. The accelerated
mean flow and the vertical vortices in the wake region aid in the scour process by helping
transport sediment out of the region. Even though the upstream flow is "steady" there are
random bursts of water motion that occur in turbulent flow and instabilities that cause an
oscillation of the axis of the horseshoe vortex. This results in a scour process that is somewhat
unsteady. Bursts of sediment being transported away from the structure can be observed. For
the purpose of analysis, however, the processes are usually considered steady or at least quasi
steady. Under clearwater conditions, scour depths increase with increasing flow velocity and
the maximum clearwater scour depth occurs at the threshold of sediment movement.
Observations of local scour processes in the laboratory have indicated a significant change
when the upstream velocity exceeds Uc. For noncohesive and uniform materials, the sediment
size is described by the median particle size, d5o. A critical mean velocity, Uc can be found for
a given stream water depth and d5o from Shields diagrams. The ratio U/Ut is an indication of
the flow intensity relative to that needed to initiate sediment motion on a flat bed away from the
structure. Local scour that occurs when the upstream velocity, U, is less than Uc is called clear
water scour and the scour that occurs for U greater than U, is called live bed scour. With clear
water scour the depth of the scour hole continues to grow until equilibrium is reached.
Equilibrium is a condition when the combination of the temporal mean bed shear stress and the
turbulent agitation near the bed is no longer able to remove bed material from the scour hole at
the pier. With live bed scour, the equilibrium scour depth is reached when the time average
amount of sediment entering the scour hole is equal to the time average amount of sediment
leaving the hole.
A second local maximum occurs at an even higher velocity. Melville (1975) indicated that
the second maximum exceeds the first for fine, ripple forming sediments ( mean grain size d5o
< 0.6 mm ). He attributes this to a reduction in the scour at U/Uc = 1 caused by sediment
being transported into the scour hole due to increased shear stress resulting from the ripples. To
test this hypothesis we performed two tests, with the same two cylinders ( 4.5" and 6.6"
diameters). In both tests the sediment in the vicinity of the cylinders had a d5o = 0.278 mm and
a sorting, a = 1.6. Both tests were performed under identical conditions except in the second
test the sediment surface layer upstream of the cylinder was replaced by a plywood board with
sand d50 = 0.278 glued to the surface. In the first test ripples formed as expected. If the effect
of the ripples on the hydrodynamics and or sediment transport impacts the equilibrium scour
depth there would be a substantial difference between the equilibrium scour depth for the two
tests.
The second test actually produced a slightly smaller scour depth, but the difference was
within experimental error. Thus, the scour was essentially the same. Even though this is just one
test, it does suggest that the reduced scour depths for finer sediments is due to some mechanism
other than the ripples.
The U/Uc plots presented in the Melville's paper show a second local maximum that is
greater than the one occurring at U/Uc for fine sediments. At flow velocities greater than
threshold, the scour depth first decreases as ripples and then dunes form on the approach flow
bed. The formation of these bed features are associated with a sharp increase in total bed shear
stress and a corresponding increase in the amount of sediment being transported into the scour
hole. Once bed features have formed on the approach flow bed, the transport of bed material
into the scour hole from upstream will become more variable, i.e., greater amounts of sediment
will be dumped into the scour hole each time a ripple or dune crest passes through it. The
transport of bed material into the hole can be considered to have steady and fluctuating
components with the periodicity of the fluctuating component being related to the wavelength
of the bed features. With increasing flow velocity, the scour depth eventually reaches a minimum
value. This minimum probably occurs at the stage of minimum dune wavelength when the scour
hole is subjected to frequent avalanches of sediment and there is insufficient time for removal
from the scour hole, of sediment dumped into it in one avalanche, before the next avalanche
arrives. Thereafter the dune formation progressively flattens as the dune wave length increases
and the frequency of avalanches into the scour hole decreases, i.e., the frequency of the
fluctuating component of sediment transport decreases. The second peak, called the transition
flat bed peak occurs when the dune formation on the approach bed has been completely eroded
away so that the fluctuating component of sediment transport due to the passage of dunes has
disappeared. In terms of bed shear stress, the transition flat bed corresponds to the stage at
which the form drag component of shear stress vanishes. At higher velocities, the occurrence
of antidunes on the approach bed has the effect of reducing the scour depth. For a uniform
nonripple forming sediment, the maximum scour depth occurs at the threshold condition.
However, in the case of ripple forming sediments, the transition flat bed peak is believed by
some researcher to be greater than the threshold peak. The reason for this is thought to be the
result of the effect of ripple formation on the approach bed. Experiments to verify these results
by University of Florida researchers (using the large tilting flume at Colorado State University)
are planned for next year. If the proper quantity of sediment (for the velocity ratio, U/U, ) is
not being transported into the scour hole, it will be artificially too deep or shallow. In the
limiting case where the upstream supply of sediment is cut off completely, the equilibrium scour
depth will reach its greatest value.
Ettema (1980) observed the dependence of scour depth on d5o/D (he actually worked with
D/d50). The data that were available at that time only covered the range 0.01 < d5o/D < 0.1. In
this range of d5o/D the nondimensional scour depth decreases with increasing d5o/D. Recent data
obtained at the University of Florida covers the range 0.00104 < d5o/D < 0.01. In this range
the nondimensional scour depth increases with increasing d5o/D. Thus, the scour depth appears
to go through a maximum value at about d5o/D = 0.01. Unfortunately, existing laboratory data
does not extend below d5o/D = 0.0001 and it is in this range that most prototype structures fall.
