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Georgia Department of Transportation Office of Materials and Research
GDOT Research Project No. 2002 Final Report
LABORATORY AND 3D NUMERICAL MODELING WITH FIELD MONITORING OF REGIONAL BRIDGE SCOUR IN GEORGIA
Submitted by
Terry Sturm1, Fotis Sotiropoulos1, Mark Landers2, Tony Gotvald2, SeungOh Lee1, Liang Ge1, Ricardo Navarro1, and Cristian Escauriaza1
1School of Civil and Environmental Engineering Georgia Institute of Technology
Atlanta, GA 30332
and
2U. S. Geological Survey 3039 Amwiler Rd. Suite 130
Atlanta, GA 30360
August 2004
TECHNICAL REPORT STANDARD TITLE PAGE
1. Report No. FHWA-GA-04-2002
2. Government Accession No.
3. Recipient's Catalog No.
5. Report Date August 2004
4. Title and Subtitle Laboratory and 3D Numerical Modeling with Field Monitoring of Regional Bridge Scour in Georgia 6. Performing Organization Code
7. Author(s) Terry Sturm, Fotis Sotiropoulos, SeungOh Lee, Liang Ge, Ricardo Navarro, Cristian Escauriaza (Georgia Institute of Technology)
Mark Landers2, Tony Gotvald, (U.S. Geological Survey)
8. Performing Organ. Report No.: 2002
10. Work Unit No.
9. Performing Organization Name and Address School of Civil and Environmental Engineering; Georgia Institute of Technology; Atlanta, GA 30332 U. S. Geological Survey; 3039 Amwiler Rd. Suite 130; Atlanta, GA 30360
11. Contract or Grant No.
13. Type of Report and Period Covered Final; 2000-2004
12. Sponsoring Agency Name and Address Georgia Department of Transportation Office of Materials and Research 15 Kennedy Drive Forest Park, Georgia 30297-2534
14. Sponsoring Agency Code
15. Supplementary Notes Prepared in cooperation with the U.S. Department of Transportation Federal Highway Administration. 16. Abstract Field measurements, laboratory modeling, and 3D numerical modeling of scour around bridge foundations were combined and applied to specific bridges in Georgia in order to elucidate the physics of the scouring process and improve scour predictions. Field data were collected at four Georgia bridge sites using fixed instrumentation and mobile instrumentation. These data include continuous scour measurements at several locations around a single pier at each site and continuous velocity measurements at two sites. Two bridges were modeled in the laboratory, including the full river bathymetry. Also, sediments sampled at the foundations of 10 Georgia bridges were tested in the laboratory to obtain erodibility parameters. Finally, a comprehensive 3D numerical model was applied to the bridges in this study. The field results revealed several important aspects of bridge scour processes, including the dynamics of live-bed scour, simultaneous occurrence of contraction and pier scour, and cyclical scour and fill associated with the tidal cycle. The 3D model was validated by laboratory measurements and revealed details of the complex flow field around natural river bridge foundations. Comparisons of laboratory scour depths with existing scour formulas highlighted the difficulties in scaling of scour depths from laboratory to field; however, a successful modeling strategy was applied. The laboratory model not only reproduced measured maximum scour depths in the field for bank-full and extreme flood events, but also the details of cross-sectional changes immediately upstream of the bridge. The laboratory erosion tests illustrated the regional variability of erosion parameters and the variability associated with sediment stratification at a particular site. Erosion parameters were successfully correlated with some easily measured sediment properties. Continuing studies will focus on contraction scour and the development of a scour prediction methodology that incorporates the knowledge gained from combined field, laboratory, and numerical studies.
17. Key Words Bridge scour, numerical modeling, sediment properties
18. Distribution Statement
19. Security Classif. (of this report) Unclassified
20. Security Classif. (of this page) Unclassified
21. No. of Pages 158
22. Price
Form DOT 1700.7 (8-69) *A color edition of this report is available at http://topps.dot.state.ga.us/homeoffs/fpmr.www/internal/b-admin/research/r-rpts-online.shtml.
i
ACKNOWLEDGMENTS
The authors gratefully acknowledge the expert guidance and assistance provided by David Jared,
Special Research Engineer, of the Georgia DOT Research Office throughout the project as well
as the support and valuable suggestions offered by Sam Teal of the Bridge Design Office. The
assistance of Tom Scruggs and Shannon Shaneyfelt of the Geotechnical Bureau in obtaining the
Shelby tube cores is greatly appreciated. The project was also made possible by the support of
Georgene Geary, State Materials and Research Engineer; Rick Deaver, Chief of Research and
Development; and Paul Liles, State Bridge Engineer.
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EXECUTIVE SUMMARY
Field measurements, laboratory modeling, and 3D numerical modeling of scour around bridge foundations have been successfully combined and applied to specific bridges in Georgia in order to elucidate the physics of the scouring process and improve scour predictions. Field data have been collected at four bridge sites in Georgia using fixed instrumentation in combination with mobile instrumentation. These data include continuous scour measurements at several locations around a single pier at each site as well as continuous velocity measurements at two of the sites. Two of these bridges have been modeled in the laboratory including the full river bathymetry. In addition, sediments sampled at the foundations of 10 bridges in Georgia have been tested in the laboratory to obtain erodibility parameters. Finally, a comprehensive 3D numerical model, including a novel approach to grid generation for bridge foundations in natural rivers and a state-of-the-art turbulence submodel, have been applied to the bridges in this study. The field results have revealed several important aspects of bridge scour processes including the dynamics of live-bed scour, simultaneous occurrence of contraction and pier scour, and cyclical scour and fill associated with the tidal cycle. In addition, the field data have proved to be invaluable for comparison with laboratory model results and have validated the need for additional continuous and simultaneous measurements of scour depths and flow fields. The 3D numerical model has revealed details of the complex flow field around natural river bridge foundations including large-scale coherent vortex shedding in the vicinity of the bridge foundations with multiple vortices having axes parallel and perpendicular to the bed. The 3D model has been validated by laboratory measurements of both velocity profiles and turbulence characteristics in the vicinity of the bridge pier bents. In addition, the 3D model has been demonstrated to be a powerful tool for understanding not only the flow field but the coupling between the flow field and measured scour patterns. Comparisons of laboratory scour depths with existing scour formulas have highlighted some of the difficulties in scaling of scour depths from the laboratory to the field; however, a successful modeling strategy has been applied in which the model sediment size is selected to obtain approximate Froude number similarity in the clear-water scour regime while maintaining geometric similarity of depths and bridge dimensions at a reasonably large ratio of model pier size to sediment diameter. The laboratory model successfully reproduced not only measured maximum scour depths in the field for both bank-full and extreme flood events, but also the details of cross-sectional changes immediately upstream of the bridge. The laboratory erosion tests illustrated the regional variability of erosion parameters as well as the variability associated with sediment stratification at a particular site. Erosion parameters were successfully correlated with some easily measured sediment properties. These advances in field data collection, 3D numerical modeling, and laboratory modeling of bridge scour, as well as in measurement and prediction of sediment erodibility properties, point the way to improved scour prediction techniques to be finalized in Phase 2 of this research.
iii
TABLE OF CONTENTS
Page No. ACKNOWLEDGMENTS i EXECUTIVE SUMMARY ii LIST OF FIGURES vi LIST OF TABLES x CHAPTER 1. INTRODUCTION 1
MOTIVATION 1 BACKGROUND 3 RESEARCH OBJECTIVES 8 ORGANIZATION OF THE REPORT 9
CHAPTER 2. FIELD DATA COLLECTION 10
FIXED FIELD INSTRUMENTATION 10 MOBILE FIELD INSTRUMENTATION 11 STREAMBED SEDIMENT SAMPLING 12 FOUR SELECTED SITES 12
Chattahoochee River near Cornelia, GA 12 Site Description 12 Fixed Field Instrumentation 14 Data Collected 14
Ocmulgee River at Macon, GA 17 Site Description 17 Fixed Field Instrumentation 20 Data Collected 20
Fint River at Bainbridge, GA 24 Site Description 24 Fixed Field Instrumentation 25 Data Collected 26
Darien River at Darien, GA 28 Site Description 28 Fixed Field Instrumentation 29 Data Collected 30
CHAPTER 3. LABORATORY MODEL STUDIES
INTRODUCTION 33 MODELING CONSIDERATIONS 33 EXPERIMENTAL METHODS 35
Model Construction 35 Experimental Instrumentation 41 Experimental Procedure 43
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Page No.
EXPERIMENTAL RESULTS 43 Summary of Data 43 Approach Velocity and Turbulence 47 Near-Field Turbulence Intensity 48 Scour Contours and Near-Field Velocities 50 Comparison of Laboratory Scour Data with Prediction Formulas 54
CHAPTER 4. THREE-DIMENSIONAL NUMERICAL MODELING 59
INTRODUCTION 59 NUMERICAL METHOD 61 GRID GENERATION FOR COMPLEX BATHYMETRY AND OBSTRUCTIONS 61 APPLICATION OF THE 3D MODEL 64 CONCLUSIONS 73
CHAPTER 5. SEDIMENT EROSION PROPERTIES 74
INTRODUCTION 74 SEDIMENT EROSION RESISTANCE 74 EROSION MEASUREMENTS 79 EROSION RELATIONSHIPS 82 EXPERIMENTAL METHODS 82
Sample Locations and Properties 82 Laboratory Flume Measurements 85
RESULTS AND ANALYSIS 88 Observed Erosion Behavior 88 Experimental Results 88 Prediction of Critical Shear Stress and Erosion Rate Constant 92 Critical Shear Stress 93 Erosion Rate Constant 97 Discussion 100
CHAPTER 6. COMPARISONS OF NUMERICAL MODEL, LABORATORY, AND FIELD RESULTS 102
INTRODUCTION 102 NUMERICAL MODEL VALIDATION 103 Chattahoochee River near Cornelia 103 Flint River at Bainbridge 106 Ocmulgee River at Macon 109 FLOW STRUCTURES AND SCOUR 111 COMPARISONS OF LABORATORY AND FIELD RESULTS 116
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Page No. Chattahoochee River near Cornelia 116 Flint River at Bainbridge 120 SUMMARY 123
CHAPTER 7. SUMMARY AND CONCLUSIONS 125 REFERENCES 130 APPENDIX A. EROSION AND SOIL PROPERTY TEST RESULTS 135
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LIST OF FIGURES
Figure Page No.
2.1. Chattahoochee River near Cornelia, GA. 13
2.2. Fathometer and velocity meter layout at Cornelia. 14
2.3 Fathometer data from Cornelia. 15
2.4 Cross-section comparison at the upstream side of the bridge at Cornelia. 16
2.5. Layout of surveyed cross-sections at Cornelia. 17
2.6. Particle size distribution of bed material samples at Cornelia. 18
2.7. Ocmulgee River at Macon, GA. 19
2.8. Fathometer layout for Ocmulgee River at Macon, GA. 20
2.9 Fathometer data from Macon. 21
2.10 Cross-section comparison at the upstream side of the bridge at Macon. 22
2.11. Layout of surveyed cross-sections at Macon. 23
2.12. Particle size distribution of bed material samples at Macon. 23
2.13. Flint River at Bainbridge, GA. 24
2.14. Fathometer and velocity meter layout at Bainbridge. 26
2.15. Cross-section comparison at Bainbridge, GA. 27
2.16. Layout of surveyed cross-sections at Bainbridge. 27
2.17. Particle size distribution of bed material samples at Bainbridge at left (L), right (R), and center (C) of main channel for cross section numbers shown in Fig. 2.16. 28
2.18. Darien River at Darien, GA. 29
2.19. Fathometer layout at Darien. 30
2.20. Fathometer data from Darien. 31
2.21. Fathometer data at downstream side of left bridge fender. 31
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Figure Page No.
2.22. Layout of surveyed cross-sections at Darien. 32
2.23. Particle size distribution of bed material samples at Darien. 32
3.1. Sketch of central pier bent of Chattahoochee River bridge near Cornelia, GA with prototype elevations and dimensions. 37
3.2. Sketch of central pier bent of Flint River bridge at Bainbridge with prototype elevations and dimensions. 39
3.3. Model of Chattahoochee River bridge near Cornelia. 40
3.4. Model of Flint River bridge at Bainbridge. 40
3.5. Scour development with time for Chattahoochee River model. 46
3.6. Longitudinal and vertical relative turbulence intensity profiles at approach section for Chattahoochee River model. 48
3.7. Longitudinal and vertical relative turbulence intensity profiles at approach section for Flint River model. 48
3.8. Near-field turbulence intensities for Chattahoochee River model. 49
3.9. Shaded scour contours and velocity vectors after scour at 40 percent of the approach depth for bank-full flow in the Chattahoochee flat-bed model. 51
3.10. Shaded scour contours and velocity vectors after scour at 40 percent of the approach depth for bank-full flow in the Chattahoochee River model. 51
3.11. Scour contours and velocity vectors after scour for bank-full flow in Flint River flat-bed model. 53
3.12. Scour contours and velocity vectors after scour for flood flow in Flint River model. 55
3.13. Comparison of measured scour depths in Chattahoochee River flat-bed model with scour prediction formulas for bank-full flow. 57
3.14. Comparison of measured scour depths in Chattahoochee River model with scour prediction formulas for bank-full flow and flood flow. 57
3.15. Comparison of measured scour depths in Flint River flat-bed model with scour prediction formulas for bank-full flow. 59
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Figure Page No.
3.16. Comparison of measured scour depths in Flint River model with scour prediction formulas for flood flow. 59
4.1. Numerical geometry of a single bent of piers on natural river reach. 62
4.2 Overset grid system. 62
4.3. Dimensionless velocity-time history at two different points A and B. 66
4.4. Visualization of instantaneous flow field in the vicinity of bridge piers. 67
4.5. Bridger piers mounted on flat bed. 69
4.6. Streamwise velocity contours. 70
4.7. Snapshot of instantaneous streamlines of the large-scale flow. 70
4.8. Instantaneous streamwise velocity contours. 72
4.9 Turbulence kinetic energy profile. 72
5.1. Shields diagram for direct determination of critical shear stress of coarse-grained sediments. 77
5.2. Shelby tube core sample locations. 84
5.3. Recirculating flume for erosion testing. 86
5.4. Erosion rate vs. applied shear stress relationships for sediment samples with erosion rates up to 1.1 kg/m2/s. 90
5.5. Erosion rate vs. applied shear stress relationships for sediment samples with erosion rates up to 0.06 kg/m2/s. 91
5.6. Comparison of the measured and predicted critical shear stress parameter using Eq. 5.6. 96
5.7 Comparison of measured data and calculated values using Eq. 5.6 plotted on Shields’ diagram format. 97
5.8. Comparison of the measured data and calculated values for erosion rate constant s1 using Eq. 5.9. 99
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Figure Page No.
5.9. Comparison of the measured data and calculated values for erosion rate constant s2 using Eq. 5.10. 100
6.1. Comparisons of streamwise velocity profiles (location F1, F2, …, F6 left to right) at relative elevations of 0.6, 0.4, and 0.2 times the depth from top row downward. 104
6.2. Comparisons of turbulence kinetic energy. 106
6.3. Flint River Bridge Layout (a), and measurement cross-sections (b). 107
6.4. Comparisons of streamwise velocity profiles at locations from S1 to S6 (left to right)
and at water depths of 0.45, 0.3, and 0.1 times the depth (top to bottom row). 108
6.5. Snapshot of the streamlines at the Flint River bridge, including the footings in the simulation. 109
6.6. Geometry of the four overlapped grids around a single bent of the Ocmulgee River bridge piers . 110
6.7. Visualization of instantaneous flow field in the vicinity of the bridge piers. 110
6.8. Time-averaged streamwise velocity profiles at locations S1, S2, and S3 (left to right) and at water depths of 0.5, 0.3, and 0.1 times the depth from top to bottom row. 111
6.9 Distribution of scour depth at the equilibrium state. 113
6.10 Flow patterns near river bed. 113
6.11 Comparison of scour in prototype and laboratory cross sections at Cornelia. 117
6.12. Comparison of velocities between field and laboratory measurement at given distances from left side of the central pier bent. 118
6.13. Comparison of field and laboratory measurement of scour depths and Sheppard’s equations for Chattahoochee River, near Cornelia, GA. 119
6.14. Comparison of scour cross sections at Flint River bridge from laboratory model and Tropical Storm Alberto. 121
6.15. Comparison of field and laboratory measurement of scour depths and Sheppard’s equations Flint River at Bainbridge, GA. 123
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LIST OF TABLES
Table Page No.
2-1. Flood-frequency discharge data for Cornelia. 13
2-2. Flood-frequency discharge data for Macon. 19
2-3. Flood-frequency discharge data for Bainbridge. 25
3-1. Model studies conducted. 35
3-2. Raw experimental data for Chattahoochee River bridge near Cornelia, GA. 44
3-3. Dimensionless experimental data for Chattahoochee River bridge near Cornelia, GA. 44
3-4. Raw experimental data for Flint River bridge at Bainbridge, GA. 45
3-5. Dimensionless experimental data for Flint River bridge at Bainbridge, GA. 45
5-1. Location of samples and description of physiographic regions. 84
A-1. Linear, piecewise linear and exponential critical shear stress values for the erosion rate vs. applied shear stress models. 136
A-2. Linear, piecewise linear and exponential slope coefficients for the erosion rate vs. applied shear stress models. 137
A-3. Results of erosion tests and soil property tests on Murray County sample. 138
A-4. Results of erosion tests and soil property tests on Towns County sample. 139
A-5. Results of erosion tests and soil property tests on Habersham County sample. 140
A-6. Results of erosion tests and soil property tests on Haralson County sample. 141
A-7. Results of erosion tests and soil property tests on Bibb County sample. 142
A-8. Results of erosion tests and soil property tests on Wilkinson County sample. 143
A-9. Results of erosion tests and soil property tests on Effingham County sample. 144
A-10. Results of erosion tests and soil property tests on Decatur County sample. 145
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Table Page No.
A-11. Results of erosion tests and soil property tests on Berrien County sample. 146
A-12. Results of erosion tests and soil property tests on McIntosh County sample. 147
1
CHAPTER 1. INTRODUCTION
MOTIVATION
Bridge scour is a significant transportation problem because of the monetary damage and
possible loss of life that it can cause when it results in bridge foundation failure. The damage
caused by tropical storm Alberto in Georgia in 1994 is a case in point. Tropical storm Alberto
dumped as much as 28 in. of rainfall in parts of central and southwest Georgia from July 3-7,
1994, and caused numerous bridge failures and highway closings as a result of the 100-yr flood
stage being exceeded at many locations along the Flint and Ocmulgee Rivers. Approximately 18
ft of foundation scour occurred at the U.S. Highway 82 crossing of the Flint River near Albany,
Georgia (Stamey 1996). Total damage to the Georgia Department of Transportation highway
system was approximately 130 million dollars (Richardson and Davis 2001). Bridge failures can
also lead to loss of life such as in the 1987 failure of the I-90 bridge over Schoharie Creek near
Albany, New York; the US 51 bridge over the Hatchie River in Tennessee in 1989; and the I-5
bridges over Arroyo Pasajero in California in 1995 (Morris and Pagan-Ortiz 1999).
Prevention of bridge scour damages and possible loss of life hinges on having the
capability of predicting expected bridge scour. Unfortunately, such predictions remain a
challenging problem because of the complex interaction of the river flow with the obstruction
presented by the bridge foundation and with the erodible bed of the river. As the approach flow
encounters a bridge foundation it rolls, via the action of the foundation-induced adverse pressure
gradient, to form multiple large-scale vortices whose axes may be parallel (horseshoe vortices) or
perpendicular (tornado and/or whirlpool-type vortices) to the bed. These unsteady, large-scale
flow structures in conjunction with a broad range of turbulent scales control the sediment
2
transport in the vicinity of the foundation and are responsible for the growth of scour holes
(Raudkivi, 1986; Dargahi, 1990, 1989; Melville, 1997). The complexity of such scour-inducing
flow phenomena has hampered satisfactory analysis and prediction procedures in the past. In
addition, bridge scour prediction has to be applicable to extreme hydrologic events and widely
varying river characteristics.
Previous attempts at solving the problem of scour prediction have been piecemeal at best.
Currently, scour prediction is based on formulas that have been developed from laboratory
experiments in flumes having unrealistic geometry. Furthermore, these formulas have been
applied using unproven scaling techniques to extrapolate from the model to the prototype. In
addition to the shortcomings of previous laboratory work, field verification of predicted scour
has been very limited even though notable efforts have been made using the latest in mobile
instrumentation techniques by the USGS (Landers and Mueller 1996). Long-term monitoring of
the scour process at particular bridge sites, including multiple spatial points of scour-depth
measurement with simultaneous real-time velocity monitoring, is practically nonexistent. A
further deficiency in current scour prediction methodology is that the terrific strides made in the
last decade or so in computational fluid dynamics (CFD), both in terms of computing power and
new computational methods, have yet to be applied in any comprehensive way to the problem of
bridge scour, despite the success enjoyed by CFD techniques in other areas of engineering.
Parola et al. (1997) have concluded that an integration of field studies, numerical model studies,
and laboratory studies is needed to make a significant advancement in bridge scour prediction
methodology and scour countermeasure design.
In addition to deficiencies in previous scour studies due to the lack of an integrated
approach, scour prediction in Georgia is further complicated by the wide degree of variability in
3
physiographic regions, from the piedmont to the coastal plain, that have very different geologic
and topographic characteristics. The sediment erodibility and the type of flow field driving the
scouring process are highly regional because of these differences in geology and topography.
This research addresses the need for improving current bridge scour prediction
methodologies with particular reference to the State of Georgia. A comprehensive research
approach, consisting of 3D numerical modeling integrated with laboratory and field
measurements, is implemented to resolve multiple problems of scour prediction. The overall
purpose of the research is to develop a prediction methodology that will substantially reduce the
expense of foundations for new bridges and avoid the costly replacement of some existing
bridges due to anticipated scour that is overestimated by current prediction procedures. This
report summarizes the results of Phase 1 of the research and outlines the remaining tasks for
completion of a proposed comprehensive scour prediction methodology in the upcoming Phase 2
of the research.
BACKGROUND
Several factors make bridge scour prediction in Georgia particularly challenging. The state of
Georgia includes a number of unique physiographic regions from the piedmont to the coastal
plain that have very different geologic and topographic characteristics. For example, one of the
most important parameters of any scour prediction technique is the critical shear stress for
initiation of motion. While critical shear stresses are relatively well known for cohesionless
sands and gravels, the contribution of clays to form cohesive sediments results in difficulties
with respect to characterization of bed stability. Furthermore, sediment bed consolidation and
layering of sediments of different types both result in stratified sediment beds that have stability
properties that change with depth as scour occurs. The wide variety of sediments in Georgia
4
make this problem of particular interest when formulating scour prediction equations, and failure
to be able to predict bed stability parameters can lead to significant errors in the prediction of
equilibrium scour depth.
In addition to sediment variability, the differences in topography throughout Georgia lead
to very different flow characteristics that can vary from local abutment scour caused by a bridge
on a wide, heavily vegetated floodplain in the coastal plain to contraction scour on relatively
narrow streams in the piedmont, or to contraction scour caused by tidal bridges subject to storm
surges on the coast. With this degree of variety in flow situations, it becomes difficult for a
single hydraulic model, especially if it is one-dimensional, to adequately forecast the relevant
velocities and/or shear stresses that are driving the scouring process.
