UFL/COEL99/012
TEMPORAL DEVELOPMENT OF CLEAR WATER LOCAL SCOUR AROUND CYLINDRICAL PIERS by
Edward Albada Thesis
1999
TEMPORAL DEVELOPMENT OF CLEAR WATER LOCAL
SCOUR AROUND CYLINDRICAL PIERS
By
EDWARD ALBADA
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
1999
ACKNOWLEDGMENTS
First and foremost I would like to express my gratitude towards Dr. D. Max
Sheppard for his encouraging words and thoughts, without which this thesis would not have developed into what it has, and for the countless opportunities given to me in furthering my academic career. It has truly been a pleasure working with such a compatible, easygoing, laidback professor with whom I share so many common interests.
I am also grateful to Sterling Jones with the FHWA and Shawn McLemore and Rick Renna with the FDOT for funding this work, especially Sterling Jones for the use of his data.
I must also thank the Massachusetts crew, the COB Laboratory crew, and all the professors for all the time spent explaining various subjects, both inside and out of the classroom, and of course, Becky and Helen, without whom we would all be lost.
Thanks also go to my roommates who lived with me at 1928 1 st Aye, as well as my fellow students from all over the world, for making my entire graduate education enjoyable. Particularly, Tom, Thanasis, Lisa, Wendy, Bill, Matt, Roberto, Guillermo, Erica, Al, and Nicolas. I intend to visit all of you in your countries eventually.
To Nicole you were the reason I returned to Gainesville. I thank you for the
wonderful times we have shared together whatever the future holds for us I will always love you.
Finally to my family Mom and Dad, Laurens & Kelly, and my grandmothers thank you for the support and encouragement from near and afar.
TABLE OF CONTENTS
pM,,e
A CKN O W LED GM EN TS .................................................................................................. ii
LIST OF TA BLES ............................................................................................................... v
LIST OF FIGU RES ............................................................................................................ vi
KEY TO SYM BOLS ......................................................................................................... ix
ABSTRA CT ....................................................................................................................... xii
CHAPTERS
I IN TRODU CTION .......................................................................................................... 1
2 BACKGROUND AND LITERATURE REVIEW ........................................................ 7
2.1 Background ....................................................................................................... 7
2.2 Scour Form ation for Steady Flow .................................................................. 10
2.3 Effect of the V arious Param eters .................................................................... 16
2.3.1 Effect of V elocity Ratio U/U .............................................................. 16
2.3.2 Effect of A spect Ratio yo/b .................................................................. 20
2.3.3 Effect of Sedim ent to Pier Size D5o/b .................................................. 21
2.4 Literature Review ........................................................................................... 22
3 EX PERIM EN TA L PROCEDU RES ............................................................................ 33
3.1 Introduction .................................................................................................... 33
3.2 Equipm ent ....................................................................................................... 33
3.2.1 Flum e ................................................................................................... 34
3.2.2 Electronic Apparatus ........................................................................... 37
3.2.2.1 A coustic transducers ............................................. I ................. 37
3.2.2.2 Electrom agnetic current m eters ............................................. 38
3.2.2.3 D igital therm om eter ............................................................... 38
3.2.2.4 Cam eras ................................................................................. 39
3.2.3 Test Setup ........................................................................................... 39
3.2.4 M odels ................................................................................................ 40
3.2.5 Sedim ent ............................................................................................. 40
3.3 Laboratory Test Procedure ............................................................................. 42
3.3.1 Bed Preparation .................................................................................. 42
3.3.2 Laboratory Procedure ......................................................................... 42
4 DA TA REDU CTION AN D AN A LY SIS .................................................................... 43
4.1 Raw D ata ........................................................................................................ 43
4.2 D ata Adjustm ent and Sm oothing ................................................................... 44
4.3 Experim ent Sum m aries .................................................................................. 46
4.4 A nalysis of Data ............................................................................................. 49
5 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ................................ 73
5.1 Sum m ary ......................................................................................................... 73
5.2 Conclusions .................................................................................................... 74
5.3 Recom m endations .......................................................................................... 78
APPENDICES
A IND IV IDU A L CURV E FITS ...................................................................................... 82
B SEMILOG PLOTS OF SCOUR DEPTH VERSUS TIME ......................................... 95
C SCOU R H OLE CON TOU R PLOTS .......................................................................... 99
REFEREN CES ................................................................................................................ 103
BIO GRAPHICA L SKETCH ........................................................................................... 106
LIST OF TABLES
Table page
4.1 Summary of experiments completed at USGS Laboratory........................... 47
4.2 Summary of experiments completed at FHWA Laboratory ......................... 48
LIST OF FIGURES
Figure page
2.1 Diagram showing forces on a particle resting on the bed ..................................... 8
2.2 Shields' diagram ................................................................................................... 9
2.3 Diagram showing flow vortices around pile in flow .......................................... 12
2.4 Downflow variation with depth from Ettema (1980) .......................................... 13
2.5 Dependence of nondimensionalized scour
depth on velocity ratio for two sediment sizes ................................................. 17
2.6 Changes in bed features with increasing velocity from Snamenskaya (1969) ......... 19
2.7 Dependence of equilibrium scour depth on aspect ratio for which
U/Uc and d50/b are held constant ................................................................... 20
2.8 Variation of scour depth on d50/b with U/Uc=I and y0/b>3.0 ......................... 22
3.1 Aerial schem atic of flum e ................................................................................... 35
3.2 Schematic figure of the crosssection of flume ......................... 35
3.3 Detail of MTA arrangement used in smallpier experiments ............................. 38
3.4 Photograph of cameras used for the 0.114 m pile in casing ............................... 39
3.5 Grain size distribution for sand #1 (d50 = 0.22 mm) .......................................... 41
3.6 Grain size distribution for sand #2 (d50 = 0.80 mm).......................................... 41
4.1 Scour depth versus time plots for the video and acoustic transponder data.
(b=0.305m, d50=0.80mm, y0=l.268m, and U=0.381m/s) .............................. 44
4.2 Comparison between raw and adjusted scour depth data ................................... 46
4.3 Smoothed scour history plots for all UF/USGSBRD Laboratory experiments ...... 47
4.4 Smoothed scour history plots for all FHWA Laboratory experiments.............. 49
4.5 Comparison of ds/dse versus time for USGS Laboratory experiments............. 50
4.6 Equilibrium scour depth versus time for equilibrium for USGS
Laboratory experiments .............................................................. 51
4.7 Plot of ds/dse versus tlte for USGS Laboratory experiments........................ 54
4.8 Rate of scour (dldt(ds/dse)) versus ds/dse for all experiments ...................... 55
4.9 Power spectrum of turbulent bursts in the horseshoe vortex
in a wind tunnel from Baker (1978) ................................................. 58
4. 10 Plot of rate of scour versus scour depth showing increasing pier diameters .....62
4.11 Author's hypothesis of the relative contributions of the mechanisms on
the rate of scour ....................................................................... 64
4.12 Diagrams representing early and later stages of scour................................ 66
4.13 Plot of equilibrium scour depth versus t90 for all experiments..................... 69
4.14 Plot of equil ibrium. scour depth versus fl. for all experiments ...................... 70
4.15 Plot of equilibrium scour depth versus f2 for USGS Laboratory experiments...71 Ai Curve fit of smoothed data for experiment 3........................................... 82
A2 Curve fit of smoothed data for experiment 4........................................... 83
A3 Curve fit of smoothed data for experiment 6........................................... 84
A4 Curve fit of smoothed data for experiment 9........................................... 85
A5 Curve fit of smoothed data for experiment 11 ......................................... 86
A6 Curve fit of smoothed data for experiment 12 ......................................... 87
A7 Curve fit of smoothed data for experiment 13 ......................................... 88
A8 Curve fit of smoothed data for experiment 57 ......................................... 89
A9 Curve fit of smoothed data for experiment 74 ......................................... 90
Al0 Curve fit of smoothed data for experiment 86......................................... 91
AII Curve fit of smoothed data for experiment 126 ....................................... 92
A 12 Curve fit of smoothed data for experiment 128 ....................................... 93
A13 Curve fit of smoothed data for experiment 133 ....................................... 94
Bi Semilog plot of scour depth versus time for experiment 3............................ 95
B2 Semilog plot of scour depth versus time for experiment 4............................ 96
B3 Semilog plot of scour depth versus time for experiment 6............................ 96
B4 Semilog plot of scour depth versus time for experiment 9............................ 97
B5 Semilog plot of scour depth versus time for experiment 11.......................... 97
B6 Semilog plot of scour depth versus time for experiment 12 ......................... 98
B7 Semilog plot of scour depth versus time for experiment 13 ......................... 98
Ci Scour hole contour plots for experiment 3.............................................. 99
C2 Scour hole contour plots for experiment 4............................................. 100
C3 Scour hole contour plots for experiment 6............................................. 100
C4 Scour hole contour plots for experiment 9............................................. 101
C5 Scour hole contour plots for Experiment I I........................................... 101
C6 Scour hole contour plots for Experiment 12........................................... 102
C7 Scour hole contour plots for Experiment 13........................................... 102
KEY TO SYMBOLS
AI particle area constant
A2 particle volume constant
b pile width (diameter)
B channel width
c exponent related to bed load
C constant
Cd drag coefficient
Cwr rectangular weir coefficient
d16 sediment size for which 16 percent of bed material is finer
ds0 median sediment diameter
d84 sediment size for which 84 percent of bed material is finer
d, scour depth
dse equilibrium scour depth
f frequency
fl function
f2 function
Ff frictional force
F, normal force
Fr Froude number
Frc critical Froude number
g acceleration of gravity
H head over the weir
Ki constant
K flow intensity factor
L length of pier
N, sediment number
Nsc critical sediment number for sediment removal
P power
Pw weir height
qs discharge per unit width
Q discharge
r radial distance
Re* boundary Reynolds number
s relative sediment density
St Strouhal number
te time required for scour depth to reach equilibrium
t90 time required for scour depth to reach 90% equilibrium
U mean depth average velocity
U0 angle component of velocity
u*C critical bed friction velocity
u velocity near bed
u, bed shear velocity
u*C critical bed shear velocity
V pier downflow velocity
w width of flume
yO depth of flow
rate at which particles in stagnation plane are transported A dune height
Xdune width
0 angle of attack of flow
v kinematic viscosity of water
p density of water
Pm density of mixture
1:, Shields' parameter
TO bed shear stress
co frequency
7's specific weight of sediment
7m specific weight of mixture
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science TEMPORAL DEVELOPMENT OF CLEAR WATER LOCAL SCOUR AROUND CYLINDRICAL PIERS By
Edward Albada
August 1999
Chairman: Dr. D. Max Sheppard
Major Department: Coastal and Oceanographic Engineering
When a bottom mounted structure such as a bridge pier is located in an erodible sediment and is subjected to water flow, local scour will occur provided the flow velocity is sufficiently large. The local scour processes are complex and vary in relative magnitude as the scour hole develops. The rate at which scour occurs is equally complex and difficult to predict. For a steady flow velocity the scour hole will deepen with time until an equilibrium depth is reached.
Both the equilibrium scour depth and the rate at which the hole develops is
important in the design of structures that will experience scour. This thesis analyzes local scour time history data for a number of long duration experiments. The structures are circular piles with diameters ranging from 0. 1 14m to 0.914m. The University of Florida tests were performed at the USGSBRD Laboratory in Turners Falls, Massachusetts. The FHWA tests were performed at the Turner Fairbanks Laboratory in McLean, Virginia.
Attempts are made to determine the parameters affecting the rate of scour, the variation of rate with scour hole depth, and the time required to reach equilibrium. Using observations made of the dependencies of various parameters on the rate, a predictive method for determining the scour depth at any time based on the conditions of the experiment is presented.
CHAPTER 1
INTRODUCTION
1. 1 Motivation
There is a long history in the use of rivers and bridges as means of transportation. Initially, rivers were used to carry goods both downstream and upstream because of the advantages of waterbased transport. Eventually, over time, as more settlements flourished inland away from both coasts and rivers, the need arose for landbased transport and the very rivers that were once beneficial to transportation became hindrances. Bridges were developed to connect the banks between which the rivers flowed.
The development of bridge design has become very technical and involved, but for most bridges support comes in the way of piles driven into the bed upon which the bridge sits. The piles hinder the natural flow of the river, and as a result water is forced to accelerate around the piles, and sediment surrounding the piles becomes scoured out, creating a depression. This depression must be accounted for in assuring the structural stability of the pile for a specified storms condition.
