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Prediction of local scour depth near multiple pile structures

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Prediction of local scour depth near multiple pile structures
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UFLCOEL-94011
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Copps, Thomas Hohmann, 1966-
University of Florida -- Coastal and Oceanographic Engineering Dept
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English
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xi, 111 leaves : ill. ; 29 cm.

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Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF ( lcsh )
Coastal and Oceanographic Engineering thesis, M.E ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (M.E.)--University of Florida, 1994.
Bibliography:
Includes bibliographical references (leaves 109-110).
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Typescript.
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Vita.
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This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
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by Thomas Hohmann Copps.

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University of Florida
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UFL/COEL-94/011

PREDICTION OF LOCAL SCOUR DEPTH NEAR MULTIPLE PILE STRUCTURES by
Thomas Hohmann Copps Thesis

1994




PREDICTION OF LOCAL SCOUR DEPTH NEAR MULTIPLE PILE STRUCTURES
By
THOMAS HOHMANN COPPS

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING
UNIVERSITY OF FLORIDA

1994




ACKNOWLEDGMENTS
My most sincere gratitude is extended to my supervisory committee chairman, Dr. D. Max Sheppard. His continuous support and his insight have permitted this study to become a reality. My thanks also go out toward Dr. Daniel Hanes and Dr. Robert Thieke for serving on my supervisory committee. My appreciation also extends to Dr. Robert Dean for including me in many of his ongoing field studies.
Jim Joiner, Vernon Sparkman, Chuck Broward, Danny Brown, and the other members of the Coastal and Oceanographic Laboratory also deserve my thanks for their assistance. Also deserving my heartfelt appreciation are Kalish, Ben, Ashraf, Ash, Max, and many others who made the work enjoyable.
I am also grateful to Mr. Roberto Perez, P.E. and Mr. Rick Renna, P.E. of the Florida Department of Transportation, as well as Mr. Sterling Jones of the Federal Highway Administration, for their financial support and professional interest.
Many others deserve a hearty thank you for making long days seem short. My fellow coastals, including Paul, Ken, Eric, Chris, Mark, Al, Sue, Darwin, Eduardo, and Gaucho, were a team in classes and research. Additional gratitude goes out to Becky, Helen, Laura, and so many other people with gifts for brightening lives.
Finally, words cannot express my gratitude toward my mother and my sister for their patience and lifelong support.




TABLE OF CONTENTS
ACKN OW LED GEM EN TS .......................................................................................... ii
LIST OF TABLES ....................................................................................................... v
LIST OF FIGURES ..................................................................................................... vi
KEY TO SYM B OLS ................................................................................................... ix
ABSTRACT ................................................................................................................ xi
CH APTER 1 INTR ODUCTION ................................................................................ I
1. 1 Types of Scour ........................................................................................... 2
1.2 Current Approach Toward Predicting Scour ............................................... 4
1.3 Problem Approach ...................................................................................... 5
1.3.1 Areas of Study ............................................................................. 5
1.3.2 Problem Breakdown .................................................................... 7
CHAPTER 2 BACKGROUND AND LITERATURE SURVEY ............................... 10
2.1 Scour Related Hydrodynamics .................................................................. 10
2.2 Effects of Flow Qualities on Scour ........................................................... 13
2.3 Scour D ependence on Structure Shapes ................................................... 16
2.4 Effect of Sediment Characteristics on Scour ............................................ 19
2.5 Rate of Scour ........................................................................................... 22
CH APTER 3 EXPERIMENTAL APPROACH .......................................................... 25
3.1 Equipment ................................................................................................ 25
3. 1.1 Flume ......................................................................................... 26
3.1.1.1 Flow Control ............................................................... 27
3.1.2 M odels ....................................................................................... 28
3.1.3 Sediment .................................................................................... 31
3.2 Laboratory Experiments ........................................................................... 34
3.2.1 Preparation ................................................................................ 35
3.2.2 Test Procedure ........................................................................... 36
3.2.3 Profile M easurements ................................................................. 38
3.3 Required Tests ......................................................................................... 39
3.3.1 Category One Tests ................................................................... 40
3.3.2 Category Tw o Tests ................................................................... 42
3.3.3 Category Three Tests ................................................................. 44




CHAPTER 4 RESULTS AND DEVELOPMENT OF PREDICTIVE EQUATIONS.47
4.1 Scour Profiles .......................................................................................... 47
4. 1.1 Single Pile Profiles .................................................................... 48
4.1.2 M ulti le Pile Profiles ................................................................. 52
4.2 Single Pile Analysis ................................................................................... 63
4.3 Scour at N o Pile Cap Structures ............................................................... 66
4.3.1 Effective W idth .......................................................................... 68
4.3.2 Scour D epth A nalysis ................................................................ 74
4.4 Scour at Pile Cap Structures ..................................................................... 82
CH APTER 5 CON CLU SION S .................................................................................. 89
5.1 Applicability of R esults to Prototype Scale ............................................... 90
5. 1. 1 H ydraulic Effects ....................................................................... 91
5.1.2 Sedim ent Effects ........................................................................ 91
5.2 A pplying Equations .................................................................................. 93
5.2.1 Alternate Physical Conditions ..................................................... 93
5.3 Future Investigations ................................................................................ 95
5.3.1 Structure G eom etry ................................................................... 95
5.3.2 R ate of Scour ............................................................................. 96
APPENDIX A RATE OF SCOUR DEVELOPMENT ..................... : ........................... 98
APPEN D IX B EX PERIM EN TAL D ATA ............................................................... 105
REFEREN CE LIST .................................................................................................. 109
BIO GRAPI-11CAL SKETCH ..................................................................................... III
iv




LIST OF TABLES
3.1 Category One Tests ......................................................................................... 40
3.2 Category Tw o Tests ........................................................................................ 42
3.3 Category Three Tests ...................................................................................... 45
4.1 M easured and Predicted Circular Pile Scour D epths ........................................ 63
4.2 M easured and Predicted Square Pile Scour D epths .......................................... 64
B. 1 Results of Category One Tests ...................................................................... 106
B.2 Results of Category Tw o Tests ...................................................................... 107
B .3 Results of Category Three Tests .................................................................... 108




LIST OF FIGURES

2.1 Illustration of Horseshoe Vortex, Side View .................................................... 11
2.2 Illustration of Horseshoe Vortex, Top View .................................................... 12
2.3 Scour Depth Dependence on Mean Velocity (Other Parameters Constant) ....... 15
2.4 Illustration of Single Pile (Circular or Square) ................................................. 17
2.5 Scour Depth Dependence on Water Depth
(U/Uc, Other Param eters Constant) ................................................................. 17
2.6 Scour Dependence on Normalized Mean Grain Size
(H/D, U/Qc constant (Sheppard, 1994) ............................................................ 20
2.7 Armoring Effects on Maximum Scour Depth
D ata From B aker (19 8 6) ................................................................................. 22
2.8 Armoring Effects on Effective Critical Velocity
D ata From B aker (19 8 6) ................................................................................. 23
3.1 Upstream View of No Pile Cap Structure ........................................................ 28
3.2 Upstream View of Pile Cap Structure .............................................................. 29
3.3 Dimensions (in.) of Typical Pile Cap Model ................................................... 29
3.4 Pile Cap on 2 4X 5 Structure ............................................................................ 30
3.5 Gradation Curve for Section One Sand ............................................................ 32
3.6 Location of Sand Volumes in Test Section (Not To Scale) .............................. 33
4.1 Single Pile Scour in Shallow Flow, Front View (D=2.0 in., H=4.2 in.) ........... 47
4.2 Single Pile Scour in Shallow Flow, Side View (D=2.0 in., H=4.2 in.) ............. 48
4.3 Single Pile Scour in Deep Flow, Front View (D=2.0 in., H=8.5 in.) ................ 51
vi




4.4 Single Pile Scour in Deep Flow, Side View (D=2.0 in., H=8.5 in.) ............. 51
4.5 Single Pile Scour in Shallow Flow, Front View (D=1.25 in., H=4.2 in.) ......... 52
4.6 Single Pile Scour in Shallow Flow, Side View (D=1.25 in., H=4.2 in.) ..... 52 4.7 Single Pile Scour in Deep Flow, Front View (D=1.25 in., H=8.5 in.) ....... 53
4.8 Single Pile Scour in Deep Flow, Side View (D=1.25 in., H=8.5 in.) ........ 53
4.9 Scour Hole at 2 3X4 Arrangement, Front View (a/D=3.0, H=4.2 in.) ....... 54
4.10 Scour Hole at 2 3X4 Arrangement, Side View (a/D=3.0, H=4.2 in.) ........ 55
4.11 Scour Holes at 3X8 Arrangement, Front View (a/D=3.0, H=8.5 in.) ........... 56
4.12 Scour Holes at 3X8 Arrangement, Side View (a/D=3.0, H=8.5 in.) ............. 56
4.13 Scour Hole at 3X8 Arrangement, Front View (a/D=1.0, H=8.5 in.) ........ 57
4.14 Scour Hole at 3X8 Arrangement, Side View (a/D=1.0, H=8.5 in.) ............... 58
4.15 Scour Hole at 5X8 Arrangement in Shallow Flow, Front View
(a/D =3.0, H =4.2 in.) .................................................................................... 59
4.16 Scour Hole at 5X8 Arrangement in Shallow Flow, Side View
(a/D =3.0, H =4.2 in.) .................................................................................... 59
4.17 Scour Hole at 5X8 Arrangement in Deep Flow, Front View
(a/D =3.0, H =8.5 in.) .................................................................................... 60
4.18 Scour Hole at 5X8 Arrangement in Deep Flow, Side View
(a/D =3.0, H =8.5 in.) .................................................................................... 60
4.19 Scour Hole at 7X8 Arrangement, Front View
(a/D =3.0, H =8.5 in.) .................................................................................... 61
4.20 Scour Hole at 7X8 Arrangement, Side View
(a/D =3.0, H =8.5 in.) .................................................................................... 61




4.21 Scour Depths at No Pile Cap Models in Deep Flow ......................................... 68
4.22 Scour Depths at No Pile Cap Models in Two Flow Depths .............................. 69
4.23 Scour Depths at All No Pile Cap Models Tested .............................................. 71
4.24 Normalized Scour Depths at No Pile Cap Structures ....................................... 74
4.25 No Pile Cap Scour Depths and Relative Widths ............................................... 75
4.26 Scour at n--5 Structures, Fit To Equation 4.7 .................................................. 77
4.27 No Pile Scour Depths Fit to Equation 4.15 ...................................................... 78
4.28 Relative W idths and Resulting C, Values ......................................................... 79
4.29 No Pile Cap Scour Data Fit to Equation 4.17 .................................................. 80
4.30 Multiple Pile Scour Depths and Pile Cap Locations ......................................... 83
4.31 Normalized Scour Depths and Pile Cap Locations
(Pile Cap Bottom At or Above Initial Bed Level) ............................................. 84
4.31 Normalized Scour Depths and Pile Cap Locations ........................................... 86
5.1 Scour Depth Dependence on Mean Grain Size ................................................. 91
A. 1 Scour Development for Single Piles
(Circular and Square, D=2.0 in., H=4.2 in.) ..................................................... 99
A.2 Scour Depth at Front Piles of 5X8 No Pile Cap Structure (H=4.2 in.) ............ 100
A.3 Scour Depth at Side Piles of 5X8 No Pile Cap Structure (H=4.2 in.) .............. 101
A.4 Scour Depth 5X8 No Pile Cap Structure (H=8.5 in.) ..................................... 103
A.5 Scour Depth 5X8 Structure, h2 =2.69 in. (H=8.5 in.) ..................................... 103
A.6 Scour Depth 5X8 Structure, h, =0.00 in. (H=8.5 in.) ..................................... 104




KEY TO SYMBOLS
a pile spacing (centerline to centerline)
C aspect ratio coefficient
Cf discharge coefficient
C. pile shape scour depth coefficient
C,5' circular pile scour depth estimate ratio
Cs' square pile scour depth estimate ratio
C1 flow depth coefficient
C2 flow depth and scour depth attenuation
D pile width (diameter)
de scour depth near a circular pile
d. scour depth near a square pile
d.npc scour depth near a no pile cap structure
d.pc scour depth near a pile cap structure
d..-n measured 7 hr. circular pile scour depth
de.at extrapolated 26 hr. circular pile scour depth
d.7 n measured 7 hr. square pile scour depth
d..at extrapolated 26 hr. square pile scour depth
D50 mean grain diameter
D50T mean grain diameter for Section Two Top sand




D1) D2, DP, D4
g
H
H*
K1, K2, K3
m
n
Q
s
U UC
x
Y
Z
CY
C'2
0

effective width of multiple pile structure sediment grain size coefficients acceleration of gravity flow depth
pile cap level above undisturbed bed head level
flow velocity coefficients number of pile columns downstream number of pile rows across the flow discharge
pile spacing coefficient mean flow velocity critical mean flow velocity distance downstream from front of structure distance to right of structure's left comer distance below undisturbed sediment level sediment variation value sediment variation value of Section Two Top sand sediment variation value, alternate value weir notch angle




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 Engineering PREDICTION OF LOCAL SCOUR DEPTH NEAR MULTIPLE PILE STRUCTURES By
Thomas Hohmann Copps
August 1994
Chairperson: Dr. D. Max Sheppard Major Department: Coastal and Oceanographic Engineering
A method of predicting the maximum equilibrium scour depth near multiple pile structures is developed. The equations developed for this purpose are based on a series of laboratory scour experiments in which attempts were made to achieve scour depths that represent both the maximum potential scour as well as the equilibrium depths. The approach makes use of the well studied problem of local scour near a single cylinder, thereby accounting for the sediment and environmental related parameters. Building on this theory, the predictive equations developed in this study account for the scour dependence on the geometry of increasingly complex structures. Scour at the following structures is studied: a single square pile, an arrangement of multiple square piles, and such an arrangement complete with a pile cap emergent from the flow. The specific design of the models representing these structures is general so that the results may be used in a wide range of applications.




