UFL/COEL99/003
LOCAL STRUCTUREINDUCED SEDIMENT
SCOUR AT PILE GROUPS
By
Wendy L. Smith
February, 1999
LOCAL STRUCTUREINDUCED SEDIMENT SCOUR AT PILE GROUPS
By
WENDY L. SMITH
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
1999
ACKNOWLEDGMENTS
My sincere gratitude is extended to Dr. D. Max Sheppard as my advisor and chairman of my
supervisory committee and Dr. Daniel Hanes and Dr. Ashish Mehta for serving on my committee.
I would also like to thank Justin Rostant for his assistance, dedication, and endless enthusiasm which
made this research easier and more enjoyable. My thanks also go to the staff at the Coastal and
Oceanographic Laboratory, Danny Brown, and Bill Studstill for their spirited assistance with all of
the models and equipment for this research.
I am also grateful to Mr. Sterling Jones of the Federal Highway Administration for his
financial support and professional interest.
I would also like to express my heartfelt appreciation to all of the people who supported me
through this challenge, including my family, Tom, Lisa, Eric, Tom, Matt, Pete, Ed, Joel, Tiffany,
Carrie, and Becky.
TABLE OF CONTENTS
ACKNOWLEDGMENTS ..................................................... ii
KEY TO SYMBOLS ........................................................ v
ABSTRACT ..................................................... viii
CHAPTERS
1 INTRODUCTION ....................................................... 1
2 SCOUR PROCESSES ................................................... 3
Flow Around a Single Cylindrical Pile ....................................... 4
Parameters ......................... .................................... 6
Flow Around Pile Groups ............................................... 9
Parameters ..................... ....................................... 11
3 SCOUR PREDICTION .................................................. 14
Equations for Predicting Maximum Equilibrium Scour Depth At Single Piles ........... 19
University of Florida equation ......................................... 19
HEC18 scour prediction equation ....... ............................... 21
Equations for Predicting Maximum Equilibrium Scour Depth Around Pile Groups ....... 24
4 TIME DEPENDENCE OF SCOUR ....................................... 29
5 DESIGN LOCAL SCOUR DEPTHS AT PILE GROUPS ....................... 33
Illustration of Model Use .................................................. 38
Example 1 ....................................................... .. 38
Example 2 .......................................................... 40
6 EXPERIMENTAL PROCEDURES ........................................ 43
iii
Flum e .............................................................. 44
Test Preparation ..................................................... 50
Test Conditions ....................................................... 55
Test Results ...................................... ................... 56
7 RESULTS AND CONCLUSIONS ......................................... 68
APPENDIX ............................................................... 74
REFERENCES ............................................................ 80
BIOGRAPHICAL SKETCH ................................................. 84
I";
* 'I
i
:

KEY TO SYMBOLS
A crosssectional area of the flow
a skew angle
b diameter/width of a single pile
ci.6 coefficients for the University of Florida scour prediction equation
c empirical coefficient for equation 39
D* effective diameter/width of pile group
D,6 sediment size
Dso median sediment diameter
D,4 sediment size
Dgo sediment size
d,, maximum equilibrium scour depth
d,(a) maximum equilibrium scour depth for a pile group at skew angle a
dse(a = 0) maximum equilibrium scour depth for a pile group at zero skew angle
ds, maximum equilibrium scour depth around an equivalent solid pier
dse submerged pile group
maximum equilibrium scour depth of a submerged pile group
d,,g maximum equilbrium scour depth around a skewed pile group
Fr Froude number
g acceleration due to gravity
H dune height
H flow head (equation 61)
h* manometer reading
HPB height of pile above the bed
k, Nikuradse roughness
K. skew angle correction factor/ parameter
Kh degree of submergence parameter
K, spacing correction factor (equation 313)
K, shape parameter (equation 53)
KV, spacing parameter
KI shape correction factor
K2 skew angle correction factor
K3 bed condition correction factor
K4 bed armoring connection factor
K5, K6 empirical coefficients (equation 310)
L length of pier
m number of piles in line with the flow
n number of piles normal to the flow
Q flow rate
s distance between the pile centerlines
S.F. safety factor
Normalizing parameter based on effective width of pile group
a sediment size distribution
t, the time required for the scour hole to develop to a depth at which the
increase in depth does not exceed 5 percent of the pier diameter in the
succeeding 24 hours
U depth averaged approach flow velocity
Uc critical velocity associated with incipient sediment motion
w width of pier
WP projected width of a pile group onto a plane normal to the flow
yo depth of approach flow
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
LOCAL STRUCTUREINDUCED SEDIMENT SCOUR AT PILE GROUPS
By
Wendy L. Smith
May 1999
Chairperson: D. M. Sheppard
Major Department: Coastal and Oceanographic Engineering
The objective of this thesis is to investigate local scour at pile groups in order to
accurately predict the maximum clearwater equilibrium scour depth. The differences
between the scour mechanisms and the fluid, flow, sediment, and structure parameters
influencing scour depth for single piles and pile groups are discussed. The assumption is
made that the relationships between these parameters that have been established for single
cylindrical piles are also valid for pile groups. An attempt is made to relate scour depths at
pile groups to those at a single cylindrical piles by determining an "effective width" of the
pile group that may be applied to the predictive equation for a single cylindrical pile. The
additional structure characteristics influencing scour at pile groups include: spacing, group
configuration, shape, skew angle, and degree of submergence. To investigate these effects,
flume tests were conducted on pile groups with varying spacing, configuration, skewness to
the flow, and degree of submergence. It was determined that spacing, configuration, shape,
and skew angle all influence the "effective width" of the structure. The influence of each was
determined based on laboratory tests conducted for this thesis and the relationships
developed by previous researchers. As a component of a complex bridge pier, the degree of
submergence of the pilings was also investigated to determine the influence on scour depth.
A relationship was determined based on test results where the height of the pile group was
varied relative to a constant water depth. These results may be used in conjunction with the
results of the tests currently being conducted by the Federal Highway Administration on the
other components (pile cap and pier) to determine the total local scour depth of a complex
bridge pier.
CHAPTER 1
INTRODUCTION
Frequently, bridge failure is due to excessive scour, the removal of sediment around the
bridge piers. Excessive scour can cause the piles to be undermined and no longer support the bridge.
Design against this type of failure is based on the prediction of the maximum depth of scour. Thus,
the accuracy of this prediction is important because underpredicting can result in structural damage
and possible loss of life, while overpredicting can waste millions of dollars in over design.
The phenomenon of scour around bridge piles has been investigated by numerous researchers
over several decades. Most of the research was conducted on single cylindrical piles in cohesionless
sediment under steady flow conditions. As a result of these laboratory experiments, it is now
possible to predict maximum scour depths for a wide range of laboratory scale structures with the
use of empirical equations. Because of the volume of work and the level of understanding of the
scour processes around simple cylindrical piles, these data sets are valuable for quantifying the
effects of many of the relevant factors influencing the scour depth.
However, bridge designs are often more complex, using multiple pile bridge piers. The scour
mechanisms for multiple pile bridge piers are much more complex than for a simple, cylindrical pile
and thus design scour depths are more difficult to predict. This is especially true when the piles are
not aligned with the flow. In order to investigate scour around complex bridge piers, it is important
to understand the scouring processes and the hydrodynamic effects of the flow around the structure.
2
The objective of this research was to build and improve upon the existing methods and
procedures for estimating design scour depths for complex pier geometries by investigating scour
at groups of square piles. This work investigates subaerial and submerged rectangular pile group
arrays both inline and skewed to the flow.
CHAPTER 2
SCOUR PROCESSES
Scour is the removal of sediment caused by flow over an erodible bed. When the flow
velocity exceeds the value needed to produce the critical shear stress of the bed material, bedload
transport is initiated. The mechanisms of scour at bridgelike structures are usually separated into
three categories:
bed degradation,
constriction scour, and
local scour.
Bed degradation is the general erosion of bed material throughout the waterway. This
degradation could change the slope, elevation, and/or contours of the bed, altering the flow.
Constriction or contraction scour is that caused by a reduction in the crosssectional area of
the flow, i.e., the presence of a large obstruction in a narrow waterway, constricting the flow. The
reduction of flow area causes an increase in velocity and bed shear stress at that location. In practice,
the scour caused by constriction is considered negligible when the area of the obstruction is less than
approximately 10 percent of the waterway crosssectional area.
Local scour is that due to the alteration of the flow field by the obstruction (e.g., a bridge
pier). Local scour is initiated when these effects produce bed shear stresses that exceed the critical
value for the bed sediment.
4
For a bed of cohesionless sediment, there are two types of local scour: clearwater and
livebed. Clearwater scour refers to local scour that occurs when the upstream bed shear stress is
below the value needed to initiate sediment motion on a flat bed. Equilibrium scour depth is reached
when the bed shear stress in the scour hole is reduced to the critical value. Livebed scour occurs
when the upstream bed shear stress exceeds that required for sediment transport. In this case,
equilibrium scour depth is reached when the quantity of sediment leaving the scour hole is equivalent
to that which is entering the hole.
