• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 Key to symbols
 Abstract
 Introduction
 Scour processes
 Scour prediction
 Time dependence of scour
 Design local scour depths at pile...
 Experimental procedures
 Results and conclusions
 Time history scour plots
 Reference














Title: Local structure-induced sediment scour at pile groups
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Title: Local structure-induced sediment scour at pile groups
Series Title: Local structure-induced sediment scour at pile groups
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Language: English
Creator: Smith, Wendy L.
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Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
    Key to symbols
        Page v
        Page vi
        Page vii
    Abstract
        Page viii
        Page ix
    Introduction
        Page 1
        Page 2
    Scour processes
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
    Scour prediction
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
    Time dependence of scour
        Page 29
        Page 30
        Page 31
        Page 32
    Design local scour depths at pile groups
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
    Experimental procedures
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
    Results and conclusions
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
    Time history scour plots
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
    Reference
        Page 80
        Page 81
        Page 82
        Page 83
Full Text



UFL/COEL-99/003


LOCAL STRUCTURE-INDUCED SEDIMENT
SCOUR AT PILE GROUPS






By

Wendy L. Smith


February, 1999












LOCAL STRUCTURE-INDUCED 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
HEC-18 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 cross-sectional 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 3-9

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 6-1)

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 3-13)

K, shape parameter (equation 5-3)

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 3-10)

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 STRUCTURE-INDUCED 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 under-predicting can result in structural damage

and possible loss of life, while over-predicting 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 in-line 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 bridge-like 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 cross-sectional 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 cross-sectional 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

live-bed. 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. Live-bed 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 2-1):

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 2-1. 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 square-nose pile will have scour depths about 20 percent greater than a sharp-nose pile and 10

percent greater than either a cylindrical or round-nose 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 non-cylindrical 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 2-2

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 2-2. 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 2-3).


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 2-3. 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 low-pressure 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 in-line piles. Both groups were composed of uniform-diameter 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 in-line 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 in-line piles. Hannah examined

1x2, 2x1, 2x2, and 2x3 arrays of in-line 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 in-line 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 structure-induced 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 non-dimensional

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 non-dimensional 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) (3-1)







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

counter-rotating 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 3-1).

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 live-bed 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 live-bed conditions. But Melville

(1984) and Raudkivi (1986) found that the peak scour depth in the live-bed range could be larger

than that at transition if the sediment is in the ripple-forming range (Dso < 0.6 mm). Figure 3-2 is

a schematic drawing of the general variation of relative scour depth with U/Ut for the clearwater and

live-bed 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 non-dimensional scour depth, ds/b, increased

with decreasing Do/b until Do/b reached a value of 0.04-0.05. 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 3-3. 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 3-1. Variation of relative local scour depth with y/b



Clearwater Live-bed

Dso/b = 0.016


dse/b


Dso/b = 0.0003


yo/b= const.


U/UL


Figure 3-2. Variation of relative scour depth with U/Uc







19

U/UC = constant
Dso/b = constant


Figure 3-3.


-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 3-2) 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 3-2, 3-3, 3-4, and 3-5 in its most recent form. Table 3-1 shows the most recently

determined coefficients.

djb = S.F.- f,(yjb) f, (U/U,)" f,(D5/b) (3-2)

fi(yob) = ci tanh (c2, y/b) (3-3)

f2(U/U,) = 1 + c3 (U/U,) + c4 (U/U,)2 (3-4)

f3(D5o/b) = logo(Do/b) expi{c, [-logo (Dso/b)] "6 (3-5)


Table 3-1. Coefficients for equations 3-2, 3-3, 3-4, and 3-5


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 over-prediction 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 3-foot diameter pile in a 20-foot wide by 21-foot

deep flume. Sheppard recommends that, at present, if D,/b is less than 3.1x10'3 that Dsb be set to

3.1x10-3 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 3-4. 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 3-6 for a square pile.


d,jb (square pile) = 1.1 djb (cylindrical pile) (3-6)


HEC-18 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 (HEC-18) "Evaluating Scour at Bridges" (1996).










dJb=2.0 K, K2 K3 K4 (yo/b)0.5- (Fr)0.43 (3-7)

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 live-bed 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 3-2. 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 3-3. 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 plane-bed conditions, the

maximum scour may be 10 percent greater than predicted (30 percent if large dunes exist).


