• TABLE OF CONTENTS
HIDE
 Report documentation page
 Title Page
 Acknowledgement
 Table of Contents
 List of Figures
 List of Tables
 List of symbols
 Summary
 Introduction
 Vertical structure of suspensioin...
 Approach to vertical transport...
 Experiments
 Application to Lake Okeechobee
 Conclusions and recommendation...
 Appendix A: Description of cores...
 Appendix B: Concentration profiles...
 Appendix C: Time-concentration...
 Bibliography






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 89/019
Title: Fine sediment erodibility in Lake Okeechobee, Florida
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Permanent Link: http://ufdc.ufl.edu/UF00076149/00001
 Material Information
Title: Fine sediment erodibility in Lake Okeechobee, Florida
Series Title: UFLCOEL
Physical Description: xix, 140 p. : ill. ; 28 cm.
Language: English
Creator: Hwang, Kyu-Nam
Mehta, A. J ( Ashish Jayant ), 1944-
University of Florida -- Coastal and Oceanographic Engineering Dept
South Florida Water Management District
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainsville Fla
Publication Date: 1989
 Subjects
Subject: 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.
Statement of Responsibility: by Kyu-Nam Hwang, Ashish J. Mehta.
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.
 Record Information
Bibliographic ID: UF00076149
Volume ID: VID00001
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: oclc - 21708702

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Table of Contents
    Report documentation page
        Unnumbered ( 1 )
        Unnumbered ( 2 )
    Title Page
        Title Page
    Acknowledgement
        Acknowledgement
    Table of Contents
        Table of Contents 1
        Table of Contents 2
        Table of Contents 3
    List of Figures
        List of Figures 1
        List of Figures 2
        List of Figures 3
        List of Figures 4
    List of Tables
        List of Tables 1
        List of Tables 2
    List of symbols
        Unnumbered ( 14 )
        Unnumbered ( 15 )
        Unnumbered ( 16 )
        Unnumbered ( 17 )
        Unnumbered ( 18 )
    Summary
        Unnumbered ( 19 )
        Unnumbered ( 20 )
        Unnumbered ( 21 )
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
    Vertical structure of suspensioin under waves
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
    Approach to vertical transport problem
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
    Experiments
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
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        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
    Application to Lake Okeechobee
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
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    Conclusions and recommendations
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
    Appendix A: Description of cores from Lake Okeechobee
        Page 102
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    Appendix B: Concentration profiles from settling tests
        Page 128
        Page 129
        Page 130
        Page 131
        Page 132
        Page 133
    Appendix C: Time-concentration relationship from erosion tests
        Page 134
        Page 135
        Page 136
    Bibliography
        Page 137
        Page 138
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Full Text


REPORT DOCUMENTATION PAGE
1. Report No. 2. 3. Recipient's Accession No.


4. Title aod Subtitle I. Report Date
FINE SEDIMENT ERODIBILITY IN LAKE OKEECHOBEE, FLORIDA November 1989
6.

7. Author(s) 8. performing Organization Report No.
Kyu-Nam Hwang
Kyu-Nam Hwang UFL/COEL-89/019
Ashish J. Mehta
9. Performing Organization Name and Address 10. project/Task/Work Unit No.
Coastal and Oceanographic Engineering Department Lake Okeechobee Phosphorus
University of Florida Dynamics Study. Task 4.4
11. Contract or Grant No.
336 Weil Hall
Gainesville, FL 32611 1. of Reprt
13. Type of Report
12. Sponsoring Organization Name and Address
South Florida Water Management District
P.O. Box V, 3301 Gun Club Road Final
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 qual-
itative agreement with observed trends in profile evolution at muddy coasts. Characteristic
features are the formation of a strong gradient in suspension concentration termed the lu-
tocline, 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 Classif. of the Report 20. U. S. Security Classif. of This Page 21. No. of Pages 22. Price
Unclassified Unclassified 159









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 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 N 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 thick-
ness 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 concen-
tration 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 Dy-

namics 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 pro-

vided 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 Spark-

man, 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

SUMMARY ................. .. ...... ............... 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 EXPERIMENTS .................................. 27

4.1 Introduction ................ ........ ............ 27

4.2 Characterization of Sediment . . . . . ... 27

4.2.1 Particle Size Distribution . . . . . ... 29

4.2.2 Organic M 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 M odel ................. ................. 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 description .. . . .. . . . 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 Wa-
ter 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 . . . . 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
G radient, . . . . . . . . 25

