PB83-223362
Modeling Fine Sediment
Transport in Estuaries
Florida Univ., Gainesville. Coll. of Engineering
Prepared for
Environmental Research Lab.f Athens, GA
Jun 83
U.S. DEPARTMENT OF COMMERCE
National Technical Information Service
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EPA-600/3-83-045
June 1983
MODELING FINE SEDIMENT TRANSPORT IN ESTUARIES
by
E. J. Hayter
A.-.J-. Mehta
Coastal and Qceanographic Engineering Department
College of Engineering
University of Florida
Gainesville, Florida 32611
Grant No. R-80668401
Project Officer
Robert B. Ambrose, Jr.
Technology Development and Applications Branch
Environmental Research Laboratory
Athens, Georgia 30613
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30613
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TECHNICAL REPORT DATA
(Please read Inductions on the reverse before completing)
1. REPORT NO.
EPA-600/3-83-045
2.
4. TITLE AND SUBTITLE
Modeling Fine Sediment Transport in Estuaries
5. REPORT DATE
June 1983
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
E.J. Hayter and A.J. Mehta
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
College of Engineering
Coastali and Oceanographic Engineering Department
University of Florida
Gainesville FL 32611
10. PROGRAM ELEMENT NO.
CARBIA,
11. CONTRACT/GRANT NO.
R806684010
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Research Laboratory—Athens GA
Office of Research and Development
U.S. Environmental Protection Agency
Athens GA 3061 3
13. TYPE OF REPORT AND PERIOD COVERED
Fi nal
14. SPONSORING AGENCY CODE
EPA/600/01
15. SUPPLEMENTARY NOTES
16. ABSTRACT •
A sediment transport model (SEDIMENT 1I1A) was developed to assist in predicting
the fate of,chemical pollutants sorbed to cohesive sediments in rivers and estuaries.
Laboratory experiments were conducted to upgrade an existing two-dimensional, depth-
averaged, finite element, cohesive sediment transport model.. The utility of SEDIMENT
IIIA was demonstrated by laboratory resuspension and deposition tests and simulations
of the sedimentation processes in a hypothetical canal. The effect of salinity in
these simulations also was examined. The model should enhance capabilities for pre-
dicting water quality impacts and for analyzing sedimentation management issues. The
improved transport descriptions should be useful in making more reliable predictions
of the fate of dissolved and sorbed pollutants discharged into an estuary or harbor
by stormwater runoff or industry releases, thus assisting in the evaluation of water
pollution control options. The enhanced descriptions should also be useful in pre-
dicting the movement of dredged material released in open marine waters, identifying
harbor sites in estuaries and bays where shoaling is minimized, predicting changes in
sedimentation that may result from proposed changes or developments of an estuary or
harbor, and estimating shoaling rates and maintenance dredging requirements in areas
of low flow.
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RELEASE TO PUBLIC
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EPA Form 2220-1 (9-73)
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NOTICE
THIS DOCUMENT HAS BEEN REPRODUCED
FROM THE BEST COPY FURNISHED US BY
THE SPONSORING AGENCY. ALTHOUGH IT
IS RECOGNIZED THAT CERTAIN PORTIONS
ARE. ILLEGIBLE, IT IS BEING RELEASED
IN THE INTEREST OF MAKING AVAILABLE
AS MUCH: INFORMATION AS POSSIBLE;
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DISCLAIMER
Although the research described in this report has been funded wholly
or in part by the United States Environmental .Protection Agency through
Grant Number R80668401 to the University of Florida, it has not been sub-
jected to the Agency's required peer and policy review and therefore does
not necessarily reflect the views of the Agency and no official endorse-
ment should be inferred.
ii
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FOREWORD
As environmental controls become more costly to implement and the
penalties of judgment errors become more severe, environmental quality
management requires more efficient management tools based on greater
knowledge of the environmental phenomena to be managed. As part of this
Laboratory's research on the occurrence, movement, transformation, im-
pact and control of environmental contaminants, the Technology Develop-
ment and Applications Branch develops management or engineering tools
to help pollution control officials achieve water quality goals through
watershed management.
Heavy metals, insecticides, herbicides, and other organic compounds
can be transported.into natural waters on fine sediment materials. Storage
of river waters for agricultural, urban and industrial uses will reduce
sediment inflows to estuaries as water resources become scarce. The effects
of reduced sediment inflows must be evaluated to ascertain minimum water
quality management needs. This report describes an improved transport
model for simulating the erosion and deposition of cohesive sediments in
estuaries and the effect of salinity on these transport processes. By
modeling the movement of fine .sediments in a water body of concern, pre-
dictions can be made of the fate of sorbed pollutants.
William.!. Donaldson
Acting Director
Environmental Research Laboratory
Athens, Georgia
111
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ABSTRACT
Laboratory experiments were carried out to determine: 1) the
resuspension characteristics of partially consolidated, flow-deposited
cohesive sediment beds under turbulent flows, 2) the effects of salinity
on the rates of erosion of these beds, and 3) the effects of salinity on
the rates of deposition and the settling velocity of suspended cohesive
sediments under turbulent flows. The experimental results together with
other available information have been used to upgrade SEDIMENT III, a
two-dimensional, depth-averaged finite element cohesive sediment
transport model. The purpose of the new model, SEDIMENT IIIA, is to
assist in the prediction of the fate of pollutants sorbed to cohesive
sediments in rivers and estuaries.
Resuspension tests conducted in a rotating annular flume and in a
straight recirculating flume at the University of Florida using
kaolinite and a natural mud revealed that flow-deposited beds are
stratified with respect to bed shear strength and density and can
consist of unconsolidated stationary suspensions, partially consolidated
beds and settled, fully consolidated beds. Both the cohesive shear
strength and the bed density increase with increasing period of
consolidation. When subjected to an excess bed shear stress, stationary
suspensions erode almost instantly, while partially and fully
consolidated beds undergo surface (aggregate by aggregate) erosion. An
empirical expression for the rate of surface erosion of partially
consolidated beds, that is analogous to the rate expression which
results from a heuristic interpretation of the rate process theory of
chemical reactions, was derived. This rate expression indicates that
the rate of erosion varies exponentially with the excess bed shear
stress. The rate of erosion of settled beds is linearly proportional to
the excess shear stress.