CHAPTER 1
INTRODUCTION
Most bridges and other large structures constructed over water are supported by a network of individual piles, or by a footing which is itself supported by individual piles. Such an arrangement can provide for water passage through the structure, resulting in a reduced hydraulic load on the structure when compared with one supported by a larger single pile. In addition, each pile in the multiple pile arrangement provides individual bed support against this load. Critical in design, then, is to ensure that the length of each pile imbedded in the bed material is sufficient for support of the structure, even as the level of the bed changes. Therefore, accurate prediction of the sediment level at multiple pile structures is necessary for design.
There are a number of reasons why the sediment level may change relative to the footings. Perhaps the most critical to the success or failure of the structure is the aggravation or degradation of the bed due to changes in the entire flow field. When caused by natural changes, such as inlet migration or the meandering of a river, this effect can be difficult to predict. As a result, conservative design of structures is imperative when this potential exists.




1. 1 Tnes of Scour
In addition to global bed changes, the bed level can change because of the presence of the structure, an effect known as scour. There are two types of scour, contraction scour (sometimes called general scour) and local scour.
Contraction scour results when the cross sectional flow area is significantly reduced in a particular locality, which may or may not be due to the presence of the structure. With the resulting accelerated flow comes a local increase in the shear stress on the bed, so the potential exists for the bed to be lowered. When scour has lowered the bed dramatically in a particular region, this is called a scour hole.
In contrast to contraction scour, which is merely induced by constriction of the flow, structure-induced local scour, or simply local scour, is caused by a modification of the flow near the structure due to its presence. The nature of the flow determines the nature of the scour.
Unsteady flows such as those induced by waves can cause significant local scour. Laboratory data indicates (Wells, Sorenson, 1970) that wave induced scour on a single cylinder has a maximum expected depth about equal to one pile diameter. These values are small compared with the maximum scour depths experienced with steady or quasi-steady flow such as river flow, tidal flow, or even storm surge induced flow.
Therefore when waves are accompanied by a significant background current, it can be assumed that the steady flow is the dominant component in terms of equilibrium scour depths. When waves and steady flow interact, "the effect of waves may be limited




to reducing the flow velocity necessary for initiation of scour and increasing the initial rate of scour, without significantly affecting long term scour depths" (Wells, Sorenson, 1970, p.76).
In comparison, local scour associated with steady or quasi-steady flow can be more significant. Unlike that induced by waves, steady flow local scour features relative steadiness in the mechanisms that lead to a net sediment removal. This condition can persist until a large scour hole has developed.
Research has identified two categories of (steady flow induced) local scour: clearwater scour and live-bed scour. Clearwater scour is characterized by the absence of sediment transport upstream of the structure; an increased bed shear stress in the vicinity of the structure creates a scour hole. In the case of live-bed scour, sediment transport occurs across the entire bed, including well upstream of the structure. Structure-induced live-bed scour is characterized by a locally higher bed shear stress near the structure, resulting in local net sediment removal. The value of the transitional bed shear stress above which bedload sediment transport occurs, and thus live-bed scour can occur, is a function of the characteristics of the bed material. At some critical mean flow velocity, Uc, this transitional shear stress is attained. Far-field velocities below U0 may result in clearwater scour, and velocities above U0 may result in live-bed scour. An
understanding of the proximity of conditions to this transition velocity is critical to a complete study of scour behavior.




1.2 Current Approach Toward Predicting Scour
When scour potential exists, current structure design frequently utilizes scour predictive equations based on a limited data set. Furthermore, the current level of scour understanding is historically often not reflected in many authors' interpretations of that data.
In bridge design, the Federal I-Eghway Administration's scour predicative equations are contained in the document known as "Hydraulic Engineering Circulars, Evaluating Scour at Bridges", or simply "IHEC- 18 (Richardson et al., 199 1). According to trends observed by authors on scour, some factors which recent research shows to be significant in determining scour depth are not accounted for in the IHEC-18 equation. Also, in terms of scour near multiple pile structures, these equations in no way account for the particular geometry. Therefore, a need exists for an improved scour predictive equation based on an expanded set of data for scour around such structures.
Serious potential exists for local scour to result in catastrophic failure of a structure when the possibility of scour is not properly accounted for in the structure's design. In two studies of 383 bridge failures caused by catastrophic floods, the Federal Highway Administration indicates that local scour is responsible for about half of these failures (Brice, et al. 1978). In these FHWA reports, some of the local scour associated failures occur as debris or ice impedes on the piles, increasing load forces and local and contraction scour. Many other failures stem from poor design, which indicates misunderstanding and underestimation of local scour.




5
1.3 Problem Approach
In the interest of improving structure design, the main focus of this study is the formulation of appropriate equations for predicting the scour depth adjacent to multiple pile structures.
Approaching such a problem is difficult in two ways. Firstly, there is almost no limit to the areas of study to be investigated in analyzing the structures' scour potential. That is, there are many quantities that influence scour depths, all of which could not be investigated in this study. Those quantities deemed most pertinent to the scour process must be delineated for inclusion in the study. After identifying those parameters to be analyzed with regards to their effect on the resulting scour depth, a difficulty also arises in consecutively dealing with such a wide range of factors. Therefore the problem must be broken down into smaller, more manageable interrelationships between specific parameters and the resulting scour depths.
1.3.1 Areas of Study
Further identifying the focus of this research, this study aims at predicting the maximum depth of the equilibrium local scour in the vicinity of typical multiple pile structures. By concentrating on maximum scour, the focus of the study is narrowed in several ways. Firstly, the research is involved with only the scour depth at the scour hole's deepest point. Therefore, the particular bathymetry of the scour hole, which can be very complex, is not directly considered. This eliminates the possibility of applying




the predictive equation toward estimating the total volume of sediment displaced due to local scour.
There exists another way in which limiting the research to maximum scour narrows the focus of the study. In the interest of satisfying conservative design practices, this thesis focuses on the greatest scour depth in any conditions to which the structure may reasonably be subjected. Therefore, for each structure, the experimental conditions represent as closely as possible those that are believed to produce the greatest scour depth attainable in the laboratory. If these conditions were not achieved in the laboratory, the results are extrapolated to the conditions of interest. The impact of this is that the predictive equations are conservative in that they yield a scour depth greater than that most likely to occur.
Finally, by dealing only with equilibrium scour, the approach disregards the scour rate and concentrates only on the final, stable scour depth. This approach eliminates some of the complexities associated with the rate at which local scour occurs.
Because local scour is affected by such a great number of variables, some of the important variables are not considered in this initial study. For example, whereas the skew angle between a structure and the incident flow is considered to affect the scour depth, analysis is limited to structures aligned with the flow. Further limiting the structures considered, any study of a footing's pile cap will be limited to those caps which are emergent from the water surface. The pile caps are consistent in shape, based on current bridge design practice. Furthermore, the number of piles downstream is not directly considered, and tests are run with a sufficiently long structure that any increase




7
in length would not be expected to affect the maximum scour depth, which takes place near the front of the structure. Despite these limitations, the models studied represent a great many structures built today, particularly in shallow waters.
Aside from these areas, the focus of this study is concentrated with regards to the scour regime that is modeled and analyzed. Most if not all scour researchers believe that if equilibrium scour depth is plotted versus depth mean (upstream) velocity a local maximum will occur at the transition from clearwater to live-bed conditions. This local maximum in scour depth is generally taken to be the absolute maximum although some researchers have found a larger local maximum in the live-bed range for fine sediments (Melville, 1985). The results presented in this thesis are based on the assumption that maximum local scour occurs at the transition from clearwater to live-bed conditions. However, due to the manner in which the data is presented, many of this study's results could be valid even if the maximum does not occur at U/U&=1.
1.3.2 Problem Breakdown
The approach for predicting scour depth is further simplified by carefully breaking the problem into smaller, interrelated levels of increasing complexity. The lowest level is the formulation of an equation representing the maximum depth of equilibrium scour for a single square pile, based on the size of the pile and the flow and sediment conditions. This is an extension of scour prediction for a circular pile, whose scour qualities are widely studied and relatively well understood. Some scour variables which are independent of the shape of the particular structure, such as flow velocity, can be accounted for in this step. Increasing the level of complexity, predicting scour depth




adjacent to multiple square piles builds on the understanding of that for a single pile. This arrangement represents the completed structure without a wetted pile cap, and will be known hence as the "no pile cap structure". Finally, the representation of scour near the more complex structure, the multiple pile arrangement complete with a pile cap (i.e. a "pile cap structure"), builds on the understanding of scour near the corresponding no pile cap structure.
Scour prediction for a circular pile is predicted by an equation developed by Sheppard and Ontowijo (1994). In part, this empirical formula makes use their data and that of other authors, providing a fairly extensive data set. The quality of data from other sources is carefully analyzed in terms of their laboratory procedures before inclusion in the data set used in the development of the predictive equation. Analysis of square pile data enables the development of a simple relationship between scour depths for square piles in terms of scour depths for circular piles.
Because this equation accounts for flow and sediment properties, it is used in the development and application of the scour predictive equation for a no pile cap structure. As a result, the scour prediction equation for such a pile group is a function of only the following geometric variables: the number of piles normal to the flow, the separation distance between the piles, and the effective aspect ratio (i.e. the water depth divided by the structures "effective width", to be defined and discussed in Chapter Two).
The scour depth for the pile cap structure is normalized by the no pile cap results for the same pile arrangement and flow conditions. Therefore, the effective structure width and flow conditions are accounted for. The general shape of the pile cap is




9
consistent from test to test. Thus, this final level of complexity involves only the height of the bottom of the pile cap from the undisturbed bed level.




CHAPTER 2
BACKGROUND AND LITERATURE SURVEY
Although accurate scour prediction may still be in an early stage of development, many authors have conducted laboratory investigations into the mechanisms that cause or affect scour. Most of the laboratory tests have involved a relatively simple structure in a sand bed subjected to steady flow. These tests have resulted in the identification of scour producing mechanisms, and have isolated the effects of a wide variety of scour related variables. In using data from a variety of authors, attention must be paid to their laboratory procedures. The following review is selected from authors who have conducted their research with suitable equipment and techniques to warrant their results to be identified as pertinent to this research.
2. 1 Scour Related Hydrodynamics
One of the early and more exhaustive investigations into the mechanics of local scour originates from Colorado State University (Shen et. al., 1966). Current research corroborates their findings that "the don-Anant feature of the flow around the upstream half of the cylinder (or other blunt nosed pier) is the 'horseshoe vortex' system which develops at the base of the pier." This horseshoe vortex develops with the pressure distribution along the front of the structure, which is associated with the bottom




11
boundary layer illustrated in Figures 2.1 and 2.2. Due to the reduced upstream velocities near the bed, the stagnation pressure on the face of the structure is lower near the bed, inducing a downflow just ahead of the structure. At the bed this flow advances upstream, and matures into a vortex whose axis is horizontal. This vortex separates from the structure on the sides and flows downstream. When viewed from above its shape and the shape of the resultant scour profile motivate the name horseshoe vortex.
Steadr Current Vortex Sheading
,Water Surface
Horseshoe Vortex
Figure 2.1 Illustration of Horseshoe Vortex, Side View
Flow visualization by Ramos (1993) reveals the horseshoe vortex to be of impressive strength when the bed is horizontal (undisturbed). Development of the scour hole alters the local hydrodynamics. Melville (1975) states that the size and the circulation of the horseshoe vortex increases, and the velocity near the bottom of the hole decreases, as the scour hole develops. Such a velocity observation would explain why the scour process slows as the hole deepens. On the other hand, observations made




12
in the present study cannot corroborate that the vortex diameter increases as the scour hole develops.
Horseshoe Vortex
Wake Region
Figure 2.2 Illustration of Horseshoe Vortex, Top View
Once the sediment is picked up from the bed by the horseshoe vortex, Bruesers, et al. (1968) describe other flow characteristics contributing to the sand's removal from the vicinity of the structure. The first such factor described is the acceleration around the sides of the structure, such as that predicted by potential flow theory. This may be the only scour mechanism in the case of a very streamlined structure, in front of which a horseshoe vortex may not develop. Finally, Shen et. al. (1977) describe both an upflow behind the structure and also the structure's wake vortex region, which features vertical rotation axes. While these contribute less than the horseshoe vortex to the dislodging of grains from the bed, their effect is to remove the suspended sediment from the region of the structure.




