Citation
Fine sediment erodibility in Lake Okeechobee, Florida

Material Information

Title:
Fine sediment erodibility in Lake Okeechobee, Florida
Series Title:
UFLCOEL
Creator:
Hwang, Kyu-Nam
Mehta, A. J ( Ashish Jayant ), 1944-
University of Florida -- Coastal and Oceanographic Engineering Dept
South Florida Water Management District
Place of Publication:
Gainsville Fla
Publisher:
Coastal & Oceanographic Engineering Dept., University of Florida
Publication Date:
Language:
English
Physical Description:
xix, 140 p. : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Sediment transport -- Florida -- Okeechobee, Lake ( lcsh )
Bed load ( lcsh )
Sedimentation and deposition -- Florida -- Okeechobee, Lake ( lcsh )
Turbidity ( lcsh )
Coastal and Oceanographic Engineering thesis M.S
Coastal and Oceanographic Engineering -- Dissertations, Academic -- UF
Genre:
government publication (state, provincial, terriorial, dependent) ( marcgt )
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references.
General Note:
Sponsor: South Florida Water Management District.
General Note:
"November 1989."
Funding:
This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
Statement of Responsibility:
by Kyu-Nam Hwang, Ashish J. Mehta.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
All rights reserved, Board of Trustees of the University of Florida
Resource Identifier:
21708702 ( OCLC )

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Full Text
REPORT DOCUMENTATION PAGE
1. Report No. 2. 3. Recipient's Accession No.
4. Title aod Subtitle 1. Report Date
FINE SEDIMENT ERODIBILITY IN LAKE OKEECHOBEE, FLORIDA November 1989
6.
7. Author(s) 8. performing organization Report No.
Kyu-Nam Hwang UFL/COEL-89/019
Ashish J. Mehta
9. Performing Organization Name and Address 10. project/TaskWork Unit No.
Coastal and Oceanographic Engineering Department Lake Okeechobee Phosphorus
University of Florida namics Study. Task 4.4
11. Contract or Grant No.
336 Weil Hall
Gainesville, FL 32611 13. T of Report
12. Sponsoring Organization Name and Address
South Florida Water Management District Final
P.O. Box V, 3301 Gun Club Road
West Palm Beach, FL 33402
14.
15. Supplementary Notes
16. Abstract
Resuspension of sediment at the bottom of Lake Okeechobee composed of fine-grained
material has been examined. A sediment transport model was used to simulate likely trends in the evolution of the vertical suspended sediment concentration profile resulting from wave action, and the corresponding eroded bed depth was calculated through mass balance. Requisite information on characteristic parameters and relationships related to fine sediment erodibility were derived from field sampling of bottom sediment in the lake,
and through laboratory experiments using this sediment and lake water.
Simulated sediment concentration profiles under "storm" waves exhibit an evident qualitative agreement with observed trends in profile evolution at muddy coasts. Characteristic features are the formation of a strong gradient in suspension concentration termed the lutocline, and a fluid mud layer near the bed. The concentration over approximately 80 % of the water column down from the surface is typically quite low throughout, and most of the sediment is elevated to a relatively small height above the bed. Upward entrainment of the lutocline is constrained by the submerged weight of the high concentration layer below the lutocline, and by the lack of a strong mechnisrn for upward diffusion. As expected, simulation of the "post-storm" calm, assuming no wave action, results in a depression of
the elevated lutocline and bed reformation.
17. Originator's Key Words 18. Availability Statement
Erosion
Fine sediment
Lake mud
Lake Okeechobee
19. U. S. Security Clasaif. of the Report 20. U. S. Security Classif. of This Page 21. No. of Pages 22. Price
Unclassified I Unclassified o 159 1 P




It is emphasized that measurement of sediment concentration at or near the water surface alone, neglecting near-bed high concentration suspension dynamics, can lead to an order of magnitude underestimation of the erodible bed depth. Gleason and Stone (1975) measured a surface concentration of 102 mg L-1 at a site with a water depth of 4.6 m during a storm in Lake Okeechobee and suggested bed material erosion of 2.3 mm assuming uniform water column concentration. Considering the characteristic features of the vertical concentration profile, however, the simulated results suggest that the erodible bed thickness in the lake is likely to be on the order of 2 cm corresponding to surface concentration of 102 mg L-1.
Through an operational definition of the fluidized mud layer thickness, bulk densities defining the upper and lower levels of the fluid mud layer have been determined to be 1.0023 g cm-3 and 1.065 g cm-3, respectively. Applying these values to the bottom density profiles as identified from bottom cores, the thickness of the fluid mud layer is found to range from
5 cmn to 12 cm, which is consistent with values reported by Gleason and Stone (1975).
The thickness of the fluid mud layer arising from wave action and associated rise of the lutocline have also been examined through model simulations with and without the initial presence of fluid mud over the bed. The thickness of the resulting fluid mud layer in both cases was of the same order (10 cm in the former case and 8 cm in the latter), while the average concentration of this layer in the former case was somewhat higher than in the latter case ('- 40 g L in the former case versus 20 g L-1 in the latter). During resuspension the fluid mud layer rises rapidly, with the rise of the lutocline to a certain height being dependent upon the intensity of wave action.
On the other hand, bed erosion continues to occur as long as the applied wave bottom stress amplitude exceeds the bed shear strength, thus supplying eroded sediment mass to the fluid mud layer and resulting in an increment in the concentration of this layer.
An effort has been made to establish the correspondence between the erodibile mud thickness due to resuspension during storm wave action, and the fluidized mud zone thickness as identified from bottom cores. The actual thickness of this "active" mud surficial layer at a site will of course depend on the intensity and frequency of wave action, water depth and the thickness and character of the bottom mud. The thickness of this active mud layer (fluidized mud thickness plus erodible bed thickness) in Lake Okeechobee appears to be on the order of 10 cm below the mud-water interface during calm conditions.
An evident conclusion is that accurate measurement of instantaneous vertical concentration profiles is vitally important in studies on bottom sediment-induced turbidity, and in establishing the erodible thickness of the bed by wave action. Such profiling, when carried out effectively, can also yield valuable information on the microstructure of fine sediment suspension. Furthermore, it is essential to track the evolution of the near-bed suspended sediment load, since this non-Newtonian "slurry" is usually responsible for sedimentation problems in many episodic environments, and is likely to be highly significant in governing phosphorus release during resuspension events in the lake.




UFL/COEL-89/019
FINE SEDIMENT ERODIBILITY IN LAKE OKEECHOBEE, FLORIDA
by
Kyu-Nam Hwang Ashish J. Mehta

Sponsor:
South Florida Water Management District P.O. Box V, 3301 Gun Club Road West Palm Beach, FL 33402

November, 1989

---




ACKNOWLEDGMENT

This investigation was conducted as a part of the Lake Okeechobee Phosphorus Dynamics Study funded by the South Florida Water Management District, West Palm Beach, Florida (SFWMD). The authors wish to acknowledge Brad Jones and Dave Soballe of SFWMD for their assistance and Dr. Ramesh Reddy for coordinating the University of Florida team effort. Acknowledgement is also due to Dr. Robert Kirby and Prof. Paul Visser for their principal participation in the field effort, and to Dr. Mark Ross, who provided a copy of his numerical model which is used in a modified form in this study. Thanks are extended to the staff of the Coastal Engineering Laboratory, particularly Vernon Sparkman, for help with the laboratory experiments. Graduate assistant Xueming Shen carried out laboratory core analysis.




TABLE OF CONTENTS
ACKNOWLEDGMENT ................................. ii
LIST OF FIGURES .................................... vi
LIST OF TABLES .................................... x
LIST OF SYMBOLS ................................... xii
SUM M ARY ........................................ xvii
CHAPTERS
1 INTRODUCTION ................................... 1
1.1 Significance of Problem ............................. 1
1.2 Objective and Scope ............................... 2
1.3 Outline of Upcoming Chapters ......................... 3
2 VERTICAL STRUCTURE OF SUSPENSION UNDER WAVES ......... 5
2.1 Typical Features of Concentration Profile ................... 5
2.2 Evolution of Concentration Profile ........................ 7
2.3 Erodible Thickness of Mud Bed ......................... 8
3 APPROACH TO VERTICAL TRANSPORT PROBLEM ............. 10
3.1 Governing Equation ............................... 10
3.2 Bed Fluxes .. .. ... ... ... ... ..... ... .. ... .. ... 13
3.2.1 Erosion . . . . .. . .. . . . .. . . . . . .. 13
3.2.2 Deposition ................................ 14
3.3 Settling Velocity ................................. 16
3.3.1 Free Settling ................ ............... 17
3.3.2 Flocculation Settling ........................... 19




3.3.3 Hindered Settling . . . . . . . . . . . . . . 19
3.3.4 Settling Flux . . . . . . . . . . . . . . 19
3.4 Diffusive Flux . . . . . . . . . . . . . . . . . 20
3.4.1 W ave Diffusion . . . . . . . . . . . . . . . 20
3.4.2 Stabilized Diffusion . . . . . . . . . . . . . 22
4 EXPERIM ENTS . . . . . . . . . . . . . . . . . 27
4.1 Introduction . . . . . . . . . . . . . . . . . . 27
4.2 Characterization of Sediment . . . . . . . . . . . . 27
4.2.1 Particle Size Distribution . . . . . . . . . . . . 29
4.2.2 Organic Material . . . . . . . . . . . . . . 32
4.2.3 Mineralogical Composition . . . . . . . . . . . 33
4.3 Bed Properties . . . . . . . . . . . . . . . . . 33
4.3.1 Field and Laboratory Work . . . . . . . . . . . 34
4.3.2 Bulk Density and Shear Strength Profiles . . . . . . . 36
4.4 Settling Tests . . . . . . . . . . . . . . . . . 39
4.4.1 Procedure . . . . . . . . . . . . . . . 39
4.4.2 Settling Velocity Calculation . . . . . . . . . . . 42
4.4.3 Test Conditions . . . . . . . . . . . . . . . 42
4.4.4 Results and Discussion . . . . . . . . . . . . 44
4.5 Erosion Tests . . . . . . . . . . . . . . . . . 57
4.5.1 Introduction . . . . . . . . . . . . . . . 57
4.5.2 Annular Flume . . . . . . . . . . . . . . . 57
4.5.3 Procedure . . . . . . . . . . . . . . . 58
4.5.4 Test Condition Summary . . . . . . . . . . . . 61
4.5.5 Results and Discussion . . . . . . . . . . . . . 62
5 APPLICATION TO LAKE OKEECHOBEE . . . . . . . . . . 75
5.1 Introduction . . . . . . . . . . . . . . . . . . 75




5.2 Numerical Model. .. .. .. ... ... ... ... ... ... ... .... ..75
5.2.1 Modeling Procedure. .. .. .. ... ... ... .... ... ... ..75
5.2.2 Data used for Modeling. .. .. .. ... ... .... ... ... ....79
5.3 Results and Discussion. .. .. .. .. ... .... ... ... ... ... ....85
5.3.1 Evolution of concentration profile. .. .. .. .. ... ... .... ..85
5.3.2 Erodible depth. .. .. .. ... ... ... ... .... ... ... ..87
6 CONCLUSIONS AND RECOMMENDATIONS .. .. ... ... ... ... ....97
6.1 Conclusions. .. .. .. ... ... ... ... ... ... .... ... ... ..97
6.2 Recommendations .. .. .. ... ... ... ... .... ... ... ... ..101
APPENDICES
A DESCRIPTION OF CORES FROM LAKE OKEECHOBEE.............. 103
B CONCENTRATION PROFILES FROM SETTLING TESTS..............129
C TIME-CONCENTRATION RELATIONSHIP FROM EROSION TESTS ... 135 BIBLIOGRAPHY............................................ 137




LIST OF FIGURES

2.1 Instantaneous Vertical Concentration and Velocity Profiles, an Idealized
D escription 6
2.2 Vertical Suspended Sediment Profiles Obtained before, during and after
the Passage of a Winter Cold Front at a Wave- Dominated Coastal Site
in Louisiana. (adapted from Kemp and Wells, 1987) . . . . . 7
2.3 a) Relationship Between Uniform Suspension Concentration, C., in Water Column of Depth hl, and The Corresponding Thickness, h2, of Bed of Concentration Cb; b) High concentration suspension layer between
low concentration suspension and bed . . . . . . . . . 9
3.1 A Schematic Description of Settling Velocity Variation With Suspension
Concentration of Fine-Grained Sediment . . . . . . . . . 18
3.2 Nonlinear Relationship Between Diffusive Flux, Fd, and Concentration
Gradient, '9C . . 25
az
4.1 Sediment Sampling Sites in Lake Okeechobee . . . . . . . 28
4.2 Fine-grained and Coarse (Composite) Particle Size Distributions from
Sites 1, 2, 3, 4 and 5 31
4.3 Bottom Core Sampling Sites in Lake Okeechobee (In the text a prefix
OK and a suffix VC are added to denote these sites) . . . . . 35
4.4 Bulk Density and Vane Shear Strength Variations for Site OK2VC 37
4.5 Bulk Density and Vane Shear Strength Variations for Site OKIOVC 38
4.6 Vane Shear Strength Variation with Bulk Density based on all Bottom
Core Sam ples 38
4.7 Scale Drawing of the Settling Column . . . . . . . . . 41
4.8 Grid Indexing used in the Settling Velocity Calculation Program . . 43
4.9 Concentration Profiles from Settling Test 1; Initial Concentration of 1.8
9 L 1 46
4.10 Concentration Profiles from Settling Test 3; Initial Concentration of 14.1
g L -1 46




4.11 Concentration Profiles from Settling Test 6; Initial Concentration of 23.7
9 L 1 47
4.12 Concentration Profiles from Settling Test 11; Initial Concentration of
19.9 g L .. 47
4.13 Settling Velocity and Settling Flux Variations with Concentration for
Site 1 51
4.14 Settling Velocity Variation with Concentration for Sites 2, 4 and 5 . 52
4.15 Settling Velocity Variation with Concentration for Sites 3 and 6 . . 53
4.16 Seasonal Comparison (March, 1988 versus October, 1988) of Settling
Velocity Variation with Concentration at Site 1 . . . . . . . 54
4.17 Spatial Comparison of Settling Velocity Variations with Concentration
for Sites 1, 2, 3, 4, 5 and 6 55
4.18 Speed Calibration Curves for Ring and Channel of the Annular Flume 59
4.19 Time-Concentration Relationship in Test 3 . . . . . . . . 63
4.20 Time-Concentration Relationship in Test 4 . . . . . . . . 64
4.21 Time-Concentration Relationship in Test 6 . . . . . . . . 65
4.22 Time-Concentration Relationship in Test 5 . . . . . . . . 66
4.23 Composite Erosion Rate Variation with Bed Shear Stress for Tests 1,2
and 3 at a Mean Density of 1.1 g cm-3 . . . . . . . . . 69
4.24 Erosion Rate Variation with Bed Shear Stress for Test 4 . . . . 70
4.25 Erosion Rate Variation with Bed Shear Stress for Test 5 . . . . 71
4.26 Erosion Rate Variation with Bed Shear Stress for Test 6 . . . . 72
4.27 Critical Shear Stress, re, Variation with Bed Bulk Density, PB . . 73
4.28 Erosion Rate Coefficient, em, Variation with Bed Bulk Density, PB - 74
5.1 Definition Sketch for Grid Schernatization . . . . . . . . 77
5.2 Typical Bulk Density Variation of the Bottom Mud Layer in Lake Okeechobee; Type 1 82
5.3 Typical Bulk Density Variation of the Bottom Mud Layer in Lake Okeechobee; Type 2 82
5.4 Typical Bulk Density Variation of the Bottom Mud Layer in Lake Okeechobee; Type 3 83