Previous approaches to developing scour prediction equations have relied on laboratory
models, which in some instances have not properly modeled the field situation, especially in the
case of bridge abutments located on the floodplain in compound channel flow. However,
previous experimental work at Georgia Tech sponsored by Georgia DOT and FHWA in a large
flume of compound section has resulted in an improved methodology for predicting abutment
scour in compound channels (Sturm and Janjua 1994; Sturm and Sadiq 1996; Sturm 1998,
1999a,b). This methodology relies on estimates of a discharge contraction ratio rather than a
geometric contraction ratio in order to account for flow redistribution between the approach and
bridge contraction sections that depends on the lateral variability in velocity and depth in a
natural channel in overbank flow. Questions remain, however, on the "scaling issue" of applying
results from laboratory models to the field. Even laboratory models with realistic cross-sectional
shapes use sediment sizes and flow rates to reproduce a sediment mobility parameter, V/Vc ,
which represents the ratio of the approach velocity to the critical value for initiation of motion.
5
Froude numbers are maintained in the subcritical range, but exact reproduction of the Froude
number is not usually attempted because some laboratory results indicate that the Froude number
has a smaller effect than the sediment mobility parameter. This modeling strategy has never
been fully validated except on an ad hoc basis with comparisons between scour predictions,
which are based on laboratory scour formulas, and measured field scour. In most cases, the
available field data displays too much variability to provide definitive comparisons, and so the
scaling issue remains unresolved. The advantage of laboratory models is that a wide range of
flow conditions can be investigated in a controlled experimental design to isolate the effects of
individual independent variables on the scour process.
During the last decade many investigations have been conducted to collect and analyze
field scour data at bridges during flood conditions. These studies have helped to set limits on
laboratory-derived equations, and have provided insight into the range of complex hydraulic and
sediment conditions that are encountered in the field. However, bridge scour investigations
focused on field studies alone are limited in that they provide data for only a very few conditions
(floods) at a given site, or they rely on measurements of remnant scour holes without adequate
knowledge of the hydraulic conditions causing the scour. Field data sets do not permit engineers
to evaluate the scour effects of a series of floods in which causative parameters, such as velocity
and sediment type, are altered.
In this study, field measurements of bridge scour are made with fixed instrumentation
that records velocity and bed depth continuously at specific points; and mobile instrumentation
that is deployed during high-flow events to record bathymetry and velocity field data through a
bridge reach. Fixed instrumentation provides continuous time series data when crews are not
deployed to collect data. This information is vital to understand overall processes of scouring and
6
infilling at a bridge site. A typical limitation to fixed instrumentation data sets is the inability to
distinguish local scour from contraction scour. Because fixed instrumentation is always on a flow
obstruction, such as a pier, it measures the change in bed elevation due to both local and
contraction scour. In order to quantify local scour, channel geometry around the local obstruction
is needed. In order to quantify contraction scour, one must have some measure of average bed
elevation changes from upstream of the hydraulic influence of the bridge, through the bridge to
downstream of the hydraulic influence of the bridge. This can be accomplished for larger streams
from boats deployed during flood events. A further advantage of mobile deployed measurements
(accompanying fixed instrumentation) is that detailed 3-dimensional velocity field data sets are
collected through the study reach. These are particularly valuable because of the 3-dimensional
numerical modeling that is part of this investigation. Detailed field data sets, such as those
collected in this study, have been the most informative field data collected for understanding
scour processes (Landers and Mueller 1996).
Both field and laboratory data collection have limits in the range of scenarios that can be
observed. This problem can be overcome by use of a numerical model of bridge scour, having
adequate complexity and computational accuracy to represent complex scour processes; and
having adequate observed laboratory and field data to permit calibration and refinement to
represent reality. A three-dimensional numerical model using modern Computational Fluid
Dynamics (CFD) techniques is needed to fully understand the complexity of bridge foundation
flows. CFD methods have been successfully applied to a number of real-life engineering
problems (Neary et al. 1999; Sinha et al. 1998) but have yet to be utilized to their full potential to
tackle the scour problem. A few preliminary simulations have been reported in the literature
(Olsen and Melaan 1993; Dou et al. 1996), but they all lack the level of modeling rigor and
7
sophistication required to reproduce the multiple facets of the phenomenon. More specifically,
these studies have adopted very simplistic turbulence modeling strategies and have, thus, failed
to reproduce even the broad qualitative features of the flow in the vicinity of the foundation.
Recently, however, very sophisticated turbulence models, capable of quantitatively accurate flow
predictions, have been developed and successfully applied to calculate a wide range of complex,
3D flows with vortices (Sotiropoulos and Patel 1994, 1995a,b; Sotiropoulos and Ventikos 1998).
The first attempt to apply such a model to bridge abutment flows was reported by Sotiropoulos et
al. (1999). Their numerical results provided the first in-depth insights into the complexities of
bridge foundation flows and demonstrated the feasibility of advanced CFD modeling for
developing predictive models of scour.
It is important to point out that fully three-dimensional CFD models, such as the one
developed by Sotiropoulos et al. (1999), promising as they may be, are presently suitable only
for academic computations. This is because the computational times they require are, even with
today’s very powerful supercomputers, far too excessive for them to be useful as engineering
design tools. Yet such models provide the only alternative for obtaining the in-depth
understanding of the physics of bridge-foundation flows needed for refining the predictive
capabilities of simpler engineering models—such as the 1D models used extensively in the
design of bridge foundations today. It is in this spirit that an advanced three-dimensional CFD
model, employed in conjunction with field and laboratory studies, can be an invaluable
engineering tool that can make an immediate and very significant contribution to the present-day
state of the art.
8
RESEARCH OBJECTIVES
The overall objective of the research described in this report is to improve bridge scour
predictions using one-dimensional (1D) methods by combining physical modeling in the
laboratory, field monitoring, and three-dimensional (3D) numerical modeling. The specific
objectives of the research are:
(1) Monitor selected bridges in the field using fixed instrumentation, mobile
deployments of instrumentation from boats, and historic scour-surface evaluation;
(2) Physically model in the laboratory two particular bridge sites that are also
undergoing detailed field monitoring, validate the physical models, and test the
models over a wide range of flow conditions;
(3) Apply a 3D numerical model, which is being developed in separate research
sponsored by NSF, to two existing bridge sites having detailed instrumentation for
validation of the model with field and laboratory data collected in this research;
(4) Apply the 3D numerical model to simulate the flow fields at additional bridge sites
that have more limited instrumentation;
(5) Characterize sediments in general physiographic regions of Georgia in terms of their
erodibility;
(6) Combine the knowledge gained from the field, laboratory, and numerical modeling
into an improved 1D scour prediction methodology specific to various regions of
Georgia.
9
ORGANIZATION OF THE REPORT
The results of the field scour data collection program, the laboratory model studies, and the 3D
numerical model studies are given in Chapters 2, 3, and 4, respectively. Chapter 5 summarizes
the results of flume erodibility tests made on Shelby tube sediment samples collected by GDOT
at 10 representative bridge sites in Georgia. Comparisons of laboratory and field results for
velocity and scour depths as well as detailed comparisons of velocity and turbulence fields
measured in the laboratory with those predicted by the numerical model are discussed in detail in
Chapter 6. Finally, a summary and conclusions are provided in Chapter 7 in which the unique
observations associated with combined field, laboratory, and numerical model studies are
summarized, and their implications with respect to a proposed scour prediction methodology to
be completed in Phase 2 of the research are discussed.
10
CHAPTER 2. FIELD DATA COLLECTION
FIXED FIELD INSTRUMENTATION
Fixed field instrumentation has been installed at four bridge sites, which represent
various sediment types and physiographic regions in Georgia. USGS gaging stations are located
at these sites. Detailed fixed instrumentation has been installed at two of the sites. One of the
detailed field instrumentation sites is located in the coastal plain (Bainbridge), and the second
site is located in the Piedmont Province (Macon). Less detailed fixed instrumentation has been
installed at the remaining two sites (Darien and Cornelia). The detailed sites have the following
equipment:
• stage sensor;
• cross-channel two-dimensional velocity sensor;
• fathometer array to record streambed elevation;
• raingage;
• data logger and controller for each device;
• solar panel and instrumentation shelter; and
• satellite telemetry.
The less detailed sites have the same equipment except for the velocity sensor.
The fathometers are attached to the bridge piers in order to monitor the changes in bed
elevation around the bridge pier. Water velocity is also a critical bridge scour parameter that is
used to quantify the available scour energy. The cross-channel velocity sensor provides two-
dimensional velocity for a series of points across the channel in the bridge-approach section. The
sensor is mounted at a fixed location and aimed across the channel. The velocity meter uses
11
acoustic-Doppler technology and has its own system controller on site. Velocities are recorded at
15-minute intervals.
MOBILE FIELD INSTRUMENTATION
A mobile scour data-collection system has four components: instruments to measure
velocity and channel-geometry data; instruments to deploy equipment in the water; an instrument
to measure the horizontal position of the data collected; and a data storage device. For this
investigation, an acoustic Doppler current profiler (ADCP) is deployed from a manned boat and
used to measure three-dimensional velocity profiles. A recording digital fathometer is used to
measure channel depths. Horizontal position is measured using a kinematic differential Global
Positioning System (GPS). Some of the parameters collected with the mobile instrumentation
include:
• detailed channel geometry at and near the bridge;
• approach-flow velocities over the study reach;
• water-surface slope during flood events;
• visual analysis and notes on the surface velocity direction, channel and overbank
roughness, and vegetation cover;
• approximate measurements of the extent and composition of debris;
• photographs of channel and bridge at flood and low-flow conditions;
• water temperature;
• bridge and pier geometry; and
• bed sediment samples and soil boring logs from the bridge crossing.
All data is recorded and used to interpret and extend the data collected by the fixed
instrumentation, and for the 3D numerical modeling component of this investigation.
12
STREAMBED SEDIMENT SAMPLING
Bed-material characteristics are important determinants of streambed erodibility and bed-
material transport conditions. The objective for any of the collection techniques is to ensure that
a representative sample is collected. The BMH-53 or BMH-80 hand samplers are used to collect
the samples in sand-bed streams that can be waded. A BM-54 is used to collect samples in sand-
bed streams that are too deep to be waded. Procedures are not well defined for sampling
cohesive bed-materials, but a BMH-53 or similar cylinder sampler may be used on streams that
can be waded. The type of sampler used will always be noted with the bed-material data.
Sampling locations were selected to ensure samples are representative of the bed material
controlling the sediment-transport processes in the study reach. In streams with cohesive beds,
sediment in the zone of scour was sampled. Bed material samples were collected from several
locations both in the bridge approach and the bridge sections, including in local scour holes.
Bed-material samples were analyzed by the Georgia Institute of Technology laboratories for
grain-size distribution and other properties related to bridge scour.
FOUR SELECTED SITES
Chattahoochee River Near Cornelia, Ga (02331600)
Site Description
The first site chosen for the research project is the Chattahoochee River near Cornelia,
Georgia. The USGS has been gaging stage and streamflow at this site since 1957. The gage is
located at the Georgia Highway 384 (Duncan Bridge Road) bridge at the Habersham-White
County line in Northeast Georgia. The drainage area at this site is 315 square miles. The
channel in the vicinity of the bridge is a long quiet pool about 160 feet wide at lower flows. The
pool extends from the rock ledge control about 500 feet downstream of the bridge to about 3,000
13
feet upstream of the bridge. The banks will overflow at higher stages onto a flat but narrow
floodplain. The control is a rock ledge, which runs diagonally from the right bank downstream to
the left bank. The bridge piers consist of four concrete square columns, which rest on concrete
footings buried below the streambed (Fig. 2.1). There is one bridge pier located in the center of
Figure 2.1. Chattahoochee River near Cornelia, GA.
the channel and one bridge pier on each of the banks. The bridge piers are aligned with the flow.
The peak discharge of record is 26,400 cubic feet per second, which occurred on March
12, 1963. The 2-year flood event at this site is about 11,800 cubic feet per second, and the 500-
year flood event is about 39,600 cubic feet per second as shown in Table 2-1.
Table 2-1. Flood-frequency discharge data for Cornelia.
Recurrence Interval (years)
Discharge (cfs)
2 11,800 10 21,500 50 29,400
100 32,600 500 39,600
14
Fixed-Field Instrumentation
The fixed-field instrumentation at this site consists of four fathometers, an acoustic
velocity meter, a raingage, and a stage sensor. The acoustic velocity meter, raingage, and stage
sensor are interfaced with a Data Collection Platform (DCP), which logs readings from the
sensors every 15 minutes. The DCP transmits the 15-minute data from each of the sensors every
four hours using satellite telemetry. The four fathometers are interfaced with a data logger, which
logs the readings from the fathometers every 30 minutes. The fathometers are attached to the
center bridge pier and monitor the bed elevation changes occurring around the bridge pier. The
velocity meter is attached to the nose of the center bridge pier and monitors two-dimensional
velocities at three points across the approach bridge section (Fig. 2.2).
Figure 2.2. Fathometer and velocity meter layout at Cornelia.
Data Collected
Due to drought conditions during the 2-year study, data was collected during five
moderate highwater events at the Cornelia site. The peak discharges for these events ranged from
3,400 to 13,600 cfs. The 13,600 cfs event is slightly greater than the 2-year recurrence interval
for this site. The event resulted in two additional feet of scour in comparison to the pre-existing
15
scour hole at the nose of the pier as shown in Fig. 2.3. The peak velocity recorded by acoustic
velocity meter during the July 2003 event was approximately 7 feet per second. The event of
July 2003 peaked early in the morning. The stage was already falling when the crew with the
mobile instrumentation arrived, and the boat and ADCP could not be deployed in the water due
to the falling stage. However, velocity distribution and cross-section profile data were collected
from the upstream side of the bridge as the stage was falling.
Figure 2.3. Fathometer data from Cornelia.
Chattahooche River near Cornelia, GAJuly 1-3, 2003
1120
1121
1122
1123
1124
1125
1126
6 6.5 7 7.5 8 8.5 9
Time (days)
Bed
Elev
atio
n (fe
et)
0
2000
4000
6000
8000
10000
12000
14000
Disc
harg
e (c
fs)
16
The 13,600 cfs event that occurred in July 2003 was modeled in the hydraulics laboratory
at Georgia Tech. The results from the laboratory models are shown in Chapter 3, and the data
comparisons between the field and model data are shown in Chapter 6. A historic discharge
measurement was made at the site in 1961 at a discharge of 13,100 cfs, which is very close to the
peak discharge of the July 2003 event. A cross-section comparison was made at the upstream
side of the bridge for both the July 2003 and December 1961 event as shown in Fig. 2.4. The
maximum scour that occurred during the July 2003 event was within one foot of the scour that
occurred during the discharge measurement that was made in December of 1961. The shapes of
the scour hole around the center bridge pier were also similar for both events indicating
recurrence of the same extent of scour for the same discharge after repeated infilling between
floods.
1110
1115
1120
1125
1130
1135
50 100 150 200 250 300
Width (feet)
Bed
Ele
vatio
n (f
eet)
12-Dec-61 13-Jun-03 2-Jul-03
Figure 2.4. Cross-section comparison at the upstream side of the bridge at Cornelia.
17
Eleven cross-sections of the river and floodplain were surveyed along the channel reach
near the bridge as illustrated in Fig. 2.5. The position of the bridge piers was determined using a
differential Global Positioning System (GPS). The cross-sections and pier placement data were
used to construct the laboratory and three-dimensional computer models. Bed material samples
were also collected at three of the cross-sections. The particle size distributions of the collected
bed material samples are shown in Fig. 2.6.
Figure 2.5. Layout of surveyed cross-sections at Cornelia.
Ocmulgee River At Macon (02213000)
Site Description
The second site chosen for the project is the Ocmulgee River at Macon, Georgia. The
USGS has been gaging stage and streamflow at this site since 1895. The gage is located at the
Fifth Street Bridge (Otis Redding Bridge) in Macon. The drainage area at this site is 2,240
square miles. The channel upstream of the bridge is straight for about 1,000 feet and straight for
18
Figure 2.6. Particle size distribution of bed material samples at Cornelia.
about 1,500 feet downstream of the bridge. The streambed is smooth and sandy. The right bank
is high and is not subject to overflow. The left bank is subject to overflow at high stages, but the
highway fill confines all flow to the bridge opening. The control is a shifting sand streambed.
The bridge piers consist of four cylindrical columns that rest on concrete footings, which are
buried below the streambed. As shown in Fig. 2.7, there is one bridge pier in the center of the
channel one bridge pier at each of the banks. All three bridge piers are aligned with the flow.
The peak discharge of record is 107, 000 cubic feet per second, which occurred on July 6,
1994. The 2-year flood event is about 28,500 cubic feet per second, and the 500-year flood event
is about 108,400 cubic feet per second as shown in Table 2-2.
PARTICLE-SIZE DISTRIBUTION (Chattahoochee River)
0
10
20
30
40
50
60
70
80
90
100
0.010.1110
Particle Size (mm)
Perc
ent P
assi
ng (%
)
Section 10-3/3 Section 10-Right Bank Section 10-Left Bank Section 7-3/3Section 7-2/3 Section 7-1/3 Section 2-2/3 Section 2-1/3
19
Figure 2.7. Ocmulgee River at Macon, GA.
Table 2-2. Flood-frequency discharge data for Macon.
Recurrence Interval (years)
Discharge (cfs)
2 28,500 10 56,200 50 79,200
100 88,300 500 108,400
20
Fixed-Field Instrumentation
The fixed-field instrumentation at the Macon site consists of six fathometers and a stage
sensor. The stage sensor is interfaced with a DCP, which transmits 15-minute data from each of
the sensors every hour. The six fathometers are interfaced with a data logger, which logs the
readings from the fathometers every 30 minutes. Five fathometers are attached to the center
bridge pier, and one fathometer is located at the nose of the pier on the right bank (Fig. 2.8).
Figure 2.8. Fathometer layout for Ocmulgee River at Macon, GA.
Data Collected
Data was collected during multiple moderate highwater events. The highest peak
discharge of these events was 25,500 cfs, which is below the 2-year occurrence interval for this
site. During this 25,500 cfs event in May of 2003, three additional feet of scour occurred around
the center bridge pier as shown in Fig. 2.9. During a smaller event in March 2003, velocity
distribution data were collected at various cross-sections throughout the channel reach using an
Acoustic Doppler Current Profiler (ADCP). The peak discharge during this March 2003 event
was 20,300 cfs.
21
Figure 2.9. Fathometer data from Macon.
A historic discharge measurement was made at the upstream side of the bridge during a
highwater event in March of 1998. The peak discharge during this event was 65,000 cfs. The
cross-section from this historic measurement was compared with cross-sections collected at the
upstream side of the bridge during this study as shown in Fig. 2.10. The historic cross-section
Ocmulgee River at Macon, GAMay 1-18, 2003
265
266
267
268
269
270
0 2 4 6 8 10 12 14 16 18Time (days)
Bed
Ele
vatio
n (f
eet)
500
5500
10500
15500
20500
25500
Dis
char
ge (c
fs)
22
shows 10 feet of contraction scour. The peak velocity measured during this event was nearly 10
feet per second.
Figure 2.10. Cross-section comparison at the upstream side of the bridge at Macon.
Seven cross-sections were surveyed throughout the channel reach and were used to
construct the three-dimensional model (Fig. 2.11). Bed material samples were taken at four of
the cross-sections. The particle size distributions of the collected bed material samples are shown
in Fig. 2.12.
240
250
260
270
280
290
300
310
320
330
-20 30 80 130 180 230 280 330 380 430
Station (feet)
Bed
Ele
vatio
n (f
eet)
22-Mar-03 21-May-03 21-Jul-03 10-Mar-98
23
Figure 2.11. Layout of surveyed cross-sections at Macon.
Figure 2.12. Particle size distribution of bed material samples at Macon.
OCMULGEE RIVER AT MACON, GEORGIACUMULATIVE PARTICLE-SIZE PLOT
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0.010.1110Particle Size (mm)
Perc
ent P
assing
Cross Section #1 Cross Section #2Cross Section #3 Cross Section #4
24
Flint River At Bainbridge (02356000)
Site Description
The third site chosen for the research project is the Flint River at Bainbridge, Georgia.
The USGS has been gaging stage and streamflow at this site since 1908. The gage is located at
the Business Highway Route 27 Bridge in Bainbridge. The drainage area at this site is 7,570
square miles. The channel is fairly straight for several thousand feet upstream and has a sharp
bend about 500 feet downstream. The site is affected by backwater from the Jim Woodruff
Reservoir at lower stages. At higher stages, the backwater is negligible, and the banks overflow
onto a very wide and flat floodplain. The bridge piers consist of two square concrete columns
that rest on very large square concrete footings (Fig. 2.13). The large footings protrude from the
streambed. There are two bridge piers in the main channel and both are aligned with the flow.
Figure 2.13. Flint River at Bainbridge, GA.
The peak discharge of record is 108,000 cubic feet per second, which occurred on July
14, 1994. The 2-year flood event is about 30,900 cubic feet per second, and the 500-year flood
event is about 122,000 cubic feet per second as given in Table 2-3.
25
Table 2-3. Flood-frequency discharge data for Bainbridge.
Recurrence Interval (years)
Discharge (cfs)
2 30,900 10 58,100 50 83,700
100 94,900 500 122,000
Fixed-Field Instrumentation
The fixed-field instrumentation at this site consists of seven fathometers, a raingage, two
acoustic velocity meters, and a stage sensor. The stage sensor, raingage, and acoustic velocity
meters are interfaced with a DCP, which logs readings from the sensors every 15 minutes. The
DCP transmits the 15-minute data from each of the sensors every four hours using satellite
telemetry. The seven fathometers are interfaced with a data logger, which logs the readings from
the fathometers every 30 minutes. Four fathometers are attached to the left center bridge pier,
and three fathometers are attached to the right center bridge pier (Fig. 2.14). The fathometers
monitor the change in bed elevation around the bridge piers. An acoustic velocity meter is
attached to the nose of the left center pier, and measures two-dimensional velocities at three
points across the approach bridge section. A second acoustic velocity meter is attached to the
downstream end of the left center bridge pier. This velocity meter measures a one-dimensional
velocity at point in the center of the main channel. This one-dimensional velocity is used as an
index velocity to determine the discharge.
26
Figure 2.14. Fathometer and velocity meter layout at Bainbridge.
Data Collected
Due to the drought conditions during the study, no highwater events occurred at this site.
So there were no pertinent data collected at this site. However, a historic discharge measurement
was made during the peak discharge of record in 1994. The discharge measurement contained a
velocity distribution and cross-section elevations at the upstream side of the bridge. Georgia
Tech physically modeled this event, and the velocity distribution and cross-section compared
very well as shown in Chapter 6. Several historic cross-sections are shown in Fig. 2.15, including
the cross-section obtained during the peak discharge of record in July of 1994. The cross-section
from the 1994 flood shows as much as 10 feet of scour when compared with previous and recent
cross-sections to identify the bed elevation that would occur in the absence of local scour.
Five cross-sections were surveyed and used to construct the model. The railroad bridge
upstream of the bridge was also surveyed and used in the modeling (Fig. 2.16). Bed material
samples were collected at four cross-sections, and the particle size distribution of the collected
bed material samples are shown in Fig. 2.17.
27
40
50
60
70
80
90
100
0 100 200 300 400 500 600 700 800 900
Width, feet
Elev
atio
n, fe
et
10-Mar-80 14-Jul-94 12-Jul-94 21-Mar-01 20-Mar-02
Figure 2.15. Cross-section comparison at Bainbridge, GA.
Figure 2.16. Layout of surveyed cross-sections at Bainbridge.
28
Figure 2.17. Particle size distribution of bed material samples at Bainbridge at left (L), right (R), and center (C) of main channel for cross section numbers shown in Fig. 2.16.
