Citation
Local sediment scour at large circular piles

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Title:
Local sediment scour at large circular piles
Series Title:
UFLCOEL-99016
Creator:
Pritsivelis, Athanasios, 1973-
University of Florida -- Civil and Coastal Engineering Dept
Place of Publication:
Gainesville Fl
Publisher:
Coastal & Oceanographic Engineering Program, Dept. of Civil and Coastal Engineering]
Coastal & Oceanographic Engineering Program, Dept. of Civil and Coastal Engineering
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English
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xv, 118 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Scour and fill (Geomorphology) ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (M.S.)--University of Florida, 1999.
Bibliography:
Includes bibliographical references (leaves 114-117).
General Note:
Cover title.
Statement of Responsibility:
by Athanasios Pritsivelis.

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Full Text
UFL/COEL-99/016

LOCAL SEDIMENT SCOUR AT LARGE CIRCULAR PILES
By
ATHIANASIOS PRITSIVELIS
Thesis

1999




LOCAL SEDIMENT SCOUR AT LARGE CIRCULAR PILES

By
ATHANASIOS PRITSIVELIS
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

I would like to express my deepest gratitude to my advisor and committee
chairman Dr. D. Max Sheppard. His continuous support and his insight have permitted this study to become a reality. I would like also to thank Dr. Mufeed Odeh, P.E., head of the Engineering Section at the USGS Laboratory part of my committee, for his support during my 14-month stay in Massachusetts. My thanks also go out toward Dr. Robert Dean and Dr. Robert Thieke for serving on my supervisory committee.
John Noreika, Stephen Walk, Phil Rokasah and the other members at the USGSBRD Laboratory in Massachusetts also deserve my thanks for putting up with me and helping me on the practical parts of the experiments. Also deserving my deepest appreciation are Tom Glasser and Edward Albada for helping me, sometimes working 15 hours, with the experiments.
Sidney Schofield, Jim Joiner, Vernon Sparkman, Chuck Broward, and the other members of the Coastal and Oceanographic Engineering Laboratory also deserve my thanks for their assistance, as well as Chris Jette for answering all my questions about transducers fast and efficient.
I am also grateful to J.S. Jones, P.E. with the Federal Highway Administration and Shawn McLemore, P.E., and Rick Renna, P.E., with the Florida Department of Transportation for their financial support for this research and their interest and helpful suggestions.




Many others deserve a hearty thank you. My fellow students, including Ed, Roberto, Guillermo, Hugo, Tom, Bill, and Erika, for the help on classes. Additional gratitude goes to Becky, Helen, Laura, and so many other people at the department.
Finally, I want to express my deepest gratitude to my parents, George and Vasiliki, and my sister Helen for their patience and lifelong support.




TABLE OF CONTENTS
pne
A CKN OW LED GM EN TS .................................................................................................. ii
LIST OF TABLES ............................................................................................................. vi
LIST OF FIGURES ........................................................................................................... vii
KEY TO SYM BOLS ........................................................................................................ xii
A BSTRA CT ...................................................................................................................... xv
CHAPTERS
1 INTRODU CTION .......................................................................................................... 1
2 BACKGROUND AND LITERATURE REVIEW ........................................................ 7
Description of the Flow Field Around a Pier ................................................................. 7
Scour Form ulation for Steady Flow ............................................................................... 9
Effect of the V arious Param eters ................................................................................. 11
Effect of A spect Ratio y,)b .................................................................................... 11
Effect of V elocity Ratio U/U c ................................................................................ 13
Effect of Sedim ent to Pier Size D 50/b .................................................................... 17
Effect of Sedim ent Gradation cr ............................................................................. 19
Effect of Pier Properties (Shape and A lignm ent) .................................................. 21
3 EXPERIM EN TA L APPROA CH ................................................................................. 24
Facilities and Instrum entation ...................................................................................... 24
Facilities ................................................................................................................. 24
Instrum entation ...................................................................................................... 28
V elocity m easurem ent ...................................................................................... 28
W ater level m easurem ent ................................................................................. 29
Tem perature m easurem ent ............................................................................... 29
A coustic transducers ........................................................................................ 30
V ideo m easurem ents ........................................................................................ 32
M easurem ent setup .......................................................................................... 35




Point gauging ................................................................................................... 36
M odels .................................................................................................................... 36
Sedim ent ................................................................................................................ 38
4 EXPERIMENTAL DATA REDUCTION AND ANALYSIS ..................................... 41
Experim ental Pprocedure ............................................................................................. 41
D ata R eduction ............................................................................................................. 43
Processed D ata Results ................................................................................................ 44
D iscussion of Results ................................................................................................... 56
5 COMPARISON OF LOCAL SCOUR PREDICTION EQUATIONS ........................ 58
Scour Prediction Equations .......................................................................................... 58
Com pilation of Local Scour D ata ................................................................................ 65
Com parative A nalysis .................................................................................................. 67
Field D ata Exam ple ...................................................................................................... 85
6 SCALING MODEL SCOUR DEPTHS TO PROTOTYPE CONDITIONS ............... 89
7 SU M M A RY A N D CON CLU SION S .......................................................................... 96
Sum m ary ...................................................................................................................... 96
Conclusions .................................................................................................................. 98
R ecom m endations for Future W ork ............................................................................. 99
APPENDICES
A EFFECTS O F TH E W EIR ........................................................................................ 100
B FLO W U N IFO RM ITY .............................................................................................. 103
C EX PERIM EN TA L D A TA ........................................................................................ 105
D COMPARISON OF METHODS CALCULATING CRITICAL DEPTH
A V ER A G E V ELO CITY ........................................................................................... 109
REFEREN CES ................................................................................................................ 114
BIO G R APH ICA L SK ETCH ........................................................................................... 118




LIST OF TABLES
Table p Lge
2.1 Shape factor for pier nose, taken from HEC-18 (1995)................................ 22
2.2 Other factors for pier shapes............................................................. 22
2.3 Correction factor K2 for angle of attack 0 of flow, where L is the length of the pier
and b the width, taken from HEC- 18 (1995)........................................ 23
3.1 Table with values of (-log (D5o/b)) before sand availability ......................... 37
3.2 Table with values of (-log (D5o/b)) for the piles and sediment used in the tests ...38 4.1 Parameters for the experiments conducted............................................. 41
6.1 Cases for model and prototype .......................................................... 93
A. 1 Prototype and model dimensions ...................................................... 100
C. 1 Experimental data....................................................................... 105




LIST OF FIGURES

Figure pageC
1. 1 Effects of local scour on a bridge pier
(taken from University of Louisville web site)........................................ 3
2.1 Schematics of the vortices around a cylinder ............................................ 8
2.2 General relationship between equilibrium scour depth and
water depth when other parameters are held constant .............................. 12
2.3 General relationship between equilibrium scour depth and velocity
when other parameters are held constant ............................................ 14
2.4 Dependence of scour depth on mean velocity for two types of sediment........... 16
2.5 Dependence of equilibrium scour depth on ratio of sediment diameter
to structure diameter for 1 > U/U,,> 0.9 and yj/b > 2.5 ........................... 18
2.6 Influence of a on scour depth, taken from Melville and Sutherland (19 88)........ 19 2.7 Graphic relationship between a and K~, taken from Chiew (1984) ................. 20
2.8 Alignment factor K2 for rectangular piers, taken from Laursen. (1958)............. 21
3.1 Aerial photograph of the S.0. Conte Laboratory ...................................... 25
3.2 Schematic figure of the setup for the experiments..................................... 26
3.3 A test pile with the instrumentation..................................................... 31
3.4 Detailed view of the arrays for the small structures ................................... 31
3.5 Detailed view of the arrays for the large structures.................................... 32
3.6 Picture of the cameras for the 0. 114 m (4.5 in) pile ................................... 33
3.7 Picture of the cameras for the 0.305 m (12 in) pile .................................... 34




3.8 Picture of the cameras for the 0.92 m (36 in) pile ............................................... 34
3.9 Diagram of the measurement system ................................................................. 35
3.10 Cross-Section of the 0.92m (36 in) pier ............................................................. 37
3.11 Gradation Curve for Sand No. 1 (D50 = 0.22 mm) ............................................. 39
3.12 Gradation Curve for Sand No. 2 (D50 = 0.80 mm) ............................................. 40
4.1 Elevation contour plot of the equilibrium scour hole for Experiment No. 1
(b = 0.114 m, D50 = 0.22 mm, yo = 0.186 m and U = 0.290 m/s) ................... 45
4.2 Elevation contour plot of the equilibrium scour hole for Experiment No.2
(b = 0.305 m, D50 = 0.22 im, Yo = 0.190 m and U = 0.305 m/s) ................... 45
4.3 Elevation contour plot of the equilibrium scour hole for Experiment No.3
(b = 0.920 m, D50 = 0.22 mm, Yo = 2.268 m and U = 0.325 m/s) ................... 46
4.4 Elevation contour plot of the equilibrium scour hole for Experiment No.4
(b = 0.920 m, D50 = 0.80 mm, Yo = 2.402 m and U = 0.454 m/s) ................... 46
4.5 Elevation contour plot of the equilibrium scour hole for Experiment No.5
(b = 0.920 m, D50 = 0.80 mm, Yo = 0.866 m and U = 0.335 m/s) ................... 47
4.6 Elevation contour plot of the equilibrium scour hole for Experiment No.6
(b = 0.305 m, D50 = 0.80 Min, Yo = 1.305 m and U = 0.381 m/s) ................... 47
4.7 Elevation contour plot of the equilibrium scour hole for Experiment No.7
(b = 0.114 m, D50 = 0.80 mm, yo = 1.280 m and U = 0.388 m/s) ................... 48
4.8 Equilibrium profiles of scour hole for Experiment No. 1
(b = 0.114 m, D50 = 0.22 mm, Yo = 0.186 m and U = 0.290 m/s)
a) Inline profile, and b) Normal profile ........................................................... 49
4.9 Equilibrium profiles of scour hole for Experiment No.2
(b = 0.305 m, D50 = 0.22 mm, yo = 0.190 m and U = 0.305 m/s)
a) Inline profile, and b) Normal profile .......................................................... 50
4.10 Equilibrium profiles of scour hole for Experiment No.3
(b = 0.920 m, D50 = 0.22 mm, Yo = 2.268 m and U = 0.325 m/s)
a) Inline profile, and b) Normal profile ........................................................... 51