5.5 Typical Bulk Density Variation of the Bottom Mud Layer in Lake Okeechobee; Type 4 .. .. .. .. ... .... ... ... ... ... ... ...83
5.6 Simulated Evolution of Suspension Concentration Profile in Run 1 . 88
5.7 Simulated Evolution of Suspension Concentration Profile in Run 2 . 89
5.8 Simulated Evolution of Suspension Concentration Profile in Run 3 . 90
5.9 Simulated Evolution of Suspension Concentration Profile in Run 4 . 91
5.10 Simulated Settling of Suspended Sediment under No-Wave Condition:
Extension of Run 1. .. .. .. .. ... ... .... ... ... ... ....92
5.11 An Operational Definition of Fluid Mud Zone .. .. .. ... ... ....93
5.12 Simulated Evolution of Suspension Concentration Profile Starting with
no Initial Concentration over the whole Water Column. .. .. .. .. ..95
A.1 Bulk Density and Vane Shear Strength Variations for Site OK4VC ..121
A.2 Bulk Density and Vane Shear Strength Variations for Site OK5VC ..121
A.3 Bulk Density and Vane Shear Strength Variations for Site OK6VC ..122
A.4 Bulk Density and Vane Shear Strength Variations for Site OK9VC ..122
A.5 Bulk Density and Vane Shear Strength Variations for Site OK12VC ..123
A.6 Bulk Density and Vane Shear Strength Variations for Site OK13VC ..123
A.7 Bulk Density and Vane Shear Strength Variations for Site OK14VC ..124
A.8 Bulk Density and Vane Shear Strength Variations for Site OK15VC ..124
A.9 Bulk Density and Vane Shear Strength Variations for Site OK17VC ..125
A.10 Bulk Density and Vane Shear Strength Variations for Site OK22VC ..125
A.11 Bulk Density and Vane Shear Strength Variations for Site OK23VC ..126
A.12 Bulk Density and Vane Shear Strength Variations for Site OK28VC ..126
A.13 Bulk Density and Vane Shear Strength Variations for Site QK29VC ..127
B. 1 Concentration Profiles from Settling Test 2; Initial Concentration of 2.8
g L1.. .. .. .. ... .. ... ... .. ... ... .. ... ... ....129
B.2 Concentration Profiles from Settling Test 4; Initial Concentration of 5.0
g L1.. .. .. .. ... .. ... ... .. ... ... .. ... ... ....129




B.3 Concentration Profiles from Settling Test 5; Initial Concentration of 2.8
9 L -1 130
BA Concentration Profiles from Settling Test 7; Initial Concentration of 2.7
9 L -1 130
B.5 Concentration Profiles from Settling Test 8; Initial Concentration of 3.2
9 L -1 131
B.6 Concentration Profiles from Settling Test 9; Initial Concentration of 6.5
g L -1 131
B.7 Concentration Profiles from Settling Test 10; Initial Concentration of
13.6 g L .. 132
B.8 Concentration Profiles from Settling Test 12; Initial Concentration of 1.9
9 L -1 132
B.9 Concentration Profiles from Settling Test 13; Initial Concentration of 4.6
g L-1 133
B.10 Concentration Profiles from Settling Test 14; Initial Concentration of
11.9 g L-1 133
C.1 Time-Concentration Relationship from Erosion Test I . . . . . 135
C.2 Time-Concentration Relationship from Erosion Test 2 . . . . . 136




LIST OF TABLES

4.1 Sediment Characteristics ....... .......................... 32
4.2 Settling Test Conditions ....... .......................... 43
4.3 Values of Characteristic Coefficients and Parameters For W, and F, . 50
4.4 Erosion Test Conditions ....... .......................... 61
4.5 Values of PB, eM, and ro ................................. 72
5.1 Hydrodynamic Conditions ....... ......................... 80
5.2 Values of Ab, f, and rb ....... ........................... 85
A.1 Bulk Density and Vane Shear Strength Variations for Site OK2VC 104
A.2 Bulk Density and Vane Shear Strength Variations for Site OK4VC 105
A.3 Bulk Density and Vane Shear Strength Variations for Site OK5VC 106
A.4 Bulk Density and Vane Shear Strength Variations for Site OK6VC 106
A.5 Bulk Density and Vane Shear Strength Variations for Site OK9VC 108
A.6 Bulk Density and Vane Shear Strength Variations for Site OK10VC 109
A.7 Bulk Density and Vane Shear Strength Variations for Site OK12VC 110
A.8 Bulk Density and Vane Shear Strength Variations for Site OK13VC 111
A.9 Bulk Density and Vane Shear Strength Variations for Site OK14VC 112
A.10 Bulk Density and Vane Shear Strength Variations for Site OK15VC 113 A.11 Bulk Density and Vane Shear Strength Variations for Site OK17VC 113 A.12 Bulk Density and Vane Shear Strength Variations for Site OK20VC 115 A.13 Bulk Density and Vane Shear Strength Variations for Site OK22VC 116 A.14 Bulk Density and Vane Shear Strength Variations for Site OK23VC 116




A.15 Bulk Density and Vane Shear Strength Variations for Site OK28VC 118
A.16 Bulk Density and Vane Shear Strength Variations for Site QK29VC 119




LIST OF SYMBOLS

Ab = Horizontal water motion (amplitude) at the bottom a = Settling velocity coefficient a. = Coefficient defining critical shear stress for mass erosion a. = Coefficient defining critical shear stress for surface erosion b = Settling velocity coefficient; Minor radius of a water particle orbit bm = Coefficient defining critical shear stress for mass erosion
b, = Coefficient defining critical shear stress for surface erosion C = Sediment suspension concentration (mass/unit volume) C = Time mean concentration C, = Sediment concentration below which free settling occurs C2 = Sediment concentration corresponding to maximum settling velocity C3 = Sediment concentration corresponding to maximum settling flux Cb = Concentration of the eroded or deposited bed C, = Initial suspension concentration CD = Drag coefficient
C1 = Average concentration of fluid mud layer C1 0 = Average concentration of fluid mud layer at initial time CT = Temperature correction factor C' = Instantaneous concentration component about mean
C, = Coefficient defining critical shear stress for surface erosion D = Molecular diffusivity
d = diameter of spherical sediment particle




d25 = Sediment grain size diameter of 25 % greater than (by weight) fraction d50 = Sediment grain size diameter of 50 % greater than (by weight) fraction d75 = Sediment grain size diameter of 57 % greater than (by weight) fraction E = Turbulent momentum diffusivity F = Sediment flux Ft = Turbulent diffusion flux of sediment Fb = Vertical bed flux of sediment Fd = Vertical diffusion flux of sediment F, = Vertical erosional flux of sediment F = Vertical depositional flux of sediment F. = Vertical settling flux of sediment F.o = Maximum vertical settling flux of sediment Ft = Turbulent diffusion flux f,, = Wave friction factor G1 = Specific gravity of fluid G, = Specific gravity of sediment particle g = Acceleration due to gravity
H = Heavyside function ; Wave height h = Water depth
K = Turbulent mass diffusivity K. = Vertical mass diffusivity for neutral flow K_. = Vertical mass diffusivity for stratified flow k = Wave number k = Vertical unit vector
kj = Settling velocity coefficient k2 = Settling velocity coefficient k. = Equivalent bed roughness




L = Wave length
1 = Prandtl's mixing length m = Eroded sediment mass per unit bed area; settling velocity coefficient ml = Coefficient defining erosion rate coefficient for mass erosion N = Total number of classes n = Settling velocity coefficient; Manning's coefficient P = Percentage of sediment finer by weight p = Probability of deposition
P1 = Coefficient defining bulk density variation with bed depth p2 = Coefficient defining bulk density variation with bed depth p3 = Coefficient defining bulk density variation with bed depth p4 = Coefficient defining bulk density variation with bed depth Ra = Hydrometer reading R, = Corrected hydrometer reading R, = Reynolds number R! = Flux Richardson number R, = Gradient Richardson number St = Turbulent Schmidt number 81 = Coefficient defining surface erosion rate 82 = Coefficient defining surface erosion rate T = Wave period t = Time variable
0 = Velocity vector with cartesian components U'1 = Instantaneous component vector about mean u = Velocity component in x-direction U = Time mean velocity in x-direction




Ub = Maximum near-bed orbital velocity in x- direction u* = Friction velocity in x-direction v = Velocity component in y-direction V = Time mean velocity in y-direction W = Mass of sediment W, = Sediment settling velocity Wrn = Maximum settling velocity of sediment W~n = Minimum settling velocity of sediment W.0 = Maximum settling velocity of sediment W = Time mean velocity in z-direction z = Longitudinal cartesian coordinate direction; log average of sediment concentration y = Lateral cartesian coordinate direction z = Elevation variable Zb = Mobile/stationary fluid mud interface; eroded or deposited bed depth z/ = Thickness of fluid mud layer zfo = Thickness of fluid mud layer at initial time a = Settling velocity coefficient; stabilized diffusivity constant aw = Wave diffusivity constant ,8 = Settling velocity coefficient; stabilized diffusivity constant; wave diffusivity constant #I "= Wave diffusivity constant l = Wave diffusivity constant p = Fluid density p3 = Bulk density at upper fluid mud interface PB = Bulk density Al = Bulk density at lower fluid mud interface Pa = Sediment granular density p,, = Water density




A = Dynamic viscosity of fluid
V = Kinematic viscosity of fluid
6 = Erosion rate
Ei = Erosion resistance defining parameters c M = Erosion rate coefficient cMs = Erosion rate coefficient for surface erosion eMm = Erosion rate coefficient for mass erosion a = Wave frequency
rb = Applied bed shear stress rce = Critical bed shear stress for erosion rce., = Critical bed shear stress for surface erosion rce., = Critical bed shear stress for mass erosion rTd = Critical shear stress for deposition rcm = Maximum critical shear stress for deposition ,r,, = Minimum critical shear stress for deposition ro = Bed shear strength r = Vane shear strength




SUMMARY

Resuspension of sediment at the bottom of Lake Okeechobee composed of fine-grained material has been examined. A sediment transport model was used to simulate likely trends in the evolution of the vertical suspended sediment concentration profile resulting from wave action, and the corresponding eroded bed depth was calculated through mass balance. Requisite information on characteristic parameters and relationships related to fine sediment erodibility were derived from field sampling of bottom sediment in the lake, and through laboratory experiments using this sediment and lake water.
Simulated sediment concentration profiles under "storm" waves exhibit an evident qualitative agreement with observed trends in profile evolution at muddy coasts. Characteristic features are the formation of a strong gradient in suspension concentration termed the lutocline, and a fluid mud layer near the bed. The concentration over approximately 80 % of the water column down from the surface is typically quite low throughout, and most of the sediment is elevated to a relatively small height above the bed. Upward entrainment of the lutocline is constrained by the submerged weight of the high concentration layer below the lutocline, and by the lack of a strong mechnism for upward diffusion. As expected, simulation of the "post-storm" calm, assuming no wave action, results in a depression of the elevated lutocline and bed reformation.
It is emphasized that measurement of sediment concentration at or near the water surface alone, neglecting near-bed high concentration suspension dynamics, can lead to an order of magnitude underestimation of the erodible bed depth. Gleason and Stone (1975) measured a surface concentration of 102 mg L-1 at a site with a water depth of 4.6 m during a storm in Lake Okeechobee and suggested bed material erosion of 2.3 mm assuming

xvii




uniform water column concentration. Considering the characteristic features of the vertical concentration profile, however, the simulated results suggest that the erodible bed thickness in the lake is likely to be on the order of 2 cm corresponding to surface concentration of 102 mg L'.
Through an operational definition of the fluidized mud layer thickness, bulk densities defining the upper and lower levels of the fluid mud layer have been determined to be 1.0023 g cm-3 and 1.065 g cm-3, respectively. Applying these values to the bottom density profiles as identified from bottom cores, the thickness of the fluid mud layer is found to range from
5 cm to 12 cm, which is consistent with values reported by Gleason and Stone (1975).
The thickness of the fluid mud layer arising from wave action and associated rise of the lutocline have also been examined through model simulations with and without the initial presence of fluid mud over the bed. The thickness of the resulting fluid mud layer in both cases was of the same order (10 cm in the former case and 8 cm in the latter), while the average concentration of this layer in the former case was somewhat higher than in the latter case (- 40 g L-1 in the former case versus ~- 20 g L-1 in the latter). During resuspension the fluid mud layer rises rapidly, with the rise of the lutocline to a certain height being dependent upon the intensity of wave action. On the other hand, bed erosion continues to occur as long as the applied wave bottom stress amplitude exceeds the bed shear strength, thus supplying eroded sediment mass to the fluid mud layer and resulting in an increment in the concentration of this layer.
An effort has been made to establish the correspondence between the erodibile mud thickness due to resuspension during storm wave action, and the fluidized mud zone thickness as identified from bottom cores. The actual thickness of this "active" mud surficial layer at a site will of course depend on the intensity and frequency of wave action, water depth and the thickness and character of the bottom mud. The thickness of this active mud layer (fluidized mud thickness plus erodible bed thickness) in Lake Okeechobee appears to be on the order of 10 cm below the mud-water interface during calm conditions.

xviii




An evident conclusion is that accurate measurement of instantaneous vertical concentration profiles is vitally important in studies on bottom sediment-induced turbidity, and in establishing the erodible thickness of the bed by wave action. Such profiling, when carried out effectively, can also yield valuable information on the microstructure of fine sediment suspension. Furthermore, it is essential to track the evolution of the near-bed suspended sediment load, since this non-Newtonian "slurry" is usually responsible for sedimentation problems in many episodic environments, and is likely to be highly significant in governing phosphorus release during resuspension events in the lake.