The dependence of the scour depth on this parameter could explain why scour depths
observed in prototype situations appear to be less than that predicted by equations developed
from laboratory data and do not include this parameter. There is not sufficient data for values
of d5s/D < 0.01 to draw definite conclusions at this point but d5s/D could be an important
parameter in translating laboratory data to field conditions. In the work reported in this paper
the independent parameters are velocity ratio, U/Uc, aspect ratio, H/D, and sediment diameter
to structure diameter ratio, d5o/D.
Prediction of Scour Near Single Piles In Steady Currents
CHAPTER II
LITERATURE SURVEY
1.1 Mechanism of Local Scour
The basic mechanism creating the local scour around a bridge pile has been identified as
the system of vortices which develop around the pile. The strength and size of the vortex system
depends on the bluffness of the pier. The vortices have been separated into components identified
as:
Horseshoe Vortex and Downflow
A blunt nose pier causes the formation of a stagnation pressure field about its stagnation
plane. If the pressure field is strong enough, a threedimensional separation of the boundary
layer takes place at the base of the pier. The boundary layer rolls up into a vortex ahead of and
along the sides of the pier. This secondary flow is called a horseshoe vortex. Raudkivi, (1983)
described the horseshoe vortex in local scour as resembling a very thick rope caught by the pier
with its end trailing downstream. When a hole has been excavated by the downflow which is
caused by the stagnation pressure on the upstream side of the pier, the oncoming flow separates
at the edge of the hole, creating a circulation or roller within the scour hole, known as the
horseshoe vortex. Ettema (1980) noted that the velocity of the downflow, occurring on the base
of the scour hole, increases as the scour hole forms and deepens. At a certain depth of scour the
downflow attains a peak strength and thereafter it gradually decreases as the scour hole deepens.
The depth of scour at which the strength of downflow occurring on the base of the scour reaches
a peak value is dependent on the approach flow to the scour hole and the relative parameter,
ds0/D.
Development of Horseshoe Vortex and Scour Hole
The development of the scour hole occurs at the sides of the piers. Ettema ( 1980)
observed that the initial small indentations occurred at about + 45 degrees to the direction of
the undisturbed flow. This corresponds closely to the location of the maximum bed shear stress
measured on a fixed plane bed surface around a cylindrical pier. These tiny holes, on either side
of the pier, propagate rapidly upstream around the perimeter of the pier and eventually meet on
the upstream centerline of the pier to form a shallow hole in front of the pier. As soon as the
hole is formed, the action of both the downflow and the horseshoe vortex begin to erode the bed
material. Melville ( 1975) described the development of horseshoe vortex as follows:
"The horseshoe vortex is initially small and roughly circular in cross section and comparatively
weak".
With the formation of the scour hole, the vortex rapidly grows in size and strength as
additional fluid attains a downward component and the strength of the downflow increases.
The horseshoe vortex moves down into the developing scour hole and expands as the hole
enlarges. As the scour hole enlarges further, the circulation associated with the horseshoe vortex
increases, due to its expanding cross sectional area but at a decreasing rate.
Development of Wake Vortices
Wake vortices are generated when the flow separates at the sides of the pier, and the
unstable shear layers formed roll up into eddy structures. This upflow has a suction effect on
the bed. The material is then swept downstream by the flow. The way in which the wake
vortices erode the bed material is analogous to that in which a tornado lifts objects from the
ground. The amount of sediment removed by the wake vortex system is relatively small
compared to that removed by the horseshoe vortex system.
11.2 Factors Affecting Local Sediment Scour Near Single Pile Piers
Local scour around bridge piers is dependent on many parameters, most of which are
interrelated. This means that the influence of one particular parameter on the depth of the scour
hole may be surpassed by that of the others.
In selecting dimensionless group parameters to represent the mechanisms of scour in term of
these quantities :
The maximum equilibrium scour hole depth (dse)
The cylinder diameter (D)
The depthmean velocity in the bottom boundary layer (U)
The critical depthmean velocity for grain movement (Uc)
The mean sediment grain size diameter (ds)
The sediment mass density (ps)
The water mass density (p)
The water depth (H)
The bottom boundary layer thickness (6)
The dynamic viscosity of water (IA)
The acceleration of gravity (g)
These parameters can be grouped into different categories. The relationship between the scour
depth and the parameters can be summarized in terms of dimensionless parameters as follows:
11.2.1 Flow Velocity Ratio (U/U)
In order to understand the effect of flow velocity on local scour depth, one must
understand sediment transport processes. When the average shear stress on the bed of a sediment
channel exceeds the critical tractive stress for the bed material, the particles on the bed begin
to move. The total amount of sediment in motion can be divided into two parts: bed load and
suspended load. Bed load is the condition when particles move in contact with the stationary bed.
In other words, the particles are transported in the flow either by rolling along or sliding over
the sediment bed or by jumping into the flow when it obtains an upward impulse as it comes into
contact with stationary grains on the bed. Suspended load is where the particles are carried in
suspension by turbulent fluctuation of the flow. There are other processes which occur in
sediment transport which will affect the structure of a stream bed; namely overpassing and
embedment. Overpassing is described as the transport of exposed particles over the immobile,
often flat bed. The overpassing particles can be larger or smaller than the bed material.
Embedment, on the other hand, is described as the burial of an overlying exposed grain in the
bed material. The larger exposed grain causes the formation of a hole in front of itself and rolls
forward into the hole to be buried in the sediment surrounding it.
Consider a particle resting on a flat bed subject to a steady flow. When the flow
velocities are small the grains will not move, but when the flow velocity becomes large enough,
the driving forces on the sediment particles will exceed the stabilizing forces, and the sediment
will start to move.