4.11 Equilibrium profiles of scour hole for Experiment No.4
(b = 0.920 m, D50 = 0.80 mm, Yo = 2.402 m and U = 0.454 m/s)
a) Inline profile, and b) Normal profile .......................................................... 52
4.12 Equilibrium profiles of scour hole for Experiment No.5
(b = 0.920 m, D50 = 0.80 mm, Yo = 0.866 m and U = 0.335 m/s)
a) Inline profile, and b) Normal profile .......................................................... 53
4.13 Equilibrium profiles of scour hole for Experiment No.6
(b = 0.305 m, D50 = 0.80 mm, Yo = 1.305 m and U = 0.381 m/s)
a) Inline profile, and b) Normal profile .......................................................... 54
4.14 Equilibrium profiles of scour hole for Experiment No.7
(b = 0.114 m, D50 = 0.80 mm, Yo = 1.280 m and U = 0.388 m/s)
a) Inline profile, and b) Normal profile .......................................................... 55
5.1 Local scour depth dependence on velocity, as proposed by Sheppard (1997) ......... 65
5.2 Comparison of equations for clearwater data ..................................................... 69
5.3 Comparison of equations for live-bed data ........................................................ 70
5.4 Comparison of measured and calculated scour for clearwater data for
(A) Garde et al. (1993), and (B) Ahmad (1953) equations ............................ 71
5.5 Comparison of measured and calculated scour for clearwater data for
(A) Breusers et al. (1977), and (B) Chitale (1962) equations ......................... 72
5.6 Comparison of measured and calculated scour for clearwater data for
(A) Froehlich (1988), and (B) Gao et al. (1992) equations ............................. 73
5.7 Comparison of measured and calculated scour for clearwater data for
(A) Hancu (1971), and (B) HEC- 18 (1995) equations ................................... 74
5.8 Comparison of measured and calculated scour for clearwater data for
(A) Inglis-Blench (1962), and (B) Jain and Fischer (1979) equations ............ 75
5.9 Comparison of measured and calculated scour for clearwater data for
(A) Laursen and Toch (1956), and (B) Melville (1997) equations ................. 76
5.10 Comparison of measured and calculated scour for clearwater data for
(A) Shen et al. (1969), and (B) Sheppard et al. (1995) equations ................... 77
5.11 Comparison of measured and calculated scour for live-bed data for
(A) Ahmad (1953), and (B) Breusers et al. (1977) equations ......................... 78




5.12 Comparison of measured and calculated scour for live-bed data for
(A) Chitale (1962), and (B) Froehlich (1988) equations........................... 79
5.13 Comparison of measured and calculated scour for live-bed data for
(A) Gao et al. (1992), and (B) Hancu (1971) equations ........................... 80
5.14 Comparison of measured and calculated scour for live-bed data for
(A) HEC- 18 (1995), and (B) Inglis-Blench (1962) equations .................... 81
5.15 Comparison of measured and calculated scour for live-bed data for
(A) Jain and Fischer (1979), and (B) Laursen and Toch (1956) equations ....82
5.16 Comparison of measured and calculated scour for live-bed data for
(A) Melville (1997), and (B) Shen et al. (1969) equations........................ 83
5.17 Comparison of measured and calculated scour for live-bed data
for Sheppard et al. (1995) equation................................................... 84
5.18 Comparison of equations for Experiment No. 3
(b = 0.920 mn, D50 = 0.22 mm, yo, = 2.268 mn and U =0.325 m/s)................. 86
5.19 Comparison of equations for example of field conditions ........................... 87
6.1 Fitting curves for the scale factor using equation (6. 1)................................ 91
6.2 Regions for the model and prototype cases............................................. 92
6.3 Data fitting curves for the scale factor.................................................. 94
A. 1 Positions of velocity profile collection................................................ 101
A.2 Flow profiles of the model at certain distances from the entrance of the flume ....l101 B.1I Contour plots of velocity for the 1.22 mn (4 ft) water depth......................... 104
B.2 Contour plots of velocity for the 2.44 mn (8 ft) water depth......................... 104
C. 1 Scour history for Experiment 1......................................................... 105
C.2 Scour history for Experiment 2......................................................... 106
C.3 Scour history for Experiment 3......................................................... 106
CA4 Scour history for Experiment 4......................................................... 107




C.5 Scour history for Experim ent 5 .............................................................................. 107
C.6 Scour history for Experim ent 6 .............................................................................. 108
C.7 Scour history for Experim ent 7 .............................................................................. 108
D. I Relationship between critical shear velocity and median grain diameter .............. 109
D.2 Comparison of the methods for calculating Uc in respect to
(A) Grain Median Diameter, (B) Temperature, and (C) Relative Roughness ... III




KEY TO SYMBOLS

b pile width (diameter)
bm model pile width
bp prototype pile width
B channel width
c exponent related to bed load
Cwr rectangular weir coefficient
D16 sediment size for which 16 percent of bed material is finer
D50 median sediment diameter
D5om model median sediment diameter
D84 sediment size for which 84 percent of bed material is finer
D50 p prototype median sediment diameter
dse equilibrium scour depth
dseJ() equilibrium scour depth for a sediment with a given a
dse m model equilibrium scour depth
dse p prototype equilibrium scour depth
Fr Froude number
Frc critical Froude number
g acceleration of gravity
H head over the weir




K pier shape factor
K1 factor for shape of pier nose
K2 factor for angle of attack of flow
Kd sediment-size factor
KI flow intensity factor
K, pier-shape factor
KyD flow depth-pier width factor
K, pier-alignment factor
K., factor for the gradation of sediment
L length of pier
Lm model scale length
Lp prototype scale length
Pw weir height
q discharge per unit width
Q discharge
R ratio of model to prototype D50/b
Rep pier Reynolds number
Re, wall Reynolds number
s relative sediment density
S scale factor
SG geometric scale factor
U mean depth average velocity
Ue critical depth average velocity




U'e velocity for the initialization of sediment movement around the
structure
u, bed shear velocity
u*C critical bed shear velocity
VC velocity for the initialization of sediment movement around the
structure
Yo depth of flow
Cl, CC2 coefficients of scale factor, SF, related to b/D50 of prototype
0 angle of attack of flow
It dynamic viscosity of water
v kinematic viscosity of water
p density of water
Ps density of sediment
G gradation of sediment
T bed shear stress
factor for pier shape




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 SEDIMENT SCOUR AT LARGE CIRCULAR PILES By
Athanasios Pritsivelis
August 1999
Chairman: Dr. D. Max Sheppard
Major Department: Coastal and Oceanographic Engineering
Local sediment scour experiments were performed with three circular pile diameter (0.114 m, 0.305 m, and 0.920 m) and two sediment grain sizes (D50 = 0.22 mm and 0.80 mm) under clearwater scour conditions. The results were analyzed and combined with data from other researchers to form two data sets, one for clearwater and one for live-bed conditions. These data sets were used to evaluate and compare 14 different scour prediction equations. The 0.92 m diameter pile was then considered to be a prototype pile and the other, smaller piles models of the prototype. The model and prototype data were then used to obtain the proper model to prototype scale factor for computing the equilibrium scour depth for the prototype from the model results. The scale factors are represented in plots of scale factor versus D50 (model)/ D50 (prototype) for various values of sediment to pile diameter ratio for the prototype.




CHAPTER 1
INTRODUCTION
When designing hydraulic structures, one must consider many aspects, which are important for the functionality and mostly for their safety and the safety of the people depending on them.
Some of the aspects considered are (Pilarczyk, 1995):
1. Function of the structure; erosion is not always the problem as long as the
structure can fulfill its function,
2. Physical environment; the structure should offer the required degree of
protection against hydraulic loading, with an acceptable risk and, when possible,
meet the requirements resulting from landscape, recreational and ecological
viewpoints,
3. Construction method; the construction costs should be minimized to an
acceptable level and legal constrictions must be adhered to,
4. Operation and maintenance; it must be possible to manage and maintain the
hydraulic structure.
From all these aspects, the cost of construction and maintenance is generally the
controlling factor. In the case of bridge design, local scour around the piles of the bridge is one of the factors that contribute to the total construction and maintenance cost and is important in the estimation of stability of the structure. Underprediction can result in




costly bridge failure and possibly in the loss of lives, while overprediction can result in millions of dollars wasted on a single bridge.
Scour in general is caused by changes in the characteristics of flow, which lead to changes in the sediment transport in the area of interest. There is an equilibrium scour depth associated with a given set of environmental conditions (water depth, sediment density and size, flow velocity, etc.). When the environmental conditions change (e.g. a change in flow velocity), the scour depth progresses toward the new equilibrium depth. If the new conditions are maintained for a sufficiently long period of time the new equilibrium scour depth is reached. Scour caused by a structure (e.g. a pile) can be divided into two categories: general (or contraction) and local. As a first approximation, the scour caused by each process can be added to obtain the total scour. Of the two types of scour, local scour is the least understood.
General scour happens when the cross sectional area of the flow at a particular
location is reduced due in most cases to the presence of a new structure. This results in an increase in flow velocity and bed shear stress and increases the potential for erosion of the area. This type of scour is well understood and there are a number of methods for predicting these scour depths.
Local or structure induced scour is caused by the structure itself. A picture of local scour around a structure (bridge pier) is shown on Figure 1. 1. The main causes of local scour are
1) an increase in mean flow velocities in the vicinity of the structure 2) the creation of secondary flows in the form of vortices and 3) the increased turbulence in the local flow field.




Two kinds of vortices are observed: Wake vortices, downstream of the points of flow separation on the structure and horizontal vortices at the bed and free surface, due to pressure variations along the face of the structure. Those phenomena, although relatively easy to observe, are difficult to quantify mathematically. Some researchers (Shen et al., 1969) have attempted to describe this complex flow field mathematically but with little success. A number of numerical solutions have also been attempted but with limited success.

Figure 1.1 Effects of local scour on a bridge pier
(taken from a Bridge Scour Site, 1998)




Historically, scientists and engineers have used scale models in order to predict complex prototype phenomena. This requires a knowledge and understanding of the modeling laws for the particular situation (i.e. a knowledge of the pertinent dimensionless groups for the processes involved), in order to extrapolate the measured values for the model to prototype conditions. Ideally, the values of the salient dimensionless groups are made the same in the model as they are in the prototype. This, however, is not always possible and when it is not the extrapolation process becomes more difficult. For local structure induced scour, the processes are characterized by three dimensionless groups,
-,U, and D, where b is the diameter of the pile, yo is the water depth, U in the b 'U C b
mean depth average velocity, Uc is the critical depth average velocity and D50 is the median sediment diameter. It is normally easy to configure the model so as to make the first two groups the same for the model and prototype but due to lower limits on the sediment diameter (before the sediment becomes cohesive) the third group usually cannot be properly scaled. In many locations, such as Florida, the sediment is sand with a prototype D5o between 0. 1 and 0.4 mm. and the structures can be large (on the order of 10 to 20 mn in width). For a geometric scale of 40, the model sediment D50 would have to be as small as 0.0025 mm, which is in the cohesive range, where the scour properties are significantly different (and less understood). The problem is then, how to predict the prototype scour depth from the scour depth measured in the model study. The most common procedure used to date has been to simply use the prototype-to-model geometric




5
scale (i.e. d,,p = dse Note that this ignores the differences in D50 for the model
m LM b
( LP )).
and prototype and the impact of this difference on the scour depth.
Most scour prediction relationships, such as the Colorado State University (CSU) relation, (currently used in the FHWA Hydraulic Engineering Circular No. 18) and the University of Florida (UF) equation (Sheppard et al., 1995) are empirical. Many of these equations are relatively accurate in predicting local scour for laboratory scale structures but are very conservative in their estimates of scour depths for prototype structures. There is a significant amount of scour data in the literature for small structures but very little for prototype size structures in a controlled environment.
One of the objectives of the work reported in this thesis is to provide local scour data for large circular piles. Laboratory experiments were conducted for three pile diameters, two different sediment sizes and a range of water depths. The results of those experiments along with other data from various researchers were then used to compare 14 different scour prediction equations. This data set was also used to obtain the scale factor for estimating prototype scour depths from measured model scour depths.
To better understand the problem of local scour, Chapter 2 reviews the current state of knowledge of local scour. The primary mechanisms are reviewed first followed by the formulation of the most important dimensionless groups for local scour.
Chapter 3 gives a detailed description of the experiments performed and the
procedures used. Seven experiments were conducted with three pile diameters and two sediment sizes. The experiments were run for approximately 24 hours beyond the point at which the scour depth ceased to increase.