CHAPTER 1
INTRODUCTION
1.1 Significance of Problem
The critical need to predict the turbidity in water due to fine-grained sediment suspension under wave action over mud deposits for sedimentation and erosion studies, as well as sorbed contaminant transport, is well known. Since fall velocities of fine sediment particles are very small, they can be easily transported by hydrodynamic flows such as waves and currents. The presence of these particles in the water column affects accoustic transmission, heat absorption and depth of the eutrophic zone (Luettich et al., 1989). Because these sediments also have a strong affinity for sorbing nutrients and toxic chemicals, sediments which have been deposited on the bottom may function as a source of contaminants to the water column if they are disturbed by eroding forces resulting, for instance, from wave action. An outstanding example of a water body for these problems is Lake Okeechobee, the largest shallow lake in Florida. This lake shows typical signs of artificial eutrophication mainly due to increased phosphorus loading associated with the surrounding region.
The transport processes of fine sediments are particularly important in a wave dominated environment (e. g., in shallow lakes and estuaries), since they may repeatedly settle to the bottom and be resuspended throughout the water column by periodic forces such as astronomical tides or by episodic forces such as storm events. The accurate prediction of fine sediment transport behavior, which is typically performed through numerical solutions of the sediment mass transport equation, is strongly contingent upon an understanding of the structure of the vertical profile of sediment concentration and interaction with the flow field. However, modeling of fine sediment transport is limited by the knowledge of physical mechanisms relating the response of mud beds to wave action. Waves tend to loosen the




2
mud deposit and generate steep suspension concentration gradients, making the sediment load near the bottom typically orders higher than that near the surface. Neglecting this characteristic of sediment concentration profiles under wave action can therefore lead to significant errors in calculating the associated flux of sediment mass and consequently in estimating the erodibility of mud deposit.
It is therefore highly instructive to examine the vertical structure of concentration and its interaction with the wave flow field in order to make a comparison with field observed trends on the erodible depth of deposit. Through analysis of laboratory and field measurements within a descriptive frame work for the vertical concentration profile and erodible bed depth, an attempt is made in this study to approach the problem in a manner such as to hopefully yield useful information on the depth of erosion.
1.2 Objective and Scope
The objectives of this study were as follows:
1. To simulate prototype trends in the evolution of fine sediment concentration profiles
due to fine-grained bed material load by progressive, nonbreaking wave action.
2. To estimate the corresponding depth of bottom erosion as determined by the response
of the muddy sediment deposit to eroding forces caused by waves.
3. To examine a possible connection between the erodible mud thickness thus obtained
and the fluidized mud zone thickness determined from bottom coring, with specific
reference to Lake Okeechobee.
The scope of this study was therefore defined as follows:
1. Erosion and deposition of fine sediment beds under waves was considered in a physically realistic but simplified manner in order to simulate prototype trends in concentration profile evolution.
2. Field data collection and laboratory experiments were conducted with Lake Okeechobee bottom sediment, in order to determine relevant parameters including erosion




and deposition relationships to serve as input data to simulate the concentration profile evolution and to estimate the depth of bottom erosion in a physically realistic
manner.
3. In developing the simple vertical concentration structure model, only vertical transport
fluxes were considered. Diffusive flux was determined on the basis of classical mixing length theory, introducing the effects of stratification of bulk density to diffusion. The strong variability of the settling velocity with sediment concentration was accounted
for in calculating the deposition flux.
1.3 Outline of Upcoming Chapters
Chapter 2 describes the idealized vertical structure of suspended sediment concentration profile and its evolution trend under waves. This chapter also suggests a reasonable method to calculate the erodible thickness of mud deposit as related to vertical variation of suspension concentration. In Chapter 3, the theoretical approach to the vertical transport process is briefly presented in order to develop the numerical model for determining the vertical structure of suspension concentration. The settling-diffusion equation for vertical transport is given as the governing equation, including bed fluxes, diffusion and settling. Chapter 4 presents the objectives, procedures and results from field data collection and laboratory experiments with the following themes: 1) Characterization of lake sediment through the particle size, organic material and mineralogical composition analyses. 2) Measurements of bulk density and vane shear strength to evaluate bed properties. 3) Settling velocity determination under quiescent condition. 4) Determination of erosion rate for given bed densities and bed shear stresses, using an annular flume. Chapter 5 describes the application of the vertical transport model to Lake Okeechobee, using the experimental data obtained in Chapter 4. This chapter also includes the modeling procedure used, based on the theory described in Chapter 3, as well as simulated results for the evolution of concentration profile and erodible bed thickness under waves and under no wave condition. Conclusions, recommendations for future research and miscellaneous closing comments are




4
given in Chapter 6. Appendix A presents vertical descriptions and profiles of bulk density and shear strength of core samples collected from various sites in Lake Okeechobee. Appendices B and C contain concentration profiles obtained during the settling column tests and annular flume erosion tests, respectively.




CHAPTER 2
VERTICAL STRUCTURE OF SUSPENSION UNDER WAVES
2.1 Typical Features of Concentration Profile For the fine-grained suspended sediments, a key feature of vertical concentration profiles is the occurrence of steep vertical gradients with concentration that can be orders higher near the bottom than at the water surface (Maa and Mehta, 1987). Figure 2.1 shows the instantaneous vertical concentration distribution in terms of the turbulence-mean concentration C(z, t) profile, as well as the corresponding horizontal orbital velocity u(z, t) profile of non-breaking progressive waves. Here z is the vertical coordinate and t is time. In order to focus on the various sediment transport mechanisms influencing the vertical concentration distribution, the idealized concentration profile is presented with only two significant steep concentration gradients.
As depicted in Figure 2.1, the uppermost layer is the mobile suspension layer, which has a relatively low concentration. The mobile suspension layer is differentiated from the fluid mud layer by a steep concentration gradient commonly termed the lutodline (Parker and Kirby, 1982). The lutocline is a pycnocline representing a sharp density gradient due to sediment. Formation of lutoclines is due to the entrainment of the mud/water interface resulting from the effects of shear-induced upward diffusion which is strongly stabilized by the negative buoyancy of the high concentration suspension combined with hindered gravitational settling. Below the lutocline, there is a fluid mud layer which has a relatively high concentration suspension. The lower gradient defines the cohesive bed wherein there is sufficient interparticle contact to result in a finite measurable effective stress (Parker, 1986). Within the cohesive bed, the deforming bed is separately identified from the stationary bed, since wave orbital motion penetrates into the cohesive bed, which in turn may then undergo




MWL

Mobile
Suspension
X
W Entrainment Settling
lne ormation
Fluildization Fluid Mud
Consolidation Deforming Bed
Stationary Bed
Figure 2.1: Instantaneous Vertical Concentration and Velocity Profiles, an Idealized Description
elastic deformation and subsequent fluidization (Maa, 1986). The deforming bed layer thus develops between fluid mud above and a stationary bed below.
In a general sense, three processes which govern the concentration profile are erosion, deposition and bed consolidation. For cohesive sediments, however, it is not always easy to define terms such as erosion and deposition unambiguously, since the sediment and fluid mixture does not always exhibit a drastic discontinuity between bed and suspension. For example, both gravitational settling of sediment onto the lutocline and formation of the bed by dewatering of fluid mud may be thought of as deposition type processes, while fluidization of the cohesive bed as well as entrainment of fluid mud due to hydrodynamic forcing can be considered to be erosion type phenomena. Knowledge of the sediment transport components, identified in Figure 2.1, is briefly summarized in Chapter 3.




100 1 1 1 1 1 1 1 1
Time
C (hr)
E 80 B 0 Pre-frontal
0 o 22.8)
A 24.1 Frontal
z a 68.5 Post-frontal
2 60
D
wj 40
10.1 100 101
CONCENTRATION (gL-1)
Figure 2.2: Vertical Suspended Sediment Profiles Obtained before, during and after the Passage of a Winter Cold Front at a Wave- Dominated Coastal Site in Louisiana. (adapted from Kemp and Wells, 1987)
2.2 Evolution of Concentration Profile
A representative illustration of suspension concentration profile evolution by wave action over coastal mud fiats is presented by the data of Kemp and Wells (1987), as shown in Figure 2.2. Out of the four instantaneous (turbulence-mean), vertical concentration profiles for suspended sediment, profile A represents pre-frontal condition, profiles B and C during the passage of a winter cold front and profile D post-frontal. The data were obtained over a three day period at a site on the eastern margin of the Louisiana chernier plain where the tidal range is less than 0.5 m. Wave height during front passage was on the order of 13 cm and period 7 sec. Of particular interest is the development of a near-bed, high concentration suspension layer by the frontal wind-generated waves (profiles B and C), which was previously absent (profile A). The post-frontal profile D further suggests that this layer may have persisted following the front, conceivably due to the typically low rate at which such a layer




dewaters. The suspension concentration in the upper water column was higher following the front than during the front, possibly due to sediment advection from a neighboring area of higher turbidity.
Concentration profiles qualitatively similar to those shown in Figure 2.2 have been reproduced in laboratory flume tests involving wave action over soft muddy deposits (Ross, 1988). Notable features were the development of a rapidly saturated fluid mud layer next to the bottom, the occurrence of a persistent lutocline, and relatively low concentrations in the upper column. Furthermore, the upper column profile was observed to be approaching equilibrium at a very low rate. These laboratory observations are supportive of concentration profiles measured in the field by Kemp and Wells (1987).
The elevation of the stabilized lutocline is largely determined by a balance between the rate of turbulent kinetic energy input and the buoyancy flux determined by the sediment settling rate. Diffusion due to the wave field is characteristically slow above the lutocline in the water column, so that the concentration there increases to modest levels only. It follows that surface concentrations are not necessarily representative of what occurs at the bottom.
2.3 Erodible Thickness of Mud Bed
The formation of a high concentration fluidized layer of sediment at the bottom is characteristic of wave-influenced environments. The presence of such a layer with a marked lutocline is not restricted to estuaries and coastal waters, but can also exit in fresh water lakes as reported by Wolanski et al. (1989). In lakes such layers are episodically generated, but due to relatively low rates of dewatering, they may be more common and persistent than previously thought.
Gleason and Stone (1975) reported a concentration value of 102 mg L at the water surface during a storm event in the southern part of Lake Okeechobee, Florida. By assuming the entire water column of 4.6 m depth had a vertically uniform concentration of 102 mg L-1, they reported an erodible bed thickness of 2.3 mm (see Figure 2.3a) which seems unrealistically small.




102 mg0
Cs 102 mngL Low
h1=4.6 mn Concentration
hi Cs b 20 gE Suspension
h2Cb High Concentration
h2 Suspension
T -Bed
(a) (b)
Figure 2.3: a) Relationship Between Uniform Suspension Concentration, C8, in Water Column of Depth hi, and The Corresponding Thickness, h2, of Bed of Concentration Cb; b) High concentration suspension layer between low concentration suspension and bed
On the other hand, on the basis of an examination of bottom cores from the same lake Gleason and Stone (1975) concluded that a "fluid zone" comprised of a sediment deposit of a thickness on the order of 7 20 cm probably occurs near the bed in this lak~e. Since fluidized mud is easily entrained by waves (Maa and Mehta, 1987), it is instructive to determine the depth of erosion by considering the sediment erosion /deposition caused by wave-induced bottom stress to ascertain the significance of the fluid zone in relation to turbidity generation and mud erosion potential. These issues are elaborated upon in the upcoming chapters.




CHAPTER 3
APPROACH TO VERTICAL TRANSPORT PROBLEM
3.1 Governing Equation
The temporal and spatial variations of suspended sediment concentration in the water column subjected to wave action are essentially governed by the mass conservation equation. By considering a differential control volume and equating the time rate of sediment accumulation inside the volume to the net flux of sediment through its boundaries in the cartesian coordinates (x, logitudinal: y, lateral: and z, vertical positive downwards from the water surface), the mass conservation equation for suspended sediment concentration can be written as
aC -V F (3.1)
where C(x, y, z,t) is the instantaneous sediment concentration (mass of sediment/volume of suspension) and f is the sediment flux vector. No decay term is of course needed in this equation since suspended sediment mass can be assumed to be conservative. The flux, F arises from fluid motion, molecular diffusion and sediment settling: f= 0C DVC + WCk (3.2)
where i! is the fluid velocity vector, D the molecular diffusivity (assumed isotropic), W, the settling velocity of the sediment and k the vertical unit vector.
It is usual to express Equation 3.1 in terms of time averaged values. In turbulent flow both fluid velocity and sediment concentration are random variables and these may be separated into (ensemble) mean and fluctuating components:
0 = 0 + 0' (3.3)




11
C = + C' (3.4)
Inserting these terms into Equation 3.2 and averaging over time results in
F= lC + U'C' DVC + W,Ck (3.5)
The second term on the right of this equation represents flux by turbulent movement. By analogy with the molecular diffusion, the turbulent diffusion flux (Ft) is commonly assumed to be proportional to the gradient of mean concentration:
F = U7c, = -. -VC (3.6)
where k is a diffusivity vector with cartesian coordinate components (K., Ky, K.). By adding the flux due to the turbulent diffusivity, the time averaged Equation 3.1 becomes a__C_ = -V(17C DVZ K. VZC + WZC k) (3.7)
at
Since turbulent diffusivity is much greater than molecular diffusivity, the terms corresponding to the latter are usually neglected in the above equation (McCutcheon, 1983). By rearranging Equation 3.1, the following reduced equation is obtained ac a (w'?c)_ V
+ U VC+ =I?) = VI (3.8)
at
which can also be expanded as
az azU a- a[(w, + vi)J a2U aU a z (3.9)
O-'- X +u +V + -a Z KZ 2 + -2 +K-2
+~a aza(39
Since the present analysis is concerned with the vertical structure of sediment concentration, only the vertical transport terms need to be evaluted. In fact, Ross (1988) shows through non- dimensional scaling that in a typical coastal settling the horizontal and vertical advection terms and horizontal diffusion terms can be neglected in a simplified analysis. This allows Equation 3.10 to be reduced to aC a-(Fd + F.) = -(K. C W,C) (3.10)
at az az az




12
where the overbars (denoting time average values) have been omitted. Equation 3.10 implies that the two most important terms affecting temporal changes in concentration are the vertical gradient in gravitational settling flux, F,, and upward diffusive flux, Fd. Since advective effects have been neglected in this equation, the treatment inherently becomes somewhat restrictive as a result. However, it is advantageous to highlight the role of vertical mass fluxes in simulating wave-induced turbidity.
Boundary conditions at the water surface and sediment bed must be defined for the solution of Equation 3.10.
Surface boundary condition
At the water surface, z = 0, the net zero flux condition is essential so that F(O,t) = Kac
K5-) I, -W.C 1,0= 0 (3.11)
This means there is no net transport across the free surface and, therefore,
diffusion flux always counterbalances the settling flux.
Bed boundary condition
At the sediment bed, z = zb, it is essential to define a bed flux term, Fb
(mass of sediment per unit bed area per unit time) as concerns erosion (F,) and deposition (Fp) fluxes. Consequently, the bed boundary conditions are specified
as
Fb(Zb,t) F, Fp (3.12)
& -" Fd I., Fp --F. (3.13)
The magnitudes of Fe and Fp are typically based on bed shear stresses relative to threshold erosion and deposition shear stress values, respectively. It is evident then that the characteristics of the concentration profile are quite sensitive to the time histories of erosion and deposition, since these represent the source or
sink to the total mass in suspension.