13
The scour removal potential of the horseshoe vortex or any other sediment removal feature is related to its effect on the magnitude of the bed shear stress. Greater bed shear stress has an increased dislodging force on sand grains, which results in a larger scour hole (Ramos, 1993). The relationship between this dislodging force and its efficiency in removing sediment is dependent on several qualities of the grains: mean diameter (D,,), diameter variability, and the density and roughness of the sediment material. Although the approach taken in this thesis does not directly isolate and investigate for all of these variables, an understanding of the processes involved ensures that no critical parameters are overlooked.
2.2 Effects of Flow Qualities on Scour
Most scour researchers note the impact that water velocity has on the depth of local scour. Early attempts to understand this relationship were focused on quantifying the structure Reynolds or Froude number (Shen et. al. 1966). Although the importance of these parameters on the hydrodynamics of such a systemis well documented, Breusers et al. (1977) were discouraged when they attempted to obtain correlations between these parameters and equilibrium scour depths. They report that "no correlation with Reynolds or Froude number was obtained." This was a surprise to these authors because they understood that scour depth is a function of vortex strength, which depends on the hydrodynamics, and thus on the value of the Reynolds or Froude number.




Consideration of the current level of understanding of sediment transport gives insight into the shortcomings of such scour verses velocity investigations.
Insight into scour behavior can be achieved by integrating the experimental results with the critical tractive force approach to sediment transport by Shields (1936). Shields states that a critical bed shear stress exists, above which bedload transport of sediment may occur. Comparing drag force on a sand grain with its weight (and its angle of repose), Shields developed an empirical formula for the critical shear stress of sand. Furthermore, the Prandtl-Von Karman formula predicts the mean velocity in an open channel with a rough bottom, based on the bed shear stress (Sleath, 1984). Combining these approaches allows prediction of a critical mean velocity, Uc, below which no upstream bedload sediment transport occurs. Flows (away from the structure) above Uc result in global bedload transport, and any scour that occurs near the structure is referred to as live-bed scour. If the upstream velocity is less than Uc, then any scour is classified as clearwater scour. Thus the value of the critical velocity separating these scour regimes, Uc, is a function of both the water depth and the sediment parameters.
Local scour appears to depend on the ratio of the mean velocity to critical mean velocity, U/Uc. Bruessers et al. (1977) developed this relationship by dimensional analysis, but applied no detailed analysis into the nature of the dependency. Hanna (1978) used appropriate Uc values in investigating his extensive clearwater scour experiments, and concludes that scour is initiated near U/Uc = 0.5 and reaches a maximum depth at U/Uc = 1.0. Melville (1985) further investigated scour and U/Uc relationships and generally verifies the findings of Hanna, explaining that when U/Uc > 1




the bedload transport provides a supply of sand into the scour hole, reducing its equilibrium depth. He describes a scour depth versus U/Uc relationship like that shown in Figure 2.3, which applies best in the range of velocities below and near U/Uc = 1.

clearwater scour

live-bed scour

0.20 0.60 1.00 1.40
U/U
c

Figure 2.3 Scour Depth Dependence on Mean Velocity (Other Parameters Constant)
In Melville's (1985) study of live-bed scour he concludes that the scour versus U/Uc relationship is more complex in the live bed regime. Furthermore, he reports equilibrium scour to exceed the depths attained at U/U. = 1 by as much as 45% at very high velocities. He attributes the complexities and local maxima of live bed scour depth to migration of bedforms past the region of the structure. In prototype, these velocities may correspond to higher values than expected in the areas where structures are typically placed. Experimentally, research into live-bed scour is always difficult and in many cases impossible due to the facility not allowing the transport of large quantities of sediment.




2.3 Scour Dependence on Structure Shape
The majority of scour data in the literature pertains to scour around a single circular cylinder in cohesionless sediment. This provides a valuable data set for quantifying the effects of many variables, but provides limited insight into the dependence of local scour on a structure's shape.
The wetted shape of a circular cylinder in a flow, shown in Figure 2.4, may only be varied by changes in the aspect ratio, i.e. the water depth, H, divided by the cylinder diameter, D. Bruesers et al. (1977) report on the findings of five authors who all found the dependency of normalized cylinder scour depth, de/D, to be highly dependent on aspect ratio for values of H/D less than 3 or 4. All proposed that the depth of scour is proportional either to tanh(H/D) or (H/D)c, where 0.25 de tanh (H)
Despite the preponderance of scour studies around circular cylinders, a number of authors have studied effects of other shapes. Typically, studies have focused on effects of streamlining the structure. Paintal and Garde (1956) report that the shape of a structure's upstream nose is particularly important in determining the degree of scour development, with deepest scour occurring when the nose is square. Other authors such




17
as Melville and Dongol (1992) studied the effects on scour of wetted shape alterations caused by accumulation of debris or ice on the pile.
H D
Figure 2.4 Illustration of Single Pile (Circular or Square)
. ....... ........ ........ i........ ........ ........
0 2 4 6
H/D
Figure 2.5 Scour Depth Dependence on Water Depth (U/Uc, Other Parameters Constant)
The increase in scour depth (for a long structure) with an increase in the skew angle between the structure and the flow is reported by many authors, such as Chabert and Endeldinger (1956).




In scour studies of multiple structures, or of a multiple pile structure, less data exists. Hanna (1978) reports on 69 scour experiments; some on single cylindrical piles and some on groups of up to six piles. All of the pile group tests were conducted at the same depth and flow velocity, and the data from these tests provides good insight into scour dependency on the layout of the piles in such groups. It is determined that for piles close to one another, scour depth decreases with an increase in spacing. No attempt to formulate a predictive scour equation was made.
For multiple piles with a submerged pile cap, some scour data is provided by Ramos (1993). In this study, both the hydrodynamics and scour around a specific arrangement of 36 square piles were analyzed, with variations in the height and design of the pile cap. From the resulting data, some idea of both the nature of the vortices near such a structure and the resulting bed shear stresses can be obtained. Furthermore, these experiments provide insight into the scour depth dependency on the placement and design of the pile cap.
Specifically regarding multiple pile bridge footings, Jones (1989) conducted tests for the FHWA on a variety of geometries, some of which represented two existing bridges that had proven to be particularly sensitive to sediment scour. The results of the tests were used to determine an effective geometry of such footings for application in existing scour predictive equations. It was concluded that appropriate, conservative estimates of equilibrium scour depth for multiple pile footings can be obtained by applying the equations described in the IHEC-18 document, and using as a width value the width of an individual pile multiplied by the number of piles normal to the flow.




Although these results account for the number of piles and thus are useful in bridge design, such a technique does not directly account for the particular geometry of the footing, i.e. the pile separation or pile cap location.
2.4 Effect of Sediment Characteristics on Scour
In addition to properties of the flow and the geometry of the structure, the characteristics of the sediment influence scour depths. As mentioned, the bed shear stress value that will initiate bedload transport is a function of the effective grain diameter of the bed. The value of this critical shear stress has been empirically determined for a wide range of mean grain diameters. Since the depth dependent critical mean flow, Uc, is a function of this critical bed shear stress, the value of Uc depends on the bed's mean grain size.
Although scour depth appears dependent on the flow velocity normalized by the critical velocity, U/Q, and U0 depends on the bed's mean grain size, there exists another way in which scour depth is dependent on the average sediment size. For various sediment sizes, the scour depth can be different with variations in the bed's mean grain size; even as U/U0 is held constant. This was first identified by Raudkivi and Ettema (1977), who found that within a certain range of mean grain diameters, finer sand produces less scour. They attributed this to ripple formation and its resulting fill into the scour hole.
Baker (1986) correlated scour depth dependence on mean grain size by concentrating on scour as a function of the value of D/D50. Applying such an analysis to




the data of Raudiviki and Ettema (1977), it was concluded that within a range of relatively high D50/D values, increasing this value results in decreased scour. Sheppard and Ontowirjo (1994) concluded that within a lower range of D50D values, increasing this value results in an increased scour depth. Quantifying such results is challenging because of the scarcity of data in which only D50/D varies, with little variation in the velocity, aspect ratio, or sediment gradation (to be discussed later in this section).
Nevertheless, Sheppard and Ontowirjo (1994) conclude that the laboratory experiments show a dLD vs. log(D5/D) curve such as that in the domain labeled "laboratory range" in Figure 2.6. Typically, in the case of a prototype footing, the sediment is approximately the same size as in the laboratory, but the scale of the structure would be much larger. Clearly, significant scour is observed in such prototype situations. Therefore, Sheppard and Ontowirjo conclude that in the prototype range of Ds/D values, the curve levels off (in some way) as shown on the left side of Figure 2.6.
In the interest of predicting the maximum equilibrium scour at a single cylinder, Sheppard and Ontowirjo (1994) fit the entire range of applicable data to curves representing the scour dependence on aspect ratio, velocity ratio, and sediment size to structure diameter ratio. To account for each of these they formulated the following relationship
ds i E nfiUrs .3,
According to the relationships illustrated in Figures 2.3, 2.5, and 2.6
(0C =tan(H)




21
f2() -KI +K2Q) + K(,)

f,(2) =Di+D2[log(i)] D+D3[log C5) 2 +D4[logTh ) 1 3
Fitting Equation 2.1 to the existing data, the constants result in the following values K1 = 1.00, K2=-2.87, K3= 1.44 D1 = 1.24, D2 =9.88, D3 =4.56, D4 =0.55

2
0
Figure 2.6

prototype range

laboratory range

* I I I I
-5 0
log (D50 / D)
Scour Dependence on Normalized Mean Grain Size (H/D, U/U, constant (Sheppard, 1994))

Another factor influencing scour depth is the degree of grain size variation. When there is a significant gradation in grain sizes, the potential exists for the removal of smaller grains, leaving coarser grains to armor the scour hole. At a bed shear stress




below the critical value for this coarse sand, these grains remain, and there is a supply of finer sediment from upstream. Therefore, scour depths decrease with an increase in sediment gradation. This was first reported by Raudkivi and Ettema (1977). Baker (1986) quantifies not only the scour depth dependency on sediment gradation, but also its effect in increasing the value of UfUc that yields a scour depth maximum, shown in Figures 2.7 and 2.8. Correlation of this dependency is complicated by the variety of formulae with which authors report ca, the value representing sediment variation.
2.2
2.0
1.6 . . . .
1.4 . . . . . .
increasingly non-uniform
1.2
1.0 2.0 3.0 4.0 5.0 6.0
a
(Sediment Gradation)
Figure 2.7 Armoring Effects on Maximum Scour Depth Data From Baker (1986)
2.5 Rate of Scour
Due to this study's emphasis on equilibrium scour, the rate at which that scour depth is attained is not of direct interest. Emphasizing the scour's equilibrium value may




yield conservative depth estimates, because in real applications flows severe enough to potentially result in damaging scour are often limited to storms or other episodic events. At least in tidal water, the duration of these extreme flows is usually short, often shorter than the duration of the tests in this study.
2.2- *...... .........
1.8 . . .. . . .
1.4
increasingly
non-uniform
1.0 2.0 3.0 4.0 5.0 6.0
0T
(Sediment Gradation)
Figure 2.8 Armoring Effects on Effective Critical Velocity Data From Baker (1986)
Nevertheless, there is one area in which some understanding of the scour rate must be achieved in order to model and interpret scour studies directed at representing equilibrium scour depths. To quantify equilibrium scour depths from test results, a conversion factor must be determined to extrapolate from the shorter tests scour depths that would result after longer duration. For example, Hanna (1978) reports that scour depths after 7 hours are 88% those measured after 24 hours. Similarly, such an




24
extrapolation can estimate equilibrium depths after finite-duration experiments. These extrapolation techniques make use of an understanding of scour rate.