Chapter 4 presents the experimental results and the data processing procedures. In line and normal scour hole profiles are presented along with contour plots of the scour holes.
Chapter 5 presents a comparison of a number of scour prediction equations using clearwater, live-bed and a typical example of field data. The equations are compared on their ability to predict those data and the results are shown with line and scatter plots.
In Chapter 6 the problem of scaling model scour depths to prototype conditions is examined. A scaling factor that depends on D50m and D50 is presented.
Finally, a summary of the work conducted for this thesis, along with some conclusions and recommendations for future work is given in Chapter 7.




CHAPTER 2
BACKGROUND AND LITERATURE REVIEW
Bridge scour has received a lot more attention this past decade and a number of
advances have been made. Many researchers have conducted laboratory experiments in order to improve the accuracy of equilibrium scour depth prediction. Most of these tests were done with simple structures, like a single pile, in a horizontal sand bed subjected to a steady flow. These experiments succeeded in identifying the physics of the local scour processes. Recently, there has been an increase in the research on local scour at more complex piers.
2.1 Description of the Flow Field Around a Pier
This section discusses the flow field near a cylindrical pile in a steady flow, as seen from various researchers. The flow field in the immediate vicinity of a structure is quite complex, even for simple structures such as circular piles. The dominant feature of the flow is the large-scale eddy structure, or system of vortices that develop about the pier. That system is the basic mechanism of local scour, and has been recognized by many investigators (e.g. Shen et al., 1966, Melville, 1975).
It has been found that depending on the type of pier and flow conditions, the eddy structure can be composed of one or more of the basic systems, which comprise the horseshoe vortex and the wake vortex systems. It has also been identified that the acceleration of the flow around the pier is a factor in the early stages of local scour.




8
The horseshoe vortex system is developed at the base of the structure. The term "horseshoe" is derived from the shape that the system takes as viewed from above. It wraps around the structure and tails downstream, as shown in Figure 2.1. Shen et al. (1966) describe the horseshoe vortex system very accurately. The main cause of this system is the stagnation pressure difference developed at the nose of the structure. If the difference is large enough, there is a downward flow, which rolls up ahead of the toe of the structure to form the horseshoe vortex system. The system in its simplest form is composed of two vortices, a large one, adjacent to the structure, with a small counter vortex. A more complicate system consists of multiple small counter vortices, which are unsteady and periodically shed and are swept downstream. Clearly, the geometry of the structure is important in determining the strength of the system, although it is not steady for all kinds of structures. Blunt nosed structures create the most energetic vortex system.
,. d o, ... ,n o ..........,...,.
I SteaeX u$rent V dilex
,eloCly Profile i eHorseho Vort
Water Surfirc
%4r
Bound.r '
Layer '
." Wake Region
Horseshoe Vorlex __"_,_ _-___.
SIDE VIIEW TOP rJI-W

Figure 2.1 Schematics of the vortices around a cylinder




Melville (1975) measured mean flow directions, mean flow magnitude, turbulent flow fluctuations, and computed turbulent power spectra around a circular pier for flatbed, intermediate and equilibrium scour holes. He found that a strong vertical downward flow developed ahead of the cylinder, as the scour hole enlarged. The size and circulation of the horseshoe vortex increased rapidly and the velocity near the bottom of the hole decreased as the scour hole was enlarged. As the scour hole develops, the intensity of the vortex decreases and reaches a constant value at the equilibrium stage.
Although the horseshoe vortex is considered the most important scouring
mechanism for steady flows, the wake vortex system is also important. Wake vortices are created by flow separation on the structure. Large scour holes may also develop downstream from piers, when the horseshoe vortex system does not form, as demonstrated by the experiments of Shen et al. (1966). With their vertical component of flow, wake vortices act somewhat like a tornado in removing the bed material, which is then carried downstream by the mean flow.
2.2 Scour Formulation for Steady Flow
In order to formulate quantitative relationships to predict local scour, there has to be a distinction between clearwater and live-bed scour. Clearwater scour is the local scour that occurs when the flow velocity is below the value needed to initiate sediment motion on the flat bed upstream from the structure. Live-bed scour occurs when the flow velocity exceeds the value needed to initiate sediment motion upstream of the structure. The sediment is assumed to be cohesionless and the term local scour is assumed to be the depth of the deepest point around the structure.




The equilibrium scour depth depends on the fluid and sediment properties, the flow parameters, and characteristics of the structure, e.g.
dse = f[p, p, g, D50, uC, p yo, U, b, h(pier)], (2.1) where
dse is the equilibrium scour depth,
p and Ps are the density of water and sediment respectively,
g is the dynamic viscosity of water (depends on temperature),
g is the acceleration of gravity,
D50 is the median diameter of the sediment,
a is the gradation of sediment,
yo is the depth of flow upstream of the structure,
U is the depth average velocity,
b is the pier diameter/width normal to the flow,
h(pier) is a function that depends on the shape and the alignment of the pier in the
flow.
The most important dimensionless groups for local scour can be obtained from the quantities given in Equation 2.1. These eleven quantities can be expressed in terms of three fundamental dimensions: force, length and time. According to the Backingham I theorem, 11 3 = 8 independent dimensionless groups exist for this situation. An example of these eight groups is shown in Equation 2.2.
---f 'U p, Ub U D50




Of these eight groups, the following six are considered the most important as shown in Equation (2.3)
bs fryoU kD50,o- pir(23
ds Kb'U~' C b (rJ 23
where U, is the critical depth averaged velocity (the velocity required to initiate sediment motion on a flat bed).
2.3 Effect of the Various Parameters
The aspects of scour processes described by the various dimensionless groups are
understood as a result of numerous laboratory experiments. These groups are described in the following paragraphs.
2.3.1 Effect of Aspect Ratio y/b
The effect of flow depth on scour depth is significant. Observations (Ettema 1980, Chiew 1984) have shown that, for shallow flows, the scour depth increases with increasing depth of flow up to a point beyond which no effect is observed. The above is generally accepted by many researchers e.g. Laursen and Toch (1956), Neill (1973). Cunha (1970). As Ettema (1980) states, the effect of the flow is due to the impact it has on the formulation of the surface and bottom vortices located at the upstream side of the pier. The pressure differences along the nose of the pier cause a surface roller at the top and the horseshoe vortex at the bottom. The two rollers rotate to opposite directions. In principle, as long as they do not interfere, the local scour depth is independent of the depth of the flow. With decreasing depth, the surface roller interferes with the downflow, making it weaker. Other reasons are the influence of the sediment bar behind the structure




for small values of yo/b and the fact that the portion of the flow that is diverted into the hole, diminishes for low values of ydb (Ettema, 1980).
Another researcher, Bonasoundas (1973) concluded that the effects of the flow depth were insignificant for yo/b > 1 to 3. However, his experiments were only run for two hours and thus equilibrium depths could not have been achieved. Basak (1975), Hancu (1971), White (1973), Chabert and Engeldinger (1956) and Jain and Fischer (1979) observed the same general behavior for live-bed conditions.
Laboratory data (Ettema 1980, Chiew 1984, etc.) indicate that, if the other two parameters (U/lU and D50/b) are held constant, the equilibrium scour depth increases rapidly with yo/b until a value of 2.5 to 3 and then remains constant. This is shown schematically in Figure 2.2.
2.5
2
1.5
I
0.5
0 1 2 3 4
y0/b
Figure 2.2 General relationship between equilibrium scour depth and water depth when other parameters are held constant




2.3.2 Effect of Velocity Ratio U/U,
The critical depth average velocity, Uc, is important since it is the velocity at which sediment movement is initiated on a flat bed upstream of the structure. A better understanding of critical velocity can be achieved, by examining the forces acting on a sediment particle subjected to a steady flow (Shields, 1936). Shields states that a critical bed shear stress exists, above which there is movement of the sediment at the bottom. Comparing the drag force on a grain with its submerged weight, Shields developed an empirical formula for the critical shear stress. From the shear stress, the shear velocity, U*.= can be computed. For a fully developed velocity profile, the Prandtl-Von
Kdtrmdtn formula can be used to compute the depth averaged velocity as a function of the shear velocity and bed roughness (Sleath, 1984). From the above, the critical depth averaged velocity, Uc, can be calculated. For flow velocities higher than this value, the local scour is defined as "live-bed scour." "Clearwater scour"~ is defined as the local scour that occurs for velocities less than the critical value.
Several different methods have been used by researchers to estimate the value of critical depth averaged velocity and their results can differ significantly. Note that in comparing data from different researchers, it is important that the same method be used for all the data. A brief description of the more common methods for computing Uc is given in Appendix D along with a comparison of their predicted values.
The depth of equilibrium local scour is closely related to the mean depth average
velocity. It is evident from published literature that under clearwater conditions, the local scour increases almost linearly with the approach velocity. Breusers et al. (1977)




developed the relationship between scour depth and the ratio of U/Uc by dimensional analysis, but applied no detailed analysis into the nature of the dependency. Hanna (1978) found out that scour is initiated around u,/u., = 0.5, where u- is the bed shear velocity and u-c is the critical bed shear velocity and reaches a maximum value for u,/uc equal to unity. Other data, that show that the initiation of scour depth starts at around 0.4-0.5Uc, for circular piles, come from Chabert and Engeldinger (1956) and Ettema (1980). Most of the laboratory data seem to follow Figure 2.3.
Clearwater Live-bed
Conditions Conditions
< -

-0.4-0.5

1
U/UJC

Figure 2.3 General relationship between equilibrium scour depth and velocity
when other parameters are held constant




As for live bed conditions (U/Uc > 1.0); the results are even more difficult to obtain. The difficulty resides in the fact that the experiments are difficult to perform and the results hard to interpret. Early researchers related the relative scour depth dse/b to the Froude number. Most of the conclusions drawn state that for a given flow depth, the scour depth increases with increasing velocity. Later researchers e.g. Chabert and Engeldinger (1956), Laursen (1962) etc. found that as the velocity increased beyond the critical velocity, Uc, the scour depth decreases by about 10%. Further increases in velocity increase the scour depth until a second peak is reached. The decrease of scour depth after the initiation of live-bed conditions was believed to be caused by infill of the scour hole due to movement of the bed. Hancu (1971) conducted a series of live-bed scour experiments and concluded that the local scour depth is independent of the flow velocity for live-bed conditions. This conclusion is similar to that of Breusers et al. (1977).
Ettema (1980) stated though that there is a dependence of both clearwater and livebed equilibrium local scour depth on velocity. He concluded that the maximum value for live-bed local scour can be lower or higher than the one for the clearwater depending on the type of sediment (Figure 2.5). He thought that for ripple-forming sediments (D50 < 0.6 mm), the deepest scour hole is for live-bed conditions, while for non ripple-forming sediments, the deepest scour depth occurs at transition from clearwater to live-bed conditions. His explanation for the above distinction is that "shallower maximum depths of local scour generally occur for ripple-forming than for non ripple-forming bed materials, because the formation of ripples on the approach bed alters the roughness of the bed, creates a low level of sediment transport into the scour hole, affects the boundary




layer separation at the pier and consequently changes the strength of the horseshoe vortex". Sheppard (1997) concluded that the condition that defines which peak (clearwater or live-bed) is higher depends on the ratio of median diameter of the sediment and pier diameter, D50/b, and not on whether the sediment was ripple-forming.
Non ripple-forming sediment
I