Flow Around a Single Cylindrical Pile
The placement of a bridge pile in cohesionless sediment under a uniform, steady flow creates
numerous hydrodynamic effects (figure 21):
horseshoe vortices at the base and in front of the pile,
downflow on the front edge of the pile,
bow wave at the surface on the upstream side of the pile,
upflow in the wake region,
wake vortices behind the pile, and
higher flow velocities (spatially accelerated flows around the pile).
The introduction of a pile in a uniform, steady flow causes the flow to increase in velocity
as it flows around the pile. The increased velocity (and corresponding increased shear stress)
initiates scour at the sides of the pile which develops into a scour hole at the pile. The size of the
scour hole increases as the surrounding sediment avalanches into the hole and is carried away by the
Bow Wave
Horseshoe
Vortex
A Upflow
SWake
S C Vortices
/
Figure 21. Flow patterns associated with local scour
accelerated flow. A horseshoe vortex is formed by the vertical gradient in stagnation pressure on
the leading edge of the pile. As the hole deepens, flow separation occurs at the edge of the scour
hole causing a downflow at the front of the pile which enhances the horseshoe vortex at the base of
the pile. This vortex is swept around the sides where it narrows in cross section and trails
downstream creating a "horseshoe" shape when viewed from above. Numerous researchers (Hannah
1978, Nakagawa and Suzuki 1975, Gosselin 1997, Shen et al. 1966, Melville 1975) have concluded
that this horseshoe vortex is the primary mechanism of local scour.
Once a sediment particle is put into suspension by the horseshoe vortex, it is swept around
the side of the pile. As more sediment is removed, the scour hole is expanded in both width and
depth. The horseshoe vortex grows in diameter as the hole deepens, descending into the hole.
Melville (1975) observed that as the size and circulation of the horseshoe vortex increases, the
Stern Wave
,
6
strength of the vortex decreases, reducing the velocity near the bottom of the hole, thus the scour
process slows as the hole deepens.
Other hydrodynamic effects that aid in the removal of sediment are the bow wave, upflow
in the wake region, and wake vortices. A bow wave is the rise in flow surface as the kinetic energy
of the flow is converted into potential energy at the pile. This creates a surface vortex that rotates
opposite to the horseshoe vortex. A pressure difference on the bed from the front to the back of the
pile can cause groundwater flow from upstream to downstream. Some researchers think that this has
an impact on the rate and depth of local scour. Vertical (wake) vortices are formed at the structure
just downstream of the points of flow separation on the pile. Just as in tornadoes, these vortices have
a vertical flow component in their interior.
The general principles of local scour due to these effects are:
the rate of scour will equal the difference between the capacity for transport out of
the scour hole and the rate of supply to the hole,
the rate of scour will decrease as the flow section is enlarged due to the scour, and
there will be a limiting extent to the scour depth that depends on the structure shape
and size, the sediment properties, and the flow conditions.
Parameters
Because of the complexity of the flow and sediment transport processes, analytical treatment
of scour has not produced meaningful results. Numerous researchers have investigated the simplest
case of scour around a single cylindrical bridge pile (Jones, Sheppard, Ettema, Melville, Chiew,
Hannah, Gosselin, Shen, Bruesers, and others). Most of them agree that the scour depth produced
7
by flow around a single cylindrical pile in cohesionless sediment depends the parameters which
characterize the critical shear stress of the bed, energy of the flow, and the size and strength of the
vortices:
fluid: density and viscosity,
flow: depth of approach flow, approach flow velocity,
sediment: size, density, shape, grain size distribution, and
structure: size, shape.
The critical shear stress governing sediment transport is a function of the fluid properties
(density and viscosity), flow depth (vertical velocity distribution), sediment properties (grain size,
shape, and density), and bed roughness (ripples, dunes, etc.). The bed roughness affects the kinetic
energy of the flow near the bed and the roughness is a function of the sediment size and bed forms.
It is this roughness along with the depth averaged flow velocity that defines the shape of the
upstream velocity profile and boundary layer and thus, the bed shear stress. The size of the surface
vortex depends directly on the magnitude of the stagnation pressure generated by the approach flow
along the pile's centerline.
The size of the pile governs the size of the vortices. The larger the pile, the larger the
horseshoe vortex. It has been found (Melville and Sutherland 1988, Mostafa et al. 1995b) that if the
pile is not cylindrical, the shape has an impact on the equilibrium scour depth. Streamlining the
upstream edge of a pile reduces the strength of the horseshoe vortex, thereby reducing scour depth.
Streamlining at the downstream end reduces the strength of wake vortices also reducing scour depth.
A squarenose pile will have scour depths about 20 percent greater than a sharpnose pile and 10
percent greater than either a cylindrical or roundnose pile (Richardson and Richardson 1989).
8
Often, piles are subjected to flows that approach from an angle (to the sides of the pile). This
may be due to the bridge being skewed to the waterway or the result of a shift in flow direction under
storm conditions. The angle between the pile (at design conditions) and the flow direction is called
the flow skew angle. As the skew angle changes, the shape of a noncylindrical pile changes relative
to the flow and alters the local flow field, thus influencing the scour depth.
Laursen and Toch (1956) is probably the best known research on the influence of skew angle
on scour depth for single, solid structures. They investigated rectangular piers, varying the skew
angle (a) and aspect ratio (Uw) where L is the length of the pier and w is the width. Figure 22
shows the influence of a and L/w. KI is defined as the ratio of the projected width of the pile (at
skew angle) to the width at zero skew angle. These curves are based on both laboratory and field
data; however, no data was presented in their plot.
Mostafa et al (1995b) conducted numerous experiments (120) at the University of Iowa and
the University of Alexandria in an attempt to better predict the scour depth at piers skewed to the
flow. Single rectangular and oblong piers with the same pier width were tested, varying Uw for
skew angles between 0 and 900. They found that the Laursen and Toch curves underpredict the
maximum equilibrium scour depth for rectangular piers at large skew angles (a > 500).
0 15
30 45 60
Angle of Attack in Degrees
75 90
Figure 22. Flow skew angle correction factor by Laursen and Toch (1956)
Flow Around Pile Groups
The scour processes for flows around single cylindrical piles in a cohesionless sediment have
long been recognized (Laursen and Toch 1956, Shen et al. 1966, Melville 1975, Nakagawa and
Suzuki 1975, Breusers et al. 1977, and others) for steady flow conditions. However, the flow field
is much more complex when there is more than one pile and they are in close proximity to each other
(figure 23).
Y I/w 16
0 I 4/~'~4~\1
 0% 01, 12_
Wo
10
Hannah (1978) studied local scour at cylindrical pile groups under uniform, steady flow
conditions, concluding that local scour at these groups is affected by four basic mechanisms:
reinforcing,
sheltering,
shed vortices, and
compressed horseshoe vortices.
Reinforcing
and
Sheltering
A
(b Upflow
Figure 23. Flow around multiple piles in close proximity
For a pile group where the piles are spaced such that the scour holes overlap, the vortices
around the piles interact with each other, and thus the downstream piles reinforce scour at the
Bow Wave
Horseshoe
Vortex
I
11
upstream piles. The downstream piles also aid the scouring at the upstream piles by decreasing the
exit slope of the scour hole and lowering the bed level behind the hole. This reduces the energy
required (in the scour hole) to transport material out of the hole. As pile separation distance
increases, reinforcing of the vortices diminishes.
A sheltering effect is observed when an upstream pile blocks the flow to the downstream pile,
reducing the approach flow velocity (and thus the shear stress), causing less scour to occur at the
downstream pile. This sheltering effect limits the scour behind the front piles, but with development
of the hole, material from the rear of the pile is eroded both by the shed vortices and by sliding into
the scour hole and being removed by the vortex system.
Shed vortices are the eddies that usually form just downstream of the point of flow separation
on the pile. These vortices provide lowpressure pockets that assist in lifting sediment from the
scour hole, aiding in the scour process at piles in the path of the vortices.
When piles are in close proximity, the trailing arms of the horseshoe vortices are compressed.
This results in an increase in the velocity of the vortex and a corresponding increase in bed shear
stress and scour.
Parameters
The scour depths produced at pile groups are also influenced by the size and shape of the
structure through the skew angle, pile spacing, and group configuration (number and arrangement
of piles). However, all of these structure parameters are interrelated, complicating scour depth
analysis.
12
Skew angle. Zhao (1996) studied the effects of skew angle on scour depth at 3x8 arrays of
cylindrical and square inline piles. Both groups were composed of uniformdiameter piles with
constant pile spacing. The skew angle, a, was varied between 0 and 900. Zhao observed the
changing influence of the scour mechanisms as the skew angle varied. When the skew angle was
small (a < 150 for cylindrical and < 200 for square piles), the compressed horseshoe vortex
dominated the scour process and the maximum scour depth occurred near the front of the pile group.