The importance of predicting the equilibrium depth of scour cannot be
understated. Underprediction can result in the collapse of the bridge, resulting in expensive delays, loss of property and even fatalities. On March 10, 1995, the Interstate 5 bridge over Arroyo Pasajero in California collapsed as a result of scour during a flood
2
event, killing seven people (Truhlar & Telis, 1997). Brice and Blodgett (1978) determined that approximately half of 383 bridge failures studied were caused by local scour, most of them due to erroneous equilibrium depth predictions. The added cost for ensuring the structural integrity of a bridge easily outweighs the expense of having to replace the bridge once it has failed. However, overprediction can result in unnecessary expense and can add to the construction time needlessly. For the proposed Bonner Bridge over Oregon Inlet in North Carolina, a 20 percent reduction in the estimated equilibrium scour depth can save close to a million dollars in construction costs (D. Dock, Parsons Brinkerhoff, Raleigh, NC, personal communication, March 1998).
The complexities of the river flow, with chaotic turbulence and erratic bank
behavior make scour prediction extremely difficult. The very parameters with which the engineers work are usually determined statistically for a specified storm condition which may or may not occur during the designed lifetime of the structure. Thus, the success or failure of the design is largely dependent on the probability of a storm event that is more severe than the one used for design.
Streambed erosion in the vicinity of bridges can be divided into the following additive components:
1) Longterm aggradation and degradation. Aggradation and degradation are
erosion or deposition of sediment in the riverbed due to a change in the
equilibrium of the river upstream and/or downstream of the bridge site. These elevation changes occur independently from the presence of the bridge, and are
attributed to either natural or maninduced processes affecting the path of the
river, the sediment concentration, or the flow intensity. Factors that contribute to
long term aggradation and degradation include channelization, changes in downstream hydraulic control, cutoffs or meander loops, regulation or diversion of stream flow, changes in basin rainfallrunoff characteristics, climate changes, gravel mining from the stream bed, dams, reservoirs, changes in basin land use, and catastrophic floods (Landers & Mueller, 1996). Aggradation and degradation are generally slow processes, but the longterm trend must be evaluated for the lifetime of the structure.
2) Contraction Scour. Contraction scour is the erosion of sediment due to the
reduction in the channel flow area of the river, either by natural obstructions created in the course of the river or manmade supporting structures such as roadway embankments which project into the channel. In keeping with the law of continuity, a decrease in the channel width will increase the velocity of the river to maintain a constant water discharge. The increase in velocity correspondingly increases the shear stress on the bed, and sediment is eroded. The removal of bed material gradually increases the channel depth (thus increasing the crosssectional area of the river) until equilibrium is reached balancing the shear stress due to the velocity of the stream and critical shear stress for the onset of particle mobility. The increase in flow velocity caused by contraction scour can also affect local scour around the bridge piers significantly once a transition is made from a clearwater to a livebed condition when a certain critical velocity is exceeded. The differences between clearwater and livebed scour will be discussed further in this chapter.
3) Local Scour. Local scour is caused by vortices and eddies which are
created by the disturbance of the flow pattern around structures such as bridge
piers. The pier effectively becomes an obstruction to the flow, forcing the flow to
accelerate around it. This acceleration initiates the scour process. The main scouring mechanism is controlled by a horseshoe vortex system, formed as a
result of flow separation from the leading edge of the scour hole. The mechanics
of local scour are more thoroughly described in Chapter 2.
Both equilibrium scour depth and the time rate of scour are dependent on the
velocity of the water flow. Unless specified otherwise, flow velocity in this thesis refers to the depthaveraged velocity for fully developed flow. At low velocities, the shear stress on the bed is not large enough to initiate sediment transport. As the velocity increases past a critical value, transport of bed material is initiated. Clearwater scour is defined as local scour which occurs when the flow velocity is below the value needed to initiate sediment motion on the flat bed upstream of the structure. Note that the upstream velocity need not exceed the critical velocity for clearwater scour to occur.
Livebed scour is local scour that occurs when the flow velocity exceeds the value needed to initiate sediment motion (suspended and/or bedload) upstream of the structure (Sheppard, 1998). The critical velocity for the transition between the two conditions can be obtained from the modified Shields curve and is dependent upon various parameters such as the water density and viscosity, sediment density and size, bed roughness, and water depth.
Keeping all other parameters constant, scour first begins at about 0.45 times the critical velocity for a circular pile. Increasing the velocity results in a deepening of the
equilibrium scour hole, until a peak depth is reached at the critical velocity. Further increases of the current velocity into the livebed range initially reduce the equilibrium depth of scour. The presence of the scour depth peak at the critical velocity has led researchers to conduct the majority of scour experiments with velocities in the clearwater range, so that data may be extrapolated to the peak depth at the critical velocity.
Most of the scour research completed to date has been in the prediction of equilibrium scour depth, which is used in design computations. However, the time required for the scour process to reach equilibrium can be much longer than the duration of many storm events. Thus, for many bridge piers situated in locations with short flood duration, the hydraulic calculations for the foundations may be in error.
The objective of this thesis is to devise a methodology for the prediction of the temporal rate of clearwater scour around cylindrical piers in the hope that design scour depths may become more accurately predicted. Data from laboratory experiments performed over a range of conditions is used in the formulation.
Chapter 2 describes the mechanics of local scour, and details the various
nondimensional parameters that influence the scour processes. A literature survey on the current knowledge and hypothesis concerning the time rate of scour is then presented.
A description of the experiments performed in the USGSBRD Laboratory is
presented in Chapter 3. The methods for both the scour and hydrodynamic data that were collected are described.
Chapter 4 is devoted to the interpretation of the data collected from the
experiments. A prediction equation for the time rate of scour is presented using the observations obtained from the data.
6
A summary of the work and conclusions reached are described in Chapter 5. Also contained in this chapter are recommendations for further study.
CHAPTER 2
BACKGROUND AND LITERATURE REVIEW
2.1 Background
A brief review of the most important local scour mechanisms is given prior to
discussing the research leading up to the work presented in this thesis. Also, a literature review of known works associated with the time rate of local scour is reviewed.
Submerged particles initially at rest on the bed are brought into suspension as a result of forces acted upon them by the action of the fluid flow. The resisting moment is surpassed by the hydrodynamic moment of forces about the center of gravity of the particle. The hydrodynamic forces include buoyancy, lift, and drag, while the resisting forces are the weight, and normal and frictional forces from neighboring particles. A force diagram is shown in Figure 21. Note the normal force (Fn) and frictional force (FF) at each point of contact with neighboring particles. Equating the various moments, a dimensionless shear stress called the Shields parameter can be obtained: TO PmU. (2.1)
= is m )d5o (Ys m)'P50
lFlow A Buoya~1y
Figure 21. Diagram showing forces on a particle resting on the bed.
The value of r, which corresponds to the initiation of motion is dependent on the angle of repose of the sediment, as well as the flow conditions, and flow regime. Shields performed laboratory experiments measuring sediment transport for various values of rz., and extrapolated back to the point of vanishing sediment transport (Julien, 1998). His data led to the modified Shields curve, shown in Figure 22, where r. is plotted as a
function of the boundary Reynolds number Re..
wegh
I
II
*
U,
1.00
  : I
I~~~~~ ~ ~ ~ ~ 1 1 II 111 1 1 111 1 1 F
I I I f l
2  ~1
 i ,0. :. 1. 100.
0.10
Figure 22.
0.1 1.0 1110 100.0
Boundary Reynolds Number, Re= uc*d5dYv Shields' diagram.
100
0.0
The critical velocity is therefore a function of the sediment, fluid and flow characteristics. The sediment characteristics are the relative bed roughness (the Nikuradse roughness length divided by the median sediment diameter), sediment density, and median diameter. The fluid properties are viscosity and density. The flow characteristics are the water depth and velocity (and acceleration for unsteady flows).
As mentioned in Chapter 1, the critical depth averaged velocity represents the
division between clearwater and live bed conditions. For live bed conditions, sediment transport is occurring throughout the bed, and various bed features can be formed. These bed features undergo significant metamorphosis with increasing velocity, from a smooth bed to ripples to dunes to flat beds to antidunes. The primary variables that affect the bedforms are the flow velocity, water depth, bed particle size, particle fall velocity and
the slope of the energy grade line. Numerous researchers have classified the bedform transitions for various parameters (Julien, 1998). The bedforms may migrate into the local scour hole and vary the scour depth with time. As a result, the equilibrium scour depth for live bed scour is defined as the point where the sediment leaving the scour hole is equal to that entering.
2.2 Scour Formation for Steady Flow
Clear water scour starts when the bed shear stress upstream of the structure is sufficient to initiate sediment motion at the structure and ends when the critical shear stress is reached. The lower limit is an approximate value that depends primarily on the structure shape (Hancu, 1971 and Ettema, 1980). In clearwater scour, material surrounding the pile is gradually scoured out at a decreasing rate until the hole is deep enough not to permit any further removal, and the equilibrium scour depth is attained.
Local scour develops as a result of a number of flow mechanisms that combine to remove sediment near a structure. The relative importance of the mechanisms changes as the scour hole progresses thereby changing the rate of scour. These mechanisms can be described as follows.
The scour process initiates on the sides of the pier, approximately 450 to the direction of the incoming flow (Ettema, 1980). Shear stress measurements made by Hj orth (1975) indicate that these locations correspond to local maximum bed stresses. However, Melville (1975), in a separate but similar experiment, discovered the maximum stresses to be at locations 1000 to the flow direction. The holes formed on either side of the cylinder propagate upstream (as sediment cascades into the newly formed depressions) to meet in the front of the pier, and downstream to meet behind the pier.
A bluntnosed pier causes the formation of a variation of stagnation pressure
about its stagnation plane directly in front of the pier (Chiew, 1984). The velocity profile of the approaching flow is such that at the bottom the velocity is zero, and increases with elevation to the airwater interface. As the flow encounters the bridge pier, the logarithmic velocity profile exerts a pressure at the top of the pier greater than near the bed, thus inducing a downflow in front of the pier. Tison (1937) and Hjorth (1975) have also shown that the downflow is also caused by the curvature of the streamlines around the pier. The downflow impinges on the bed and is directed upstream. The approaching flow meets this redirected downflow and a horseshoe vortex is formed, named after the shape of the vortex (viewed from above) as it is swept downstream. A horseshoe vortex is also formed when the oncoming flow separates at the edge of the depression created initially by the downflow, inducing a circulation within the scour hole (Chiew, 1984). The downflow and the horseshoe vortices are believed to be the primary mechanisms for scour around bridge piers. A bow wave or rolling vortex is also formed at the head of the flow obstruction. Vertical vortices called wake vortices are generated as a result of the flow separation on the sides of the pier, effectively aiding the lifting of sediment into suspension much like a tornado. A diagram showing the local scour mechanism is shown in Figure 23.
Bow Wave Stern Wave
, Wake
.4:) Vortices
Horseshoe
Vortex Downflow
Figure 23. Diagram showing flow vortices around pile in flow.
The downflow has been identified as the leading cause of scour (Shen at al, 1965), acting as a vertical jet on the bed. Ettema (1980) measured the variation of the downflow strength as the scour hole deepens, and found that the velocity of the jet initially increases with the development of the hole, reaching a maximum when the scour depth ratio (ds/b) is between 0.8 and 1 before decreasing (Figure 24). He also found that the strength was dependent on the approach flow (flow velocity and water depth) and the diameter of the cylinder.
.0
Y/b
1.0
The downflow and horseshoe vortex erodes the sediment and the hole expands in width and depth. Avalanches occur as the angle of the side of the hole becomes too great, widening the depression even more. Measurements have shown that the slope of the equilibrium hole corresponds to the angle of repose of the sediment.
The horseshoe vortex is initially weak and small in crosssection. As the scour
hole develops, the downflow velocity increases and the vortex grows in size and strength. Melville (1975) postulates that the circulation associated with the vortex increases as the
scour hole enlarges due to the expanding crosssection, fueled by the quantity of fluid supplied by the downflow. The downflow, initially being a function of the upstream flow, eventually attains a peak value and then decreases with further deepening of the scour hole as described earlier. The strength of the circulation of the vortex correspondingly grows weaker and weaker, decreasing the rate of erosion until equilibrium is reached. Equilibrium can thus be defined as the depth for which the downwardly directed jet in front of the pier is not strong enough to dislodge particles resting on the bottom of the hole.