Darien River At Darien (02203598)
Site Description
The fourth site chosen for the project is the Darien River at Darien, Georgia. The USGS
began gaging stage and streamflow at this site in January 2002. The gage is located at the
Georgia Highway 17 bridge in Darien. The channel is fairly straight in the vicinity of the bridge.
The flow at this site is tidally affected and is confined in a 400 foot wide channel. The bridge
piers consist of three rectangular concrete columns, which rest on very large square concrete
footings (Fig. 2.18). The footings protrude from the streambed. The mid-sections of the columns
PARTICLE-SIZE DISTRIBUTION (Flint River)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0.0010.010.1110
Particle Size (mm)
Perc
ent P
assin
g
2R - No material 2C 2L 3R3C 3L 4R 4C4L 5R 5C 5L
29
are connected with a flange. There are four bridge piers in the main channel. Two of the bridge
piers near the right bank are protected with wooden bridge fenders while the others are not.
Figure 2.18. Darien River at Darien, GA.
Fixed-Field Instrumentation
The fixed-field instrumentation at this site consists of seven fathometers, a raingage, and
a stage sensor. The stage sensor and raingage are interfaced with a DCP, which logs readings
from the sensors every 15 minutes. The DCP transmits the 15-minute data from each of the
sensors every four hours using satellite telemetry. The seven fathometers are interfaced with a
data logger, which logs the readings from the fathometers every 30 minutes. Three fathometers
are attached to the left bridge fender, two fathomers are attached to the right bridge pier, and two
fathometers are attached to the left center pier (Fig. 2.19). The fathometers monitor the change in
bed elevation around the bridge fenders and piers.
30
Figure 2.19. Fathometer layout at Darien.
Data Collected
Fathometer data were continuously collected at Darien. During the tide cycle, one foot of
scour and fill was seen on a few occasions at a couple of the fathometer locations as shown in
Fig. 2.20. The scour and fill coincided with the tide cycle. Overall, the scour and fill seen on a
daily basis was minimal. However, on a yearly basis the scour and fill was as much as five feet at
one of the fathometer locations (Fig. 2.21).
Nine cross-sections throughout the channel reach were surveyed and used to construct the
models (Fig. 2.22). The position and dimensions of the bridge fenders were also surveyed and
incorporated into the models. Bed material samples were taken at five locations near the bridge,
and the particle size distribution of these bed material samples are shown in Fig. 2.23.
31
Figure 2.20. Fathometer data from Darien.
Figure 2.21. Fathometer data at downstream side of left bridge fender.
Darien River at Darien, GAMay 29, 2002 - June 2, 2002
-19.0
-17.0
-15.0
-13.0
-11.0
-9.0
-7.0
-5.0
-3.0
-1.0
130 130.5 131 131.5 132 132.5 133 133.5 134 134.5 135Time (days)
Bed
Ele
vatio
n (fee
t)
4
6
8
10
12
14
Gag
e Hei
ght (
feet
)
32
Figure 2.22. Layout of surveyed cross-sections at Darien.
Figure 2.23. Particle size distribution of bed material samples at Darien.
PARTICLE-SIZE DISTRIBUTION (Darien River)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0.010.1110 Particle Size (mm)
Perc
ent P
assi
ng
Downstream Fender Upstream Fender Downstream Bridge Upstream Bridge Front of Pier
33
CHAPTER 3. LABORATORY MODEL STUDIES
INTRODUCTION
Although numerous formulas for the prediction of bridge pier scour depths have been developed
based on laboratory experiments as summarized by Melville and Coleman (2000) or Sturm
(2001), for example, considerable doubt remains concerning their applicability to large-scale
prototypes. Scour-depth estimates based on laboratory data tend to overestimate actual pier scour
depths measured in the field (Landers and Mueller 1996). This situation is partly due to the
sediment scale effect that limits the size of the sediment that can be used in the laboratory
without it becoming so fine-grained that interparticle forces that may not exist in the field
become dominant in the laboratory (Ettema et al. 1998).
This chapter discusses laboratory modeling considerations with respect to bridge scour
and gives the results of laboratory scale model studies conducted in the Georgia Tech Hydraulics
Laboratory. The two field sites that were modeled in the laboratory are the Chattahoochee River
bridge near Cornelia, Georgia and the Flint River bridge at Bainbridge, Georgia which were
described in Chapter 2. Each site was modeled at two different physical scales for two sediment
sizes. Both bank-full and extreme flood flows were modeled.
MODELING CONSIDERATIONS
Dimensional analysis of the pier scour problem produces (Ettema et al. 1998, Sturm 2001):
),,,,,( 1
50
1 FrVV
db
by
KKfbd
cs
sθ= (3.1)
in which ds = scour depth; b = pier width; Ks = shape factor; Kθ = skewness factor; y1 = approach
depth; V1 = approach velocity; Vc = critical velocity; d50 =median sediment size; and Fr =
approach Froude number. For strict dynamic similarity, all of the dimensionless parameters on
34
the right-hand side of Eq. 3.1 should be the same in model and prototype. However, as a
practical matter, choosing a length scale ratio such that the model will fit in a laboratory results
in the impossible situation of d50 becoming so small that a cohesive sediment would be necessary
to satisfy equality of the ratio b/d50 . A similar dilemma arises in the case of modeling
contraction scour. To further complicate matters, a sand-bed river is likely to be in the live-bed
scour regime (V1/Vc > 1) which is difficult to model in the laboratory because of the sediment
that must be fed or recirculated to the flume in order to maintain the unknown upstream sediment
transport rate.
The modeling compromise utilized in this study was to maintain approximate Froude
number similarity with equality of y1/b values while selecting the sediment size such that clear-
water scour was obtained near the maximum of V1/Vc = 1.0 as a conservative approach. The
experimental plan proceeded in two stages with two different physical model scales for each
bridge. In the initial stage, a flat mobile-bed model was constructed at a larger scale for the
purpose of making detailed velocity and turbulence measurements around the main pier bent for
comparison with the numerical model results and for measuring scour depths to be compared
with accepted scour prediction formulas. These initial-stage models, referred to as flat-bed
models, were intended to reproduce bank-full flows rather than flood flows, and the Froude
number was allowed to take on larger values than occurred in the prototype. In the second stage
of the model studies, smaller-scale models referred to as river models were constructed to
include the complete river bathymetry and bridge geometry for reproducing both bank-full and
extreme flood events (100-yr and 200 yr). A smaller sediment size was used to achieve close
Froude number similarity in the range of V1/Vc = 0.7 – 1.0. A summary of the model study
conditions is given in Table 3-1.
35
Table 3-1. Model studies conducted.
Bridge Model Type of Model Scale of Model Sediment Size, mm Flow Conditions Chattahoochee R. near Cornelia
Flat Bed 1:23.3 3.3 mm Bank-full
Chattahoochee R. near Cornelia
River Model 1:40 3.3 mm, 1.1 mm Bank-full, 100-yr
Flint R. at Bainbridge
Flat Bed 1:50 3.3 mm Bank-full
Flint R. at Bainbridge
River Model 1:90 1.1 mm Alberto (200-yr)
EXPERIMENTAL METHODS
Model Construction
Experiments were conducted in a 4.2 m wide by 24.4 m long flume with a mobile sediment bed
in which models of the Chattahoochee River bridge near Cornelia, Georgia and of the Flint River
bridge at Bainbridge, Georgia were constructed. Two median sediment sizes of d50 = 3.3 mm and
1.1 mm were utilized. Each sediment was relatively uniform in size distribution with a geometric
standard deviation, σg = 1.3.
In the flat-bed model studies, the mobile bed was leveled between temporary walls of
cinder blocks to form a flat bed with a channel width of 8.0 ft and a working channel length of
60 ft in which only the main-channel pier bent was placed. In the river model studies, the
complete river bathymetry was modeled with a fixed-bed approach channel followed by a
mobile-bed working section in which the bridge embankment and pier models were placed. In
the river models, the approach section was approximately 40 ft long with a 5-ft long working
section and then an approximately 10-ft long exit section for sediment deposition. The river
bathymetry was modeled by cutting plywood templates that reproduced the surveyed cross-
sections that were shown in Chapter 2 and then leveling the bed to match the templates. The
36
templates were left in place in the fixed-bed section, but in the moveable-bed section they were
installed and removed after the bed was shaped for each experimental run. Fiberglass was used
for the fixed bed in the Chattahoochee River model and a single layer of the 3.3-mm gravel was
fixed to it by spraying it with several layers of polyurethane. For the Flint River model, the full
depth of the 3.3-mm gravel bed was simply molded to the plywood templates and a surface layer
was fixed with polyurethane. This proved to be a more flexible scheme for moving different
models in and out of the flume.
The initial velocity and turbulence measurements were made for a fixed bed in the
vicinity of the model pier bent. This was achieved by spraying polyurethane on the gravel to hold
it in place. For subsequent scour experiments, the fixed-bed section was removed and the bed
was made completely mobile, but no scour occurred upstream of the pier bent because conditions
for incipient live-bed scour were not exceeded.
The central pier bent for the Cornelia bridge is shown in Fig. 3.1 with prototype
dimensions. It was modeled at a scale of 1:23.3 for the flat-bed model and at a scale of 1:40 for
the river model as shown previously in Table 3-1. The inner piers are tapered as shown in the
figure. They are the original piers in existence before widening of the bridge occurred. The outer
rectangular piers, which have a width of 3.5 ft and a length of 4.0 ft in the flow direction, were
added when the bridge was widened. The spacing between the two inner piers is 16.0 ft, and
between the outer and inner piers it is 6.75 ft. The inner piers are connected by a solid web that
extends from an elevation above low-water stage to an elevation near the 100-yr high-water
stage. The footings were also modeled at the same scale as the piers and placed at the correct
elevation relative to the channel bed as shown in Fig. 3.1.
37
Upstream
55.8 ft
44.5 ft
17.0 ft
Top of the bed (EL= 1126 ft)
2yr flood flow(Q=13500 cfs)
100 yr flood flow(Q=31700 cfs)
24.8 ft
14.0 ft5.0 ft
6.75 ft 16.0 ft 11.75 ft
10.0 ft11.5 ft3.5 ft 2.0 ft2.0 ft 14.0 ft
C
C'
D
D'
B
B'
A
A'
(a) Profile.
SEC.A-A' SEC.B-B' SEC.C-C' SEC.D-D'
13.75 ft
3.5 ft
2.25 ft
53.55 ft
10.67 ft
3.5 ft
48.85 ft
2.75 ft
3.17 ft 3.17 ft
2.25 ft
13.75 ft
50.44 ft
3.5 ft
2.0 ft
46.95 ft
2.75 ft
10.67 ft
Top of the bed (EL= 1126 ft)
14.0 ft
14.0 ft
24.8 ft
100 yr flood flow(Q=31700 cfs)
2yr flood flow(Q=13500 cfs)
(b) Sections.
Figure 3.1. Sketch of central pier bent of Chattahoochee River bridge near Cornelia, GA with prototype elevations and dimensions.
38
The main channel pier bent of the Flint River bridge at Bainbridge is shown in Fig. 3.2. It
was modeled at a scale of 1:50 for the flat-bed model and at a scale of 1:90 for the river model.
The pier bent consists of two identical piers that are 6 ft square in cross section with a spacing in
the flow direction of 49 ft centerline to centerline. The footings are stepped as shown in the
figure. The high water flood that was modeled for this case occurred due to Tropical Storm
Alberto in 1994 with an estimated return interval of 200 years.
Photographs of the river models for the Chattahoochee River bridge at a 1:40 scale and
the Flint River bridge at a scale of 1:90 are shown in Figs. 3.3 and 3.4, respectively. The riprap
on the embankments is shown in Fig. 3.3 for the Chattahoochee River bridge. The central pier
bent in the middle of the river is the only one that experienced any significant scour, and so it is
the bent for which scour results are given subsequently. The left floodplain can be seen just
downstream of the bridge and it is relatively narrow there as well as upstream of the bridge. The
downstream rock sill that serves as a control for low flows as discussed in Chapter 2 was also
modeled although it is not shown in the photograph.
The four bents of the Flint River bridge can be seen in Fig. 3.4 (a) as well as the old
embankment on the left side of the bridge opening which remained in place after the new bridge
was built. This embankment blocked the flow around the leftmost pier but directed some flow
toward the pier that is second from the left in the photograph. However, the third pier from the
left is located in the deepest part of the main channel, and it experienced the greatest scour
depths which are reported subsequently in this chapter. The upstream railroad bridge was
modeled and is shown in Fig. 3.4 (b). The left embankment of this bridge effectively blocked
much of the approach flow to the highway bridge in the left floodplain. Flow visualization
showed that flow in the right floodplain did not affect scour around the primary pier in the study.
39
Upstream
Top of the bed (EL= 57.6 ft)
Bankfull flow(Q=45000 cfs)
Alberto (7/12/94)(Q=107000 cfs)
43.1 ft
53.3 ft76.3 ft
55.0 ft
6.0 ft
15.7 ft
A
A'
(a) Profile.
Top of the bed (EL= 57.6 ft)
Bankfull flow(Q=45000 cfs)
Alberto (7/12/94)(Q=107000 cfs)
43.1 ft
53.3 ft
15.7 ft10.0 ft
21.8 ft
18.8 ft
6.0 ft
SEC. A-A'
(b) Section.
Figure 3.2. Sketch of central pier bent of Flint River bridge at Bainbridge with prototype elevations and dimensions.
40
(a) Bridge section looking downstream (b) River and bridge looking downstream from the right bank. from left floodplain.
Figure 3.3. Model of Chattahoochee River bridge near Cornelia.
(a) Bridge section looking downstream from (b) Railroad bridge looking downstream left bank including old embankment. to highway bridge.
Figure 3.4. Model of Flint River bridge at Bainbridge.
41
Experimental Instrumentation
The water supply to the flume was provided from a large constant-head tank through a 12-in.
diameter pipe that can deliver up to 10 ft3/s to the head box of the flume. A flow diffuser,
overflow weir, and baffles in the flume head box provided stilling of the inflow to reduce
entrance effects and produce a uniform flume inlet velocity distribution. A flap tailgate
controlled the tailwater elevation. Water recirculated through the laboratory sump from which
two pumps continuously provided overflow to the constant-head tank. In the 12-in. supply pipe,
discharge was measured by a magnetic flow meter (Foxboro 9300A) with an uncertainty of
±0.05 ft3/s.
An instrument carriage was mounted on horizontal steel rails and was moved along the
flume on wheels driven by a cable system and electric motor. Velocities and turbulence
quantities were measured with a 3D down-looking SonTek 10 MHz acoustic Doppler
velocimeter (ADV) as well as the 3D down-looking SonTek 16 MHz MicroADV. To measure
velocities and turbulence quantities near the piers and in the floodplain, a 2D and a 3D side-
looking SonTek MicroADV were utilized. The ADVs were attached to the instrument carriage
on a mobile point gage assembly that could be accurately positioned in all three spatial
dimensions. The 10 MHz ADV has a sampling volume of 0.015 in.3 while the sampling volume
of the MicroADV is approximately 0.005 in.3. The measuring volume is located 2.0 in. away
from the probe where velocities are measured based on the Doppler frequency shift of acoustic
signals reflected from small scattering particles moving at the same speed as the water. The
sampling frequency of the 10 MHz ADV was chosen to be 25 Hz, while a higher sampling
frequency of 50 Hz was possible with the MicroADV. A sampling duration of 2 minutes was
used at each measuring location.
42
Velocities and turbulence quantities were measured over the temporarily fixed bed prior
to scour at relative heights above the bed of approximately 0.04, 0.1, 0.2, 0.4, and 0.6 times the
flow depth throughout the flow field including both near-field and far-field locations relative to
the bridge pier bent resulting in a total of approximately 750 measuring points for a single
experiment. In addition, detailed approach velocity profiles and turbulence quantities were
measured using a combination of the down-looking and side-looking ADVs.
Although Voulgaris and Trowbridge (1998) have demonstrated in flume experiments that
the ADV can measure both mean velocities and Reynolds stresses within 1 percent of the
measurements made by a laser Doppler velocimeter (LDV) and can describe the vertical
variation of Reynolds stresses according to accepted open channel flow results, the occurrence of
noise in measurements below a level of about 1.2 in. above the bed can cause problems. Some of
this noise is flow-related and can be attributed to high levels of both turbulence and mean
velocity shear near the bed. In addition, electronic noise can originate from errant reflections due
to the measuring volume being too close to the boundary and from boundary interference when
the return signal from the boundary interferes with the signal from the measuring volume (Lane
et al. 1998). One method of dealing with this noise is to filter the data according to the value of a
correlation coefficient that is a measure of the coherence of the return signals from two
successive acoustic pulses (Martin et al. 2002, Wahl 2002).
In this study it was found that the velocity and turbulence measurements near the bed
suffered from the same noise problems as experienced by other investigators, especially in the
near-field shear zone that experienced high turbulence levels. Accordingly, the data were filtered
by first requiring that the correlation coefficient of each sample in the 2-minute time record
exceed a value of 70 percent as recommended by the manufacturer (SonTek 2001) for obtaining
43
turbulence statistics. In some cases, the filtering resulted in a large number of data points being
rejected from a given time record, so an entire two-minute record was rejected if the average
correlation coefficient fell below 70 percent.
Experimental Procedure
After completion of the flow field measurements over a fixed bed, the mobile sediment
bed was installed in the vicinity of the central pier bent, and scour experiments were conducted.
The flume was slowly filled to a depth larger than the test depth so as to prevent scour while the
test discharge was set. Then the tailgate was lowered to achieve the desired depth of flow.
Measurements of scour depth as a function of time at a fixed point were measured with the ADV
to determine when equilibrium had been reached. Then the flow rate was reduced while keeping
the scoured bed submerged, and the bed elevations were mapped in detail using the ADV feature
of acoustically pinging the bottom to measure the distance from the sampling volume to the bed.
Based on comparisons with point gage measurements, this method allowed the measurement of
bed elevation with an uncertainty of ±0.05 in. Some bed elevations very close to the pier were
measured directly with a point gage.
EXPERIMENTAL RESULTS
Summary of Data
Measured data for the Chattahoochee River bridge are presented in Table 3-2 as raw data and in
dimensionless form in Table 3-3. The raw data for the Flint River bridge are given in Table 3-4
with the data in dimensionless form summarized in Table 3-5. The raw data include the
measured discharge (Q), sediment size (d50), pier width (b), approach depth (y1), approach
velocity (V1), scour depth (ds), duration of scour experiment (T), and calculated scour
equilibrium time (Teq) according to the relationship developed by Melville and Chiew (1999).
44
Table 3-2. Raw experimental data for Chattahoochee River bridge near Cornelia, GA. (b = pier width, y1 = approach flow depth, V1 = approach velocity, ds =scour depth, T = duration of scour, Teq = equilibrium time from Melville and Chiew, 1999).
1FB = flat-bed model 2RM = river model
Table 3-3. Dimensionless experimental data for Chattahoochee River bridge near Cornelia, GA (Fr = approach Froude number, Vc = critical velocity).
Run Model Scale Fr V1 /Vc y1 /b b/d50 ds /b No. Type Ratio 1 FB 0.043 0.350 0.64 3.62 13.9 1.23 2 FB 0.043 0.367 0.70 4.16 13.9 1.77 3 FB 0.043 0.511 0.91 3.32 13.9 2.91 4 FB 0.043 0.416 0.78 3.91 13.9 2.62 5 FB 0.043 0.404 0.74 3.72 13.9 2.17 6 FB 0.043 0.463 0.83 3.40 13.9 2.79 7 FB 0.043 0.399 0.76 4.16 13.9 2.25 8 FB 0.043 0.438 0.83 4.16 13.9 2.91 9 FB 0.043 0.602 1.07 3.32 13.9 2.93 1 RM 0.025 0.391 0.75 7.09 8.2 2.32 2 RM 0.025 0.429 0.82 7.09 8.2 2.33 3 RM 0.025 0.526 0.84 4.07 8.2 3.28 4 RM 0.025 0.557 0.88 3.95 8.2 2.96 5 RM 0.025 0.301 0.75 3.95 24.5 1.92 6 RM 0.025 0.334 0.83 3.95 24.5 2.22 7 RM 0.025 0.401 1.00 3.95 24.5 2.51 8 RM 0.025 0.232 0.71 7.04 24.5 2.22 9 RM 0.025 0.255 0.78 7.04 24.5 2.19
Scale Q d50 b Y1 V1 ds T Teq Run No.
Model Type Ratio (cfs) (mm) (ft) (ft) (ft/s) (ft) (hrs) (hrs)
1 FB1 0.043 6.92 3.3 0.151 0.546 1.468 0.185 24 25 2 FB 0.043 8.42 3.3 0.151 0.628 1.652 0.267 32 29 3 FB 0.043 8.42 3.3 0.151 0.502 2.054 0.440 36 37 4 FB 0.043 8.42 3.3 0.151 0.591 1.816 0.396 36 33 5 FB 0.043 8.42 3.3 0.151 0.561 1.717 0.328 36 31 6 FB 0.043 8.42 3.3 0.151 0.514 1.885 0.421 36 34 7 FB 0.043 9.63 3.3 0.151 0.628 1.793 0.339 36 32 8 FB 0.043 10.21 3.3 0.151 0.628 1.968 0.440 38 35 9 FB 0.043 10.21 3.3 0.151 0.502 2.422 0.443 37 41 1 RM2 0.025 4.50 3.3 0.089 0.628 1.760 0.205 48 20 2 RM 0.025 5.00 3.3 0.089 0.628 1.930 0.206 48 22 3 RM 0.025 2.45 3.3 0.089 0.360 1.790 0.290 48 23 4 RM 0.025 2.45 3.3 0.089 0.350 1.870 0.262 48 24 5 RM 0.025 1.35 1.1 0.089 0.350 1.010 0.170 48 32 6 RM 0.025 1.50 1.1 0.089 0.350 1.120 0.197 47 36 7 RM 0.025 1.66 1.1 0.089 0.350 1.347 0.222 47 41 8 RM 0.025 2.50 1.1 0.089 0.623 1.040 0.197 47 31 9 RM 0.025 3.00 1.1 0.089 0.623 1.143 0.194 47 34
45
Table 3-4. Raw experimental data for Flint River bridge at Bainbridge, GA. (b = pier width, y1 = approach flow depth, V1 = approach velocity, ds =scour depth, T = duration of scour, Teq = equilibrium time from Melville and Chiew, 1999).
Scale Q d50 b Y1 V1 ds T Teq Run No.
Model Type Ratio (cfs) (mm) (ft) (ft) (ft/s) (ft) (hrs) (hrs)
1 FB1 0.020 7.71 3.3 0.120 0.50 1.708 0.164 48 26 2 FB 0.020 7.72 3.3 0.120 0.53 1.584 0.124 48 24 3 FB 0.020 8.85 3.3 0.120 0.52 1.762 0.175 48 27 1 RM2 0.011 1.50 1.1 0.068 0.500 0.810 0.071 48 17 2 RM 0.011 1.65 1.1 0.068 0.500 0.950 0.120 96 22 3 RM 0.011 1.80 1.1 0.068 0.500 1.100 0.190 96 27
1FB = flat-bed model 2RM = river model
Table 3-5. Dimensionless experimental data for Flint River bridge at Bainbridge, GA (Fr = approach Froude number, Vc = critical velocity).