When the skew angle was large (a > 200 for cylindrical and > 25 for square piles), the interaction
of the wake vortices from the upstream piles on downstream piles dominated and the maximum
scour depth occurred along the upstream side of the pile group. Zhao also found differences in the
maximum equilibrium scour depth of the skewed pile groups based on the shape of the pile. The
maximum depth occurred at a skew angle of 250 for cylindrical piles and approximately 700 for the
square piles. The scour depth at skewed pile groups not only varies for different pile shapes and
skew angles, but for different pile spacings as well.
Pile spacing. Pile spacing influences the vortices created around the piles which interact with
each other and the acceleration of the flow due to constriction created by the adjacent piles. These
effects are greatly influenced by the distance between the piles. Salim and Jones (1996) and
Sheppard et al. (1995a) studied these effects by looking at the ratio s/b where s is the distance
between the pile centerlines and b is the diameter/width of a single pile.
Salim and Jones investigated groups of square piles in inline arrays of 3x3, 3x5, and 4x5,
varying s/b between 1.5 and 10. Sheppard et al. examined square pile groups in arrays of 3x2, 3x3,
13
and 3x8, varying s/b between 1 and 9. Both researchers observed an increase and then a decrease
in scour depth as s/b increased from 1 to about 3. For values of s/b greater than 3, the scour depths
continued to decrease out to approximately 10 where the scour depth was that of a single pile.
Group configuration. The arrangement of the piles and number of piles normal to the flow
influence the hydrodynamics around the pile group due to the changes in the size of the structure and
the interaction of the vortices due to the number of piles.
Salim and Jones (1996) investigated the effects of pile arrangements by looking at square
piles in a staggered array, 5 piles long and alternating between 3 and 4 piles wide. They found that
the group behaved similarly to an equivalent solid structure, even as the structure was rotated with
respect to the flow direction. However, at certain angles, the piles lined up with one another, making
the structure appear much smaller.
Copps (1994) and Hannah (1978) investigated the influence of the number of piles normal
to the flow, n. Copps analyzed 3x8, 5x8, and 7x8 arrays of square inline piles. Hannah examined
1x2, 2x1, 2x2, and 2x3 arrays of inline cylindrical piles. They both concluded that an increase in
the number of piles normal to the flow (increasing the effective width of the structure) increases
scour depth. It was observed that this effect decreases as spacing between the piles increases.
Hannah's (1978) research also included an investigation of the influence of the number of
piles in line with the flow, m, on scour depth. He concluded that for inline pile groups, m has only
a minor effect on the maximum depth of scour.
CHAPTER 3
SCOUR PREDICTION
There has been an increased interest in the prediction of structureinduced scour in the last
decade. As a result of numerous laboratory experiments, it is now possible to predict equilibrium
scour depths for a limited range of laboratory scale structures through the use of empirical equations.
The variables that must be included in a scour predicting equation are those that characterize the
primary local scour mechanisms.
Several researchers (Melville and Sutherland 1988, Sheppard 1998, Raudkivi 1986, and
Ettema 1980) have examined the influence of the numerous parameters influencing scour around a
single cylindrical pile. Most agree that the primary fluid, flow, sediment, and structure parameters
that influence scour depth near single piles in cohesionless sediments are:
depth of approach flow, y,,
sediment size, Dso,
sediment size distribution, a,
depth averaged approach flow velocity, U,
critical velocity associated with incipient sediment motion, Uc, and
structure width, b.
However, these researchers have come to different conclusions regarding the dimensionless
groups formed from these parameters that should be used to predict the equilibrium scour depth, d,,.
15
Melville and Sutherland used the parameters, b/D0o, yjb and U/Uc to characterize nondimensional
equilibrium scour depth, d]/b. They concluded that as b/Dso exceeded a value of 25, the scour depth
becomes independent of this parameter (even though some of their own data showed dependence
beyond that value). Sheppard et al. (1995b), using the data from several researchers including their
own, found the nondimensional equilibrium scour depth dependence on the reciprocal of this
parameter, Dso/b, to go beyond the range reported by Melville and Sutherland. Others have
concluded that scour depth is dependent on other dimensionless groups such as Froude Number.
Because the number of parameters associated with the scour process is quite large, there have
been numerous empirical equations for predicting scour depths. Jones (1984) compared the
equations available at that time and found the results to be quite different. Even the best correlations
have a reasonable amount of scatter in the data plots. A number of factors have contributed to scatter
in laboratory data. These include: conducting tests for too short a duration to obtain equilibrium
depths, not measuring (or at least not reporting) some of the important variables; not measuring
and/or not maintaining uniform compaction of sediments from one experiment to the next, etc.
Therefore, even though a large number of experiments appear in the literature, only a portion of the
data are usable for creating or evaluating predictive equations.
Using only data from laboratory experiments of sufficient duration that equilibrium scour
depths were achieved, Sheppard has found that the data for single cylindrical piles correlates well
with the dimensionless parameters y/b, U/Uc, and Do/b.
d,/b = f(y/b, U/Uc, D,5b) (31)
16
yjb. The flow depth to structure diameter ratio (y,/b) describes the relationship between the
surface and bottom horizontal vortices at the upstream side of the pile, i.e., the interaction of the
counterrotating surface vortex near the water surface and the horseshoe vortex at the base of the
pile. When yjb is small, the flow associated with the surface vortex interacts with and weakens the
horseshoe vortex at the base of the pile. It is generally accepted by researchers (Laursen and Toch
1956, Sheppard 1998) that the relative scour depth (djb) increases as the relative flow depth (y/b)
increases until a certain limiting value of yjb is reached, after which the relative scour depth is
independent of y/b. The limit expressed by most researchers is in the range of 2< yjb< 3.
Laboratory data (Ettema 1980, Sheppard 1998) indicates that if the other two parameters
(U/Uc, D,/b) are held constant, the relative scour depth increases rapidly with yo/b from zero. It then
approaches a constant value when yo/b reaches between 2.5 and 3.0, indicating that when the flow
depth to structure diameter ratio exceeds this value it no longer has an influence on the scour depth
(figure 31).
ULU,. The depth averaged approach flow velocity to critical velocity ratio (U/U,) is a
measure of the flow intensity. The critical velocity is that associated with critical shear stress at the
point of incipient sediment transport. Critical velocity is a function of the fluid properties (density
and viscosity), flow depth (vertical velocity distribution), sediment properties (grain size, shape, and
density), and bed roughness (ripples, dunes, vegetation, etc.).
Laboratory data (Sheppard 1998, Hannah 1978, Ettema 1980, Melville 1984) shows that for
single cylindrical piles, local equilibrium scour is initiated at approximately U/Uc = 0.45 and
increases rapidly with increasing U/Uc up to transition from clearwater to livebed conditions (U/Uc
=1). Early researchers of local scour (Jain and Fischer 1980) concluded that the maximum
17
equilibrium scour depth occurs at the transition from clearwater to livebed conditions. But Melville
(1984) and Raudkivi (1986) found that the peak scour depth in the livebed range could be larger
than that at transition if the sediment is in the rippleforming range (Dso < 0.6 mm). Figure 32 is
a schematic drawing of the general variation of relative scour depth with U/Ut for the clearwater and
livebed regimes.
DsA. The median sediment diameter to structure diameter ratio (D5o/b) is actually the ratio
of two Reynolds Numbers, one based on the sediment grain diameter and one on the structure
diameter. Both Reynolds numbers are important in characterizing the flow and sediment transport
in the vicinity of the structure.
Baker (1986) and Ettema (1980), using the data of Raudkivi and Ettema (1977), concluded
from their clearwater scour data that the equilibrium nondimensional scour depth, ds/b, increased
with decreasing Do/b until Do/b reached a value of 0.040.05. For values less than this, the scour
depth was thought to be independent of Dsob. Sheppard et al. (1995b), using data from several
researchers (including Ettema, 1980) and their own (collected at the University of Florida), found
the scour depth dependence to extend to lower values of D5sb as shown in figure 33. Note that both
y/b and U/Uc are held constant in this plot.
The reduction in scour depth with decreasing values of Do/b is very important since 1) most
prototype situations have very small values of Do/b and 2) this relationship is needed to properly
interpret laboratory data from model scour tests. Sheppard et al. are presently conducting
experiments with larger piles in order to extend the data to even smaller values of Do/b.
U/U = constant
0 D5o/b = constant
0 I I
0 1 2 3 4
yo/b
Figure 31. Variation of relative local scour depth with y/b
Clearwater Livebed
Dso/b = 0.016
dse/b
Dso/b = 0.0003
yo/b= const.
U/UL
Figure 32. Variation of relative scour depth with U/Uc
19
U/UC = constant
Dso/b = constant
Figure 33.