Table 3-4. Bed condition correction factor, K3

Bed condition Dune Height (m) K3
Clearwater scour NA 1.1
Plane-bed 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 Dso-size 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 (3-8)



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* = (n-1)-b/(s/b)c +b (3-9)


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 + (n-1) (s/b)"' exp{K6 (s/b 1)2} (3-10)


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 in-line 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 HEC-18. 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 in-line

cylindrical piles and a 3x8 array of in-line 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) (3-11)


where d,(a) = the maximum equilibrium scour depth for the pile group at skew angle a and

ds(a--0) = the maximum equilibrium scour depth for the same pile group at zero skew angle. Figure

3-5 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 3-1). 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 3-5.


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

in-line 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, (3-12)


where d., = the scour depth around the skewed pile group;


+


60 75 9







28

K,= a spacing correction factor (equation 3-13); 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) (3-13)


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

live-bed 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 4-1).

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 24-hour 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 time-dependent 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 4-1. Scour depth as a function of time in the live-bed and clearwater regimes










To exemplify the variation in scour depth as a function of time, figure 4-2 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 1.18x10-3. 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 4-3 and 4-4 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
6-day test
single cylindrical pile
b = 6 inches


1 2 3 4 5 6
time (days)

Figure 4-2. 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 4-3. 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 6-day test
3x8 square pile array
70 skew angle
3.0 projected width = 28.8 inches


1 2 3 4 5 6
time (days)
Figure 4-4. Time history of scour around an array of square piles skewed 70 to the flow


after 26 hours
= 81% d,,




USGS Flume
5-day 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 live-bed 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 (5-1)

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 over-conservative for centerline distances-to-

diameter ratios greater than about 3.

In this analysis, W, is the sum of the (non-overlapping) 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(1-b/Wp)(s/b 1)33/exp(0.015(s/b)2) (5-2)










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 5-1. K,, pile spacing parameter


Figure 5-1 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 HEC-18. K, for cylindrical piles

is equal to 1. However, for non-cylindrical 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 sharp-nose shaped piles from HEC-18 and data from












1.1 -






0.9-


0.8

0 0.4 0.8 1.2 1.6
ac (radians)

Figure 5-2. 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 +0.811a-7t/4|4 (5-3)

Figure 5-2 depicts this relationship.

The D* computed from WpKYK, (equation 5-1) 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 HEC-18 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 none-the-less important.

As a component of a composite structure such as a complex bridge pier (figure 5-4), 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) (5-4)


The scour depth's dependence on pile height is found in equation 5-5 (and figure 5-3) 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.


(5-5)


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 5-3. Kbvs Hpg/,


I = 3.5D* for y > 3.5 D*

= Yo for 0 y, < 3.5 D* (5-6)


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 5-4). 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 5-4. 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

5-2 with b/Wp = 0.144 and s/b = 3, K, = 0.98.

K, is determined from equation 5-3 where a = 180 = 0.314 radians. K, = 0.89.

The effective diameter is calculated by equation 5-1 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

3-2) with the given flow and sediment conditions;

dD* = 1.35- f, f2 f3

f, = 4.81- tanh(l- (5/3.84) = 4.147 (equation 3-3)






40

f, 1 + (-2.87 1) + 1.43 (1)2 = -0.44 (equation 3-4)

f,= logo (0.22mm/3.84 m) exp{-0.18 [-logjo (0.22mm/3.84m)]209} =-0.106

(equation 3-5)


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 5-5. 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

5-4 and 5-5). The prototype conditions (figure 5-5) 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

5-2 with b/Wp = 0.207 and s/b = 6, K, = 0.71.

K, is determined from equation 5-3 where a = 5' = 0.0873 radians. K, = 1.04.

The effective diameter is calculated by equation 5-1 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

3-2) with the given flow and sediment conditions;

dJD* = 1.35- f, f2 f,

f, = 4.81. tanh(l1 (7/3.56) = 4.625 (equation 3-3)

f = 1 + (-2.87 1) + 1.43 (1)2 = -0.44 (equation 3-4)

f3= log,0 (0.22mm/3.56 m) exp{-0.18[-logIo (0.22mm/3.56m)]209} =-0.112

(equation 3-5)

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 5-6, 4r = y, = 7.0 m







42

H-Ipg~ = 5.0/7.0 = 0.71

From equation 5-5, Kh = 0.78

By equation 5-4, 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

in-line 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 USGS-BRD 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 6-1 through 6-5) 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 20-foot 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

6-6).

Flow in this recirculating flume is driven by a 100 horsepower pump (figure 6-4) 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 6-3).