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 OK1OVC 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
g 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
g 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- . . . ... 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, rTe, 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 Schematization . . ..... 77

5.2 Typical Bulk Density Variation of the Bottom Mud Layer in Lake Okee-
chobee; Type 1 ................... .. ......... 82

5.3 Typical Bulk Density Variation of the Bottom Mud Layer in Lake Okee-
chobee; Type 2 ................... ............ 82

5.4 Typical Bulk Density Variation of the Bottom Mud Layer in Lake Okee-
chobee; Type 3 ... ... .. ... .. ... .. .. ... ..... 83










5.5 Typical Bulk Density Variation of the Bottom Mud Layer in Lake Okee-
chobee; 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 OK29VC 127

B.1 Concentration Profiles from Settling Test 2; Initial Concentration of 2.8
g L-1 ............ .. ....... ... ........... 129

B.2 Concentration Profiles from Settling Test 4; Initial Concentration of 5.0
g L-1 ...................... .............. 129










B.3 Concentration Profiles from Settling Test 5; Initial Concentration of 2.8
g L -1 . . . . ...... . . .. 130

B.4 Concentration Profiles from Settling Test 7; Initial Concentration of 2.7
gL-1 .................. .................. 130

B.5 Concentration Profiles from Settling Test 8; Initial Concentration of 3.2
g 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
g L- ........................ ..... ... ....... 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 1 . ... 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 re . . . ................... 72

5.1 Hydrodynamic Conditions ........................ .... .. 80

5.2 Values of Ab, f, and rb ....... ................ .... .. 885

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


L









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

A.16 Bulk Density and Vane Shear Strength Variations for Site OK29VC 119














LIST OF SYMBOLS


Ab = Horizontal water motion (amplitude) at the bottom

a = Settling velocity coefficient

am = 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

C1 = 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

Co = Initial suspension concentration

CD = Drag coefficient

Cj = Average concentration of fluid mud layer

Cfo = 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

Fp = 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

Kn = Vertical mass diffusivity for neutral flow

K, = Vertical mass diffusivity for stratified flow

k = Wave number

k = Vertical unit vector

kl = Settling velocity coefficient

k2 = Settling velocity coefficient

k, = Equivalent bed roughness












L = Wave length

I = Prandtl's mixing length

m = Eroded sediment mass per unit bed area; settling velocity coefficient

mi = 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

pi = 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

Rc = Corrected hydrometer reading

Re = Reynolds number

Rf = Flux Richardson number

Ri = Gradient Richardson number

St = Turbulent Schmidt number

es = Coefficient defining surface erosion rate

82 = Coefficient defining surface erosion rate

T = Wave period

t = Time variable

U = Velocity vector with cartesian components

U' = 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

Wm = Maximum settling velocity of sediment

Wn = Minimum settling velocity of sediment

Wo = 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

zf = Thickness of fluid mud layer

zfo = Thickness of fluid mud layer at initial time

a = Settling velocity coefficient; stabilized diffusivity constant

a, = Wave diffusivity constant

/8 = Settling velocity coefficient; stabilized diffusivity constant; wave diffusivity constant

/i = Wave diffusivity constant

#2 = Wave diffusivity constant

p = Fluid density

ps = Bulk density at upper fluid mud interface

pB = Bulk density

Pi = Bulk density at lower fluid mud interface

p, = Sediment granular density

p, = Water density













p = Dynamic viscosity of fluid

v = Kinematic viscosity of fluid

e = Erosion rate

Ei = Erosion resistance defining parameters

eM = Erosion rate coefficient

EM., = Erosion rate coefficient for surface erosion

eM.m = Erosion rate coefficient for mass erosion

a = Wave frequency

rb = Applied bed shear stress

re, = Critical bed shear stress for erosion

rTe., = Critical bed shear stress for surface erosion

rTe., = Critical bed shear stress for mass erosion

red = Critical shear stress for deposition

r,m = Maximum critical shear stress for deposition

rn = Minimum critical shear stress for deposition

r, = Bed shear strength

r7 = 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 qual-

itative agreement with observed trends in profile evolution at muddy coasts. Characteristic

features are the formation of a strong gradient in suspension concentration termed the lu-

tocline, 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 mechanism 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-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 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 thick-

ness 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 concen-

tration 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 suspen-

sion 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 sedi-

ments 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 domi-

nated 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 measure-

ments 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 physi-

cally realistic but simplified manner in order to simulate prototype trends in concen-

tration profile evolution.