A cohesive sediment bed schematization algorithm and an erosion
algorithm have been developed. Based on an interpretation of typically
observed Eulerian time-concentration records in estuaries, erosion is
considered to occur during accelerating flows. Likewise, deposition is
considered to occur during decelerating flows. The erosion algorithm
simulates mass erosion of stationary suspensions and the surface erosion
of partially consolidated and settled beds. The bed schematization
includes these three bed sections, and divides each section into
discretized layers. The amount of sediment eroded from the bed or
deposited onto the bed in each element is determined, and the thickness
and the structure of the bed in that element are adjusted accordingly.
Consolidation of the bed due to overburden is accounted for by first
filling up the top stationary suspension layers and then the partially
consolidated layers as deposition occurs.
A deposition algorithm has been developed. This algorithm
integrates the concepts proposed by various investigators and represents
a unified model of this process. Deposition is predicted to occur when
the bed shear stress is less than the maximum depositional shear
stress, t, . The rate of deposition is dependent, among other
factors, u^Sfi the bed shear stress and the settling velocity of the
suspended sediment.
iv
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The bed shear strength was found to vary with the salinity S of the
eroding fluid for salinities less than 2 ppt. The shear strength
increased linearly in the range ~0 < S < 2.ppt. For S > 2 ppt, no
further increase in the bed shear strength was observed. Consequently,
the rate of erosion decreased with increasing salinity up to 2 ppt,
where it became practically invariant with respect to salinity.
The rates of deposition of the natural mud were found to increase
with increasing salinity. A power relationship between the settling
velocity, VI , and the salinity, of the form W « S0**3, was determined
from analysis of deposition tests conducted at salinities ranging from 0
to 35 ppt and under bed shear stresses varying from 0.0 to 0.30 N/m2.
The utility of the model is shown by simulations of laboratory
resuspension and deposition tests and of the sedimentation processes in
a 10 km hypothetical canal. The effect of salinity in these simulations
has been described.
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TABLE OF CONTENTS
Page
ABSTRACT .. iv
LIST OF FIGURES viii
LIST OF TABLES xiii
ACKNOWLEDGEMENT .. xiv
CHAPTER
I. INTRODUCTION..... 1
1.1. Estuarial Fine Sediment Dynamics. 1
1.2. Significance of Clays in Pollutant Transport 7
1.3. Purpose of Study 14
1,3.1. Need for Research. 14
1.3.2. Predictive Modeling. 15
1.3.3. Objectives and Scope of Investigation 21
II. MODELING CONSIDERATIONS 23
2.1. Significance of Important Physical Factors in
Estuarial Transport.... 23
2.2. Governing Equations.... 34
2.2.1. Convective-Oiffusive Transport Equation....... 34
2.2.2. Initial and Boundary Conditions 38
2.2.3. Solution of Governing Equation .^ 39
2.3. Description of Selected Transport Model....... 41
2.4. Model Modifications 42
2.5. Fine Sediment Bed.... 44
2.5.1. Introductory Note 44
2.5.2. Bed Schematization 50
2.6. Erosion of Fine Sediment Bed *... 54
2.6.1. Introductory Note... . 54
2.6.2. Erosion Algorithm..... 68
2.7. Deposition of Fine Sediment 72
2.7.1. Introductory Note..... 72
2.7.2. Deposition Rates 86
2.7.3. Deposition Algorithm 88
vi-
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2.8. Influence of Salinity on Estuarial Sediment