A manometer measures the water elevation upstream of a sharp-crested 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


(6-1)







45

The flow rate in ft3/s is calculated using the equation for a sharp-crested weir, calibrated for this

flume:
Q = 24.96 H.'5 (6-2)

where H is in feet.

The upstream depth averaged velocity is calculated by:

U = Q/A (6-3)

where A is the cross-sectional 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 6-1. UF flume: flow straighteners, screen, weir, and energy dampening devices


Figure 6-2. UF flume: main section exit, sluice gate






























Figure 6-3. UF flume: sluice gate, turning vanes


Figure 6-4. UF flume: pump















Energy Dampening
Devices and
Flow Straighteners


Figure 6-5. 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

0-4------- ----------
20I I I I I

0-

1.00 0.10 0.01
Grain Size (mm)

Figure 6-6. UF flume grain size distribution


The USGS flume (figures 6-7 through 6-10) 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 30-foot 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 6-11). The remainder of the flume is filled with a coarse base material

covered by a filter material and a 1-foot 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 sharp-crested 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 6-7. USGS flume with base material (prior to placement of test sediment)









































Figure 6-8. 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
S-0 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 6-11. 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 live-bed 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 6-1. Photographs of the tests,

before and after each experiment, are depicted in figures 6-12 through 6-31. Time-history 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 6-12. Test 1, Hpg/yo = 1/4, 900 skew angle, before test


Figure 6-13. Test 1, Hpg/yo = 1/4, 900 skew angle, after test






























Figure 6-14. Test 2, Hpg/yo = 1/4, 00 skew angle, before test


Figure 6-15. Test 2, Hpg/yo = 1/4, 00 skew angle, after test








60






























Figure 6-16. Test 3, Hpg/yo = 1/2, 900 skew angle, before test


Figure 6-17. Test 3, Hpg/yo = 1/2, 900 skew angle, after test


~I;~JIF~
..
k






























Figure 6-18. Test 4, Hpg/yo = 1/2, 00 skew angle, before test


Figure 6-19. Test 4, Hpg/yo = 1/2, 0 skew angle, after test






























Figure 6-20. Test 5, Hpg/yo = 3/4, 900 skew angle, before test


Figure 6-21. Test 5, Hpg/yo 3/4, 900 skew angle, after test







63






















Figure 6-22. Test 6, Hpg/yo = 3/4, 00 skew angle, before test


Figure 6-23. Test 6, Hpg/yo = 3/4, 00 skew angle, after test





























Figure 6-24. Test 7, Hpg/yo = 1, 0 skew angle, before test


Figure 6-25. Test 7, Hpg/yo = 1, 0 skew angle, after test
































Figure 6-26. Test 8, Hpg/yo = 1, 900 skew angle, before test


Figure 6-27. Test 8, Hpg/yo = 1, 900 skew angle, after test
































Figure 6-28. Test 9, Hpg/yo = 1, 700 skew angle, after test


Figure 6-29. Test 9, Hpg/yo = 1, 700 skew angle, after test































Figure 6-30. Test 10, s/b = 6, 0 skew angle, before test


Figure 6-31. 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 7-1. The effective width of

the pile group was computed based on the model developed in chapter 5 (equation 5-1). Figures 7-1,

7-2, and 7-3 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 3-2 without the safety factor) to determine dse for an equivalent diameter single

cylindrical pile. Equation 5-4 was then applied to account for the degree of submergence of the pile

groups. Figure 7-4 shows the submerged pile data on the Kh curve. Figure 7-5 shows good

agreement between the measured and predicted (without the safety factor) non-dimensional scour

depths. Figure 7-6 shows the data with the safety factor in equation 3-2 applied. The model

conservatively over-predicts 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 7-1. 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 7-2. 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 7-3. 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 7-4. 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 7-5. Predicted vs. measured non-dimensional 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 7-6. Predicted vs. measured non-dimensional 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 in-line 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 A-l. Test 1


Submerged Piles Hpg = 1/4 yo
SkewAngle = 90'


II I I I
1 2 3 4 5 6
Time (days)

Figure A-2. 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 A-3. 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 A-4. Test 4
















Submerged Ries Hpg = 3/4 yo
SkewAngle = 0


1 2 3 4 5 6


Time (days)

Figure A-5. Test 5


Submerged Piles Hg = 3/4 yo
SkewAngle = 90'


1 2 3
Time (days)


4 5 6


Figure A-6. 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 A-7. Test 7


Suberged Piles Hpg = y
SkewAngle = 90


1 2 3 4 5 6
Time (days)


Figure A-8. 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 A-9. Test 9


Submerged Piles H = y
SkewAngle = 0
s/b=6


1 2 3
Time (days)


4 5 6


FigureA-10. Test 10


Submerged Rles Hp = Yo
SkewAngle = 70













REFERENCES


Baker, R.E. 1986. "Local Scour at Bridge Piers in Non-Uniform Sediment." University of Auckland,
Department of Civil Engineering, Report No. 402, Auckland, New Zealand.