Run Model Scale Fr V1 /Vc y1 /b b/d50 ds/b No. Type Ratio
1 FB1 0.020 0.426 0.75 4.17 11.1 1.37 2 FB 0.020 0.385 0.69 4.38 11.1 1.03 3 FB 0.020 0.431 0.77 4.33 11.1 1.46 1 RM2 0.011 0.202 0.57 7.35 18.8 1.04 2 RM 0.011 0.237 0.67 7.35 18.8 1.76 3 RM 0.011 0.274 0.78 7.35 18.8 2.79
1FB = flat-bed model 2RM = river model
The scour depths reported in Tables 3-2 and 3-4 are the maximum scour depths in front
of the most upstream pier in the main pier bent. Approach velocities and depths given in these
tables were measured upstream of the pier at a distance of 10 pier widths. The corresponding
dimensionless variables for each experimental run as identified in Eq. 3.1 are given in Tables 3-3
and 3-5. The critical velocity in the sediment mobility factor V1/Vc is calculated from Keulegan’s
equation with an equivalent sand-grain roughness of ks = 2d50. It is important to note that at the
same value of y1/b, a smaller sediment size produces a smaller Froude number and a larger value
of b/d50 for the same range of values of V1/Vc as shown in Table 3-3, for example, for Runs RM 1
and RM 8.
46
The duration of the scour experiments is given in Tables 3-2 and 3-4 as well as the
calculated equilibrium scour time for maximum clear-water scour according to the relationship
developed by Melville and Chiew (1999). In general, the experimental scour durations are equal
to or greater than the equilibrium times. In fact, in most cases the scour experiments were
continued well beyond the estimated equilibrium time.
0.0
0.1
0.2
0.3
0.4
0 10 20 30 40 50
Time, hr
Scou
r dep
th,
ft
Exp. IExp. IIRegression
(a) Scour depth development with time in repeated experiments.
0
1
2
3
1.E+03 1.E+04 1.E+05 1.E+06
V c t /y 1
d s /b
Exp. IExp. IIRegression
(b) Dimensionless scour depth development with dimensionless time.
Figure 3.5. Scour development with time for Chattahoochee River model (Replicates of Run FB 8 with V1/Vc = 0.83 and y1/b = 4.2).
47
The development of scour depth with time is shown in Fig. 3.5 (a) for two replicated
experiments in the Chattahoochee River flat-bed model (Run FB 8). The scour has clearly
reached equilibrium, and more importantly the data in Fig. 3.5 (a) show that the scour depth can
be reproduced in identical experiments with an uncertainty of approximately ±0.01 ft, or about
one grain diameter, if care is taken to level the bed to the same initial position. The scour
development with time is shown in dimensionless form in Fig. 3.5 (b), and it follows a linear
trend with the logarithm of dimensionless time as found by other investigators (Ettema 1980,
Sturm 1998, Cardoso and Bettes 1999).
Approach Velocity and Turbulence
The relative longitudinal and vertical turbulence intensities at the location of the approach
section to the main pier bent are shown in Fig. 3.6 for the Chattahoochee River model (Run FB
8) and in Fig. 3.7 for the Flint River model (Run RM 1) as typical examples. The longitudinal
and vertical turbulence intensities are shown in these figures nondimensionalized by the
longitudinal point velocity u as a function of relative height above the bed z/H where H =
approach flow depth. The experimental data are compared with accepted experimental
relationships for rough boundaries in open channel flow obtained by other investigators (Nezu
and Nakagawa 1995, Nikora and Goring 2000). Although there are some outliers close to the
bed, the data are within the experimental uncertainty of the accepted experimental relationships.
The comparisons shown in Figs. 3.6 and 3.7 are important not only because they verify the
acceptability of the turbulence measurements in the approach flow, but also because they provide
a baseline for comparison with turbulence intensities that exist in the near field of the pier bent
where scour occurs.
48
Turbulence intensity in x-direction
0
0.1
0.2
0.3
0.4
0.5
0 0.2 0.4 0.6 0.8 1z/H
u'/u
10MHz ADVNezu and Nakagawa (1993)Nikora and Goring (2002)
Turbulence intensity in z-direction
0
0.1
0.2
0.3
0.4
0.5
0 0.2 0.4 0.6 0.8 1z/H
w'/u
10MHz ADVNezu and Nakagawa (1993)Nikora and Goring (2002)
Figure 3.6. Longitudinal and vertical relative turbulence intensity profiles at approach section for Chattahoochee River model (Run FB 8).
Turbulence intensity in x-direction
0
0.1
0.2
0.3
0.4
0.5
0 0.2 0.4 0.6 0.8 1z/H
u'/u
10MHz + 2D side ADVNezu and Nakagawa (1993)Nikora and Goring (2002)
Turbulence intensity in z-direction
0
0.1
0.2
0.3
0.4
0.5
0 0.2 0.4 0.6 0.8 1z/H
w'/u
10MHz + 2D side ADVNezu and Nakagawa (1993)Nikora and Goring (2002)
Figure 3.7. Longitudinal and vertical relative turbulence intensity profiles at approach section for Flint River model (Run RM 1).
Near-Field Turbulence Intensity
Turbulence intensities were measured for the flat-bed Chattahoochee River model at the 14
locations shown on the left and right sides of the main pier bent as shown in Fig. 3.8 (a) where
y/b is approximately ±2. For purposes of comparison, all turbulence intensities are
nondimensionalized by the mean approach velocity (U0) and are shown in Fig. 3.8 (b) for the
49
(a) Measuring locations.
z/HLeft side of piersRight side of piers
0
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 1
u'/U
0
1 2 3 4 5 6
0
0.1
0.2
0.3
0.4
0.5
0 0.5 1
7
0
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 1
u'/U
0
8 9 10 11 12 13
0
0.1
0.2
0.3
0.4
0.5
0 0.5 1
14
(b) Longitudinal turbulence intensity relative to approach velocity U0.
z/HLeft side of piersRight side of piers
0
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 1
w'/U
0
1 2 3 4 5 6
0
0.1
0.2
0.3
0.4
0.5
0 0.5 1
7
0
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 10
0.1
0.2
0.3
0.4
0.5
0 0.5 1
w'/U
0
8 9 10 11 12 13
0
0.1
0.2
0.3
0.4
0.5
0 0.5 1
14
(c) Vertical turbulence intensity relative to approach velocity U0.
Figure 3.8. Near-field turbulence intensities for Chattahoochee River model (Run FB 8).
-10 -5 0 5 10 15 20
x/b
-5
0
5
y/b
U
1 148
50
longitudinal direction and in Fig. 3.8 (b) for the vertical direction. The measured turbulence
intensities are close to the edge of the near field or wake zone and show a maximum near the bed
in absolute terms since the reference approach velocity U0 is a constant. The horizontal
turbulence intensity is roughly of the order of 10 percent of the mean approach velocity while the
vertical turbulence intensity is of the order of 5 percent of the mean approach velocity. Of
particular interest is the increase in turbulence intensities on the right side of the pier bent in
comparison to the left side for positions downstream of location 8 as defined in Fig. 3.8 (a). This
is the result of a slight skewness of the approach flow which is discussed in more detail in
Chapter 6.
Scour Contours and Near-Field Velocities
Fig. 3.9 shows the equilibrium scour contours for the same flat-bed Chattahoochee River model
run (FB 8) for which the turbulence intensities were given in Fig. 3.8. Superimposed on the scour
contours are the near-field velocity vectors measured after scour at a height above the bed of 40
percent of the depth.
Although the maximum scour depth for the experimental run shown in Fig. 3.9 is in front
of the upstream pier, scour holes are also evident in front of the downstream pier as well as
between the two inner piers underneath the solid web. Immediately downstream of the first and
fourth piers and underneath the inner pier web, a region of deposition, or less scour, can be
observed. This scour pattern will be explored in more detail in Chapter 6 in which the computed
three-dimensional velocity field is compared with the laboratory scour and velocity
measurements. The horizontal velocity vectors in Fig. 3.9 show the characteristic decrease in
magnitude associated with the approach to the pier stagnation line at a location of approximately
two pier widths upstream of the first pier. In addition, the velocity vectors at this location are at
51
an angle to the centerline of the pier bent as the flow bends around the pier bent and separates to
form a wake zone. The horizontal velocities are very small between the piers as well as in the
downstream wake of the bent until the wake velocity defect gradually begins to recover in the
downstream direction.
-10 -5 0 5 10 15 20
x/b
-10
-5
0
5
10
y/b
ds/b
-3.0
-2.7
-2.4
-2.1
-1.8
-1.5
-1.2
-0.9
-0.6
-0.3
0.0
0.3
V/V1 = 1.0
Figure 3.9. Shaded scour contours and velocity vectors after scour at 40 percent of the approach depth for bank-full flow in the Chattahoochee flat-bed model (Run FB 8).
-10 -5 0 5 10 15 20
x/b
-10
-5
0
5
10
y/b
-3.0
-2.7
-2.4
-2.1
-1.8
-1.5
-1.2
-0.9
-0.6
-0.3
0.0
0.3
ds/b
V/V1 = 1.0
Figure 3.10. Shaded scour contours and velocity vectors after scour at 40 percent of the approach depth for bank-full flow in the Chattahoochee River model (Run RM 5).
52
Scour contours and velocities after scour are shown for the Chattahoochee river model
case (Run RM 5) in Fig. 3.10 which is also for bank-full flow as in Fig. 3.9 for the flat-bed
model. The values of V1/Vc and b/d50 are not the same in Figs. 3.9 and 3.10, so only the scour
patterns and velocity vectors relative to the approach velocity are compared here while the scour
magnitudes will be discussed in the next section. The velocity field for the river model in Fig.
3.10 is not as uniform across the channel because of the river bathymetry, so the effect of the
obstruction caused by the pier bent on the near-field velocities is slightly different. In addition,
there is a greater skewness of the approach velocity with respect to the centerline of the pier bent
in the case of the river model. The angle of attack for the river model was measured to be 4.3°
while it was only 1.8° for the flat-bed model. This becomes apparent in the scour pattern in front
of the upstream pier in Fig. 3.10 in which the scour hole is offset to the right of the centerline of
the pier bent. Scour is less underneath the web between the inner piers in both Figs. 3.9 and 3.10,
and the continuity of the scour trench surrounding the pier bent is similar in both cases.
Scour patterns and velocity fields for the Flint River flat-bed model and river model are
given in Figs. 3.11 and 3.12, respectively. While there is an obvious scour hole in front of the
upstream pier, the deepest scour for the flat-bed model at bank-full flow (y1/b = 4.4) occurs in
two symmetric scour holes between the piers as shown in Fig. 3.11 (a). The velocity field after
scour in Fig. 3.11 (a) clearly shows the deceleration of flow as the upstream pier is approached
and the very small velocities between piers, but the horizontal velocity field does not explain the
scour pattern between piers. A closer look at the velocity components after scour in two cross
sections located just upstream of the first pier and between the two piers is given in Figs. 3.11 (b)
and 3.11 (c), respectively. The downflow induced by the first pier is still evident in Fig. 3.11 (b)
at the end of scour along with very small velocities near the bottom of the scour hole. However,
53
-5 0 5 10 15
x/b
-5
0
5
y/b
-1.8
-1.5
-1.2
-0.9
-0.6
-0.3
-0.0
0.3
0.6
ds/b
A
A'
B
B' V/V1 = 1.0
(a) Scour contours and velocity vectors after scour at 40 percent of the depth.
6 4 2 0 2 4 6
y/b
-2
0
2
4
z/b
V/V1 = 0.24
Right sideLeft side
(b) Velocity vectors at cross section A-A’ after scour.
6 4 2 0 2 4 6
y/b
-2
0
2
4
z/b
V/V1 = 0.24
Right sideLeft side
(c)Velocity vectors at cross section B-B’ after scour.
Figure 3.11. Scour contours and velocity vectors after scour for bank-full flow in Flint River flat-bed model (Run FB 2).
54
in Fig. 3.11 (c) there is an upwelling between the piers at the centerline of the pier bent with two
counter-rotating vortices on either side that coincide with the symmetric scour holes.
Scour patterns and the velocity field for flood flow (y1/b = 7.4) in the Flint River for the
river model are shown in Fig. 3.12. In this case, the symmetric scour holes disappear and the
deepest scour is in front of the upstream pier with scour of a lower magnitude between piers.
Skewness is a factor in this case since the angle of attack was measured to be 6.4° which in
combination with the river bathymetry helps to explain the small wake scour hole to the right of
the downstream pier and the deposition area also to the right and considerably downstream of the
pier bent. However, the most surprising difference in comparison with the flat-bed model can be
seen in Figs. 3.12 (b) and 3.12 (c) which show the velocities in cross sections upstream of the
first pier and between piers. There is an obvious secondary flow near the bed moving across the
cross section to the left which may originate from the floodplain flow joining the main channel
flow in the bridge opening or may be the result of the gradual bend in the river just upstream of
the bridge. In summary, there are significant three-dimensional flow effects in both the flat-bed
and river models, but they are due to different sources and they result in very different scour
patterns.
Comparison of Laboratory Scour Data with Prediction Formulas
To conclude this chapter on laboratory modeling, it is useful to compare the measured laboratory
scour depths at different model scales and for different sediment sizes with accepted clear-water
scour formulas. The scour depths being compared are at the nose of the upstream pier in the pier
bent. In the figures that follow, the measured dimensionless values of scour depth, ds/b, are
plotted together with predictions from scour formulas that include corrections for the
independent nondimensional variables listed in Eq. 3.1. The HEC-18 formula does not include
55
-20 -15 -10 -5 0 5 10 15 20 25
x/b
-10
-5
0
5
10
y/b
-1.1-0.9-0.7-0.5-0.3-0.10.10.30.50.70.91.11.3
ds/b
V/V1 = 1.0
A
A'
B
B'
(a) Scour contours and velocity vectors after scour at 40 percent of the depth.
10 8 6 4 2 0 2 4 6 8 10
y/b
0
2
4
z/b
V/V1 = 0.5
Left side Right side
(b) Velocity vectors at cross section A-A’ after scour.
10 8 6 4 2 0 2 4 6 8 10
y/b
0
2
4
z/b
V/V1 = 0.5
Left side Right side
(c) Velocity vectors at cross section B-B’ after scour.
Figure 3.12. Scour contours and velocity vectors after scour for flood flow in Flint River model (Run RM 1).
56
the effect of V1/Vc , while both the Sheppard and Melville formulas do not include the influence
of the Froude number. Accordingly, the plots of the dimensionless scour depths are given as a
function of V1/Vc with the value of the approach Froude number shown as a label on each data
point. Results are presented in separate figures for the flat-bed model and the river model
because the values of b/d50 are different in the two cases, and they have a significant effect in the
Sheppard and Melville formulas (reduction in predicted scour for values of b/d50 less than about
25). On the other hand, the value of b/d50 is not a factor in the HEC-18 formula. Finally, both
bank-full and flood flow experimental runs are included in the figures with values of y1/b
approximately equal to 4.0 and 7.0, respectively, for both the Chattahoochee River and the Flint
River. These values of y1/b are large enough that they have almost no influence in the Sheppard
and Melville formulas, while the value of y1/b appears explicitly in the HEC-18 formula
regardless of its value.
The comparison between measured and predicted scour depths for the flat-bed
Chattahoochee model (1:23.3 scale) at bank-full flow is shown in Fig. 3.13. The data points at
low values of V1/Vc are bounded above by the Sheppard and Melville formulas. As V1/Vc
continues to increase, the data points approach the HEC-18 formula which is considerably above
the other two formulas for this case. The values of the Froude number also become rather large at
the higher values of V1/Vc. This is a consequence of the larger model sediment size (3.3 mm)
which also produces smaller values of b/d50. These values of the Froude number are considerably
higher than the field value for bank-full flow which is approximately 0.33.
Figure 3.14 shows the scour depth comparisons for the river model of the Chattahoochee
River (1:40 scale). The sediment size for these data is 1.1 mm which results in a value of b/d50 of
57
0.0
1.0
2.0
3.0
4.0
5.0
0.5 0.6 0.7 0.8 0.9 1.0 1.1V 1 /V c
d s/ b
Flatbed model, b/d50=13.9Sheppard (2003), b/d50=13.9Melville (1997) , b/d50=13.9HEC-18(1995), b/d50=13.9
0.35
Fr=0.600.510.44
0.46
0.42
0.400.40
0.37
Figure 3.13. Comparison of measured scour depths in Chattahoochee River flat-bed model with scour prediction formulas for bank-full flow (y1/b = 4.0).
0.0
1.0
2.0
3.0
4.0
5.0
0.5 0.6 0.7 0.8 0.9 1.0 1.1V 1 /V c
d s/ b
River model, b/d50=24.5Sheppard (2003), b/d50=24.5Melville (1997) , b/d50=24.5HEC-18 (1995), b/d50=24.5, y1/b=7.0HEC-18 (1995), b/d50=24.5, y1/b=4.0
0.300.23 0.33
Fr=0.40.26
Figure 3.14. Comparison of measured scour depths in Chattahoochee River model with scour prediction formulas for bank-full flow and flood flow (y1/b = 4.0 and 7.0).
58
24.5 at which there is almost no influence on predicted scour depths in the Sheppard and
Melville formulas. Another result of the smaller sediment size is a range in the laboratory Froude
number values that is smaller and more comparable to the prototype value. There is good
agreement between the measured data and all three scour prediction formulas in Fig. 3.14.
The comparison between measured and predicted scour depths for the flat-bed Flint River
model (1:50 scale) at bank-full flow is shown in Fig. 3.15. As for the Chattahoochee model
results in Fig. 3.13, the Sheppard and Melville formulas agree with the measured scour depths at
small values of V1/Vc, but the corresponding HEC-18 formula predictions are well above the
measured values because of the small values of b/d50 for the 3.3 mm sediment size. The
difference in this case is that measurements were not made at very high values of V1/Vc so that
the Froude numbers are not excessively large.
Fig. 3.16 shows the scour depth comparisons for the Flint River model (1:90 scale)
utilizing the 1.1 mm sediment at flood flow stage (y1/b = 7). As in Fig. 3.14 for the
Chattahoochee River model, the Sheppard and Melville scour prediction formulas provide
reasonable predictions of the scour depth, while the HEC-18 formula overpredicts the scour
depth somewhat more than in Fig. 3.14 because the model value of b/d50 is less than 25. The
Froude numbers in Fig. 3.16 for the Flint River model remain relatively low and comparable
with the field value of 0.25.
Further comparisons of laboratory scour depths with field values are made in Chapter 6.
The results of this chapter indicate that good comparisons with the Melville and Sheppard
formulas can be obtained even at different model scales if the model sediment size is small
enough that values of the Froude number do not become too large. The HEC-18 formula, on the
other hand, tends to overpredict the scour depth for most of the measurements that were made.
59
0.0
1.0
2.0
3.0
4.0
5.0
0.5 0.6 0.7 0.8 0.9 1.0V 1 /V c
d s/ b
Flatbed model, b/d50=11.1Sheppard (2003), b/d50=11.1Melville (1997) , b/d50=11.1HEC-18(1995), b/d50=11.1
Fr=0.3
0.430.43
Figure 3.15. Comparison of measured scour depths in Flint River flat-bed model with scour prediction formulas for bank-full flow (y1/b = 4.0).
0.0
1.0
2.0
3.0
4.0
5.0
0.5 0.6 0.7 0.8 0.9 1.0V 1 /V c
d s/ b
River model, b/d50=18.8Sheppard (2003), b/d50=18.8Melville (1997) , b/d50=18.8HEC-18 (1995), b/d50=18.8
0.20
Fr=0.27
0.24
Figure 3.16. Comparison of measured scour depths in Flint River model with scour prediction formulas for flood flow (y1/b = 7.0).
60
CHAPTER 4. THREE-DIMENSIONAL NUMERICAL MODELING
INTRODUCTION
The flow features around bridge foundations on natural river reaches are largely determined by
the geometry of the structures, and by the complex bathymetry of the river. There is a large
disparity between the chacteristic length scales of the river flow and those produced by the
bridge foundation. The existence of bridge piers and abutments in the flow introduces vortex
shedding from the concrete walls to the already highly three-dimensional and strongly turbulent
flow existing in the river.
To simulate the flow around bridge foundations, a novel state-of-the-art numerical solver
has been developed which has the following features:
1) It resolves accurately and efficiently the intricate geometric details of real-life bridge
foundations, which typically consist of multiple bundles of piers with complex geometry;
2) It accounts for the large-scale topography of the river reach where the bridge is
embedded;
3) It captures the large-scale dynamics of the coherent vortex shedding, modeling the small
scale turbulence with statistical turbulence models.
The numerical model simulates the turbulent flow by solving the unsteady Reynolds-averaged
Navier-Stokes (URANS) equations along with the standard k-ε model. Overset or Chimera grid
techniques are employed in the calculations to deal with the arbitrarily complex geometry of the
problem. The following sections provide detailed descriptions of the numerical model that was
developed as well as the results that were obtained from the numerical simulations.
61
NUMERICAL METHOD
The 3D, incompressible, URANS and turbulence closure equations are formulated and solved in
generalized, curvilinear coordinates in strong conservation form. The governing equations are
discretized in space using the three-point, central, second-order accurate, finite-volume scheme.
Third-order, fourth-difference, matrix-valued artificial dissipation terms (Lin and Sotiropoulos
1997) are explicitly added to the discrete equations to suppress grid-scale oscillations. The
discrete equations are integrated in time using a second-order-accurate, dual- or pseudo-time-
stepping, artificial compressibility scheme. The equations are integrated in pseudo time using the
Beam-and-Warming approximate-factorization scheme in conjunction with V-cycle multigrid
and local-pseudo-time-stepping for faster convergence. At the inlet, fully-developed turbulent
flow distributions for the mean-velocity field and the turbulence quantities are specified. Non-
reflecting, characteristic-based boundary conditions are applied at the outlet boundary to allow
vortical structures to exit the flow domain without distortion. The free surface is treated as a flat,
rigid lid. Wall functions are used to account for the wall roughness and flow turbulence near all
solid walls. The developed numerical solver is parallelized to take full advantage of modern
computational power. Typically, 15 pseudo-iterations are required to reduce all residuals by three
orders of magnitude, and a total number of 3000 physical time steps are required to obtain a
statistically converged solution.
GRID GENERATION FOR COMPLEX BATHYMETRY AND OBSTRUCTIONS
An example of the complex geometries of interests is given in Fig. 4.1, which shows the actual
river bathymetry of a reach of the Chattahoochee River near Cornelia, GA with a single bent of
bridge piers mounted on the bed. The bent consists of four rectangular piers located one behind
the other along the flow direction. There is a web connecting the two middle piers which does
62
not extend all the way to the channel bed. The actual bridge foundation consists of three such
bents across the bridge span. In this study, the focus is on the single-bent case. In the following
section, the overset grid method is described in the context of the flow around the bridge
foundation of the Chattahoochee River case.
Figure 4.1. Numerical geometry of a single bent of piers on natural river reach.
(a) (b)
Figure 4.2 Overset grid system.