The driving forces on a sediment particle resting on other particles on an originally plane
horizontal bed are the lift forces and those due to the tractive stress To (horizontal).
The horizontal drag, FD, created by the flow, consists of skin friction acting on the
surface of the grain and forms drag due to a pressure difference on the upstream and
downstream side of the grain because of flow separation. The horizontal drag can be expressed
as follows:
FD= p CD ' d
FD=p C^ d2 U2
where:
U is characteristic velocity near the bed
d is the grain diameter
CD is the drag coefficient which is known to depend on the local Reynolds number.
The drag coefficient, CD is also dependent on the shape. The shape effects are accounted for
sufficiently well by using the fall diameter. The fall diameter of a particle is defined as the
diameter of a sphere having the same settling velocity in water at 24C.
Figure 11.2.1 Schematic drawing of force balance on a submerged particle
A lift force, FL, in excess of natural buoyancy is also created by the flow. This lift is
partly due to the curvature of the streamlines which locally will decrease the pressure to a value
lower than the hydrostatic pressure at the top of the grains. Further, the flow separation also
induces a positive lift force on the grains. The lift force can be expressed by the following
equation.
FL= p CL d2 (U2)
in which U is the friction velocity due to the friction directly acting on the bed surface ( skin
friction), and CL is non dimensional coefficients. U is the flow velocity at a distance of the order
of magnitude d from the bed.
The stabilizing forces can be modeled as frictional forces acting on a particle. For a non moving
particle resting on the bed this cannot exceed the lifting forces.
Fs = pg (s1) d3 = W6
in which W is the submerged weight of the particle, and p, is the maximum friction between the
~v
grain and the surrounding grains. This can be taken as equal to
C/s = tan (0,)
where:
08 is the static friction angle (angle of repose) for the sediment.
The particle can remain resting on the bed without moving as long as the driving forces are
smaller than the maximum retarding force. This means that the particle will not move as long
as U is smaller than Uc, where Uc is determined by:
1 CD d 2 d (s 1) pg Is
2P CO4 d 2 6 (d
2 As 4
(s 1) g d CD 3
The term on the lefthand side of equation above is called the critical Shields parameter, 0c, and
is defined by
02
c(s1) g d
The righthand side of equation above is a constant quantity which Shields found to be of 0.05
for certain roughness of Re. Recall that the Reynolds number, Re, based on the grain diameter
is :
Re L d
v
Thus, the Shields diagram that relates Shields parameter and Reynolds number will provide the
threshold value,0c as a function of Re.
Regarding the mechanism of sediment transport, we can conclude that the critical depth
mean velocity (U,) is a function of the sand diameter and mass density, water mass density and
bottom boundary layer thickness. In a case where the water depth is less than or equal to the
bottom boundary layer thickness, the water depth can be used to compute Uc.
It has been shown by previous researchers that the scour depth in the clear water
condition increases almost linearly with increasing velocity from a value U/Uc = 0.5 and
reaches a maximum at the Critical (Threshold) velocity of the bed sediment. Limited data for
clear water scour collected in this study are consistent with this trend. Among the available data
that show this trend are those of Chabert and Eldinger (1956), Ettema (1980) and Chiew (1984).
11.2.2 Aspect Ratio (H/D)
The Horseshoe vortex formed near a structure is important in defining the equilibrium
scour depth. The parameter used to characterize the vortex is the aspect ratio, 6/D.
For depths less than about 7 m the boundary layer thickness (b) can be replaced by water depth,
H. Therefore, the parameter used here to characterize the vortex is the aspect ratio of H/D.
(Chiew, 1984).
11.2.3 Sediment Grain Size to Structure Diameter Ratio (d5o/D)
The measured values of the temporal average scour depth, dse/D in uniform sediment
at a cylindrical pier presented by Ettema (1980) show the influence of d5o/D, on the equilibrium
scour depth. Ettema (1980) found that for clear water scour the influence of sediment size is
significant if the relative size d5o/D of sediment and pier is higher than 0.040.05 and that for
smaller d5o/D the scour depth is independent of sediment size.The latter is contrary to the results
from recent experiments conducted at the University of Florida.
With the combined data set from Ettema and the University of Florida there appears to
be a continuous, consistent trend in the dependence of nondimensional scour depth on d5o/D.
This could be an important parameter in translating laboratory results to prototype conditions
since the other two parameters U/Uc and H/D are approximately the same size for model and
prototype conditions. On the other hand the ratio dso/D is quite different for model and
prototype. The scour depth dependencies on this d50/D could explain why scour depths observed
in prototype situations appear to be less than that predicted by equation developed from
laboratory data and do not include this parameter. There is not sufficient data for values of d5o/D
< 0.01 to draw definite conclusions at this point and needs to be investigated further.
Prediction of Scour Near Single Piles In Steady Currents
CHAPTER III
DATA ANALYSIS METHODS
III.1 Method of Fitting the Data
The primary objective of this report is to obtain an empirical equation for the local
sediment scour depth near a circular cylinder in a cohensionless sediment in a steady flow. The
assumed dominant independent dimensionless parameters are U/Uc, H/D and d5o/D. The
nondimensional scour depth is ds /D. Thus the equation will have the form:
dse U H d0
D UC' D' D
In order to gain insight into the form of the dependence of scour depth on these
parameters dse /D was plotted versus each of the three parameters for constant values of the other
two parameters. The plots are shown in figure III.1 to figure III.3. The nature of dependence
of nondimensional scour depth on U/Uc and H/D has been established for some time but this is
not the case for d50/D due to a shortage of data for the smaller values of d5o/D. Recent
experiments at the University of Florida have supplied some of the data needed to establish this
relationship as shown in figure III.3. Two experiments were conducted specifically for this
report: one experiment to establish the point (value of U/Uc) at which local scour is initiated and
one to obtain scour data for a lower value of d5o/D. The rationale behind the overall form of the
predictive equation is discussed below. The discussion is divided according to independent
variables, i.e the functional dependence of the normalized scour depth on each of the three
parameters is discussed separately.