The flow around a circular pile encounters an increasing pressure as it progresses around the sides (i.e. an adverse pressure gradient). This pressure gradient slows the flow adjacent to the pile until at some point it comes to rest and "separation" occurs. The location of the point of separation is not stable and oscillates in time. Vortices form downstream of the point of separation and can either remain attached to the pile or separate and flow downstream depending on the pile Reynolds number (Ub/v). The shedding of the vortices from the pier occurs alternatively in a periodic manner, in what is known as the Krmdn vortex trail.
The Strouhal number, a measure of the ratio of inertial forces due to the
unsteadiness of the flow to the inertial forces due to velocity changes in spatial variations of the flow field, can be used to describe the frequency of shedding. The Strouhal number is given by
St = wb (2.2)
U
where co = frequency of operation,
b = cylinder diameter, and
U = mean approach flow velocity.
Melville (1975) determined that vortex shedding occurs at a Strouhal number
varying from 0.229 to 0.238. He also noticed that the shedding frequency decreases with increasing depth. The wake vortices, with their vertical axes and lowpressure center, assist in the removal of sediment placed in suspension by the downflow and horseshoe vortices in a manner similar to tornadoes.
Melville (1975) further theorized that the arms of the horseshoe vortex oscillate laterally and vertically at the same frequency of the shedding wake vortices. He describes the sequence of the coupling of the two vortex systems during one period:
The decreased pressure within an individual castoff vortex draws up fluid from
the horseshoe vortex region, pulling the vortex arm with it. As this first wakevortex passes downstream, the arm of the horseshoe vortex recedes back into the
scour hole, while the other arm of the vortex is similarly affected by the second
wake vortex shed from the other side of the cylinder. (Melville, 1975, p. 195)
Behind the structure there is a relatively calm region sheltered from the upcoming flow. Sediment that is put in motion by the horseshoe scour vortex and not removed from the scour hole by the wake vortices will deposit in this area to form. a characteristic mound behind the pier. Sediment interacting with the wake vortices will be carried with them downstream, initially experiencing a vertical displacement due to the upward flow associated with the low pressure in the center of the vortex system. As the wake vortices progress downstream they lose energy and slow down and the sediment redeposits on the bed.
A list of the variables associated with the complex mechanisms contributing to erosion can be assembled. The temporal rate of scour around a cylindrical bridge pier in
a cohiesionless, erodible bed is a function of the fluid and sediment properties, pier characteristics, flow parameters and time. The fluid properties are mass density and the dynamic viscosity. The sediment properties are mass density, size and size distribution, and particle shape. Pier characteristics include pier shape and surface roughness. The flow parameters are water depth, velocity, velocity distribution and acceleration (for unsteady flows).
2.3 Effect of the Various Parameters
These variables can be combined to form independent dimensionless groups (the number of which is given by the Buckingham nr theorem). The subset of these groups that best describe the local scour processes is still a subject of debate. Different researchers use different dimensionless groups to present their results. Sheppard (1996) has found that the equilibrium scour depth can be expressed in terms of the three groups U/Uc, yO/b, and d5O/b.
2.3.1 Effect of Velocity Ratio U/Uc
The velocity ratio U/Uc has been examined thoroughly. For circular cylinders, the depth of the local scour hole increases almost linearly from a U/Uc value of approximately 0.45 to the transition critical velocity, where a maximum clearwater peak is attained. For the model tests that have been conducted for U/Uc greater than one (i.e. in the livebed range), the equilibrium scour depth is seen to decrease to a minimum before reaching another peak at some higher value of U/Uc. The nature of livebed scour with increasing velocity appears to be dependent on the sediment to structure diameter ratio (d50b). As the ratio drops, the clear water peak first increases then decreases while the live bed peak tends to remain relatively constant for fixed values of yO/b. A typical
plot of nondimensional scour depth dse/b versus U/Uc for two nondimensionalized sediment particle sizes (d50/b) is shown in Figure 25.
Clearwater Livebed
Dso50/b = 0.016
dse/b
yo/b = const.
U/uc
Figure 25. Dependence of nondimensionalized scour depth on velocity ratio for
two sediment sizes.
Scour initiates at a velocity ratio of about 0.450.5. This can be attributed to the increase in velocity of the flow around the pier, in so much as doubling the magnitude of the approach flow to surpass the critical threshold on either side of the pier. From potential flow theory the 0 component of the velocity on the cylinder can be expressed as Uo =U(1 + (b/2) sin9 0, (2.3)
where U is the upstream flow velocity, and b is the cylinder diameter. At rb/2 and sin0=1 (900 to the approach flow), Uo reaches a maximum value of 2U, or twice the upstream velocity.
As the upstream velocity is increased to beyond the critical value for the incipient motion, bedload transport occurs throughout the bed. The bedload and suspended sediment transport affects the logarithmic velocity profile and decreases the stagnation pressure gradient on the upstream face of the pier. Since the magnitude of the pressure gradient supplies the energy to the downflow and horseshoe vortex, the rate of scour decreases immediately after the velocity of the incoming flow changes from clear water to live bed. Upon further increase in velocity the equilibrium depth reaches a minimum before increasing once again. One possible explanation for the apparent minimum in scour depth in the livebed range is for at that velocity ratio where the minimum is located, there is a transition in the sedimentcarrying capacity as the flow is able to actively transport suspended sediment as well as bedload.
The formation of the secondary livebed peak is thought to occur at the point where the bed flattens (Sheppard, 1998). The transition of the bed from dunes to a flat bed can be seen in the graph by Snamenskaya (1969) in Figure 26. The Froude number is plotted versus the flow velocity normalized by the sediment fall velocity. The parameter is the dune height to length ratio and is a measure of the dune steepness. From this graph, the transition of the bed with increasing velocity is divided into seven distinct sections, with the livebed peak occurring in region six.
In the livebed range, the scour depth dependence on U/Uc relies heavily on a
third parameter, d50/b. Analysis done by Sheppard (1998) indicates that for larger water depths (yO/b>2.5), although the location of the live bed maximum appears to be independent of grain size (remaining relatively constant at dse/b2. 1), the maximum of the scour depth at the critical velocity fluctuates with varying d50/b.
U
1.5 1.0 0.5
.....IM
.i  .
0.lift
1 10 100 1000 10000
Figure 26. Changes in bed features with increasing velocity, taken from
Snamenskaya (1969).
Most data collected on circular pile bridge scour have been performed in the clear water range, as the maximum equilibrium scour depth was assumed to be attained at the transition between clearwater and live bed conditions. The lack of controlled, accurate experiments in the livebed range is due in part to the generation of bedforms. In small flumes, the height of the bed forms can be of the same order as the scour hole. Thus, differentiating between local scour and bed forms can be difficult and the results misleading.
UAU
1. Flat Dunes
2. Ripples
3. Dunes
4. Steep Dunes
5. Dune Distribution
6. Smooth Bed
7. Antidunes
2.3.2 Effect of Aspect Ratio yO/b
The aspect ratio, yO/b, is a significant factor if the water depth is relatively
shallow. Laboratory data indicate the equilibrium scour depth increases, with increasing values of yO/b, from zero to approaching a constant value when yO/b is about 2.5 to 3 (Figure 27), when the other factors U/Uc and d50/b are held constant.
2.00
100 0.00
U /Uc = constant d50 / b = constant
0.00 2.00 4.00
YO/b
Figure 27. Dependence of equilibrium scour depth on aspect ratio for which
U/Uc and d50/b are held constant.
The reasoning behind the shape of the curve is as follows. At low water depths, the surface roller that forms at the free surface may interfere with the horseshoe vortex formed at the base of the pier. These two vortices have opposite axes of rotation, so the
effect of their interaction yields a reduction in their individual strengths. On increasing the water depth, the distance separating the center of rotation of the two vortices is increased, until eventually there will be no interaction between them. This occurs at a water depth ratio y0/b ,2.5.
Effect of Sediment to Pier Size D50/b
The dependence of the scour depth on the third parameter d50/b is not fully
understood. Sheppard (1996) postulates that the parameter d50/b is actually a function of the ratio of two different Reynolds numbers, one based on the sediment diameter and the other on the structure diameter:
d0 d50U
50 V (2.4)
b bUV '
where the velocity near the bed (u) is related to the depth averaged velocity (U) for a fully developed flow.
There exists a limit as to the smallest size of the median diameter that can be used in the laboratory. This is due to the cohesive behaviour of fine sediment (d50<0.06 mm). Additionally, sediment finer than about 0.6 mm will form ripples as a result of the small relative size of the particles to the viscous sublayer formed by the flow (Ettema et al., 1998). These characteristics of smaller sediment behave differently to larger sediment found in streambeds, and thus cannot be accurately used in modeling prototype situations.
As sediment used in model tests are frequently of the same order in size as found in prototype piers, the data collected for d50/b is comprehensive for small diameter piles from laboratory tests, and meagre for larger, prototype piles. From the tests that have
been completed, the dependence of d50/b on the equilibrium scour depth is shown in Figure 28, for constant values of U/Uc and yO/b.
3.00 2.00
2,0
1.00
0.00
Figure 28.
UIIUo .0I
o b o.
4 3 2 0
og 10(d50 / b)
Variation of scour depth on d50/b with U/Uc=l and yO/b>3.0.
The graph indicates that for a given pier width, an increase in the sediment size will first increase the scour depth until a maximum is reached, then decrease the depth.
2.4 Literature Review
Research on the local scour phenomenon to date has mainly concentrated on the determination of equilibrium scour depth. The temporal rate of scour has not been given the same attention since bridge designers have tended to seek an equation predicting the
final depth for design rather than understand the underlying processes that govern the development of the scour hole. Additionally, reliable and unobtrusive methods for measuring the scour depth over time have only recently been adopted.
Shen et at (1966) was one of the first to address the variation of scour with time. They conducted tests with a single cylindrical pile and a single sediment size, and varied the water depth and approach flow velocity. They plotted the ratio of scour depth to the flow depth versus a parameter which incorporated a quantity that depends on the flow, the Froude number, and time. They were, however, unable to observe any trends in their data.
They then defined t75 as the time required to reach 75% of the equilibrium scour depth. Incorporating the work of Chabert and Engeldinger (1956), they plotted t75 versus the velocity squared for all of the experiments. From this rather scattered plot, they concluded that the time required to reach 75% of equilibrium increases with increasing sediment size, and decreasing velocities.
Later in a separate paper, Shen et al (1966) fit the equation d, = K ln(K2t) to his data set and arrived at the following equation: lb = 2.5Fr0 ( b O.6 (e) (2.5)
where m=O.O26e'2"932yo and (2.6)
E /Y0FrO33 lnIUYJ. (2.7)
Nakagawa and Suzuki (1975) formulated a temporal rate model, using the assumption that the horseshoe vortex is the principle scouring mechanism and the strength and scale of it remains constant during the scouring process. They derived
equations representing circulation in the approach flow and in an area bounded by an imaginary triangle on the lower half of the pier. By equating these, they found an expression for the bottom velocity in terms of the depth averaged flow velocity. A sediment transport rate was formulated using a probabilistic technique and volumetric representation, which included the shear stress on the bed. They observed a small ridge of sediment around the immediate vicinity of the pier from where most of the scour seemed to be taking place. The radial distance to the edge of this sediment buildup was observed to be constant throughout the process at one quarter of the pier diameter. By assuming that all scour takes place in this region and is replenished by sediment sliding down from the sides of the hole, they could represent the rate of sediment being supplied to the hole. Using the continuity equation, they derived the following expression for t andd,
~KiJ2dP t 1+2K1 (dj2+ 3(lKdtan 3b (2.8)
where K 0.25,
A, particle area constant,
A2 = particle volume constant and
F= rate which particles in the stagnation plane are transported out the hole.
When the results of the equation are compared to laboratory data, the equation follows the initial phase of scour well, but does not follow the asymptotically approaching equilibrium phase.
Carstens (1966) tried to model the rate of scour using data of Chabert and Engeldinger (1956). HeI assumptions included
1) the boundary layer thickness was negligible in the area of active scour,
2) the velocity distribution was a function of the geometry of the hole and the
structure, and
3) the hole was shaped like an inverted right cone with an angle equal to the
angle of repose of the sediment.