6 4 2 0
log (Dso/b)
Variation of relative scour depth with Dso/b
Equations for Predicting Maximum Equilibrium Scour Depth Around a Single Pile
University of Florida equation
Sheppard et al (1995b) developed the following empirical predictive clearwater scour depth
equation for a single cylindrical pile in a cohesionless sediment, penetrating the water surface, and
subjected to a steady flow. The assumption is made that the relative scour depth can be expressed
as a product of three functions (equation 32) of the relevant dimensionless parameters discussed
above, y/b, U/Uc, and D5,b.
The coefficients in this equation were determined by a regression analysis and have been
confirmed with more recent and reliable data. The equation allows for a safety factor (S.F.) to be
20
added so as to be an envelope or design equation rather that one that best fits the data. It is shown
in equations 32, 33, 34, and 35 in its most recent form. Table 31 shows the most recently
determined coefficients.
djb = S.F. f,(yjb) f, (U/U,)" f,(D5/b) (32)
fi(yob) = ci tanh (c2, y/b) (33)
f2(U/U,) = 1 + c3 (U/U,) + c4 (U/U,)2 (34)
f3(D5o/b) = logo(Do/b) expi{c, [logo (Dso/b)] "6 (35)
Table 31. Coefficients for equations 32, 33, 34, and 35
c, c2 c3 C4 c5 c6 S.F.
4.81 1.0 2.87 1.43 0.18 2.09 1.35
The safety factor ensures conservative overprediction of scour depths. Figure 3 4 shows
the accuracy of this equation.
It should be noted that data from controlled laboratory tests do not exist for large structures,
so it is uncertain how well laboratory results predict scour at prototype scale structures. For
prototype situations, U/U, and y/b will be approximately the same as those for laboratory studies,
however, the value of D,/b can be significantly smaller for the prototype. For this reason, Sheppard
et al are presently conducting experiments with a 3foot diameter pile in a 20foot wide by 21foot
deep flume. Sheppard recommends that, at present, if D,/b is less than 3.1x10'3 that Dsb be set to
3.1x103 when using the equation.
3
,*..
*
.o C2= 1.0
Ca c3= 2.87
S.* c4 = 1.43
cs = 0.18
.c6 = 2.09
S.F. = 1.35
0 I 1 I
0 1 2 3
dseb measured
Figure 34. djb measured vs. d,jb predicted
The effect of pile shape has been accounted for by the use of a multiplicative coefficient such as that
shown in equation 36 for a square pile.
d,jb (square pile) = 1.1 djb (cylindrical pile) (36)
HEC18 scour prediction equation
The current method recommended by the Federal Highway Administration (FHWA) for
predicting design scour depths at bridge piles uses an equation based on the one developed at
Colorado State University by Richardson et al. (1988). This equation is presented in the FHWA
Hydraulic Engineering Circular No. 18 (HEC18) "Evaluating Scour at Bridges" (1996).
dJb=2.0 K, K2 K3 K4 (yo/b)0.5 (Fr)0.43 (37)
where Ki = shape correction factor for pile nose shape;
K2 = skew angle correction factor;
K3 = bed condition correction factor;
K4 = correction factor for armoring by bed material size; and
Fr = Froude number = U/(gyo)5.
This equation is for both livebed and clearwater conditions.
The shape correction factor, KI, estimates the influence of the shape of the upstream edge of
the pile. However, for skew angles greater than five degrees, K, = 1.0.
Table 32. Shape correction factor, KI
square nose round nose circular cylinder group of sharp nose
cylinders
1.1 1.0 1.0 1.0 0.9
The skew angle correction factor, K,, adjusts the predicted scour depth based on aspect ratio
and skewness to the flow. The following table estimates the influence of skew angle based on the
aspect ratio (L/b) where L is the pile length and b is the pile width.
Table 33. Skew angle correction factor, K,
K,
Skew Angle L/b = 4 Ub = 8 L/b = 12
0 1.0 1.0 1.0
15 1.5 2.0 2.5
30 2.0 2.75 3.5
45 2.3 3.3 4.3
90 2.5 3.9 5.0
The bed condition correction factor, K3, results from the fact that for planebed conditions, the
maximum scour may be 10 percent greater than predicted (30 percent if large dunes exist).
Table 34. Bed condition correction factor, K3
Bed condition Dune Height (m) K3
Clearwater scour NA 1.1
Planebed and Antidune NA 1.1
flow
Small dunes 3 > H 0.6 1.1
Medium dunes 9 > H > 3 1.2 to 1.1
Large dunes H > 9 1.3
24
The bed armoring correction factor, K4, decreases the predicted scour depth due to armoring
of the scour hole by bed materials in which D5so 0.06 meters. This factor is necessary because it has
been observed that finer grains are transported away from the structure at a lesser velocity than is
required to remove Dsosize sediment, thus leaving larger grains to "armor" the scour hole. Jones
developed an equation for determining K, based on velocity ratio and grain size, D9g from research
conducted for FHWA by Molinas at Colorado State University.
The Froude number characterizes the local energy or hydraulic gradients driving the flow into
or around the scour hole. It expresses the relative sizes of the stagnation pressure at the leading edge
of the pile (U2/2g) and the flow depth, y,. The acceleration due to gravity is g.
Fr = U/(gyo)0.5 (38)
Equations for Predicting Maximum Equilibrium Scour Depth Around Pile Groups
One approach to predicting scour depths at pile groups associates an "effective width" or
diameter of the group and computes the scour depth for a single structure using this diameter. A
circular pile was chosen as the single structure in this work because it is the best understood and
most researched structural shape. The assumption is made that the local scour at a pile group is
related to the local scour that would occur for a single cylindrical pile subjected to the same fluid,
flow, and sediment conditions. It is also assumed that the group has a similar functional dependence
on the independent parameters with the exception that an "effective diameter/width", D*, must be
used in place of b. The functional dependence of the "effective diameter" on the group properties
(number of piles, spacing, etc.) must then be determined.
25
Copps (1994) examined the effective width of pile groups as a function of pile diameter
(width) to centerline spacing (s/b), and the number of piles normal to the flow (n), and developed
the relationship:
D* = (n1)b/(s/b)c +b (39)
where the value of c (0.55) was determined from a regression analysis of University of
Florida (UF) laboratory data. This equation was modified by Sheppard et al. (1995a) to the
following form:
D*/b = 1 + (n1) (s/b)"' exp{K6 (s/b 1)2} (310)
where K5 and KI were evaluated using regression analysis of experimental data (collected at
UF) to be 0.27 and 0.05, respectively.
However, these equations are only applicable to inline pile groups (i.e. pile arrays that are
in rows and columns) which are aligned with the flow (no skew angle). It has been well documented
(Laursen and Toch 1956, Chabert and Engeldinger 1956, Hannah 1978, Mostafa et al. 1993, 1995b,
1996, Zhao and Sheppard 1996, Salim and Jones 1996) that skewness of a pile group to the flow
direction has a significant influence on the maximum depth of local scour due to the increased
effective size of the structure and the added complexity of the flow field. For pile groups skewed
to the flow, Jones (1989) concluded that pile groups that project above the stream bed can be
analyzed conservatively by representing them as a single width structure equal to the projected width
of the piles, ignoring the clear spaces between the piles. This is currently the methodology used in
26
predicting the maximum equilibrium scour depth in HEC18. It should be noted that the duration
of his tests was only 4 hours.
The most comprehensive research on the influence of skew angle on scour depth at pile
groups was done by Zhao (1996). Zhao studied the effects of skew angle for a 3x8 array of inline
cylindrical piles and a 3x8 array of inline square piles both with s/b = 3. Six tests were conducted
on each of the circular and square pile groups with the skew angle varying between 0 and 90. The
duration for each test was 26 hours, the time at which Zhao had estimated the scour depth had
achieved 90 percent of the maximum equilibrium scour depth. Zhao defined a skew angle correction
factor, K. to account for the skewness of a pile group:
K. = dse(a)/d,,(0) (311)
where d,(a) = the maximum equilibrium scour depth for the pile group at skew angle a and
ds(a0) = the maximum equilibrium scour depth for the same pile group at zero skew angle. Figure
35 shows the variation of K, with the skew angle for both the square and cylindrical pile groups.
All of his tests were conducted at U/Uc values between 0.60 and 0.66.
It should also be noted that as the skew angle (and effective width of the structure) increased,
yo was held constant for these tests. Thus, y/D* fell far below the value at which scour depth is
independent of this parameter (see figure 31). In addition, as the effective width of the group
increased, a longer time was needed to reach maximum equilibrium scour depth. Thus, 26 hours was
not a sufficient duration to accurately determine the maximum equilibrium scour depth at large skew
angles.
+ X8 =Ampie70
A US se pilegim
Larne Sarm for Vb l3.14
220  IC.1IK2for bb3.14
1.80
1.40 A
/ /
+, +
1.400 a
/
T 1
1' 3
I I530 4
Figure 35.