Batuca, D., and B. Dargahi 1986. "Some Experimental Results on Local Scour Around Cylindrical
Piers for Open and Covered Flows." Proceedings of the Third International Symposium on River
Sedimentation.

Breusers, H.N., G. Nicollet, and H.W. Shen 1977. "Local Scour Around Cylindrical Piers." Journal
of Hydraulic Research 15, no.3: 211-52.

Chabert, J., and P. Engeldinger 1956. "Etude des affouillements autour des piles de points Rep.,
Laboratoire National d'Hydraulique, Chatou, France.

Chiew, Y.M. 1984. "Local Scour at Bridge Piers." Department of Civil Engineering, University of
Auckland Report to National Roads Board, New Zealand.

Chiew, Y.M., and B.W. Melville 1996. "Temporal Development of Local Scour at Bridge Piers."
Proceedings of the ASCE North American Water and Environment Conference, Anaheim, CA
(August).

Copps, T.H. 1994. "Prediction of Local Scour Depth Near Multiple Pile Structures." Master's thesis,
UFL/COEL-94/001, Coastal and Oceanographic Engineering Department, University of Florida,
Gainesville, FL.

Ettema, R. 1980. "Scour at Bridge Piers." Ph.D. Dissertation, Department of Civil Engineering,
University of Auckland, Auckland, New Zealand, Report No.216.

Ettema, R., B.W. Melville, and B. Barkdoll 1996. "Pier Width and Local-Scour Depth." Proceedings
of the 1996 ASCE North American Water and Environment Congress.

Gosselin, M.S., and D.M. Sheppard 1995. "Time Rate of Local Scour." Proceedings of the ASCE
1" International Conference on Water Resources Engineering, San Antonio; TX 1: 775-79.









Gosselin, M.S. 1997. "The Temporal Variation of Clear Water Local Scour Around a Single Circular
Cylinder." Ph.D. Dissertation, Department of Coastal and Oceanographic Engineering, University
of Florida, Publication No. TR-114.

Hannah, C.R. 1978. "Scour at Pile Groups." Department of Civil Engineering, University of
Canterbury. Master of Engineering Report, No.78/3.

HEC-18. 1996. "Evaluating Scour at Bridges." Hydraulic Engineering Circular No. 18, Third
Edition, U.S. DOT, FHWA, Pub. No. FHWA-IP-90-017, revised February 1996.

Jain, S.C., and E.E. Fischer 1980. "Scour Around Bridge Piers at High Flow Velocities." Journal
of Hydraulic Engineering, 106, no. HY11 (November).

Johnson, P.A., and E.F. Torrico 1994. "Scour Around Wide Piers in Shallow Water." 73rd Annual
Meeting of the Transportation Research Board (January).

Johnson, P.A. 1996. "Pier Scour at Wide Piers." Proceedings of the 1996 ASCE North American
Water and Environment Congress.

Jones, J. S. 1984. "Comparison of Prediction Equations for Bridge Pier and Abutment Scour."
Transportation Research Record 950, Second Bridge Engineering Conference, Volume 2,
Transportation Research Board, Washington, D.C.

Jones, J. S. 1989. "Laboratory Studies of the Effects of Footings and Pile Groups on Bridge Pier
Scour." Proceedings of the Bridge Scour Symposium (October). Report Number FHWA-RD-90-
035: 3401-60.

Laursen E.M., and A. Toch 1956. "Scour at Bridge Crossings." Iowa Highway Research Board
Bulletin No.4, Iowa Institute of Hydraulic Research, Iowa State Highway Commission, and the
Bureau of Public Roads (May).

Melville, B.W. 1975. "Local Scour at Bridge Sites." University of Auckland, School of Engineering,
Auckland, New Zealand, Report no.117.

Melville, B.W. 1984. "Live-Bed Scour at Bridge Piers." Journal of Hydraulic Engineering, 110,
no.9 (September).

Melville, B.W., and A. J. Sutherland 1988. "Design Method for Local Scour at Bridge Piers."
Journal of Hydraulic Engineering, ASCE 114(10): 1210-1226.