63
The idea of the overset grid method is to divide the original complex flow domain into
several small subdomains which are simple for grid generation. These subdomains are allowed to
overlap with other subdomains. The overset grid layout used for the site on the Chattahoochee
River near Cornelia, GA is illustrated in Fig. 4.2. As shown in Fig. 4.2(a), a curvilinear grid
system, which will be referred to as the background grid hereafter, is used to discretize the river
reach---denoted as Subdomain 1 in Fig. 4.2(a). Other four subdomains, Subdomain 3, 4, 5, and 6
as shown in Fig. 4.2(a), are employed to discretize the four bridge piers mounted on the river bed
and the web connecting the two middle piers. Such a grid layout allows, on the one hand,
resolution of all essential flow features resulting from the river bathymetry with the background
grid, while the grids used in the other subdomains make it possible to cluster grid nodes in the
vicinity of solid walls, where the majority of the unsteady flow physics occur. Due to the
disparity in spatial scales between the river reach and the pier bent, there is a large discontinuity
between the grid spacing of the background grid (Subdomain 1) and that of Subdomains 3, 4, 5,
and 6 used to discretize the piers. As shown in Tang et al. (2003), large discontinuities in mesh
spacing across subdomain interfaces tend to introduce spurious oscillations in the computed flow
variables and in general lead to inaccurate solutions. In order to remedy this problem, yet another
subdomain, Subdomain 2 in Fig. 4.2(a), is embedded between the background grid and the pier-
bent grids. Grid nodes are distributed uniformly in this subdomain and their total number is
selected such that the spatial resolution of this grid alleviates the large discontinuity between the
coarse resolution of the background grid and the very fine resolution of the pier-bent grids. Grid
embedding with Chimera overset grids allows both the large-scale flow features controlled by
the river topography and the complex unsteady flow induced by the piers to be taken into
account without requiring excessively large grid sizes.
64
The solutions on the original complex domain are obtained in an iterative manner.
Governing equations are first solved separately in each subdomain and the solutions
commnunicate with the neighboring subdomains through interpolation on the subdomain
interfaces. The interface interpolation is implemented in two steps. First, the location of each
grid node on the interface relative to the other domains is determined using a Newton method,
which is an iterative method to obtain a numerical solution of a system of equations of the form
f(x) = 0. This grid connectivity information can be performed as a preprocessing step and stored
for use during the calculation. The second step is the interpolation of the flow variables from
Subdomain 1 (which contains the background flow field information) to the interface of interest.
A second-order interpolation scheme is used to maintain the overall solver accuracy. The code
developed for this study features both standard trilinear interpolation for all flow variables at grid
interfaces (Steger and Benek 1987) as well as the so-called mass-flux based interpolation
approach developed in Tang et al. (2003).
APPLICATION OF THE 3D MODEL
The developed numerical solver was applied to study the 3D unsteady turbulence flows of the
following cases. In all these cases, the actual geometry of the bridge foundations was used. They
were either mounted on the actual river bathymetry or on flat river beds:
1) Bridge in the Chattahoochee River near Cornelia, GA:
a. Single pier bent mounted on the actual river bed;
b. Single pier bent mounted on a flat river bed;
c. Two pier bents mounted on a flat river bed.
2) Single pier bent of the Flint River foundation mounted on a flat river bed.
3) Single pier bent of the Ocmulgee River foundation in Macon, GA, mounted on a flat bed.
65
Only results from Case 1 are presented in this section in order to demonstrate the general
capabilities of the numerical model and underscore the complexity of hydrodynamics in the
vicinity of real-life bridge foundations. Results from all three cases will be presented in Chapter
6 in the numerical model validation section.
The grid shown in Fig. 4.1 is used to study the flow through the Chattahoochee River
reach. The calculations are carried out for flow parameters that are typical for the specific reach,
where the bulk velocity is about 7 ft/s.
First, the capacity of the developed numerical solver for resolving the flow unsteadiness
in the vicinity of bridge foundations is illustrated. In Fig. 4.3, the calculated time histories of the
velocity component along the y axis at two points in the flow are shown. Point A is located in
Subdomain 6 just downstream of the last pier while Point B is located in the background grid
(Subdomain 1)---for point locations (see Fig. 4.2). As seen in Fig. 4.3, following an initial
transient of approximately 200 time units, the flow at Point A attains an oscillatory, periodic
state. In stark contrast, the flow at Point B reaches a quasi-steady state after the initial transition--
-a very weak unsteady fluctuation persists at this point but its amplitude is only a very small
fraction of the mean vertical velocity at Point B. This is consistent with the fact that a) the
location of point B is far away from the bridge foundations; and b) the grid resolution in the
background region is really coarse and designed to provide the background flow features for the
bridge foundations. Note that this flow unsteadiness was captured under steady inflow velocity
conditions. The flow unsteadiness is excited naturally by the large-scale vortex shedding induced
by the bridge foundations.
66
Figure 4.3. Dimensionless velocity-time history at two different points A and B (U0 = approach velocity; T = b/U0; b = pier width).
To illustrate the complexity of the large-scale flow in the vicinity of the piers, Fig. 4.4
shows two snapshots of instantaneous velocity magnitude contours and three-dimensional
streamlines at the corresponding instants of time. This figure illustrates clearly the complexity of
the flow in the vicinity of the piers. Features such as the unsteady meandering of the shear layers
around the bent and the unsteadiness of the recirculating flow regions in the pier wakes are
clearly evident in these results. The effect of the complex river bathymetry on the pier hydraulics
is also apparent. Note that for both instants in time, the instantaneous velocity contours are
highly asymmetric. The velocities are considerably higher and the vortex shedding is more
intense on the left side of the pier bent (as viewed looking downstream) due to the fact that the
approach flow is skewed by about 5° relative to the streamwise axis of the bent. Obviously such
complex flow patterns cannot be accurately simulated without taking into account the complexity
of the ambient bathymetry. As shown in Fig. 4.4(b), highly unsteady, coherent vortical structures
with axes perpendicular and parallel to the bed are seen to appear and disappear continuously
throughout one period of the flow.
67
(a) Velocity contours. (b) 3D streamlines.
Figure 4.4. Visualization of instantaneous flow field in the vicinity of bridge piers.
The above results clearly reveal the existence of large-scale coherent vortex structures in
the vicinity of the bridge foundations. In order to further understand the complex flow physics in
these regions, the flow is studied by replacing the complex river bed bathymetry with a flat bed
in cases 1(b), 2, and 3—for this configuration laboratory experiments were carried out and the
data from these experiments are used to validate the numerical model in Chapter 6 of this report.
The incoming flow is assumed to be aligned with the axis of the bridge piers. The same incoming
flow velocity as in the laboratory experiments is used for the numerical simulations.
68
The grid system used for this calculation is shown in Fig. 4.5(a). As illustrated in Fig.
4.5(b), where the time history of spanwise velocity components at two different points located on
the symmetric plane of the pier-bent axis is shown, the flow unsteadiness is captured. After an
initial transient stage, the flow approaches a periodic state, and this flow unsteadiness is
sustained throughout a long calculation time span. Juxtaposing the two snapshots of resolved
streamwise velocity contours shown in Fig. 4.6(a) with the time-averaged flow at the horizontal
plane shown in Fig. 4.6(b) clearly shows that unsteadiness in the flow originates due to the
Kelvin-Helmoltz type instability of the shear layers emanating from the upstream corner of the
foundation and the intense vortex shedding in the wake. The transverse flapping and meandering
of the wake flow is clearly evident in the two snapshots in this figure. Furthermore, it should be
noted that the time-averaged flow field shown in Fig. 4.6(b) exhibits a high degree of symmetry
with respect to the streamwise axis of the foundation, thus suggesting that the simulated time
interval is suffcient for obtaining statistically-converged mean flow.
69
(a) Overset grid layout. (b) Time history of spanwise velocity.
(c) Measurement and comparison locations.
Figure 4.5. Bridger piers mounted on flat bed.
70
(a) Streamwise velocity contours at two different time instants on a horizontal plane.
(b) Time-averaged streamwise velocity contours.
Figure 4.6. Streamwise velocity contours.
Figure 4.7. Snapshot of instantaneous streamlines of the large-scale flow.
71
Fig. 4.7 shows a snapshot of streamlines in the vicinity of the bridge piers. The complex
coherent vortex structures are clearly reproduced in this figure. In front of the first bridge pier on
the upstream side, the flow is smooth and organized with the horse-shoe vortex forming in the
area of conjunction between the downward flow and the riverbed. The flow behind the first
bridge pier is extremely complex, dominated by multiple tornado-like vortices. These vortices
are the result of the wake flow of the front pier and the solid wall of the following bridge piers.
The snapshot clearly illustrates the result of the interaction of the flow and the bridge
foundations, and these complex vortex structures are anticipated to play an important role in the
formation of the local scour hole.
Another case study to be presented is the flow around two bents of bridge piers mounted
on a flat riverbed. The geometries of the piers and the distance between these two bents are based
on the site near Cornelia, GA. The streamwise velocity contours on a horizontal plane just below
the water surface are shown in Fig. 4.8. As seen in this figure, despite the relatively large
distance between the two bents, there appear to be very weak interactions of the vortical
structures emanating from the solid walls of the piers. To quantify the interaction, the total
turbulence kinetic energy obtained from the numerical solution is calculated. Fig. 4.9 shows the
turbulence kinetic energy profile along the depth direction at four locations on both sides of the
right-hand pier bent (see Fig. 4.8 for locations). These locations are symmetric about the
symmetry axis of the bent. If the flow between these two bent structures has very weak or no
interaction, these profiles are anticipated to be symmetric on both sides. However, as shown in
Fig. 4.9, they are asymmetric suggesting that the turbulence structure in the vicinity of the two
bents is affected considerably by their mutual interaction in spite of their relatively large spacing.
72
Figure 4.8. Instantaneous streamwise velocity contours.
Figure 4.9 Turbulence kinetic energy profile (see Figure 4.5 (c) for locations).
73
CONCLUSIONS
The results presented in this chapter point to the following conclusions:
1) The flows around natural river bridge foundations are naturally unstable and highly three-
dimensional. Large-scale coherent vortex shedding exists in the vicinity of the bridge
foundations with multiple vortices having axes both parallel and perpendicular to the bed;
2) Both the river bathymetry and the presence of multiple pier bents can influence the flow
patterns considerably and need to be taken into account if realistic flow predictions are to be
obtained.
3) The numerical model developed in this research is a powerful engineering simulation tool for
elucidating the complex flow physics of real-life bridge foundation flows. As will
subsequently be shown, the insights into the flow structures provided by the numerical model
facilitate the understanding and interpretation of the results from laboratory experiments for
foundations mounted on deformable beds.
74
CHAPTER 5. SEDIMENT EROSION PROPERTIES
INTRODUCTION
Shelby tube sediment samples collected from the foundations of ten (10) bridges located in the
state of Georgia were tested in the laboratory to find their erosional behavior and the correlation
of erosion parameters with sediment properties in order to improve the prediction of scour
around bridge foundations. These sites were spatially distributed in order to fall into different
major river basins and in different physiographic regions. Flume measurements were performed
using a rectangular, tilting, recirculating flume that was modified to receive Shelby tube samples
in the flume bottom that could be extruded upward as erosion occurred. Regression analysis was
performed on erosion rates as a function of applied shear stress to determine the parameters of
the erosion function. The resulting parameters, the critical shear stress and the erosion rate
constant, were correlated with soil properties and physiographic regions, and the results are
reported in this chapter. Additional details can be found in the thesis by Navarro (2004).
SEDIMENT EROSION RESISTANCE
The size of the particles being eroded is the principal factor that influences the type of forces
involved in resisting erosion. For coarse sediments with low content of fine particles (smaller
than 76 microns) gravity forces govern the process. Alternatively, when fine sizes are present in
the bed material, additional forces become important. For instance, for particle sizes smaller
than 10 microns or clay sizes, electrical forces make their appearance. In addition, the particle-
fluid interaction cannot be disregarded. The ionic concentration and pH of the fluid affect
particle charges; therefore the erosion process becomes dependent on the chemistry of the pore
water (Ravisangar et al. 2001).
75
As the particles get smaller, electrical forces have more effect on the erosion resistance
because electrical forces are highly dependent on the particle’s specific surface area, which is
defined as the surface area per unit volume or mass of the particle. Given that specific surface
area increases as the size decreases, and that it is greater for platy particles than for spherical
particles, an abrupt change in the behavior of the forces takes place as the size changes from silty
to clay-size material. Silty material is the result of mechanical weathering and therefore
maintains a rounded shape. On the other hand, clay has platy structures with high values of
specific surface area. As a result, the interparticle forces that resist the hydrodynamic drag force
and erosion include the gravitational force, Coulombian attraction, van der Waals attraction and
double layer repulsion. Short range forces, such as hydration forces and Born repulsion, may
also be important in determining the net overall attractive or repulsive force between clay
particles (Mahmood et al. 2001).
The gravitational force manifests itself as the submerged weight of the sediment particle,
and it is the only force resisting erosion for coarse-grained sediments. Erosion is caused by the
hydrodynamic force consisting of lift and drag components produced by a viscous fluid moving
around a particle. Both surface drag and form drag contribute to the total drag force. The
movement of coarse-grained particles is produced when the hydrodynamic force overcomes the
submerged weight. The hydrodynamic force in the sediment transport literature is often
represented simply by the applied shear stress (τ), or force per unit surface area. The applied
shear stress for steady uniform open channel flow can be measured at the threshold of movement
of sediment particles on the channel bed and defined as the critical shear stress, τc which can be
given in dimensionless form as (Sturm 2001)
⋅==
⋅−=
νρτ
γγτ
τd
fd
cc
ws
cc
2/1
*2*)/(
Re)(
(5.1)
76
in which γs - γw = submerged specific weight; d = particle diameter; ρ = water density; ν =
kinematic viscosity; τ*c = Shields Parameter; and Re*c = critical boundary or particle Reynolds
number. These last two parameters were presented by Shields for the initiation of sediment
motion in the widely known Shields Diagram. The first parameter (τ*c) can be interpreted as the
ratio of the hydrodynamic force per unit area to the gravitational force per unit volume. The
second parameter (Re*c) represents the ratio of the particle diameter to the thickness of the
viscous sublayer. In the definition of the last two parameters the diameter and the critical shear
stress are included, which impedes the direct calculation of the critical shear stress for a given
diameter. The introduction of a third dimensionless parameter, given by [0.1Re*c2/τ*c]1/2,
eliminates this restriction. The result of that analysis can be given in the form (Julien 1995)
⋅⋅−==
3/1
2
3
*3*)1(
ντ dgSGdfc (5.2)
in which d* = dimensionless particle diameter and SG = specific gravity. The functional
relationship suggested by Eq. 5.2 has been developed experimentally by many investigators for
coarse-grained sediments and it is shown in Fig. 5.1.
77
0.01
0.1
1
0.1 1 10 100 1000Dimensionless Diameter, d *
Shie
lds P
aram
eter
, τ*c
Figure 5.1. Shields diagram for direct determination of critical shear stress of coarse-grained sediments (after Sturm 2001).
For fine-grained materials, in addition to gravitational forces opposing the movement,
interparticle forces start to act. Among these can be mentioned Coulombian attraction, van der
Waals attraction, and double layer repulsion. Coulombian attraction acts when there are counter
electrical charges interacting. Edges of clay particles that have a positive charge are attracted to
the negative face of the mineral. Van der Waals attraction is a result of the nonuniform charge
distribution on adjacent molecules. The closer the particles can move towards each other, the
stronger that this force will be. Its value depends on the shape of the interacting particles. The
double layer repulsion force makes erosion more likely. This force acts to cause particle
repulsion, making erosion by hydrodynamic forces easier. It depends on the ionic concentration
of the environment more than any other factor. As a result of this dependence, when ionic
concentration changes, this force changes and affects the equilibrium of the system. Coulombian
78
and van der Waals forces will redistribute to form a new equilibrium state with a new particle
arrangement.
The relative contribution of the interparticle forces depends on the size and structure of
sediments. For example, considering two relevant forces, gravitational and van der Waals, it can
be shown that the gravity force is overwhelmed by the van der Waals force for particles smaller
than 60 microns (Santamarina 2001). Thus, the applied hydrodynamic drag force, which is a
combination of surface and form drag as well as turbulent bursts near the bed, must overcome
not only the gravitational forces but also the much larger interparticle forces for fine-grained
sediments.
The arrangement of the sediment particles is an important determinant of erosion.
Sediments that form a well-arranged structure will have great erosion resistance than sediments
that do not. The arrangement of particles depends on pH and ionic concentration conditions
present when they are deposited. Fine-grained platy particles have three main associations:
Edge-to-Face, Edge-to-Edge, and Face-to-Face. Edge-to-Face (E-F) arrangements are governed
by Coulombian forces presented by the contrary charge of the faces and edges of the particles.
Face-to-Face (F-F) arrangements are present when sedimentation occurs at high concentrations
and the van der Waals force prevails over double layer repulsion. Edge-to-Edge (E-E) are
transition arrangements of the other two structures given that there is not a dominant force that
governs the final structure.
Ravisangar et al. (2001) analyzed the influence of sediment pH on bed structure
formation and on initial erosion rates in flume experiments on kaolinite sediment. For different
pH conditions, kaolinite sediments have different bed structures and therefore different values of
bulk density and water content. Initial erosion rates were measured for those structures with the
79
following results. For pH conditions below 5.5, Edge-to-Face associations predominate. As the
pH increases, the bed structure becomes weaker, corresponding to Edge-to-Edge associations
dominating the structure. At pH conditions above 7, the sediment particles associate as Face-to-
Face increasing resistance to erosion. In terms of erosion resistance, the strongest associations
were E-F and F-F, while erosional strength was less in the transition stage.
Mahmood et al. (2001) performed experiments on attachment and detachment of particles
in porous media columns and calculated interparticle forces for platy particles including van der
Waals forces, electrical double layer forces, hydration forces and Born repulsion. An
interparticle force model was developed using the actual shape of kaolinite particles (hexagonal
platelet-like), and it produced results consistent with experimental observations. The force
magnitudes followed the decreasing sequence F-F > E-F > E-E, which is the same sequence
observed by Ravisangar et al. (2001) in flume erosion experiments for kaolinite. In addition, the
pH value observed for the maximum in the percent detachment was around 5, where E-E
associations predominate.
Because most of the sediments sampled at bridge foundations in this project consisted of
some fraction of fine-grained sediments, the interparticle forces just discussed are an important
consideration in determining erosion resistance. Despite the advances that have been made in
calculation of interparticle forces, experimental evaluation is still the only viable alternative to
estimating erosion resistance. As a result, flume experiments were conducted to evaluate the
relative erosion resistance of the sediment samples.
EROSION MEASUREMENT
The most important measures of erosion are the critical shear stress and the erosion rate of the
sediment when it is resuspended and transported at higher shear stresses. Different types of
80
experimental equipment have been used to measure erosion properties. These include the linear
recirculating flume, rotating annular flume and submerged impinging jet, among other devices.
Briaud et al. (1999), developed an apparatus called the erosion function apparatus (EFA), which
can test Shelby tube samples by introducing them into a rectangular duct having a cross section
50.8 mm high and 101.6 mm wide. In addition to laboratory measurements, in situ erosion
measurements have also been attempted as in the case of Ravens and Gschwend (1999) who
performed measurements of sediment erodibility in Boston Harbor. Still, the most common
devices to study sediment erosion phenomena experimentally are the linear recirculating flume
and the rotating annular flume.
The linear recirculating flume (Partheniades 1965; McNeil et al. 1996; Dennett et al.
1998; Ravisangar et al. 2001) used in this study is basically a straight open channel with an open
section at the bottom through which a sample of the erodible material is introduced. The flow
conditions in the channel are adjusted in order to assure fully developed, uniform, turbulent flow
as well as to apply a known shear stress at the bed. A piston is used to extrude the sample into
the flume as it is eroded. The height of the material eroded is recorded continuously as well as
the time during which it occurs, which when multiplied by the cross sectional area of the sample
results in the volumetric or gravimetric, if sediment density is known, erosion rate corresponding
to the specified flow conditions. A similar procedure is followed by Briaud et al. (1999), with
the difference that the flow through the sample is pressurized.
EROSION RELATIONSHIPS
Many attempts have been made to relate erodibility to bulk variables of the sediment and pore
fluid, and to the conditions of the flow. Among these contributors are McNeil et al. (1996), who
made measurements of erosion of undisturbed bottom sediments. Since erosion properties vary
81
spatially throughout a nonhomogeneous material, they were measured as a function of depth.
McNeil et al. (1996) found the most important sediment parameters that affect the erosion
phenomenon are the bulk density, water content, average particle size, and organic content.
Among the fluid characteristics that affect the erodibility, pH was already mentioned for the
results of Ravisangar et al. (2001). It was found that the erosion resistance depends on the bed
structure, which in turn is dependent on the pH of the pore water.
Zreik et al. (1998) and Hoepner (2001) attempted to relate erosional behavior to more
conventional measures of soil strength. Zreik et al. (1998) compared the erosional and
mechanical strength of deposited fine sediment. Mechanical strength was measured in a manner
similar to the conventional fall cone, where a cone is released from the sediment surface and
penetrates by its own weight for a period of time. Their results showed that erosional strength
was one order of magnitude smaller than mechanical strength. Two hypotheses are presented by
Zreik et al. (1998): first, the resistance to erosion is governed by the weakest of the individual
bonds between flocs, while mechanical resistance is governed by the group of bonds between the
flocs available in the sheared sediment mass. Second, for the erosional phenomenon, turbulent
eddies in the flow accumulate greater energy that causes sporadic motion of individual flocs
before the bulk shear strength of the bed is mobilized. Hoepner (2001) related the stability of
fine sediments tested in flume experiments to rheometer measures of yield stress and found that
the measured yield stress can be a practical index to predict the erosional strength of undisturbed
sediment.
Briaud et al. (2001) using their EFA (Erosion Function Apparatus) measured the erosion
rate of fine grained soils, finding that the most common shape of the erosion rate vs. applied
shear stress curve is concave up. However, straight and convex shapes were also found. The
82
convex shape was associated with the change of mechanism from surface to mass erosion.
Briaud et al. (2001) also correlated the erosion function with soil properties. One of the curve-
fitting parameters involved, the critical shear stress, is thought to increase when the soil unit
weight, plasticity index, soil shear strength, or fines content increase; and to decrease when the
void ratio, soil swell, dispersion ratio, soil temperature or water temperature decrease. However,
poor correlations were found with the plasticity index, undrained shear strength, and percent
passing the #200 sieve, for example. On the other hand, the initial slope of the erosion rate vs.
applied shear stress curve showed an encouraging relationship with the critical shear stress.
The dissimilar approaches to finding a unique relationship for the erosion resistance of
sediments is due to the difficulty in characterizing the microstructure based on the macro
properties of the material. This is in particular difficult for fine-grained sediments for which the
Shields relationship does not apply. Microstructure properties such as interparticle distance or
particle arrangement are not easily converted into particle size distribution and bulk density. In
addition, the nonhomogeneity of natural sediments adds more uncertainty in the measured
sediment properties. These problems force the use of experimental work to measure soil
erodibility although an analytical approach can provide a better understanding of the
phenomenon.
EXPERIMENTAL METHODS
Sample Locations and Properties
The Georgia Department of Transportation (GDOT) supplied the sediment core samples tested in
this project. The flume experiments were conducted on material collected according to ASTM
(D 1587-00): Standard practice for thin-walled tube sampling for geotechnical purposes. In this
project, thin-walled tubes were used with a diameter of 76.2 mm (3 in.), length of 910 mm (36
83
in.) and wall thickness of 1.65 mm (0.065 in.). The crews from GDOT were told the foundation
depth of the bridges, and they chose the most convenient drilling method and the sampler
insertion method. Boring logs were provided for each of the sites where the samples were
extracted. After receiving the samples, they were sealed and stored in a constant temperature
room vertically confined inside a wooden box, until the soil and flume tests were ready to begin.
Ten bridge sites in the state of Georgia were chosen for collection of samples from their
foundations on which to perform flume tests and measure soil characteristics. Flume tests were
executed with the objective of finding the particular critical shear stress and erosion rate constant
at the respective site. A number of soil properties were measured including size distribution,
water content, bulk density, organic matter, and liquid and plastic limit for the fine-grained
samples. These sites were geographically distributed in such a way that they fell into different
river basins and into different physiographic regions.