13
3.2 Bed Fluxes
The bed fluxes are the overall source and sink components of sediment mass in the evolution of the vertical suspension profile, corresponding to the deposition flux, F,,, and the erosion flux, F,. In the natural environment, it is often difficult to separately identify the phases of the deposition and those of the erosion as a consequence of the time-dependent nature of the flow field. For the purpose of mathematical modeling, however, deposition and erosion of fine cohesive sediment must be provided as separate, bed shear stress dependent, relationships.
3.2.1 Erosion
The erosional behavior of a mud bed depends on four principal factors: physico-chemical properties of the mud, chemical properties of the eroding fluid, flow characteristics, and bed structure (Parchure and Mehta, 1985). Bed erosion occurs when the resultant hydrodynamic lift and drag forces on the sediment at or below the bed interface exceed the resultant frictional, gravitational and physico-chemical bonding forces of the sediment grain or particle.
Erosion of cohesive sediment beds can be classified in two modes, surface erosion and mass erosion (Mehta, 1986). In the former mode, erosion occurs by separation of individual sediment particles from the bed surface as the hydrodynamic erosive forces exceed the frictional, gravitational and cohesive bed bonding forces. In the latter mode, the bed fails at some level beneath the bed surface where the bulk shear strength is unable to withstand the induced stress. Sometimes, in this case, erosion occurs by dislodging the large pieces of the soil.
Surface erosion is the typical mode in low concentration environments with mild to moderate flow conditions. At higher concentrations, which usually take place under more severe flow conditions, mass erosion often becomes dominant. This type of erosion is preceded by bed fluidization, under erosive flow conditions, in which a large degree of soil structural breakdown occurs. Such behavior is particularly evident under oscillating flows




due to waves (Alishahi and Krone, 1964), and erosion occurs to a depth where the bed shearstrength and the bed shear stress are equal.
Through the bed scour process, which results in decreasing bed elevation, erosion continues until the applied shear stress acts on the bed layer with equal or higher bed shear strength. Typically in prototype environments, the bed shear strength generally increases with depth in the upper few centimeters and it becomes comparatively uniform over depth below that level.
The time rate of increase of suspended sediment mass per unit bed area, m, may be described in a functional form as
F, = am = f(rb r,61,621,... ,N) (3.14)
where rb is the bed shear stress, r, the bed shear strength and ri are other erosional resistance defining parameters. Equation 3.14 implies that the erosion flux is mainly determined by the excess shear stress, Irb r.
Expression for the erosion flux for surface erosion under wave action (Maa, 1986) is given as
F.)m r-e (3.15)
Tee
where eM is the erosion rate when rb = 2r., and re = r, is the critical shear strength for surface erosion. Since shear strength of a uniform bed does not vary with depth, the erosion flux (Fe) remains constant, represented by eM, under a constant rb. Equation 3.15, although obtained from surface erosion studies, may be used for simulating mass erosion in an approximate way. For mass erosion, the rate coefficient, eM, is typically much larger than that for surface erosion under comparable conditions and must be evaluated either experimentally or by calibration against available data for specific eroding conditions.
3.2.2 Deposition
The rate of deposition, Fp, is obtained from (Mehta, 1988b) dm
Fp "- dt =-_pW, (3.16)




15
where p is defined as the probability of deposition, W, is the settling velocity and C is the near-bed suspended sediment concentration. The probability of deposition, p, is described by
p= H(l (3.17)
Ted
where rb is the bed shear stress, red is a critical shear stress for deposition and H(-) is a heavyside function represented as H = 1 when rb < red and H = 0 when Tb Trcd.
The concept of deposition probability, originally attributed to Krone (1962), implies that deposition occurs through the sorting of sediment aggregates which occurs because of the high rates of flow shearing near the bed boundary. When the aggregates are strong enough to withstand the near-bed shear stress, they stick to the bed and, if not, they are disrupted and resuspended.
For non-uniform sediment the settling velocity is usually represented by its distribution, 4(W,), and its dependence on suspension concentration is considered on a class by class basis. Integrating Equation 3.16 under these conditions, Mehta and Lott (1987) suggested the following solution for the instantaneous concentration (C(t)) C N rb Woen aWsl
C .O(Wj)exp-H[1 Tt ) -- (3.18)
where
eln( ) (3.19)
ln()
and C, is the initial suspension concentration, N is the total number of classes, 4(W) is the frequency distribution of settling velocity with maximum value Wern and minimum value Won, h is the water depth, and r, and rn are the maximum and minimum values, respectively, of the critical shear stress for deposition, rTi.
For rb ? rcm no initially suspended sediment will deposit, while for rb _< Tcn the entire mass of suspended material will finally deposit. A consequence of settling by class is that for Tn < Tb < rcm a fraction of the initially suspended sediment for which r < rb will not deposit at steady state. A further consequence is that the size of the particles remaining in suspension will differ from the size in the deposit at steady state.




16
If the properties of the settling sediment are uniform, then N = 1 and r, =cm --= r Consequently Equation 3.18 reduces to
C = b W,
- exp [-H(I (3.20)
A typical value for red is considered to be 0.1 N m-2 (Mehta, 1988b). The settling velocity, W,, is the critically important parameter in specifying Fp, and is discussed further in the following section.
3.3 Settling Velocity
The settling velocity of cohesive sediment strongly varies with concentration in suspension. Moreover, the settling velocity is a function of the suspension and not exclusively of the sediment (Mehta, 1988a).
Aggregation occurs as a consequence of interparticle collision and cohesion of particles. Cohesion depends primarily on the mineralogical composition and the cation exchange capacity of the sediments (van Olphen, 1963). Collision frequency is dependent on Brownion motion, fluid shearing, and differential settling. Among these facters contributing to aggregation, fluid shearing seems to be the most important. Differential settling, however, becomes the most dominant factor under quiescent settling conditions such as at the time of slack water in estuaries (Mehta, 1988a). Brownion motion in natural environments is the least significant mechanism of the three (Krone, 1962).
Aggregated sediments or flocs have peculiar characteristics which differ from those of primary individual particles. Their relative particle density is reduced by the interstitial trapped water, and this causes a reduction in settling velocity. However, their shape and size become more spherical and larger with correspondingly reduced drag. Since the reduction in drag and increased size are much more significant than the decrease in density, the settling velocities of the flocs are substantially higher than those of individual particles.
Figure 3.1 is a descriptive plot of the relationship which may typically be found between the settling velocity, W., and the suspended sediment concentration, C. Also shown is the variation of the corresponding settling flux, F. = W8C. The settling velocity regime can be




conveniently divided into three sub-ranges depending upon the concentration. These are identified as free settling, flocculation settling and hindered settling. A short description of the physical characteristics of each regime is given below.
3.3.1 Free Settling
Free settling occurs in the range of C less than C1 as identified in Figure 3.1. In this range the particles or aggregates settle independently without mutual interference and the settling velocity no longer depends on concentration. For cohesive sediments, the upper concentration limit, C1, is considered to be in the range of 0.1 to 0.3 gL-1 (Mehta, 1988a).
The terminal velocity of individual sediment particles is determined by a force balance between drag and net negative buoyancy. For a spherical particle of diameter d, the settling velocity over the entire range of Renolds number, R,, is expressed as W2= 4 gd (pa p.) (3.21)
3 CD p.
where CD is the drag coefficient, g is the gravity acceleration, and pa and p,,, are sediment and fluid densities, respectively.
In the Stokes range (X~ < 0.1) the drag coefficient is given by
CD = 24(3.22)
and the settling velocity is given by Stokes law (Vanoni, 1975) W- gd2 (pa p.) (3.23)
18v p,,
where v is the kinematic viscosity of the fluid. For large R~, CD is still a function of R, but cannot be expressed analytically.
The influence of the particle shapes on the settling velocity is typically expressed by an effective particle diameter. As this diameter is used, Equation 3.23 can be considered to be valid for the fine sediment in dispersed or flocculated conditions (Ross, 1988).

I




C, C2 C3

CONCENTRATION

C4;
Negligible Settling

Figure 3.1: A Schematic Description of Settling Velocity Variation With Suspension Concentration of Fine-Grained Sediment




3.3.2 Flocculation Settling
Between concentrations C, and C2, identified as the flocculation settling range, increasing concentration leads to increasing interparticle collision and consequently enhanced aggregation. This in turn means that the settling velocity increases with concentration due to the formation of stronger, denser and possibly larger aggregates.
In the flocculation settling range, the typical relationship of the settling velocity to the concentration is
W.= klC* (3.24)
Theoretically, a is 4/3 as indicated in Figure 3.1, although the actual value typically varies between about 0.8 and 2 (Krone, 1962; Mehta, 1988a). The proportionality coefficient,
kcan vary by an order of magnitude depending upon sediment composition and flow environment.
3.3.3 Hindered Settling
At concentrations in excess of C2, the occurrence of an aggregate network hinders the upward transport of interstitial water. Consequently, W, decreases with increasing C (Kynch, 1952) as indicated in Figure 3.1. This is commonly termed hindered settling.
The general expression for the settling velocity in the hindered settling region is
W, = W..[l k2(C C2)1" (3.25)
where W,, is the maximum settling velocity that corresponds to C2, k2 is the inverse of the concentration in excess Of C2 at which W, = 0 and theoretically 6 is 5. At concentrations greater than C4 there is negligible settling.
3.3.4 Settling Flux
The behavior of the settling flux, F., is also shown in Fig. 3.1. Although the settling velocity decreases at concentrations in excess of C2, F, increases with C up to C3 where it attains a peak value of F,,. This is due to the minuscule decrease of settling velocity




20
between C2 and C3 in comparison with the increase of concentration. At values of C higher than C3 the flux also decreases relatively rapidly with increasing C.
3.4 Diffusive Flux
3.4.1 Wave Diffusion
There have been many attempts to estimate the mass diffusivity (or eddy diffusivity), K, as related to the momentum diffusivity (or eddy viscosity), E. Analogous with the dynamic viscosity u, in Stokes' law for laminar flow, momentum diffusivity for the Reynolds stress in turbulent flows is defined by
IV. = -PU:U;. = (3.26)
where rij are the components of the turbulent shearing tensor, puu. are the components of the Reynolds stress tensor, p is fluid density, and Eij represent the components of the momentum diffusivity tensor. If turbulence is isotropic, Eii = Ei= 0 and E1, = E = E. It should be noted that E is approximately proportional to the first power of the mean velocity Ui, since viscous forces in turbulent flow are approximately proportional to the square of the mean velocity rather than to its first power as in laminar flow (Schlichting, 1979). Consequently, E is not a property of the fluid like viscosity (p) for laminar flow, but is a property of the flow and depends on the mean velocity. The ratio between mass (K) and momentum (E) diffusivities is commonly expressed by the turbulent Schmidt number St=E (3.27)
For many fine sediment related practical applications it may be assumed that St = 1 (Teeter, 1986). Consequently, this means the turbulent momentum diffusivity can be taken to be
equal to the mass diffusivity.
The most commonly applied expression of vertical variation in mass diffusivity for
turbulent unidirectional flow was developed by Rouse (Vanoni, 1975). Under wave action, however, the expression for the mass or momentum diffusivity has not been fully clarified yet.
Since the oscillation of waves plays an important role in the diffusion process, the solution for




21
the diffusivity problem becomes more complicated. Kennedy and Locher (1972), Hwang and Wang (1982), and Maa (1986) have reviewed currently popular expressions for diffusivity under waves. There seems to be little consistency in the forms. Although most investigators have treated diffusivity as constant, laboratory experiments suggest that diffusivity varies with depth in the water column (Bhattacharya, 1971).
A plausible expression for the diffusivity under waves is given by Homma et al. (1962). By direct analogy to the mixing length theory, they gave the following expression: K -(3.28)
where P is a empirical constant, b is the minor radius of a water particle orbit, u is the horizontal component of orbital velocity, and z is the vertically downward negative at the water surface. As pointed out by Kennedy and Locher (1972), however, several shortcomings have been found in this expression. Again, Homma et al. (1965) presented a modified equation, introducing a mixing length, 1, and following the hypothesis of von Karman in the form
au
= I A-a (3.29)
Since in the linear wave theory u is given as H cosh k(h + z) (3.30)
u 2- sinh kh
diffusivity is calculated as
Ha sinh3 k(h + z)
K = 62 k sinh kh cosh2 kh(h + z) (3.31)
where 62 is a constant and equal to #2/2, H the wave height, a the wave frequency, and k the wave number.
Another plausible expression is given by Hwang and Wang (1982). They indicate, in the determination of diffusivity under wave field, Prandtl's mixing theory may not be applicable due to the large scale of the wave motion. Emphasizing the dominant role of the vertical components of wave induced particle velocity in the diffusion process, they assume that




22
diffusivity is proportional to the vertical velocity component of wave motion as well as the vertical excursion of the water particle, thus expressing the diffusivity as K = a w(z) 2b(z) (3.32)
where a, is a constant and w(z) is the vertical orbital velocity. Again using linear wave theory, w and b are given as
= Ha sinh k(h + z) (3.33)
w = 2 sinh kh
b = H sinh k(h + z) (3.34)
2 sinh kh
and substituting Equations 3.33 and 3.34 into Equation 3.32, the following expression for K is obtained
K = cwaH2sinh k(h + z) (3.35)
2 sinh2 kh
This equation is considered as a promising expression, based on energy dissipation consideration, for diffusivity under wave action (Ross, 1988). Thimakorn (1984) also gave a diffusion coefficient similar to that given by Hwang and Wang (1982) to predict vertical concentation profiles for the suspension of natural clay in a wave flume.
It should be noted that Equation 3.35 is not applicable inside the wave boundary layer. Effects of the boundary layer next to the bed greatly increase the vertical mixing under waves due to the relatively large velocity gradients and shear (Neilson, 1979). However, diffusion in this layer is often neglected since it is very small (Maa, 1986). Outside the boundary layer, the velocity amplitude gradients increase with distance above the bottom to a maximum at the surface. This is the basis of Equation 3.35 given above.
3.4.2 Stabilized Diffusion
Suspended fine sediments increse the bulk density of suspension and lead to the vertical variation of suspension density. Bulk density, PB, is related to suspension concentration, as
PB =P + C(1 ) (3.36)
P "




23
where p,, and p, are the water and sediment granular densities, respectively. When the bulk density increases upwards the stratification is stable and it becomes unstable when the density variation is reversed.
Stratification due to bulk density variation alters the vertical fluid momentum and mass mixing characteristics. Furthermore, the diffusivities of momentum and mass are not affected in the same manner, the former usually having larger values (French, 1985; Oduyemi, 1986). In the case of flow with stable density stratification, vertical diffusion of mass and momentum are impeded because the stabilizing gravitational force of sediment suspension acts against the destabilizing shear induced force. If the density gradient is large enough, upward diffusion can be largely suppressed and will result in the formation of a stable interface (lutocline) with pratically no mixing between two layers.
For turbulence under conditions of local equilibrium, the most obvious measure of stability is given by the flux Richardson number (Abraham, 1988) Rf, which represents the mixing efficiency (the efficiency of the conversion from turbulent kinetic energy to potential energy):
Rf = (3.37)
PB OZ) S)
where Rj is the gradient Richardson number defined as Z (3.38)
PB (10U)2
where g denotes gravity acceleration, and z represents the vertically downward positive axis. Positive values of R! indicate stable stratification, negative values denote unstable stratification, and R/ = 0 corresponds to a neutral (non-stratified) condition. The dimensionless quantity R! clearly determines the relative role of buoyancy in the generation of turbulent energy. In the case of R! < 0, turbulent energy is increased and for Rf > 0, buoyancy becomes negative, indicating that kinetic energy is lost. If a positive Rf becomes large enough, it leads to complete suppresion of all turbulence. For simplicity of treatment in this study, the turbulent Schmidt number, St, will be assumed to be equal to one, so that Rf =R.