Processes ..... 90
2.8.1. Effect of Salinity of Interparticle Forces.... 90
2.8.2. Effect of Salinity on Bed Structure.... 95
2.8.3. Effect of Salinity on Surface Erosion 96
2.8.4. Effect of Salinity on Coagulation 106
2.8.5. Effect of Salinity on.Deposit!on.. 113
2.9. Convergence and Stability of the Numerical Scheme 124
2.10. Model Limitations 125
2.11. Model Applicability 126
2.11.1. Water Quality Problems...... 126
2.11.2. Sedimentation Management Problems 126
III. SIMULATION OF FINE SEDIMENT TRANSPORT PROCESSES 12k.
3.1. Introductory Note 128
3.2. Simulation of Laboratory Erosion Tests.. 128
3.3. Simulation of Laboratory Depositional Tests........... 131
3.4. Simulation of Sedimentation Processes in
an Artificial Canal :. T36
IV. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 141
4.1. Summary and Conclusions....... 141
4,2. Recommendations for Future Research..... 145
V. REFERENCES 147
APPENDIX
A. Model Flow Chart of SEDIMENT IIIA.... 161
B. User's Manual 172
B.I. Oata Required for Model Use. 173
B.2. Description of Field Oata Collection Program.... 185
B.3. Description of Laboratory Sediment Testing Program.... 187
C. Characterization of Factors Involved in the Study of
Erosion of Fine Sediments 190
VII
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LIST OF FIGURES
Figure
1.1. Schematic Representation of Transport and Shoaling
Processes in the Mixing Zone of a Stratified Estuary,
including Ebb Predominance Factors (after Mehta and
Hayter, 1981) 2
1.2. Longitudinal Salinity and Suspended Sediment Concentrations
1n th* Hooghly River F.stuary (India) (after Mehta and
Moyter, mi)....... 6
1.3. Time and Depth Variation of Suspended Sediment Concen-
tration in Savannah River Estuary (after Krone, 1972) 8
1.4. Schematic Representation of the Physical States of Fine
Sediment in Estuarial Mixing Zone (after Mehta et a].,
1982a) 8
1.5, Variation of Heavy Metal Concentration with Sediment
Particle Size (after Salomons and Mook, 1977) 10
1.6. Time and Depth Variation of Salinity in Savannah River
Estuary (after Krone, 1972) 17
1.7. Time Variation of Chloride Concentration in a.Pacific
Ocean Estuary Due to Stormwater Runoff (after Orlob
et_jl_., 1967) : 17
1.8. Interactions of Tidal and Estuarial Sediment Transport
Processes (after Owen, 1977) 18
2.1. Monthly Salinity Distributions in the Cumbarjua Canal
Goa, India; Ebb; --<.-- Flood (after Rao
et_^l_., 1976) , 24
2.2. Variation of Chloride Concentration in San Francisco Bay
and Sacramento-San Ooaquin Delta-September 1955 (after
Orlob JUI-, 1967) 25
2.3. Salinity of the Surface Waters of the Pamlico River
Estuary as a Function of the Distance from the Railroad
Brodge at Washington, N.C. (after Edzwald et_jiU, 1974)...,. 26
2.4. Computed Longitudinal Salinity Profile in the Yangtze
River Estuary as a Function of the Distance Downstream
from Jiang Zhen Dong for Two River Discharges: Q =
33000 cms and 45500 cms (after Huang et al., 1980) 26
vi 11
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2.5. A Plot of Raw Vlscometer Data Obtained from the U.S. Army
Corps of Engineers Philadelphia District Sample (after
Krone, 1963) 31
2.6. Coordinate System 34
2.7. z/H vs. p/p for Avonmouth, Brisbane and Grangemouth Muds
(after Oixit, 1982) 47
2.8. z/H versus p/p for Consolidation Periods (a) Less than
48 Hours and (b) Greater than 48 Hours (after Dixit, 1982).. 47
2.9. Bed Shear Strength Observed as a Function of Depth (after
Parchure, 1980) 48
2.10. Variation of Critical Bed Shear Strength, tc, with
Depth (after Dixit, 1982) 49
2.11. Bed Schematization used in SEDIMENT IMA.. 51
2.12. Hypothetical Shear Strength Profile Illustrating
Determination of Bed Layers Thicknesses 51
2.13. Typical Laboratory Determined Relationship between
Surface Erosion Rate E and Time-mean Bed Shear Stress T
(after Mehta, 1981) 57
2.14. Example of Relationship between Surface Erosion Rate E
and Bed Shear Stress t. Data of Christensen and Das
(1973) for Grundite (after Mehta, 1981). 58
2.15. ert Data of Partheniades (1962), Series I and II
(After Mehta, 1981) 58
2.16. Dimensionless E-t Relationship Based on Results of
Ariathurai and Arulanandan (1978) (after Mehta, 1981) 60
2.17. Relative Suspended Sediment Concentration versus Time
for a Stratified Bed at Bed Shear Stress -^ =0.207 N/m2
(after Mehta and Partheniades, 1979)..... 60
2.18. Schematic Representation of the Selected Methodology for
the Variation of the Applied Bed Shear Stress During
Bed Preparation and Resuspension Tests (after Mehta
et^li.., 1982a) 62
2.19. Variation of Suspension Concentration with Time for
Tdc » 48 Hours (after Dixit, 1982).. 64
2.20. C^) versus ^ for Three Values of T^, using Kaolinite
in Salt Water (after Mehta jt__a_T., 1982a)....., 65
ix
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2.21. Normalized Rate of Erosion, e^e^, versus Normalized
Excess Shear Stress, (^^c(z)/rc(i), using Kaolinite in
Tap Water (after Mehta _et..al_., 1982a) 66
2.22. Normalized Rate-.of Erosion, e^/e^, versus Normalized
Excess Shear Stress, (t^-vc(z)/tc(z), using Kaolinite in
Distilled Water (after Mehta jt_jil_., 1982a),..* 67
2.23. Ratio C/C0 versus Time t for Kaolinite in Distilled Water
(after Mehta and Partheniades, 1975). 75
2.24. Ratio Ceq/C0 versus 8ed Shear Stress tb (after Mehta and
Partheniades, 1975) 75
*
2.25. Relative Steady State Concentration C in Percent Against
* eq
Bed Shear Stress Parameter -t-1 (after Mehta and
Partheniades, 1975) 77
2.26. C* in Percent versus t/t50 for Kaolinite in Distilled
Water (after Mehta and Partheniades, 1975) 79
*
2.27. Log tg0 versus tb for Kaolinite in Distilled Water (after
Mehta and Partheniades, 1975) 80
2.28. og versus Tb for Kaolinite in Distilled Water (after Mehta
and Partheniades, 1975). 80
2.29. Settling Velocity, Ws, versus Suspended Sediment Concen-
tration, C, for San Francisco Bay Mud (after Krone, 1962)... 82
2.30. Settling Velocity, Ws, versus Suspended Sediment Concen-
tration, C, for Yangtze River Estuary Mud (after
Huang et_jU, 1980) 83
2.31. Settling Velocity, Ws, versus Suspended Sediment Concen-
tration, C, for Severn Estuary Mud (after Thorn, 1981) 83
2.32. Effect of Size and Settling Velocity of Elementary
Particles on the Coagulation Factor of Natural Muds
(after Bellessort, 1973) 85