Four main physiographic regions can be roughly identified in Georgia. They are the
Valley and Ridge, the Blue Ridge, the Piedmont and the Coastal Plain regions. Samples were
collected from each of these regions. Fig. 5.2 shows the location of the sites identified by the
county in which the bridge is located. Table 5-1 provides further information on the bridge
locations and physiographic regions in which they are found.
84
Figure 5.2. Shelby tube core sample locations (Digital Environmental Atlas of Georgia, Alhadeff et al. 2000).
Table 5-1. Location of samples and description of physiographic regions.
Sample Number
County Location Physiographic Section
Major Land Resource Area
Latitude and
Longitude 1 Murray US 411 over Mill
Creek Southern Valley and Ridge Section
Southern Appalachian
34.8189º, 84.7647º
2 Towns SR 288 over Fodder Creek
Southern Blue Ridge Section
Blue Ridge 34.9275º, 83.7625º
3 Habersham Duncan Bridge Rd over Chattahoochee River
Southern Piedmont Section
Southern Piedmont 34.5406º, 83.6228º
4 Haralson US 27 over Tallapoosa River
Southern Piedmont Section
Southern Piedmont 33.8642º, 85.2097º
5 Wilkinson SR 57 over Oconee River
Sea Island and East Gulf Coastal Plain Section
Southern Coastal Plain
32.7817º, 82.9586º
6 Bibb US 80 / 5th St over Ocmulgee
Southern Piedmont Section
Sand Hill 32.8380º, 83.6212º
7 Effingham I-95 (NBL) over Savannah River
Sea Island Section Atlantic Coast Flatwoods
32.2351º, 81.1540º
8 Decatur SR 1b / Calhoun St over Flint River
East Gulf Coastal Plain Section
Southern Coastal Plain
30.9061º, 84.5886º
9 Berrien SR 76 over Withlacoochee River
East Gulf Coastal Plain Section
Southern Coastal Plain
31.1769º, 83.3225º
10 McIntosh US 17 over Darien River
Sea Island Section Atlantic Coast Flatwoods
31.3675º, 81.4364º
85
In addition to the material collected from the ten sites, two samples were prepared to
calibrate the erosion measurements and to provide reference measurements on coarse sediments.
The first was bed material collected from Peachtree Creek inside the Atlanta metro area with low
clay content. The second reference material tested was a pure commercial sand having no silt or
clay content with a median size of 1.16 mm and a coefficient of uniformity of 1.5, which is the
ratio of the diameter of the particles corresponding to 60% and 10% finer on the cumulative
particle-size distribution curve.
Laboratory Flume Measurements
Shown in Fig. 5.3 is the rectangular, tilting, recirculating flume which was utilized to erode the
core samples. It is located in the hydraulics laboratory at the Georgia Institute of Technology.
The flow in the flume can be driven by either of two variable-speed pumps for low or high flows.
The flume is 20 ft long, 1.25 ft wide, and a maximum of 1.25 ft deep. The flume bed has fixed
small gravel (d50 = 3.3 mm) to assure a fully-developed boundary layer in fully-rough turbulent
flow. At the end of the flume there is a holding tank with a volume of 67 ft3, which feeds both
pumps. Only one pump is operated at a time. A 6 in. diameter pipe circulates the flow from the
large pump to the head box of the flume, which contains an elliptical wall transition and flow
stilling devices. On the other side of the flume, a 4 in. diameter pipe feeds water from the small
pump into the head box. The small pump is a progressing cavity pump for slurries while the large
pump is a low-speed, large-impeller centrifugal pump designed for solids pumping.
86
Figure 5.3. Recirculating flume for erosion testing.
The operating variables of the flume are flow rate, slope and flow depth. The flow rate is
adjusted based on the rotational speed at which the pump is operating. Flow calibration tables
were developed in previous research (Ravisangar 2001 and Hoepner 2001). The 4 in. pump has
a working range from 0.12 – 0.52 cfs, while the 6 in. pump develops flow rates from 0.50 – 2.5
cfs.
87
The tilting flume can be set at slopes between 0 and 0.02 ft/ft. The slope is measured by a
slope counter, which counts the revolutions of the gear mechanism that raises and lowers the
flume.
The flow depth is set using either the tailgate for subcritical cases or the upstream sluice
gate for supercritical flow. The values of the normal depth were determined in an initial set of
experiments as the asymptotic approach depth of gradually-varied flows. Depths were then set
to normal depth during erosion experiments because that guarantees a uniform flow and allows
calculation of the bed shear stress by the uniform flow formula. The resulting calculated shear
stresses were found to agree with values obtained from velocity profiles measured by a laser
Doppler anemometer as shown by Ravisangar (2001). The bed shear stresses ranged from 0.4 Pa
to 21 Pa (0.008 to 0.438 lb/ft2).
To measure the erosion rate of a sample, the Shelby tube is placed below a circular
opening in the bottom of the flume, and the position of the piston used to extrude the sample as
erosion occurs is tracked by a linear variable differential transformer (LVDT). As the material is
eroded over the exposed area of the Shelby tube sample, which is a circle approximately 3 in. in
diameter, the operator pushes the sample upward with the piston, maintaining the sediment
surface level with the top of the gravel bed of the rectangular flume. The material eroded is
recorded as the mass per unit area removed per unit time based on piston displacement as a
function of time measured by the LVDT and the measured dry density of the sample. Uniform
sand was tested in the flume, and the erosion rate values were found to be reproducible, while the
measured critical shear stress agreed with the Shields’ value within the range of experimental
uncertainty (Navarro 2004).
88
RESULTS AND ANALYSIS
Observed Erosion Behavior
The observed erosion fell mainly in two of the three modes of erosion identified by
Mehta (1991). At low shear stresses, just above the critical shear stress, single particles were
dislodged over the entire bed, which is identified as surface erosion. The other type of erosion
observed in this study was mass erosion, which occurred at shear stress values greater than those
that created surface erosion. In this last case, the material failed along a plane, transporting all
the material above it. Even though these two mechanisms could be distinguished, there was not
a clear line of demarcation between them. These two mechanisms usually coexist but the
predominance of one over the other is likely to depend on the amount of fine material present in
the sediment and the size of the fine material.
Experimental Results
Among the many empirical relationships between erosion rate and shear stress for fine-grained
sediments that have been proposed, as summarized by Mehta (1991), three were explored in
detail: linear, exponential and power. Two of them, linear and exponential, showed the best
agreement with the experimental data and were included in the analysis based on their goodness
of fit and the standard error of the erosion parameters. For those relationships, seventeen
sediment samples out of the thirty-one samples on which soil classification tests were performed
had acceptable erosion rate vs. applied shear stress relationships. An acceptable relationship was
defined as one having a coefficient of determination greater than 0.50 (R2 > 0.50). This criterion
was applied to the two best regression models, which were piecewise linear and exponential
relationships.
89
The linear model was first proposed by Kandiah (1974), and it is given by
−⋅=
c
cMEτ
ττ (5.3)
in which E = erosion rate; M = erosion rate constant; τ = applied shear stress; and τc = critical
shear stress. In this study, a piecewise linear relationship was developed to better fit the data. The
exponential model has been proposed in several forms (see Mehta 1991), but the form used in
this study is given by
−⋅
⋅= c
ca
c eEE τττ
(5.4)
in which Ec = critical erosion rate; a = erosion rate constant; τ = applied shear stress; and τc =
critical shear stress.
The critical shear stress is defined in the linear model by the extrapolation of the best-fit
line for erosion vs. applied shear stress to an erosion rate equal to zero. Flow conditions under
this critical value of shear stress produce insignificant erosion. In the exponential model, a value
of negligible erosion rate has to be specified in order to find the intercept and thus the critical
shear stress, given that it is an asymptotic model. The critical erosion rate for the exponential
model is defined in this study as the value of erosion rate that gives a minimum least squares
error between the critical shear stress values found by linear regression and by exponential
regression. This value of the erosion rate was found to be 0.00190 kg/m2/s, which is acceptable
given that it is approximately twice the value of the minimum erosion rate that could be
measured.
Fig. 5.4 shows the erosion test results for the first group of sediments for which measured
erosion rates reached 1.1 kg/m2/s. The solid lines are the best-fit linear and piecewise linear
models, and the dashed lines are the best-fit exponential models. Each sample is identified by
90
the county in which it is located as given previously in Table 5-1 and by the depth of the sample
layer. Fig. 5.5 shows the measured erosion rates and their best-fit models for erosion rates up to
0.06 kg/m2/s. In some cases, the data follow a single linear relationship rather than a piecewise
linear one.
The values of critical shear stress and erosion rate constants for each sample are
summarized in Appendix A in Tables A-1 and A-2, respectively. The linear regression model
gives a standard error in the critical shear stress of 0.45 Pa compared to 0.57 Pa for the
exponential model, and so the critical shear stress from the linear model is used in subsequent
regression analyses. The relative uncertainty in the erosion rate constants for the two models is
29% for the linear model and 22% for the exponential model.
0.001900.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20
Applied Shear Stress (Pa)
Eros
ion
Rat
e (K
g/m
2 /s)
Ptree Creek
Murray 3'-4'
Towns 7' - 8'
Habersham 12' - 12' 6"
Haralson 12' - 15' 5''
Effingham 21' - 22'
McIntosh 10' - 12'
Critical Erosion
Figure 5.4. Erosion rate vs. applied shear stress relationships for sediment samples with erosion rates up to 1.1 kg/m2/s (samples identified by county and depth except for Peachtree Creek in Atlanta metro area; see Fig. 5.2).
91
0.001900.00
0.01
0.02
0.03
0.04
0.05
0.06
0 5 10 15 20
Applied Shear Stress (Pa)
Eros
ion
Rat
e (K
g/m
2 /s)
Towns 5' - 5' 6"
Towns 6' - 7'
Habersham 11' - 12'
Habersham 12' 6" - 14'
Wilkinson 36'6" -37'6"Bibb 25' - 25' 8"
Bibb 30' 8" - 31' 4"
Bibb 31' 4" - 32'
Decatur 20'-20'4"
Critical Erosion
Figure 5.5. Erosion rate vs. applied shear stress relationships for sediment samples with erosion rates up to 0.06 kg/m2/s (samples identified by county and depth; see Fig. 5.2).
Overall, the linear regression model, or piecewise linear regression model, showed good
agreement with the data. This type of model is certainly easier to manipulate and fewer
parameters have to be defined, which makes it more robust to apply in predictions. However, the
range of applicability of the linear models is more limited. For larger ranges of shear stress
values, piecewise linear models are required, although this increases the number of parameters to
specify. The location of the break point for the piecewise linear model is based on judgment
applied to the plotted data and on maximizing the coefficients of determination of each segment.
Linear models are preferred for low increments of the applied shear stresses beyond the critical
value, and they are more accurate in finding the critical shear stress values using the first part of
the piecewise relationships.
92
The exponential model describes a more realistic shape of the erosion rate function over
the full range of low to high shear stresses. This model is asymptotic to the shear stress axis and
an additional variable, the critical erosion rate, has to be defined. The critical erosion rate value
acts as an axis intercept for the model in order to find the critical shear stress. The value of the
critical erosion rate has to satisfy the physical restriction of the minimum laboratory erosion rate
that can be measured in the laboratory apparatus, as well as provide a consistent intercept for
determining the critical shear stress in the exponential model.
Results for all of the sediment properties measured for each sample are also given in
Appendix A in Tables A-3 through A-12 along with a map of the sample location, a
classification into soil types, and the relative percentage by weight of sand, silt, and clay in each
sample. The sediment properties included in the tables are dry density, void ratio, bulk density,
water content, specific gravity, organic matter, liquid limit, plasticity index, and median grain
size.
Prediction of Critical Shear Stress and Erosion Rate Constant
The best group of independent variables for prediction of critical shear stress and the erosion rate
constant of the sediment samples was determined using MINITAB statistical software to perform
simple and multiple linear regression analysis.
Among the sediment parameters measured for all the sites, the following were included in
the statistical analysis: bulk density (kg/m3), water content (decimal fraction), organic matter
content (decimal fraction), median sediment size (mm), clay content (decimal fraction) and fines
content, defined as the sum of the clay and silt content (decimal fraction).
The soil parameters that were measured but not included in the statistical analysis were
the specific gravity, the liquid limit, and plastic limit. The specific gravity was excluded because
93
of its low variability. The liquid limit and plasticity showed some correlation since, for example,
the most resistant material (Berrien Co.) had by far the largest values of liquid and plastic limit.
However, only eight of the seventeen data points were classified as plastic material, too few to
perform confident regression analysis.
In order to verify the goodness of fit of the regression models, statistics such as the
coefficient of determination, the adjusted coefficient of determination, the Mallow’s Cp, and the
estimated standard error of the model were evaluated.
Critical Shear Stress
The statistics mentioned above are utilized to assess the goodness of fit and the goodness of
prediction of a regression model in order to choose the best model for prediction of critical shear
stress. In the first multiple linear regression model considered, the predictors selected are
• bulk density (kg/m3),
• water content (decimal fraction),
• organic matter (decimal fraction),
• median size (mm),
• clay content (decimal fraction), and
• fines content (decimal fraction).
The response variable is the critical shear stress found from the intercept of the first segment of
the piecewise linear regression relationship between erosion rate and shear stress.
For the linear model applied to critical shear stress, one outlier point was identified,
which was the sample from McIntosh County. The material from this site can be considered
unusual because of its content of shells. After removing this point, fines content is the best
predictor, followed by organic matter and median sediment size. It should be mentioned that the
94
clay content was expected to be a better predictor variable than fines content given that at clay
sizes the change to platelet-like shape magnifies the interparticle forces. Also, Kamphuis and
Hall (1983), who performed initiation of motion tests on consolidated fine sediments, found that
the shear stress required to initiate motion increases with increases in the clay content. However,
for the data obtained in this study, the fines content is a better predictor variable.
Given the limited number of data points (16), it was decided to use a maximum of three
predictors in a regression model. Considering the values of the model statistics, the models with
three variables perform better, and the best-fit linear model with three predictors is given by
5037.24.617.2576.0 dOMFinesc ⋅+⋅−⋅+=τ (5.5)
in which τc = critical shear stress, Pa; Fines = decimal fraction of fine material by weight; OM =
decimal fraction of organic matter by weight; and d50 = median grain size, mm.
The performance of the regression equation of measured vs. predicted shear stress gives a
value of R2 = 0.72, and the standard error of estimate in the critical shear stress is 3.1 Pa which is
greater than the estimated experimental uncertainty of 0.5 Pa. This means that there is additional
unexplained variation that cannot be accounted for by the experimental uncertainty.
An alternative three-parameter model with about the same performance as Eq. 5.5
brought in bulk density as a replacement for median grain size. However, the regression equation
shows a decrease in critical shear stress with an increase in the bulk density, which contradicts
the results obtained by other researchers (Mehta 1991, Krone 1999, Ravisangar et al. 2001, and
Briaud et al. 2001). They have found that a more compact or denser fine material will better
resist erosion. This contradiction can be explained for the sediments tested in this study, which
are a mixture of fine and coarse sizes, by the different bulk density values of the sand and the
clay. Consider that the bulk density of pure sand is higher than for clay. In the case of pure clay
95
samples, they become more resistant as their density increases as found by other investigators.
However, for mixtures of clay and sand material having higher bulk density than clay alone, the
critical shear stress may not be higher because of the presence of sand which reduces the
interparticle forces. For this reason, bulk density is not a clear predictor variable for mixed
sediment layers.
A third regression model that was tried was a two-variable model that utilized
nondimensional variables for comparison with the Shields diagram for coarse sediments in the
form given by Fig. 5.1 with τ*c = Shields parameter = τc/(γs − γ)d50 as a function of the
dimensionless particle diameter d* = [(SG − 1)gd503/ν 2]1/3 where SG = specific gravity of the
sediment and ν = kinematic viscosity of the fluid.
Unlike Shields’ data, the natural sediment exposed to erosion around bridge foundations
is a mixture of both fine and coarse sediments with varying magnitudes of interparticle forces
that can affect the comparison. The best two-variable predictor model that includes log d* also
includes Fines content (decimal fraction) as the second variable. This analysis includes all 17
data points and explains the behavior of the sample from McIntosh Co. The regression equation
is given by
337.0*
67.2* 10586.0 −⋅ ⋅⋅= dFinescτ (5.6)
For this regression relationship, the standard error in the log of the Shields parameter is 0.3 and
R2 = 0.89. It is of interest to note that experimental data for silt-size particles (crushed quartz)
plots on the Shields diagram with an exponent on d* of −0.39 which is close to the value in Eq.
5.6 (Sturm 2001). Fig. 5.6 shows the comparison between the measured and predicted critical
Shields parameter using Eq. 5.6.
96
0.01
0.1
1
10
100
0.01 0.1 1 10 100
Predicted Shields Parameter, τ *c
Mea
sure
d Sh
ield
s Par
amet
er, τ
*c
R2 = 0.89
Figure 5.6. Comparison of the measured and predicted critical shear stress parameter using Eq. 5.6.
Fig. 5.7 shows the results plotted using the Shields diagram coordinates given previously
as Fig. 5.1. It can be observed that the measured values close to the Shields curve correspond to
sandy material with low fines content. For the special case used to calibrate the flume testing
with uniform sand material, which is similar to the material used to develop the Shields curve,
the data point falls within the upper range of the Shields curve. Either Eq. 5.6 or Fig. 5.7 is
recommended to estimate the critical shear stress value of sediment when its fines content and
size are known.
97
10% fines
30%
50%
70%
90%
0%
74%
56%52%50%
56%40%
17%29%22%
25%5%
7%1% 3%
13%10%
0.01
0.1
1
10
100
1000
0.01 0.1 1 10 100 1000Dimensionless Diameter, d * = [(SG-1)gd 50
3 / ν 2 ] 1/3
Shie
lds P
aram
eter
, τ*=
τ c/(γ
s − γ
)d50
Shields Measured
Figure 5.7. Comparison of measured data and calculated values using Eq. 5.6 plotted on Shields’ diagram format.
Erosion Rate Constant
For excess shear stress relationships, the second parameter of importance is the erosion rate
constant. This constant, called “M” in the linear model (Eq. 5.3), and “a” in the exponential
model (Eq. 5.4), quantifies the relative increase in the erosion rate as the response for an increase
in the applied shear stress above its critical value. In the linear case, M is defined as the erosion
rate predicted for an applied shear stress equal to twice the value of the critical shear stress.
Because of the relatively poor correlation found between the erosion rate constants a or M and
sediment properties, a possible correlation was also sought using slightly different expressions as
suggested by Lee et al. (1994) for the erosion rate dependence on shear stress. They proposed a
linear model of the form
)(1 csE ττ −= (5.7)
98
in which s1 represents the erosion rate predicted for a unit increment above the critical shear
stress. Similar definitions can be stated for the exponential case. The proposed erosion rate
relationship for the exponential case becomes
)(2 csceEE ττ −= (5.8)
Six possible forms of the erosion rate constants given by M, s1, log s1, a, s2, and log s2 were
studied. The best expression found for the erosion-rate constant in the linear case is using the
logarithm of the response variable, log s1, where s1 is in (kg/m2/s)/Pa. The best predictors are the
logarithm of the fines content, log Fines, where Fines is given as a decimal fraction, and the
dimensionless particle diameter, d*. The expression is given by
*0305.011.11 1000191.0 dFiness ⋅− ⋅⋅= (5.9)
which applies for values of Fines > 0. Eq. 5.9 has a coefficient of determination of R2 = 0.79, and
a standard error in log s1 of 0.42.
In Fig. 5.8, Eq. 5.9 for the erosion rate constant s1 is compared with the laboratory data
using a plot similar to the Shields diagram. The dimensionless diameter d* is plotted on the x-
axis, while on the y-axis the erosion constant s1 replaces the value of the dimensionless shear
stress. It is of interest to note that the values for s1 found by Hoepner (2001) for an estuary mud
collected from the Providence River in Rhode Island agree well with the proposed relationship.
This material had values of d* between 0.25 and 0.5, and Fines content between 84 and 99%.
99
100%
32%
10%
3%
56%
50%52%
74% 56%40%
17%
7%10%
22%
5%
29%
25%
1%
13%
3%
1% fines
estuary mud
0.001
0.01
0.1
1
10
0.1 1 10 100Dimensionless Diameter, d * = [(SG-1)gd 50
3 / ν 2 ] 1/3
Eros
ion
Con
stan
t, s 1
, (kg
/m2 /s
)/Pa.
Measured estuary mud (Hoepner 2001)
Figure 5.8. Comparison of the measured data and calculated values for erosion rate constant s1 using Eq. 5.9.
Analyzing the results in Fig. 5.8, it can be observed that for d* < 1.5, which corresponds
to the upper limit of the silt-size range, the erosion rate constant depends only on the fines
content. For larger values of d*, it depends on both fines content and d*.
The best-fit relationship found to estimate the erosion rate constant s2 for the exponential
model is linear. It relates the value of s2 with Fines and d*, and it is given by
*2 0794.060.144.1 dFiness ⋅+⋅−= (5.10)
which applies for materials with Fines content higher than 5%. Four out of the thirteen
measured relationships between erosion rate and shear stress had a poor exponential fit. The
coefficient of determination for the best-fit relationship given by Eq. 5.10 is R2 = 0.74. Although
Fines content does not seem to play a very important role according to the statistical output, it is
included as a predictor given that it has been shown to be the most important variable in the
100
analysis of both the critical shear stress and the erosion rate constant for the linear model. The
results are presented in graphical form in Fig. 5.9. The regression relationship seems to follow
the same trends as for s1 shown previously in Fig. 5.8.
50%
90%
50%56% 52%
74% 56%17%
40%29%
10%
22%
25%
13%
3%
10% fines
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0.1 1 10 100Dimensionless Diameter, d * = [(SG-1)gd 50
3 / ν 2 ] 1/3
Eros
ion
Con
stan
t, s 2
, Pa
-1.
Measured
Figure 5.9. Comparison of the measured data and calculated values for erosion rate constant s2 using Eq. 5.10.
Discussion
Given the limited experiments performed, it must be emphasized that these results are applicable
only to sediments collected from similar environments. The material studied came from bridge
foundations at depths from 1 to 35 ft deep below the top of the river bed and was usually
consolidated. The relationships that were developed to estimate the critical shear stress and
linear erosion rate constant are encouraging. The relationship found for the exponential erosion
rate constant is less reliable than the others, but it has the advantage of describing the erosion rate
over a wider range.
101
In studying the geographic distribution of the results for critical shear stress given in
Appendix A along with the sediment properties, it is difficult to discern definitive regional trends
in the data. What is clear, however, is the considerable stratification with depth of erosion and
other sediment properties for the same sample. In general, the critical shear stress in the Valley
and Ridge and the Piedmont Provinces ranges between approximately 3 and 10 Pa (0.063 and
0.21 lbs/ft2) as long as the percent fines is less than about 50%, but considerable variability is
obvious within each sample and from sample to sample. On the other hand, in the Sea Island
Section and the East Gulf Coastal Plain, larger percentages of clay can give rise to very high
values of critical shear stress. As shown in this chapter, the unifying explanatory variables for
critical shear stress are the median sediment size and the percent fines, which can be used along
with the results presented in Appendix A to provide general guidance on scour resistance. In the
case of high-risk bridges, individual site-specific erosion tests are recommended.