2. Field data collection and laboratory experiments were conducted with Lake Okee-

chobee bottom sediment, in order to determine relevant parameters including erosion










and deposition relationships to serve as input data to simulate the concentration pro-

file 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 concentra-

tion 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) Mea-

surements 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 ap-

plication 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 con-

centration 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. Ap-

pendices 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 concen-

tration 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 concentra-

tion 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 lutocline (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


L








MWL


Mobile
Suspension


Iu Entrainment Settling
Lutocline ormation
,S,~- LZ----------
Fluuidization Fluid Mud

Consolidation Deforming Bed
-"------------------- --------
Stationary Bed


Figure 2.1: Instantaneous Vertical Concentration and Velocity Profiles, an Idealized De-
scription

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 fluidiza-

tion 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.









10 0 1 1 1 1 1 1 1 1
Time
C (hr)
E 80 0 Pre-frontal
0 o 22.8
B--- 24.1 Frontal
zO 68.5 Post-frontal
2 60-
D


L0
UJ 40-
A Lutocllne

0 1 1 I I I I I1 I I I I1 1 1
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 ac-

tion over coastal mud flats 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 previ-
ously 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 re-

produced 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 equi-

librium 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-1 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 mgL



Cs= 102 mgL' Low
hi = 4.6 m Concentration
hi C Cb 200 gSuspension
Cb= 200 gL

I h High Concentration
"""c'. Suspension
-h2 Lb -Bed


(a) (b)

Figure 2.3: a) Relationship Between Uniform Suspension Concentration, C,, in Water Col-
umn 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 lake. 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 equa-

tion. 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:


S= UC 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:


U = 0 + U' (3.3)







11
C = + C' (3.4)

Inserting these terms into Equation 3.2 and averaging over time results in

F = OC + 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:


t = U'C' = -K VC (3.6)

where K is a diffusivity vector with cartesian coordinate components (K., Ky, Kz). By

adding the flux due to the turbulent diffusivity, the time averaged Equation 3.1 becomes

_C = -V(0C DVC K. VC + WCk) (3.7)
at

Since turbulent diffusivity is much greater than molecular diffusivity, the terms corre-

sponding 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 V2 (3.8)
at az

which can also be expanded as

aC aC aC a[(w, + iw)C a 2 a0U aC (3.
+ +v + = K + K + K-, 3.9)
9t 8x 8y 9z 922 Qy" 8z*

Since the present analysis is concerned with the vertical structure of sediment concen-

tration, 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 verti-

cal advection terms and horizontal diffusion terms can be neglected in a simplified analysis.

This allows Equation 3.10 to be reduced to

ac 8a a ac
aC (Fd + F.) = -(K, W,C) (3.10)
at 8z 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(Ct) = a
F(0,t)= K |Io -W,C I,,= 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)

Fe = Fd Ib ; 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, Fp, 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 fric-

tional, 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 pre-

ceded 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 con-

tinues 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
am
F, = = f (r r,,ex,e2,... ,eN) (3.14)

where rb is the bed shear stress, r, the bed shear strength and er are other erosional resistance

defining parameters. Equation 3.14 implies that the erosion flux is mainly determined by

the excess shear stress, rI r,.

Expression for the erosion flux for surface erosion under wave action (Maa, 1986) is

given as

Fe = EM(rb (3.15)
Tee

where eM is the erosion rate when rb = 2ree and e,, = 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= -pWC (3.16)


i








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(1 (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 red.

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 Won Ws
S= (W,)exp H[1 )) t (3.18)
0en i= h
where
= )en (3.19)
ln( )
and Co is the initial suspension concentration, N is the total number of classes, 4(Wj,)

is the frequency distribution of settling velocity with maximum value W,, and minimum

value Wn, h is the water depth, and r,, and ren are the maximum and minimum values,

respectively, of the critical shear stress for deposition, rei.

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 Ten < Tb < rem a fraction of the initially suspended sediment for which rT < 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 rcn = rcm = rcd.