Velocity Ratio, U/Ue
As can be seen in figure III.1 the dependence of the normalized scour depth on U/Uc
in the range from zero to slightly above one can be expressed as a quadratic such as:
dse U U
S= ao + a, ( ) + a2 ( 2
D U U
where ao, a, and a2 are coefficients to be determined by the data.
There is sufficient evidence that a local maximum in this relationship occurs at U/Uc = 1. The
data also indicate that local scour is initiated at about U/Uc = 0.45 to 0.5 regardless of the value
of H/D or d5o/D. This information was used in analyzing the data.
dse/D vs U/Uc
HID and d50/D constant
3.00
2.50
2.00 
S1.60  . . .
XI.50
1.00 ...........................................
0.50 
0.00
0.00 0.20 0.40 0.60
U/Uc
0.80 1.00 1.20
Figure III.1 Plot of dse/D vs U/Uc
Aspect Ratio, H/D
As discussed earlier in this report the aspect ratio is believed to be the appropriate
parameter to characterize the horseshoe vortex. The data shows that the effect of this parameter
on the normalized scour depth is one of attenuation, i.e. in deep water (relative to the diameter
of the structure) the parameter has no effect on the scour depth but as the depth decreased the
scour depth is attenuated. This suggests a hyperbolic tangent type dependence as in the following
equation:
ds tanh (c
where c, is a coefficient to be determined by the data.
It seems logical (and the data support the fact) that the scour depth should approach
zero as H/D approaches zero.
dse/D vs H/D
U/Uc, d50/D are constant
3.00
2.50
2.00 
W 1.50
1.00
0.50 
0.00
0.00
1.00 2.00 3.00 4.00 5.00
H/D
Figure III.2 Plot of d,,/D versus H/D
Reynolds Number Ratio, dso/D
The scour data seem to correlate well with the ratio d5o/D. This parameter can be thought
of as a ratio of Reynolds Number based on the grain diameter, (Ubdso/v) to the Reynolds
Number based on cylinder diameter,(UD/P). The near bottom velocity, Ub, is assumed to be
proportional to the depth mean velocity, U and the kinematic viscosity of water, would be the
same in both Reynolds Numbers. Data by Ettema ( 1980) and Chiew ( 1984) for larger values
of d5o/D ( in the range of 0.025 to 0.5) showed a decreasing normalized scour depth with
increasing d5o/D with a local maximum occurring at about d5s/D = 0.01. Data from experiments
performed at the University of Florida for 0.00107 < d5o/D < 0.008 ( Figure III.3) showed that
for values of d5o/D < 0.01 the scour depth increases with increasing d5o/D. When this data is
plotted on semilog coordinates (i.e. d,gD versus log(d5o/D)) it appears to be such that a cubic
equation such as the following would be appropriate:
d d d
= bo + b, log ( ) + b2 log 2( ) + b3 log
where bo, b,, b2 and b3 are coefficients to be determined from the data.
dse/D vs log (d50/D)
H/D = 5 and UIUc = 0.85
3.00
2.50
2.00
w 1.50
1.00
0.50
0.00
4.1
00
3( 50
vD
2.00
log (d50/D)
Figure III.3 Plot of dJD versus dso/D

.............................................. ....... ...........................
 .. ............................... .................
........................ i   
.............       
Predictive Scour Depth Equation
The complete equation will thus have the form :
dse tan H U U) 2]r dbo
D = tanh (clD)[ao + a( )) + a( [bo + bD log (D)
d d
+ b2 log 2( ) + b3 log (
) .+b3log3()]
Note that this equation is highly nonlinear and in general would be difficult to use in a least
squares curve fit of the data. If, however, sufficient data exists for large values of H/D such that
tanh(c, H/D) 1, then the problem becomes tractable. From figure III.2 it appears that the
value of ci = 1 for a reasonable range of U/Uc and d5o/D. This being the case the scour data
obtained for small values of H/D can be extrapolated to the values that would have occurred if
the aspect ratio had been large. This greatly extends the data available for this analysis. The next
step in this analysis is to select scour data with constant values of d5s/D such that the expression:
[bo + b, log ( d) + b2 log 2( ) +b3 log 3( d)]
becomes a constant, say k,. For this data the problem becomes one of finding the best fit for the
equation:
dse U U
s k, [ao+al( ) a2( )2]
or
S[klao + kal( ) + ka2( ) 2]
A least squares fit of the data will produce values of the products klao ,kiaj and kla2 .