He equated the rate of sediment transport to the volumetric rate of change of the hole. By using geometrical equations to define the volume of the hole, and determining an appropriate sediment transport function, he arrived at the following equation: d' 5 d 4 tan d
4.14 E 6(N' N2C Y2 lb)+Ulb24
tn0(d a ),( (2.9)
+ bj (ta l)db)+ (tan 0) Y d Inj+
32 32 64 tan 0
where Ns = YU  g is defined as the sediment number, and N5c is the sediment number corresponding to the lowest value for which scour will occur. The derivation of the constants in the equation was based on a small range of laboratory data, which did not take into consideration the effect of varying sediment size.
In his dissertation, Ettema (1980) identified three distinct stages of local scour over time. The initial phase is from a planar bed to the erosional phase. This phase is dominated by the acceleration of the flow around the pier. When the erosional phase initiates, the downflow and horseshoe vortex become the leading mechanisms. The horseshoe vortex, rapidly growing in size, eventually becomes submerged in the scour hole. The final phase, the equilibrium phase, represents the stage at which equilibrium is reached for the given conditions.
Ettema (1980) looked at the temporal rate problem in a mathematical approach. He approximated the half of the upstream scour hole by half an inverted frustum of a right circular cone with side slopes equaling the angle of repose of the sediment. From this, volume and surface area equations for a cone were used. He described an entrainment zone, from the cylinder to about midway up the scour hole slope, from which sediment is observed to be removed by the horseshoe vortex. He assumed that when a layer of particles is removed from the entrainment zone, complete transport away from the scour hole takes place, and the surface of the scour hole is immediately replenished by particles sliding down from above. Also, bed particles were assumed to be spherical, and sediment porosity was neglected.
Using these assumptions, Ettema (198 0) described the rate of sediment transport out of the scour hole as:
q., = E (# particles entrained) x (volume/particle) x (entrainment probability). (2.10) The effective number of particles entrained per unit area is a product of the total number of particles per unit area by the ratio of particles on the surface of the semicircular scour hole to the particles on the surface of the entrainment zone. Regarding the surface area of the entrainment zone, two simplifying assumptions were considered:
1) the surface area is proportional to the pier diameter and varies with the
depth of the scour hole
2) the surface area is proportional only to the pier diameter.
Ettema explains the first assumption is valid for the initial phase of scour, while the latter assumption is valid for the later erosional phase. By assuming the probability function is
independent of particle size, and that the angle of repose is constant, Ettema arrived at the following relationship:
a(ds/b) Ic D3 (2.11)
or the rate at which the normalized scour depth increases with time is proportional to the mean particle size divided by the cube of the pier diameter.
Ettema then fitted two straightline segments for the principle erosional phase, each having the form
dSb = K1in{ob((DX U )}+lnK (2.12)
where K1 and K2 are functions of U/Uc, d50/b, and the corresponding phase of scour.
While some insight regarding the scour rate problem was gained by Ettema's model, more work is needed in relating the dependent parameters to the equation coefficients. Also, while the erosional phase of scour is described, there is no mention of the scour development in the initial or equilibrium phases.
Yanmaz and Altmbilek (1991) formulated an equation using a similar derivation to Carstens (1966). They used a more recent sediment pickup function, and performed 71 flume tests to determine coefficients for the sediment transport out of the hole. Their final equation for the rate of scour was dds 3000OFud5o(2d, +btan) (2.13)
S 075 ( .3
dt rNCo (t4a (n ) (d 2 + db tan )
S D (ano) / C,50
Later in a separate paper, the authors state that the equation is good only within the limits of the flume data they tested, because of the extreme sensitivity of the drag coefficient determination.
Johnson and McCuen (1991) assumed the scour rate could be represented as a function of the difference of the strength of the downflow velocity and the critical velocity. Using experimental data, they fitted an equation relating the downflow to the cylinder diameter, water depth, and approach velocity. The critical velocity was found by equating the shear stress on the bed to the resistive force (component of weight along the slope of the hole). Adjustments were made to account for sediment gradation and turbulence. Their final equation took the form: Ad, = C, I 1 C4U(i eCsbyo) [C' 2(2p gdsino +C7Gsi)/ (2.14)
The constants CI through C8 were found using a nonlinear least squares method and laboratory data. The scour depth can be solved for each chosen incremental time step. The shortcomings of this formulation lie in the negligence of other scour mechanisms that contribute to the erosional rate.
Sumer et al. (1992) used livebed scour data to analyze the scour rate in steady currents. Their final equation includes the equilibrium scour depth, and is of the form: d= de (1 e,IT)
T b2yO C U2 12.2 (2.15)
2000b g(sl)d3 ,g(s1)d)
The authors recommend a value of 1.01.5 times the pier diameter for dse if the equilibrium scour depth is unknown. The equation is based entirely on livebed scour data.
Kothyari et al. (1992) provided an algorithm to outline a procedure for calculating the time required to scour an incremental depth. They incorporated the work of Paintal (1971) to determine the time required for a single particle to moe. Assuming the main
scouring mechanism is the horseshoe vortex, they used experimental data to devise a relationship for the diameter of the vortex as a function of the pier diameter and water depth. Following the work of Melville (1975), they represented the increase in area of the horseshoe vortex as it descends into the scour hole as a function of the scour hole and initial vortex area. Coefficients were determined using flume data, which was obtained by the authors for a wide range of conditions. The algorithm basically computes the initial vortex size, shear stress on the bed, and probability of movement for one particle. The time required to move the particle is then added to the cumulative time, and the scour depth is increased by one sediment diameter. Shear stress is again calculated and if it falls below the initial value, the loop begins a new cycle. However, the authors admit that their estimation of the size of the horseshoe vortex using the thickness of the separated boundary layer may not be precise.
Gosselin (1997) conducted experiments using both erodible and fixed beds. He measured velocity vectors in and around the scour hole using an Acoustic Doppler Velocimeter. Using results from the experiments, he simulated the development of the scour hole over time from a threedimensional NavierStokes equation solver program. The simulations were in turn used to develop a method to predict the scour depth over time based on volumetric changes as well as energy considerations of the scour hole. His analysis of the velocity vectors of the horseshoe vortex is comprehensive, however the apparatus used was unable to pick up the higherfrequency turbulent fluctuations.
Chiew and Melville (1996) performed 35 experiments, varying pier diameters, sediment sizes, flow depths, and approach velocities. Motivated by the lack of consistency of test durations completed by previous researchers, they defined a 'time to
equilibrium' (te) as the time taken for which the rate of development of the scour hole does not exceed five percent of the pier diameter in a 24 hour period.
Graphical analysis of their results show interesting trends. A plot of scour depth normalized by equilibrium scour depth versus time normalized by time for equilibrium shows a family of curves with increasing velocity ratio in the direction of increasing scour depth (or decreasing time), demonstrating the significance of time in the measurement and estimation of scour depth. On a separate plot, time to equilibrium was plotted versus pier diameter, holding the water depth constant. For a given velocity ratio, time to equilibrium increases with increasing pier diameter. Also from the same graph, it can be seen that the time to equilibrium increases with the velocity ratio for a given pier diameter. The reasoning behind this observation is somewhat unclear. An increase in the velocity ratio correspondingly increases the energy of the flow and its capacity to transport sediment, which should decrease the time required for equilibrium. However, the increased velocity ratio would result in deeper equilibrium scour depths, which would increase the time required to reach equilibrium. The authors explain that the increased transport capability of the flow has a lesser effect on the time to reach equilibrium, and the effect of the increased time to develop the deeper scour hole is dominant.
The authors also plotted a nondimensional parameter t.=Ut/b versus UIUc, from which they determined the empirical relation: te =3 3104 (U 4.(/Y (2.16)
which is valid for .5 U/Uc:!l .0. Thus, for a given structure diameter and approach velocity ratio, a time required for equilibrium can be obtained. Then for any given time, a scour depth can be read off the previous graph described earlier. The authors, however,
admit their results require further research and are only based on their limited laboratory data.
In a later paper by the same authors, Melville and Chiew (1999) use additional
data and the same parameters to develop an equation for the scour depth as a function of equilibrium scour depth and time. They found that both the equilibrium scour depth and the time to reach equilibrium depended on the same parameters. Plotting the parameters ds/dse versus t/te as in the previous paper, the authors arrived at the following expression for the temporal development of the scour depth: d se =exp{ 0.03[U Uln( ]1.6 (2.17)
A plot of the relation of the nondimensional parameter to and the aspect ratio y0/b show striking similarities to a similar plot of dse/b versus y0/b, in that there is an apparent limit to the influence of the water depth on t*. The following equation for the dependence was given:
0.25
t. =1.6x 106 .b for y0/b<6 and (2.18)
t. = 2.5 x 106 for y0/b>6. (2.19)
The dependence of t* on U/Uc was plotted and an equation given: t. = 4.17 x 106 (U U 0.4) for 0.4
t. = 2.5 x 106 for b/d50>100.
(2.22)
By combining the effects of the water depth and the flow intensity, the resulting equations can be written for t,:
te = 48.26bu(U 0.4) for yO/b>6 and (2.23)
te =030.89/ 0.4XYJ for yO/b<6. (2.24)
If the various flow and structure variables are known, the equilibrium scour depth and time to reach equilibrium can be calculated. The scour depth at any point in time can then be computed.
CHAPTER 3
EXPERIMENTAL PROCEDURES
3.1 Introduction
This chapter contains a description of the flume, equipment, and procedures that were used in obtaining the data for analysis. The descriptions include precautionary procedures so as to ensure accurate replication, thus minimizing errors due to differences in test conditions.
The choices of the dimensions of the piers as well as the sediment size used were made due to the lack of data of the independent parameter d50/b. As mentioned earlier, using flume data to relate to prototype situations encounters the problem of scaling the sediment size. There exists a minimal limit for which the sediment used in the model cannot exceed, due to the cohesive nature of small diameter particles. Thus, sediment used in model situations often has to be of the same order as that in the prototype. Most data collected on the d50/b parameter fall in the range 0.0006<60<03162. The lower boundary has been limited by the size of the pier that flumes can accommodate. The test data analyzed in this thesis used pile diameters as large as 0.914 ra that extends and sediment diameters as small as 0.22 ra (yielding d5O/b values as small as 0.0002).
The quantities measured during the experiments were water temperature and elevation, flow velocity, and scour depth. The scour depth was measured using two different instruments during the test and the scour hole was point gauged on completion
of each test after the water was drained. Two methods were used so as to provide a backup in case one of the systems malfunctioned.
3.2 Equipment
3.2.1 Flume
The flume is located at the USGSBRD S.0. Conte Anadromous Fish Research Laboratory in Turners Falls, Massachusetts. The flume itself has three separate channels, of which only the main center channel was used. That channel has a width of 6.1 m, a length of 38.6 m, a maximum depth of 6.4 m and a zero bed slope. Schematic drawings of the flume and sediment arrangement for the experiments are shown in Figures 31 and 32.
Water used in the flume comes from a reservoir on the Connecticut River that was built to supply a hydro electric power plant a short distance from the laboratory. The water is discharged into the Connecticut River downstream of control structures. The head difference between the reservoir and river below the structures (approximately 10.67 m) drives the flow in the flume that can be as large as 9.91 m3/s.
Originally designed for studying the migration of anadromous fish, various
modifications were necessary to adapt the flume for use in bridge scour experiments. A vertical weir was constructed at the end of the channel with variable height so as to
Flow Intake from Reservoir
r 126
Test (hannel
flow
I A
A Modelre r
flow

Plan View
NOT TO SCALE
All dimensions in feet
V
10
20
j 10
o
Flow Discharge To Connecticut River
Clearwater Scour Test Setup Figure 31. Aerial schematic of flume.
NOT TO SCALE
All dimensions in feet
Test Sediment 6
Section AA *[
126 >1
 I
Filter M~terial Base SeJiment Test Sediment Base Sejiment Section BB
Figure 32. Schematic figure of the crosssection of flume.
w
_ . M
control the water depth and discharge inside the flume. Also, a flow straightener was installed at the entrance of the flume to ensure uniformity of the flow.