Consequently Equation 3.18 reduces to

C rb W,
exp [-H(1- (3.20)
Co Ted h
A typical value for red is considered to be 0.1 N m-2 (Mehta, 1988b). The settling velocity,

W,, is the critically important pamameter 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 suspen-

sion. 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 ca-

pacity of the sediments (van Olphen, 1963). Collision frequency is dependent on Brownion

motion, fluid shearing, and differential settling. Among these factors contributing to ag-

gregation, 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, = WC. 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, Re, is expressed as

2 4 gd (p, p) (3.21)
3 CD pw

where CD is the drag coefficient, g is the gravity acceleration, and p, and p, are sediment

and fluid densities, respectively.

In the Stokes range (Re < 0.1) the drag coefficient is given by

24
CD = (3.22)
R,

and the settling velocity is given by Stokes law (Vanoni, 1975)

W = d (p, p) (3.23)
18v p,

where v is the kinematic viscosity of the fluid. For large Re, 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;
I


Negligible
Settling


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










3.3.2 Flocculation Settling

Between concentrations Ci and C2, identified as the flocculation settling range, in-

creasing 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. = kiC" (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,

kI, can 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.o[l k2(C C2)]" (3.25)


where W,o 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 Fo. This is due to the minuscule decrease of settling velocity








20

between C2 and Cs in comparison with the increase of concentration. At values of C higher

than Cs 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 p, in Stokes' law for laminar flow, momentum diffusivity for the Reynolds stress

in turbulent flows is defined by

= -pu -.= -pa (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 = Ejj = 0 and Eij = Eji = E.

It should be noted that E is approximately proportional to the first power of the mean

velocity U, 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= 3b[- [ (3.28)


where # 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-U (3.29)

Since in the linear wave theory u is given as

H cosh k(h + z) (3.30)
u = -a- (3.30)
2 sinh kh

diffusivity is calculated as

Ha sinh3 k(h + z)
K = 2k sinh kh cosh2 kh(h + z)

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 = ac 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) (33)
2 sinh kh
H sinh k(h + z) (334)
b = (3.34)
2 sinh kh

and substituting Equations 3.33 and 3.34 into Equation 3.32, the following expression for

K is obtained
H2sinh k(h + z) (3
2 sinh2 kh

This equation is considered as a promising expression, based on energy dissipation con-

sideration, 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

concentration 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 increase 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)
Ps







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 practically 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):
gw'p' R3
R = (3.37)
PBu''() St
where R, is the gradient Richardson number defined as

S=- (3.38)
PB ( )2
where g denotes gravity acceleration, and z represents the vertically downward positive axis.

Positive values of Rf indicate stable stratification, negative values denote unstable stratifi-

cation, and Rf = 0 corresponds to a neutral (non-stratified) condition. The dimensionless

quantity Rf clearly determines the relative role of buoyancy in the generation of turbulent

energy. In the case of Rf < 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 suppression 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 typ-

ically of the Munk and Anderson (1948) form as
K1
K = ( (3.39)
S(1 + #")a

where K, and K, are the vertical mass diffusivities for stratified and neutral flows, respec-

tively, and a and P are generally non-negative empirical constants. Note that for positive a

and f, increasing density gradient (a- ) leads to increasing Ri 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 = -K. (3.40)
ac

which indicates direct dependence of Fd on s-. In the presence of density stratification, by

substituting Equation 3.38 into 3.39, the diffusive flux becomes

K,, C
Fd = Kn a (3.41)
(1+ -PP)- az

From Equations 3.36 and 3.38, it is obvious that RA 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 9,

reaches a maximum and then slowly decreases. For very high values of -, the gradient

of the diffusive flux, aFd/8(Q ) becomes zero and, with stabilized perturbations and local

minima in mixing, a lutocline is developed in the vertical concentration profile. Conse-

quently, the formation of lutocline is strongly related to the nonlinear dependence of Fd on

9. Since the sediment settling acts against the vertical mixing, the growth and stability of





















0.004



E

m 0.003


X Kn
K K )
ri (1+3.33 R,)1-5
2 0.002
0

LL
U-
SV mK= -- Kn--
W 0.001 (1+4.17 R,)2


w
z

0.000 I I i I i I
0.0 0.2 0.4 0.6 0.8

CONCENTRATION GRADIENT -J (kg i4)



Figure 3.2: Nonlinear Relationship Between Diffusive Flux, Fd, and Concentration Gradient,
ac
8z








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 char-

acteristic 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 transport. Mehta et al.