Flow skew angle (degrees)
Skew angle correction factor
Salim and Jones (1996) investigated two groups of square piles at various skew angles in
order to determine a skew angle correction factor for pile groups. One group was a 3x5 array of
inline piles and the other was a staggered design, 5 piles long and alternating between 3 and 4 piles
wide. Spacing between the piles was varied for different tests with the staggered array. The
experimental results showed that the skew angle correction factor for a group of square piles is
reasonably close to that for a solid pier with the same overall width to length ratio. They defined K,
as:
K = (dd/K)/d, (312)
where d., = the scour depth around the skewed pile group;
+
60 75 9
28
K,= a spacing correction factor (equation 313); and
d,s = the scour depth around an equivalent solid pier, set at the same skew angle.
The spacing correction factor was determined empirically to be:
K, = 0.47 (1 e'") + e 5(b) (313)
where s is the center to center spacing of piles and b is the width of a single pile.
It now appears that much of the earlier work on the influence of flow skew angle on scour
depths at pile groups is of limited value due to 1) the duration of the tests being insufficient to allow
the accurate prediction of equilibrium depths, 2) water depths being less than 3D* for some of the
skew angles, and 3) the flume width being too narrow for the effective width of the structure. That
is, if there is a scour depth dependence on y/D*, as most researchers believe, then as the skew angle,
a, is increased, the effective structure width, D*, increases and thus the value of yJD* decreases.
If yo/D* decreases below a value of approximately 3, then the equilibrium scour depth is reduced
below the value it would have been were this not the case. This must be taken into consideration in
analyzing much of the earlier data by most of the researchers.
CHAPTER 4
TIME DEPENDENCE OF SCOUR
Due to the complexity of local scour processes, the majority of research has concentrated on
determining the maximum equilibrium scour depth for given flow and sediment conditions while
relatively few researchers have delved into the dependence of these processes on time. It has been
determined that the time to reach an equilibrium depth is dependent on the scour regime. For
clearwater scour, the rate of scour slowly approaches an asymptotic value (equilibrium). For
livebed scour, the depth of scour oscillates around the equilibrium value with an amplitude equal
to the amplitude of the sand waves migrating into and out of the scour hole (figure 41).
Chiew and Melville (1996) investigated the time required to reach equilibrium scour depth
for clearwater conditions in an attempt to standardize the criteria for determining the equilibrium
value. Data was collected from 35 experiments using single cylindrical piles covering a wide range
of cylinder diameters, flow depths, and approach flow velocities. The experiments were run for a
sufficient duration to ensure that the maximum equilibrium scour depth had been reached. The time
when the scour hole develops to a depth at which the increase in depth does not exceed 5% of the
pier diameter in the succeeding 24hour period was defined as te. They found that the time to reach
equilibrium is dependent on flow and structure characteristics. The flow energy available for
scouring can be characterized by the mean approach flow velocity, U, and pile size, b. The pile size
affects the strength of the horseshoe vortex and the associated vertical flow components of scour.
30
The data showed that t, increased with increasing U/Uc, holding other variables constant. This is
because greater velocity ratios are associated with greater depths of scour, therefore, it would take
longer to reach equilibrium.
The duration of the tests (and pile sizes) used thus far for analysis have varied widely.
Hannah's tests were run for 7 hours, Jones' for 4 hours, Copps' for 26, Mostafa et al. for several
hours, and Zhao's for 26 hours. According to the results of the timedependent investigations, the
time effects can be significant and the use of shorter duration tests for larger structures can lead to
confusing results. Scour tests with too short a duration are one of the major causes of scatter in
published data.
d
se, live
lS
Live Bed Scour
Clear Water Scour
Figure 41. Scour depth as a function of time in the livebed and clearwater regimes
To exemplify the variation in scour depth as a function of time, figure 42 shows the time
history data of an experiment conducted for 6 days in the clearwater regime in the flume at the
University of Florida. The structure was a single cylindrical pile with a diameter of 6 inches, yf/b
of 3.2, U/UI of 0.93, and D5o/b of 1.18x103. In 4 hours, the scour depth had reached approximately
66% d.. In 7 hours, the scour depth had reached approximately 73% d,,. And in 26 hours, the scour
depth had reached approximately 90% dse. However, these ratios change with fluid, flow, sediment,
and structure parameters. Figures 43 and 44 show how the size of the structure changes these
percentages.
after 26 hours
= 90% d,,
after 7 hours
 = 73% d.,
after 4 hours
= 66% d.,
University of Florida
6day test
single cylindrical pile
b = 6 inches
1 2 3 4 5 6
time (days)
Figure 42. Time history of scour around a single cylindrical pile
10.0
8.0
after 7 hours
= 68% d,.
= 58% d,,
10.0
8.0
2.0 
0.0
1 2 3 4 5 6
time (days)
Figure 43. Time history of scour around an array of square piles normal to the flow
15.0
12.0 
12. aftertr 26 hours
= 73% d,,
9.0 after 7 hours
=55% d.,
"C after 4 hours
' = 48% d. USGS Flume
o 6.0
U 6day test
3x8 square pile array
70 skew angle
3.0 projected width = 28.8 inches
1 2 3 4 5 6
time (days)
Figure 44. Time history of scour around an array of square piles skewed 70 to the flow
after 26 hours
= 81% d,,
USGS Flume
5day test
8x3 square pile array
b = 10 inches
CHAPTER 5
DESIGN LOCAL SCOUR DEPTHS AT PILE GROUPS
A more generalized method for predicting local scour depths at pile groups is proposed in
this chapter that accounts for pile size, spacing, flow skew angle, and, where applicable, the degree
of submergence of the piles. As discussed earlier in this thesis, local scour processes are very
complex, even for seemingly simple structures such as single cylindrical piles. For pile groups, the
flow is more complex and there is much less scour data for these structures reported in the literature.
In addition, most of the data that exists for pile groups is only for clearwater flow conditions while
there is substantial data for single cylindrical piles in both the livebed and clearwater regimes. For
this reason, it was decided that, at least until more data is available, the best way to estimate scour
depths at pile groups is to continue to relate it to the scour that would be produced by a circular pile
with the equivalent or "effective" diameter of the group, D*.
The problem then becomes one of determining the effective diameter, D*, for the group.
From the work of Salim and Jones (1996) and Copps (1994) it is known that D* is a function of pile
size, shape, centerline spacing, and the number and arrangement of piles. It is assumed that these
effects can be treated separately as indicated in the following equation:
D*/Wp =KIpK (51)
where W, = the projected width of the piles onto a plane normal to the flow and upstream
of the structure, accounting for size, and the number and arrangement of piles;
34
K, = the parameter that accounts for the centerline spacing between the piles; and
K, = the parameter that accounts for the shape of the piles.
W,. Jones (1989) suggested that the effective width of a pile group could be conservatively
approximated by the projected width of the group, ignoring the clear spaces in between. This works
well for certain centerline spacings, but is increasingly overconservative for centerline distancesto
diameter ratios greater than about 3.
In this analysis, W, is the sum of the (nonoverlapping) projected widths of each pile onto
a plane normal to the flow and upstream of the forward most pile. Note that only the portion of the
projected width that is not "blocked" by upstream piles is counted. This method accounts for the
number of piles, the arrangement of the piles, and the change in the width of a pile as it is skewed
to the flow. Because this method accounts for the skew angle, a skew angle correction factor is not
needed in the predictive equations. This approach seems to work well for the limited (but reliable)
data that is available at this time.
K,. Y corrects the effective width of a pile group based on pile centerline spacing. Similar
to the findings of Salim and Jones (1996) and Sheppard et al. (1995a), the value of K, decreases
with increased spacing, thus decreasing the effective width of the pile group. At an s/b value of 1,
the piles are touching, and the group acts as a single pile. As the centerline spacing is increased, the
influence will gradually decline until a value of approximately 10 at which point the piles act
independently and the effective diameter, D*, is the width of a single pile, b. The following
relationship was found to work well for computing K, as a function of s/b and b/W,.
Kp = 1 0.003078(1b/Wp)(s/b 1)33/exp(0.015(s/b)2) (52)
1.00
0.80
0.60
b/WVp = 0.5
0.40
b/Wp = 0.334
0.20
b/Wp = 0.125
0.00
1 3 5 7 9 11
s/b
Figure 51. K,, pile spacing parameter
Figure 51 shows this equation plotted for three different values of b/Wp. Note that both Salim and
Jones and Sheppard et al found a modest increase in D* for s/b values between 1 and 3. More data
is needed in this range of s/b in order to verify this finding and to quantify it.