Only a section in the middle of the channel was completely filled with test
sediment. This section had a length of 9.75 mn, and was located a distance 19.5 mn from the channel entrance. Gravel (d50;z9.5 mm) was used as filler below the test sediment for the remainder of the flume. The bed was lowered and covered with gravel for the first
8.5 m from the entrance in order to promote a faster development of the velocity profile and to prevent the development of dunes that would have resulted from the j etting of water through the flow straightener. The test sand was separated from the gavel by a filter material with a 0. 1 mim opening. *In total, 3 56 mn3 of gravel and 212 m 3 of test sediment were used.
The discharge in the flume was calculated using the equation:
Q = Cwr Y 23itwH3 (3.1)
where Cwr, is the rectangular weir coefficient, w is the flume width, and H is the head over the weir. For most flume channel situations, the viscous and surface tension effects are negligible compared to the geometric effect, and the weir coefficient can be computed using
Cwr.=061+ .7 P (3.2)
where P,, is the height of the weir (Rouse, 1946 and Henderson, 1966).
3.2.2 Electronic Apparatus
The electronic apparatus used for monitoring the scour depth were acoustic transponders and video cameras mounted inside the piers. Electromagnetic current meters were used to measure the velocity of the flow. A digital thermometer was used to measure the temperature of the water.
3.2.2.1 Acoustic transducers
Acoustic transducers were used to record scour depth as a function of time. By
emitting pressure pulses directed at the hole, the distance from the transducer to the scour hole can be calculated by measuring the time it takes for the pulses to travel from the sensor to and from the bed. Twelve sensors were used, arranged in 3 arrays of 4 sensors each, as shown in Figure 33. The Multiple Transducer Arrays (MTA) were positioned at the front and at angles of 83' on either side of the structure. The MTAs were mounted a few centimeters below the water surface so as not to interfere with the dynamics of the scour development. The distance from the arrays to the bed directly under the crystals was measured continuously and recorded at predetermined intervals throughout the experiments.
Different MTA arrays were used for small and large pile diameters. For the small piles, the sensors 2.5 cm in diameter and spaced 4 cm apart. For the large pile, the sensors were 4 cm in diameter and spaced 8 cm apart. The frequency of the acoustic system used was 2.25 MHz.
MTA for small pile diameters (0.5 to 1 ft. diameter)
side view (crosssection) front view (crosssection)
mounting OngOsi
1 1.57in (4 M 0375 in T (0.95 cm)
2.25 MHz transducers
top view \
2.50 in.
(6.3 n)
~[ ]SEATEK
6.4 in (163 cr by: Chris Jette' 32497
Figure 33. Detail of MTA arrangement used in smallpier experiments.
3.2.2.2 Electromagnetic current meters
Two electromagnetic velocity meters (MarshMcBimey Models 523 and 511) were used to measure the velocity of the flow. These meters accurately measure the horizontal components of velocity. The sensors have no moving parts, and are therefore less susceptible to fouling or clogging by foreign matter.
3.2.2.3 Digital thermometer
A digital thermometer was used to periodically check the temperature of the water during the experiments.
3.2.2.4 Cameras
Two miniature video cameras were placed inside the piles on a vertically
traversing devise. The speed of the traversing mechanism was adjusted to match the scour rate so that the cameras were directed at the watersediment interface in the scour hole. A photograph of the video recording equipment used in the smaller pile is shown in Figure 34.
3.2.3 Test Setup
The velocity meters, water level indicator, and digital thermometer were all
connected to a personal computer with a 486 processor. The computer was programmed to take oneminute data samples every halfhour throughout the tests.
Figure 34. Photograph of cameras used in the 0. 114 m pile in casing.
The acoustic transducers were connected to a SeaTek Control Box, which converts the signals from the acoustic sensor into digital numbers representing the distances from the sensors to the bed. The Control Box was connected to a second 486 personal computer. Communication between the computer and Control Box was accomplished with a communication software package (CrosstalkTm). Ten second samples of data were recorded every ten minutes throughout the experiments.
3.2.4 Models
Cylindrical piers of varying diameter were used in all of the experiments. The
first pier had a diameter of 0.92 mn, the second 0.31 mn, and the third 0. 114 mn. The largest pier stood 5.5 m high, and was made out of Polypropylene with two Plexiglas windows. Measuring tapes were located inside the pile near the windows in view of the cameras. Steel channels secured the pier from deformation under the water pressure. The other piles were made out of Plexiglas, and stood 3.35 mn tall. In order to reduce the forces on the large pile it was flooded during the experiments and the cameras placed inside a waterproof case.
3.2.5 Sediment
Tests were performed with two different sediment diameters. The sizes used were 0.22 mm and 0.80 mm. The sand was sieved by the supplier to provide as near a uniform
grain size as possible. The sigma (a = P84/ ) for the two sands were 1.51 and 1.29, respectively. Graphs showing grain size distributions are given in Figures 35 and 36.
d84 = 0.32 mm dso = 0.22 mm d16 = 0.14mm
diameter (mm)
Figure 35. Grain size distribution for sand #1 (d50=0.22 mm)
d84 =1.07 mm d5o = 0.80 mm d16 = 0.64 mm
0.1 1
diameter (mm)
Figure 36. Grain size distribution for sand #2 (d50=0.8 mm)
3.3 Laboratory Test Procedure
A description of the experimental procedure including preparation of the bed prior to each test is given below.
3.3.1 Bed preparation
First, the gravel was placed in the flume, using buckets attached to an overhead crane. After leveling, the filter material was placed on top of the gravel. The test sediment was then placed on top of the gravel followed by the installation of the structure and the placement of sediment in the test area. The sediment was compacted every 2030 cm with a diesel compactor and a hand tamper next to the structure.
3.3.2 Laboratoly Procedure
The electronics and computers were positioned on a wooden observation platform that spanned the width of the flume at the test section. The platform had dimensions of 3.05 in x 6.10 in with an opening forte pile. All electronics were run through a series of tests to ensure everything was working before the experiment was started. The flume was then filled with water. Care was taken not to disturb the leveled bed as the flume filled. When the water overflowed the weir at the end of the flume, the experiment was ready to start.
The sluice gates were opened slowly so as to increase the flow of water to the
desired water level and flow velocity. Adjustments made to both gates were necessary so as to achieve the correct velocity reading on both velocity meters.
The tests were run approximately 24 hours beyond the point where scour was no longer detected. Then the gates were shut, and the water was slowly drained. A mapping of the scour hole was then performed with a point gauge.
CHAPTER 4
DATA REDUCTION AND ANALYSIS
Time dependent, local scour data collected from clearwater experiments
performed at the USGSBRD Laboratory in Turners Falls, Massachusetts are described and analyzed in this chapter. Data collected by J. Sterling Jones at the FHWA Turner Fairbanks Laboratory in McLean, Virginia are also used in the analysis. Certain trends were observed and are depicted graphically.
The USGS Laboratory experiments are somewhat unique in that
1) Their duration was such that there was no question about their equilibrium scour
depths and
2) They include one of the largest test structures used in steady flow laboratory
experiments.
This analysis has revealed a number of interesting correlations and the formulation of a predictive relationship for the rate of scour.
4.1 Raw Data
The development of the scour hole was measured by acoustic pingers as well as video cameras set up inside the piers connected to a VCR. Both methods allowed for unobtrusive measurements to be performed, however, they both had limitations as well.
For the experiments where the acoustic transponders were working properly there was good agreement between the results from the two methods, as shown in Figure 41.
4Camera 1
E Camera 2
x Pinger
0 20 40 60 80 100
Time (hrs)
Figure 41. Scour depth versus time plots for the video and acoustic transponder
data. (b=0.305m, d50=0.80mm, yO=l.268m and U=0.381m/s)
4.2 Data Adiustment and Smoothing
Local scour is not a smooth, continuous process but rather a sequence of events involving the local removal of sand followed by an avalanche of the surrounding
sediment into the scour hole. In order to enhance the analysis of the data it was smoothed both visually and mathematically.
Most of the data was collected from the video recordings, with the pinger data
mainly used as a check. Missing data due to the cameras dipping below recordible levels were connected as accurately as possible. The lack of scour deepening due to the sediment sticking to the cylinder was corrected by adjusting the scour history to achieve a smooth curve. Finally, minor discontinuous jumps in the acoustic readings were assumed to be due to foreign particles carried in by the river and the corresponding data points were rejected.
Another adjustment had to be made to the scour data so that the deepest
equilibrium scour depth was attained. Neither the acoustic data nor the video data achieved the deepest scour depth, found after point gauging the bed on completion of the experiment. This was because the location of measurement did not coincide exactly with the deepest point. It was assumed that the time taken for equilibrium to be reached at the measured site was the same as for the point of maximum scour.
For this adjustment, a Matlab program was written. First, the equilibrium scour depth had to be determined from the raw data. Because the experiments were run for such a long period of time, the level as to where the hole had stopped scouring was obvious. The time for equilibrium was then determined by finding the time at which the deepest scour occurred first on the scour time history plot. Dividing the difference in the maximum scour depth and the measured equilibrium depth by the time for equilibrium yields an incremental scour addition for each time step. By this method, the time for equilibrium stays the same, while the maximum equilibrium scour depth is attained.
Figure 42 shows the original data and the adjusted data for the deepest equilibrium point for experiment # 12.
.. ..... Adjusted Data Raw Camera DataI
45
40
S30 S25
"~20 S15
0
5
0
0 20 40 60 80
time 0Mr)
Figure 42. Comparison between raw and adjusted scour depth data.
4.3 Experiment Summaries
As mentioned earlier, a total of seven experiments involving circular piles were completed. The experiments differ mainly in cylinder diameter, sediment size, and water depth, with minor variations in the UIUc parameter. Table 41 below shows the 'conditions of each experiment performed.
Table 41. Summary of experiments completed in the USGS Laboratory
Exp # b (m) Dso (mm) yO (m) U (m/s) Uc (m/s) T (o C) U/Uc dse (m)
3 0.114 0.22 1.186 0.290 0.316 18.0 0.918 0.1336
4 0.305 0.22 1.190 0.305 0.315 18.0 0.968 0.2586
6 0.914 0.22 2.268 0.325 0.326 17.1 0.996 0.3683
9 0.914 0.80 2.402 0.454 0.464 1.0 0.979 0.9271
11 0.914 0.80 0.866 0.335 0.411 1.0 0.815 0.6375
12 0.305 0.80 1.268 0.381 0.431 1.2 0.884 0.4039
13 0.114 0.80 1.280 0.388 0.429 3.9 0.904 0.1885
The scour depth versus time plots for all experiments are given in Figure 43.
+Exp 6  Exp12 Exp11 xExp9
Exp3  Exp4 +Expl3
0 50 100 150 200 250 300
Time (hrs)
Figure 43. Smoothed scour history plots for all UF/USGSBRD Laboratory experiments.
All the curves show a high initial rate of scour, which slowly decreases until an equilibrium depth is reached.
Incorporating the FlIWA Laboratory data provides valuable information about the effects of UIUc and the sediment particle size. Jones used the same structure with the same water depth for all of his experiments. The effects of an individual parameter could be investigated without having to account for changes in the other variables. Table 42 summarizes Jones' data.
Table 42. Summary of experiments completed at FHWA Laboratory
Exp # b (M) Dso (Mm) YO (M) U U(Ws) Uc(mWs) T (0C Q U/Uc Dse (m)* 57 0.152 1.2 0.267 0.340 0.455 ?0.747 0.181
74 0.152 2.4 0.267 0.427 0.649 ?0.658 0.124
86 0.152 2.4 0.267 0.429 0.649 ?0.661 0.127
126 0.152 5.0 0.267 0.713 0.919 ?0.776 0.267
128 0.152 2.4 0.267 0.544 0.649 ?0.838 0.236
134 0.152 1.2 0.267 0.422 0.455 0.927 10.225
*Estimated from extrapolation of data.
The scour plots for the Jones data are shown in Figure 44. Although the duration of the experiments are quite long (up to 6 days) and the scour seems to be leveling off, a finite equilibrium scour depth cannot be accurately determined from the raw data presented.