Ripple-forming sediment

-0.4 0.5
1

U/UC

Figure 2.4 Dependence of scour depth on mean velocity for two types of sediment




2.3.3 Effect of Sediment to Pier Size D50/b
The effect of this parameter was not recognized until recently. Laursen and Toch
(1956) stated "exactly the same depth of scour should result in the model, no matter what velocity or sediment is used, as long as there is general bed load movement and the Froude number is everywhere less than unity". However they added "because secondary effects of velocity and sediment size which could not be detected in the limited range of the laboratory data may become important at large scale, the validity of this conclusion can only be tested by model-prototype conformity studies". The results of the model study by Chitale (1962), Ahmad (1962) support the conclusions drawn by Laursen and Toch (1956) concerning the effect of sediment on scour depth. Krishnamurthy (1970) also stated that the effect of sediment size is negligible for high Froude number and large pile sizes.
The data from Chabert and Engeldinger (1956) show a small effect of sediment size on scour depth. Nicollet and Ramette (1971) extended the experiments of Chabert and Engeldinger (1956) and showed that the sediment size has a considerable effect. Raudkivi and Ettema (1977) decided to hold U/Jc and yo/b constant and change D50/b. Even though their data showed effects of sediment size, they attributed the changes to ripple formation and it was not given further thought. Baker (1986) correlated scour depth with b/D50 using the data from Raudkivi and Ettema (1977) and found that there is a correlation between the two values. Ettema's (1980) clearwater data showed that the influence of sediment size is significant, if the ratio of b/D50 is less than 20-25 and that for higher values the scour depth is independent of sediment size. A similar study to determine the scour depth dependence on D50/b was conducted by Sheppard and Ontowirjo (1994).




Using their data and that due to Ettema (1980) and Chiew (1984), they found that the effect of sediment size is as shown in Figure 2.5. The value of dse/b increases and then decreases with increasing values of D50/b. Sheppard (1997) assumed that one possible explanation for why the laboratory data correlate so well with the parameter D50/b is that it is actually the ratio of two different Reynolds numbers, one based on the sediment grain diameter (and the associated near bed shear velocity) and one on the structure diameter and the depth average velocity. Both Reynolds numbers are important in characterizing the flow and sediment transport in the vicinity of the structure.
3
2.5 + +
2+ +
+
% 1.5 +
1 ++
0+ +
0.5
+ Ettema (1980)]
1 0 UF/USGS
0- I I I
-4 -3 -2 -1
log(D5sb)
Figure 2.5 Dependence of equilibrium scour depth on ratio of
sediment diameter to structure diameter for 1 > U/U, > 0.9 and y0/b > 2.5




2.3.4 Effect of Sediment Gradation ;
For a given structure and flow, the equilibrium scour depth is very dependent on the sediment gradation. Experiments carried out by Nicollet and Ramette (1971) and a more extensive study by Ettema (1976) showed that the equilibrium scour depth decreases as the stardard deviation of the particle size distribution increases for clearwater scour conditions. For live-bed tests conducted by Baker (1986) and plotted by Melville and Sutherland (1988), there was a reduction as well but not as much as for clearwater and for values of U/U. > 4, the effect was almost independent of the gradation of the sediment (Figure 2.6). It is believed that the main effect of a is in the formation of an armor layer around the upstream perimeter of the pier reducing the scour hole depth.
2.?.
dse/b. I I
4 ., .. 1
0 1,.0 2,0 3o 5,.60,
UfUc
Figure 2.6 Influence of a on scour depth, taken from Melville and Sutherland (1988)




Ettema (1980) replotted his previous data as K, versus a, where K, is the coefficient in the equation
d s e ( C a K ( b 1 ( 2 .9 )
w here o = ,
de (o-) is the equilibrium clearwater scour depth for a sediment with a given a,
b
d,. is the equilibrium scour depth for uniform sediment (a < 1.6).
b
The graph is reproduced in Figure 2.7. The data is grouped by sediment type (rippleforming, D50 < 0.6 mm or non ripple-forming, D50 > 0.6 mm). K, varies from 1.0 for uniform sediments to less than 0.25 for sediments with a large gradation.
Oo
\.-)Ripple d5I0-(ml
Forming 10.55
0.75 Sediments W 0.85
:i + 9- 1.10
0.50 Non Ripple
?0- Forming
A Sediments 0,25-

Figure 2.7 Graphic relationship between a and K0, taken from Chiew (1984)




2.3.5 Effect of Pier Properties (Shape and Alignment)
The shape of the pier and its orientation to the flow can have a significant effect on the equilibrium scour depth. The shape and orientation effect can be accounted for with coefficients multiplied times the equation for a circular cross-section pier.
dse K2 d (2.10)
b b Jcircular pier
Values for K1 for common geometric pier cross-sections are given in Tables 2.1 and
2.2. The effect of flow skew angle (pier orientation) can be seen in Table 2.3 and Figure
2.8, taken from HEC-18 (1995) and Laursen (1958) respectively.
7
6
3
2
0 is45, 0 7590
ANGLE OF ATCK 0 (Degrees)
Figure 2.8 Alignment factor K2 for rectangular piers, taken from Laursen (1956)




Table 2.1 Other factors for pier shapes
Laursen Chabert And And
Tison Toch Engeldinger Neill Venkatadri Shape in plan L/a (1940) (1956) (1956) (1973) (1965)

Lenticular
Parabolic nose
Triangular nose, 600 Triangular nose, 900
Elliptic Ogival
Joukowski Rectangular

Circular

1.00

0.67 0.41
0.86 0.76 1.40

1.00
0.97 0.76
0.91 0.83
1.11 1.11

0.56 0.75 1.25

Table 2.2 Shape factor for pier nose, taken from HEC-18 (1995)
Shape of pier nose KI Square Nose 1.1
Round Nose 1.0
Circular Cylinder 1.0 Group of cylinders 1.0 Sharp Nose 0.9

0.73
0.92 0.86 1.11

1.00

1.00




23
Table 2.3 Correction factor K2 for angle of attack 0 of flow,
where L is the length of the pier and b the width, taken from HEC-18 (1995)
Angle J L/b=4 I L/b=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




CHAPTER 3
EXPERIMENTAL APPROACH
This chapter includes a detailed description of the experiments performed as part of this work, as well as a description of the equipment and instrumentation used.
3.1 Facilities and Instrumentation
The equipment used in the experiments is divided in four categories. The first is the facilities, which includes the flume and the equipment used to place and remove the sediment. The second is the instrumentation used to measure the water properties, flow conditions and scour depth. The third category is a description of model piers and the last category is a description of the sediment used in the experiments.
3.1.1 Facilities
All experiments were conducted in a flume located at the U.S. Geological Survey Biological Research Division, S.0. Conte Anadromous Fish Research Laboratory (referred to here as USGS-BRD Laboratory) in Turners' Falls, Massachusetts. The primary purpose of this laboratory is to study the behavior and biology of anadromous fish and to conduct research on fish passages. This is the first time the flume has been used for sediment scour research. An aerial view of the laboratory is shown on Figure 3. 1. The flume area of the laboratory has three parallel open channels. The main channel, located in the middle, has a width of 6.1 mn (20 ft). The two side channels have widths of




3.05 m (10 ft). All three channels have a length of 38.6 m (126.5 ft) and a depth of 6.4 m (21 ft). A not-to-scale, schematic drawing of the flume area in the Engineering Building is shown in Figure 3.2. Only the 6.1 m wide main channel was used for the work reported here.

Figure 3.1 Aerial photograph of the S.O. Conte Laboratory

The laboratory is located between a hydropower stationcanal and the Connecticut River. The flow in the flume is generated by the head difference between the canal and the Connecticut River. There is an intake pipe connecting the flume and the canal. The flow passes through grates to filter the water entering the flume. The flow is controlled by four sluice gates with dimensions of 1.22 m x 1.22 m (4 ft x 4 ft). Two of the gates are located at the north wall and one on either side at the north end. The gates are controlled with electric motors that raise or lower them individually. Discharge as large as 350 cfs




Flow Intake from Reservoir

126 I

NOT TO SCALE
All dimensions in feet

Flow Discharge To Connecticut River

Clearwater Scour Test Setup

NOT TO SCALE
All dimensions in feet

j I y 21
Test Sediment 61
Section A-A

126

Filter Material

Base Sediment

Test Sediment

Base Sediment

Section B-B

Figure 3.2 Schematic figure of the setup for the experiments

i 06 -




can be achieved with the two main sluice gates with an additional 50 cfs from the other two gates (depending on the canal and river elevations).
For the purpose of the work reported in this thesis, a weir was placed at the
downstream end of the flume to control the water level and volumetric discharge. Model tests were performed to determine how far upstream of the weir, the velocity profiles were affected (see Appendix A). It was determined that the weir has minimal effect on the velocity profiles in the test section.
The discharge, Q, over a rectangular weir occupying the entire width of the flow B can be computed using the equation
Q =C.,r 2/i2BH3, (3.1)
3
where Cwr, is the rectangular weir coefficient. From dimensional analysis arguments, it is expected that Cwr, is a function of Reynolds number (viscous effects), Weber number (surface tension effects) and the ratio of water head over the weir to the weir height, L1IP, In most practical situations, the Reynolds and Weber numbers effects are negligible, and the following expression can be used (Rouse 1946, Blevins 1984) Cwr, = 0.611+ 0.075-H (3.2)
Pw
More precise values of Cwr, can be found in the literature (Henderson, 1966).
At the upstream entrance of the flume, a 5.5 mn (18 fi) high flow straightener was installed to maintain uniformity of the flow over the width of the flume. The flow straightener consists of vertical wood slats with a 25% opening. The setup was successful




in that it produced near uniform flow across the flume for the range of water depths and velocities used in the experiments (see Appendix B for details).
In order to reduce the volume of the relatively expensive, uniform diameter sand, gravel with a D5o of approximately 0.48 cm (3/8 in) was used as a filler away from the test area (Figure 3.2). A filter cloth with a mean diameter opening of 0. 1 mmn was placed over the drains in the floor of the flume and between the sand and the gavel. An additional advantage of the gravel was the reduction of the drain time for the flume. A total of 360 m 3 of gravel and 205 m 3 of test sediment were used. In order to prevent sediment transport near the entrance of the flume, where the water was jetting from the openings in the flow straightener, gravel was placed on the bed for the first 8.5 mn (28 ft). This hastened the development of a fully developed velocity profile and prevented the formation of sand dunes that would have occurred due to the increased velocities near the flow straightener.
3.1.2 Instrumentation
The instrumentation for the data collection is composed of the instruments, for the measurement of the water temperature and elevation, flow velocity and scour depth. The instruments are described below.
3.1.2.1 Velocity measurement
Two commercially available electromagnetic current meters were used to measure the velocity during the tests [Marsh-McBimey Models 523 (0.5 in sensor) and 511 (1.5 in sensor)]. The water velocity was measured at the same two horizontal locations upstream of the test structure for all the experiments. The meters were located a distance of 1.52 m (5 ft) from the sides of the flume and approximately 5 meters upstream from the center of




the test structures. The vertical position of the velocity sensors were such that they were at the point of depth averaged velocity for a fully developed velocity profile, which is approximately yd3 from the bed. The time over which the velocity was averaged was increased until the measurement was steady. This value was found to be one minute. Velocities at the same elevation of the sensors were also measured using an impeller type current meter (Ott-meter). This instrument was also used during the experiments to check the electromagnetic meters. The duration of the measurement at each location was one minute. The accuracy of the electromagnetic and impeller meter measurements was estimated to be 1 cm/s and 0.5 cm/s respectively.
3.1.2.2 Water level measurement
A water pressure sensor was used to measure the water level during the tests. The water level was measured at the same location for all the experiments downstream of the test structure and approximately seven meters upstream of the weir. The time over which the water level was averaged was one minute. The accuracy of the water level measurement was estimated to be 0.5 cm.
3.1.2.3 TeMperature measurement
A temperature sensor was used to measure the water temperature during the tests. The temperature was measured at the same location for all the experiments, which was close to the test structures. The meter was located a distance of approximately three meters downstream from the test area and close to the wall of the flume. The time over which the temperature was averaged was one minute. The accuracy of the temperature measurement was estimated to be 0.050C.