CHAPTER 3
EXPERIMENTAL APPROACH
The description of the experimental approach is comprehensive so that the tests' conditions may be fully understood. This allows proper evaluation of the data and permits reproduction of the tests.
All of the major equipment used is described in full, along with the complete experimental procedure. The results of the test are particularly sensitive to certain procedural steps, so these are reported in detail.
In addition, the descriptions of the models to be tested and the test conditions are outlined. A complete description is given of the strategy used to obtain the necessary data for the development of the scour predictive equation.
3.1 Equipment
The equipment used in the experiments is described in three categories. The first is the flume and the equipment used to generate the proper flow and to measure the results. The second category is the models themselves. Some mention is made of the strategy used in determining the particular models to study. Finally, the nature of the sediment used in the experiments is described, along with the method of obtaining such sediment.




3. 1.1 Flume
All experiments were conducted in the flume located in the hydraulics laboratory of the Civil Engineering Department of the University of Florida. The flume is equipped with a 100 hp. pump capable of a discharge rate of 38.8 ft.3sec., although practical limitations reduce the possible flow rate to about 12 ft.3/sec. Flow from the pump passes through a vertical gate (referred to as the head gate), which provides control of the volumetric discharge.
Upon jettison into the flume the water is contained in a holding area, which is taller than the surrounding flume. A manometer is provided to measure the water level (the head) in this section. From this area a V-notched Thompson weir permits water passage to the flume's main section. In order to generate straight and consistent flow, four arrays of PVC pipes are placed in the flume, two upstream and two downstream of the weir. Each of the 5400 pipes in these arrays are six inches long and two inches in diameter.
The main flow channel of the flume is 2.5 ft. deep, 8 ft. wide, and 108 ft. long. The center 20 ft. is the windowed test section, whose base is 1.13 ft. deeper than the surrounding flume to provide space for a sand bed. Above the main flume rides an electric carriage, providing a stable platform for observations and measurements of the test section. At the downstream limit of this flume lies a vertical gate (the tailgate) for control of water depth. Below this, the flow is redirected into a smaller, lower return channel in which the water passes back to the pump's holding basin.




3.1.1.1 Flow control
Generally, volumetric flow is controlled with the head gate and water depth is controlled with the tail gate. Although these provide ultimate flow control, explicit manipulation of either flow rate or flow depth is difficult. This is due to the fact that any change in the depth alters the head difference across the pump, which changes the flow rate, in turn affecting the depth. This control sensitivity results in slight variability in flow conditions within and between tests.
Flow depth measurement is made on a scale located near the test section. Measurement of the head level behind the weir gate is made with a built in manometer.
The value of the volumetric discharge over the weir (and past the test section) is found from the value of the head level behind the weir. Potential theory states that the discharge is:
Q = C, .1 2g (H*) 2. 5tanh(~ (3.1)
where Cf is a coefficient whose value is to be empirically determined, 0 is the notch spread angle, and H* is the head level upstream of the weir.
Previous to this study the flow rate over the weir was calibrated by the University of Florida Civil Engineering Department. In this calibration, the surface of the flume was divided into 25 grid locations. At each of these locations, flow velocities were recorded at five depths chosen to represent the mean flow rate. The resulting volumetric flow calibrated for the manometer reading follows




Q =2.84(H*)2.5l4 (3.2)
where H*, the effective head (in ft.), is the following function of in', the manometer reading
_* m /-5.62 (3.3)
3.1.2 Models
Two classes of structure models are used in scour studies. The first class consists of single piers, both square and cylindrical. The second class of models is geometrically scaled models of multiple pile footings, some specifically representing particular applications, and some more general in shape.
Each of the models in the first class, the single piles, is designed so that its scour data may pertain to one or more of three applications. Figure 2.4 shows a single pile as it is tested in the flume.
The first application of the single pile models, for which cylinders are designed, is comparison with data from other authors to provide insight into the procedures and equipment used in the tests. These are also designed to provide necessary data points where needed to improve the understanding of the scour process (as it applies to scour at cylinders).
The second application of the first class of structures pertains to tests on one particular square pile model. This model features D=1 .25 in., and represents a single pile




of the same width as the piles that make up the second class of models: those that represent multiple pile footings.
The third application, for which both square and circular piles may be used, is in the developing of a comparative study of the local scour attributed to piles of the two shapes (in the same conditions). Therefore square and circular single pile models with the same width are tested.
Regarding the second class of structures, the multiple pile arrangements, those whose scour depths are used in development of the predictive equation are more general in shape, with a rectangular arrangement of nXm piles.
When no pile cap is present in the flow, the effective shape of the model is illustrated in Figure 3. 1. This view is from the front, but Figure 3.1 would apply to a side view if 8 piles were shown (given that m--8). The piles are square, with D=1.25 in. Most models feature a spacing of a/D=3.0. Above the flow, the piles are held in a pile cap, with set screws used for support.

n piles

Figure 3.1 Upstream View of No Pile Cap Structure




30
When the pile cap is in the flow, the appearance of the model is shown in Figure 3.2. The value of h2 represents the height of the emergent cap from the undisturbed bed level. In the case of a 5X8 structure, the dimensions of the pile cap are shown in Figure 3.3. The dimensions in Figure 3.3 pertaining to the piles and their arrangement apply to both pile cap models and no pile cap models. Generally, only the outside width dimension varies with alternate models; for example, a 3X8 model also features a=3.75 in. centerline to centerline pile spacing.
i H
Flow
hE2
n piles
Figure 3.2 Upstream View of Pile Cap Structure
.D 29.25 E] [] o] o] o] o] E E ]a3.75 Flow
irectionD 180T
D = 1.25

Figure 3.3 Dimensions (in.) of Typical Pile Cap Model




The second class of structures also consists of less general shapes of pile cap structures; these are geometrically scaled 1:24 from existing bridge designs. With regards to these, the dimensions of D, a, and the pile cap overhang are the same as shown in Figure 3.3. However, their arrangement is often somewhat different. A typical example is Figure 3.4, whose arrangement is labeled 2 4X5 because it is the equivalent of 2 4X5 pile caps joined by a separator. Vertically, the bottom and top of this separator is flush with the other sections of the pile cap.
Z--8.75 18.00
Fl3 0 03 0 03 0 0 0 0 0
Flow 13 0] E3 13 13 13 13 13 13 El
5.00 14.25
Direction 00 00 03 13 13 0 0 0 0 1
0 00 0 31Oj 0
Figure 3.4 Pile Cap on 2 4X5 Structure
For particular tests, more specific descriptions of the dimensions of the piles and the arrangements of the multiple pile structures follow later in this chapter, in which the specific tests are described in 3 categories.
3.1.3 Sediment
Three types of sand are used in the test section. The downstream 12 ft. of the test section is designated section one, and the sand in this section is called Section One sand. Section one is the portion of the test section into which each model was placed, so the scour occurs in Section One sand. This sediment is intended to be as uniform as




possible, to be representative of typical bridge conditions, and to be practical for use in the flume. The entire volume of Section One sand was produced by sieving fine raw sand in 25 lb. batches for 15 minutes. That volume remaining in between the screens of diameter 0.250 mm. and 0.595 mm is designated Section One sand.
The resulting grain size distribution for Section One sand is shown in Figure 3.5. Its statistical analysis is as follows
Mean grain size diameter
D0= 0.278mm. (3.4)
Grain size variation value
D84
0 51 1.637 (3.5)
Alternate grain size variation value (formula applied by some authors)
02=T- 1.938 (3.6)
The sieving required to produce Section One sand is extensive and costly. Therefore, the remainder of the test section contains alternate sediment. The surface sand of section two, called Section Two Top sand, is chosen to minimize its transport toward the models. Therefore, Section Two Top sand is sieved (quickly) to yield a




consistently large grain size diameter. The resulting analysis of Section Two Top sand follows

T
D50 = 1.42mm.
YT = 84 1.33
D16

100-I
80- -40- ...
40D50=0278mm a = 1.637
20- -0-

0.10 1.00
Sieve Diameter (mm.)

(3.7) (3.8)

10.00

Figure 3.5 Gradation Curve for Section One Sand
Section Two Top sand extends across section two in its uppermost 3 inches. The lower 10 in. of section two are filled with a sand volume referred to as Section Two Bottom sand. Since it lies below the anchoring layer of Section Two Top sand, its diameter is arbitrary. Figure 3.6 shows the positioning of the sand volumes in the test section.




flow
Two Top
Two Bottom One
Figure 3.6 Location of Sand Volumes in Test Section (Not To Scale)
This approach requires that the Section One sand be a dynamic part of the scour process and that the other sand be static. Thus in terms of interpreting either sediment related flow qualities or the results of tests, only the characteristics of Section One sand are of interest. In other words, since only Section One sand is in the vicinity of the structure, any sediment dependent characteristics, such as a test's critical mean flow velocity, are evaluated with regards to Section One sand.
3.2 LaboratoU Experiments
In order to achieve consistent results that correctly reflect the impact of varying specific conditions from test to test, strict adherence to a well planned experimental procedure is critical. Any inconsistency in data stemming from inadequate procedure results in an inappropriate scour predictive equation. Therefore, greatest care was taken in preparing for and conducting each experiment.




3.2.1 Preparation
In the interest of consistent results, a series of procedural steps was developed that best prepares the equipment for a quality scour experiment. Many additional duties were required over the course of the experiments, such as irregular maintenance and repair on the flume and pump. The consistent major procedural steps (beginning with a dry flume) follow.
First the pump and the flume's structure are prepared for the run. During the tests, regular maintenance on these insured that no failure would occur. The pump is oiled and greased as necessary. The flume (flow straighteners and screen) is cleaned as necessary for quality flow.
Next the test section is cleared and the model (or models) is inserted. At this point, the quality of the sand in section one is given a cursory inspection and any (very small) volume of the larger upstream sediment is carefully removed and replaced by additional Section One sand. In addition, any larger objects in the bed are removed at this time (it shall be explained in Chapter Four that paint chips were found to initiate ripple formation). The sand is cleared away and the model is placed on the floor of the test section with the proper skew angle to the flume.
With the model in place, the sand is redistributed to approximately the floor level of the upstream and downstream flume. After this the entire volume of sand is compacted using an upright hand held steel compactor. In areas nearer the structure or more disturbed between tests, the compacting is exhaustive. This ensures that the sand best represents a naturally settled bed, yielding the most consistent scour depths. The




sand within each multiple pile structure is compacted by externally driving objects down upon the sand surface. If a pile cap is to be on the structure, and to be too low to permit this technique, then it is left elevated at this stage.
Requiring more precision is the final leveling of the initial sand bed. The leveling is executed with a series of long smooth objects of wood and steel. Special attention is paid to surficial compaction of any areas across which removal or addition of sand disturbs the previously compacted sand. In the case of multiple pile structures, the first sand to be leveled is the sand between and immediately around the set of piles. The greatest possible care is taken to ensure that the initial level of the sand will be the same as the level upstream and downstream of the floor of the flume. This is done with a set of scales painted on outer piles, whose zero level corresponds with the depth of the test section. Any lowering of the pile cap takes place at this point, taking care that the pile cap is level and at the intended height. Following this, the remainder of the sand is brought to the same level. The degree to which the sand is level is indicated by the scale on the piles as well as similar markings on the flume's walls. Between these, extensive use is made of level indicators to ensure a consistent initial bed.
Finally, the water depth of the flume is raised. Special attention is paid toward reduced filling rates to ensure that no scour occurs in this stage.
3.2.2 Test Procedure
In the course of conducting the various scour experiments, attention is paid to the degree to which variations in the test methodology affect the test's results. Of primary concern is ensuring that the velocity never exceed the critical velocity, which




37
would initiate live-bed sediment transport and affect the nature of the bed for the duration of the test. An example of such an effect would be the transport of the upstream anchoring layer of sand into the region of the structure, which would lead to armoring and reduced scour depths. This would occur at velocities well above critical velocities (for the Section One sand).
The formation of ripples is the primary effect to be avoided by continuously keeping velocities below the critical value. Over the course of the tests, upstream ripples proved to be an ongoing issue, whose development often seems to coincide with excessive water velocity. It appears that ripples result if the water velocity exceeds the critical velocity, however momentarily. Despite the fact that ripples often appeared to be initiated by objects in the bed, lower velocities seem to reduce the likelihood of their appearance. Upon gaining some experience, it was determined to use U=0.9 Uc as a target velocity, with possible variations upon observation of the bed during the run.
Adjusting the flow to the desired velocity and depth generally results in flow oscillations. Because emphasis is placed on restricting these oscillations in a way that avoids velocities below the critical value, the goal at startup is reduced volumetric flow and increased depth compared with the desired values. Therefore at startup both the head gate and the tail gate are lower than expected levels for the test.
After startup the levels of the gates are adjusted until acceptable flow is achieved. This could take minutes or hours.
Throughout the run, the flow conditions and scour depth are recorded. Hourly readings are made of the head level, recorded on the manometer. At the same times, the




water level is recorded, along with the current value of U[Uc from the flow equation. The final value of U/Uc arrives from the average of the individual values derived from the depth and manometer readings. In addition to these, the water temperature is recorded each hour.
Also frequently recorded is the scour depth at the structure. For single pile structures, this reading comes from the front or left of the pile. For multiple pile structures, the scour depth is recorded at each of the front and left piles. The recording is taken from scales painted on the structure, the same scales that are used in determining the zero sand level.
The duration of most runs is 26 hours. Based on observations of the scour development, this duration seems to result in scour depths reasonably close to equilibrium values.
Upon completion of the run, the pump is stopped with the tailgate lowered to ensure moderate flow. A discharge pump drains the flume, and the test section is left to gravity drain from a side valve.
3.2.3 Profile Measurements
At this time the profile of the resulting scour hole may be measured. The profile data are taken with a vernier point gauge attached to the carriage. This simple but accurate instrument measures the Z-value of the bed location, which is zero at the level of the initial bed and positive upward. Thus for a given location, the value of the scour depth is -Z. The X-axis lies in the direction of the flow, positive downstream. Therefore, side view figures appear as a reflection of the actual structure as measured.