49
I Exp74  Exp126 0 Exp57 +Exp134 +Exp86 a Exp128
30
25
20 15 o 10
cdo
0
0 50 100 150 200
Time (hrs)
Figure 44. Smoothed scour history plots for all FHWA Laboratory experiments
4.4 Analysis of Data
Analyzing Jones data proved to be challenging due to the lack of equilibrium depths. Scour plots have always taken the shape of approaching the maximum scour depth asymptotically. The equilibrium depth and time had to be estimated by manually continuing the scour plots until the rate of scour leveled off. Time for equilibrium was especially difficult to predict as the rate of scour decreases to minimal values as a maximum scour depth is approached. Defining t90 as the time required for 90% of the maximum scour depth to be completed, both the USGS Laboratory data and the data received from Jones could be compared with better accuracy. However, due to the
uncertainties in the equilibrium depth, analysis of Jones data was limited to the initial scour rates.
The plot shown below is of the nondimensionalized parameter ds/dse (scour depth divided by the max scour depth) versus time. For this plot, all curves approach ds/dse=l at varying times. What is interesting is that the experiments reach ds/dse=l in order of increasing equilibrium scour depth. In other words, smaller equilibrium scour depths are attained in less time than larger scour depths. This indicates a dependence of the rate of scour on the maximum scour depth.
*__Ex6  Expl2 N Expl1 xExp9
*Exp3 Exp4 +Exp 13
1.2
0.8
0.6
0.4
0.2
0 J
0 50 100 150 200 250 300
Time (hrs)
Figure 45. Comparison of ds/dse versus time for USGS experiments
This dependence is accentuated in the comparison of equilibrium scour depth versus time required to reach equilibrium. An almost linear relationship can be seen joining the individual points in the plot shown in Figure 46.
300
.250
E200
S100
E50 94
0
0 20 40 60 80 100
Equilibrium Scour Depth (cm)
Figure 46. Equilibrium scour depth versus time for equilibrium for USGS
experiments.
The basis for the time to equilibrium's dependence on the equilibrium scour depth comes from the mechanisms that govern the scour process. The maximum nondimensional scour depth (dselb) has been shown to be dependent on the parameters d50/b, U/Uc, and yO/b. If the two phenomena are related, as can be deduced from the above plots, then the same parameters must also influence the time to equilibrium. This makes intuitive sense as the time required for one particle to move a certain distance must be dependent on such variables as the water velocity, the size of the particle and the water depth.
As the number of data points used for the formulation of the equation describing the deepest scour depth far exceeds the number of experiments containing scour time history data, finding a relationship between the maximum scour and the time required for
equilibrium is valuable. Including the maximum scour depth equation in the analysis carries with it a greater sense of confidence due to the amount of research concentrated on the subject. It also alleviates the need to model the time required for equilibrium based on just seven experiments, an impossible task considering the numerous factors involved in this complicated process. However, the basis of the relationship between the time and maximum equilibrium depth must be determined from the very same seven experiments, and although the relationship is simplified by having just two independent variables (dse and te), the lack of a more comprehensive data set requires that the results be used with caution.
Additionally, considering the time required to reach equilibrium alone effectively ignores changes in the rate of scour as the scour hole develops. In comparing the maximum scour depth to the equilibrium time, valuable information on the initial rates is lost as the time required to reach equilibrium effectively averages the variations in scour rate. Substantial differences in the behavior of each experiment that are important in understanding this complex phenomenon are ignored.
Empirical curve fits to the data were obtained with the help of a 2D curve fit program (TableCurve 2D TM) The time history data for each of the experiments are therefore individually described by an equation. The benefit of this is that either the scour depths or their respective rates can be plotted and compared on the same axis. All experiments at the USGS Laboratory were fitted with the equation: d,. a b~ ')+ (I Ct),(4.1) dsc
where unique values for the coefficients a,b,c,d,and f were obtained for each experiment. This equation was chosen for its ability to fit the raw data for every experiment, and for
its simplicity in form and ease of differentiation. Jones' data were also fitted with individual equations describing the scour depth versus time. Equilibrium scour depth for each experiment had to be estimated from the scour depth versus time plots. Due to differences in the general shape of the scour history plots, a different equation was used for Jones' data:
d, ( a+ct') (4.2)
d = ( + btO5) *
See Appendix A for plots of the individual curve fits.
Variations in the initial rates for each experiment can be seen in Figure 47 of the normalized parameters ds/dse versus the. The advantage of using the normalized parameters is that all data must pass through both the origin and the point (1,1). With the exception of experiments 13 and 6, the plots indicate a high rate of scour for the initial time period (until about t/te=O.1), and then a smaller rate until an equilibrium depth is achieved. Experiment 13 and 6 make the transition somewhat later, at around t/te=0.2.
These transitional features have been noticed and identified by other researchers such as Ettema (1976). In his dissertation, he describes the initial phase as the transition from a planar bed to the principal erosion phase. The erosion during this phase occurs as a result of general sediment transport caused by the accelerating fluid around the structure. The erosional phase is dominated by the downflow and corresponding horseshoe vortex that descends into the increasing scour hole. As the downflow decreases, the rate of scour diminishes, and ultimately an equilibrium depth is reached. Ettema suggests the stages can best be viewed on semilog plots of scour depth versus time, which can be seen in Appendix B.
,
0.8
0.6
r 0 Exp 3
i Exp 4
0.4  <> Exp 6
A Exp 9
 (D) Exp 11
* / Exp 12
0.2 1 Exp 13
I I I
0 0.2 0.4 0.6 0.8 1
t/te
Figure 47. Plot of ds/dse and t/te for USGS experiments.
An investigation into the factors contributing to the initial rate of scour was then attempted. Jones data was included, since the primary focus was on the initial rate and not on the unfinished latter stages of the scour process. By differentiating the respective equations from the curve fitting, an equation describing the rate of scour was formulated. When this was plotted versus the normalized parameter ds/dse, the plot in Figure 48 resulted.
A
 Exp3
+ Exp 4
0 Exp 6 0.8 Exp 9
A Expll
Exp 12 0.6 Exp 13
0 Exp 57
A Exp 74
Exp 86
0.4 Exp 126 Exp 128 E Exp 134
0.2
0
0 0.2 0.4 0.6 0.8
ds/dse
Figure 48. Rate of scour d/dt(ds/dse) versus ds/dse for all experiments
A wealth of information can be gained from plots of rate of scour versus ds/dse. The Jones data, which have much larger initial rates, all are for larger sediment. This indicates a dependence on the absolute particle diameter. Looking at the individual experiments in the Jones data, the general trend is for an increased initial scour rate with increasing particle diameter. The same general trend can be seen in the USGS Laboratory data.
This noticeable trait can be explained by considering the volume of the scour hole as scour is initiated. Larger particle diameters correspond to a steeper angle of repose.
As the angle of repose dictates the slope of the scour hole and the volume of sediment removed for a given scour hole, a steeper slope would have a smaller surface area and reduced volume. The smaller surface area and volume would erode faster, hence resulting in a larger scour rate. Calculations for a 5 cm scour hole show a I I % decrease in erodible surface area in going from a 2.4 nim. to a 5 mm sediment. Using the rate plot above, for the same two sediments an increase of 25% of the respective initial rates is observed. Other factors such as the difference in U/Uc were not considered in these calculations.
The increase in the initial scour rates with increasing sediment size appear at first to disagree with observations made by other researchers. Shen et al (1966) observed that t75, or the time required for the scour hole to reach 75% of the maximum scour depth, tends to be greater for larger sediment sizes. Compared to USGS Laboratory data the time plots of Jones' data, which are for significantly larger sediment sizes than those used in the USGS experiments, show a faster scour rate followed by a slower rate which results in a long time to reach equilibrium. The same is noticed in comparing experiments 6 and 9, in which only the sediment diameter has been changed. Experiment 9, using the larger sediment, approaches equilibrium much slower than experiment 6.
In accordance with Shields' curve, an increase in sediment diameter requires a
larger critical shear stress for the onset of particle motion. Towards the end of the scour process, turbulent bursts in the horseshoe vortex near the bed become instrumental in moving the sediment out of the scour hole. A stronger burst is required to move the larger sediment. In addition to requiring a faster flow for the initiation of sediment movement, the increase in sediment size increases the scour depth, so the sediment at the
bottom of the scour hole must travel further up the face of the slope before the hole deepens. It can be assumed that the higher energy bursts required to remove the sediment occur less frequently, hence the slower rate of scour.
Baker (1978), in his dissertation, made detailed measurements of vortex flow
around the base of a cylinder. He sectioned his analysis of the horseshoe vortex into that formed by a separating laminar or turbulent boundary layer. His experiments, however, were conducted in a wind tunnel, but the basis of the horseshoe vortex system should be similar to that formed in water.
With regards to the oscillations of the turbulent 'bursts' in a laminar boundary
layer, he concluded they were caused by disturbances in the vortex system downstream of the model, but correlation was found with the frequency of the wake vortex shedding was found. For a turbulent boundary layer, which is the more likely situation for the scour experiments considered here, Baker concluded the distribution of turbulent energy with frequency within the horseshoe vortex system is determined by the energy distribution in the upstream boundary layer. He also deduced that the wake flow does not affect the spectra of the velocity fluctuations in the horseshoe vortex. A plot of Baker's horseshoe vortex spectrum is reproduced in Figure 49. Note that the form of the graph is consistent with the earlier hypothesis that the higher energy turbulent bursts occur less frequently than those with lower energy. It should be noted that the frequency of Baker's measurements is higher than what is noticed in the experiments as Baker's experiments were conducted in a wind tunnel.
101) W0
0 f(z 6
Figure 49. Baker's plot of the power spectrum of the turbulent bursts of the
horseshoe vortex in a wind tunnelVisual observations of the bursts for the 0.3 05m diameter pier also support the above hypothesis. Measurements of the frequency of the bursts were made by counting the number of bursts that occurred during a given period of time. Using the videotape observations were made midway through the scour process (ds/dse=0.5) and towards the end (ds/dse;1). No bursts were observed at the onset of the experiments when the bed was flat and the horseshoe vortex is small in size and intensity. Experiment 4, with the smaller 0.22mm sediment, had similar burst frequencies of 0.29 Hz midway through scour, and 0.30 Hz when equilibrium was approached. However, midway through the scour, sediment swept up by the vortex action was eroded away from the hole completely, whereas towards equilibrium the sediment was merely lifted up from the base of the pier and deposited on the slope, eventually cascading down the slope into the
base of the scour hole. This supports the theory noted by a number of previous researchers (Baker, Ettema, and others), that as the scour hole deepens, the strength of the horseshoe vortex decreases while its size increases.
It is also apparent from looking at the Jones experiments that the
nondimensionalized parameter U/Uc also has a direct effect on the scour rate. This can be seen from experiments 57 and 134, in which the sediment size, water depth, and structure size are all held constant while the velocity is increased. Experiment 134, which has a higher initial rate correspondingly has the greater velocity and U/U~c ratio.
The exception from the preceding argument that the scour depth is directly
dependent on the sediment size is experiment 134, in which a high rate is noticed while the sediment size is a relatively small value of 1.2 mm. However, this experiment also has a high U/Uc ratio of 0.93. The rate, which by the above argument should be less due to the smaller size sediment, is comparable to the adjacent experiments 86 and 128 having the larger sediment diameter of 2.4 mm. The effect of the difference in the particle size is offset by the increase in U/Uc. Experiments 86 and 128 both have a smaller U/Uc value in the range 0.650.66.
The dependence of scour rate on UIUc appears to be more obvious. A higher U/Uc increases the shear stress on the bed, resulting in a greater capacity for sediment removal. Bedload transport increases as particles are transported faster along the bed; consequently the rate of sediment removal from the scour hole increases. Baker (1978) describes the increase in velocity to a shift from the low to a higher frequency of the power spectra density. In other words, the greater the flow speed, the more the occurrence of higher energy turbulent bursts.
In looking at the dependence of the characteristics of the scour depth on an
increased velocity ratio, we see that although the scour depth deepens marginally, a larger change is noticed in the time required for equilibrium. This is more apparent in the Jones data, as only minor variations in U/Uc were used for the USGS experiments. Comparing similar conditions, experiment 57 and 134 used the same sediment, water depth, and pier size, the only change being with the U/UJc parameter. Experiment 57 had a U/Uc of 0.75, while experiment 134 had a U/Uc of 0.93. The average rate, computed by dividing the equilibrium scour depth by the time required for equilibrium, increased from 0. 17 cm/hr to 1.13 cm/hr. A similar comparison can be made with experiments 74 (U/Uc =0.66) and 128 (U/Uc = 0.84), where the average rates increased from 0. 15 cmlhr to 0.79 cmlhr. Thus it can be concluded that not only does the initial rate increase, the average rate also increases with higher velocity ratios.