Let kiao = c11 klai = c21 ka2, = c31
Repeating this operation for different (fixed) values of log (d5o/D) results in the following sets
of equations:
ao[ bo + b, log(dso/D), + b2 log2(dso/D), + b3 log3(d5/D), ], = c
ao[ bo + bl log(dso/D)2 + b2 log2(dso/D)2 + b3 log3(d5/D)2 ] = C12
ao[ bo + bl log(dso/D)3 + b2 log2(d5o/D)3 + b3 log3(d5o/D)3 ]1 = c13
ao[ bo + bl log(dso/D)4 + b2 log2(d5o/D)4 + b3 log3(do/D)4 ] = C14
As well as the equations for aI ,a2 can be obtained as follows:
ai[ bo + bi log(d5o/D), + b2 log2(dso/D), + b3 log3(d5o/D)1 ]2 =
aj[ bo + bi log(dso/D)2 + b2 log2(dso/D)2 + b3 log3(do/D)2 2 =
aj[ bo + bl log(d5o/D)3 + b2 log2(d5o/D)3 + b3 log3(d5o/D)3 ]2 =
a [ bo + bi log(dso/D)4 + b2 log2(d5o/D)4 + b3 log3(dso/D)4 2 =
a2[ bo + bi log(d5o/D)1 + b2 log2(d5o/D), + b3 log3(dso/D) ]3 =
a2[ bo + b, log(dso/D)2 + b2 log2(dso/D)2 + b3 log(dso/D)2 ]3 =
a2[ bo + b, log(dso/D)3 + b2 log2(dso/D)3 + b3 log3(dso/D)3 ]3 =
a2[ bo + b, log(dso/D)4 + b2 log2(dso/D)4 + b3 log3(dso/D)4 =
Thus we may solve these sets of equations to obtain solutions for ao a, a2,
from the complete form of the equation :
C21
C22
C23
c24
C31
C32
C33
C34
bo bi b2 b3
d tanh (c ) +[ao +a,( ) a2 ) 2][bo +b, log ( )
D = clb[a alog(U ) .b2( [bl3 D[
d d
+ b2 log 2( ) + b log 3( d
+ b3log()]
Prediction of Scour Near Single Piles In Steady Currents
CHAPTER IV
DATA ANALYSIS RESULTS
The plot of nondimensional scour depth versus H/D for constant value of d5s/D and U/Uc
indicates that this dependence can be approximated by a hyperbolic tangent function, i.e.
D tanh (c, )
The amount of data where d5o/D and U/Uc are both constant is limited but for this data
C, has been found to equal unity. If one assumes that Clis not dependent on d50/D or U/Uc then
the above expression can be used to adjust those data points with low values ( i.e. H/D < 4 )
to the value where dse/D no longer depends on H/D. The hyperbolic tangent function is made
to pass through the data point and the value of dse/D at H/D = 5 computed. By adjusting all of
the data points to values of H/D beyond which H/D has influence on dse/D, one can concentrate
on the other two components of the scour depth equation, i.e.
dse f(u ) f2( do
D UC D
Data for dse/D versus U/UC for constant values of d50/D and H/D indicate that local scour
is initiated at U/Uc = 0.45, that a local maximum occurs at U/U, = 1.0 and that the slope of
the curve for 0.45 < U/Uc < 1.2 can be approximated by a quadratic function of U/Uc. Plots
of dJD versus log(d5s/D) for a constant value of U/Uc and H/D suggest a cubic function
dependence of dse/D on log(d5o/D). Therefore, the form of the empirical equation to be used to
fit the dimensionless local scour depth is:
dse H U U 2b +
D =tanh (c a)[ao + a( &) + a2( )][b + b log ( )
+ b2 log 2( ) + b3 log(
D +D3g )
The procedure used for obtaining a least squares fit through the data is outlined below:
Extrapolate the data points with low values (i.e. H/D < 4 ) to the value where dse/D no longer
depends on H/D (i.e. H/D = 5) with a hyperbolic tangent function. Figure IV. 1 IV.4 show
plots of dse/D versus H/D for constant value of U/Uc and ds0/D as the data was adjusted to be
independent of H/Dd5o/D.
For constant values of d5o/D and H/D (i.e. H/D = 5) those data points will then be
approximated by a quadratic function of U/Uc. Figure IV.5 IV.8 show plots of dse/D versus
U/UC for constant values of H/D and d5s/D.
Select scour data from figure IV.5 IV.8 with constant values of U/Ut and H/D (i.e U/Ut =
0.9 and H/D = 5). These set of data can be approximated by a cubic function dependence of
dse/D on log(d5o/D). Figure IV.9 IV. 12 are plots of dJe/D versus d5o/D for constant value of
H/D and U/Uc.
Select scour data with constant values of d5o/D and H/D ( i.e. H/D = 5) from figure IV.9 
IV. 12 such that the expression:
[bo + b, log ( ) + b2 g ) 3 log l 3 )
becomes a constant, say k1. For this data the problem becomes one of finding the best fit for the
equation:
d k [aoal(U) + a2( )
A least square fit of data will produce values of the products klao ,kia, and ka2 .
Repeating this operation for N different (fixed) values of log (dso/D) results in the following sets
of equations:
ao[ bo + b, log(dso/D)i + b2 log2(d5o/D)i + b3 log3(d5o/D)i ] = kiao
a[ bo + b, log(dso/D)i + b2 log2(dso/D)i + b3 log3(do/D)i ]2 = kial
a2[ bo + bi log(d5o/D)i + b2 log2(dso/D)i + b3 log3(dso/D)i l] = kia2
A cubic least square fit will obtain solutions for ao a, a2 bo b b2 b3 from i = 1 to N
number of fixed values of log (d5o/D).
dse/D vs H/D
Constant U/Uc and log d50/D
3.00
2.50    
2.00      
2.00 
2.50 ................. ....................... ................................ .............
0.00 /  
0.00
0.00 1.00 2.00 3.00 4.00 5.00
HD
3.00
2.50
2.00
1.50
1.00
0.50
0.00
0.0
dse/D vs H/D
Constant U/Ue and log d50/D
0 1.00 2.00
3.00 4.00 5.00
Figure IV. 1 de/D vs H/D
dse/D vs H/D
Constant U/Uc and log d50/D
3.00
2.50  
2 50 0 ..... ........... .......................................... ....................