24
Classical phenomenologically based forms for mass diffusivity in stratified flow are typically of the Munk and Anderson (1948) form as K. = K. (3.39)
where K, and K,, are the vertical mass diffusivities for stratified and neutral flows, respectively, and a and P are generally non-negative empirical constants. Note that for positive a and P, increasing density gradient (aP.) leads to increasing R and consequently decreases K, relative to K,,. It means that stratification acts to reduce diffusion by damping.
Incorporating gravitational stabilization in wave diffusivity induces a high degree of non-linearity between the diffusive flux, Fd, and the vertical concentration gradient, W. The diffusive flux is expressed as
Fd=-.aC (3.40)
ac
which indicates direct dependence of Fd on -O-. In the presence of density stratification, by substituting Equation 3.38 into 3.39, the diffusive flux becomes Fd "" &R aC (3.41)
(I1 -t/P)- az
From Equations 3.36 and 3.38, it is obvious that R in the above equation is a direct function of concentration gradient, -. by virtue of the bulk density gradient term, -. As a result, Equation 3.41 indicates that if P is not zero the diffusive flux is inversely proportional to 9Z due to R, term as well as directly dependent on Due to this fact the diffusive flux is nonlinear in concentration gradient.
Figure 3.2 shows a plot of negative Fd versus 3- for the coefficient sets given by Ross(1988). As observed in the figure, the flux initially increases with low values of ac ax )
reaches a maximum and then slowly decreases. For very high values of c, the gradient of the diffusive flux, 4Fd/a(4) becomes zero and, with stabilized perturbations and local minima in mixing, a lutocline is developed in the vertical concentration profile. Consequently, the formation of lutocline is strongly related to the nonlinear dependence of Fd on 9Z Since the sediment settling acts against the vertical mixing, the growth and stability of




0.004
E
m 0.003
LO
X Kn
MK K .
. (1+13.33 R, )1.5
z 0.002
0
0 0.001 Kz = (1+4.17 R ) 2
LL.
U
W 0.001 (+.7R)
0
W
z
0.000 I I i I i l l I
0.0 0.2 0.4 0.6 0.8
CONCENTRATION GRADIENT "z (kg ni4)
Figure 3.2: Nonlinear Relationship Between Diffusive Flux, Fd, and Concentration Gradient, ac
Lz




26
the lutocline is further enhanced. This implies that lutoclines can be much more persistent in high sediment environments than other types of pycnoclines.




CHAPTER 4
EXPERIMENTS
4.1 Introduction
Field data collection and laboratory experiments were performed to determine the characteristic parameters and relationships related to the bottom fine sediment erodibility under the wave effects in Lake Okeechobee. These experiments consisted of characterization of the sediment, bed property tests, settling tests and erosion tests. Settling tests were carried out to determine the relationship between settling velocity and suspension concentration, while erosion tests were conducted to obtain relationships between the erosion rate, bed shear stress and bed density.
4.2 Characterization of Sediment
The identification of important factors characterizing the physico- chemical properties of the sediment is basically related to the prediction of cohesive sediment tranport. Mehta et al. (1986) specified essential properties of cohesive sediment in terms of grain size, mineralogical composition, percentage of organics, and the cation exchange capacity. In this section, these properties of sediment particles, except the cation exchange capacity, are discussed following a brief description of methodology for each test.
To specify the characteristics of fine sediment in Lake Okeechobee, samples were taken from the bed in March 1988 at five locations, sites 1, 2, 3, 4 and 5, identified in Figure 4.1. These samples were also used in the settling and erosion tests. Mud samples from site 1, 3 and 6 were additionally collected in October 1988 to supplement the spatial representation, and to evaluate possible effects of seasonal variations of settling properties. Water depths at each site were 3.96 m at site 1, 4.57 m at both sites 2 and 3, 4.88 m at site 4, 4.27 m at




Date of Mud Collection

Figure 4.1: Sediment Sampling Sites in Lake Okeechobee




29
site 5, and 3.35 m at site 6. The mud samples were collected by using a grab sampler and brought to the Coastal Engineering Laboratory of the University of Florida.
The mud samples were first separated into coarse and fine-grained fractions by wet sieving through No. 200 Tyler sieve with an opening of 74 pm. This procedure was necessary due to the presence of extraneous large matter in the sediment. It was found that finegrained material accounted for between 75 % to 90 % of the material. This means that the material was almost entirely in the fine size range.
4.2.1 Particle Size Distribution
The fine-grained fractions from all five locations were subjected to standard hydrometer test to obtain the grain size distribution (ASTM, 1987). The hydrometer test is a widely used method for estimating the soil particle size distribution ranging from the opening size of No. 200 sieve to around 0.001 mm. A modification was made so that the sediment was not dried initially, because Krone (1962) showed that redispersion of the flocculated sediment, once dried, remained incomplete. Therefore, the sediment used for the test was dried after finishing the hydrometer test in order to determine the total dry sediment weight required for the calculation of particle size distribution.
The procedure used for the hydrometer test is as follows:
1. A sufficient amount of wet mud was taken in a graduated cylinder (1000 ml) so that
the dry weight of the sediment was about 50 g and was mixed with 125 ml of 4 %
Calgon solution in order to disperse the sample easily.
2. The sediment mixture was allowed to stand about 16 hours, and then the sample was
dispersed by a mixer for 3 minutes.
3. The entire mixture was transferred to the sedimentation cylinder. Distilled water was
added to fill the cylinder to the 1000 mnl mark. A control cylinder was prepared and
filled with distilled water and 125 ml of the 4 % Calgon solution.




30
4. In order to mix the contents well, the cylinder of sediment suspension was carefully
shaken. Hydrometer readings, Ra, were taken after 2, 5, 15, 30, 60, 250, 1440, 2880
and 4320 minutes.
Corrected hydrometer readings, R,, were computed as R,= R. Zero correction + CT (4.1)
where CT is the temperature correction factor, and "zero correction" represents both meniscus correction and dispersion agent correction.
Since ASTM 151H soil hydrometer made by Ertco was used in the tests, the percentage of the sediment finer (by weight) was calculated from P 100000O/W) G, ](Rc GI) (4.2)
where G, is the specific gravity of the sediment particles, G1 is the specific gravity of the fluid in which soil particles are suspended, and W is the (oven-dry) mass of sediment used in the hydrometer test. The diameter of particle (corresponding to percent finer than a certain grain size in cumulative size distribution) was calculated according to Stokes' law.
Specific gravity of sediment particle (G.) in Equation 4.2 was obtained using a standard method (ASTM, 1987) by filling the sediment-water mixture into a 500 mnl volumetric flask and de- airing the mixture under high vacuum. Sediments from all sites were subjected to this measurement giving ani average value of G, equal to 2.14. Note that since G, is equal to pP,, sediment granular density becomes 2.14 g cm-3 with a given (assumed) value of
Figure 4.2 shows the grain size distribution of the dispersed sediment from sites 1 through 5. The sediments from site 1 exhibited the smallest percent (28 %) of the clay size sediment, while sediment from site 5 exhibited the largest percent (44 %) of clayey material among the five sites. The material from sites 2, 3, and 4 showed the clay size sediment to be 29 %, 40 % and 39 %, respectively. The remainder were in the silt size range.




100 I I
Site
_ 8 0 \ -2i
- ---- 3~
60 4\h
----50 --.---4
Z %
c 4 Coarse Fractlin
-(composite) LU
20.
0 I I !
104 103 102 101 100
PARTICLE DIAMETER (gim)
Figure 4.2: Fine-grained and Coarse (Composite) Particle Size Distributions from Sites 1, 2, 3, 4 and 5
Table 4.1 gives fine-grained particle size characteristics based on size distributions presented in Figure 4.2 for the fine-grained fractions at the five sites. This table shows that the dispersed median diameter, d50, ranged from 3.4 to 14.4 pm, which is in the medium silt size. The fine-grained portion of the sediment from all sites seem to be comparatively similar. However, it is also apparent that the median diameters of fine-grained fractions from sites 3, 4, and 5 in the middle of the lake were somewhat smaller than the diameters from sites 1 and 2, which are located near the Kissimmee River. Furthermore, the sorting coefficient, S, = (d76/d25)1/2, of the material from all sites appears to be relatively large, which is indicative of graded (broad) size distributions.
The coarse fractions from all sites were initially combined because they were relatively small in quantity. A large amount of shelly detritus was present in the composite sample. A standard sieve analysis was conducted on the composite sample to determine the size distribution of the coarse particles (ASTM, 1987). Sieves #20, #40, #60, #100, #140,




Table 4.1: Sediment Characteristics
Site Fine Particle Characteristics Ignition
No. d25 (pm) d4o (pum) d76 (AM) S. (pm) Loss (%)
1 15 10 2 2.7 40
2 24 15 1 4.1 36
3 13 7 0.6 4.5 43
4 8 0.4 0.7 3.4 38
-5 1 10 1 3 1 0.6 1 4.2 1 41

and #160 were selected for the analysis. Figure 4.2 also shows coarse-grained particle size distribution. The median diameter of the coarse material is 400 pum (0.4 mm).
4.2.2 Organic Material
Characterization test for the amount of organic matter in the sediment, as defined by loss on ignition, was conducted at the Soil Science Laboratory of the University of Florida, using the standard combustion method (ASTM, 1987). Initially, 50 g of fine-grained wet sample was dried in an oven for a day at 501C to remove the moisture, and cooled in a desiccator. Five grams of the dried sample were heated again for 12 hours in a combustion furnace at 5500C. This procedure ashed the organic matter in the sample. The ashed sample was carefully removed from the furnace and placed in the desiccator to cool. Then, the ashed sample was weighed again and the difference between the two weights was used to calculate the percentage of organic matter in the sediment. Table 4.1 gives the resulting percentage of organic content (loss on ignition) by weight of the sediment at sites 1 through
5.
The percentage of organic content is fairly uniform, ranging from 36 % to 41 %, and a considerable amount of organic matter is present in the sediment. The high organic fraction in the sediment is indicative of the rather low value of p, (2.14 g cm--). Since the density of a organic matter has lower value than p, for clayey soil, p, tends to be low when the organics fraction in the sediment is high. Otsubo et al. (1987) also observed this trend in the relationship between the organics fraction in the sediment and p, through the field




33
studies on the physical properties of sediment (water content, Ga, and loss on ignition) in Lake Kasumigaura in Japan. In their study they also recognized no particular seasonal or long-term change in three physical parameters for all sampling sites and suggested that the seasonal change of the organic content, including the other physical parameters, need not be considered in the sediment resuspension model. Although a comprehensive sediment sample program is still required to investigate seasonal variation of the organic content in Lake Okeechobee, this variation may in fact be negligible, following the observation by Otsubo et al. (1987).
4.2.3 Mineralogical Composition
In order to determine the predominant clay and non-clay constituents, X-ray diffraction analysis of the fine-grained fraction from site 5 was conducted in the Soil Science Laboratory. The results indicated the presence of clay minerals including kaolinite, sepiolite and montmorillonite. Kaolinite was the predominant constituent among them.
The presence of sepiolite in the sediment must be noted. This agrees with a previous report on the occurrence of sepiolite in the mineral portion of sapric horizons in a histosol south of Lake Okeechobee (Zelazny and Calhoun, 1977). Sepiolite is chemically precipitated and crystallized in alkaline sediments with significant quantities of Si and Mg (Zelazny and Calhoun, 1977). The greatest deposits of sepiolite occur throughout the world in association with non-clastic sediments such as carbonatic rocks, opal, chert, and phosphates.
The presence of quartz, a non-clay mineral, was detected in the sediment. Traces of other clay and non-clay minerals appear to be present as well, but their identification requires further confirmatory tests.
4.3 Bed Properties
Bed properties were examined through the measurements of the bed density and the vane shear strength of mud core samples. The bed density is important in assessing bed erodibility, and bed density and the vane shear strength together are important in estimating the fluidized mud thickness.




4.3.1 Field and Laboratory Work
A small vibracorer designed at the Coastal Engineering Laboratory of the University of Florida was used to collect the bottom sediments at various sites in Lake Okeechobee (Kirby et al., 1989). A total of 31 sites, which are identified in Figure 4.3, were selected. The selected sites were not strictly limited to the muddy zone but covered most relatively deep sedimentary zones in the lake, although most of them were within the muddy area.
The vibracorer basically had a concrete vibrator powered through a flexible drive from a gasoline motor on board the survey vessel. The concrete vibrator was clamped onto the top of a drill barrel. The drill barrel was 1.83 m in length and had an i. d. of 9.4 cm. It was fitted with a transparent CAB liner to contain the sample. A steel cutting shoe, plastic, petal-type core catcher and a non-return valve were fitted to permit core penetration and retention. A threaded collar on the top of the corer allowed a guide tube to be fitted. This was attached after the vessel had anchored and the corer had been hung over the side in the water. The guide tube permitted the vertical position of the corer to be maintained during drilling operations as well as allowed visual monitoring of bed penetration.
When the vibracorer was recovered, the transparent liner was capped at its base and removed from the core barrel. In circumstances where very loosely consolidated fluid mud type deposits were observed in the upper surface of the mud deposits, a Paar (DMA 35) densimeter was used on board the vessel to measure the density structure of the upper, lowly consolidated mud layers. This measurement was essential because the vertical structure of the loosely consolidated mud layers could have been easily altered during transport to the laboratory. The Paar densimeter is a small, battery operated device for accurate measurement of the density of slurries, using the principal of resonance of the vibrating sample. The frequency of resonance is directly influenced by the slurry, which is converted to density in the instrument and displayed digitally. The core liner was then capped at the top and numbered before being stored in an upright position for transport to the laboratory.




Figure 4.3: Bottom Core Sampling Sites in Lake Okeechobee (In the text a prefix OK and a suffix VC are added to denote these sites)




36
In the laboratory the cores were laid in a clamp and only the liner was cut down opposite sides with an electric saw. The core was then bisected by drawing a cheese wire down the cuts and through the sample. The bisected core was then opened so that both halves could be inspected. Shortly after cutting and before the sample could dry out to any extent, bulk density and shear strength measurements were carried out.
The bulk densities were measured gravimetrically and the shear strength measurements were conducted with a small calibrated vane, made by Wykeham Farrance Eng. (serial No. 971). Measurement was made at 5 cm increments of depth and the vane was inserted sideways into the axial (thickest) part of the halved core.
4.3.2 Bulk Density and Shear Strength Profiles
The measured bed bulk density and shear strength profiles for each site, including the descriptions of the observed vertical structure of the core mud samples, are contained in Appendix A. The profiles indicate that many of the cores had a loosely consolidated upper zone of fluid mud (in which in situ measurements of density were made). No shear strength readings are available in this low strength upper zone, first because shear strength measurements were only made in the laboratory and secondly because the strengths were below the resolution of the instrument.
In the firmer muds, it was observed that the density and vane shear strength measurements showed a close relation, despite obvious data scatter. Figure 4.4 shows density and shear strength profiles in a core sample from site 0K2 VC. From the figure it is noted that the density and shear strength values generally show an increase with depth mainly due to self-weight consolidation effects.
Other samples also showed an overall increase in density and strength with depth, while the detailed profile showed a series of sharp density and strength reversals. As shown in Figure 4.5, the vane shear strength and density peaks and troughs are generally coincident (i. e., OK10 VC). In this core, however, while the shear strength increased with depth, the density of the weak mud layers was lower at 50 cm than at 2 cm below the surface. This




SHEAR STRENGTH (N nI2)
0 2000 4000 6000
10 & Bulk Density
10 0 Shear Strength
LL
20
30
o 40
-J
w
: 50
I
0 6
u0a60 I I I I I
1.0 1.1 1.2 1.3 1.4 1.5 1.6
BULK DENSITY (g cn3)
Figure 4.4: Bulk Density and Vane Shear Strength Variations for Site OK2VC
indicates that density is not an unambiguous analog for strength, which also depends upon mud composition.
Mud densities are in the range that might be expected, ranging typically from 1.01 g cm-3 up to 1.2 g cm-3 with a maximum value of 1.3 g cm-3 in two cases examined. Sand densities are higher, reaching 1.8 g cm-S.Shear strengths reach almost 6 kN M-2 at times, which is consistent with vane shear strengths given by the Task Committee on Erosion of Cohesive Materials (1968). Through a study to find a relationship between vane shear strength and critical shear stress, the Task Committee showed that vane shear strengths measured for several different clay minerals ranged approximately from 1 kN M-2 to 9 kN m-2.
A plot of vane shear strength, r,, versus density, PB, has been produced (Fig. 4.6), showing expected scatter of data points. The mean line was drawn by eye, without recourse to the least square fit method. A best fit curve for the data intercepts the density axis




SHEAR STRENGTH (N ni2)

40
50 60o-L

1.