2.33. Repulsive and Attractive Energy as a Function of
Particle Separation at Three Electrolyte Concentrations
(after van Olphen, 1963) i. 92
2.34. Net Interaction Energy as a Function of Particle
Separation.at High Electrolyte Concentration (after van
Olphen, 1963)... 92
x
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2.35. Net Interaction Energy as a Function of Particle
Separation at Intermediate Electrolyte Concentration
(after van Olphen, 1963) . 94
2.36. Net Interaction Energy as a Function of Particle
Separation at Low Electrolyte Concentration (after van
Olphen, 1963) 94
2.37. Critical Shear Stress versus SAR for Montomorillonitlc
Soil (after Alzadeh, 1974) 97
2.38. Oimensionless Bed Density versus Bed Depth Profiles for
Salinities of 0, 1, 2, 5 and 10 ppt 100
2.39. Bed Shear Strength Profiles as a Function of Salinity 101
2.40. Surface Erosion Rate e versus Normalized Excess Shear
Stress (vV^c 102
2.41. Slope, a, Plotted Against Depth Below Bed Surface, z, as
a Function of Salinity 103
2.42. Ordlnate Intercept, EQ, Plotted Against Depth Below Bed
Surface, z, as a Function of Salinity , 103
2.43. Variation of SAR with Salinity (Sea Salt Concentration)
(after AMathural, 1974) 107
2.44. Coagulation-Dispersion Boundary Curves for (a)
Montmorillonite, (b) IHite and (c) Kaolinite at Three
pH Ranges (after Kandiah, 1974)...., 107
2.45. Comparison of the Collision Functions for Brownian, Shear
and Differential-Sedimentation Coagulation (after Hunt,
1980) 112
2.46. Effect of Salinity on Settling Velocity of San Francisco
Bay Mud (after Krone, 1962) 112
2.47. Effect of Salinity on Settling Velocity of Avonmouth Mud
(after Owen, 1970) 115
2.48. Effect of Salinity and Suspension Concentration on
Settling Velocity of Avonmouth Mud (after Owen, 1970) 116
2.49. Ratio C/C0 versus Time as a Function of the Bed Shear,
ijj, for Lake Francis Sediment with S = 5 ppt 118
2.50. Ratio Ce /CQ versus tb for Deposition Tests with Lake
Francis Sediment 118
xi
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2.51. Effect of Salinity and Bed Shear Stress on Settling
Velocity of Lake Francis Sediment , 120
2.52. Settling Velocity versus Suspension Concentration for
Deposition Test with lake Francis Sediment 122
*
?.*>3. Variation of C with Salt Concentration, S, and Bed
Shear Stress, tb 122
3.1. Comparison of Predicted and Measured Suspension Concentra-
tions versus time for a Resuspenslon Experiment..... i^g--
3.2. Demonstration of the Effect of Salinity on the Resuspenslon
Rates of a Flow Deposited Kaolinite Bed 130
3.3. Comparison of Predicted and Measured Deposition Rates for
Lake Francis Sediment at a Salinity of 0.0 ppt, and
Demonstration of the Effect of Salinity on the
Depositi on Rate T32
3.4. Comparison of Predicted and Measured Variation of C versus
(t/t50) lo<1 for Kaolinite in Distilled Water with
t* - 0.90 133
3.5. Comparison of Predicted and Measured Variation of C versus
(t/tso)1/a2 for Kaolinite in Distilled Water with
i* . 1.41 134
3.6. Comparison of Predicted and Measured Variation of C versus
(t/t50)1/02 for Kaolinite in Distilled Water with
T* « 2.70 135
3.7. Plan View of 10 km Hypothetical Canal 137
3.8. Predicted Concentration-time Record for Element 4 in
10 km Canal........ 138
3.9. Predicted Concentration-time Record for Element 5 in
10 km Canal 139
C.I. Oiagramatic Representation of the Steps in the Study of
Erosion Rates of Fine Sediments 193
xii
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LIST OF TABLES
Page
1.1. Valence and Atomic Number of Cations 1n Sediment 12
2.1. Properties of Sediment Aggregates (after Krone, 1963) 32
2.2. Principal Factors Controlling Erosion of Saturated
Cohesive Sediment Beds 55
2.3. Cation Concentrations in Processed Sodium Chloride
and Standard Sea Salt 98
A. Characterization of Sediment .. 194
8. Characterization of Pore Fluid........ 196
C. Characterization of Bed Structure 198
0. Characterization of Coagulation and Settling..... 199.
E. Erodibility Index 199
F. Characterization of Bed Shear Stress..... 200.
G. Measure of Erosion. 201
xm
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ACKNOWLEDGEMENT
The authors wish to acknowledge the significant assistance provided
by Dr. Ranjan Ariathurai to this investigation. Or. Ariathurai was a
consultant to the project and provided a copy of the SEDIMENT III fine
sediment transport model program to the investigators. He also gave
invaluable advice regarding the use of SEDIMENT III and related
experimental research. Mr. T. M. Parchure, graduate assistant, wrote
Appendix C and also contributed to some aspects of Chapters I arid II.
The investigation was supported by the U.S. Environmental
Protection Agency under Grant Number R806684010. Funds for research
work by Messers. 0. G. D1x1t (M. S. Thesis), S. 0. Hunt (M. S. project
report) and T. M. Parchure (M. S. Thesis) were partially derived from
this grant.
The authors wish to sincerely thank Mr. Robert 8. Ambrose (Project
Officer) and Dr. James W. Falco of the Environmental Protection Agency
for their involvement and guidance during the course of the
investigation.
xiy
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I. INTRODUCTION
1.1. Estuarial Fine Sediment Dynamics
Fine, cohesive sediments 1n estuaries are comprised largely of
terrigenous clay-sized particles plus fine silts. The remainder may
Include blogenic detritus, algae, organic matter, waste materials and
sometimes small quantities of very fine sand. Although in water with a
very low salinity (less than about 1 part per thousand) the elementary
sediment particles are usually found in a dispersed or "non-salt
flocculated" state, small amounts of salts are sufficient to repress the
electrochemical surface repulsive forces between the elementary
particles, with the result that the particles coagulate to form much
larger units known as aggregates. Each aggregate may contain thousands
or even millions of elementary particles and have a settling velocity
that is much larger than those of the elementary particles. The
transport properties of aggregates are affected by the hydrodynamic
conditions and by the chemical composition of the suspending fluid.
Most estuaries contain abundant quantities of cohesive sediments which
usually occur in the coagulated form in various degrees of aggregation.