However, the observation that an increase in U/Uc increases the rate and
consequently decreases the time required for equilibrium is opposite to that observed in the USGS Laboratory data, and reported by other researchers (Shen et al. (1966), Baker (1978), Melville and Chiew (1999)). Baker observed that the time required for equilibrium increases with a higher velocity ratio in the clear water range. However, the number of measurements made was few, and his methods of data collection were somewhat crude. In a more recent publication, experiments completed by Melville and Chiew (1999) agreed with the observations made by Baker. The authors note, however, that higher velocities effectively increase the potential for sediment removal, which may reduce the time required for an equilibrium depth to be reached. They also explain that the increase in velocity ratio leads to a deepening of the scour hole, which consequently
takes longer to scour. They conclude that the effect of the increased scour depth dominates over the greater capacity for sediment removal of the flow, hence the increase in the time required for equilibrium.
Focussing on the USGS Laboratory data, in experiments 3,4, and 6 the same
sediment size is used, with comparable U/Uc values (0.92, 0.97, and 0.99, respectively). However, the size of the structure increases (0. 1 14m, 0.305m, and 0.914m). From the graph, experiment 6 has the slowest rate, while experiment 3 has the largest. Thus it can be deduced that the initial scour rate varies inversely with the size of the structure.
Isolating the experiments on a separate plot in Figure 410, it can be seen that the smaller pier starts off with a larger rate, decreases rapidly until the rate is about 0. 15 s then maintains a slower relatively constant rate until equilibrium is reached. The same shape can be seen for the mediumsized pier, except the initial rate is not as high, and the transition between rates is not as abrupt. The larger pier, however, takes on a different shape in that two separate rates cannot be defined. The variation in the change of rate as scour progresses is minimal. A similar comparison can be seen from experiments 13, 12 and 9, in which d50 is also held constant and the pier diameter changes.
Another difference noted for the larger pile was the location of the maximum scourdepth. For the 0.1 14m and 0.305m piers, the maximum scour depth was located directly in front of the piers. For the larger 0.914m pier, the deepest scour occurred at locations between 45' and 60' to the front of the pier. See appendix C for the individual scour hole profiles.
0.8
8 Exp3b=0.114m
0 Exp 4 b=0.305m
S 0.6 Exp 6 b=.914m
0.4
0.2
0 II
0 4 8 12
ds
Figure 410. Plot of rate of scour versus scour depth showing increasing pier
diameter.
The general thinking behind the dynamics of the horseshoe vortex system agrees with observations made with the smaller diameter piers, in that a high scour rate precedes a lower scour rate until equilibrium is approached. The high scour rate is produced from the increased shear stress as a result of the acceleration of the flow around the structure. The scour hole develops, growing deeper as well as wider as sediment cascades down from the sides of the hole. Once the scour hole deepens, the streamlines become spread apart as the flow enters the hole signifying a reduction in velocity. The effect of the acceleration on the scour process becomes smaller as the scour hole deepens. Eventually,
the dominant mechanism switches from the accelerated flow to the horseshoe vortex system. The lower scour rate is produced by the horseshoe vortex system. The horseshoe vortex evolves as the scour hole develops. A smaller, weaker vortex forms initially when the bed is plane as a result of the variation in stagnation pressure along the leading edge of the pile. The vortex formed in this case is localized and concentrated at the base of the pier. As the scour hole develops from the accelerated flow and the surrounding sediment avalanches into the scour hole, the flow separates at the upstream edge of the newly formed hole. The flow in the hole downstream of the point of separation is such that it reinforces the strength of the horseshoe vortex. The horseshoe vortex fonned descends into the hole, and then is transported by the flow around the structure, dissipating the further it travels due to both adverse pressure gradients and viscous effects. Thus in front of the cylinder, the accelerated flow weakens and the horseshoe vortex strengthens as the scour hole develops. Further development of the scour hole results in an enlargement and weakening of the horseshoe vortex until an equilibrium depth is reached. Figure 411 shows the author's conceptions of the contributions of the acceleration and horseshoe vortex on the overall rate of scour.
The lack of a clear break in the scour rate versus scour depth for the larger
diameter pier as well as the location of the maximum scour depth can be explained as follows. The angle of repose for the sediments used in the USGS Laboratory experiments was such that the scour hole produced by the accelerated flow on the sides of the pile had only a small overlap in front of the structure. This reduced scour hole depth in front of the pile impacted flow separation on the leading edge of the scour hole and the energy that it feeds into the horseshoe vortex. The decrease in energy in the horseshoe
vortex reduces its role in the scour process and not only affects the equilibrium scour depth but the rate of scour as well. It is anticipated that these effects (more uniform scour rate with scour depth and further separation of maximum scour hole locations) will increase with increased pile diameters. Changes in the scour rate, which can be seen with the smaller piles, are anticipated until the pile diameter is large enough so that the scour holes formed from the accelerated flow do not overlap in front of the pile. For larger diameter piles the change should be minimal. For 0.2 mm diameter sand the pile diameter where this occurs is estimated to be 0.9 m.
Combined effects
Rate of Scour IV. A ... 1+;
Time
Figure 411. Author's hypothesis of the relative contributions of the mechanisms on the rate of scour.
Baker (1978) writes on the increase of the parameter b/d* (where d* is described
as the displacement thickness or 1(1 Y'U)dy, where u is the velocity inside the
0
boundary layer and U is the velocity outside the boundary layer) that the large energy carrying eddies within the boundary layer upstream of the vortex system become smaller and hence the frequencies associated with them become larger. If this is true, it provides an explanation as to why the rates decrease with an increase in pier diameter. If the pulses that drive the horseshoe vortex become smaller, even though they occur more, there will be a limit as to which mechanism becomes dominant.
The acute variation in the rate of scour after a certain depth has been achieved
may also be due to a cutoff of the horseshoe vortices from the incoming flow. It may be possible for the streamlines of the incoming flow to be diverted away from the horseshoe vortices at the bottom of the hole for scour hole having steep side slopes. This concept is based on the dynamics of a flow over a rectangular cavity (a limiting situation to an increasing slope of the scour hole), in which a trapped rotating eddy is generated inside the cavity, and streamlines of the incoming flow show only a slight deflection into the cavity as they pass over the depression. The diagrams shown in Figure 412 illustrate the concept.
The water depth dependence could not be comprehensively analyzed as all but one of the experiments were run at yO/b values large enough so as not to affect the maximum scour depth. It has been shown that the yO/b parameter has little effect on the maximum depth above values of around 2.5. The exception was experiment 11, having a yO/b of 0.95. Comparable to that experiment (having the same d50 as well as b),
experiment 9 had a yO/b of 2.62. Experiment 9 also had a higher U/Uc value (0.98 as compared to 0.82 for experiment 11). Had the yO/b parameters been equal, experiment 9 should have had a higher initial scour rate. Surprisingly, the converse was found, experiment 9 had a slightly smaller initial scour rate.
r
Figure 412. Diagrams representing early and later stages of scour showing less contribution of the incoming flow to the horseshoe vortex system as equilibrium is approached.
The general reasoning behind the effect of the yO/b parameter is that for values smaller that about 2.5, the horseshoe vortex at the base of the pier interacts with the surface roller vortex on the upstream edge of the pile and at the surface. The surface roller and horseshoe vortex have opposite rotations, the horseshoe vortex having a downward motion next to the structure. The interaction causes a decrease in the strength of both vortices, hence producing a lesser maximum scour depth. Considering this reasoning, the initial rate of scour should decrease with smaller yO/b. A decrease in yO/b reduces the strength of the horseshoe vortex, thus inferring a weaker mechanism for sediment removal. The opposite, however, was noticed. Not only did the initial rate disagree with the hypothesis; the timeaveraged rate over the respective scour depth also showed an unfavorable difference. The average scour rate, found by dividing the equilibrium depth by the time required for equilibrium, was 0.38 cm/hr for experiment 9 (having a greater water depth), while experiment 11 had an average rate of 0.54 cm/hr.
Concrete explanations as to why this happened cannot be attempted without
additional data. The variation in the rates between the two experiments was indeed small, so it could be that some unforeseen factor affected the scour process, not an unreasonable suggestion considering the number of variables involved.
The data examined in this thesis indicate a dependence of the rate of scour on the parameters b, U/Uc, and d50 as well as the equilibrium scour depth dse. The range of parameters investigated to date is not sufficient to establish the precise dependence but the trends for rate dependence on many of these parameters can be established. The equilibrium scour depth has already been shown to be dependent on the parameters U/Ujc, d50/b, and yO/b. The USGS Laboratory data shows a good correlation between the time
for equilibrium and the equilibrium scour depth. Could it be that the time required for equilibrium is solely a function of the equilibrium scour depth?
Based on the results taken from the USGS Laboratory experiments alone, this
appears to be true. However, the range of variables used in the experiments is extremely limited. All experiments were completed at high U/Uc values, and only two types of relatively small sediment sizes were used. Further experimental data are needed before a definitive relationship can be established.
Including the estimated maximum scour depth and the time required to reach 90% of this depth, the findings shown in Figure 413 below indicate that the time for equilibrium cannot be expressed solely as a function of the equilibrium depth. Although most of the variables are the same, the dependence of the equilibrium time on these variables may be different.
160
120
80*7
40 426
J34
0 1 1 1 1 1
0 20 40 60 80 100
dse (cm)
Figure 413. Equilibrium scour depth versus t90 for all experiments.
69
Using the estimated dse and t90 for Jones data in conjunction with the UF/USGSBRD data, an effort was made to find a way of expressing the data points so that a linear relationship could be found. In this way, a predictive equation can be used to estimate a scour depth for any time. Using the relationships deduced earlier from the scour rates, the expression in Equation 4.3 was obtained. A plot of this function along with the data is given in the logarithmic plot in Figure 414.
fi (yU,~ (log d50 X1 000d5 0 7(90 )5, (4.3)
where 0.45
100
: CD
100
0.1
dse (m)
Figure 414. Plot of dse versus fl using data from all experiments.
The line fitted through the data was calculated to be ln(fl) = 0.6703 In dse + 2.9666. (4.4)
However, the validity of the method for predicting t90 using the equations above is dependent on the accuracy of the estimations for the equilibrium scour depth and corresponding time required for equilibrium made for Jones' data. More confidence can be placed on equations developed from data taken from complete, accurate experiments such as those completed in the USGS Laboratory. Equations based on the USGS data alone are developed below.
A major fault of the dse versus te relationship for data taken from the USGS Laboratory experiments shown earlier was that the line joining the points did not pass through the origin. Earlier in the analysis it was shown that for the USGS experiments, as the parameter U/Uc increased, the time for equilibrium increased. It was also shown that although the initial rate increased with increasing d50, the average rate decreased, so it took longer for equilibrium to be reached. Using these observations, the following equation was proposed:
t9O = k(d50)oo5(UU dse (4.5)
Equation 4.5 is shown in Figure 415 along with the data, where t90 is in hours, and d50 and dse are in meters. The constant k is computed to be 218.55 hr/m'05.
250
~ 200
150
~ 100
50
0 0.2 0.4 0.6 0.8 1
dse (cm)
Figure 415. Plot of dse versus f2 for data collected from USGS experiments
only.
The equilibrium scour depth has been researched by a number of scientists over the last 5 decades. The most recent and accurate calculation has been that of Sheppard, which is generally accurate to within 10% of the corresponding laboratory results. Using the predicted equilibrium scour depth and the results from the graph above, an equilibrium time can be deduced. For a comparison of scour prediction equations, see Pritsivelis (1999).
Finally, using the earlier plot shown for ds/dse versus t/te, a curve was fitted for a conservative (fast rate) experiment. The following equation represents the development of the nondimnsionalized scour depth with nondimnsionalized time: dS/ a+b d (4.6)
72
where a=0.0017, b=1.1755, c=0.0745, d=2.1075
Using the equation above with the estimated scour depth and equilibrium time, a scour depth can be computed for any given time, as described in the following steps:
1) Calculate the dse using Sheppard's equation
2) Compute t90 from Equation 4.5
3) For any given t, ds can be calculated using dse and te from Equation 4.6.