2.0 ............................................. .........................................
1.00 .... .
0.50 .... ........ ...... ...
0.00
0.00 1.00 2.00 3.00 4.00 6.00
H/D
Figure IV.3 de/D vs H/D
dse/D vs U/Uc
H/D = 5 and d50/D = 0.00104
3.00
2.50  
2.50 .............0...... ..... ............. ... .............. .. ... ....
2.00
2.00 .... ..  ........ ........................................................
1.50 .................... ............... ...................... . ..........
0.50    ......
1.50
0.00
0.00 0.20 0.40 0.60 0.80 1.00 1.20
UAJc
Figure IV.5 de/D vs U/U,
Figure IV.2 de/D vs H/D
dse/D vs H/D
Constant UJUc and log d50/D
3.00
2.00 
2100  ................   ........
0.50
0.00 *.................. 
0.00
0.00 1.00 2.00 3.00 4.00 5.00
Figure IV.4 /D vs H/D
Figure IV.4 d,,/D vs H/D
dse/D vs U/Uc
H/D = 5 and d50/D = 0.001652
3.00
2.50 ..... ..
2.00 .............................
1.500 .
1.00 rl 
0.00 
0.00 0.20 040 0.60 0.80 1.00 1.20
UAJC
Figure IV.6 dJD vs U/U,
~
........................................................................ ..............
................................. I ................... .................................
   I ................... ..................
........... ..... ....................... ... .................. ... ... ... ...
                         ." ........
dse/D vs U/Uc
H/D = 5 and d50/D = 0.005473
3.00
1.50
1.00
0.50
1.00   ............
0.50       
0.00
0.00 0.20 0.40 0.60 0.80 1.00 1.20
UMUC
Figure IV.7 de/D vs U/Uc
dse/D vs U/Uc
HID = 5 and d50/D = 0.008758
[0 ................................................................... ....................
50   
10 .
10 z
10
0.00 0.20 0.40 0.60 0.80 1.00 1.20
U/UC
Figure IV.8 dse/D vs U/U,
dse'D s log Id O.Dl
1 l' ,
dseDO ,s log i d50/1D
 .'. j, I 1 1 ..
" II:lI
io
.r:
Figure IV.9 dJe/D vs d5o/D
Figure IV. 10 d,,/D vs dso/D
dse'D vs log aidO5D
r I, WI. P. "7 "
a;
dse/D S logic 150 /D
lI .I:l. I
Figure IV. 12 dse/D vs dso/D
f lj.
r I ._ i. .
u
C *l
S.'1 =
,
.1 ,
. .
I,.
4 ,
J _11 '
f. [:., .l .. ..
i;
5
I'1 I II i
I ,>
Figure IV. 11 dse/D vs dso/D
For a value of log dso/D = 0.5 we may obtain 3 different values of dse/D and U/U, as follows
(dse/D), =0.90424 for U/Ue = 0.85
(d,jD)2 =0.94459 for U/U, = 0.90
(dse/D)3 =0.96878 for U/Uc = 0.95
Thus 3 sets of equation for solution can be obtained:
(dse/D)ii = C11 + C21 (0.85), + C31 (0.85)12 = 0.90424
(dse/D)21 = C11 + C21 (0.85), + C31 (0.85)12 = 0.94459
(de/D)31 = C11 + C21 (0.85)1 + C31 (0.85)12 = 0.96878
Solve the system of equations to get the value of C11 ,C2 and C31 where in turn these
coefficients are the solutions for cubic system of equations.
ao[ bo + b, log(d5o/D)1 + b2 log2(d5o/D), + b3 log3(d5s/D)1 ]1 = cl
alj bo + bl log(dso/D), + b2 log2(dso/D), + b3 log3(dso/D), 2 = C21
a2[ bo + b, log(d5o/D), + b2 log2(dso/D), + b3 log3(dso/D) ]3 = c31
Plug in log d5o/D and C1 ,C21 and C31 the values to obtain
ao[ bo + b, (0.5) + b2 (0.5)2 + b3 (0.5)3 ]1 = 2.25
al[ bo + b, (0.5) + b2 (0.5)2 + b3 (0.5)3 12 = 6.46
a2[ bo + b1 (0.5) + b2 (0.5)2 + b3(0.5)3 ]3 = 3.23
Do the same steps as above to obtain 4 set of equations
ao[ bo + bi log(1) + b2 log2(1) + b3 log3(1) ]1 = 4.08
aj[ bo + b, log(1) + b2 log2(1) + b3log3(1) ]2 = 11.68
a2[ bo + b, log(1) + b2 log2(1) + b3 log3(1) 13 = 5.85
+ bi
+ b,
+ b,
ao[
al[
a2[
We may regro
iup these equations
ao[ bo + b, (0.5)
ao[ bo + bl (1.0)
ao[ bo + b, (1.5)
ao[ bo + b, (2.0)
b2 (1.5)2
b2 (1.5)2
b2 (1.5)2
= 4.72
= 13.49
= 6.75
(1.5)
(1.5)
(1.5)
(2.0)
(2.0)
(2.0)
Then the solution for the system of equations will be as follows
aobo = 1.2409
aobi = 9.8806
aob2 = 4.5594
aob3 = 0.5466
and also for
a, a2
albo =
ab, =
alb2 =
alb3 =
3.6137
28.3553
13.0900
1.5713
+ b2 (2.0)2 + b3 (2.0)3 ]1 = 4.4
+ b2 (2.0)2 + b3 (2.0)3 ]2 = 12.59
+ b2 (2.0)2 + b3 (2.0)3 ]3 = 6.30
in terms of ao a, a2 to obtain
+ b2 (0.5)2 + b3 (0.5)3 ]1 = 2.25
+ b2 (1.0)2 + b3(1.0)3 ]1 = 4.08
+ b2 (1.5)2 + b3(1.5)3 ]. = 4.72
+ b2 (2.0)2 + b3 (2.0)3 ]1 = 4.4
b3 (1.5)3 ]1
b3 (1.5)3 ]2
b3 (1.5)3 ]3
a2bo = 1.8074
a2bl = 14.1786
a2b2 = 6.5455
azb3 = 0.7857
Dividing ao by a, and a2 and let ao = 1 at the threshold value of U/U, thus bo b1 b2 and b3
values can be obtained as well.