Figure 4.5:
5
z
J9 CD 3
z
LU
'
C,)
'U z
G4 0

0 1.1 1.2 1.3 1.4 1.5 1.6
BULK DENSITY (g cni3)
Bulk Density and Vane Shear Strength Variations for Site OK10VC

**0
0
*0 0*
0
. ., 3.
* 0
*
* *0
.0** * .*

*0 0,

> 1 1.1 1.2 1.3 1.4
p, = 1.065g cm3 BULK DENSITY, pB(g cm )
Figure 4.6: Vane Shear Strength Variation with Bulk Density based on all Bottom Core Samples




39
at 1.065 g cm-3. At density values below 1.065 g cm-3, the shear strength becomes zero, implying that the mud behaves as a fluid.
This evidence seems to suggest that the fluid mud layers could regularly be resuspended during windy weather, while the underlying mud is relatively unaffected by erosion. The intricate and small scale lamination of the deeper mud layers supports this observation.
4.4 Settling Tests
Several methods have been used to measure the settling velocity of fine sediment in suspension. Previous studies and particular conditions for each can be found in Heltzel and Teeter (1987). Two indirect approaches which are commonly used are the bottom accumulation method and the point concentration (pipette) method. The pipette method measures the temporal change in local concentration so that Wlat can be known at a particular point, while the accumulation method records the temporal change in the actual mass flux, WC, at the bottom.
Another approach was selected to yield the settling velocity versus concentration relationship based on measuring the temporal history of the concentration profile. This method, which can be used to measure the settling velocity in settling columns, is called the concentration profile or multi-depth method (McLaughlin, 1958 ; Fitch, 1957).
The actual procedure developed by Ross (1988) was chosen. This method uses multidepth concentration sampling and numerical integration of the sediment settling equation (Mass conservation). In order to make the experimental condition similar to the field condition, water brought from Lake Okeechobee was used instead of local tap water. Mud samples for the tests were collected from six different sites within Lake Okeechobee in two different seasons. Sampling sites and times of sampling are described in section 4.4.3 and identified in Figure 4.1.
4.4.1 Procedure
Settling tests were carried out by using a specially designed 2 m tall settling column at the Coastal Engineering Laboratory. The column was originally designed by Lott (1987).




40
It consisted of a plexiglass pipe 10 cm in diameter. Tap hoses, 5 cm in diameter and 10 cm in length, were attached to the sides at nine elevations. The column configuration is shown in Figure 4.7. The following procedure was used for each test:
1. A small amount of the fine-grained sediment slurry of high concentration was placed
in a 20 liter carbuoy. The carbuoy was filled with the lake water to the marked height which represented the required volumn (15.7 liters) to fill the column. The carbuoy was then well shaken and agitated for a few minutes to premix the suspension thoroughly.
2. After a vacuum bubbler tube was inserted into the column, the premixed suspension
was poured into the column. In order to ensure uniform distribution of the suspended sediment, the suspension was vigorously mixed for two additional minutes in the
column using the bubbler tube.
3. The bubbler tube was then quickly removed and the first set of about 20 ml samples
were taken from the top hose to the bottom hose as fast as possible. Samples were collected in 50 ml glass bottles which were tightly capped, labeled, and set aside.
Samples were then taken after 5, 15, 30, 60, 120, and 180 minutes. The height and temperature of the suspension were noted at each time of sampling. The sampling
tubes were flushed before each withdrawal to ensure the removal of residues.
4. Gravimetric analysis was used to determine the profiles of concentration with depth
at each sampling time. A fixed volume of sample was taken using the pipette, then filtered by a vacuum pump, and finally dried in an oven for a day at 501C. The dried sample was then removed from the oven and cooled before weighing it on a Mettler
balance scale which could measure the weight up to 0.1 mg.
5. Dividing the weight of the dried sediment by the fixed selected volume gave the concentration of the sample at the time and depth the sample was taken. The concentration data at each time and depth were then entered into an input data file to be used for
a settling velocity calculation routine which was developed by Ross (1988).




__Tap Inner
G Diameter 5mm
0 10cm
NOTE: Tap Hoses not shown

p. - ~q

Figure 4.7: Scale Drawing of the Settling Column




4.4.2 Settling Velocity Calculation
In the quiescent conditions, the one dimensional mass conservation equation governs the vertical settling of mass, and is expressed as ac aF. a(wc) ()
8t Oz 8z
This equation relates the time rate variation of suspended sediment concentration, C(z, t), to the vertical gradient in settling flux, F, = W.C. Since the settling velocity, W,(C), varies with z, W, cannot be taken directly out of the spatial derivative.
Ross (1988) developed a computer program to calculate the sediment settling velocity at each elevation and time. The program is based on the finite difference method. The difference equation chosen for the program was as follows: Wj+1I Azi [2.+1 +~' 1[ lYj~l _bw +l, (4.4)
where xi is the log average of the sediment concentration and Az is the vertical distance between (i) th and (i + 1) th sample elevation. The term, Ati, is the time increment and j is the time index. This is shown graphically in Figure 4.8. The log average concentration is defined as
= c (Inci+1$nC) (4.5)
It should be noted that the log average, instead of the arithmetic average, was used to calculate the mid-point concentration. This is due to the trend of concentration profile, which typically shows logarithmic shape. Ross (1988) gives the details, including the boundary
conditions for solution of Equation 4.4.
4.4.3 Test Conditions
A total of fourteen settling column tests were conducted on the muds from six different
sites within the muddy zone of Lake Okeechobee. Conditions for each test are given in
Table 4.2. Locations of mud samples used for tests are identified in Fig. 4.1.
As shown in Table 4.2, the mud samples used for the first seven tests are those collected
from five different sites in Mar. 1988, as described in section 4.2. Through these tests, the




Cj
1-1

Wi Xi
S -

w1 X1

ci 1

Figure 4.8: Grid Indexing used in the Settling Velocity Calculation Program

Table 4.2: Settling Test Conditions

Note: * ** indicates no value obtained.

Test Location of Date of Mud Temp. of Variation of C
No. Mud Sample Collection Suspension (TOC) Suspension Height (cm) (g L-1)
1 site 1 Mar 1, 1988 27.4 **** 162.8 135 5 1.8
2 site 2 Mar 1, 1988 29.0- 32.0 163.3 139.8 2.8
3 site 2 Mar 1, 1988 26.3 161.7 135.2 14.1
4 site 3 Mar 1, 1988 157.5 130.0 5.0
5 site 4 Mar 1, 1988 27.0 **** 163.5 140.8 2.8
6 site 4 Mar 1, 1988 25.5 164.0 137.5 23.7
7 site 5 Mar 1, 1988 28.7- 30.8 161.3 133.5 2.7
8 site 6 Oct 28, 1988 19.0 20.9 164.3 139.8 3.2
9 site 6 Oct 28, 1988 19.6- 22.3 167.1 145.4 6.5
10 site 6 Oct 28, 1988 19.4 20.6 159.3 137.4 13.6
11 site 6 Oct 28, 1988 21.6- 22.1 163.5 141.3 19.9
12 site 1 Oct 28, 1988 22.0- 23.1 164.2 142.6 1.9
13 site I Oct 28, 1988 20.6- 19.7 171.2 150.7 4.6
14 site 1 Oct 28, 1988 21.0 24.5 174.1 152.3 11.9

T- 11




44
spatial variation of settling properties could be estimated. For tests 12 through 14, the mud sample was collected from the same location as that of test 1, but in a different season in order to evaluate possible seasonal effect on the settling properties. To supplement the spatial representation of settling properties, mud sample from site 6 was additionally collected in Oct. 1988. This sample was investigated through tests 8 to 11.
From Table 4.2, it is observed that the temperature change of sediment suspension in the laboratory colurrin was relatively small during each test, indicating the maximum variation to be 3.50C. For the tests as a whole, however, temperature varied from 19'C to 320C.
The height of sediment suspension is also given in Table 4.2. The first value given for each test represents the sediment suspension height at initial time of each test, and the other values represent heights which resulted after the final collection of samples at the last sampling time. It is noticeable that the sediment suspension heights decreased by approximately 25 cm in all tests.
Initial sediment concentration, C, used in the tests is also given in the last column of Table 4.2, and varied from 1.8 g L-1 to 23.7 g L-1. Since the settling velocity in general varies measurably with the suspension concentration, various initial concentrations were selected to obtain the settling velocities in an extensive range of the suspension concentration. The initial concentration represents the concentration at zero time immediately after mixing when the concentration was nearly uniform over depth.
4.4.4 Results and Discussion
Concentration profiles. Concentration profiles measured in selected tests are shown in Figures 4.9 through 4.12. Other profiles are contained in Appendix B. Three distinct settling regimes are apparently observed from the profiles, which Ross (1988) described as low (C < 2 g L-'), moderate, and high (C > 20 g L-1) concentration settling regimes, respectively.
Figure 4.9 shows concentration profiles from the test 1, which was conducted using mud from site I in Mar. 1988 as described in Table 4.2. This profile illustrates well the




45
settling of low concentration due to low initial concentration (1.8 g L-1). Suspension concentration decreased everywhere in the column except immediately at the bed. For example, the suspension concentration gradually decreased with time from 1.8 g L1up to approximately 0.1 g L-1 at 130 cm above the bottom of the columnn. Ross (1988) attributed this decrease to aggregate sorting during the flocculation process.
It is noted that the variation from low to high concentration occurred with no significant development of a moderate concentration region.
In Figure 4.10, concentration profiles from test 2 at an initial concentration of 14.1 g L1are shown. These profiles can be considered to be representitive of the moderate concentration settling regime. Two marked interfaces are noticed in these profiles. Both interfaces converge with time. Ross also observed these interfaces and described the upper interface in this profile as separating the concentration "thinning" layer (above) from the constant settling layer (below); and the lower layer interface indicates the beginning of hindered settling and decreasing vertical flux rates. Here, "thinning" means the decrease of the suspension concentration with time at any elevation of the column.
Finally, high concentration settling, which is generally called hindered settling, is illustrated well in Fig. 4.11. As observed in these profiles, the initial concentration was 23.7 g L-1. A characteristic feature for this regime is the corresponding decrease in sediment flux with increase in concentration. In this case, concentration increases everywhere with time and the settling occurs in mass.
In Fig. 4.12, concentration profiles from test 11 are shown. The initial suspension concentration in this test was 19.9 g L-1. It should be noticed that a lutodline representing a step gradient in the concentration profile developed shortly after the initiation of the test. For example, at 120 minutes the lutocline was 100 cm above the bottom of the column, and at 180 minutes, it was at 60 cm. Below the lutocline, the sediment was in the form of a high concentration, but not a significantly thick structured bed, since 180 minutes is typically insufficient to develop the thick structured phase by dewatering.




200
150 100 50

101 1 10 102
SUSPENDED SEDIMENT CONCENTRATION (g I1)
Figure 4.9: Concentration Profiles from Settling Test 1; Initial Concentration of 1.8 g L-1

200
E 150
z
0
-- p100
w
Wj 50

10-1

1 10

102

SUSPENDED SEDIMENT CONCENTRATION (g L1)

Figure 4.10: Concentration Profiles from Settling Test 3; Initial Concentration of 14.1 g L-1




200
150
E
0
z
0 100
I
-j
UJ 50

10-1 1 10 102
SUSPENDED SEDIMENT CONCENTRATION (g L1)
Figure 4.11: Concentration Profiles from Settling Test 6; Initial Concentration of 23.7 g L-

200
E 150
z
O
- 100
4
w
-J
wJ50

01-
101

1 10

102

Figure 4.12: gL-

SUSPENDED SEDIMENT CONCENTRATION (g L1) Concentration Profiles from Settling Test 11; Initial Concentration of 19.9




48
Settling velocity profiles. The concentration profiles from the fourteen settling tests were used to calculate the settling velocities of sediment from the six different sites. In order to determine the settling velocity at different concentrations, these profiles were entered into the numerical program for settling velocity calculation. The resulting settling velocity profiles for different sites are shown in Figures 4.13 through 4.15.
Figure 4.13 shows the settling velocity and the corresponding settling flux plots for site 1. As shown in the figure, the data were quite scattered but clearly indicated an increasing velocity region and a decreasing velocity region. The reasons for the scatter around the fitted line have been explained by Ross (1988). He attributed the scatter to a slight time variation in the settling velocity due to collision and flocculation, and limitations in the bubbler mixing procedure used for obtaining an initially uniform suspension.
The data shown in Fig. 4.13 seem to indicate a parabolic shape, which is somewhat different in comparison with the typical settling velocity profile given in Fig. 3.1, especially in flocculation settling region. Typically, the settling velocity profile in the flocculation settling region is represented by a straight line. However, in Fig. 4.13 the parabolic shape is observed to extend from the hindered settling region into flocculation settling region following similar observation by Wolanski at al. (1989). Noticing this parabolic shape, the following relationship
(, C' (4.6)
which is modified from Wolanski et al. (1989), has been developed to represent both flocculation settling and hindered settling.
It should be noted that depending on the concentration, Equations 3.24 and 3.25 can be simplified as follows:
W,= ab-2-Cn if C2 < (4.7)
W.= aCn-2m if C2 >>b (4.8)
By applying the least square fit method to the obtained settling velocity data, the four




49
unknown coefficients of a, b, n and m can be determined from these simplified forms. Referring to Fig. 4.13, Equation 4.7 represents a straight line in the flocculation settling region and Equation 4.8 in the hindered settling region. The gradient of the straight line in the flocculation settling region directly gives the value of n in Equation 4.7. The value of a in Equation 4.8 is the value of W, when the straight line in the hindered settling region intersects the vertical line at C = 1 g L-1. In Fig. 4.13, the resulting values of a, b, n and n were 33.38, 4.39, 1.02 and 1.48, respectively.
Furthermore, a simple differenciation of Equation 4.6 with respect to C gives the peak value of the settling velocity, W... The maximum value, W.0, and the corresponding C2 are defined by
W~~o = aM- 1)'- 3
W. = ab(2m 1) (4.9)
b
C2 = b (4.10)
(2- -1).2
Note that the settling flux, F., is obtained by multiplying the settling velocity with the concentration. Replacing n by n + 1 in Equation 4.6, therefore, the corresponding equation for F, is obtained as
aCn+l
F, = WC = C+ (4.11)
In the same way as before, the peak value, Fo, of the flux and the corresponding C3 can be defined by
F.o = ab *+1-2m 'k;) 2 (4.12)
2m) m
b
C3 = b (4.13)
2M 1)2
In Table 4.3, the characteristic coefficients (n, m, a and b) of Equation 4.6 are given for different sites, including the characteristic parameters (W.0, C2, F0 and C3) for the settling velocity and flux relationships.
Figure 4.14 shows the settling velocities of sediment from sites 2, 4 and 5, and the settling velocity profile obtained from Equation 4.6. There is a noticeable similarity in the




Table 4.3: Values of Characteristic Coefficients and Parameters For W, and F,
Site n m a b W,, C2 Fs. C3
No. (mm8ec-1) (g L-1) (Kgm-s eec-) (g L-1)
1 1.83 1.89 33.38 2.54 1.47 2.46 4.67 4.38
2, 4 and 5 1.02 1.48 33.38 4.39 0.73 3.18 3.30 6.43
3 and 6 1.96 1.96 33.38 4.19 0.52 4.19 2.83 7.36
flocculation settling regions for sites 2, 4, and 5, as well as in their corresponding hindered settling regions. In Fig. 4.15 the sediments from sites 3 and 6 also show similarity in the settling velocity, even though these two sediments were collected in different seasons as indicated in Table 4.2.
In Figure 4.16, the settling velocity profile for site 1 is given as a representive one in order to examine any seasonal variation. From the data it is observed that the settling velocities of sediment from site 1 were not affected by any measurable seasonal difference (Spring versus Fall). It may be surmized that the influence of season on the settling velocity of sediment in the muddy zone of Lake Okeechobee may not be significant.
In order to compare the spatial variability of the settling velocity, profiles for each of the six sites have been combined in Figure 4.17. Data from all sites show W, variation in the range of two orders of magnitude, from about 0.01 to 1 mm sec-1. At the end of the low concentration regime, W, varies approximately from 0.02 to 0.3 mm sec-1. This may be considered to represent the free settling velocity.
It is observed that the sediments from all sites seem to exhibit similar behavior in the hindered settling region, which is beyond the peak value of W, (on the order of 1 mm sec-1 at about 3 g L-1). This phenomenon may be attributed to the dominant effect of the aggregate network on dewatering rather than sediment composition on the settling behavior. However, the effect of sediment composition is clearly seen in the flocculation settling range. Site 1 shows the highest W. and sites 3 and 6 the lowest. Sites 2, 4 and 5 are intermediate but approach site 1 towards the free settling regime.