Therefore, an understanding of the transport properties of these
sediments in estuaries requires a knowledge of the manner In which the
aggregates are transported in these waters.
Fine sediment transport in estuaries is a complex process involving
a strong coupling between tides, baroclinic circulation and the
coagulated sediment. This process has been described extensively
elsewhere (Postma, 1967; Partheniades, '1971; Dyer, 1971; Krone, 1972;
Kirby and Parker, 1977; Kranck, 1980). In Fig. 1.1, a schematic
description is given. The case considered is one in which the estuary
1s stratified, and a stationary saline wedge is formed as shown.
Various phases of suspended fine sediment transport are shown, assuminq
a quasi-steady state, i.e. a tidally-averaged situation. In the case of
a partially mixed estuary, the description will be modified, but since
relatively steep vertical density gradients are usually present even in
this case, the sediment transport processes will generally remain
qualitatively similar as depicted in Fig. 1.1.
-1-
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Upstream
Sea
Riverborne Sediment
=>• ..
Upward
Entrainment
Limit of Seawater
Intrusion —
Settling
V
Net Upstream
3 Transport
Transport to Sea cz£>
*—"S—"""""'
>- Saline Wedge
Transport from Sea
Shoaling Mixing and Enhanced Aggregation
Turbidity Maximum
I /
0.1
.•/«
Ju(z,t)dt
J u(z,t)dt+ Ju(z,t)dt
Fig. 1.1 Schematic Representation of Transport and Shoaling Processes in the Mixing Zone of a Stratified
Estuary, including Ebb Predominance Factors (after Mehta and Hayter, 1981).
-------
With reference to this figure, the vertical variation of the
horizontal flows on a tidaily-averaged basis can be conveniently
described by computing the ebb predominance factor, EPF, defined as
TE
/ u(z,t)dt
EPF - -j * (1.1)
'E F
/ u(z,t)dt + / u(z,t)dt
0 0
where u(z,t) = instantaneous longitudinal current velocity at an eleva-
tion z above the bed, TE = ebb period, Tp = flood period and T = Tg +
Tp, where T * tidal period. If the strengths of flood and ebb were the
same throughout the water column, EPF would be equal to 0.5 over the
entire depth of flow. This is almost never the case; EPF is usually
less than 0.5 near the bottom, particularly in the saline wedge, and
greater than 0.5 in the upper layers. The net upstream bottom current
is due to the characteristic nature of flow circulation induced by the
presence of the wedge, which means that the strength of this current
will decrease as the limit of seawater intrusion is approached, and is
theoretically zero at the limit (node) itself (Keulegan, 1966).
Distributions of EPF at three locations - at the mouth, in the wedge and
at the node, would qualitatively appear as shown in Fig. 1.1. When
interpreted in terms of tidal flows, these distributions correspond to
the general observation that in the mixing zone of the estuary (i.e. the
region where sea water mixes with fresh water) flood flows landward at
the bottom and ebb flows seaward at the surface.
The trends indicated by the EPF distributions suggest the
dominating influence of flow hydrodynamics on .sediment movement. As
noted 1n Fig. 1.1, riverborne sediments from upstream fresh water
sources arrive in the mixing zone of the estuary. The comparatively
high degree of turbulence, the associated shearing rates and the
increasingly saline waters will cause aggregates to form and grow in
size as a result of frequent inter-particle collisions and increased
cohesion. The large aggregates will settle to the lower portion of the
water column because of their high settling velocities. Results based
on laboratory experiments show that aggregate settling velocities can be
-3-
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up to four orders of magnitude larger than the settling velocities of
the elementary particles (Bellessort, 1973). Some of the sediment will
deposit and some will be carried upstream near the bottom until periods
close to slack water when the bed shear stresses decrease sufficiently
to permit deposition. The deposited sediment will start to consolidate
due to overburden forces. The depth to which the new deposit scours
when the currents Increase after slack will depend on the bed shear
stresses imposed by the flow and the shear strength of the deposit. If
the currents during both flood and ebb are sufficient to scour all of
the new deposit, the net movement will be determined approximately by
current predominance. However, if the bed shear stress during ebb 1s
less than sufficient to suspend all of the newly deposited material, a
portion of the material will remain on the bed during ebb, and will be
resuspended and transported during the predominant flood flows,
resulting in a net upstream transport. Het deposition, i.e. shoaling,
will occur when the bed shear during flood, as well as during ebb, is
insufficient to resuspend all of the material deposited during preceding
slack periods. Some of the fine material that 1s resuspended will be
re-entrained throughout most of the length of the mixing zone to levels
above the salt water-fresh water interface and will be transported
downstream to form larger aggregates once again, and these will settle
as before. At the seaward end some material may be transported out of
the system, a portion or all of which could ultimately return with the
net upstream current. Some sediment moving upstream along the bottom
may also be derived from oceanic sources, as for example occurs in the
channel which connects the Gulf of Venezuela with Lake Maracalbo
(Partheniades, 1966). The strength of this upstream current Is often
enhanced by the inequality between the flood and the ebb flows induced
by the usually observed distortion of the tidal wave. -Inasmuch as the
low water depth is often significantly less than the depth at high
water, the speed of the propagating tidal wave, being proportional to
the square root of the depth, 1s higher at high water than at low
water. This typically results 1n a higher peak flood velocity than peak
ebb velocity and a shorter flood period than ebb period. Such a
situation tends to enhance the strength of the upstream bottom current,
and the sediment is sometimes transported to regions upstream of the
limit of seawater intrusion.
-4-
-------
The shoals formed in the mixing zone may be periodically scoured by
high freshwater discharges, and the material will deposit near the mouth
of the estuary or in the sea. During periods of low freshwater
discharge, the sediment will slowly return to the shoal area with the
net upstream current. In a typical estuary the sediment residence time
in the mixing zone is large, and the transport rates often are an order
of magnitude greater than the rate of inflow of "new" sediment derived
from,up!and or oceanic sources. The estuarial sedimentary regime is
characterized by several periodic (or quasi-periodic) macro time-
scales. These are:
a) The tidal period (diurnal, semi-diurnal, or mixed),
b) One-half the lunar month (spring to spring or neap to neap),
c) Yearly cycle,
d) Periods greater than a year, e.g. the 19 year metonic cycle.