bo = 1.2409
b, = 9.8806
b2 = 4.5594
b3 = 0.5466
a, = 2.8745
a2 = 1.4356
Therefore, we may rewrite the equation for solution in general form as follows
de H U U 2]
= tanh ( )[ 12. 8745 (U) +1. 4356 ( )2] [ 1. 2409
+ 9. 8806 log ( ) + 4. 5594 log 2( d5 + 0.5466 log ( d5
D + 0.5466 log )]
Prediction of Scour Near Single Piles In Steady Currents
CHAPTER V
SUMMARY AND CONCLUSION
This study has attempted to develop an improved local sediment scour prediction equation
for a circular cylinder in cohesionless sediments subjected to steady currents. Laboratory data
from a number of researchers has been used in the study. The flow and sediment transport
processes associated with local structure induced sediment scour are complex and the number
of dimensionless parameters involved is large.
Attempts were made to find correlation between the scour depth and several parameters
including Froude Number, Reynolds Number, velocity ratio, U/Uc, aspect ratio, H/D and
sediment diameter to structure diameter ratio, d5o/D. The best correlation was found when using
the velocity ratio, U/Uc, aspect ratio, H/D and sediment diameter to structure diameter ratio,
d5o/D, as independent parameters.
A subset of the total data set was used in obtaining the coefficients in the predictive
equation. A comparison between predicted and measured scour depth for the complete data set
is shown in table A. 1. The agreement appears to be quite good overall. It should be noted that
for some of the data not used in developing the equation, an assumption had to be made in order
to compute one or more of the variables (U/Uc, H/D or d5o/D).
A surface plot of dse/D versus U/Uc and log d5o/D is shown in Figure A. 1 for H/D = 5.
This illustrates the function's dependence on these two variables according to the empirical
equation.
The equation appears to provide a good fit to the laboratory data. For prototype
situations, U/Uc and H/D will not be significantly different from those for the laboratory studies.
The value of d5o/D will be smaller for prototype conditions (on the order of 104 to 105).
Unfortunately, the laboratory data only extends down to d5o/D = 0.00107. In the dse/D versus
log d5o/D curve fit an attempt was made to force the value of dse/D to larger ( more
conservative) value in the extrapolated region below dse/D < 0.75. Laboratory data for smaller
values of d5o and larger values of D are needed.
Prediction of Scour Near Single Piles In Steady Currents
APPENDIX A
DATA
This study has also compared the existing scour prediction equation HEC.18 and the equation
used in this report for a set of prototype conditions. For a sediment size of d5o = 0.24 mm and
15 ft water depth conditions, the critical velocity, Uc is 1.309 ft/sec. Let the Prototype condition
occur at the Critical velocity with Cylinder Pile Diameter of 6 ft. Therefore we can calculate
the equilibrium scour depth based on these two equations as follows :
The HEC.18 Equation is :
dse D ( 0.65 U 0. 43
H 2. 0 1 K2() ( )
Where :
K, for circular cylinder = 1.0
K2 for angle of attack of the flow where the angle is 0 and L/Dis 1 = 1.0
L is the length of the pile
The calculated equilibrium scour depth is :
dse = 2.0 (6 0.65 (1. 309 )0.43 = 0.32
H 15 V/32. 18 15
ds dse H 15
ds = d H = 0. 32 15 0. 8197
D H D 6
The equilibrium scour depth from our equations can be obtained as follows :
d,, H U U 2]
tanh ( )[ 1 2. 8745 ( ) +1. 4356 ( )2] [ 1. 2409
+ 9. 8806 log ( ) + 4. 5594 log 2( ) + 0. 5466 log( )]
Where :
U/Uc = 1
dso/D = 0.00013
Log(dso/D) = 3.882
Therefore, we may obtain the dimensionless scour depth, d/D :
d = tanh ( )[1 2. 8745 (1)+1. 4356 (1)][1. 2409 + 9. 8806 (3. 882)
+ 4. 5594 (3.882)2 + 0.5466 (3. 882)3] = 0.1657
The equation predicts much less scour than the HEC.18 equation. However, since no
actual data were collected we could conclude that the scour prediction by the equation was
satisfied.
The 3D surface plot of the scour dJD versus U/U, and log(d50/D) illustrates the
functional dependence on these two variables according to the empirical equation.