CHAPTER 5
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
5.1 Summar
The complex nature behind the mechanisms of local bridge scour has yet to be fully understood. This thesis attempts to gain useful insight into these mechanisms by analyzing the temporal development of scour at a cylindrical pile in a steady current. Through examination of the changes in the rate as scour, a better grasp of the driving mechanisms that control the process is achieved. Observations made in the analysis are used to construct a predictive equation to estimate local scour depths as a function of time.
Data were collected from experiments conducted at the USGSBRD Laboratory in Turners Falls, Massachusetts. A total of seven experiments were run. The experiments varied mainly in cylinder diameter and sediment size, with minor variations in water depth to pile diameter ratios and the nondimensionalized velocity U/Uc. The experiments were allowed to run until a definite equilibrium depth could be identified. The scour depth was monitored by video cameras located inside the piers, and by acoustic transponders located near the water surface. Water velocities were measured using two MarshMcBimey velocity meters. A digital thermometer and a water level indicator were also used. On completion of each experiment, a survey was made of the
scour hole by point gauging. Additional data used in the analysis came from experiments completed at the FHWA Turner Fairbanks Laboratory in McLean, Virginia under the supervision of J. Sterling Jones.
The raw data were first corrected to attain the maximum scour depth recorded on completion of each experiment by point gauging the bed. The data was then checked for inconsistencies and smoothed to assist in the analysis. For each experiment, a separate curve was fitted to the scour history data. This was done to achieve a better comparison for the initial rates of the experiments.
5.2 Conclusions
The experiments conducted in the USGS Laboratory were not originally intended for use in the investigation of time rate of scour. They were designed to investigate the dependence of the parameter d50/b on the maximum scour depth, in order to check and improve the existing predictive equations. Previously, the small size of the flumes put a restriction on the maximum size of the structure that could be tested. The expanse of the flume in the USGS Laboratory made it possible for large near prototype size piles to be tested.
Because of this, the main variations from one experiment to another were in the
size of the sediment and the diameter of the pile. All were conducted at high U/Uc values (above 0.8), and all had a yO/b parameter greater than 2. Of the three dimensionless parameters believed to describe local scour (U/Uc, D50/b and y0/b), only D50/b was varied in the USGSBRD Laboratory experiments. It was therefore not possible to examine the effects of U/Uc and yO/b on the rate at which clearwater local scour occurs using this data.
A correlation between the time required to reach equilibrium and the equilibrium scour depth was observed. However, the only time history data available in the literature for experiments with sufficient duration to reach equilibrium scour depth are those conducted at the USGSBRD Laboratory. Jones' experiments were of long duration but were all short of equilibrium. Since the scour depth versus time plot is very flat as equilibrium depths are approached it is difficult to establish the time when equilibrium is reached. Nevertheless, Jones' data were extrapolated to equilibrium and estimates made for both equilibrium depth and time. Using these approximate values it became apparent that additional factors, other than just the equilibrium depth were responsible for determining the time required to reach'equilibrium.
Using a plot of the nondimesionalized parameters ds/dse versus t/te, two distinct scour rates could be identified for each experiment. These rates can be explained by a transition of the dominant mechanism controlling the scour process. The first, stronger rate is caused by the action of the acceleration flow around the sides of the pile. Scour initiates at locations 4560' to the front of the cylinder. The hole develops, deepening and widening as sediment cascades down into the hole periodically due to slope stabilization. Flow separation occurs at the upstream end of the hole, strengthening the horseshoe vortex. The horseshoe vortex is initiated by the downflow due to the stagnation pressure gradient on the front of the cylinder. This flow is redirected to meet the incoming flow when it encounters the bed. As the scour hole deepens, the horseshoe vortex enters the hole, and grows in strength and size. Streamlines of the accelerated flow are spread apart, signifying a reduction of the velocity. After a certain depth, the dominant mechanism controlling the scour process switches from accelerated flow to the
horseshoe vortex. The effect of the horseshoe vortex is considered to be weaker than the accelerated flow and hence the transition in the rate of scour. Further deepening of the hole results in the vortex expanding in size but weakening in strength. Equilibrium is reached when the vortex is not strong enough to transport dislodged sediment out of the hole
All data from the experiments were then fitted with individual curves for better analysis of the initial rates. By differentiating the resultant equations for the normalized scour depth versus time, another equation was obtained that described the time rate of scour. Comparing this rate to ds/dse produced a number of interesting results.
An increase in particle diameter d50 increases the initial scour rate. This is
explained by a decrease in area of sediment available for scour as compared to sediment of smaller diameter because the angle of repose, which determines the slope of the scour hole, is greater. As the scour hole progresses, a larger sediment, which has a larger angle of repose, will have a steeper side slope. Thus the erodible area will be less, and the scour greater.
However, even though the initial rate increases, the time required for equilibrium increases with increasing particle diameter. The scour plots for the larger sediment are seen to approach equilibrium much slower. It is thought that at this stage of scour, turbulent bursts are instrumental in achieving equilibrium. A larger particle requires a stronger burst to be completely removed from the hole. Stronger bursts occur less frequently, hence the slower rate of scour.
Increase in the nondimensionalized parameter U/Uc will increase the initial scour rate. Greater values of U/Uc will have a larger capacity for sediment transport, and the
rate of scour increases. The effect on the overall time required for an equilibrium scour depth to be reached is inconclusive. The FHWA experiments were included in the analysis as they were performed over a wider range of velocity ratio. Using estimates for both equilibrium depth and the time required for 90% of the scour to be completed, the FHWA data indicates the time required for equilibrium decreases with increasing U/Uc. However, this observation disagrees with both the data from the USGSBRD experiments, as well as findings made by previous researchers (Shen, Baker, Melville et al.). This data shows increasing times to equilibrium with increasing U/Uc.
The scour rate plots show differences in the shape of the curves for the different size piers. The smaller piers have two distinct scour rates, whereas the larger pile has a scour rate that generally does not change significantly during the scour process. Coincidentally, the location of the deepest scour depth changes, being directly in front of the pier for the smaller cylinders and at angles 45'60' for the larger cylinder. These differences are thought to be due to a difference in the extent of the scour initiated by the accelerated flow around the sides of the pile. For the larger pile, if the scour spreading from the points of initiation on either side of the pile do not meet, a section of the hole directly in front of the pile is left relatively unscoured. This affects the flow separation, the horseshoe vortex and the energy fed into the system, which is apparent in the lack of variation in the scour rate. The flow is directed around the unscoured sediment, hence the difference in the location of the maximum scour depth. The smaller piers seem to agree with the hypothesis presented earlier.
From the preceding observations, an equation was derived so that a linear
relationship between it and the maximum scour depth could be fitted through the data.
Two equationsy*ere presented one for all the data and another for just the data taken from the USGS Laboratory experiments. Using one of the faster rate experiments for conservative reasons, a separate equation was fitted relating the nondimensionalized parameters ds/dse and tlte. Using a predictive equation to find the maximum scour depth, the time for equilibrium could be estimated. Finally for any time, a scour depth can be computed using the conservative scour plot equation.
5.3 Recommendations
The lack of data for a range of all of the important parameters affecting the rate at which local scour occurs places limits on the confidence in the descriptions and conclusions given in this thesis. In spite of these limitations a number of interesting observations were made. These include the dependencies of the sediment diameter, pile diameter, and velocity ratio on the scour rates, as well as variations in the rate changes from one experiment to another as scour progresses.
Various uncontrollable aspects of the experiments, such as the variability of the river water used and the relative inefficiency of the gates controlling the flow may have resulted in small inaccuracies in the data collected. The time rate, more so than the equilibrium scour depth, is especially sensitive to the subtle irregularities encountered.
Firstly, the initial rates were dependent on the speed at which the target velocity was reached. The gates controlling the flow of water into the flume were tricky to use. Several minutes would elapse before a steady velocity was attained. Although efforts were made to set the target velocity as quickly as possible, the time elapsed before this was accomplished must have had a bearing of the initial scour.
The source of the flow came from the Connecticut River. Several filters were
used to stop large obstacles from entering the test area. Inevitably, small particles such as silt suspended in the water column were transported into the flume. This cohesive sediment settled on the bed when the water flow had been shut off on completion of each experiment, and was carefully removed before the bed was pointgauged.
Extreme temperatures of the river water were recorded during the winter months. For two of the experiments, for example, the average temperature was a meager P C. The temperature is known to affect both the density and the viscosity of the water, thus changing the critical velocity for the onset of sediment motion. This was accounted for in the calculation of the critical velocity for each experiment, but the effect of extreme temperatures on other factors was not. It could be that the temperature also affects cohesive attraction of individual particles. It also seems likely that because both density and viscosity are affected, the dynamics of the horseshoe vortex could be altered as well, either in magnitude or shape.
The validity of the rate of scour equation derived in this thesis is not only
restricted by the narrow range of experimental data but also dependent on the accuracy of the predictive equation of the equilibrium scour depth. Although substantial research has been conducted in determining the maximum depth of scour, the possibility of error multiplies in using one empirically derived equation for use in another.
The nondimensionalized plot of ds/dse versus t/te allows the rates of the
experiments to converge at both the origin and at the point (1, 1). However, in between these points there are small differences in the rates in the individual experiments. The slower experiments were used to devise the fitted equation to which a depth can be
estimated for any time. However, a better situation for estimating the scour depth using the maximum depth and equilibrium time would be to incorporate the factors that determine the rate of the scour process as it evolves.
Clearly a detailed series of experiments dedicated to the investigation of the
temporal rate of scour is needed. The experiments have to be completed in their entirety to ensure both an equilibrium depth and time can be recorded. Nonintrusive methods of data collection such as those used in the USGSBRD Laboratory are recommended. The experiments have to be varied singly in water velocity, sediment diameter, water depth, and pier size, while holding the other variables constant.
Additionally, accurate measurements of velocity fluctuations of both the accelerated flow and the horseshoe vortex need to be completed. A laser Doppler anemometer would be the most ideal instrument for this purpose. Additionally, a study into the intensity and frequency of the turbulent bursts that dictate the final stages of scour would also be desired. Using this information, a complete understanding of the mechanism behind the scour process could be formulated.
A better understanding of the dynamics of scour can be used in devising a mathematical computer model. The very nature of the process, with the apparent turbulent bursts of the vortex removing sand periodically, appears to be very similar to a typical sediment transport model using an incremental time step. By representing the contribution of both the acceleration and the horseshoe vortex as they vary in the development of the hole, and taking the volumetric transport of the eroding sediment as well as the neighboring cascading sediment into consideration, the design of a model estimating the scour development over time is quite feasible.
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0 0
from original
APPENDIX A
INDIVIDUAL CURVE FITS The following curve fits were accomplished using the 2D empirical curvefitting program TablecurveTM.
Exp3
y=a+b(1exp(cx))+d(1exp(ex)) a=0.00045214718 b=0.19307718 c=4.2084458 d=0.82592905 e=0.1728253
1.25 1.25
*0~ I
e1
0.25  0.25
0 ._ ,_ .I
0.5 0
0.25 0. 25
0 10
Time (hrs)
Figure A1. Curvefit of data of experiment #3.
83
Exp4
y=a+b(1exp(cx))+d(1exp(ex))
a=0.00068531296 b=0.41187992 c=1.2901773
d=0.59838058 e=0.050830295
____ ____ .0.9 0.8
 0.7
0.6
 .~0.5
Figure A2. Curvefit of data of experiment #4.
84
Exp6
y=a+b(1exp(cx))+d(1exp(ex)) a=O.0013300124 b=O.1254428 c=0.5870551 d=0.9123429 e=0.05407349
1.25 1 1 1 1 1.25
I I
 I
0.75   0.75
0.5 0.5
0.25 ....0.25
Time (hlirs)
Figure A3. Curvefit of data of experiment #6.
Exp9
y=a+b(1exp(cx))+d(1exp(ex))
a=O.0016169758 b=O. 17848818 c=0.99698604 d=0.82649869 e=O.013839237
1.25 T 1.25
1 _ _1
0.75 0.75
0.5" 0.5
0.25 0.25
Time (Irs)
Figure A4. Curvefit of data of experiment #9.
Exp11
y=a+b(1exp(cx))+d(1exp(ex))
a=0.0021784218 b=0.33460626 c=0.63915118 d=0.72608262 e=0.020879841
1.25 1 1.25
0.75  0.75
0.5 I0.5
0.25 10.25
Time (Ihrs)
Figure A5. Curvefit of data of experiment #11.