Of these, the first is of course the most important since it is the
fundamental period which characterizes the basic mode of the sediment
transport phenomenon in an estuary. The second is important from the
point of view of determining net shoaling rates in many cases of
engineering interest, and by the same token the third and sometimes the
fourth time-scales are involved in considerations of long-term stability
and shoaling in estuaries.
As an example of the yearly cycle, Fig. 1.2 shows the depth-
averaged distributions of salinity and suspended sediment concentrations
In the Hooghly River estuary, India (Inset). It is observed that
following the freshet season, as the freshwater outflow is reduced, the
salinity progresses upstream at a rate of approximately 30 km/month.
Thus in November, the penetration is 40-50 km upstream of Gasper Shoals,
and in the following April the penetration distance 1s in excess of 180
km. The mean of these two profiles gives an average for the dry season,
as shown. It is observed that the turbidity maximum for the same period
occurs at a distance of 90-110 km, which is where the dry season
salinity (normalized with respect to seawater salinity) is reduced to
approximately one-tenth the seawater value.
From an Eulerian point of view, the super position of oscillating
tidal flows on the quasi-steady state transport phenomenon depicted in
Fig. 1.1 results in corresponding oscillations of the suspended sediment
-5-
-------
i I 1 I I I
Salinity
Mean (Nov.-April)
0
20 40 60 80 100 120 140
DISTANCE UPSTRLAM FROMSP*SPER SHOALS (kilometers)
160
Fig. 1.2 Longitudinal Salinity and Suspended Sediment Concentrations in the Hooghly River Estuary (India)
(after Hehta and Hayter, 1981).
-------
concentration with time as shown by the Savannah River data in Fig.
1.3. Such a variation of the suspended load ultimately results from a
combination of convective transport, diffusion, erosion and deposition.
Understanding the last two processes is crucially important and is
the thrust of most, if not all, current research. Because of the
complexity of the erosion-deposition phenomena, more than one
interpretation is possible as far as any schematic representation of
these phenomena is concerned. One such representation is shown in
Fig. 1.4. According to this description, fine sediments can exist in
four different physical states in a tidal estuary or sea: as a mobile
suspension, a stationary suspension, a consolidating bed and as a
settled bed. The last two are formed as a result of consolidation of a
stationary suspension. Stationarity here implies little horizontal
movement, although consolidation does mean that there is vertical
(downward) movement. Beds corresponding to the latter three states may
erode if the shear stress exceeds a certain critical value. Erosion of
a stationary suspension is referred to as redispersion while erosion of
a consolidating as well as a settled bed is termed resuspension.
1.2. Significance of Clays in Pollutant Transport
Substances which are known to cause discomfort, illness or death,
and substances which are carcinogenic, mutagenic or harmful to
metabolism are usually called pollutants. Thus, radioactive elements,
heavy metals, complex organic substances, certain bacteria and viruses,
etc. are all considered pollutants in a typical aquatic environment such
as an estuary. Substances affecting economic interests are also often
catagorlzed as pollutants. In this section the role of fine, cohesive
sediments in pollutant transport is qualitatively discussed.
The importance of considering the transport of cohesive sediments
in predicting the fate of pollutants introduced in a water body is
pointed out by Kirby and Parker (1973). They state that the bulk of the
pollution'load is quite often transported sorbed to these sediments
rather than in the non-sorbed state. In fact, most pollutants are
associated with particulates in one way or another. Their position in
the sediment can probably be classified into several groups: sorbed on
the mineral, oxide or hydrous oxide surfaces, bonded in"humtc materials,
-7-
-------
DECELERATING
FLOW
ACCELERATING DECELERATING
FLOW
FLOW
ACCELERATING
FLOW
DECELERATING
FLOW
0.3 m
0.6 m
1.2 m
» 2.4 m
* 4.9 m
• 7.6 m
• Surface
16
17 18
9/24/68
19 20
21 22 23 24 I
TIME OF MEASUREMENT
3 4
9/25/68
Fig. 1.3 Time and Depth Variation of Suspended Sediment
Concentration in Savannah River Estuary (after
Krone, 1972).
Suspension in Transport
| -
1 !
Deposition Redispersion Resuspension
Resuspension
i
Stationary
Suspension
Consolidating Bed
Settled Bed
Fig. 1.4. Schematic Representation of the Physical States of
Fine Sediment in Estuarial Mixing Zone (after Mehta
et al., 1982a).
-8-
-------
precipitated as metal sulfides, sorbed on the exchange sites of clay
minerals or incorporated in the detrital organic or mineral phase.
Salomons and Mook (1977) studied the concentration of trace metals
sorbed to estuarial and marine sediments. The grain size as well as the
concentration of trace metals has a considerable variation in natural
sediments. However, a positive correlation was seen between the
quantity of pollutants, i.e. heavy metals, and the amount of fine-
grained particles expressed by the percentage of particles less than
16 ^ in diameter. The results, which show an increase in the
concentration of heavy metals with decreasing grain size, are shown in
Fig. 1.5. Figure 1.5(a) shows the correlation with Al, Fe, P and K.
Fig. 1.5(b) shows the correlation with quartz, feldspar, carbonates and
organic matter, and Fig. 1.5(c) shows the correlation with Zn, Cr, Pb
and Cu. It is observed that the concentration of species increased in
the order: Al > Fe > K > P, and Zn > Cr > Pb > Cu. Linear
relationships between metal content and percentages of fractions smaller
than. 16 \tn have been reported as well by Veltman (1979).