K,. K, is the parameter that accounts for the pile shape. The influence of pile shape on
scour depth (discussed in chapter 3) has been investigated by several researchers such as Richardson
and Richardson (1989). Values for a variety of shapes are given in HEC18. K, for cylindrical piles
is equal to 1. However, for noncylindrical piles, the shape of the pile relative to the flow changes
as the flow skew angle changes. For example, a square pile at a 450 skew angle has a sharp nose
shape. Using the shape factors for square and sharpnose shaped piles from HEC18 and data from
1.1 
0.9
0.8
0 0.4 0.8 1.2 1.6
ac (radians)
Figure 52. Shape correction factor, Kfor square piles
a 700 flow skew angle test, the following expression was developed for square piles where the skew
angle, a, is in radians:
K,= 0.85 +0.811a7t/44 (53)
Figure 52 depicts this relationship.
The D* computed from WpKYK, (equation 51) can be substituted for b into the predictive
equations for a single cylindrical pile to determine the maximum equilibrium scour depth at the pile
group. Note that if the HEC18 equation is used, the shape correction factor, K,, and the skew angle
correction factor, K2, should both be set equal to 1 because they are accounted for in the K, and Wp
parameters, respectively.
If the piles are submerged, the degree of submergence is also important. Submerged pile
groups are encountered less frequently than subaerial groups, but they are nonetheless important.
As a component of a composite structure such as a complex bridge pier (figure 54), consisting of
37
a pier, pile cap, and pile foundation, they may be the greatest contributor to the scour hole. Sheppard
et aL (1995a) and Salim and Jones (1996) have independently approached the problem of predicting
local scour at complex piers by decomposing these structures into their components and attempting
to determine the scour contribution due to each component. Recently, Sheppard and Jones (1998)
have joined forces in order to produce a more unified approach to this problem. Part of the
motivation for the work on submerged pile groups in this thesis was to support this effort.
The equilibrium scour depth's dependence on the height of the pile group above the bed is
similar to its dependence on the ratio y/D*. It was determined that if the water depth is greater than
3.5 times the effective width of the pile group (D*), submerging the piles will have little affect on
the scour depth until the height of the piles falls below this value.
For those situations where the piles are submerged, a parameter K, can be used to account
for the effect of the submergence on the scour depth.
dse submerged pile group = Kb dse (D) (54)
The scour depth's dependence on pile height is found in equation 55 (and figure 53) in the
relationship between Kb and Hp,/ where Hpg is the height of the piles above the bed and i is the
normalizing factor based on the effective width of the pile group. If the water depth, yo, is greater
than 3.5D*, i equals 3.5D* and if the water depth is less than or equal to 3.5D*, is equal to the
water depth. The value of 3.5D* was arrived at empirically.
(55)
K, = 0.0011 + 2.68 (H,/il) 3.55 (Hpg~l)2 + 1.87 (Hp/4ry)3
1 
0.8
0.6
0.4
0.2
0 
0 0.2 0.4 0.6 0.8 1
Hdw
Figure 53. Kbvs Hpg/,
I = 3.5D* for y > 3.5 D*
= Yo for 0 y, < 3.5 D* (56)
Illustration of Model Use
Example 1
The following example illustrates how to use this model to predict the design scour depth
at a multiple pile bridge pier (figure 54). The prototype conditions are:
b = 0.5 meters; s/b = 3; yo = 5.0 meters; U/U= = 1; D5s = 0.22 mm; n = 3, m = 3, a = 180, and
the piles are square. The pile cap is above the water line under design conditions, thus the pile group
is subaerial.
n=3
Figure 54. Prototype multiple pile bridge pier
The projected width of the structure at a flow skew angle, a = 180, is 4.4 meters, thus, W =
4.4 meters.
To determine K,, the value ofb/W, is calculated: b/Wp = 0.5/4.4 = 0.144. Using equation
52 with b/Wp = 0.144 and s/b = 3, K, = 0.98.
K, is determined from equation 53 where a = 180 = 0.314 radians. K, = 0.89.
The effective diameter is calculated by equation 51 to be:
D* = WpK~,IK = 4.4 (m) 0.98 0.89 = 3.84 meters
Substituting this D* for b into the University of Florida scour prediction equation (equation
32) with the given flow and sediment conditions;
dD* = 1.35 f, f2 f3
f, = 4.81 tanh(l (5/3.84) = 4.147 (equation 33)
40
f, 1 + (2.87 1) + 1.43 (1)2 = 0.44 (equation 34)
f,= logo (0.22mm/3.84 m) exp{0.18 [logjo (0.22mm/3.84m)]209} =0.106
(equation 35)
d,/D*= (1.35 4.147 0.44 0.106) = 0.261
d,s.,) = 0.261 3.84 (m) = 1.0 meters
The piles extend above the water surface so KI = 1.
.. d,, = 1.0 meters
17
S
*<
" b
UU U n,
n=3
Figure 55. Prototype multiple pile bridge pier with submerged piles and no pile cap
Example 2
The following example illustrates how to use the submerged pile parameter, K, (equations
54 and 55). The prototype conditions (figure 55) are:
41
b = 1.0 meter; s/b = 6; y = 7.0 meters; U/U = 1; Dso = 0.22 mm; n = 3,m= 3, a = 5, and
the piles are square. The piles are submerged below the water line and the pile group has no pile cap.
The height of the piles above the bed, Hp,, is 5.0 m.
The projected width of the structure at a flow skew angle, a = 50, is 4.82 meters, thus, Wp =
4.82 meters.
To determine KI, the value of b/Wp is calculated: b/Wp = 1/4.82 = 0.207. Using equation
52 with b/Wp = 0.207 and s/b = 6, K, = 0.71.
K, is determined from equation 53 where a = 5' = 0.0873 radians. K, = 1.04.
The effective diameter is calculated by equation 51 to be:
D* = WpKVK, = 4.82 (m) 0.71 1.04 = 3.56 meters
Substituting this D* for b into the University of Florida scour prediction equation (equation
32) with the given flow and sediment conditions;
dJD* = 1.35 f, f2 f,
f, = 4.81. tanh(l1 (7/3.56) = 4.625 (equation 33)
f = 1 + (2.87 1) + 1.43 (1)2 = 0.44 (equation 34)
f3= log,0 (0.22mm/3.56 m) exp{0.18[logIo (0.22mm/3.56m)]209} =0.112
(equation 35)
d,/D*= (1.35 4.625 0.44 0.112) = 0.308
ds.*) = 0.308 3.56 m = 1.1 meters
Because the piles are submerged, the K, parameter must be considered.
3.5 D* = 3.5 3.56 m = 12.46 m.
3.5 D* > y, so by equation 56, 4r = y, = 7.0 m
42
HIpg~ = 5.0/7.0 = 0.71
From equation 55, Kh = 0.78
By equation 54, ds sbmergedpie group = 0.78 1.1 meters
dse submerged pie group = 0.86 meters.
CHAPTER 6
EXPERIMENTAL PROCEDURES
Ten pile group scour experiments were performed as part of the work for this thesis.
Attempts were made to avoid problems with previous experiments such as test duration, effects of
water depth, and constriction scour. Nine experiments were conducted using a 3x8 array of square
inline piles with a centerline spacing to pile diameter ratio, s/b = 3. One experiment was performed
with a 2x4 array with s/b = 6. The height of the piles above the bed was varied so as to obtain the
effect of this height on the scour depth. Four of these experiments were conducted with 3 piles
normal to the flow, 4 were conducted with 8 piles normal to the flow, 1 test with 2 piles normal to
the flow and 1 at a flow skew angle of 700. Tests at ratios of pile height above the bed (Hp) to the
flow depth (yo) of 1, 0.75, 0.5, and 0.25 were conducted. Eight of the 10 experiments were
conducted in the flume at the University of Florida and 2 in the USGSBRD flume in Turners Falls,
Massachusetts. The USGS flume was needed for some of the tests because of UF flume width and
depth limitations.
The pile group used for 9 of the tests was a 3x8 rectangular array of 1.25 inch wide square
aluminum tubes with s/b = 3. The 2x4 array was rectangular with 1.25 inch wide square piles as
well, but with s/b = 6. For the tests where the piles were submerged, the piles were bolted to an
aluminum base that was placed on the bottom of the test section. For the tests where the piles
extended above the water surface, the piles were secured at the top by an aluminum pile cap placed
44
above the water line. Scales were glued to the front of each pile in order to measure the scour depth
as a function of time.
Flume
The University of Florida flume (figures 61 through 65) is approximately 100 feet long,
2.5 feet deep, and the main section is 8 feet wide. The main section of the flume has zero bed slope.
The maximum water depth is approximately 22 inches. A 20foot long test section (which is located
midway between the entrance and exit) is 1.13 feet deeper than the rest of the channel The test
section is filled with quartz sand with a D, of 0.172 mm and a standard deviation, o, of 1.38 (figure
66).
Flow in this recirculating flume is driven by a 100 horsepower pump (figure 64) with a 38.8
ft3/second discharge capacity. The pump produces a constant discharge. Flow in the flume is
controlled with a bypass system that diverts a portion of the pump discharge back to a reservoir. The
flume is equipped with a series of flow straighteners and energy dampening devices designed to
produce a uniform flow upstream of the test section. A screen is located upstream of the test section
to ensure that no debris interferes with the test. The water depth is controlled by a sluice gate at the
downstream end of the flume (figure 63).