39
The Y-axis measures normal to the flow, positive to the right as one views a structure from the front (upstream). The zero location for both X and Y is the comer of the structure that is upstream on the side and leftmost on the front (viewed from upstream).
Sand elevation measurements are recorded over a wide range of the bed (as well as the upstream flume). Many of these are intended to report on the location of the upstream bed in order to provide insight into any irregularities in the resulting scour data. The more pertinent data consist of profile measurements directly along one side and the front of a structure. These usually show both the deepest scour recorded as well as the particular depths at each pile. Because of their significance, many of these measurements are provided in Chapter Four. Unfortunately, no effective method was devised for measuring the bed elevation within the pile groups. Nevertheless, observations indicate that the deepest scour depths are usually outside of the outermost (usually front) piles.
3.3 Required Tests
A total of 35 tests was conducted in the course of this research, and these tests fall loosely into three categories. The first category consists of scour tests conducted for an improved understanding of the dynamics of scour and for a refinement of experimental techniques. Conducted on single circular and square piles, these also provide a measure of the consistency of scour depths with those reported by other authors. The second category of scour tests were conducted on structures directly representing the proposed Roosevelt Bridge and Indian Town Road Bridge. Either




because they are skewed to the flow or else because they feature irregularly shaped pile caps, the models tested in this category of tests do not match the shape of those directly covered by the predictive equation developed here. Rather, the models studied for the purpose of the equation make up the third category.
It should be emphasized that overlaps exist between these three categories. For example, some tests are directly aimed at representing a specific application, such as category two tests, but could also appropriately be considered category three tests. Still other tests are conducted on single square cylinders (and could be considered category one tests), but the scale and conditions match category three tests. To resolve this, category three includes any test matching the description of the model shape and test conditions consistent with the tests whose data is used in formulating the predictive equation. This is so that the maximum quantity of data is utilized in developing the scour predictive equation. This data may also apply to the other categories.
To conduct the 35 tests, a total of 29 runs was needed. The quantity of runs was minimized by sometimes placing two or more of the smaller structures into the test section. This is possible when the structures are suitably small such that resulting blockage of flow would not be expected to affect scour depths. As a rule of thumb, such multiple test runs were conducted unless the cross'sectional flow area would be decreased by 10% or more. Thus contraction scour is minimized.
3.3.1 CateRoU One Tests
Category one consists of 10 tests, described in Table 3. 1, and chosen to provide data most efficiently providing insight into the scour process. Tests 1, 2, and 3 were




conducted on a 4.5 inch Plexiglas cylinder in flow conditions (depth and U/Uc value) that matched tests previously conducted in the same flume. These previous tests, conducted by Ramos (1993), were run with a different sediment. Analysis of sand from the vicinity of the scour hole in these tests indicates that the configuration of sand in the test section is suitable, because the level of transport from the upstream anchoring layer is insignificant.
Table 3.1 Category One Tests

test description H skew U/U0c duration
(in.) (deg.) (hr.)
1 4.5" cylinder 15.4 -- 0.9 7
2 4.5" cylinder 8.2 0.9 7
3 4.5" cylinder 4.1 -- 0.9 7
4 1.25" cylinder 4.2 -- 0.9 26
5 11.25" cylinder 8.5 -- 0.9 26 1
6 2" cylinder 4.2 -- 0.9 26
7 2" cylinder 8.5 _____ 0.9 26
8 2"1 square 4.2 0 0.9 26
9 2" square 8.5 0 0.9 26
ia 4.5"1 square 8.6 0 0.9 7
10b 4.5"1 square 8.6 1 0 10.9 126

The primary intention of the next group of category one tests is a comparative study of circular and square piles. Tests 4-7 are circular piles tested in flow conditions directly matching corresponding tests on multiple pile structures. For each of these tests,




a corresponding test on a square pile of the same diameter (width) is conducted. Tests 8 and 9 are the scour tests on the 2 in. square pile corresponding with tests 6 and 7. The corresponding tests on the 1.25 in. square pile are considered category three tests. Finally, test 10 offers a comparison between the scour achieved near a 4.5 in. square pier and the 4.5 inch circular cylinder of the first three tests. Test 10 was carefully measured for scour after seven hours duration, described as test number 10a.
As mentioned, many of these tests were conducted in combined runs. The structure in test 10 was run consecutively with a structure in category three, explaining why test 10 was permitted to run 26 hours (test 10b) despite the fact that comparisons with the circular cylinder are made after 7 hours. All of the tests on the 2 inch and 1.25 inch single piers were made in a mere two runs: one in shallow flow and one in deeper water. This ensures that the flow conditions are nearly identical between, for example, tests 6 and 8.
3.3.2 Category Two Tests
Category two tests, numbers 11 through 18, were conducted to supply the Florida Department of Transportation with scour depth estimates for the footings of two proposed bridges. The models were geometrically scaled by a 1:24 ratio from the designed footings, whose individual piles are 30 inches in diameter. Thus each category two structure is scaled down to an individual (square) pile diameter of 1.25 inches. In further keeping with the design of the bridge footings, the separation between piles has a value of a/D = 3.0. Furthermore, each pile cap overhangs the outermost piles by a




43
distance of 0.7 D. In addition to these qualities, each pile cap is emergent from the water.
The category two tests are described in Table 3.2. Test 12, for example, is described as a 4X5 pile arrangement, similar to the 5X8 arrangement shown in Figure 3.3. Thus the value of n, the number of piles normal to the flow, is 4; the number of piles downstream, m, is 5, and there are 20 piles altogether in the model. The pile diameter, D, (or width) is 1.25 in. The pile cap overhangs the outer rows of piles by a distance of 0.7D, and is rectangular in shape. Furthermore, the pile cap bottom in test 13 is located a height of k2 (1.33 inches) above the initial bed level, similar to the structure shown in Figure 3.2. The reason that the structure is not to be used in the predictive equation, and thus is not a category three structure, is its skew of 15 degrees to the flow.
Table 3.2 Category Two Tests

test description H skew h2 UIUc duration
(in.) (deg.) (in.) (hr.)
11 5X5 4.5 15 1.3 0.9 26
12 4X5 4.4 15 1.3 0.9 26
13 2 4X4 6.3 15 2.6 0.9 26
14 2 4X5 6.6 15 2.6 0.9 26
15 2 4X5 8.3 35 5.1 0.9 26
16 2 5X4 8.4 35 4.3 0.9 26
17 4X12 (itr) 10.4 0 5.9 0.9 26
18 4X12 (itr) 10.5 0 0 0.9 26




This general description applies to all of the models in categories one and two. Several models, however, need more description. The model in test 13, for example, is described as a "2 4X5" structure. This indicates that the model consists of two pile caps and pile groups just as the 4X5 structure described in test 12. Bridging these members is a pile cap separator, shown in Figure 3.4, which extends down to flush with the bottom of the pile caps.
Tests 17 and 18 are conducted on other structures in need of further description. Designed to represent footings on the proposed Indian Town Road Bridge, these feature the same scaling as the Roosevelt structures, but with markedly altered pile caps. In the interest of streamlining the flow, the prototypes (and thus the models) are designed not with a rectangular pile cap, but rather with a pile cap whose upstream and downstream ends are shaped to form a point. As such, their resulting scour may not compare accurately with the scour achieved at rectangular pile caps, explaining why these tests are not placed in the third category of tests.
3.3.3 Category Three Tests
The third category of tests are those whose data is used in the formulation of the scour predictive equation. They are intended to yield the maximum insight into effects on scour depths from alterations in the design of a generalized multiple pile footing.
The various tests on no pile cap models are intended to represent the effects on scour of varying either the water depth, the number of piles normal to the flow, or the pile spacing. At a given water depth, scour at several different no pile cap structures is investigated. A typical example is shown in Figure 3.3, which also shows the pile cap,




which is above the flow. In addition, for a given structure the effect of varying water depth is studied. Finally, for a structure already studied at a given water depth, a study is made of alternate pile spacing and its resulting effect on scour depth.
The studies on the structures complete with the pile cap emphasize the same arrangement and water depths as the no pile cap structure. At a given pile cap height, varying either the water depth or the structure's width (number of piles) is investigated. Furthermore, holding these steady, tests are made at different pile cap locations. Data from the Roosevelt Bridge tests is included for completeness.
Finally, at the water depths used in these tests a single pile is tested so that its depth may be used for comparison.
The category three tests are described in Table 3.3. All are directly or indirectly based on the size and shape of the "nXm" structure described in category two, but further description is required for some tests' models. The location of the pile cap, h,, in tests 19-25 is described as "npc"~, meaning that the model used is a no pile cap structure. Test 27's structure has no exposed piles; the entire structure has the outer dimensions of a 3X8 pile cap. The models in tests 19 and 20, each described as a 1.25 in. single square pile, can be regarded as a IXI no pile cap structure. The 3X8 no pile cap model in test 25 is unique in that there is no spacing between the 24 piles. Thus while all other models feature a value of aID)=3.0, the models in test 25 features aLD=1.O, providing detail regarding scour dependence on pile spacing.
Investigation is not made into the degree to which the pile cap affects scour depths for a variety of pile spacings. Each pile cap model features the spacing a/D=3, a




value common in bridge design. It is presumed that scour adjacent to pile cap structures has a greater dependence on presence of the pile cap with increased pile spacing.
Table 3.3 Category Three Tests

test description H skew h, U/Ic duration
(in.) (deg.) (in.) (hr.)
19 1.25" square 4.2 0 npc 0.9 26
20 1.25" square 8.5 0 npc 0.9 26
21 3X8 8.5 0 npc 0.9 26
22 5X8 4.2 0 npc 0.9 26
23 5X8 8.5 0 npc 0.9 26
24 7X8 8.5 0 npc 0.9 26
25 3X8 (a/D=l) 8.5 0 npc 0.9 26
26 2 3X4 4.2 0 1.3 0.9 26
27 3X8 8.5 0 -inf 0.9 26
28 3X8 8.5 0 -5.5 0.9 26
29 3X8 8.5 0 0 0.9 26
30 4X5 4.2 0 1.3 0.9 26
31 2 4X4 4.2 0 0 0.9 26
32 5X8 4.2 0 3.7 0.9 26
33 5X8 4.2 0 0 0.9 26
34 5X8 8.5 0 2.6 0.9 26
35 5X8 8.5 0 0 0.9 26




CHAPTER 4
RESULTS
The results of these tests are described in several sections. The first provides illustrations of the tests' resulting scour holes. The remaining sections deal with the analysis of the maximum scour depths, and the development of the scour predictive equations.
4.1 Scour Profiles
As mentioned in Chapter Three, the primary goal of this research is the formulation of equations predicting the maximum depth of equilibrium scour, and not analysis of the shape of the scour hole. Therefore, no quantitative analysis is made in this text of the shape of the scour hole in any of the tests.
Nevertheless, the shapes of the structure-induced scour profiles resulting from many of the tests are illustrated here so that their inspection may provide insight into the scour process. For example, the side views show that the deepest point of scour is near the front of the pile, or near the front of the upstream piles of a multiple pile structure. Many side views show the accretion of sand behind the structure. Also, from these profile views can be seen the level of interaction between the individual piles in a multiple pile structure.