Mauser and Fauth (1972) verified the presence of high
concentrations of barium, calcium, cobalt, copper, lead, mercury,
nickel, silver and zinc in sediments. Mercury has received particular
attention due to its transformation to the highly toxic methylmercury by
benthic organisms (Fagerstrom and Zernelov, 1971). According to Jones
(1972), the sources of metallic elements in the sediment are accessory
mineral sites, lithic fragments, and surface coatings on grains and clay
minerals. Changes in redox potential, pH or composition of solution
media probably bring about changes in the availability of trace
substances.
The important properties of clays which cause the adsorption of
pollutants are the large surface area to volume ratio of clay particles,
the presence of net negative electrical charges on their surfaces and
their cation exchange capacity. These properties are described below.
When a substance is subdivided into smaller and smaller units, the
ratio of surface area to volume, i.e. specific area, becomes larger and
larger. For a given particle shape the specific area is inversely
proportional to the equivalent spherical particle diameter, or Stokes
diameter. -When this diameter is reduced to 2 pm or less, the surface
-9-
-------
UJ
8 4
(a)
20 40 60 80
ui
I
UI
o
cr
0
2
L Feldspar
0
(b)
20
Organic MottW]
40 60
%< 16/xm
80
0.28
0.24
$ 020
o>
"- 0..6I
z
ui
0.12
0.08
0.04
0.0
0
(O
20 40 60 80
100
Fig. 1.5 Variation of Heavy Metal Concentration with Sediment
Particle Size (after Salomons and Mook, 1977).
-10-
-------
physico-chemical forces begin to exert a distinct Influence on the
behavior of this particle due to the large specific area and the
particle Is considered to be in the colloidal size range . Most clay
particles fall within the colloidal range in terms of both their size
and the controlling Influence of surface forces on their behavior. In
fact, the average surface force on one clay particle Is approximately
106 times greater than the force due to gravity (Partheniades, 1962).
Clays are usually platelet shaped and have a very large surface area to
volume ratio. For Instance, montmorillonite has a specific surface area
of 800 m2/gram. If all particles contained in about 10 grams of this
clay could be spread out side by side, they would cover a football field
(Mitchell, 1976). The shape in the form of platelets and the large
surface area provide a large potential for different arrangements and
trapping dissolved substances in the pore water.
Clays are primarily hydrous aluminum silicates with magnesium or
Iron occupying all or part of the aluminum positions in some minerals,
and with alkalies (e.g. sodium, potassium) or alkaline earths (e.g.
calcium, magnesium) also present as essential constituents in some of
them (Grim, 1968). Substitution of ions of one kind by ions of another
kind, with the same or different valence, but with retention of the same
crystal structure is termed isomorphous substitution. This process does
not necessarily involve replacement. In reality, the "replaced" cations
are never there and the mineral is formed with its existing proportions
of different cations in the structure. The tetrahedral and octahedral
positions in the crystal lattice can be occupied by cations other than
those in the ideal structure. Common examples are aluminum and ferrous
iron (Fe ) for magnesium. The tetrahedral and octahedral cation
distributions develop during initial formation of the mineral, and not
by later substitution (Mitchell, 1976). However, the isomorphous
substitution in all the clay minerals, except for kaollnite, gives clay
minerals a net negative charge which Is of great significance in
coagulation of clays and in adsorption of pollutants.
The cation exchange capacity (CEC) is an important property of clay
minerals by which they sorb certain cations and anions In exchange for
those already present and retain them in an exchangeable state. The CEC
of different clays varies from 3-15 meq/100 gm for kaolinite to 100-150
-11-
-------
meq/100 gm for vermiculite. Higher CEC indicates greater capacity to
adsorb other cations. The negative charge caused by isomorphous
substitution is neutralized by attracting and holding cations on the
surfaces and edges of a clay particle. These cations remain in an
exchangeable position and may in turn be replaced by other cations.
The following factors are the causes of cation exchange: 1)
substitution within the lattice structure results in unbalanced charges
in the structural units of some clay minerals, and 2) broken bonds
around the edges of the silica-alumina units give rise to unsatisfied
charges. In both cases the unbalanced charges are balanced by the
adsorbed cations. The number of broken bonds and hence the CEC
increases with decreasing particle size. Lattice distortion would tend
as well to increase the number of broken bonds. Also, the exchange
capacity increases with decreased degree of crystallinity.
The ability to replace exchangeable cations depends on the
following factors: 1) concentration: increased concentration of a
replacing cation causes greater exchange by that cation. 2) population
of exchange positions: the ease of release of an ion depends not only on
the nature of the ion itself, but also upon the nature of the
complementary ions filling the remainder of the exchange positions and
on the degree to which the replaced ion saturates the exchange sites.
3) nature of anions in the replacing solution. 4) nature of the
cation: higher the valence of the cation, the greater is its replacing
power and the more difficult it is to displace when already present on
the clay. Some of the predominantly occurring cations in sediments are
listed in Table 1.1 in the order of their valence and atomic number. In
the case of metals having the same valence, the metal with the higher
atomic number replaces the one with the lower atomic number.
0
Table 1.1. Valence and Atomic Number of Cations in Sediments
Cation
Valence
Cation
Atomic No.
Na
1
Na
11
K"
1
Al
13
Ca
2
K
19=
Cd
2
Ca
20
Zn
2
Cr
24
Hg
2
Cu
29
Cu
2
Zn
30
Pb
2,4
Cd
48
Al
3
Hg
80
Cr
2,3
Pb
82
,6
-12-
-------
Chemicals are sorbed on the sediments or are released from them
depending upon the conditions favorable for the corresponding process.
Quantities in excess of the adsorption capacity may be found in the pore
water surrounding the sediment. Some soluble substances such as phos-
phates sorb strongly on calcium carbonate, which explains why calcium
carbonate-rich sediments contain low concentrations of dissolved phos-
phates in their pore water. There are several factors which affect the
adsorption/desorption and hence the exchange rate of chemicals with
-3 +3
sediments. For instance, the adsorption isotherm of PO. -Fe system
Is controlled by the phosphate-iron ratio, the age of the complex
formed, and pH.