51
10 101
Fs 2 2m /
(C2+ b2)
-~ / 1
10
a Cn~ l
W = /* Hindered
E (C2 +b 2) Settling (n
E ;*m
*-10' z
gM
) 1001 I
zz
. 2 -n
o 10 o Flocculation
-00
(/) //Wso= 1.47 mms1 1 0.3
/ C 3 = 4.38 g'
10' I I 1 0-4
1 0 2 1 0 1 10 102
CONCENTRATION, C(gL")
Figure 4.13: Settling Velocity and Settling Flux Variations with Concentration for Site 1




10
Site
. v 2
- 0 4
Sa 5
E
0
E
- v
oM v
a v 0 D 0 V%
z
3 10-1 vo o a
(1) 0p a
- 0
0 0
'7
10-2 I lI
10-2 10-1 1 10 102
CONCENTRATION (g I1)

Figure 4.14: Settling Velocity Variation with Concentration for Sites 2, 4 and 5




53
10
Site
o 3
6
E A
1 A 8A o
00
os 0 Ao
C) o
. 01 0 - 10 o
E A 0
z 00 016
M0 lo, 0
0 6 A 0
L 0. 0 0 A 0 p 0
n ~A AA
0f AA A
0 0 0
0 *AA
0 A AA
10-2 1 1 &1 li 111 11111 09 1 0 o
10-2 10-1 1 10 102
CONCENTRATION (g L:1)

Figure 4.15: Settling Velocity Variation with Concentration for Sites 3 and 6




1
10-1

10"1 1 10

102

CONCENTRATION (g I:1)
Figure 4.16: Seasonal Comparison (March, 1988 versus October, 1988) of Settling Velocity Variation with Concentration at Site 1

10-2
10-2




10
1
10"-1
10-2

10-1

102

CONCENTRATION (g 11)
Figure 4.17: Spatial Comparison of Settling Velocity Variations with Concentration for Sites 1,2,3,4, 5 and 6

.
Site
*1
v2
o 3
o4
o 5
06
*
0 q)
1 v o 4 00 0
_ vo' oo*
a *
. o 2,4,5 0 0
_ o a Mbo 3,6 o,,8
. *
v 0 o
a~ 61en sa 11401111 t I 1III o I*II Ln

10-2




56
As described in the previous section (Fig. 4.1), site 1 is located at the northern end of the muddy zone in Lake Okeechobee and sites 3 and 6 are at the eastern end and western end, respectively. Sites 2, 4 and 5 cover the central and southern parts of the muddy zone. From the data of Fig. 4.17, therefore, it can be concluded that sediment settling occurs fastest in the northernmost zone, more slowly in the eastern and western zones, and at a moderate rate in the central and southern mud zones.
In reference to both the fine particle size distributions in Fig. 4.2 and the grain size data in Table 4.1 in previous section, it appears to be difficult to correlate the dispersed particle size with the settling velocity of the aggregated sediment. The lack of correlation between the aggregate settling velocity and the corresponding dispersed particle size is somewhat unexpected. However, it in fact makes clear a basic difference between behaviors of cohesive and cohesionless sediments, which is that unlike the case of cohesionless sediment, in cohesive sediments the settling velocity can not always be uniquely defined by particle (dispersed) size. Note that even in the relatively low salt concentration environment of Lake Okeechobee, we are dealing with aggregated sediment whose properties seem greatly influenced by the presence of nearly 40 % organic matter. Unfortunately, specific factors related to the organic constituents which affect aggregation are generally not well known.
It is noticeable that over a fairly large portion of the muddy zone, represented by sites 2, 4, and 5, the settling velocities are similar. This in turn suggests a good degree of spatial mixing of the muddy sediment due to wind generated circulation and associated wave action. This could also explain why site 1 is different, since in the narrow neck region of the lake some sheltering from the effects of wind and insufficient communication with the rest of the muddy zone thereof is likely. With regard to the low settling velocities at sites 3 and 6, hydrodynamic influence on the bottom sediment distribution is believed to be the major factor.




57
4.5 Erosion Tests
4.5.1 Introduction
In order to investigate the erosional properties of sediments from various sites in Lake Okeechobee, erosion tests were conducted at the Coastal Engineering Laboratory, using the rotating annular flume originally designed by Mehta (1973).
The erosional behavior varies both with the magnitude of the bed shear stress and the structure of the bed. Beds are commonly classified into two categories: deposited beds and placed beds. A deposited bed, which is usually composed of freshly deposited mud undergoing consolidation, generally exhibits non-uniform property variation with depth. Typically, the density and the shear strength increase with depth in the top few centimeters. The bed properties of the placed bed are comparatively uniform over the depth so that the shear strength and the density are independent of depth.
In the case of the deposited bed, the time rate of concentration variation, aClat, decreases with time and the suspension concentration approaches a final constant value. In the placed bed case, the suspension concentration increases at a constant rate with time when a given shear stress exceeds the shear strength. Thus, the rate of erosion of these beds is constant for a given shear stress. For the present experiments, placed beds were used so that the erosion rate could be directly estimated for a given shear stress and bed density.
4.5.2 Annular Flume
The basic components of the annular flume consist of a system of a rotating annular ring and an annular channel. The annular channel, which is made of 0.95 cm thick fiberglass, has a width of 20 cm, depth of 46 cm and a median radius of 76 cm. The annular ring is made of 0.6 cm thick plexiglass, having the same mean radius as the channel but narrower by 0.6 cm than the width of the channel. The ring can be suspended at any required height within the channel by means of four vertical supports which are connected to the central vertical shaft by horizontal supports.




58
A control unit with an indicator panel is provided for both the ring and the channel to enable their operation at the desired speeds. These control units had to be calibrated, since they do not give the speeds of the ring and the channel directly in rpm. Therefore, rpm measurements of the ring and the channel were carried out for given different settings on the meters using a stopwatch. Calibration curves obtained in this way are given in Figure 4.18. Other equipment for bed shear stress measurements was previously calibrated by Mehta (1973). The required bed shear stress could be obtained by adjusting the rotation speeds of the ring and the channel. The ring and the channel were rotated in opposite directions to minimize the effect of secondary currents and to provide a uniform flow in the channel.
In order to collect samples of suspended sediment, tap tubes are provided at three different elevations on the outer wall of the channel, at elevations of 8 cm, 18.5 cm and 26.5 cm above the bottom of the channel. Flume configuration and additional details on the flume may be obtained from Mehta (1973).
4.5.3 Procedure
Placed beds were prepared by pouring a thick slurry of sediment into the annular flume. In reality, in the top few centimeters the bed is usually soft and has a relatively low density with high water content (> 100 %), since the bed is composed of freshly deposited mud undergoing consolidation. However, below the upper layer of the bed, it is typically more dense and more consolidated, with a lower water content. The sediment slurry, having a density corresponding to that of a soft bed, was obtained easily by setting aside the sediment in water in a quiescent condition, which gradually increased the density of the slurry through consolidation. However, it was difficult to obtain a sediment slurry density corresponding to that of a dense bed by this process alone. Therefore, in this case, the slurry was heated in an oven at a temperature less than 50'C for approximately two days, which lowered the water content. In order to make the experimental conditions similar to the field condition, lake water was used in all experiments.




Channel y = 3.543x 0.481 Ring y = 3.412x 1.372
y : Meter Reading x : Revolution Per Minute

40 r-

20 t-

lot-

I I I I I

I I I I I

I I I I I I

REVOLUTION PER MINUTE (rpm)
Figure 4.18: Speed Calibration Curves for Ring and Channel of the Annular Flume




60
The following procedure was used for each test:
1. A thick slurry of mud was well mixed by a mixer for an hour to obtain uniform density
over the depth. In order to measure the bulk density of the slurry, a small amount of sediment was taken from the well-mixed slurry and its weight and volume were measured. The bulk density was obtained by dividing the weight of sediment by the volume. The slurry was placed over the flume bottom to uniform depth. All mud stains on the inside walls of the channel during the placement of bed were removed.
2. Lake water was then carefully added to the flume to give the desired water column
height, using a very small pump made by Cole-Parmer Instrument Company (Model No. 7568). The ring was lowered to be in complete contact with the water surface. It is very important to set the ring properly, since a shear stress is transmitted to the sediment bed during the rotation of the ring, therefore the stress magnitude depends
on the area of contact between the water surface and the ring.
3. The flume was kept in quiescence for one to three days to allow the sediment suspended
in the process of adding the lake water into the flume to settle down.
4. For the present study, six to seven different shear stresses were applied in a step-wise
manner with a increment of 0.1 N m- in accordance with the procedure described in detail by Parchure (1984). The starting shear stress was 0.05 N M-2 or 0.1 N M-2, and time duration for each shear stress was 90 minutes. The sampling times used over each 90 min duration of application of shear stress were 2, 5, 10, 15, 20, 30, 40, 50,
60, 75 and 90 minutes with an initial sample taken at the start of the duration.
5. At each sampling time, suspension samples were taken simultaneously at two different elevations to give an average suspension concentration over the entire water column.
The selected two elevations were 8 cm and 18.5 cm above the bottom of the channel.
Samples were collected in 50 ml glass bottles which were capped, labeled, and set




Table 4.4: Erosion Test Conditions
Test Date of Sediment PB Water Depth Bed Thickness Duration of
No. Collection (g CM-3) (CM) (CM) Deposition (hr)
1 Mar. 1, 1988 1.10 27 3.0 24
2 Mar. 1, 1988 1.12 23 3.0 24
3 Mar. 1, 1988 1.09 23 3.0 24
4 Mar. 1, 1988 1.19 23 1.5 24
5 Oct. 28, 1988 1.07 23 5.0 72
6 Oct. 28, 1988 1.09 1 23 1 3.5 241
aside. Care was taken to flush the sampling tubes before each withdrawl. Lake water
was periodically added to the flume to maintain a 23 em water depth.
6. Gravimetric analysis was used to determine the suspension concentration of each sample. Gravimetric analysis procedure has been described in section 4.4.1. This analysis provided time-variation of suspension concentration over each 90 min duration at a given applied bed shear stress. The concentration-time profiles were then used to estimnate the erosion rate at each given bed shear stress, and the critical shear stress for erosion, corresponding to the selected bed density, was obtained from the relationship
between the erosion rate and the bed shear stress (Mehta, 1988b).
4.5.4 Test Condition Summary
Test conditions are summarized in Table 4.4. For tests 1 through 4, the sediment used was a mixture of sediments collected from sites 1, 2, 4, and 5 in Lake Okeechobee in March 1988. The approximate proportion (percent by weight) of sediment from these four sites in the mixture was 30, 25, 25, and 20, respectively. These samples could be combined since they showed similar properties through the characterization tests and settling velocity tests. Since the sediment from site 3, however, exhibited somewhat different properties, tests 5 and 6 were conducted using the sediment collected at site 3 in October 1988. It is surmized that the erosional properties of the sediment are not affected by the seasonal difference, based on the results of the examination of seasonal variation in the settling properties.




62
In test 4, a dense bed with a bulk density of 1.19 g cm-3 was prepared. I all other tests less dense beds were used. The water column height was 23 cm in all tests except test 1, and the placed bed thickness varied from 1.5 cm to 5 cm according to the amount of sediment available for each test.
Even though a very sensitive small pump was used to add lake water into the flume, the surface of the sediment bed was disrupted and sediment particles were resuspended. Therefore, a long duration (24 hr) of deposition was required to allow the suspended sediment to settle down. In test 5, the duration of deposition was 72 hours because the sediment bed was disrupted more than in the other tests, due to low bulk density.
4.5.5 Results and Discussion
Concentration-time profile. Illustrative suspension concentration versus time profiles are shown in Figure 4.19 through 4.22. Other profiles are contained in Appendix C. As noted, in the case of the placed bed (which has uniform properties over the depth), the depth-averaged suspension concentration during erosion increased linearly with time for a constant shear stress in excess of the shear strength. This typical trend is clearly observed at high shear stresses.
Figure 4.20 shows a significant dependence of suspension concentration on the bed density in comparison with other figures. As observed, suspension concentrations for each shear stress were always less than 0.1 g L-1. The bed bulk density for this test was 1.19 g cm53, which was relatively higher than the others, as seen from Table 4.4.
Fig. 4.21 illustrates that the concentration suddenly dropped at the beginning of the second applied stress duration step from the end. The concentration drop is attributed to a change in the vertical concentration profile, possibly as a consquence of a change in the inter-particle collision frequency at the beginning of the step (Parchure, 1984).
In most profiles the suspension concentration shows a different trend at low shear stresses, where the concentration shows a nearly constant value and sometimes even a decreasing trend with time. For example, such a trend is easily observed in the first three




2.0 1.0 0.0
0

TIME (mins)
Figure 4.19: Time-Concentration Relationship in Test 3

100 200 300 400 500




0.4

0.3

0.2

0.1

0.0L
0

0 1 I B I I 0 I 14 '1. b I =
0.15N m2 O.25N m-2 1O.35N m- 2 1o.45N m 2 0.55N m2 0.65N m2 0.75N m2
O 0 0 0
(0

SI ,

100

200

300

400

TIME (mins)
Figure 4.20: Time-Concentration Relationship in Test 4

.4 64

500

600




0.6
0.15N m'2 0.25N m- 2 0.35N m 2 0.45N m-2 0.55N m2 0O.65N mn2 0.75N m- 2 CD
- 0.5
O
4 0.4
- 0.3
O
0
CL)
Z 0.20
F**
z
U .1 *
0~0
CL Cl) 0.0"
0 100 200 300 400 500 600
TIME (mins)

Figure 4.21: Time-Concentration Relationship in Test 6




V) I-1
0)
z
0
z
w C.)
C-)

TIME (mins)