A manometer measures the water elevation upstream of a sharpcrested rectangular weir.
The manometer reading, h*, is in centimeters. The following equation is used to calculate the flow
head, H, in centimeters:
H = h* 15.95
(61)
45
The flow rate in ft3/s is calculated using the equation for a sharpcrested weir, calibrated for this
flume:
Q = 24.96 H.'5 (62)
where H is in feet.
The upstream depth averaged velocity is calculated by:
U = Q/A (63)
where A is the crosssectional area of the flow in ft2 calculated at the test section.
A movable carriage sits atop the flume on rails, able to traverse the length of the flume. The
carriage provides a stable platform from which observations are made. A video camera system
collects the time history scour data from the carriage. The camera is mounted inside of a long PVC
tube with a plexiglass plate on one end. The plexiglass end extends just below the water surface.
From this vantage point, the camera can view the scour at the front piles. A control system was
designed to turn on the lights, video camera, and VCR at specified times and durations to record
scour depths as a function of time. Both the time interval between recordings and the duration of
the recording can be changed. A VCR records the scour depths at the piles in the camera's view
(using the scales attached to the piles) and the time of the measurement. The camera is directed at
the region of anticipated maximum scour depth, thus the camera does not have to be moved during
the test. At the start of the test, the scour activity is recorded for 15 continuous minutes, then for one
minute periods at varying intervals that are increased as the test progresses and the scour rate
decreases.
Figure 61. UF flume: flow straighteners, screen, weir, and energy dampening devices
Figure 62. UF flume: main section exit, sluice gate
Figure 63. UF flume: sluice gate, turning vanes
Figure 64. UF flume: pump
Energy Dampening
Devices and
Flow Straighteners
Figure 65. Schematic drawing of the University of Florida Civil Engineering flume
Weir
Screen
49
100 r  F 1 1I .
I II I I I I I 1 2
I I I I I II I 11 116Ii0.l34p n I
1 1 I I I 1 11 1 I I4 I
8 0  III 
i 60 V 
40         
 40  A  
o 4 I I I I
111 l1 I l1 l I I I
04 
20I I I I I
0
1.00 0.10 0.01
Grain Size (mm)
Figure 66. UF flume grain size distribution
The USGS flume (figures 67 through 610) has three channels. All channels are 126 feet
long and 21 feet deep. The main channel is 20 feet wide and is located between the other two 10 feet
wide channels. The main channel was used for all of these experiments. The channel has zero bed
slope. A 30foot long test section is located about 2/3 of the channel length from the entrance. The
test section of the flume is 6 feet deep, filled with quartz sand with a D50 of 0.22 mm and a standard
deviation, a, of 1.57 (figure 611). The remainder of the flume is filled with a coarse base material
covered by a filter material and a 1foot layer of the test section sediment.
The flow is generated by a head difference between the entrance and exit section of the flume.
Control structures in the Connecticut River create the head difference between the flume entrance and
exit. Screen filters upstream of the flume prevent debris from interfering with the test. The flow
50
depth is controlled by the height of a sharpcrested weir at the downstream end of the flume. The
average velocity was calculated from the water elevation above the weir (head) and measured with
two electromagnetic current meters located 2/3 of the depth from the water surface upstream and on
either side of the structure. After the water flows through the flume, it is discharged back into the
river downstream of the control structures.
Observations are made from a fixed platform located above the test section. Scour depths are
measured using two cameras mounted to the platform. One is located upstream, viewing down in
front of the test structure. The other camera is located to the side of the structure, viewing the scour
from the side. The cameras are mounted inside of streamlined PVC and plexiglass housings designed
and constructed in the Coastal Engineering Laboratory at the University of Florida for this
application. A video system, identical to the one used for the UF tests, is used to record the scour
depths (read from scales located on the front of the piles) as a function of time.
Test Preparation
To prepare for the tests, the models are set in the center of each test section and the sand is
compacted with an electric compactor in the UF flume and a diesel powered compactor in the USGS
flume. Attempts were made to obtain a uniform and repeatable compactness of the sediment similar
to that found in a natural setting. The sand is then leveled throughout the USGS flume and to the
surrounding fixed bed in the UF flume. The flumes were then filled slowly so as not to disturb the
sand. Photographs and slides were taken upon completion of leveling to document the condition of
the bed before testing.
LRrr
Figure 67. USGS flume with base material (prior to placement of test sediment)
Figure 68. USGS flume with test sediment and 3x8 structure
Flow Intake from Reservoir
I
Test channel A
4 \ Y 
41 4
SA Model Area
Plan View
NOT TO SCALE
All dimensions in feet
Flow Discharge
To Connecticut
River
flow
flow
 >
flow B
flow +
10
10
)w
SI
m m I
20
Water
Test Sediment
NOT TO SCALE
All dimensions in feet
H = 9' for 3' pile
H = 4' for 4.5" and 12" piles
Section A
Section B
H 21
6
55
100 T IT I 7 1 I T 7_ r  l
' \ '1o'=0.2dmri I
b I I I o I1
80 17 1  
I I I I I. I I 3
60
S0 I I I L\ l l I I
S 40
SI iii I\I 1 I I
20 111 I \ J_ l _
i i I I I I I
1.00 0.10 0.01
Grain Size (mm)
Figure 611. USGS flume sediment grain size distribution
Test Conditions
All of the tests aimed to maintain a U/U, velocity ratio at slightly less than transition from the
clearwater to livebed regime (0.9). The critical depth averaged velocity was determined from
Shield's parameter based on the water density, viscosity, and depth; median sediment diameter and
density; and bed roughness. For all tests, the sediment density for quartz sand is assumed to be 2650
kg/m3.
To maintain this condition, the temperature was closely monitored and used to determine the
fluid density and viscosity properties. Minor adjustments to the flow velocity were made during the
tests in an attempt to maintain constant upstream bed shear stress and U/Uc. That is, as ripples formed
on the upstream bed, the bed roughness changed causing minor changes in bed shear stress and thus
56
in the critical velocity. The tests were run until such time that no increase in scour depth was
observed for a period of 24 hours to ensure that the maximum equilibrium scour depth had been
reached. This duration varied from test to test.
While the automated video recorded the time history of scour depth, the water depth,
temperature, manometer reading, and scour depths were manually collected and recorded periodically.
After each test, a vernier point gage was used to survey the test section to obtain a complete picture
of the scoured bed.
Test Results
The test conditions and measured results are presented in table 61. Photographs of the tests,
before and after each experiment, are depicted in figures 612 through 631. Timehistory plots of
the scour depths are included in Appendix A.
Relative bed
Test# Hp Hp (in) Temp C roughness Uc (ft/s) U (ft/s) U/U
Test # Hp H (in) o in) Do ( ) (ave) (ave) (ave)
ks/Dso
1 '/ 3.50 14.00 0.172 31.6 10 0.82 0.75 0.92
2 % 3.50 14.00 0.172 32.9 7.5 0.81 0.74 0.91
3 /2 7.25 14.50 0.172 32.1 7.5 0.85 0.76 0.90
4 2 7.38 14.75 0.172 32.5 7.5 0.84 0.77 0.92
5 % 11.56 15.40 0.189 33.0 7.5 0.84 0.74 0.88
6 % 11.00 14.70 0.189 32.1 7.5 0.89 0.81 0.91
7 1 15.00 15.00 0.172 29.8 10 0.83 0.79 0.95
8 1 47.28 47.30 0.220 24.8 10 1.13 1.08 0.96
9 1 47.16 47.20 0.220 24.8 10 1.13 1.00 0.89
10 1 15.00 15.00 0.172 30.8 10 0.82 0.74 0.90
Test # Skew angle n m b s/b Test duration dse measured
(minutes) (inches)
1 90 8 3 1.25 3 3506 3.0
2 0 3 8 1.25 3 4467 2.7
3 90 8 3 1.25 3 6918 4.5
4 0 3 8 1.25 3 5406 3.8
5 90 8 3 1.25 3 6499 5.75
6 0 3 8 1.25 3 2327 4.0
7 0 3 8 1.25 3 5759 5.2
8 90 8 3 1.25 3 6710 9.5
9 70 3 8 1.25 3 8190 14.96
10 0 2 4 1.25 6 3899 3.35
.... ; T?