3.1.2.4 Acoustic transducers
Two different transducer arrays were used for the temporal measurement of the
scour, one for the smaller structures and another one for the large structure. Both arrays consisted of three elements, each of which contained four crystals. The transducers are called Multiple Transducer Arrays or simply MTAs. They were positioned at the front of the structure and at angles of 830 from the front. Their height from the sandy bottom varied according to the water depth but they were always underwater and as close as possible to the surface so as not to interfere with the scour process. For most of the experiments, the transducers were located 10 cm. (4 in) from the water surface. The MTAs were custom built for this application by SeatekTm. For a more detailed description of the system, see Jette and Hanes (1997).
The arrays for the small pile diameters consisted of four 2.25 MHz transducers with
4 cm separation between the elements. The transducers were 2.5 cm in diameter. The footprint at a range of 0.9 m (3 ft) was 5 cm. (which means a 1.5 degrees spread angle of the acoustic beam). The arrays for the large pile diameters consisted of four 2.25 MHz transducers with 8 cm separation between elements. The transducers were 4.0 cm. in diameter. The footprint at a range of 2.7 m (9 ft) was 8.7 cm. The arrays were made of anodized aluminum.
The MTAs were mounted on each structure with an aluminum ring. The rings were fastened at a certain height and each of the three arrays was positioned on the ring at predetermined positions. Figure 3.3 shows the mounting of the transducers and cameras and Figures 3.4 and 3.5 show the details of the transducers.




i-

Plan View

Figure 3.3 A test pile with the instrumentation
MTA for small pile diameters (0.5 to 1 ft. diameter)

front view (cross-section) In0 7 (0 5 i.)
2.25 MHz transducers
[ SEATED
S41, (161 Drawn b: Chs JetteI 3-24-97

Figure 3.4 Detailed view of the arrays for the small structures

C9 mpra/

FLOW

top view
o o

side view (cross-section)




MTA for large pile diameters (greater than 1 ft.) 1/2 scate side view (cross-section) front view (cross-section)
mounting ring
- 31 sr~isu t-.4 0.1in
top vew
I SEATED
Figure 3.5 Detailed view of the arrays for the large structures
3.1.2.5 Video measurements
The video measurement consisted of the video equipment, the mechanisms to control them and the stepper motor for the movement of the cameras inside the piers. Although it was used as a backup measurement, it proved to be very reliable. Two cameras were used to monitor the rate of scour by moving vertically inside the piers. The mechanism for support and moving of the cameras was the same for all the piers but the carriage for the cameras changed according to the diameter of the pier (Figures 3.6 3.8). The controller for the traverse mechanism was designed to allow traverse speeds from
1 Omn/h to 1 mm/h. The mechanical part consisted of a threaded rod, which supported the cameras, and was connected to a stepper motor, the speed of which could be set by the controller. The rod had the appropriate length so the cameras could follow the sand-water interface during the scour process.




The output from the video cameras was sent to the VCR. A second controller was programmed to turn on the lights and record one minute of video at specified intervals throughout the experiments. After the end of the recording time, the video and lights were turned off and the system put in a stand-by mode until the next recording time. The controller also switched between cameras during the recording session.

Figure 3.6 Picture of the cameras for the 0.114 m (4.5 in) pile




Figure 3.7 Picture of the cameras for the 0.305 m (12 in) pile

Figure 3.8 Picture of the cameras for the 0.92 m (36 in) pile




3.1.2.6 Measurement setup
Two personal computers with 486 processors were used for data acquisition. One
was used for velocity, water elevation and temperature and one for the acoustic transducer measurements of the scour depth. The first computer was programmed to take one-minute samples of velocity, water elevation and temperature every 30 minutes. The data were written to a file on the hard drive. The second personal computer was connected to the acoustic transducers through a control box (SeaTek Control Box). The purpose of this box was to gather the signals from all 12 crystals and convert them to distances from the transducer to the bed. The communication between the personal computer and the acoustic control box was done with the software, CrosstalkT, a serial/parallel/modem communication package. The data was viewed on a computer screen and stored in files. Data were sampled for ten seconds every ten minutes. A diagram of the measurement system is shown in Figure 3.9.
P Mechanical M
V #Traverse
SeaTek VCR
Control Box
Inside Camera/VCR
Control Box
AcousticTime/Day
Water Digital Transducers

Figure 3.9 Diagram of the measurement system




3.1.2.7 Point gauging
After every experiment, the scour hole was surveyed with a point gauge system. The system was composed of a square array of steel beams that spanned the width of the flume with a side length of 6.1 mn (20 fi). The point gauge system was located on an aluminum carriage that moved along tracks on the steel beams. The point gauge was connected to a string potentiometer and voltage source so that the vertical position was indicated by an electrical potential in mV. The horizontal and vertical accuracies of the measurements were estimated to be 0.5 cm and 0.5 mm. respectively.
3.1.3 Models
The models used in these experiments were piles with cylindrical cross-sections. The pile diameters were 0.114 in (4.5 in), 0.305 mn (12 in) and 0.92 mn (36 in) with lengths that exceeded the water depth. They were attached to the floor of the flume and given lateral support near the top by a bridge that spanned the width of the flume above the water.
The 0.92 mn (3 ft) diameter pile was 5.5 mn (18 ft) high. It had two Plexiglas windows fitted for scour visualization at angles of 45' from the front of the pile (Fig. 3. 10). To prevent the pile from distorting in shape, steel channels were attached to the walls inside of the pier. Measuring tapes were glued to the inside faces of the piles at locations where they could be seen by the inside video cameras. The 4.5 in and 12 in piles were constructed of Plexiglas. Both were 3.3 5 mn (11 ft) in length.




0.92 m (36 in) diameter pipe
Aluminum
carrier
Waterproof case with cameras
Figure 3.10 Cross-section of the 0.92m (36 in) pier
The rationale behind the pile diameter used in the experiments is as follows. The
0.92 m diameter was the largest standard diameter that could be used in the 6.1 m wide flume without creating significant contraction scour. Even this diameter exceeded the "rule of thumb" limit of 10% of the flume width. The second factor used in sizing the piles was the need to maintain the same D50/b ratio using different values of D50 and b. At the time that the piles were being designed, the uniform diameter sand sizes that were available were 0.20 mm and 0.65 mm. This would have produced D50/b ratios as shown in Table 3.1.
Table 3.1 Table with values of (-log (D50/b)) before sand availability D50 (mm)
b (in) 0.20 0.65
0.920 3.66 3.15
0.305 3.18 2.67
0.114 2.76 2.24




By the time the sand was purchased, the available uniform sand sizes changed to
0.22 mm and 0.80 mm. This resulted in D50/b ratios as shown in Table 3.2. Even though these ratios were not as close as planned, they were sufficient to test the dependence of equilibrium local scour depth on the parameter D50/b.
Table 3.2 Table with values of (-log (D5ofb)) for the piles and sediment used in the tests
D5o (mm)
b (in) 0.22 0.80
0.920 3.62 3.06
0.305 3.14 2.58
0.114 2.71 21
3.1.4 Sediment
Two sand sizes, 0.22 mm and 0.8 mm, were used in these experiments. Experiments with all three piles were performed with each of the two sediments. Near uniform sediment diameters were used, since (under clearwater conditions) the greatest scour depths occur in uniform diameter sediments. The sand was purchased from a vendor in Rhode Island that had a system for producing near uniform diameter sand.
The grain size distributions for the two sand sizes are shown in Figures 3.11 and
3.12. Their properties are summarized as follows: Sand No. 1
D50 '=0.22 mm
- =1.51
Mineral content = Quartz Mass density = 2650 k g/in3




Sand No. 2 D50 = 0.80 mm
F 8= -1.29
Mineral content = Quartz Mass density = 2650 kg/m3

100
806040-

0.01

D84 = 0.32 mm

D50 = 0.22 nim

20 -[ D16 = 0.14 mm

I I I I I 11I1I
0.1
diameter (mm)

I I I I I1 I1I I
1

Figure 3.11 Gradation Curve for Sand No. 1 (D50 = 0.22 mm)




40
100
D84 = 1.07 mm
80
60
Dso= 0.80 mm
40
20- D16=0.64mm
0
0.1 1 10
diameter (mm) Figure 3.12 Gradation Curve for Sand No. 2 (D50 = 0.80 mm)




CHAPTER 4
EXPERIMENTAL DATA REDUCTION AND ANALYSIS
This chapter contains the results from the experiments performed at the USGS-BRD Laboratory in Turners' Falls, Massachusetts, as part of the work for this thesis. The techniques and procedures used in performing these experiments and in reducing and analyzing the data are also included.
4.1 Experimental Procedure
The sediment, flow and structure parameters used in the experiments are summarized at Table 4.1 below.

Table 4.1 Parameters for the experiments conducted
Experiment No _D50 (mm) b (in) yo (in) U (mis) Uc (mis) U/lJc
1 0.22 0.114 1.22 0.300 0.333 0.90
2 0.22 0.305 1.22 0.300 0.333 0.90
3 0.22 0.92 2.29 0.320 0.355 0.90
4 0.80 0.92 2.29 0.447 0.497 0.90
5 0.80 0.92 0.90 0.403 0.448 0.90
6 0.80 0.305 1.22 0.414 0.460 0.90
7 0.80 0.114 1.22 0.414 0.460 0.90

To assume consistent results, a series of procedural steps were developed for the
data collection. The procedures are divided into a) the pre-test, b) during test, and c) posttest steps.