4. 1.1 Single Pile Profiles
In order that the profile data be shown in its accurate location with respect to both square and circular piles, consistent location of the (front, left) "zero" location is essential. For circular cylinders the zero point is the location of the front left comer of a corresponding square cylinder. Therefore, it is disjoint from the cylinder but provides accurate correlation with the profile data from square cylinders of the same width. The zero location for multiple pile arrangements is the front left comer of the pile cap (even if the pile cap is out of the water in the test).
The range of data point locations for the single piles is limited by the various structures that were used to hold them in place. As a result, sometimes the scour holes shown in Figures 4.1 through 4.8 were not measured out to a location were the level of their scoured bed is equal to the initial bed level.
Figure 4.1 shows the front view (i.e. looking downstream) of the scour hole around 2 in. piles, both square and circular, in a water depth of 4.2 in. The view is taken across the front of the structure, as close as possible to the pile (usually about 0.3 inches in front of the structure). The pier is shown along with the water line (W. L.) and the level of the initial sand bed (S. L.). As expected, the scour hole in front of the square pile is deeper than that in front of the circular pile, presumably due to the efficient development of the horseshoe vortex before a flat face.
This front view is noteworthy in two ways. The first is the asymmetry of both of the scour holes away from the structure. This could reflect variations either in the flow




49
or in the bed. Most likely, upstream ripples are responsible for the asymmetry in this case, for they were widespread in the run from which both of these tests originate.
6.0
4.0- W. L.
Pile Shape
2.0- ------ circular
- square
N
0.0 -- --- S. L.
-2.0
-4.0
-4.0 -2.0 0.0 2.0 4.0 6.0
Y (in.)
Figure 4.1 Single Pile Scour in Shallow Flow, Front View (D=2.0 in., H=4.2 in.)
Also noteworthy in Figure 4.1 is the location difference of the deepest point of scour for the two tests. In the early stages of scour, the scour hole is nearly symmetric in front of a (skew-free) structure, either round and square. The deepest scour is at the front comers, and at the front center there is a significant peak. After the scour hole grows, this peak usually disappears. Usually, but not always, the deepest point is still at one of the comers of the pile. Based on many scour observations, it seems that the different appearance of the scour hole immediately in front of the two piers in Figure 4.1 is not necessarily due to only their shape difference. Complexities in the flow and sediment processes can contribute to a variety of scour hole shapes.




50
The side view of the resulting scour in front of the piers in the same two tests is shown in Figure 4.2. Near the pier, the scour profiles closely resemble one another in shape. Like the front profile, Figure 4.2 shows that the location of deepest scour varies from the square pile to the circular pile. Farther from the piles, Figure 4.2 shows the two scour holes to ascend at essentially the same slope. This slope has an angle of 38 degrees from the horizontal, presumed to equal the angle of repose. At least at the steepest area of the slope, this angle is consistent from test to test in front of the structure.
6.0
4.0- W. L.
Pile Shape
------ circular
2.0- square
N
0.0- S. L.
-2.0
4.0
-12.0 -8.0 4.0 0.0 4.0
X (in.)
Figure 4.2 Single Pile Scour in Shallow Flow, Side View (D=2.0 in., H=4.2 in.)
Farther up the slope and also upstream of the scour hole, the difference in bed levels are obvious between the two tests. It is doubtful that these variations are related to structure shape, as experience indicates minimal effect of structure shape on the bed




profile this far upstream. Also, the likelihood that initial sand level differences are responsible for this effect is minimal due to the great care taken to ensure that the initial bed is at a constant level from one test to another (in fact these tests were made in the same run).
Rather, Figures 4.1 and 4.2 show the effect of upstream ripples. An upstream ripple field appeared on the bed in this particular run despite all countermeasures. In front of the square pile's scour hole is a ripple peak, and in front of the circular pile's scour hole is a ripple trough. When these upstream ripples occur in a test, a condition not uncommon with such fine sediment, the effect of the ripples on the equilibrium scour depth is largely unknown. In fact, as ripples move past the area the concept of a stable equilibrium scour depth may be somewhat inappropriate. It is conjectured that the effect of these ripples is more severe on the depth of scour adjacent to structures of this size, in comparison to the much larger multiple pile structures with their corresponding larger scour holes.
Figures 4.3 and 4.4 show the side and front profiles of the scour hole near the same two structures when subjected to an 8.5 in. flow depth. Generally, the shape and size of the scour holes are similar to those resulting from the shallower flow. The front view, Figure 4.3, shows ripples to exist in front of the scour hole. Possibly because of these ripples, the circular pile scoured slightly deeper than did the square pile.
Conducted in the same two runs, shallow and deep water, were the two tests on the smaller square piles, shown in Figures 4.5-4.8. Of these, the results of the tests on square piles are critical to the development of the scour predictive equation because




these piles represent a single pile from the multiple pile structures, tested in the same water depths. Therefore, these scour depths will be compared with those attained near the multiple pile structures in the same depth. This (to be explained further in this chapter) is how the scour dependence on the geometry of such a structure is isolated.
Like the tests on the larger piles, which were conducted in the same runs, these tests also featured ripples. In fact, ripple effects on these scour depths may be more severe with these piles, because of the piles' smaller size in comparison with the ripple size.
4.1.2 Multiple Pile Profiles
The appearance of the scour holes near multiple pile structures (both with and without a pile cap) is similar from test to test. All profiles show the deepest scour to occur near the front of the structure, and the sediment level to become much shallower (or even accreted) toward the downstream end. Furthermore, whereas the tests differ in the specific location of the deepest scour along the front of the structure, all show the deepest scour to occur at the piles rather than in the space between.
The model of the Roosevelt Bridge footing illustrated in Figures 4.9 and 4.10 shows typical scour behavior. This model is the 2 3X4 structure, with the pile cap located 1.33 in. above the initial sand bed, as shown. The flow depth is 4.2 in.
The front view, Figure 4.9 shows the deepest scour to occur on the left side of the central front pile. The side view, Figure 4. 10 shows the deepest scour along the side to occur at the second pile back, although the front, center scour is deeper. The dual structures such as this one typically exhibit the type of scour behavior shown, with two




W.L.
8.0
Pile Shape
4.0 circular
square
0.0 -' S. L.
-4.0 __'_'
-8.0 -4.0 0.0 4.0 8.0 12.0
Y (in.)
Figure 4.3 Single Pile Scour in Deep Flow, Front View (D=2.0 in., H=8.5 in.)
W.L.
8.0
Pile Shape
4.0 circular
square
N
0.0 -- ----------------- S.L.
-4.0 -I I I
-4.0 -2.0 0.0 2.0 4.0
X (in.)
Figure 4.4 Single Pile Scour in Deep Flow, Side View (D=2.0 in., H=8.5 in.)




Pile Shape
------circular
square

-- S. L.

-4.0 0.0 4.0
Y (in.)

Figure 4.5 Single Pile Scour in Shallow Flow, Front View (D=1.25 in., H=4.2 in.)

Pile Shape
-- - circular
square
- - - - - - - - - - -

I I I 1 I
-6.0 -4.0 -2.0
X (in.)

W. L.
-----------------------S. L.

I I I I
0.0 2.0 4.0

Figure 4.6 Single Pile Scour in Shallow Flow, Side View (D=1.25 in., H=4.2 in.)

-4.0

0.0-+-

-2.0
-4.0-

-8.0




W.L.
-- S.L.

0.0 2.0 4.0 6.0
Y (in.)

Figure 4.7 Single Pile Scour in Deep Flow, Front View
(D=1.25 in., H=8.5 in.)

8.0 4.0

00 -

W.L.
S.L.

x (in.)

Figure 4.8 Single Pile Scour in Deep Flow, Side View
(D=1.25 in., H=8.5 in.)

Pile Shane
circular square

0.0-+

' I
-2.0




56
almost distinct scour holes. When such a structure is not skewed to the flow, the front hole is considerably deeper, as shown. In the case of a skewed structure, the deepest point is sometimes near the front of the rear group of piles.

W. L.

-30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0
Y (in.)
Figure 4.9 Scour Hole at 2 3X4 Arrangement, Front View
(a/D=3.0, H=4.2 in.)

8.0-

[ I I I I
-20.0 0.0 20.0 40.0 60.0
X (in.)
Figure 4.10 Scour Hole at 2 3X4 Arrangement, Side View
(a/D=3.0, H=4.2 in.)




The scour around the similar 3X8 structure is shown in Figures 4. 11 and 4.12. The data shown is from two tests: the no pile cap test and the test in which the cap is located at the initial sediment bed level, shown in the illustrations. The front view shows that although the location of the outer ripples and the deepest point of scour vary somewhat between the two tests, the scour holes are generally very similar. The deepest scour is adjacent to the piles, and small peaks exist in the space between.
10.0
W. L.
5.0
-5.0
-30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0
Y (in.)
Figure 4.11 Scour Holes at 3X8 Arrangement, Front View (aID=3.O, H=8.5 in.)
The side view also shows similar scour holes. Irregularities in profile data, like the ripple in front of the no pile cap scour hole and the deep scour in front of the third pile in the pile cap group, appear exaggerated with the different horizontal and vertical scales. Finally, the view shows the accretion of sand behind the structures.
The views of scour near another structure with three piles normal to the flow is shown in Figures 4.13 and 4.14. As shown, the model tested is a no pile cap model with




58
a/D = 1; so there is no space between the piles. The frontal appearance of the scour hole is similar to that resulting from a single pile test.
15.0
10.0
W. L
5.0
-5.0 -- - n iea
-20.0 0.0 20.0 40.0 60.0
X (in.)
Figure 4.12 Scour Holes at 3X8 Arrangement, Side View (aJD=3.O, 11=8.5 in.)
For structures tested with 5 piles normal to the flow, sets of profile data for the two water levels tested are shown in Figures 4.15-4.18. For each of the water levels, data is shown from tests with no pile cap, the pile cap on the initial bed, and the pile cap located off the bed, as illustrated. The front and side profile shapes are typical, and show deeper scour occurring with lower pile cap levels. It is not obvious from either side profile that there is a relationship between the volume of sand accreted behind the structure and the size of the scour hole, although this must be the case. In many tests much of the accretion of sand occurs directly behind the structure or a long distance behind the structure. Thus, much of the sand may accrete in locations other than those shown.




-15.0
Figure

-W.L.
S.L.

-10.0 -5.0 0.0 5.0 10.0 15.0
X (in.)

4.13

Scour Hole at 3X8 Arrangement, Front View
(a/D=1.0, H=8.5 in.)

W.L.

0.0 -- -=1 S. L.
-5.0 -

'I I
-20.0 0.0 20.0 40.0
x (in.)

Figure 4.14 Scour Hole at 3X8 Arrangement, Side View
(a/D=1.0, H=8.5 in.)

15.0 10.0
5.0-

-40.0




4.0 -- W.L.
0.0I .. .. . S.L.
% %
-4.0- Pile Cap Level
! .------- no pile cap
-8.0 h2 = 3.75"
- h2 = 0.00"
I I I'
-20.0 0.0 20.0 40.0
Y (in.)
Figure 4.15 Scour Hole at 5X8 Arrangement in Shallow Flow, Front View (a/D=3.0, H=4.2 in.)

W.L.

Pile Cap Level
------- no pile cap
-h2= 3.75"
- h2 = 0.00"

-20.0 0.0 20.0 40.0
X (in)
Figure 4.16 Scour Hole at 5X8 Arrangement in Shallow Flow, Side View (a/D=3.0, H=4.2 in.)




10.0 0.0
-10.0
-20.0
Figure 4.17

10.0
. 0.0
-10.0

W. L.
rS.L.

-10.0 0.0 10.0 20.0 30.0 40.0 50.0
Y(in.)
Scour Hole at 5X8 Arrangement in Deep Flow, Front View
(a/D=3.0, H=8.5 in.)

-20.0 0.0 20.0 40.0
X (in.)

Figure 4.18 Scour Hole at 5X8 Arrangement in Deep Flow, Side View (a/D=3.0, H=8.5 in.)




62
The profile of the scour hole near the largest pile group studied, the 7X8, is shown in Figures 4.19 and 4.20. The scour hole is deeper and larger than those around the smaller structures. Nevertheless, the shape of the scour hole is generally similar.

-20.0 0.0 20.0 40.0
Y (in.)
Figure 4.19 Scour Hole at 7X8 Arrangement, Front View
(a/D=3.0, H=8.5 in.)

-40.0 -20.0

.L

0.0 20.0 40.0 60.0 80.0
X (in.)

Figure 4.20 Scour Hole at 7X8 Arrangement, Side View
(a/D=3.0, H=8.5 in.)