, 'c.. ;'. .* ,
.X. ^* .^ .* \
Figure 612. Test 1, Hpg/yo = 1/4, 900 skew angle, before test
Figure 613. Test 1, Hpg/yo = 1/4, 900 skew angle, after test
Figure 614. Test 2, Hpg/yo = 1/4, 00 skew angle, before test
Figure 615. Test 2, Hpg/yo = 1/4, 00 skew angle, after test
60
Figure 616. Test 3, Hpg/yo = 1/2, 900 skew angle, before test
Figure 617. Test 3, Hpg/yo = 1/2, 900 skew angle, after test
~I;~JIF~
..
k
Figure 618. Test 4, Hpg/yo = 1/2, 00 skew angle, before test
Figure 619. Test 4, Hpg/yo = 1/2, 0 skew angle, after test
Figure 620. Test 5, Hpg/yo = 3/4, 900 skew angle, before test
Figure 621. Test 5, Hpg/yo 3/4, 900 skew angle, after test
63
Figure 622. Test 6, Hpg/yo = 3/4, 00 skew angle, before test
Figure 623. Test 6, Hpg/yo = 3/4, 00 skew angle, after test
Figure 624. Test 7, Hpg/yo = 1, 0 skew angle, before test
Figure 625. Test 7, Hpg/yo = 1, 0 skew angle, after test
Figure 626. Test 8, Hpg/yo = 1, 900 skew angle, before test
Figure 627. Test 8, Hpg/yo = 1, 900 skew angle, after test
Figure 628. Test 9, Hpg/yo = 1, 700 skew angle, after test
Figure 629. Test 9, Hpg/yo = 1, 700 skew angle, after test
Figure 630. Test 10, s/b = 6, 0 skew angle, before test
Figure 631. Test 10, s/b = 6, 00 skew angle, after test
CHAPTER 7
RESULTS AND CONCLUSIONS
The results of the pile group experiments are presented in table 71. The effective width of
the pile group was computed based on the model developed in chapter 5 (equation 51). Figures 71,
72, and 73 show the data on the W,, K, and K, plots. This D* and the flow and sediment
parameters from each experiment were then applied to the University of Florida scour prediction
equation (equation 32 without the safety factor) to determine dse for an equivalent diameter single
cylindrical pile. Equation 54 was then applied to account for the degree of submergence of the pile
groups. Figure 74 shows the submerged pile data on the Kh curve. Figure 75 shows good
agreement between the measured and predicted (without the safety factor) nondimensional scour
depths. Figure 76 shows the data with the safety factor in equation 32 applied. The model
conservatively overpredicts the scour depths.
This model works exceptionally well for the available (reliable) scour data on pile groups.
However, due to the limited amount of such data (i.e. long duration, deep water, limited constriction
scour), additional tests are needed to investigate the effects of skew angles and pile spacing on
submerged and subaerial pile groups.
Submerged piles are one component of complex bridge piers. The results of this study can
be used in conjunction with models being developed by Sheppard and Jones (1998) to estimate each
component's contribution to local scour depth.
ddJD* d//D* dsD*
Test D* (in) Yo (inches) D0 (mm) UUc Hpg (n) (in) Hpg Kh predicted w/o measured predicted
w/o SF SF with SF
1 11.37 14.00 0.172 0.92 0.70 3.50 14.00 0.25 0.43 0.30 0.26 0.41
2 4.26 14.00 0.172 0.91 1.22 3.50 14.00 0.25 0.52 0.63 0.63 0.86
3 11.37 14.50 0.172 0.90 0.71 7.25 14.50 0.50 0.65 0.46 0.40 0.62
4 4.26 14.75 0.172 0.92 1.23 7.38 14.75 0.50 0.73 0.90 0.89 1.21
5 11.37 15.42 0.189 0.88 0.74 11.57 15.42 0.75 0.83 0.61 0.51 0.83
6 4.26 14.67 0.189 0.93 1.28 11.00 14.67 0.75 0.77 0.99 0.94 1.33
7 4.26 15.00 0.172 0.95 1.25 15.00 14.91 1.01 1.00 1.25 1.22 1.69
8 11.37 47.28 0.220 0.96 0.94 47.28 39.80 1.19 1.00 0.94 0.84 1.27
9 24.61 47.16 0.220 0.89 0.61 47.16 47.16 1.00 1.00 0.61 0.61 0.82
10 2.38 15.00 0.172 0.90 1.46 15.00 8.33 1.80 1.00 1.46 1.41 1.97
skew
Test skew Wpn) s/b K,p K D* (in)
angle a D(in)
1 90 10.00 3 0.98 1.16 11.37
2 0 3.75 3 0.98 1.16 4.26
3 90 10.00 3 0.98 1.16 11.37
4 0 3.75 3 0.98 1.16 4.26
5 90 10.00 3 0.98 1.16 11.37
6 0 3.75 3 0.98 1.16 4.26
7 0 3.75 3 0.98 1.16 4.26
8 90 10.00 3 0.98 1.16 11.37
9 70 28.83 3 0.97 0.88 24.61
10 0 2.50 6 0.82 1.16 2.38
0 10 20
Projected Width (in)
Figure 71. Wp plotted for test results
b/Wp = 0.5
b/Wp = 0.334
b/Wp= 0.125
1 3 5 7 9 11
s/b
Figure 72. Test data on K. curve
1.00
0.80
0.60
0.
V)
0.40
0.20
0.00
1.2
1.1
ir 1
0.9
0.8
0 0.4 0.8 1.2
a (radians)
Figure 73. Test data on K, curve
1
0.8
0.6
0.4
0.2
0
0 0.2 0.4
Hp/
0.6 0.8 1
Figure 74. Test data on K, curve
._ 1.2 no safety
/factor
0 0.8
1 08 0 skew angle
0 O 0 90 skew angle
X 0 skew, s/b = 6
0.4 A 70 skew angle
0 i I
0 0.4 0.8 1.2 1.6 2
dse/D* measured
Figure 75. Predicted vs. measured nondimensional scour depth, without safety factor
with a safety
factor: S.F. = 1.35
* 0 skew angle
0 90 skew angle
X 0 skew, s/b = 6
* 70 skew angle
0 0.4 0.8 1.2 1.6
ds/D* measured
Figure 76. Predicted vs. measured nondimensional scour depth, with safety factor
The results showed the anticipated correlation between effective size of the pile group and
the duration to reach dse. The larger the size, the deeper the scour depth, and the longer the time
needed to reach dse. For the 4 arrays which had 8 piles normal to the flow, the degree of
submergence influenced the time required to reach ds. As the pile height was reduced, the scour
depth decreased, and less time was needed to reach dse. The 4 arrays having 3 piles normal to the
flow also displayed this trend of decreasing scour depth with reduced pile height, however, the time
required to reach d, varied with pile height (i.e. the shortest pile group required a longer time to
reach ds than some of the taller pile groups under the same fluid, flow, and sediment conditions).
This may have been due to equipment problems causing the scour depths to be recorded at
inconsistent intervals of time, thus the d, may have been reached before the time it was documented.
Portions of this model were developed based on previous researchers findings which may
have been subject to the problems discussed throughout this thesis: insufficient test duration, small
values of U/U,, small values of y/b, etc. which produce inaccurate values of ds. Other portions were
developed based on limited data. Thus, further research is needed to fully investigate the effects of
the skewness of a pile group, spacing of the piles, and the number of piles normal to and inline with
the flow, in which these problems have been corrected.
APPENDIX
TIME HISTORY SCOUR PLOTS
6.0 
5.0
" 
a)
S4.0
c
0
3.0 
0 
1.0
0.0 
6.0 
5.0
'O' 
0)
5 4.0
c
c. 3.0 
0)
CO
S2.0
1.0 
0.0
Suberged Piles H = 1/4 yo
SkewAngle = 0
I I I I
1 2 3 4 5 6
Time (days)
Figure Al. Test 1
Submerged Piles Hpg = 1/4 yo
SkewAngle = 90'
II I I I
1 2 3 4 5 6
Time (days)
Figure A2. Test 2
*
T
6.0 
5.0
U,
_ 3.0
a)
2.0 
8 2.0
u,
1.0 
0.0
Submerged Piles Hp = 1/2 y,
SkewAngle = 0(
I I I I
1 2 3 4 5 6
Time (days)
Figure A3. Test 3
6.0
5.0
C,
5 4.0
c

S3.0
2.0
0
CO
1.0
0.0
Submerged Piles H = 1/2 yo
SkewAngle = 90'
1 2 3
Time (days)
4 5 6
Figure A4. Test 4
Submerged Ries Hpg = 3/4 yo
SkewAngle = 0
1 2 3 4 5 6
Time (days)
Figure A5. Test 5
Submerged Piles Hg = 3/4 yo
SkewAngle = 90'
1 2 3
Time (days)
4 5 6
Figure A6. Test 6
6.0
5.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
1 2 3 4 5 6
Time (days)
Figure A7. Test 7
Suberged Piles Hpg = y
SkewAngle = 90
1 2 3 4 5 6
Time (days)
Figure A8. Test 8
Surged Piles Hpg =
SkewAngle = 0
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
15.0
12.5
10.0
7.5
5.0
1 2 3 4 5 6
Time (days)
Figure A9. Test 9
Submerged Piles H = y
SkewAngle = 0
s/b=6
1 2 3
Time (days)
4 5 6
FigureA10. Test 10
Submerged Rles Hp = Yo
SkewAngle = 70
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