(1986) specified essential properties of cohesive sediment in terms of grain size, mineralogical

composition, percentage of organic, 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 fine-

grained 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 ml 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, Re, were computed as

Re = R. Zero correction + CT (4.1)


where CT is the temperature correction factor, and "zero correction" represents both menis-

cus 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

(1l00000W) G. ,
P 1[ ](R G) (4.2)
G, G1

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 ml volumetric flask

and de- airing the mixture under high vacuum. Sediments from all sites were subjected to

this measurement giving an average value of G, equal to 2.14. Note that since G, is equal

to p,/p., sediment granular density becomes 2.14 g cm-3 with a given (assumed) value of

p", = 1 gcm-3.
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
....... 1 "
C- 80- 2\
-2


S60 --4- \4
0 ---- 5 \ V\\

540 -.
U Coarse Fraction .
(Composite) *

S20 :


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 pre-

sented in Figure 4.2 for the fine-grained fractions at the five sites. This table shows that

the dispersed median diameter, dso, 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, = (d7s/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) dso (pm) d75 (pm) So (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 10 3 0.6 4.2 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 pm (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 500C 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-S). Since the density

of a organic matter has lower value than p, for clayey soil, p, tends to be low when the

organic fraction in the sediment is high. Otsubo et al. (1987) also observed this trend

in the relationship between the organic fraction in the sediment and p, through the field








33

studies on the physical properties of sediment (water content, G,, 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 Labora-

tory. 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 measure-

ments showed a close relation, despite obvious data scatter. Figure 4.4 shows density and

shear strength profiles in a core sample from site OK2 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 nm2)
0 2000 4000 6000
EI I

0 & Bulk Density
0 10 Shear Strength


20

| 30-


o 40
-J
w
m
: 50
I.-
C.
0 60 I I I I
1.0 1.1 1.2 1.3 1.4 1.5 1.6
BULK DENSITY (g cm'3)

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-S 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 -

60 -


1.


Figure 4.5:

S5

z

J-
4




CD 3
z
w
U,
cc
2

(0 -
C)
M
4

'U
X 1

UJ
z
G4 0


0 1.1 1.2 1.3 1.4 1.5 1.6
BULK DENSITY (g cmn3)

Bulk Density and Vane Shear Strength Variations for Site OK10VC


* *
*
*


. .: ..
* 0


**
0* *
r o 'oo

m


& *


0
Og


> 1 1.1 1.2 1.3 1.4

= 1.065g cm'3 BULK DENSITY, pB(g c 3)

Figure 4.6: Vane Shear Strength Variation with Bulk Density based on all Bottom Core
Samples








39

at 1.065 g cm-S. 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 aC/at can be known at a

particular point, while the accumulation method records the temporal change in the actual

mass flux, W,C, at the bottom.

Another approach was selected to yield the settling velocity versus concentration rela-

tionship 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 concen-

tration profile or multi-depth method (McLaughlin, 1958 ; Fitch, 1957).

The actual procedure developed by Ross (1988) was chosen. This method uses multi-

depth concentration sampling and numerical integration of the sediment settling equation

(mass conservation). In order to make the experimental condition similar to the field con-

dition, 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 50C. 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 concen-

tration 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 C 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)
(4.3)
8t 8z 8z

This equation relates the time rate variation of suspended sediment concentration, C(z, t),

to the vertical gradient in settling flux, F, = WC. 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+ = -I + + 1W.- l w+ )j+ (4.4)

where x 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
S= C (Inci+in C) (4.5)

It should be noted that the log average, instead of the arithmetic average, was used to cal-

culate 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
I-1


Wi Xi
S -
I-1


i Xj


i1
1+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 Co
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 1 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 -1.








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 column was relatively small during each test, indicating the maximum

variation to be 3.50C. For the tests as a whole, however, temperature varied from 190C 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, Co, 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 concentra-

tion. 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 1 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 L-1 up to

approximately 0.1 g L-1 at 130 cm above the bottom of the column. 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 L~' are shown. These profiles can be considered to be representative 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 illus-

trated 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 lutocline 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


10-1 1 10 102
SUSPENDED SEDIMENT CONCENTRATION (g C1)


Figure 4.9: Concentration Profiles from Settling Test 1; Initial Concentration of 1.8 g L-1


200


E 150

z
0
F 100

S5
w 50


01-
10-1


1 10


102


SUSPENDED SEDIMENT CONCENTRATION (g .1)


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












200


150
E

z
100

IU
-j 50
UJ 50


10-1 1 10 102
SUSPENDED SEDIMENT CONCENTRATION (g L'1)