102
CHAPTER 6. COMPARISONS OF NUMERICAL MODEL, LABORATORY, AND FIELD RESULTS
INTRODUCTION
First, in this chapter, the numerical model is validated by presenting comparisons between
measured and computed mean velocity and turbulence kinetic energy profiles. Due to space
considerations, detailed comparisons are shown only for the Chattahoochee River site near
Cornelia and only a small sample of comparisons is included for the Ocmulgee and Flint River
sites. It should be noted, however, that for all three cases the comparisons between predictions
and laboratory measurements lead to essentially the same conclusion; namely, that the numerical
model can capture most experimental trends with good accuracy. After presenting the validation
of the numerical model the computed flowfields are analyzed in tandem with the laboratory
scour experiments to elucidate the physical mechanisms that contribute to local scour and to help
interpret the laboratory results.
Secondly, laboratory and field results are compared for a measured bank-full flow at the
Chattahoochee River site and an extreme historical flood event at the Flint River site (the 200-yr
flood resulting from Tropical Storm Alberto in 1994). These comparisons focus on the river-
model results rather than the flat-bed model results because the full three-dimensional
bathymetry is reproduced in the river models. In the course of these comparisons, the laboratory
scour and velocity measurements are validated with the field data and further insights into the
laboratory scale-up problem are discussed.
103
NUMERICAL MODEL VALIDATION
Chattahoochee River near Cornelia
The flow around a single bent of the Cornelia site bridge piers mounted on a flat bed are
extensively studied both numerically and experimentally. In the experiments, the mean velocity
and turbulence kinetic energy distributions for the flat-bed model near the bridge foundations
were measured in addition to the scour hole bathymetry at equilibrium. Before presenting the
comparisons, it is important to mention that a series of numerical sensitivity studies were carried
out in order to demonstrate that the numerical results are free of numerical errors due to
insufficient grid resolution and other numerical parameters. For that reason, calculations were
carried out on three different grid systems with different grid resolutions and different sizes of
flow domains. Comparisons of the results from these different grid systems show that all of them
agree well with each other and approach the same result. Therefore, in the following
comparisons, numerical solutions are given for only one grid system.
Fig. 6.1 shows the comparison of measured and computed streamwise velocity profiles at
various locations upstream, within, and downstream of the piers (for detailed comparison
locations see Fig. 4.5(c)). The profiles show velocity variations in the transverse, y, direction at
various streamwise locations and at three different depths. It is important to note that the
measured velocity profiles are not perfectly symmetric and uniform. Moreover, the degree of
non-uniformity in the measured profiles appears to vary with depth. On further investigation of
the measured direction of the approach velocity vectors relative to the piers, it was discovered
that there was a slight skewness of about 1.8° clockwise in the approach velocity vector relative
to the pier centerline. This may have been due to inherent construction tolerances in setting the
piers relative to the approach flow or due to a slight asymmetry in the approach flow itself. This
104
small degree of incoming flow skewness is hardly detectable in flow visualization. However, in
order to examine its effects on the flow, especially the effects on turbulence structures, flows
with different incoming directions were investigated. In the first case, the flow is aligned with
the bridge pier centerline and in the second case, the flow is skewed 1.8° clockwise.
Comparisons of the simulated and measured velocity profiles are shown in Fig. 6.1 in which the
red line depicts the aligned case while the green one corresponds to the skewed flow simulation.
Fig. 6.1 reveals that the numerical model captures most trends observed in the experiments with
very good accuracy. For instance, both the reduction of the centerline velocity as the flow
approaches the pier bent and the growth of the wake between and downstream of the piers are
predicted with good accuracy by the numerical model. It is also observed in the comparisons in
Fig. 6.1 that effects of the flow skewness can only be seen in the more downstream portion of the
bridge pier bent, with larger discrepancies in the wake region.
Figure 6.1. Comparisons of streamwise velocity profiles (location F1, F2, …, F6 left to right) at relative elevations of 0.6, 0.4, and 0.2 times the depth from top row downward (circles: lab data; red curves: aligned flow; green curves: skewed flow).
105
In stark contrast to the relatively small effect of the flow alignment on the mean velocity
distribution, the experimental and computational results reveal a rather dramatic effect of even a
small misalignment on the turbulence structure in the vicinity of the piers. Fig. 6.2 shows the
calculated and measured profiles of total turbulence kinetic energy in the vertical direction at
several streamwise locations to the left and right of the bridge pier bent (locations are marked as
P1 to P4 in Fig. 4.5(c)). A remarkable feature of the measured kinetic energy profiles, which are
shown by symbols, is the large asymmetry of the turbulence structure with respect to the
streamwise axis of symmetry of the pier bent. At the first location (P1) the measured kinetic
energy profiles to the right and left of the pier bent are nearly identical and in good agreement
with the simulations. Further downstream, however, the kinetic energy to the right side of the
pier bent rises sharply in the outer layer yielding a highly asymmetric turbulence structure. The
numerical simulations of the aligned flow case, on the other hand, yield a symmetric turbulence
structure, which is to be expected since the simulated conditions are perfectly symmetric.
However, unlike the limited effects on the time-averaged velocity distribution, the slight
misalignment of incoming flow has a considerable effect on the distribution of the turbulence
kinetic energy. As depicted by the green lines, the simulated result of the skewed flow exhibits
qualitatively the main trend observed in the data: the steep rise of turbulence kinetic energy on
the right side of the piers and the gross asymmetry of the turbulence structure.
106
Figure 6.2. Comparisons of turbulence kinetic energy (circles: lab data, red curves: aligned flow; green curves: skewed flow).
As suggested by the above results, the numerical model can capture the apparent
sensitivity of the turbulence structure to even a relatively small misalignment of the pier bent
with respect to the approach flow. Yet, significant discrepancies between the measured and
computed turbulence kinetic energy profiles remain even for the skewed flow simulation. These
discrepancies may be due to the fact that the exact state of the approach flow in the laboratory
experiment is not known. As indicated by the mean velocity profiles shown in Fig. 6.1 at the
most upstream measurement stations, the approach flow in the laboratory exbibits small but
clearly visible spanwise variations. Unless these variations can be quantified in sufficient detail
to be incorporated into the model boundary conditions it is unlikely that improved predictions of
the turbulence structure can be obtained.
Flint River at Bainbridge
The flow around a single bent of the Flint River bridge piers mounted on a flat river bed is also
studied both numerically and experimentally. In the experiments, the mean velocity distribution
and equilibrium scour depths were measured for the flat bed near the bridge piers. The first
simulations shown here are based on the initial state of the river bed in which it is flat and the
107
footings are not exposed. The following comparisons are focused on the numerical solution with
a grid discretization consisting of 4 subdomains containing approximately 1×106 elements. Fig.
6.3(a) shows the two grids around the piers and the intermediate grid connecting them. The
locations of the six cross-sections where results of the simulations are compared with
experimental data are shown in Fig. 6.3(b).
Fig. 6.4 shows the comparison of measured and computed streamwise velocity profiles at
six locations upstream, within, and downstream of the piers (sections S1 to S6). These
comparisons are similar to those for the Chattahoochee River site. The comparison between the
profiles of measured and computed velocities, at three vertical positions near the bed, shows
reasonably good agreement. The largest disparities between the computed and observed profiles
occur at section S4 between the piers at 30% of the total depth, but the wake comparisons at
section S6 are quite good.
Figure 6.3. Flint River Bridge Layout (a), and measurement cross-sections (b).
108
Overall, for the Flint River Bridge, the numerical model can capture the characteristics of
the mean velocity profiles observed in the experiments, especially the reduction in the velocity at
the centerline and the velocity profiles in the wake of the piers.
At the equilibrium scour state, the bridge footing is exposed to the flow. This change may
drastically change the flow status and the capacity for scouring; therefore, it is of fundamental
importance to study the flow with footings exposed. A new case, in which the footings along
with the bridge piers are mounted on a flat river bed, is generated to investigate the more
complex flow. As shown in the instantaneous streamlines for this simulation, depicted in Fig.
Figure 6.4. Comparisons of streamwise velocity profiles at locations from S1 to S6
shown in Fig. 6.3 (left to right) and at water depths of 0.45, 0.3, and 0.1 times the
depth from top to bottom row (circles: measurements; curves: numerical simulation).
109
6.5, the foundations of each pier have a considerable influence over the flow patterns at the bed,
producing recirculating zones behind the footings and decreasing the velocity in the wake. It is
worthwhile to note that the river bed is not flat at equillibrium scour, and the actual flow may
differ from what is presented here. Nevertheless, this simulation once again illustrates the strong
capability of the 3D numerical model to handle complex pier geometry.
Ocmulgee River at Macon
A single bent of four cylindrical piers at the Ocmulgee River bridge in Macon GA is simulated
over a flat bed, in which the solution domain is discretized in 5 overlapped subdomains as seen
in Fig. 6.6. The complexity of the flow features in this simulation required an increase in the grid
resolution in order to find a solution free of numerical errors. Satisfactory results were obtained
with a grid consisting of approximately 2×106 elements.
Figure 6.5. Snapshot of the streamlines at the Flint River bridge,
including the footings in the simulation.
110
From the results it can be observed that the flow features obtained in this simulation are
similar to the other two cases. The flow is characterized by unsteady coherent structures which
form a shear layer in the direction parallel to the pier bent. In Fig. 6.7(a), instantaneous
streamwise velocity contours show periodic vortex shedding in the wake flow. Fig. 6.7(b) shows
the typical unsteady tornado-like vortices, which appear and disappear continuously behind the
piers. Time-averaged streamwise velocity profiles are shown in Fig. 6.8.
(a) Streamwise velocity contours. (b) 3D streamlines.
Figure 6.7. Visualization of instantaneous flow field in the vicinity of the bridge piers.
(a) (b)
Figure 6.6. Geometry of the four overlapped grids around a single bent
of the Ocmulgee River bridge piers .
111
Figure 6.8. Time-averaged streamwise velocity profiles at locations S1, S2, and S3 shown in Fig. 6.6 (left to right) and at water depths of 0.5, 0.3, and 0.1 times the depth from top to bottom row.
Experimental measurements of velocity profiles for the Ocmulgee River site will be
conducted in the GDOT Phase 2 project, and detailed comparisons between experiments and
numerical simulations will be made.
FLOW STRUCTURES AND SCOUR In this section, links are established between the complex hydrodynamics induced by the bridge
piers, as obtained from the numerical simulations, and the scour patterns that result under the
same flow conditions in a laboratory experiment with the same piers installed on an erodible bed.
Since the numerical computations have assumed a fixed flat bed, the discussion herein is only
qualitative. It is aimed at underscoring the complexity of the hydrodynamic processes that drive
the scouring process in real-life bridge foundations and at providing guidance for future
extensions of the model to develop a numerical scour-prediction tool. All the subsequent
discussion will focus on the Cornelia site.
112
The equilibrium scour patterns obtained from the laboratory experiments are shown in
Fig. 6.9. As seen in this figure, a scour trench develops that surrounds the entire foundation with
the deepest scour occurring upstream of the first pier. Another region of relatively deep scour
within this trench is also observed just upstream of the last pier. It is important to note the overall
asymmetry of the scour patterns, which becomes more pronounced downstream of the first pier.
Such asymmetry is in accordance with the previously discussed impact of approach flow
skewness on the structure of the foundation-induced turbulence.
Most available sediment transport models employ the concept of critical bed shear stress,
the so-called Shields parameter, to define the threshold for incipient sediment grain motion. It
would, thus, be instructive to examine the simulated bed shear stress contours for the flat-bed
case because that would tend to identify regions in the flow where the scouring process is
initiated. The calculated time-averaged shear velocity contours are shown in Fig. 6.10(a). Two
pockets of maximum shear velocity are observed at the two upstream corners of the first pier.
The calculated shear velocity levels within these pockets are at least one order of magnitude
greater than the shear velocity levels within the rest of the foundation. This trend is to be
expected since the last three piers are embedded within the wake of the first pier and the flow in
their vicinity is, thus, dominated by large-scale, three-dimensional separation and flow reversal.
The pockets of large shear velocity correlate well with the region of maximum scour depth
surrounding the first pier.It is evident from Figs. 6.9 and 6.10(a), however, that the distribution
of bed shear stress alone cannot account for the complexity of the scour patterns observed in the
experiment. To further elucidate the role of foundation-induced hydrodynamics on scour, Fig.
6.10(b) shows contours of vertical time-averaged velocity at a horizontal plane very close to the
channel bottom (0.01H). The vertical velocity component is a good indicator of the complexity
113
Figure 6.9 Distribution of scour depth at the equilibrium state.
(a) Friction velocity. (b) Vertical velocity.
(c) Limiting streamlines.
Figure 6.10 Flow patterns near river bed.
114
and three-dimensional structure of the vortical patterns near the foundation. For example, a
pocket of negative vertical velocity component near a pier indicates that the flow along the
obstacle is directed toward the bed. For continuity to be satisfied, however, such a pocket of
downflow must be accompanied by a horizontal flow along the bed directed away from the
obstacle, which would tend to sweep bed material away from the obstacle and promote scour.
Alternatively, a pocket of positive vertical velocity around a pier suggests a vertical upwelling
along the pier away from the bed and must be accompanied by a region of horizontal flow
directed toward the obstacle. Such secondary flow patterns would tend to sweep bed material
toward the obstacle and lead to local deposition. To better illustrate these flow patterns at the
horizontal plane, Fig. 6.10(c) shows the limiting streamlines (or skin-friction lines)
corresponding to the vertical velocity contours shown in Fig. 6.10(b). As seen in Figs. 6.10(b)
and (c), the region of negative vertical velocity around the first pier is indeed accompanied by a
horizontal flow along the bed directed away from the pier. The topology of the limiting
streamlines in this region, which consists of the C-shaped separation line surrounding the
obstacle, the saddle node delineating the approach and near-obstacle flows, and the half saddle
node on the upstream face of the obstacle, is characteristic of the horseshoe vortex system
induced by the pier. Similarly, the pocket of positive vertical velocity at the downstream end of
the first pier is indeed accompanied by a near-wall flow directed toward the pier, which emanates
from the half saddle node on the upstream face of pier number 2. It is also worth noting from
Fig. 6.10(c) the complexity of the topology of the limiting streamlines around piers 2, 3, and 4,
which is characterized by the presence of pairs of saddle foci in the wake of each pier. These
saddle foci tend to sweep flow toward each pier and are thus the footprints on the bed of
vertically oriented, tornado-like vortices.
115
Juxtaposing now the near-bed flow patterns shown in Fig. 6.10(a)-(c) with the observed
scour map shown in Fig. 6.9 reveals that the region of deepest scour at the front of the upstream
pier (pier 1) correlates well with the pocket of negative vertical velocity, the associated region of
near-bed flow away from the pier, and the two pockets of maximum bed shear stress. The second
region of deep scour located at the face of the most downstream pier (pier 4) correlates well with
the pocket of negative vertical velocity even though no appreciable levels of shear velocity exist
in this region.
Another interesting feature of the scour patterns visible in Fig. 6.9 is the characteristic C-
shaped structure of the bed-elevation contours at the downstream end of piers 1 and 4, which
reveals the presence of two small ridges of local sediment deposition with less scour adjacent to
the ridges. These ridges appear to correlate well with the pockets of positive vertical velocity in
the downstream end of piers 1 and 4, thus, supporting the previous qualitative discussion on the
role of local hydrodynamics in the sediment transport processes.
As remarked at the start of this section, the discussion herein is only qualitative. The
simulated flow patterns for the flat bed case can only provide some indication as to where and
how scour will originate. The complex deformation of the channel bed in the vicinity of the
foundation, as revealed by the experiments, will undoubtedly alter the local hydrodynamics
which will in turn affect the rate of sediment transport and deposition. The discussion in this
section, however, serves to clearly underscore that simplistic sediment transport models relying
exclusively on the concept of shear stress in excess of critical bed shear stress may not be
adequate for modeling scour at real-life bridge foundations.
116
COMPARISONS OF LABORATORY AND FIELD RESULTS
Chattahoochee River near Cornelia
The comparisons in this section rely on a modeling strategy that is the outcome of the
comparisons made between laboratory scour measurements and accepted pier scour formulas in
Chapter 3. The 1:40 scale laboratory river model was constructed as a Froude-number model
with equality of y1/b values. The sediment size was selected to be 1.1 mm to obtain clear-water
scour near the maximum of V1/Vc = 1.0 at approximately the same Froude number as the
prototype for the bank-full and the 100-yr flood flows. Approach Froude numbers, Fr, do not
change very much for this range of events. The model sediment size results in a value of b/d50 =
24.5 in the laboratory at which several pier scour formulas indicate almost no effect of this
parameter. The comparisons discussed next refer to experimental run RM 5 in Tables 3-1 and 3-2
for which y1/b = 4.0, b/d50 = 24.5, V1/Vc = 0.75, and Fr = 0.30. The corresponding values of the
dimensionless parameters in the field for the bank-full event of July 2, 2003 are y1/b = 4.0, b/d50
= 1570, V1/Vc = 4.38, and Fr = 0.33.
Laboratory measurements of scour contours and velocity vectors (before scour) at a
relative height above the bed of 0.4 were shown previously in Fig. 3.10 for the bank-full flow of
13,600 cfs that occurred on July 2, 2003. The flood recurrence interval for this event is
approximately 2 years. The field fathometer measurements of bed elevation with time were
shown previously in Fig. 2.3 throughout the hydrograph for this event. The greatest scour occurs
in front of the nose of the upstream pier in agreement with the laboratory results, but there is an
obvious infilling of the scour hole on the recession side of the hydrograph after a constant
elevation is reached indicating equilibrium live-bed scour. Relatively little scour occurs on the
117
right side of the upstream pier, but measurable scour is apparent around the sides of the most
downstream pier.
Measured channel cross sections just upstream of the bridge for several flow events are
compared with the laboratory experiments in Fig. 6.11. The event of June 13, 2003 was a very
small one, but it established the reference bed elevation of 1126 ft prior to the occurrence of the
flood event on July 2, 2003. There is relatively close agreement between the field cross sections
for the events of 1961 and July 2, 2003 which had almost identical discharges. Good agreement
is also shown in Fig. 6.11 between the laboratory cross section measured after scour and the field
cross sections for these two flood events measured near the time of peak discharge. The obvious
disagreement is the occurrence of what are apparently dunes to the left of the pier for the live-
bed scour in the prototype because the laboratory model measurement was taken for clear-water
scour.
1105
1115
1125
1135
50100150200250300
Station, ft
Ele
vatio
n, ft
Experiment(Q=1.35cfs)12/12/1961(Q=13100cfs)7/2/2003(Q=13600cfs)6/13/2003
EL 1126 ft
Right BankLeft Bank
Figure 6.11 Comparison of scour in prototype and laboratory cross sections at Cornelia site just upstream of the bridge looking downstream (field events and model Run RM 5).
118
Comparisons between laboratory and field measurements of velocity to the left of the
central bridge pier are shown in Fig. 6.12 for the bank-full event of July 2, 2003. There is close
agreement between the laboratory velocities scaled up with Froude number similarity and the
field measurements made during the flood with the fixed acoustic Doppler instrument.
0
2
4
6
8
13.9 ft23.8ft33.6ft
Distance from left side of pier
Vel
ocity
, ft/s
Field measurement (7/2/2003) River model (Q=1.35 cfs)
2.3% 1.3%% diff.= 0.8%
Figure 6.12. Comparison of velocities between field and laboratory measurement at given distances from left side of the central pier bent.
The dimensionless maximum pier scour depths are shown in Fig. 6.13 for three
laboratory clear-water scour experiments with differing values of V1/Vc all less than 1.0 but with
constant values of y1/b = 4.0 in agreement with the bank-full flood event. The values of the
Froude number are shown next to each data point. The data point shown in Fig. 6.13 with a
laboratory Froude number of 0.30 is the one that represents the laboratory results that have been
compared favorably with field data in all previous figures, and it agrees relatively closely with
the prototype Froude number of 0.33. Also shown in Fig. 6.13 are the pier scour formulas of
Melville (1997) and Sheppard (2003) for clear-water scour in the laboratory with b/d50 = 24.5
119
and y1/b = 4.0. There is good agreement between the laboratory data and these two clear-water
scour formulas. However, the prototype is in the live-bed scour regime for the bank-full event
with d50 = 0.7 mm and b/d50 = 1570, which is obviously quite different than the model value.
Accordingly, the proposed live-bed scour formula of Sheppard (2003) obtained from scour data
in a large flume is compared with the field scour depth in Fig. 6.13, and the results agree
reasonably well considering that Sheppard’s formula has been extrapolated beyond the
maximum range of his data of b/d50 = 564. His large-flume data suggest that very large values of
b/d50 which occur in the field diminish the maximum clear-water scour depth with approximately
a straight line drawn by his formula between the reduced maximum clear-water scour depth and
the live-bed scour peak at which the bedforms become flat or plane bed.
0.0
1.0
2.0
3.0
4.0
5.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0V 1 /V c
d s/ b
Lab River model, b/d50=24.5Sheppard (2003), b/d50=24.5Melville (1997) , b/d50=24.5Field Measurement, b/d50=1570Sheppard (2003), b/d50=1570
0.30Fr=0.33
0.400.33
Figure 6.13. Comparison of field and laboratory measurement of scour depths and Sheppard’s equations for Chattahoochee River, near Cornelia, GA (y1/b=4.0).
120
Flint River at Bainbridge
A modeling strategy similar to that adopted for the Chattahoochee River site was applied
to the Flint River site for the historical event associated with Tropical Storm Alberto in 1994
which was a 200-yr event (107,000 cfs). In contrast to the bank-full event modeled for the
Chattahoochee River, this site allowed the modeling of an extreme flood event for comparison
with historical field measurements. The sediment size was 1.1 mm in a 1:90 scale model with a
Froude number similar to that in the field but in the clear-water scour regime. The 1:90 scale was
necessary to capture the very wide floodplains at this site. In addition, the upstream railroad
bridge and the abandoned embankment of the old highway bridge were included in the model in
order to reproduce the approach flow conditions as closely as possible (see Chapter 3). The
comparisons discussed next refer to experimental run RM 1 in Tables 3-3 and 3-4 for which y1/b
= 7.4, b/d50 = 18.8, V1/Vc = 0.6, and Fr = 0.20. The corresponding values of the dimensionless
parameters in the field for the flood event of July 1994 are y1/b = 6.2, b/d50 = 4800, V1/Vc = 5.94,
and Fr = 0.25. The value of y1/b in the model is slightly higher than in the field in order to obtain
model flow depths large enough for ADV velocity measurements; however, accepted scour
formulas show a negligible effect of this difference in y1/b on scour depths. The corresponding
values of ds/b are 1.04 in the model and 1.07 in the field.
Cross sections and velocity distributions measured in the model and the field are
compared in Fig. 6.14. The initial bed in the laboratory was leveled according to the cross
section measured in March 2001 which is similar to the cross section measured in March 2002
and also in 1980 at the location of the third pier from the left (Station 500 ft) as shown
previously in Fig. 2.15. Most of the pier scour measurements were made at this pier because it
showed the greatest scour due to Tropical Storm Alberto. The bed appears to be at an
121
equilibrium elevation near the top of the upper footing both before Alberto and then several
years after Alberto.
The laboratory model run designated as Run RM 1 in Tables 3-3 and 3-4 was repeated
and both cross sections measured after scour are shown in Fig. 6.14 as Experiments I and II.
They are virtually identical within the experimental uncertainty of scour depth measurement in
the model. When compared to the field measurement made on July 12, 1994, there is remarkable
similarity in the cross sections not only at the pier at Station 500 but also with respect to the
deposition that occurs to the right of this pier around Station 560.