63
4.2 Single Pile Analysis
Because the strategy for predicting scour around multiple pile structures is based on the predicted single square pile scour depth, it is essential that scour around single piles be well understood.
As described in Chapter Two, the analysis of the scour around single cylinders has been rather complete. In particular, equation 2.1 by Sheppard and Ontowijo (1994) makes use of a wide range of single pile data, so it is perhaps the most suitable scour predictive equation. Therefore, equation 2.1 may be used to predict the value of deBut the multiple (square) pile structure predictive equations are based on d., the predicted scour depth for a single pile that is square, not circular. Therefore, an equation predicting depth of scour for a square pile is necessary. In order to make use of the understanding of scour adjacent to circular piles, the prediction of d. is based on that of de. The following form is used
d, = C, d, (4.1)
where C,, is a coefficient whose value is empirically derived.
One appropriate method of evaluating C, would be to compare the tests that are conducted on piles of the two shapes, of the same width and in the same conditions. However, there is a scarcity of such data.
In order to use more data to evaluate C., the following technique is applied to utilize all of the pile data from this study. First, the scour depth results of those circular




64
pile tests that were conducted for 7 hr., d,.7, are extrapolated to 26 hr. scour depths, d.at. This is done by applying equation 4.2, developed by Hanna (1978). Next, each value of d.a is compared with that predicted (for the same conditions) by equation 2.1, d.pred, shown in Table 4.2. The average of these values is Ce', as described in equation 4.3. Similarly, the scour depths measured at the square piles, ds.a, are compared with the depths predicted (for a cylinder) by equation 2.1, de.pred, shown in Table 4.2. The average of these values is C.', as described in equation 4.4. This procedure accounts for any differences in test conditions by applying these conditions into equation 2.1.

de.7hr
de.act : 0.88

(4.2)

Table 4.1 Measured and Predicted Circular Pile Scour Depths
test de.act de.pred de.acJde.pred
(in.) (in.)
1 3.84 5.82 0.66
2 6.26 5.94 1.05
3 4.65 4.55 1.02
4 1.87 2.41 0.78
5 2.23 2.44 0.91
6 3.09 3.38 0.91
7 4.42 3.52 1.26




65
C/ [de'act -0.94
de.pred
C'l=[ ds'act
d$.pred

(4.3) (4.4)

Table 4.2 Measured and Predicted Square Pile Scour Depths

test ds.,c ds.pred ds.a/d.pred
(in.) (in.)
8 3.42 3.38 1.01
9 3.59 3.52 1.02
10b 5.74 5.58 1.03
19 3.1 2.41 1.29
20 2.99 2.44 1.23

Finally, C.' and Cs' are compared. The ratio between these is assumed to account for the geometric difference between square and circular piles. The effect of this geometric difference on scour depth is used to evaluate C. as in equation 4.5. Therefore, the predictive equation for square pile scour is equation 4.6, where de is the predicted scour depths for a circular pile of the same width with matching flow and sediment conditions.

(4.5)

C s = 1.2 ds= 1.2.de

(4.6)




66
4.3 Scour at No Pile Cap Structures
As described in Chapter Two, the maximum local scour depth near a structure is believed to primarily depend on the water depth (as HID), the water velocity (as UfUJ), the relative mean grain size (as D5I/D), and the geometry of the structure. To a large degree, the effects of the first three of these have been determined by investigating scour near a single pile, so the scour determination near a multiple pile structure uses these results and concentrates on the effects of the structure's geometry.
With regards to the no pile cap structure, in this chapter a predictive equation is developed, accounting only for the geometric wetted shape of the pile group. It predicts the difference in scour of such a structure in comparison to that of a single square pile in the same flow conditions, such as equation 4.6. Thus the depth of scour for the no pile cap structure can be predicted. This is the motivation for referring to the equation for the no pile cap structure as the scour predictive equation, despite the fact that it only accounts for the geometry.
There are several ways in which an arrangement of piles without a pile cap may present various effective geometries to the flow. The number of piles normal to the flow, n, and its relationship with scour depth are investigated here. The number of piles downstream, m, determines the effective length of the structure. As previously addressed, effects on scour of various ma values was not investigated; a representative value of m--8 was chosen for study. In addition to this the pile spacing, a/D, was studied for its impact on scour depths. Also, since a multiple pile arrangement has a shape that is




67
vastly different from that of a single pile, the depth of flow is considered to affect its wetted geometry in ways similar to, but not identical to, the effects of a single pile's aspect ratio. Therefore, the depth of flow is included in deriving the geometric scour dependence, even though HID is already included in the depth of flow for a single pile. Finally, structure skew angles to the flow were not studied.
Therefore, the form of the predictive equations must account for all of these geometric effects (except skew and the value of in). One approach would be to explicitly include an expression for each of n, a/D, and H. Separate studies of the dependency of scour on each of these would yield the particular nature of their expressions, and thus the form of the predictive equations themselves. This would be similar to the approach taken by Sheppard and Ontowirjo (1994) in developing the predictive equation for a single cylinder.
In order to streamlAine the equations, an alternative approach is taken. This approach makes use of the fact that scour depths are so critically dependent on the width of a structure, so much so that pile scour depths are usually presented normalized by the pile width.
Similarly, in this analysis of the no pile cap structure, its depth of scour is considered to be highly dependent on its width. However, the appropriate value to use to represent its width is not immediately clear for such a complex structure. Because of the interdependence between scour depth and structure width, the resulting scour depths are used to derive the formula for the "effective width", D*, for the various structures. Scour dependence on the number of piles normal to the flow and the pile spacing is used




68
to formulate D*, which is then a function of these geometric parameters. Thus the value of D* is essentially empirical.
In further relating the approach toward multiple pile arrangements with that toward single piles, the effect of various water depths on the resulting scour is assumed to follow the same trend with the two classes of structures. Pile group scour depth is considered to be dependent on I)*, similar to considering scour depth dependent on H/D for a single cylinder.
The tests conducted on the no pile cap structures are described in Table 3.3. Because tests 20 and 21 are tests on a single square pile, these are viewed as lxi, no pile cap structures. The other arrangements are nX8 piles with a/D=3.0, except test 26 where a/D =1.0. Two water depths are investigated.
4.3.1 Effective Width of No Pile Cap Structure
The development of an expression for D*, the effective width, is the first step toward the development of the no pile cap scour predictive equation. Since scour is dependent on the width of the structure, it is expected that the value of D* will represent the structure's potential for scour.
The parameters of study affecting the wetted geometry of the no pile cap structure are the number of piles normal to the flow, the pile spacing, and the water depth. In determination of the effective width, it is reasonable to assume that the number of piles and their spacing are the critical geometric factors. Therefore, these are included in the formula for D*, along with the width of a single pile. By observing the




69
relationship between the depth of scour at a no pile cap structure, d.npc, and the values of n and a/D, the form of D* is derived.
The relationship between the depth of scour and the number of piles is best shown in the results of the no pile cap tests in 8.5 in. water depth, shown in Figure 4.21. The first data point, n= 1, is the depth at a single pile. The remaining data points are on structures with pile arrangements 3X8, 5X8, and 7X8.
7.0 .. .. . . . . . . . . . .. .
6.0 . . . . . . . . . . .. .
* Water Depth and Pile Spacing
* V-- H=8.5" aID=3.O
3.0 -. . . . . . . .. .
13 5 7
n (number of piles)
Figure 4.21 Scour Depths at No Pile Cap Models in Deep Flow
Regarding the development of D*, Figure 4.21 shows deeper scour with an increased number of flow-normal piles. Furthermore, Figure 4.21 shows this dependence to weaken as the structure gets very wide. Presumably at some number of flow-normal piles, the local flow acceleration due to blockage is a maximum, and additional piles




70
would not change the flow rate either between the central piles or around the outermost piles.
In other flow depths, it seems reasonable to assume that the scour dependence on number of piles would reflect this trend. Two of these structures, the single pile and the n--5 arrangement, were tested in a shallower (4.2 in.) depth for comparison. The comparative results are shown in Figure 4.22. Like the results in the deeper water, increased scour depth can be seen with increased number of piles. However, the dependence on water depth is shown to be much more critical with the larger structure (in fact, the single pile scoured slightly deeper in the shallower flow).
-d 5.0 .. .. . . . .. . . . . .. .
Water Depth~ and Pile Spacing
--k- H=4.2" a'fl=3.O'
3.0 .. ........ V- H=8.5" aID=3.O
1 3 5 7
n (number of piles)
Figure 4.22 Scour Depths at No Pile Cap Models in Two Flow Depths
This lends support to the approach of considering the larger, more complex structures to have an effective width value. The width of the single piles, at 1.25 in., is




relatively small; in the two water depths studied, the values of H/D are 3.4 and 6.8. Recalling that the scour predictive equation for a single pile (cylinder) represents water depth as a tanh(H/D) relationship, these values of H/D are clearly on the flat portion of such a curve. Therefore, for the given value of D (for a single pile), it is not surprising that the scour depths were approximately the same.
However, for the larger structures, with n--5, in the same water depths the scour depths differ significantly. Assuming that a similar depth and scour relationship applies, then, the effective values of the aspect ratio are much lower for the two multiple pile structures than for a single pile. Therefore the effective values of the no pile cap tests' aspect ratios fall below the flat region of the curve, and depth of scour is more dependent on the flow depth. Therefore, the effective value for the pile group's width is not D, but is some larger value, D*.
It is presumed, then, that the shape of the width vs. scour depth curve in Figure 4.22 depends more on the water depth for higher values of n. Therefore, the degree of curvature of this curve would be higher in shallower waters, and in deeper waters this curve would be more linear.
The complete data set on no pile cap scour depths is shown in Figure 4.23. Like Figures 4.21 and 4.22, the data shows investigations into scour dependence on both number of normal piles as well as water depth. Figure 4.23 also shows the results of the investigation into pile spacing. Each model in the tests previously discussed features a pile spacing value of a/D=3 .0, representing common current bridge design. As shown




in Figure 4.23, deeper scour resulted from the test conducted on the 3X8 structure (in deeper water) when a/D=1.0, or there is no space between the piles.
7.0 .................................................
6.0
40.0 ..... ............. Water.D..h d Pile Spadn .
- .7 H=8.5- a/D=3.0
3.0 .......... .. ....... H =8.5' a .0
I I I I I I
1 3 5 7
n (number of piles)
Figure 4.23 Scour Depths at All No Pile Cap Models Tested
Based on these observations, then, a no pile cap structure is effectively wider with an increased number of piles normal to the flow. Such a structure is also effectively wider with a reduction in the pile spacing, matching scour trends observed by Hanna (1978). The form of D* should reflect these trends.
Other features of the form of D* are intuitively apparent. If there is no pile spacing then the apparent width is equal to the actual width, so if a/D = 1, then D*=nD. Furthermore, as pile separation becomes very large, the scour holes become independent and D*=D.




73
In order to reflect these bounds, the following form of effective width is investigated
D*- (n-1)D +D (4.7)
where s is some value to be determined from scour data.
The most successful approach toward determining the value of s is based on comparison of scour depth results from the two tests on the 3-pile-wide structures, both in the deeper flow. The assumption is made (temporarily) that the effective aspect ratios of the two tests are high, so the depth of scour is not dependent on the depth of flow. The other test conditions are essentially matching between the two tests. According to this approach, then, the normalized scour depths (d.npc/D*) of the two no pile cap tests are expected to equal one another. Therefore
(d.npc) ) (d.npc (4.8)
test 22 = D* )test 26
so
(D*)22 (d.npc)22
(D*)26 (d.npc)26
Inserting the values of pile spacing and resulting scour from these two tests yields
(3-1).1.25+1.25
3.0s 4.68 (4.10)
(3-1).1.25+1.25 5.42
1.OS




solving for s
s=O.55
Therefore, the effective width, D*, is
D*= (nID+D (4.11)
4.3.2 Scour Depth Analysis
Whereas Figures 4.21, 4.22, and 4.23 plot scour depth against number of piles normal to the flow, a more strategic approach can be used to isolate various scour dependent parameters. This makes use of the effective width concept, and also of a set of assumptions regarding the nature of the scour depth dependency on the depth of flow for no pile cap structures.
Figure 4.24 shows the same data using the approach intended to isolate the various geometric parameters. The assumption is now made that the effective aspect ratio, IUD* is significant, and the scour depths are shown with respect to this value. The scour depth for the no pile cap structure, d.npc, is shown normalized by the appropriate value of d., the depth of scour for a single pile in the same water depth and conditions. By this approach, the flow conditions are accounted for, and the value of d.npc/d. is assumed to depend only on the geometry of the no pile cap structure.
Therefore, the normalized scour depths for the two single pile tests are d.npc/ds--1.0. In this text, subsequent figures will not feature these data points, for their primary role is for the purpose of normalizing the scour depth of the multiple pile structures.