Mostafa, E.A., A.A. Yassin, R. Ettema, and B.W. Melville 1993. "Local Scour at Skewed Bridge
Piers." Hydraulic Engineering '93. Proceedings of the 1993 Conference. 1:1037-42.











Mostafa, E.A., A.A Yassin, R. Ettema, ard B.W. Melville 1995a. "Parametric Approach for the
Estimation of Bridge Pier Non-Alignment Effect on Maximum Equilibrium Scour Depth."
Alexandria Engineering Journal 34, no. 4 (October).

Mostafa, E.A., A.A. Yassin, R. Ettema, and B.W. Melville 1995b. "Systematic Investigation of
Skewness Effect on Maximum Equilibrium Scour Depth at Skewed Bridge Piers." Alexandria
Engineering Journal 34, no. 3 (July).

Mostafa, E.A., A.A. Yassin, R. Ettema, and B.W. Melville 1996. "Simplified Approach for the
Prediction of Maximum Equilibrium Scour Depth at Skewed Bridge Piers." Alexandria Engineering
Journal 35, no. 2 (March).

Nakagawa, H., and K. Suzuki 1975. "An Application of Stochastic Model of Sediment Motion to
Local Scour Around a Bridge Pier." Proceedings of the 16h IAHR Congress, Sao Paulo, Brazil,
2:228-35.

Ontowirjo, B. 1994. "Prediction of Scour Near Single Piles in Steady Currents." Master's thesis,
UFL/COEL-94/001, Coastal and Oceanographic Engineering Department, University of Florida,
Gainesville, FL.

Raudkivi, A.J., and R. Ettema 1977. "Effects of Sediment Gradation on Clear Water Scour." Journal
of the Hydraulics Division, 103, no. HY10 (October).

Raudkivi, A.J. 1986. "Functional Trends of Scour at Bridge Piers." Journal of Hydraulic
Engineering, 112, no.1 (January).

Richardson, E.V., D.B. Simons, and P.Y. Julien 1988. "Highways in the River Environment." 2nd
ed. U.S. Dept. of Transportation, FHWA, Ft. Collins, CO.

Richardson, E.V., and J.R. Richardson 1989. "Bridge Scour." Proceedings of the Bridge Scour
Symposium, October 17-19, 1989, Report No. FHWA-RD-90-035.

Salim, M., and J.S. Jones 1996. "Scour Around Exposed Pile Foundations." Proceedings of the
ASCE North American Water and Environment Conference, Anaheim, CA (August).

Shen, H.W., V.R. Schneider, and S.S. Karaki 1966. "Mechanics of Local Scour." Civil Engineering
Department, Colorado State University, Fort Collins, CO Pub. No.CER66HWS22.

Sheppard, D.M., G. Zhao, and T.H. Copps 1995a. "Local Scour Near Multiple Pile Piers in Steady
Currents." Proceedings of the 1' International Conference on Water Resources Engineering, San
Antonio, TX. 1804-08.









Sheppard, D.M, G. Zhao, and B. Ontowirjol995b. "Local Scour Near Single Piles in Steady
Currents." Proceedings of the ASCE Water Resources Engineering Conference, San Antonio, TX.

Sheppard, D.M. 1998. "Conditions of Maximum Local Scour." Compendium of Scour Papers from
ASCE Water Resources Conferences, Eds. E.V. Richardson and P.F. Lagasse (September 1998).

Sheppard, D.M., and J.S. Jones 1998. "Scour at Complex Pier Geometries." Compendium of Scour
Papers from ASCE Water Resources Conferences. Eds. E.V. Richardson and P.F. Lagasse
(September 1998).

Sumer, B.M., N. Christiansen, and J. Fredsoe 1992. "Time Scale of Scour Around a Vertical Pile."
Proceedings of the 2nd International Offshore and Polar Engineering Conference, San Francisco, CA.
308-15.

Yanmaz, M., and D. Altinbilek 1991. "Study of Time-Dependent Local Scour Around Bridge Piers."
Journal of Hydraulic Engineering 117, no.10: 1247-68.

Zhao, G. 1996. "The Effect of Flow Skew Angle on Local Sediment Scour Near Pile Groups."
Master's thesis, UFL/COEL-96/001, Coastal and Oceanographic Engineering Department, University
of Florida, Gainesville, FL.

Zhao, G., and D.M. Sheppard 1996. "The Effect of Flow Skew Angle on Sediment Scour Near Pile
Groups." Proceedings of the 1996 ASCE North American Water and Environment Congress.




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