Before scour tests could be performed in the USGS-BRD flume, the bed had to be prepared. First the gravel was put in place. Dividers in the flume made this task easier. The next step was to place filter material on top of the gravel to separate it from the test sediment. The following step was to install the structure. Next the test sediment was placed on top of the gravel and in the test section. The sediment was compacted every 20 to 30 cm with a diesel driven mechanical compactor and hand tampers in the area near the structure. The bed was then leveled. An observation platform that spanned the width of the flume at the test section was mounted in the flume. The platform could be moved vertically to accommodate the range of water depths used in the experiments. The next step was to install and test the data collection equipment. The flume was then filled with water up to the level of the weir. Care was taken so as not to disturb the bed or initiate scour at the test structure. The water was then allowed to stand at this level, until the air trapped in the sediment was released. This ranged from 4 to 10 hours.
The experiment was started by opening the gates until the desired water level and flow velocity were reached. The water level and velocity were checked throughout the experiment and minor adjustments were made when necessary. The speed of the video camera traversing mechanism was also adjusted during the experiment to account for the changing rate of scour.
When no scour depth changes were observed for approximately 24 hours, the
experiment was terminated and the flume drained. The procedure took two to three hours. Pictures of the scour hole were taken from six positions around the pile. The scour hole was then point gauged and the structure was removed. At the end of the tests with the first sediment, the test sand was loaded into 0.76 in 3 (1.0 yd 3) polypropylene bags and




removed from the flume. The second sand was then placed in the flume using the same procedure as for the first sand.
4.2 Data Reduction
The quantities measured during these experiments were water temperature, water elevation, flow velocity and scour depth. The scour depth was measured using two different instruments during the test (acoustic and video) and a third method was used at the end of each test after the water was drained from the flume (point gauge).
The data for temperature and water elevation were written to a file on the hard drive of a personal computer (PC) used for data collection. At the end of each experiment, each of the three data sets were averaged over the time span of the test.
The data from the two velocity meters were also written to the hard drive on the
same PC. The two data sets were averaged individually over the time duration of the tests. The average from the individual gauges were then averaged to obtain the value associated with that experiment. An impeller velocity meter (Ott meter) was used to check the electromagnetic meters.
The video data were stored on one or more videocassettes for each experiment. After each experiment, the video tapes were viewed and the scour depth versus time was recorded.
The acoustic transducer data were written to a file on the hard drive on a second PC. The data collected had to be filtered in order to remove those signals that did not correspond to scour hole depth. These were caused by acoustic reflection from suspended sediment and other particles in the flow and zero readings when the return signal was not




detected. The filtering was accomplished with the help of a computer program called SMSO, which allowed the data to be displayed and edited graphically. The acoustic transducer ran continuously throughout the experiment and ten seconds of data was sampled and recorded every ten minutes.
After the test was completed and the flume was drained, the entire scour hole was surveyed with a point gauge. The (x, y) position of the tip was recorded along with the voltage output from a string potentiometer, which was proportional to the vertical positions of the gauge. The initial position of the bed was established by the initial tape reading from the video cameras inside the pile. Then the voltage readings were converted into distances from the undisturbed bed to the elevation of the scour hole at each horizontal (x, y) position. The origin of the coordinate system was located at the center of the pile and the initial, undisturbed bed. The survey extended to the flat portion of the bed beyond the scour hole.
4.3 Processed Data Results
The processed data are presented in summary tables and graphs. A table in Appendix C gives the summary of all the experiments conducted along with graphs showing the scour depth versus time for both the video and acoustic transducers (when both are available).
Contour plots of the equilibrium scour holes for all seven experiments are presented on Figures 4.1 to 4.7. Equilibrium scour profiles inline and normal to the flow for all seven experiments are given in Figures 4.8 to 4.14.




Z (in)
-1
0
-1
-2

-20 -10 0 10 20 30
X (in)
Figure 4.1 Elevation contour plot of the equilibrium scour hole for Experiment No.1
(b = 0.114 m, D50 = 0.22 mm, Yo = 0.186 m and U = 0.290 m/s)
50-!:!::
50
Z (in) 4 O
30- O0
-5 0
2 20- 0
-0 -0-9 0
-1
-4 -1 o
-6-30 -20 -10 0 10 20 30 40 50 60 70
X (in)
Figure 4.2 Elevation contour plot of the equilibrium scour hole for Experiment No.2
-8(b = 0.305 m, D = 0.22 mm, o = 0.190 m and U = 0.305 m/s)
T-9 -0
-10 -0
-11 -50
-30 -20 -10 0 10 20 3'0 40 5'0 6'0 70 X (in)
Figure 4.2 Elevation contour plot of the equilibrium scour hole for Experiment No.2
(b = 0.305 m, D50 = 0.22 mm, yo = 0.190 m and U = 0.305 m/s)




Z (in) 40
5
3 200 0
-3
-5 -20
-7
-9 -40. .........
-13 -60
-14
-15
-o -o -Io 6 20 40 X (in)
Figure 4.3 Elevation contour plot of the equilibrium scour hole for Experiment No.3
(b = 0.920 m, D50so = 0.22 mm, Yo = 2.268 m and U = 0.325 m/s)

C

8

0 -60 -40 -20

0 20 40 60
X(in)

Figure 4.4 Elevation contour plot of the equilibrium scour hole for Experiment No.4
(b = 0.920 m, D50 = 0.80 mm, Yo = 2.402 m and U = 0.454 m/s)

Z (in)
2 -2
-6
-10 -14 -18
-22
-26 -30
-34
-37




Z (in)
6 2 -2
-6
-1
-1z
-2

X (in)

Figure 4.5 Elevation contour plot of the equilibrium scour hole for Experiment No.5
(b = 0.920 m, D50 = 0.80 mm, Yo = 0.866 m and U = 0.335 m/s)

Z (in) H6
A

10 2( X (in)

Figure 4.6 Elevation contour plot of the equilibrium scour hole for Experiment No.6
(b = 0.305 m, D50 = 0.80 mm, Yo = 1.305 m and U = 0.381 m/s)




48
Z(in) 030
2
20
0
31 10
-2 z
-3
-5 -20
-6
--6 -30-7
-8 -40-8
-fo 6 1'0 20 30 40 50 X(in)
Figure 4.7 Elevation contour plot of the equilibrium scour hole for Experiment No.7
(b = 0.114 m, D50so = 0.80 mm, yo = 1.280 m and U = 0.388 m/s)




108
6
4
2
0
-2
-4 -

-4 -~

-30 -20I
-30 -20

a) Inline profile

10
8
6
4
2
0
-2
-4

--I-

'-30 -20
-30 -20

b) Normal profile
Figure 4.8 Equilibrium profiles of scour hole for Experiment No. 1
(b = 0.114 m, D50 = 0.22 mm, Yo = 0.186 m and U = 0.290 m/s)
a) Inline profile, and b) Normal profile

Flow
--------------

-10

0

10
X (in)

20

30I 30

' I40 40

Flow
0

-10I
-10

' I
10

' I
0
Y (in)

' I
20

'30 30




Flow

-40 -30 -20 -10 0 10 20 30 40 50 60 70 X (in)
a) Inline profile

Flow
0

0 -4- -

-60 -40 -20 0 20 40 60
Y(in)
b) Normal profile
Figure 4.9 Equilibrium profiles of scour hole for Experiment No.2
(b = 0.305 m, D50 = 0.22 mm, Yo = 0.190 m and U = 0.305 m/s)
a) Inline profile, and b) Normal profile




Flow

-70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 X (in)
a) Inline profile

-80 -60 -40 -20 0
Y (in)

20 40 60 80

b) Normal profile
Figure 4.10 Equilibrium profiles of scour hole for Experiment No.3
(b = 0.920 m, D50 = 0.22 mm, Yo = 2.268 m and U = 0.325 m/s)
a) Inline profile, and b) Normal profile




-80 -60 -40 -20 0 20 40 60 80
X (in)

a) Inline profile

-80 -60 -40 -20 0
Y (in)

20 40 60 80

b) Normal profile
Figure 4.11 Equilibrium profiles of scour hole for Experiment No.4
(b = 0.920 m, D50 = 0.80 mm, Yo = 2.402 m and U = 0.454 m/s)
a) Inline profile, and b) Normal profile




-80 -60 -40 -20 0 20 40 60 80
X (in)
a) Inline profile

-80 -60 -40 -20 0
Y (in)

20 40 60 80

b) Normal profile
Figure 4.12 Equilibrium profiles of scour hole for Experiment No.5
(b = 0.920 m, D50 = 0.80 mm, Yo = 0.866 m and U = 0.335 m/s)
a) Inline profile, and b) Normal profile




-30 -20 -10 0 10 20 30 40
X(in)

50 60

a) Inline profile

-50 -40 -30 -20 -10 0 10 20 30 40 50 Y (in)
b) Normal profile
Figure 4.13 Equilibrium profiles of scour hole for Experiment No.6
(b = 0.305 m, D50 = 0.80 mm, Yo = 1.305 m and U = 0.381 m/s)
a) Inline profile, and b) Normal profile




-20 0 20 40
X (in)

a) Inline profile

10 8
6
4
2
N 0
-2
-4
-6
-8
-5

Flow
0

I I I I I I I I
50 -40 -30 -20 -10

I I I I I I I
10 20 30 40 50

Y (in)

b) Normal profile
Figure 4.14 Equilibrium profiles of scour hole for Experiment No.7
(b = 0.114 m, D50 = 0.80 mm, yo = 1.280 m and U = 0.388 m/s)
a) Inline profile, and b) Normal profile

I

--------------

------------




4.4 Discussion of Results
The most unique aspects of the local scour experiments conducted during the work of this thesis have to do with the size of the structure tested and the duration of the tests. The 0.92 m (36 in) diameter pile is one of the largest, tested under controlled steady flow conditions. Any questions regarding the equilibrium depths were eliminated by continuing the tests until no measurable change in the scour hole was observed.
Several interesting observations were made regarding the scour hole at the large diameter piles. The location of the deepest point in the hole was different from that for the smaller piles. For the 0.114 m (4.5 in) and 0.305 m (12 in) diameter piles, the equilibrium scour hole was more uniform in depth from the side to the front (upstream edge) with the deepest point being directly in front of the pile. The deepest point in the scour hole at the 0.92 m pile was between 45' and 60' from the front. There are several possible explanations for this. One might be the fact that the slope of the pressure distribution along the circumference of the pile is smaller for large diameter piles than for small diameter piles. Another possible reason is that the effect of the horseshoe vortex seems to be diminished for the large piles. The scour holes from the accelerated now do not extend to the front of the large structure, thus the horseshoe vortex is deprived of the energy, caused by flow separation at the upstream edge of the scour hole.
Note that there was a slight asymmetry of the scour hole (see for example Figure 4.11). This is believed to be due to the slightly higher velocity on the west side of the flume. Flow profiles for the 1.22 m (4 ft) and 2.44 m (8 ft) water depths that show this asymmetry are given in Appendix B.




Ripples in the test section for the first two experiments can be also observed (Figures
4.1 and 4.2). The reasons for their formation are various. The sand, used in these experiments, was very fine (0.22 min), and ripples are common for sediments with 1)50:!
0.6 mm. Another reason is that those experiments were conducted at conditions very close to live-bed conditions, so there may have been brief periods of time, when the flow exceeded the critical value, U,
The other reason is the presence of a big sand dune, which did not affect the
formation of the scour holes, but helped initiate the ripples. This sand dune was formed initially near the flow straightener due to velocities greater than Uc. The flow straightener had an opening of 25% of the total cross section, so the velocities were up to four times greater than the velocity downstream. Those conditions formed a sand dune that could travel downstream but its speed was very small and it did not affect any of the results. This problem was later corrected by substituting gravel for sand just downstream of the flow straightener.