2.2 n=7
V Relative Depth and Pile Spacing
n=fi5 A H/Di3.4 aADff3.0
V V 11D68 a/D3.0
1.8 V V H/D-6.8 a/Dl.0
n5 V
1.4
n-1 n=1
1.0 A V
I I i I
0.0 2.0 4.0 6.0 8.0
H/D*
Figure 4.24 Normalized Scour Depths at No Pile Cap Structures
The same associations that were noticed in the previous illustrations of the resulting scour depths are apparent in Figure 4.24; increased scour results from an increase in the values of either I-I/D* or n, or a decrease in the value of a/D. Nevertheless, this presentation of the data is still confusing, concealing the independent contributions of each of these geometric parameters.
In order to simplify this approach, the concept of a relative width is defined
Relative width = D
D
The same data (minus the results from the single pile tests) are shown in Figure 4.25, plotted with respect to II/D* and showing the values of the relative widths. The




76
assumption is made that the normalized value of d.npc is a function of only 2 variables: IHD* and D*/D.
* Relative Width
2.4 ...... : ...... ...... . ..... : D /D =428
* !i D/D=3.19
* D/D=3.00
* *D/D=2.09
2. ..... ..... .. .... .. .. I ... ... /
2.0
. . . ... . . ... .. . . . . ... . ... . . .
1.2 . . . ... ... . . .. . . .. . ... . . .
I I i I I
0.0 1.0 2.0 3.0 4.0
H/ D*
Figure 4.25 No Pile Cap Scour Depths and Relative Widths
The data points shown as circles are from the 2 tests conducted on the model featuring 5 piles across the flow. They indicate that curves of equal D*/D would ascend generally up and to the right on a plot such as Figure 4.25. Determining the shape of such a curve is difficult because of the scarcity of data points.
At this point the assumption is made that the scour dependence on water depth for a no pile cap structure mimics that for a cylinder. Therefore, the expression correlating the depth of scour and the water depth is represented by
d.npc
=f[tanh (4.12)




The form of this function is further defined by recalling that the intent of this equation is for the purpose of predicting scour at typical bridge footings; typically these feature significant pile spacing. For such a structure, at shallow water depth, the scour holes adjacent to the individual piles are small. At a very shallow depth, then, the scour holes at the individual piles are so small that they are independent from one another. Therefore, at very small values of HD*, d.npc is equal to d., the scour depth at a single pile (and at very shallow water, d, approaches 0). For a given value of D*/D, then, the resulting form of the depth dependence for the normalized scour depth follows
d = I f Cl tah(CH) (4.13)
where C1 and C2 are constants to be determined by the data. Therefore the following equalities exist
Peak value of d.npC 1 + C1
ds
Attenuation on depth of flow = C2
The curve in equation 4.13 is fit to the only two data points with the same value of D*/D, shown in Figure 4.26. The resulting curve is
d.npc H
-= +3.9 tanh (0376-) (4.14)

so for n=5, C1=3.19 and C2=0.376.




2 . . . . . . .
. ... . . . ... . . ... .
1.0 .......................... ........
0 D*/D = 3.19
1 + 3.19 tanh(O.376 H/D*)
0.0 I I I
0.0 2.0 4.0 6.0
H/D*
Figure 4.26 Scour at n=5 Structures, Fit To Equation 4.7
A form of this same equation is fit to the other data points. The number of data points does not permit exactly the same technique to be used with each D*/D value, so for these both C1 and C2 cannot be solved explicitly. To resolve this, it is assumed that the value of C2 = 0.376 is constant for fitting equation 4.13 to the various values of D*/D. By constraining the value of C2 and treating C, as a variable, it is postulated that for a given effective aspect ratio, the relative width determines the normalized scour depth, but the sensitivity of that depth to variations in HID* is constant for all such structures. The resulting equation follows
d.npc = C
1+C1" tanh (0.376H (4.15)
ds + a

. .. . . . .. . I . . . . . . . . . . .. . . . . . .
. .. . .. . .. . . . .. . . . ... . . . ... . . . .




For each data point representing a value of D*/D, the empirical value of C, can be solved from equation 4.15. These, and the resulting curves, are shown in Figure 4.27. The trend is clearly shown that decreasing values of D*/D result in decreasing values of C1. Not shown in the figure, D*/D=1.0 represents a single pile, and would correspond with d.npc/d,=1.0, and therefore C1=0.O.
3 . . . .. . . . . .. . . . . . . . . . . . . . .
3 .0 . ------. ....... ........ ..............
. . . . . . . . - - - - -
2 .0 ... ... .. .. ...
. . . . ... . . . . . ..: .. . . . .
1.0 .- .........- ., | ..
0.0:/D=2.09 C = 0.68
0.0 2.0 4.0 6.0
H/D*
Figure 4.27 No Pile Scour Depths Fit to Equation 4.15
This empirical D*/D and C, relationship is shown in Figure 4.28. The
relationship is nearly linear. Furthermore, this line appears to intercept D*/D=1.0 and C1=0.0, a necessary stipulation regarding a single pile, for the reason described above. For lines constrained to intercept this point, a least squares fit determines the equation of the line to be
C1 = 0.64(-- 1) (4.16)




2 .0 . .. . .. . .
1.50.. .. .. . .. . ... .. .
2 0 . . . .. . . . . . . .
.1.00. .. . .
0.50 .. .. . .. .. . .. ... . .. .. .

3.00 D*/D

Figure 4.28

Relative Widths and Resulting C, Values

This formula for C1 is useful in the following analysis. Because of the simidlarity of the curves shown in Figure 4.27, it is possible to numerically collapse these into a single curve. This is done by subtracting 1.0 from each curve and the dividing the curve by the value of C,. The resulting curve is applicable to all of the data, and has the following expression

= tanh (0.376C1 D*.

This curve is shown in Figure 4.29. The data points are also shown, normalized by the value of C1 predicted by equation 4.16.

(4.17)




1.0
0 ... .. ...... ... ..... .. ... ... .. . .. ... ..... . ... .
0.8 ........ ........ ....... M ....: ........ .........
0 .6 ........ ...... .. ........ ........ ........ ........
.0 .......... ... ...... ...... ...... -----OA . . . . ... . . . .. .

H/D*

Figure 4.29 No Pile Cap Scour Data Fit to Equation 4.17 Solving equation 4.17 for d.npc results in equation 4.18 d.npc = d. + C1 tanh (0.376) where C1 and D* are defined in equations 4.16 and 4.11: C1 = 0.64(- 1) (n-1)D
(a 055+
\D)

(4.18)




The predictive equation for no, pile cap structures is equation 4.18. This equation accounts for the geometric effects particular to no pile cap structures. Application of this equation toward prediction of scour depth near such a structure would require a value to be input for d., the predicted depth of scour at a single square pile. One possible resolution of this would be the use of equations 2.1 and 4.6 to predict the value of d., the depth of scour adjacent to a square pile, and equation 4.18 to predict d.npc.
4.4 Scour at Pile Cap Structures
Many designs of multiple pile footings feature a pile cap partially submerged below the mean low water level. Of those pile caps designed to be completely emergent from the water surface, many are at a level that would cause them to become partially submerged in the case of a severe flood. For this reason, the ability to predict local scour for these geometries is of utmost importance.
Such a structure presents a complex geometry. Scour depth analysis requires investigation not only into flow and sediment qualities, but also into the number of piles, their spacing, the aspect ratio, the shape of the pile cap, and also the location of the pile cap. Just as the predictive equation for the no pile cap structure uses the scour depth for a single pile, the predictive equation for a pile cap structure will make use of the scour depth for the no pile cap structure. Therefore, only the geometric features of the pile cap itself are necessary to complete the predictive equation for a pile cap structure.




83
In Chapter Three it was explained that only one class of pile cap is investigated in this study. The pile cap, like those shown in Figures 3.2 and 3.3, is rectangular and features scaled dimensions that reflect those appearing on specific current pile cap designs. It is also explained that investigations into pile cap structures are limited to analyses of those that feature a pile spacing of a/D=3 .0. With these geometric restrictions the only variable in need of study for the pile cap structure analysis is h2, the level of the bottom of the pile cap above the undisturbed bed level.
Figure 4.30 shows the results of all of the scour tests on multiple pile structures. The depth of scour for each pile cap test, d.pc, is shown plotted against hfil, the normalized pile cap elevation above the undisturbed bed. Therefore h2/JI0 refer to models with pile caps at and above the initial bed level, respectively. A model featuring h/Hf=1.0 refers to a model whose pile cap bottom location is at the water surface, to which no pile cap scour test data applies.
Observing tests on a given model in a given water depth, one trend is immediately apparent from Figure 4.30: scour depth is greater near a structure with a lower pile cap (i.e. the smaller h2.IH the larger the scour depth). Physically this could be caused by one of the following: a larger horseshoe vortex in front of the effectively larger structure, water being forced down below the pile cap, or just an accelerated flow in the constriction between the pile cap and the bottom. Any number of these effects would be greater in magnitude the lower the pile cap.




12.0 -

-1.5 -1.0 -0.5
h 2/H

ElV
V
Test Conditions *
* n-3 H-42
E] n=3 H=-8.5"
4 n-4 H -4.2 .....
A n=5 H =4.2* V n-5 H=-S.5"
* n=7 H=85

0.0 0.5 1.0

Figure 4.30 Multiple Pile Scour Depths and Pile Cap Locations
The results shown in Figure 4.30 include effects of not only pile cap location, but number of piles and water depth (other flow conditions were constant between the tests) as well. In the interest of isolating the effects of the pile cap location, this data can be compared with results from tests in the same water depth on a structure with the same pile arrangement but no pile cap. Because scour depth at a no pile cap structure is a function of the number of piles and their spacing, this technique would isolate the effects of the pile cap location.
This approach results in the relationship shown in Figure 4.3 1, which shows all data points from tests featuring pile cap locations at or above the initial bed level. Like Figure 4.30, this plot shows the pile cap location as h2/H, and shows the resulting depth

I U,

10.0 --4

8.0 -

6.0 -




85
of scour. The scour depths are normalized by the depth of scour achieved adjacent to the same arrangement of piles without the pile cap, in the same flow conditions.
1.8 .. . . .. . . .. . . .:. . . .. . . .
Test Descriptin
s%.. --5 H/D=3.4
1.6 ............. ...............
'S.'.n-5 1/D=6.8
.".. -El n-- 3 HID=6.8
01.8
0.0 0.2 0.4 0.6 0.8 1.0
h2/H
Figure 4.31 Normalized Scour Depths and Pile Cap Locations (Pile Cap Bottom At or Above Initial Bed Level)
As shown in Figure 4.3 1, this approach results in a remarkably simplified correlation. The data collapses to a single curve (at least within the accuracy limitations of the procedure). Therefore, normalizing the pile cap scour depths by the corresponding no pile scour depths eliminates all scour dependent variables except the location of the pile cap.
In this range of h/Il values, the curve describing the scour depth dependence on the location of the pile cap appears linear. End effects as the pile cap location is very near the water surface or very near the initial bed level do not appear significant; results from tests run in these conditions coincide with the linear relationship resulting from the




other tests. The equation of the average least squares fit between these points is the following
d.pc H-d1.78c 0.78H (4.19)
and the predictive equation for scour depth adjacent to such structures is equation 4.20, pertinent when h2f)>O
d.pc = d.npc [1.78 0.78 hi (4.20)
When the data points from tests featuring h/H With regards to the data featuring h/H<0, with other conditions constant the scour depth appears to vary linearly with the normalized pile cap location. The slope is different than that resulting from the data points in Figure 4.30. Evaluating this line results in equations 4.21 and 4.22, which apply when the pile cap is partially submerged in the undisturbed (initial) bed,
,dpc = 1.78 0.48-L2 (4.21)
d.npc H (.1




d = d.npc 1.78 0.48L

(4.22)

2 .8 ..................................................................
equation 4.22 equation 4.20
applies applies
2.4 ... .. . ..S.. . . . *.. . .
2 .0 -a :. ............ :........... .. ..........................
n-. .8
1.2 ....- n=3 HD=6 ....
0.8 '
-1.5 -1.0 -0.5 0.0 0.5 1.0
h2/H

Figure 4.31 Normalized Scour Depths and Pile Cap Locations
It should be noted that the data from which equation 4.22 is derived is more scarce than that which is used in deriving equation 4.20. A particularly conservative scour predictive approach could apply equation 4.20 throughout the range of pile cap positions.
Equations 4.20 and 4.22 account for the geometry pertaining only to the pile cap itself (for the given general pile cap design). For predicting maximum equilibrium scour for such structures, equation 4.18 should be used to predict d.npc. Equation 4.18 requires an estimate for the value of ds, such as that predicted by equations 2.1 and 4.6.




88
By such an application, equations 4.20 and 4.22 account for flow velocity and depth, sediment size, number of piles, pile spacing, and the pile cap location.