-6
-4
-2
0
2
4
6
8
10
0 100 200 300 400 500 600 700 800
Station, ft
Vel
ocity
, ft/s
40
60
80
100
120
140
160
180
200
Ele
vatio
n, ft
Left (SE) edge channel Right (NW) edge channel
Jul 12, 1994 (Alberto)
Field Data (USGS)Mar 21, 2001
Velocity, ft/s
Velocity, ft/s
Experiment IElevation, ft
2D ADV 2D ADV
EL. 95.24Alberto7/12/94
Experiment IIElevation, ftVelocity, ft/s
Figure 6.14. Comparison of scour cross sections at Flint River bridge from laboratory model and Tropical Storm Alberto.
122
Measured velocities in the model scaled up by the Froude number law are also compared
with field measurements in Fig. 6.14. They are in good agreement not only between the repeated
experiments I and II but also between the laboratory and field measurements. Some discrepancy
can be seen on the right side of the cross section where field velocities are smaller than
laboratory ones, but this may be due to the buildings in the right-side floodplain that were not
included in the model because they did not impact the main pier at Station 500.
The dimensionless maximum pier scour depths are shown in Fig. 6.15 for three
laboratory clear-water scour experiments with differing values of V1/Vc all less than 1.0 but with
constant values of y1/b = 7.4 in rough agreement with the flood event. The values of the Froude
number are shown next to each data point. The data point shown in Fig. 6.15 with a laboratory
Froude number of 0.20 is the one that represents the laboratory results that have been compared
favorably with field data in Fig. 6.14, and it agrees closely with the field scour depth which has a
Froude number of 0.25. Also shown in Fig. 6.15 are the pier scour formulas of Melville (1997)
and Sheppard (2003) for clear-water scour in the laboratory with b/d50 = 18.8 and y1/b = 7.4.
There is relatively good agreement between the laboratory data and these two clear-water scour
formulas. However, as in Fig. 6.13 for the Chattahoochee River, the prototype is in the live-bed
scour regime with d50 = 0.4 mm and b/d50 = 4800, and so the proposed live-bed scour formula of
Sheppard (2003) is also shown in Fig. 6.15 even though it is extrapolated beyond its range. The
results do not agree as well as in Fig. 6.13 perhaps because no attempt has been made to correct
for the effect of the footings.
123
0.0
1.0
2.0
3.0
4.0
5.0
0.5 1.5 2.5 3.5 4.5 5.5 6.5V 1 /V c
d s/ b
River model, b/d50=18.8Sheppard (2003), b/d50=18.8Melville (1997) , b/d50=18.8Field Measurement, b/d50=4813Sheppard (2003), b/d50=4813
0.20Fr=0.25
0.27
0.24
Figure 6.15. Comparison of field and laboratory measurement of scour depths and Sheppard’s equations Flint River at Bainbridge, GA (y1/b = 7.4).
SUMMARY
In this chapter the numerical model has been verified both in terms of detailed velocity
distributions and turbulence kinetic energy. The numerical model has shown that even the
slightest skewness or nonuniformity in the approach flow tends to have a magnified effect on the
turbulence characteristics. Furthermore, the numerical model shows that shear stress alone is not
sufficient to explain the scour patterns and hence the sediment transport rates. The vertical
velocity component before scour, for example, explains much of the measured scour pattern in
the vicinity of a complex pier bent that cannot be accounted for by shear stress alone.
The field and laboratory results in this chapter suggest that in some cases modeling of
live-bed scour might be done in the laboratory in the clear-water regime by preserving Froude
124
number similarity with equality of y1/b values and with b/d50 close to 25. The apparent reduction
in scour at large values of b/d50 is modeled by V1/Vc < 1.0 in the laboratory. However, additional
continuous field measurements such as those obtaned in this project are needed to extend the
predictive range of live-bed scour formulas obtained from laboratory flume data to much larger
values of b/d50 that occur in the field.
125
CHAPTER 7. SUMMARY AND CONCLUSIONS
Field measurements, laboratory modeling, and 3D numerical modeling of scour around bridge
foundations have been successfully combined and applied to specific bridges in Georgia in order
to elucidate the physics of the scouring process and improve scour predictions. In addition,
sediments sampled at the foundations of 10 bridges in Georgia have been characterized with
respect to their erodibility which has been related to easily measured sediment properties. Taken
together, the observations and results in this report will be utilized in Phase 2 of the research to
develop a scour prediction methodology that takes into account site-specific sediment erodibility
properties, time variation of scour depths, scale-up problems of laboratory scour prediction
formulas, and insights about the physics of the flow field around bridge foundations obtained
from the 3D numerical model that can be utilized in one-dimensional modeling.
While the field data collected in Phase 1 of this research have been somewhat limited by
drought conditions, several smaller storm events have been successfully measured at the
Chattahoochee River site and the Ocmulgee River site. The Chattahoochee data obtained for a
bank-full event as well as historical data collected for Tropical Storm Alberto at the Flint River
site have proven to be quite useful in comparisons with the laboratory model data. In addition,
the field data have revealed several important aspects of the bridge scour process including:
• dynamics of live-bed scour around bridge piers in which smaller events gradually fill
remnant scour holes only to be scoured out again by larger storm events;
• simultaneous occurrence of contraction scour and local pier scour and the differentiation
of the two processes based on historical cross sections;
126
• minor cyclical scour and fill during the tidal cycle at the Darien River site with more
significant scour and fill on a seasonal time scale.
The observed simultaneous contraction and local pier scour at the Ocmulgee River site will be
studied more intensely in Phase 2 of this research in the laboratory model to compare field
measurements (mobile and fixed instrumentation), laboratory measurements, and contraction
scour predictions to distinguish between the two types of scour.
The 3D numerical model has revealed a complex flow field around natural river bridge
foundations that is unstable and highly three-dimensional. Large-scale coherent vortex shedding
exists in the vicinity of the bridge foundations with multiple vortices having axes parallel and
perpendicular to the bed. Both the river bathymetry and the presence of multiple pier bents can
influence the flow patterns considerably and need to be taken into account if realistic flow
predictions are to be obtained. The numerical model developed in this research is a powerful
engineering simulation tool for elucidating the complex flow physics of real-life bridge
foundation flows.
The numerical model was successfully validated using velocity and turbulence data from
the laboratory physical models. Using the numerical model it was possible to show that even the
slightest skewness or nonuniformity in the bridge approach flow tends to have a magnified effect
on the turbulence characteristics. Furthermore, the numerical model shows that shear stress alone
is not sufficient to explain the scour patterns and hence sediment transport rates within the scour
zone. The vertical velocity component before scour, for example, explains much of the measured
scour pattern in the vicinity of a complex pier bent that cannot be accounted for by shear stress
alone. Such secondary variables will be related to more conventional hydraulic variables
obtained from the one-dimensional model HEC-RAS in Phase 2 of the research. The insights
127
into the flow structures provided by the 3D numerical model facilitate the understanding and
interpretation of the results from laboratory experiments for scour around bridge foundations and
can provide a link to one-dimensional hydraulic variables that are more easily estimated.
The laboratory model results for scour depth were compared with accepted scour
formulas, and it was found that the Sheppard and the Melville clear-water scour formulas
provide reasonable agreement with the laboratory data except at large values of the Froude
number at which the HEC-18 formula performs better. These comparisons bring into focus the
laboratory scale-up problem in which it is apparent that proper selection of the sediment size in
the model is extremely important in order to avoid violation of similarity requirements due to the
Froude number (Fr) becoming too large and the value of the ratio of pier width to sediment
diameter (b/d50) becoming too small in the laboratory.
A laboratory modeling strategy was applied to the river models in which the sediment
size was chosen to reproduce the field value of the Froude number as closely as possible in the
clear-water scour regime while maintaining the value of b/d50 as close to 25 as possible at which
it has little influence on scour depth. This strategy was proven to be successful both for a bank-
full event measured in this study at the Chattahoochee River site and an extreme historical flood
event at the Flint River site. Very good comparisons were obtained not only for maximum pier
scour depth but also for cross-sectional changes and measured velocity distributions at the
bridge. The field and laboratory results suggest that reproduction of live-bed scour scour depths
may be achieved in the laboratory in the clear-water regime by preserving Froude number
similarity with equality of y1/b values and with b/d50 close to 25. The apparent reduction in scour
at large values of b/d50 is modeled by V1/Vc < 1.0 in the laboratory. However, additional
continuous field measurements such as those obtained in this project are needed to extend the
128
predictive range of live-bed scour formulas obtained from laboratory flume data to much larger
values of b/d50 that occur in the field. An expected outcome of this effort is that predictions of
scour for smaller bridges should follow the same formulas as larger bridges if the scaling
relationships are properly developed.
The measurement of sediment erodibility in the scour flume was successful, but the
degreee of stratification of sediment properties was greater than expected. While ranges of
erodibility parameters such as critical shear stress and erosion rate constants can be defined for
physiographic regions in Georgia, they are by no means universal but nevertheless can be useful
in providing guidance in the initial bridge foundation design to prevent possible scour failure.
For a more definitive measure of erosional strength, the critical shear stress was successfully
correlated with percent fines and median sediment grain diameter as an approximate measure of
the influence of interparticle forces on the erodibility of sediments consisting of both fine and
coarse-grained fractions. This is considered to be an important step forward in characterizing
sediment resistance to scour in scour-prediction procedures. For high-risk bridges, site-specific
tests for scour resistance such as those conducted in this study are recommended.
Based on the combined field, laboratory, and 3D numerical results obtained to date, it is
clear that a scour-prediction methodology needs to incorporate the effects of sediment scour
resistance for mixed grain sizes, time variation of scour depth and resultant sediment transport
rates out of the scour hole, explanatory hydraulic variables driving the scour process as identified
by the numerical model both before and after scour, live-bed scour processes observed in the
field, and an understanding of laboratory scale-up issues. Much of the information needed to
develop such a methodology has been obtained in the Phase 1 research, but the Phase 2 research
is expected to add needed insights into contraction scour at the Ocmulgee River site, tidal
129
processes at the Darien River and Altamaha River sites, and values of one-dimensional hydraulic
parameters after scour as well as before scour to be incorporated into scour prediction formulas.
The Phase 2 research will also provide invaluable and essential field data to validate and extend
the concepts developed thus far in this study.
130
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APPENDIX A
EROSION AND SOIL PROPERTY TEST RESULTS
136
Table A-1. Linear, piecewise linear and exponential critical shear stress values for the erosion rate vs. applied shear stress models [(1) = lower line segment, (2) = upper line segment]. Linear Exponential
−⋅=
c
cMEτ
ττ
−⋅
⋅= c
ca
c eEE τττ
Critical Erosion = 0.00190 kg/m2/s τc, Pa s.e. τc R2 τc, Pa s.e. τc R2
Sand d50=1.16mm (1) 1.03 0.15 0.95 0.38 0.20 0.95 Sand d50=1.16mm (2) 2.91 0.04 0.99 Peachtree Creek 2.18 0.43 0.92 Murray 3'-4' (1) 4.05 0.50 0.75 3.14 0.63 0.81 Murray 3'-4' (2) 5.33 0.29 0.44 Towns 5'-5'6" 17.21 0.48 0.91 17.02 0.26 0.98 Towns 6'-7' (1) 11.31 1.44 0.65 12.55 0.95 0.68 Towns 6'-7' (2) 15.62 0.48 0.84 Towns 7'-8' 6.82 0.39 0.72 4.96 0.62 0.89 Habersham 11'-12' 17.35 0.84 0.57 17.57 0.78 0.56 Habersham 12'-12'6" 3.29 0.32 0.79 1.75 0.55 0.85 Habersham 12'6"-14" 4.54 0.28 0.85 4.35 0.38 0.77 Haralson 12'-15'5" (1) 5.77 0.27 0.70 4.38 0.33 0.89 Haralson 12'-15'5" (2) 8.68 0.33 0.81 Wilkinson 36'6"-37'6" 0.44 0.14 0.98 Bibb 25'-25'8" 9.68 0.29 0.79 10.08 0.31 0.66 Bibb 30'8"-31'4" 3.32 0.34 0.73 2.36 0.54 0.79 Bibb 31'4"-32' (1) 5.11 1.00 0.65 6.32 0.56 0.85 Bibb 31'4"-32' (2) 9.45 0.98 0.76 Effingham 21'-22' 3.24 0.25 0.81 Decatur 20'-20'4" (1) 7.90 0.36 0.96 7.98 0.17 0.99 Decatur 20'-20'4" (2) 9.88 0.32 0.95 McIntosh 10'-12' 17.17 0.15 0.94 15.92 0.54 0.88 Average 0.45 0.80 0.57 0.84
137
Table A-2. Linear, piecewise linear and exponential slope coefficients for the erosion rate vs. applied shear stress models [(1) = lower line segment, (2) = upper line segment]. Linear Exponential
−⋅=
c
cMEτ
ττ
−⋅
⋅= c
ca
c eEE τττ
Critical Erosion = 0.00190 kg/m2/s
M kg/m2/s s.e. M s.e./M a s.e. a s.e./a
Sand d50=1.16mm (1) 0.063 0.007 11% 0.626 0.053 8% Sand d50=1.16mm (2) 1.81 0.11 6% Peachtree Creek 0.410 0.083 20% Murray 3'-4' (1) 0.209 0.084 40% 5.12 1.45 28% Murray 3'-4' (2) 2.45 1.95 80% Towns 5'-5'6" 0.096 0.030 32% 12.7 1.9 15% Towns 6'-7' (1) 0.022 0.009 43% 7.6 2.6 34% Towns 6'-7' (2) 0.41 0.18 44% Towns 7'-8' 3.29 1.44 44% 8.2 2.0 25% Habersham 11'-12' 0.043 0.017 39% 8.3 3.3 40% Habersham 12'-12'6" 0.309 0.080 26% 2.37 0.49 21% Habersham 12'6"-14" 0.021 0.002 10% 2.33 0.30 13% Haralson 12'-15'5" (1) 0.117 0.023 20% 3.5 0.33 9% Haralson 12'-15'5" (2) 1.60 0.38 24% Wilkinson 36'6"-37'6" 0.010 0.001 11% Bibb 25'-25'8" 0.053 0.011 21% 11.0 3.2 29% Bibb 30'8"-31'4" 0.084 0.029 35% 2.74 0.82 30% Bibb 31'4"-32' (1) 0.007 0.002 33% 2.08 0.33 16% Bibb 31'4"-32' (2) 0.048 0.019 40% Effingham 21'-22' 2.53 0.87 34% Decatur 20'-20'4" (1) 0.033 0.007 21% 6.2 0.41 7% Decatur 20'-20'4" (2) 0.192 0.043 23% McIntosh 10'-12' 2.14 0.38 18% 28.7 7.6 26% Average 29% 22%
138
Table A-3. Results of erosion tests and soil property tests on Murray County sample.
Site Murray 1'-2' Murray 2'-3' Murray 3'-4' Critical Shear Stress (Pa) >21 <3 4.05
Sediment SC-SM SP-SM SM
Group Name Silty, Clayey Sand Poorly Graded Sand with Silt Silty Sand
Color Light Brown Gray Light Gray Dry Density (Kg/m3) 1693 1695 1649
e (void ratio) 0.56 0.55 0.59 Bulk Density (Kg/m3) 1993 1963 2220
Water Content 18% 16% 35% Specific Gravity 2.64 2.62 2.63 Organic Matter 3.1% 1.6% 2.4% Liquid Limit 22% NP NP Plasticity Index 5% NP NP d50 (mm) 0.0802 0.6734 0.3112 Sand 55% 90% 75% Silt 31% 7% 18% Clay 15% 3% 7%
139
Table A-4. Results of erosion tests and soil property tests on Towns County sample.
Site Towns 5' - 5' 6"
Towns 5' 6" - 6' Towns 6' – 7' Towns 7' - 8'
Critical Shear Stress (Pa) 17.21 >21 11.31 6.82
Sediment ML MH ML SP
Group Name Sandy Silt Elastic Silt with Sand Sandy Silt
Poorly Graded Sand with
Gravel Color Gray Brown Gray Brown Gray Brown Light Brown Dry Density (Kg/m3) 1099 876 1019 1588
e (void ratio) 1.44 2.03 1.68 0.71 Bulk Density (Kg/m3) 1477 1177 1369 2079
Water Content 34% - 34% 31%
Specific Gravity 2.68 2.65 2.73 2.71
Organic Matter 3.6% 2% 2% 1%
Liquid Limit 44% 51% 41% NP Plasticity Index 12% 13% 7% NP
d50 (mm) 0.032 0.020 0.047 1.19 Sand 44% 37% 50% 97% Silt 36% 39% 33% 3% Clay 20% 24% 17% 0%
140
Table A-5. Results of erosion and soil property tests on Habersham County sample.
Site Habersham 10' - 11'
Habersham 11' - 12'
Habersham 12' – 12' 6"
Habersham 12' 6" -
14'
Habersham 20' - 21'
6" Critical Shear Stress (Pa) >21 17.35 3.29 4.54 ~2.5
Sediment ML ML SM SM SP-SM
Group Name Sandy Silt Sandy Silt Silty Sand Silty Sand
Poorly Graded
Sand with Silt
Color Light Brown Light Brown Tan Tan Gray
Dry Density (Kg/m3) 1410 1473 1366 1463 1586
e (void ratio) 0.89 0.91 0.98 0.81 0.71 Bulk Density (Kg/m3) 1819 1909 1678 1893 1962
Water Content 29% 30% 23% 29% 24% Specific Gravity 2.66 2.81 2.71 2.65 2.71
Organic Matter 5.5% 4% 2% 2% 3% Liquid Limit 35% 37% NP NP NP Plasticity Index 11% 11% NP NP NP d50 (mm) 0.031 0.043 0.153 0.163 0.265 Sand 46% 48% 78% 83% 92% Silt 32% 32% 14% 11% 7% Clay 22% 20% 8% 5% 1%
141
Table A-6. Results of erosion tests and soil property tests on Haralson County sample.
Site Haralson 12’- 15’5”
Haralson 15’5”-15’7”
Haralson 15’7"-17’
Critical Shear Stress (Pa) 5.77 >12 ~3
Sediment SM SM ML Group Name Silty Sand Silty Sand Sandy Silt Color Mustard Yellow Yellow Orange Tan Dry Density (Kg/m3) 1638 1843 -
e (void ratio) 0.63 0.45 - Bulk Density (Kg/m3) 2026 2279 -
Water Content 24% - - Specific Gravity 2.67 2.68 2.82 Organic Matter 2.0% 1.3% 3.0% Liquid Limit 35% 29% 32% Plasticity Index 9% 5% 4% d50 (mm) 0.27 0.44 0.04 Sand 71% 69% 48% Silt 27% 28% 51% Clay 3% 3% 1%
142
Table A-7. Results of erosion tests and soil property tests on Bibb County sample.
Site Bibb 25' - 25' 8"
Bibb 25' 8" – 27'
Bibb 30' - 30' 8"
Bibb 30' 8" - 31' 4"
Bibb 31' 4" - 32'
Critical Shear Stress (Pa) 9.68 ~2.5 ~16.5 3.32 5.11
Sediment CL SM SC SP-SM ML
Group Name Lean Clay with Sand Silty Sand Clayey
Sand
Poorly Graded
Sand with Silt
Sandy Silt
Color Light Brown Gray Light
Brown Light
Brown Dark Gray
Dry Density (Kg/m3) 1261 1631 1596 1316 1162
e (void ratio) 1.07 0.62 0.68 1.02 1.19 Bulk Density (Kg/m3) 1749 1949 1973 1715 1513
Water Content 39% 20% 24% 30% Specific Gravity 2.62 2.64 2.69 2.66 2.54
Organic Matter 10.3% 6.5% 6.7% 6.2% 16.4% Liquid Limit 36% NP 32% NP 39% Plasticity Index 18% NP 11% NP 12% d50 (mm) 0.0074 0.250 0.111 0.159 0.036 Sand 26% 84% 59% 90% 44% Silt 40% 9% 20% 4% 33% Clay 34% 7% 21% 6% 23%
143
Table A-8. Results of erosion tests and soil property tests on Wilkinson County sample.
Site Wilkinson 36'6”-37'6” Wilkinson 37'6”-38'6” Critical Shear Stress (Pa) 0.44 >21 Sediment SP-SM CH
Group Name Poorly Graded Sand with Silt Fat Clay
Color Tan Light Brown Dry Density (Kg/m3) 1544 1657 e (void ratio) 0.70 0.58 Bulk Density (Kg/m3) 2007 2227 Water Content 30% 34% Specific Gravity 2.63 2.61 Organic Matter 0.3% 6.6% Liquid Limit NP 51% Plasticity Index NP 23% d50 (mm) 0.1803 0.004 Sand 93% 11% Silt 3% 49% Clay 4% 40%
144
Table A-9. Results of erosion tests and soil property tests on Effingham County sample.
Site Effingham 20’-21’ Effingham 21’-22’ Critical Shear Stress (Pa) >21 3.24 Sediment SC SP Group Name Clayey Sand Poorly Graded Sand Color Gray Light Gray Dry Density (Kg/m3) 1430 - e (void ratio) 0.78 - Bulk Density (Kg/m3) 1733 - Water Content 21% 21% Specific Gravity 2.54 2.64 Organic Matter 2.2% 0.0% Liquid Limit 36% NP Plasticity Index 19% NP d50 (mm) 0.3 0.45 Sand 67% 99% Silt 15% 1% Clay 18% 0%
145
Table A-10. Results of erosion tests and soil property tests on Decatur County sample.
Site Decatur 20'-20'4" Decatur 20'4"-22' Critical Shear Stress (Pa) 7.90 ~2.5 Sediment SC SM Group Name Clayey Sand Silty Sand Color Red Brown Brown Dry Density (Kg/m3) 1761 1548 e (void ratio) 0.49 0.71 Bulk Density (Kg/m3) 2114 1887 Water Content 20% 22% Specific Gravity 2.62 2.65 Organic Matter 4.8% 0.6% Liquid Limit 28% NP Plasticity Index 12% NP d50 (mm) 0.131 0.404 Sand 60% 83% Silt 9% 3% Clay 31% 14%
146
Table A-11. Results of erosion tests and soil property tests on Berrien County sample.
Site Berrien 25'-25'6"
Berrien 25'6"-27'
Berrien 30'-30'6"
Berrien 30'6"-32'
Critical Shear Stress (Pa) >21 >21 >21 >21
Sediment CH SC SM CH
Group Name Sandy Fat Clay Clayey Sand Silty Sand Fat Clay with Sand
Color Gray Tan Light Gray Brown Gray Dry Density (Kg/m3) 1065 1246 1482 1052
e (void ratio) 1.55 1.05 0.74 1.56 Bulk Density (Kg/m3) 1698 1895 1764 1716
Water Content 59% 52% 19% 63%
Specific Gravity 2.72 2.55 2.58 2.7
Organic Matter 4.6% 6.1% 5.6% 4.3%
Liquid Limit 103% 76% 22% 114% Plasticity Index 72% 39% 2% 69%
d50 (mm) <0.001 0.084 0.144 <0.001 Sand 38% 53% 72% 26% Silt 5% 23% 10% 6% Clay 57% 24% 18% 68%
147
Table A-12. Results of erosion tests and soil property tests on McIntosh County sample.
Site McIntosh 10’-12’ Critical Shear Stress (Pa) 17.17 Sediment SC Group Name Clayey Sand with Gravel (Shells) Color Black Dry Density (Kg/m3) 1298 e (void ratio) 1.00 Bulk Density (Kg/m3) 1728 Water Content 33% Specific Gravity 2.6 Organic Matter 5.7% Liquid Limit 32% Plasticity Index 16% d50 (mm) 1 Sand 87% Silt 6% Clay 7%
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