Figure 4.11: Concentration Profiles from Settling Test 6; Initial Concentration of 23.7 g L-


200


E 150

z
Z
0 100

4
-J
UJ 50


0L-
10-1


1 10


102


Figure 4.12:
gL-1


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
aC"
w= = C2 (4.6)
(C2 + b2)m
which is modified from Wolanski et al. (1989), has been developed to represent both floc-

culation 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-2mC" if C2 < b2 (4.7)

W, = aC"-2m if C2 > b2 (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. Refer-

ring 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

m 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, Wo. The maximum value, Wo, and the corresponding C2 are

defined by

(2m l)- 1 -
Wo = ab-m ) (4.9)
(2 M 1)2
b
C2 = (4.10)
(2- 1).

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+1
F, = W,C = (4.11)
(C2 + 62)m
In the same way as before, the peak value, Fo, of the flux and the corresponding Cs can

be defined by

( 2m )m--
F.o = abn+l-2m n+) 2 (4.12)
n+lJ
b
Cs = b (4.13)
(n+l
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 (Wo., C2, Fo and Cs) 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 Fo C3
No. (mm sec-1) (g L-') (Kg m- sec-1) (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-'. At the end of the

low concentration regime, W, varies approximately from 0.02 to 0.3 mm sec-'. 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



/ N 0
10
a Cn
S1 W =- /* Hindered
E (C +b) Settling 0)
E m

S* -101 z
S.. *.
*n
o 10"1 / Flocculation "* -

> 10 n


S10- 2 C/: c2 = 2.46 g L\ 91
0101
W /= 1.47 mms .3
/ C3 = 4.38 gL1


103 I I I 1 0-4
10' 2 101 1 10 102
CONCENTRATION, C(gL"1)



Figure 4.13: Settling Velocity and Settling Flux Variations with Concentration for Site 1

















10
Site
v 2
0 4
S5


I-)

E 1


v



a 0 0 v o%




0W 0
oo




10-2 I ,
10-2 10-1 1 10 102

CONCENTRATION (g I:1)


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








53










10

Site
o 3
A6




E A A
S1 A 8A

0 OA O

A

3 0A-
10 2 , o
z o OA





0 A

0 A AA


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 L'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
v 2
o 3
04
0 5
"6




v o o
00 0

o oo a
a *

M 3, 0 0 o



Po
- / | 3 o


0 0 *

J i 61t 11t ,a11 I 11 I 11 t I l I*$-I Lt


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, aC/at,

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 50C 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


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


40 r-


20 -


o10








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~2, 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-S) (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 23 3.5 24


aside. Care was taken to flush the sampling tubes before each withdrawal. Lake water

was periodically added to the flume to maintain a 23 cm water depth.

6. Gravimetric analysis was used to determine the suspension concentration of each sam-

ple. 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 es-

timate 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~- was prepared. In 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. There-

fore, 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 cm-3, 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 consequence 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 BI dI 0 1 1 I b I b
0.15N m2 0.25N 2 0.35N 2 0.45N m20.55N m2 0.65N m 0.75N m
















, m 0 *


SI


100


200


300


400


TIME (mins)



Figure 4.20: Time-Concentration Relationship in Test 4


.4 64


500


600















0.6

T, 0.15N m'2 0.25N m-2 0.35N m2 0.45N m-2 0.55N m-2 0.65N m-2 0.75N m 2
CD
- 0.5 -
O
I-
4 0.4-

Z
w

O
C) 0.3-
z
0
L)
z 0.2-
0

z 0
W 0.1-


C) 0.0 I
0 100 200 300 400 500 600
TIME (mins)


Figure 4.21: Time-Concentration Relationship in Test 6



















0)


I-
Z
0




z
<
a.)
LU
Z
0

Z
C-)
z
0

z
w

C',
Z
LU
Q.
(0
=)
0)


TIME (mins)


Figure 4.22: Time-Concentration Relationship in Test 5









duration steps in Figure 4.21. Without considering possible experimental error in the mea-

surement 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 experi-

mental 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 con-

centration 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

8m fC
a = (4.14)
at at

where e 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 (e) 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 rb = 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 M1 and M2 (for example, see Fig. 4.23)

were obtained. The line of slope M1 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, e = Fe,

and the bed shear stress is given as:


Fe = EM( 1) (4.15)
*ce







2.0
Test


cM 0 3
'E 1.5 -
o Bed Surface Erosion


u 1.0 M
-

Z Erosion of Surface "Fluff"
S0.5- o a
0 M
O o -1 /

0.0 I I
o.o ,p- l -- I --l,,o----



0.0 0.2 0.4 t Tce .s 0.6
SHEAR STRESS, (N n2)
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, ree is a erosion critical shear strength, and rb is a
bed shear stress.
For surface erosion, the erosion critical shear strength, rec.,, can be determined by
extrapolating the M2 line back to the abscissa (Parchure and Mehta, 1985). The erosion
rate coefficient, eM.,, is obtained by multiplying rce., with M2. Values of ree., 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 Tce. and eM.,. The estimated values of re,., 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 rce.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

*L-
e-
C4 0.8
'E
0)
E 0.6


0.4 -
Z
0
V) 0.2-
0

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-S is the bulk density below

which the bed was considered to be fluidized. The values of Tee.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,

Te, 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.s = a(pB pP)' + c, ; 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 pi is the bulk density

of uppermost bed level which is specified as 1.065 g cm-S. Equation 4.16 seems to be






71 I






i
7M






20





-i 15





W 10
*-

z
0
O
c 5-
w




0
0.0 0.2 0.4 0.6

SHEAR STRESS, (N ni2)


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















C.)

E
o


CM



0
O
rU
t0)


Note: indicates that these values were obtained by combining the erosion rate data re-
sulting 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 -

0.0 -
0.0 0.2 0.4 0.6

SHEAR STRESS, (N i2)

Figure 4.26: Erosion Rate Variation with Bed Shear Stress for Test 6







Table 4.5: Values of PB, eM, and ree

Test PB CM.a rce.s Tee.m
No. (g cm-) (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
Fluid Mud Bed
'E

Z Tb e m
Z bZce m
I Mass Erosion
0
z I
e 1.0 e* s' Tb "ce m
,- I Surface Erosion
Cl I


SI O
c 0.50- .--- NTce*s

'T Zb< Tce s
LU No Erosion
0.0 I I I
1.0023 1.05 1.10 1.15 1.20 1.25
BULK DENSITY (g cn3)

Figure 4.27: Critical Shear Stress, ree, Variation with Bed Bulk Density, PB

consistent with the expression, ree = ap, 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 E., = l exp T- ; surface erosion (4.18)

EM.m = i ; mass erosion (4.19)

where sl = 0.23, s2 = 0.198, mi = 224, and ps 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-2 hr-', which is very close to mi.

















103
0 Fluid Mud Bed





S* -,EM = Const = 224 (mg cri2 h1)
E 2 I Mass Erosion (Tb>Tce. m)


mto
-\ Surface Erosion
-('ce m> Tb ce s)
O-
S InEM= 0.23 exp ( 0198
10 1.1 Pg-1.00235
10


Oz
oI
cnI
W ~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 5
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 appli-

cation 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, how-

ever, 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.








76

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

rb = \fpu (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 diffusiv-

ities are then obtained through Equation 3.38. The diffusion fluxes are computed through

a forward difference scheme:

d(i) ) C( + 1) C (5.2)
Az









C ( -1)


Fd (1) Fs (i-1)




C(i)
AZ 0

Fd(1) Fs(i)


-4t---- 1--

C (i +1)
*

Figure 5.1: Definition Sketch for Grid Schematization

and the diffusion flux gradient is computed through backward differencing
dFd(i) Fd(i) F(i- 1) (5
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 flocculationn 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







78

The concentration at every grid point within the water column is then computed as

F, (i) dFd(i)
C'+At() = C'(i) + At( d + 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 < red the depositional flux Fp is obtained from Equation 3.16 with H = 1.

2. For rTe., < Tr < rce.m erosion is specified by surface erosion and an erosion flux is

obtained as follows

F = M.,(- 1) (5.8)

where both re,., and eM., 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 > rTe.m mass erosion occurs and the corresponding erosional flux is defined as

Fe = eM.m( 1) (5.9)
'ce.m

where rTe.m and eM.m 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 ,ee 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


+At = z + At b (5.10)
Cb










where Fb is the bed flux represented by Fe 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+t(n) = Ct(n) + At( + dF(n) + dF(n) (5.11)
Az, ,~n Azn

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 (Wo,) and the concentration (C1) defining the limit

of the free settling range

3. Diffusion parameters

Empirical parameter for neutral mass diffusivity (Cw)

Empirical parameters for stabilized diffusivity (a and 3)




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