CHAPTER 5
COMPARISON OF LOCAL SCOUR PREDICTION EQUATIONS
5.1 Scour Prediction Equations
Over the past 40 years, numerous studies have been conducted and many equations have been developed to predict local equilibrium scour depth. Most of these equations were based on laboratory data. In some cases, limited field data was also used. Due to the complexity of the processes involved in local scour and the large number of parameters needed to describe these processes, the predictive equations differ dramatically. In some cases, the data on which these empirical equations are based were not published. Fourteen of the more commonly referred to equations are evaluated and compared in this chapter, using two data sets, one for clearwater and one for live-bed scour conditions. The clearwater data set includes the data obtained as part of the work for this thesis.
Perhaps the most commonly used scour prediction equation in the United States is the so-called Colorado State University (CSU) equation. It is the recommended equation in the U.S. Federal Highway Administration (FHWA) Hydraulic Engineering Circular No. 18 (HEC-18) (1995). This equation is
0 b.065
dse =2.0yoK, K2 r0.43, (5.1)
where
dse is the equilibrium scour depth,




Yo is the flow depth upstream of the structure,
K1 is a correction factor for pier nose shape,
K2 is a correction factor for angle of attack flow,
b is the pier width and
U
Fr = Froude number
Values from K1 and K2 can be obtained from HEC-18 and are discussed in Chapter 2. This equation was developed by fitting laboratory data and is recommended for both livebed and clearwater conditions. In HEC-18, limiting values for the scour depth normalized by the pier diameter, dse/b, are recommended as follows: dse/b = 2.4 for Fr < 0.8 and 3.0 for Fr > 0.8.
Melville (1997) developed a scour equation based on various laboratory experiments of the form:
dse =KIKdKyDKaKS, (5.2)
where
U
->1
K, = flow intensity factor = for
U U <
b
10b>25
1.0 D50
Kd = sediment-size factor = for
0.571og 2.24 b- <25 D50) D50




b
-<0.7
2.4b Yo
KyD = flow depth-pier width factor = J2-y0b for 0.7 < b <5 KyDo YO
4.5yo b
->5
Yo
K = pier-alignment factor, and
K, = pier-shape factor.
Values for K, and Ks can be obtained from tables given in Melville and Sutherland (1988).
Hancu (1971) proposed the following scour prediction equation
dse = 2.42b 2 1 gb (5.3)
seUc gb for 0.05 < _< 0.6 where U, is calculated by the equation
gb
0.2
Uc = 1.2 (s-1)gD5o Yo) .
Dso
Equation (5.3) does not apply for values of U less than 0.5.
UC
Laursen and Toch (1956) developed design scour depth curves that were later described by Neill (1964) in equation form as dse =1.35bo7y3. (5.4)
Shen et al. (1966) used laboratory data and limited field data to develop the following clearwater scour prediction equation,




dse = 0.000223 ReO619, (5.5)
Ub
where Rep = Ub For live-bed conditions, Equation (5.5) was found to be too
V
conservative, so Shen (1971) recommended using the Larras (1963) equation, dse = 1.05bo75. (5.6)
Breusers et al. (1977) developed the following equation (which is similar to Equation (5.3) (Hancu, 1971)) dse = b f KK2 tanh YO, (5.7)
where
U
f =0 for -<0.5,
Uc
U U
f=2 -1 for 0.5<- U 1.0,
Uc Uc
U
f=1 for ->1.0,
Uc
and KI and K2 are the same as in Equation (5.1).
Jain and Fischer (1979) developed a set of equations based on their laboratory experiments. For Fr Frc > 0.2
0.5
dse = 2b(Fr Frc )0.25 (5.8)
(b
where Frc = critical Froude number Uc
- '

For Fr-Frc <0




dse = 1.85bFr025 0. (5.9)
For 0 < Fr -Fr, < 0.2, the larger of the two scour depths computed from Equations (5.8) and (5.9) are to be used.
Garde et al. (1993) developed a clearwater scour equation based on various laboratory experiments
d,, b ,0.75,, 0 .16[ 0.4 ds -0.66 b D __u V
D50 D50) D50) L (s-)gD5oj (
where Vc is the velocity for the initialization of sediment movement at the structure, which is about 0.4-0.5 U, and s is the relative sediment density. The equation given to calculate Vc is
V2 1.2( b )-0.11( Y 0.16
(s -1)gD50 1D50J D50)
Another scour prediction equation was developed by Chitale (1962), using very limited laboratory data,
- = -0.51 + 6.65Fr 5.49Fr2. (5.11)
Yo
Based on data from previous investigations for local scour at spur dikes, Ahmad
(1953) concluded that scour does not depend on grain size for the range of his data (0.1 to
0.7 mm). He stated that this might not be accurate for the entire range of the sediment sizes. Ahmad (1962) reanalyzed the work of Laursen (1962) with a special emphasis on scour in sand beds in West Pakistan and developed the following equation: dse = Kq2/3 YO, (5.12)




where K is assumed from model studies conducted by Ahmad (1962) to vary from 1.7 to
2.0 for piers and abutments. A value of 1.85 was used in the calculations made in this thesis. Also q is the discharge per unit width of the channel and all units are in English.
Inglis (1949) performed experiments on model bridge piers and developed an equation from his data. Blench (1962) reduced Inglis' (1949) formula to dse 1.8b025 qo.5 Yo 0-Y, (5.13)
where all units are in English.
Gao et al. (1992) presented empirical equations for clearwater and live bed local
scour that were used by highway and railway engineers in China for more than 20 years. The equations for clearwater and live-bed conditions are dse = 0.78Kb06 y015 -007 UUc (5.14)
Uc -U
and dse= 0.65K b 6y15D-07 U J (5.15)
respectively. K, is a coefficient for pier shape and has the values of 1.0 for cylinders, 0.8 for round-nosed piers and 0.66 for sharp-nosed piers. The critical depth average velocity, UC, the velocity for initialization of scour at the pier, Uc and the exponent c in Equation (5.15) are calculated using
U= YO 0.14 [1 76(s-1)Do +6.05E-17 D10+ 0.5,
u; = 0.645- D5 .5 and




C =( 9 "35+2'23 gD50
Froehlich (1988) compiled field measurements of local scour at bridge piers from reports of several investigations and developed the equation dse = 0.320~b Fr 0.2 0.46(b 08 (5.16)
where 4 is a pier shape factor and has the value of 1.3 for square-nosed piers, 1.0 for round-nosed piers, and 0.7 for sharp-nosed piers.
Sheppard et al. (1995) at the University of Florida developed a clearwater scour prediction equation for cylindrical piers based on laboratory data,
(5.17)
= 4.8 1tanh C 2.- 1- 2 .87 -U + 1.43 U ] log D exp { 0.18[- iog( -0 )]2.09
b)~ v _U' ( U') I ]
Based on his limited live-bed dataand data from other researchers, Sheppard (1997) concluded that a second peak in the normalized scour depth (dse/b) versus normalized velocity (U/Uj) plot occurred in the live-bed scour range and had a value of approximately 2.1 (for yo/b > 2.5). The value of U/U, where the live-bed peak occurs, is believed to coinside with the conditions, where the bed flattens. That condition has been shown to be dependent on the Froude number and the velocity normalized by the sediment fall velocity (Snamenskaya, 1969). For design purposes Sheppard (1997) recommended connecting the clearwater peak to the live-bed peak with a straight line as shown in Figure 5.1. For velocities greater than the value for the live-bed peak, the equilibrium scour depth is assumed to be the value at the live-bed peak. For values of




yo/b < 2.5, the height of the live-bed peak is computed using the equation dsY
dse = 2.1tanh bo bb
independant of Do/b
2.1 ---- ---- --

depends on Dso0/b

0.4- 0.5 1.0 (U/U)1bp
U/UC
Figure 5.1 Local scour depth dependence on velocity,
as proposed by Sheppard (1997)

5.2 Compilation of Local Scour Data

The clearwater and live-bed data sets used in this analysis were compiled from a number of sources. These include Ettema (1980), Chiew (1984), Sheppard et al. (1995),




Chabert and Engeldinger (1956), Jones (1997), Melville and Chiew (1999), Graf (1995), Shen et al. (1966), and the data obtained as part of the work for this thesis.
The data were divided into two categories, clearwater and live bed. This was done
for several reasons. The first reason is that the local scour processes are different for these two categories. In the clearwater region, there is sediment movement only around the structure, while in live-bed conditions there is movement over the entire bed. That may result even at the reduction of the scour hole for velocities just over the critical value, Uc, and is based on observations by Ettema (1980), Chiew (1984) and others. Another reason is that many of the scour prediction equations were based on curve fits to just clearwater data (Garde 1992, Sheppard et al. 1995), while others used both clearwater and live-bed data.
The criteria used in selecting the data used in this analysis were as follows. The author had to present sufficient information about the parameters of the experiment, so that the equations used in this analysis could be evaluated. In addition the duration of the experiments had to be sufficiently long that equilibrium (or near equilibrium) scour depths were achieved. The time required to reach equilibrium is not well understood, but it is known to increase with the size of the structure and (for clearwater scour) the velocity. For the purpose of this analysis a minimum of 17 hours was chosen. Only scour data for structures with a circular cross section were used, because the coefficients for other shapes of structures vary for the different equations. Another criterion was that the test sediment had to be relatively uniform in grain size. The data chosen had a gradation a less than 1.6. Using these criteria, 215 clearwater and 244 live-bed data points were compiled.




The scour depths were computed for the conditions of the test using Equations (5.1) (5.17). The value for critical depth average velocity, U", was calculated using Shields' diagram, except where stated otherwise, like for Hancu (1971), Melville (1984), HEC-18 (1995) and Gao et al. (1992). For the data where temperature was not reported, a value of 15'C was assumed. Little or no data on bedforms was available for most of the data. In the computation of U,, a relative roughness r (k/D50) was assumed to be five. For Breusers et al. (1977) and Hancu (1971), scour depths were assumed to be zero for U/u, < 0.5 and for U/UC < 0.45 for Sheppard et al. (1995). Also for Hancu (1971), some data points could not be considered due to limitations on the equation by the author.
5.3 Comparative Analysis
Predictions of the clearwater data will be discussed first. The Jain and Fischer
(1979), Laursen and Toch (1956), Gao et al. (1992) and Melville (1997) equations do a good job of predicting clearwater scour depths for smaller diameter piles but overpredict as the diameter increases. The Chitale (1962) and Ahmad (1953) equations, which depend on a limited number of parameters, overpredict most of the data, as expected. The Hancu (1971) equation underpredicts (as much as 95%) for the majority of the data points where the equation can be applied. The Breusers et al. (1977), Froehlich (1988), Garde et al. (1993), Inglis-Blench (1962) and Shen (1966) equations underpredict most of the data. The best predictions were by the HEC-18 (1995) and Sheppard et al. (1995) equations with an average overprediction of 31% and 16% respectively.
When the same equations (with the exception of Garde et al. (1992)) are used to predict the 244 live-bed scour depths, some differences are observed. The Jain and




Fischer (1979), Gao et al. (1992) and Melville (1997) equations still overpredict as the pier diameter increases. The Laursen and Toch (1956) equation gives better predictions (53% as opposed to 104% for clearwater scour). The Chitale (1962) equation still overpredicts (up to 690%) and the Ahmad (1953) equation underpredicts most of the live-bed data. The Hancu (1971) equation, which cannot be applied to all the data, still underpredicts by as much as 92%. The Froehlich (1988) and Inglis-Blench (1962) equations underpredict for the live-bed data, as they did for clearwater conditions. The Breusers et al. (1977) and Shen (1966) equations overpredict for most of the data. Again the best predictive equations are the HEC-18 (1995) and Sheppard et al. (1995) equations with mean overpredictions of 26% and 12% respectively. Both equations appear to be more accurate for live-bed conditions.
The mean of the absolute values of the predictions and the range of the predictions for all of the equations are shown in line plots of the ratio of measured to calculated scour depths are given in Figures 5.2 and 5.3 for the clearwater, and live-bed data sets respectively. The mean of the absolute value of the predictions for every equation is represented with an asterisk along the range of the prediction line. The line of absolute agreement is the dotted line passing from 1.0. The narrower the range and the closer the mean of the absolute value is to the line of absolute agreement, the better is the equation. Scatter plots of calculated versus measured scour depths for all the equations are given in Figures 5.4 5.17.