2.5
1
0 4
Figure A. 1 Surface Plot of d,,/d versus dso /D and U/U,
0.5 2
\og
UNIV. OF FLORIDA
U/Uc H/D d50/D logd50/D dsefit/D dse/D Diff
0.98 0.913333 0.002432 2.614 1.012148 1.136111 0.109112
1.05 1.826667 0.002432 2.614 1.321284 1.530556 0.136729
0.9 2.105 0.005473 2.26181 1.691158 1.755682 0.036752
0.84 2.348679 0.001652 2.78197 1.075909 0.895369 0.20164
0.83 2.366792 0.001652 2.78197 1.063819 0.849057 0.25294
0.89 2.701887 0.001652 2.78197 1.138743 0.960549 0.18551
0.9 3.368 0.008756 2.05769 1.924527 1.7 0.13207
0.78 3.404444 0.005337 2.27271 1.501292 1.486111 0.01022
0.85 3.422222 0.002432 2.614 1.294939 0.938889 0.37923
0.84 3.457778 0.002432 2.614 1.28083 1.14899 0.11474
0.83 3.484444 0.002432 2.614 1.265747 1.234848 0.02502
0.89 3.484444 0.005337 2.27271 1.715529 1.694444 0.01244
0.92 6.84 0.008756 2.05769 1.952901 2.027273 0.036686
0.49 2.348679 0.001652 2.78197 0.170962 0.154374 0.10745
0.49 3.457778 0.002432 2.614 0.203524 0.181818 0.11938
0.82 1.333333 0.001042 2.98197 0.740855 0.649351 0.14092
MELVILLE
U/Uc H/D d50/D Iogd50/D dsefit/D dse/D Diff
1.025 1.9685 0.027559 1.55974 2.17073 2.1 0.03368
0.875 1.9685 0.027559 1.55974 2.061576 2 0.03079
0.875 1.257862 0.01761 1.75424 1.7734 1.82 0.025604
1.025 1.257862 0.01761 1.75424 1.867297 1.9 0.017212
0.875 0.984252 0.01378 1.86075 1.532536 1.5 0.02169
1.025 0.984252 0.01378 1.86075 1.613679 1.6 0.00855
JAIN & FISHER
U/Uc H/D d50/D logd50/D dsefit/D dse/D Diff
0.875 0.384615 0.015385 1.8129 0.754216 0.4 0.88554
1 0.384615 0.015385 1.8129 0.795627 0.8 0.005467
D.M. CHIEW
U/Uc H/D d50/D Iogd50/D dsefit/D dse/D Diff
0.90699 0.384615 0.015385 1.8129 0.772557 0.82284 0.061109
0.99742 0.384615 0.015385 1.8129 0.795594 0.89764 0.113683
R.E. BAKER
U/Uc H/D d50/D Iogd50/D dsefit/D dse/D Diff
0.94023 3.77778 0.01333 1.87517 2.104441 1.89 0.11346
1.03306 3.77778 0.01333 1.87517 2.123205 2.12 0.00151
Table A.1
Prediction of Scour Near Single Piles In Steady Currents
APPENDIX B
CLEAR WATER EXPERIMENTS
Two experiments were conducted in the flume in the Civil Engineering Laboratory at the
University of Florida to extend the data set.The flume is 33 m (100 ft) long, 2.5 m (8 ft) wide
and 1 m (3.048 ft) deep. A 100 hp pump recirculates water through the flume with the flow rate
up to 10 ft3/sec.
The purpose of the first experiment was to determine more precisely the condition under
which scour is initiated. It was known that the local scour starts near U/Uc = 0.5 but not much
data in this range of U/Uchas been reported in the literature. The experiment was conducted with
a 6.6" diameter cylinder and sediment size d5o = 0.278 mm and a sorting, a = 1.6. The water
depth =15.5"', and flow velocity rate U/U, = 0.49. Prior to running the pump, the 6.6"
diameter cylinder was installed at the middle of the flume and the sediment bed was compacted
and leveled. The flume was then filled with water to the required depth and the water pump
started. After the pump was started, the water temperature, head across the pump and scour hole
depth were recorded at 1 hour intervals. Recordings of the scour depth were made at 1 minute
intervals for the first hour so that a time variation of the scour depth could be plotted. The
duration of the experiment was 26 hours. The water was then drained and point gauge
measurements of the scour hole conducted.
The purpose of the second experiment was to obtain scour data for small values of d5o/D.
In order to keep the contraction scour to an acceptable level the maximum diameter cylinder that
could be used was 10.5 ". This yielded a d5o/D ratio of 0.00107. The conditions of this
experiment were D = 10.5 "', H= 14 ", d50= 0.278 mm, a = 1.6. and flow velocity rate
U/U, = 0.82. The procedure used was similar to that for the first experiment but the duration
was 24 hours. Researchers have found that clear water scour rates are such that approximately
88 % of the equilibrium depth is reached in 24 hours. The results of these experiments are
presented in table A1.
BIBLIOGRAPHY
Baker, C.J. (1980) Theoretical Approach to Prediction of Local Scour Around Bridge Piers",
Journal of Hydraulic Research 18, No. 1 pp 112
Chiew, Y.M. (1984) Local Scour at the Bridge Pier Report to National Road Board,
Auckland University, Auckland, New Zealand, Report No. 216
Jain, S.C. (1981) Maximum Clear Water Scour Around Circular Piers ", JHD, Proc.
A.S.C.E., Vol 107, HY5, pp 611626
Raudkivi A.J. and Ettema R. (1983) Clear Water Scour at Cylindrical Piers ", JHE, Proc.
A.S.C.E. Vol 109, No. 3, pp 338351
Shen, H.W. (1971) Scour Near Piers Chapter 23 River Mechanics, Vol II, Colorado State
University, Fort Collins, Colorado
Shields, A. (1936) Application of Similarity Principles and Turbulence Research to Bed Load
Movement" Translated version, U.S. Dept. of Agriculture, Soil Conservation Service Coop Lab.
C.I.T.
Yalin, M.S. ( 1972) Mechanics of Sediment Transport" Pergamon Press