Figure 4.22: Time-Concentration Relationship in Test 5




duration steps in Figure 4.21. Without considering possible experimental error in the measurement of concentration, this trend can be explained by the effects of altered bed structure and occurrence of fluffy, highly organic sediment at the top bed. As noted, adding water into the flume in the manner described in section 4.5.3 caused the bed to become disturbed, following which the resuspended sediment settled down within 24 hrs. Due to this experimental difficulty, the top layer of the placed bed was essentially changed into a deposited bed. Therefore, during the erosion of this layer, the time-rate of change of suspension concentration initially decreased and finally became zero at each shear stress. Villaret and Paulic (1986) also observed such a trend and reported the placed bed in the annular flume exhibited an initial trend of steady state approach at low shear stresses.
In addition to the deposited bed behavior at the top bed layer, the effect of a very thin fluffy sediment layer at the top can explain the decreasing trend of concentration. It should be noted that the magnitude of concentration was typically very small at low shear stresses. This means that most sediment suspended at low shear stresses was possibly accounted for by the fluffy layer. The fluffy sediment may respond very sensitively to the initial shear stress application so that most of it would be suspended rapidly. Since the top layer of the bed exhibited the behavior of a deposited bed, bed erosion stopped at some level where the shear stress was equal to or less than the shear strength, and only resuspension of the deposited (as opposed to placed) sediment occurred. Therefore, the decreasing trend of concentration means that the amount of sediment resuspension was less than the amount deposited.
Another important observation in these tests was mass erosion, which usually occurred under high bed shear stress conditions and resulted in a structural breakdown of the bed at low bed densities.
An illustrative concentration profile for mass erosion is shown in Figure 4.22. This figure shows that at the highest shear stress (0.7 N M-2) the suspension concentration rapidly increased with time, which is characteristic of mass erosion. Mass erosion seems




68
to be governed by bed shear stress as well as the time-rate of change of bed shear stress (Cervantes, 1987). This type of erosion was observed in every test except in tests 1 and 3.
Erosion rate and shear strength. Erosion rate (or erosion flux) for each shear stress was obtained by converting the time variation of the suspension concentration over the depth of flow to the corresponding time variation of the eroded sediment mass per unit bed surface area. The expression for this conversion is
am=- at (4.14)
where r is the erosion rate, m is the eroded sediment mass per unit bed surface area, and h is the depth of flow.
Using Fig. 4.21, for example, to calculate the erosion rate (6) for surface erosion, the concentration difference (AC) during 1.5 hours (At) is calculated to be 0.027 g cm-S at Tb = 0.45 N m-2 over the water depth (h) of 23 cm. The substitution of AC, At and h into Equation 4.14 thus yields an erosion rate of 0.414 mg cm-2 hr-1 at Tb = 0.45 N M-2.
Excepting negative values of e due to the decreasing concentration variation for a given shear stress, erosion rate at each shear stress was calculated in the above manner and then plotted against the applied bed shear stress. The corresponding profiles of erosion rate related to bed shear stress are shown in Figs. 4.23 through 4.26. As observed from these figures, two straight fitted lines of slopes M, and M2 (for example, see Fig. 4.23) were obtained. The line of slope M, represents the "fluff" erosion of bed surface at low shear stresses and the other line represents bed surface erosion at relatively high shear stresses. The actual mass of sediment eroded due to surface fluff (possibly of predominantly organic origin) is, however, not high, and for purposes here has been neglected from further consideration.
As has been described in section 3.2.1, the relationship between the erosion rate, f:= and the bed shear stress is given as:
F, =rm(L 1)(4.15)
T*e




2.0 Test
A2
'E 1.5
U 1Bed Surface Erosion
1 1.0
c Erosion of Surface "Fluff"
0
)0.50\a
0 M,
0.0 n II I/ III
0.0 0.2 0.4 f__Tce s 0.6
SHEAR STRESS, (N ni2)
Figure 4.23: Composite Erosion Rate Variation with Bed Shear Stress for Tests 1, 2 and 3 at a Mean Density of 1.1 g cm-3 where eM is an erosion rate coefficient, r, is a erosion critical shear strength, and rb is a bed shear stress.
For surface erosion, the erosion critical shear strength, Tcc.a, can be determined by extrapolating the i2 line back to the abscissa (Parchure and Mehta, 1985). The erosion rate coefficient, rM.,, is obtained by multiplying r with Mi2. Values of r., and em., obtained through this method for each test are given in Table 4.5.
As shown in Fig. 4.23, erosion rates resulting from tests of 1, 2 and 3 were plotted to obtain the two parameters of Tcea and eM.,. The estimated values of r,,., and eM., are respectively 0.43 N m-2 and 2.8208 mg cm-2 hr-1 for a bulk density of 1.1 g cm-3 averaged from bulk densities of all three tests. In this profile, since the bulk density for each test was not very different, the erosion rate data resulting from all tests could be combined together.
For mass erosion rC.m may be considered to be equal to the applied shear stress at which mass erosion was observed. However, no reasonable method to estimate the erosion

Dow-




70
1.0
C4 0.8
EO.6
LLF
' 0.4
0
C/ 0.20
0.0
0.0 0.2 0.4 0.6 0.8
SHEAR STRESS, (N ni2 )
Figure 4.24: Erosion Rate Variation with Bed Shear Stress for Test 4
rate coefficient, em.m, has been suggested until now. Moreover, data obtained from this study were also not sufficient to determine EM.m in an acceptable manner. Therefore eM.m was assumed to be constant over a whole bed bulk density range and to be equal to eM., at PB = 1.065 g cm-s. As described in section 4.3.2, 1.065 g cm-3 is the bulk density below which the bed was considered to be fluidized. The values of Tc.m for mass erosion for each tests are also given in Table 4.5.
In order to estimate the influence of bulk density (PB) on the bed on two parameters, T., and eM, these parameters were plotted against PB and are presented in Fig. 4.27 and 4.28. As shown in Figure 4.27, which is a plot of bed shear strength against PB, yields the following relationships for the two types of erosions rce.a= as(PB pO" + Ce ; surface erosion (4.16)
Tce.m amPB + bm ; mass erosion (4.17)
where a, = 0.883, b, = 0.2, c, = 0.05, am = 9.808, bm = -9.934, and p, is the bulk density of uppermost bed level which is specified as 1.065 g cm-3. Equation 4.16 seems to be




71
~1
20
i 5
'E W 100
LU
0 re 5
w
0.0 0.2 0.4 0.6
SHEAR STRESS, (N m2)

Figure 4.25: Erosion Rate Variation with Bed Shear Stress for Test 5




C.)
E
0
m
O UJ
0
w)

Note: indicates that these values were obtained by combining the erosion rate data resulting from tests 1, 2 and 3. Note: a indicates that no mass erosion was observed.

3.0
2.5
2.0
1.5
1.0
0.5
I
0.0 A
0.0 1 I I I I, ,
0.0 0.2 0.4 0.6
SHEAR STRESS, (N 1i2) Figure 4.26: Erosion Rate Variation with Bed Shear Stress for Test 6
Table 4.5: Values of PB, em, and ree
Test PB sM.a rce.s Tee.m
No. (g cm-1) (mg cm-2 hr-1) (N m-2) (N m-2)
1 1.10 a
2 1.12 2.82* 0.43* 0.75
3 1.09 0.73
4 1.19 2.37 0.64 a
5 1.07 57.61 0.34 0.55
6 1.09 14.61 0.55 0.75




2.0 i
SFluid Mud Bed
Z I tce m
1.5 I bIce m
I b T
" I Mass Erosion
0
Z I
1.0 Ice* Tbb TCe m
- I Surface Erosion
Cl)
ccI O
0.5 - ce s
Cl) bCc s
- Tb< Tce s
a No Erosion
0.0 I I I
1.0023 1.05 1.10 1.15 1.20 1.25
BULK DENSITY (g cni3)
Figure 4.27: Critical Shear Stress, re,, Variation with Bed Bulk Density, PB
consistent with the expression, r, = apt, given by Owen (1970), while Equation 4.17 is in agreement with previous expression of the form, T = apB + b, given for surface erosion (Mehta et al., 1982; Villaret and Paulic, 1986).
In Fig. 4.28 the relationship between EM and PB is expressed as
In EM., = s exp P-n 2 ; surface erosion (4.18)
eM.m = m ; mass erosion (4.19)
where sl = 0.23, s2 = 0.198, ml = 224, and p3 is the bulk density at the upper level of the fluid mud zone selected to be 1.0023 g cm-3. The assumed value of EM.m = ml for mass erosion given in Equation 4.19 is likely to be reasonable since the calculated eM.m using data presented in Fig. 4.22, gives 239 mg cm-' hr-1, which is very close to ml.




103a
10 Fluid Mud Bed
_ I
-a I
.E
0' FM = Const= 224 (mg crni2 h1f)
E 2 I Mass Erosion (Tb>Tce. m)
102
mto .) \Surface Erosion
U. (ce m Tb zce T* s)
O
o InEM= 0.23 exp ( 0.198
I
1.0023 1.05 1.10 1.15 1.20
BULK DENSITY (g cni3)

Figure 4.28: Erosion Rate Coefficient, eM, Variation with Bed Bulk Density, PB




CHAPTER
APPLICATION TO LAKE OKEECHOBEE
5.1 Introduction
This chapter presents the application of the vertical sediment transport model to Lake Okeechobee using the theoretical aspects presented in chapter 3 and experimental data obtained in chapter 4. It must be emphasized that this is a realistic but simplified application using selected theoretical and experimental relationships to examine the evolution of vertical suspension concentrations of fine sediment in wave-dominated environments, in general. The vertical transport model was originally developed by Ross (1988). Since, however, his model did not include the calculation of eroded or deposited bed depth and the corresponding effects due to different degrees of wave action, the model was modified for these purposes. Details on modifications are described in following sections, including the modeling procedure and description of data used for simulation.
5.2 Numerical Model
5.2.1 Modeling Procedure
The vertical transport model solves equation 3.10 through a finite difference scheme, using boundary conditions 3.11 and 3.12. The model consists of an input data routine, an initialization routine, a main computation routine, a diffusion flux calculation routine, a settling flux calculation routine, a hydrodynamic calculation routine, a bed flux calculation routine and an output routine.
For each time step, the hydrodynamic routine calculates the changed the water depth of water column due to deposition or erosion, the maximum wave orbital velocities at the elevations corresponding to each grid point and the maximum wave-induced bed shear stress.




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In the linear wave theory, the maximum orbital velocity at a given depth is obtained from Equation 3.30 as presented in section 3.4.1, and the maximum bed shear stress is computed using the relation
b = b(5.1)
where f,, is the wave friction factor, p is the fluid density and ub is the maximum orbital velocity just outside the bottom wave boundary layer. In this simple form for the bed shear stress the only unknown is f.. Jonsson(1966) showed that the friction factor is dependent on the relative roughness of the boundary, and provided a diagram which gives the wave friction variation with Reynolds number and relative roughness (Dyer, 1986).
From this diagram it is possible to calculate rb, if an appropriate value for the equivalent bed roughness, k,, can be chosen. The calculation of rb from Ub, and the selection of rb obtained in this way as the erosion forcing parameter, is valid only under quasi-steady conditions in which the rates of turbulence production and dissipation in the wave boundary layer can be assumed to be in equilibrium. This assumption is therefore inherent in the present study.
Initially, the water column height h is divided into n vertical layers, and each layer is represented by grid point i which is located at the center of the layer. For example, at the top layer i = 1 and at the layer just next to the bottom i = n. A definition sketch for grid schematization is given in Fig. 5.1. Vertical spacing, Az, of each layer is equal except the vertical space, Azn, of the nth layer. The nth layer is represented initially by a fluid mud layer as noted further later, and eroded or deposited bed depth (zb) at each time step is added to Azn.
Within the water column, at elevations corresponding to grid points, i, below the water surface, the neutral mass diffusivities are calculated through Equation 3.35. Mass diffusivities are then obtained through Equation 3.38. The diffusion fluxes are computed through a forward difference scheme:
Fd(i) t- K.(i) C(i + 1) C(t) (5.2)
Az




C (I 1)
Fd 1) Fs (i 1)
- AZ
C ()
AZ 0
Fd(1) F (i)
C (I +1)
0
Figure 5.1: Definition Sketch for Grid Schematization and the diffusion flux gradient is computed through backward differencing dF (i) Fd(i) Fd(i- 1) (53)
dz Az
The settling fluxes are computed at each grid point, i, by F,(i) = W,(i)C(i) (5.4)
where W,(i) is computed as a function of concentration using Equation 4.6, or a constant value is used to compute W,(i) if the concentration falls within the free settling range. In the range of concentrations for which the settling flux increases with C (flocculation settling), the settling flux gradient is computed using backward differencing: dF, (i) F,(i) F,(i- 1) (55)
dz Az
while in the hindered flux range a forward differencing is used: dF, (i) F, (i + 1) F, (i) (5.6)
dz Az




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The concentration at every grid point within the water column is then computed as
____ dFd(i)
C'+Aly) = C'(i) + At(F + d----) (5.7)
dz dz
where At represents the time increment.
Bed fluxes are computed corresponding to one of four cases as defined by the value of the bed shear stress amplitude, rb:
1. For rb < ed the depositional flux F, is obtained from Equation 3.16 with H = 1.
2. For Tee.a < rb < re.m erosion is specified by surface erosion and an erosion flux is
obtained as follows
F,= M.(- 1) (5.8)
where both r,., and rM., are computed as functions of the sediment bulk density PB
of bed as given in Equations 4.16 and 4.18, respectively.
3. For rb > r.,. mass erosion occurs and the corresponding erosional flux is defined as Fe = em.( ) (5.9)
where Tce.m and eM.,n are also dependent on PB according to Equations 4.17 and 4.19,
respectively.
It should be noted that a bed bulk density profile with depth (for example, see Equation 5.13) is essentially required for calculating the erosion flux and eroded depth of the bed, since re and eM for both surface erosion and mass erosion vary with PB of bed. For each time step, the amount of sediment mass eroded or deposited per unit bed area (F. or Fp) is used to calculate the eroded or deposited bed depth (zb) in accordance with the given profile of bed bulk density with depth. For each time step, At, the eroded or deposited bed depth is obtained from following expression 4+At = 4 + At Fb (5.10)
Cb




where Fb is the bed flux represented by F or Fp and Cb is the concentration of the eroded or deposited bed during At corresponding to the bed bulk density profile. With this depth, the bulk density is recalculated and the height of water column (h) and Az, are redefined.
The new value of the concentration, C(n), at the grid point just above the bed which represents the fluid mud layer is computed as Ct+"'(n)= Ct(n) + AtX + dF.(n) + dFd(), (5.11)
An AZ,, AZ,,
where n indicates the grid point specifying the layer just above the bed.
5.2.2 Data used for Modeling
In order to simulate the vertical concentration profiles and the corresponding eroded depths, the vertical transport model requires the following data:
1. Hydrodynamic data
" Wave data represented by the wave period (T) and the wave height (H)
" Initial water column height (h)
2. Sediment parameters
" Sediment granular density (p.)
" Parameters of a, b, m and n used to compute the settling velocity dependence
on concentration
" Maximum settling velocity (W,) and the concentration (C1) defining the limit
of the free settling range
3. Diffusion parameters
* Empirical parameter for neutral mass diffusivity (Cf)

* Empirical parameters for stabilized diffusivity (ce and 6)