C
Froelich (1988)Gao et al. (1992)Inglis-Blench (1962)Ahmad (1953)Melville (1997)Garde et al. (1993)Chitale (1962)HEC-18 (1995)Jain & Fisher (1979)Breusers et al. (1977)Hancu (1971)Laursen & Toch (1956)Shen et al. (1966)Sheppard et al. (1995)-

comparison of 14 equations using 215 clearwater data

' fi

-4 -2 0 2 4 6 8
Ratio of calculated to measured scour
- Prediction Range Mean of Absolute Value of Scour Predictions
- Absolute Agreement Line

Figure 5.2 Comparison of equations for clearwater data

10
10

I




70
Comparison of 13 equations
using 244 live-bed data

Froelich (1988)Gao et al. (1992)Inglis-Blench (1962)Ahmad (1953)Melville (1997)Chitale (1962)HEC-18 (1995)Jain & Fisher (1979)Breusers et al. (1977)Hancu (1971)Laursen & Toch (1956)Shen et al. (1966)Sheppard et al. (1995)-

II~ II~
4~E
*

' I I I I '
-6 -4 -2 0 2 4 6 8 10
Ratio of calculated to measured scour
Prediction Range
a Mean of Absolute Value of Scour Predictions
- - - Absolute Agreement Line
Figure 5.3 Comparison of equations for live-bed data




(A) Garde et al. (1993)

Ettema (1980) Chiew (1984) UF/USGS Chabert & Engeldinger (1' Jones (1997) Melville & Chiew (1999)

0 0.3 0.6 0.9
measured scour (m)

1.2 1.5

(B) Ahmad (1953)

+ + + + + + + +
+

Ettema (1980) Chiew (1984) UF/USGS Chabert & Engeldinger (1956) Jones (1997) Melville & Chiew (1999)

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 measured scour (m)
Figure 5.4 Comparison of measured and calculated scour for clearwater data for
(A) Garde et al. (1993), and (B) Ahmad (1953) equations




1.5
1.2 -

F- 0.3
0 0.3

0.6

0.9

1.2

1.5

measured scour (m)
(B) Chitale (1962)

+ + + 2 + +

++ ++

Ettema (1980) Chiew (1984) UF/USGS Chabert & Engeldinger (1956) Jones (1997) Melville & Chiew (1999)

0 0.4 0.8 1.2 1.6 2 2.4
measured scour (m)

Figure 5.5 Comparison of measured and calculated scour for clearwater data for
(A) Breusers et al. (1977), and (B) Chitale (1962) equations

0.9
0.6-

0.3
0-

(A) Breusers et al. (1977)
,*
+ Ettema (1980)
O Chiew (1984)
A UF/USGS
A Chabert & Engeldinger (1956)
8 Jones (1997)
[] Melville & Chiew (1999)
-I- "k*




(A) Froehlich (1988)

0 0.3 0.6 0.9
measured scour (m)
(B) Gao et al. (1992)

1.2 1.5

Ettema (1980) Chiew (1984) UF/USGS Chabert & Engeldinger (1 Jones (1997) Melville & Chiew (1999)

0 0.3 0.6 0.9
measured scour (m)

1.2 1.5

Figure 5.6 Comparison of measured and calculated scour for clearwater data for
(A) Froehlich (1988), and (B) Gao et al. (1992) equations




1.5
1.2-

0.9
0.6-

0.3
0

0- I
0

(A) Hlancu (1971) + Ettema (1980)
O Chiew (1984)
* UF/USGS
A Chabert & Engeldinger (1956)
( Jones(1997)
1 Melville & Chiew (1999)

+
++
++ *
*

I I I I
0.3 0.6 0.9 1.2
measured scour (m)

' I
1.5

(B) HEC-18 (1995)

++ ++ + Ettema (1980)
+- + 0> Chiew(1984)
0.2 UF/USGS
A Chabert & Engeldinger (1956)
- e Jones (1997)
0- Melville & Chiew (1999)
0 I I I [
0 0.2 0.4 0.6 0.8 1
measured scour (m)
Figure 5.7 Comparison of measured and calculated scour for clearwater data for
(A) Hancu (1971), and (B) HEC-18 (1995) equations

+

f




1.2
0.9-

0.3

0.6

0.9

measured scour (m)
(B) Jain and Fischer (1979)

Ettema (1980) Chiew (1984) UF/USGS Chabert & Engeldinger (1956) Jones (1997) Melville & Chiew (1999)

0 0.3 0.6 0.9 1.2 1.5 1.8
measured scour (m)

Figure 5.8 Comparison of measured and calculated scour for clearwater data for
(A) Inglis-Blench (1962), and (B) Jain and Fischer (1979) equations

(A) Inglis-Blench (1962)
* *
+ Ettema (1980)
O Chiew (1984) A UF/USGS
-[+ A Chabert & Engeldinger (1956)
(D Jones (1997)
] Melville & Chiew (1999)

0.6
0.3 -

0
-0.3

1.2




(A) Laursen and Toch (1956)

2
1.6 -

* *

I I I I I

+ Ettema (1980)
O Chiew (1984)
* UF/USGS
A Chabert & Engeldinger (1956)
E Jones (1997)
] Melville & Chiew (1999)
1 I 1 I 1 I

I I I I
0 0.4 0.8 1.2
measured scour (m)

(B) Melville (1997)
**
*
*
4* + Ettema (1980)
0 Chiew (1984)
A UF/USGS
A Chabert & Engeldinger (1956)
e Jones (1997)
[] Melville & Chiew (1999)

I 0 I I
0 0.3 0.6

0.9 0.9

1.2 1.5 1.8 2.1 1.2 1.5 1.8 2.1

measured scour (m)

Figure 5.9 Comparison of measured and calculated scour for clearwater data for
(A) Laursen and Toch (1956), and (B) Melville (1997) equations

*

1.2
0.8-

0.4
0-

2.1
1.8
1.5
1.2
0.9
0.6
0.3 -

I

t




1.5
1.2-

I I
0 0.3

I I 1 1
0.6 0.9
measured scour (m)

1.2

(B) Sheppard et al. (1995)

Ettema (1980) Chiew (1984) UF/USGS Chabert & Engeldinger (1 Jones (1997)
Melville & Chiew (1999)

1.5

0 0.2 0.4 0.6 0.8 1
measured scour (m)
Figure 5.10 Comparison of measured and calculated scour for clearwater data for
(A) Shen et al. (1966), and (B) Sheppard et al. (1995) equations

(A) Shen et al. (1966)
,*
+ Ettema (1980)
O Chiew (1984)
A UF/USGS
A Chabert & Engeldinger (1956)
D Jones (1997)
] Melville & Chiew (1999)
++ ++ *

0.9
0.6-

0.3
0
0.8 -




(A) Ahmad (1953)

0 0.4 0.8 1.2
measured scour (m)

0.4 0.3
-o 0.2
0.1
0

(B) Breusers et al. (1977)

+ + A A& + +
+ +~i +

0 0.1 0.2 0.3 0.4
measured scour (m)

Figure 5.11 Comparison of measured and calculated scour for live-bed data for
(A) Ahmad (1953), and (B) Breusers et al. (1977) equations




(A) Chitale (1962)

0.8 0.6
- 0.4
0.2
0

0 0.2 0.4 0.6 0.8
measured scour (m)

(B) Froehlich (1988)
+ Shen et al. (1966)
+ Chiew(1984)
A Chabert & Engeldinger (1956)
* Graf(1995)
Sheppard (1995)

Q Q
*

0 0.2
measured scour (m)

Figure 5.12 Comparison of measured and calculated scour for live-bed data for
(A) Chitale (1962), and (B) Froehlich (1988) equations

A A AQ
A
A A A

0.4
a
S 0.20




80
(A) Gao et al. (1992)

0.8 0.6
E
S0.4
0.2
0

0 0.2 0.4 0.6 0.8
measured scour (m)

(B) Hancu (1971) + Shen et al. (1966)
+ Chiew (1984)
A Chabert & Engeldinger (1956

Sheppard (1995)

AA A A AA
A A A
A A *
AM A A AL A AA
44* AA A A
AA* A A A
A A A A~ +A + *

' I

0.1 0.:
measured scour (m)

0.3

Figure 5.13 Comparison of measured and calculated scour for live-bed data for
(A) Gao et al. (1992), and (B) Hancu (1971) equations

+ +
4 ++

0.3 -

0.2
0.1 -

i I




81
0.4 (A) HEC-18 (1995)
0.3
+ A
i+ A
A+
AA
Un +A -4p~+ A
0.2 +
* A +
0.1 A + Shenetal. (1966)
* 4A Chiew (1984)
A Chabert & Engeldinger (1956)
* Graf(1995)
9 Sheppard (1995)
0 -I r I
0 0.1 0.2 0.3 0.4
measured scour (m)
(B) Inglis-Blench (1962)
0.32
+ Shen et al. (1966)
Chiew (1984)
A Chabert & Engeldinger (1956)
Graf(1995) aSheppard (1995)
0.2
+ +
+A*_ A
/ +++ + +
0.1
0
0 0.1 0.2 0.3
measured scour (m)
Figure 5.14 Comparison of measured and calculated scour for live-bed data for
(A) HEC-18 (1995), and (B) Inglis-Blench (1962) equations




(A) Jain and Fischer (1979)

0.1
0
0.4
0.3
i
0.2
0
0
0.1
0

0 0.1 0.2 0.3 0.4 0.5
measured scour (m)

(B) Laursen and Toch (1956)

A
A *

0 0.1 0.2 0.3 0.4
measured scour (m)
Figure 5.15 Comparison of measured and calculated scour for live-bed data for
(A) Jain and Fischer (1979), and (B) Laursen and Toch (1956) equations




(A) Melville (1997)

0.6
S0.4
0. 0
0.3
S0.2 0
O
0.1
0.

0 0.1 0.2 0.3
measured scour (m)

0.4 0.5

(B) Shen et al. (1966)
+ ++ WOW1 k *A"
*
A AAA& A AAhKA AL

0 0.1 0.2 0.3
measured scour (m)

Figure 5.16 Comparison of measured and calculated scour for live-bed data for
(A) Melville (1997), and (B) Shen et al. (1966) equations

+A A AAI A
A+ + +
A




84
Sheppard et al. (1995)

0.4 0.3
0.2
0.1
0

A A

0 0.1 0.2 0.3 0.4
measured scour (m)
Figure 5.17 Comparison of measured and calculated scour
for live-bed data for Sheppard et al. (1995) equation