Schindler jt._al_. (1980) studied the effect of pH (acidity) on the
mobilization of heavy metals from the sediments. They found that
aluminum, zinc, manganese and iron were released from lake sediments at
pH 5 and 6. Concentrations of zinc in the overlying water column
exceeded 300 ^g/1.
Soule and Oguri (1974) have mentioned that an understanding of the
sorptlon and release mechanism of trace substances can only be achieved
by considering the sediment as a dynamic system where the composition
and geochemistry of the bulk materials vary through the following
processes:
a) Diffusion of Ions within the sediment
b) Reactions occurring in the interstitial water
c) Humic binding forces
d) Organic/inorganic complexes
e) Nutrient mobilization
f) Reactions at the sediment-water Interface
Molecular diffusion plays a dominant role in describing the
transport of dissolved substances especially below the zone of
bioturbation. Molecular diffusion is assumed to follow Pick's Law and
is expressed in terms of a diffusion coefficient, Ds. Despite the
importance of diffusion in diagenetic models, there have been very few
measurements of Ds for various chemical species in anoxic pore waters.
To quote Krom and Berner (1980), "we know of only three direct
determinations of the diffusion coefficient of sulfate in marine
sediments and none at all of the diffusion coefficients of ammonia and
-13-
-------
phosphate in such sediments." Krom and Berner (1980) determined the
diffusion coefficient of phosphate to be Os = 3.7 x 10"6 cm2/sec by
laboratory experiments using homogenized anoxic mud.
Mathematical models have been developed and used: 1) to describe
and predict the concentration profiles of dissolved sulfate, ammonia,
silica, phosphate, etc. in the pore waters of anoxic sediments (e.g.
Berner, 1974; Lasage and Holland, 1976; Vanderborght _et_jil_., 1977;
Murray jjt^jiU, 1978) and 2) to describe the chemical composition of
organic matter undergoing decomposition (e.g. Shollcovltz, 1973; Hartmann
et_jil__., 1973; Berner, 1977).
Mortimer (1971) showed the effect of aerobic and anaerobic status
of soil on the chemical exchange of phosphorus, manganese and iron.
With a progressive decline of 02 concentration from 2 mg/1 to analytical
zero at the sediment-water interface, first manganese and later iron was
solubilized from sediment and transferred to the water. Patrick and
Khalid (1974) studied release and sorption of phosphate by soils and
sediments under aerobic and anaerobic conditions. They found that
anaerobic soils released more phosphate to soil solutions low in soluble
phosphate and sorbed more phosphate from soil solutions high in soluble
phosphate than did aerobic soils. The difference in behavior was
attributed to the change brought about in ferric oxyhydroxide by soil
reduction.
1.3. Purpose of Study
1.3.1. Need for Research
The necessity of better understanding fine, cohesive sediment
transport in estuaries is demonstrated by examining the following two
sediment related problems.
The first pertains to water quality effects on biota. The effects
of sediments on water quality for biota include limitation of the
penetration of sunlight and the sorption of toxic compounds from
solution. The concentrations of nutrients for algae in some estuaries
are often sufficient to cause excessive algae blooms. The rate of
multiplication of algae in such estuarial waters is limited by a reduced
light supply resulting from high- turbidity caused by suspended sediment
particles. Estuarial waters are often used by industries as convenient
-14-
-------
dump sites for waste products. As discussed in the previous section,
pollutants such as heavy metals, pesticides, herbicides, and organics
are often found sorbed onto sediment materials with equilibrium between
dissolved and sorbed materials frequently favoring the sorbed phase
(Ariathurai Jill., 1977). Due to their property of cohesion, these
sediments provide a large assimilative capacity as well as the
transporting mechanism for such toxic compounds. For example, in an
investigation of the bottom sediments from several coastal marinas in
Florida, two interesting observations were made (Weckmann, 1979; Bauer,
1981). First, when comparing sediment particle size inside the basin
with that obtained immediately outside in the main body of water, it was
found that in the majority of the marinas investigated, the sediment
inside was measurably finer than that outside. Second, a similar
comparison in terms of heavy metal (e.g. Cu, Pb, Ni, Cd and Zn) content
within the basin and without indicated measurably higher concentrations
inside the basin. These two observations when correlated exemplify the
role of fine sediments in accumulating pollutant levels in estuarial
depositlonal environments such as marina basins.
Storage of river waters upstream and their diversion for agricul-
tural, urban and industrial uses will sharply reduce sediment inflows as
water resources become scarce. Therefore, it will be necessary to
predict the effects of reduced sediment inflows to ascertain the minimum
waste water management needed to achieve and maintain desirable water
quality. Several aspects of water quality problems related to sediment
contamination have been discussed in a series of papers edited by Baker
(1980).
The second problem concerns the maintenance of navigable waterways.
Under low flow velocities, sometimes coupled with turbulent conditions
which favor the formation of large aggregates, cohesive sediments have a
tendency to deposit in areas such as dredged cuts and navigation
channels, in basins such as harbors and marinas, and behind pilings
placed in water (Einstein and Krone, 1962). In addition, as noted
previously, the mixing zone between upland fresh water and sea water in
estuaries is a favorable site for bottom sediment accumulation.
Inasmuch as estuaries are often used as commerce routes to the sea, it
is desirable to be able to accurately estimate the amount of dredging
-15-
-------
required to maintain navigable depths in these water bodies, and also to
predict the effect of new estuarial development projects such as the
construction of a port facility or dredging of additional navigation
channels.
The influence of salinity on fine sediment erosion, deposition and
transport (e.g. as shown in Fig. 1.4), must be considered for the
following reason: the structure of aggregates has been found to be
dependent on the salinity for salinities lower than about 10 ppt (Krone,
1962; 1978). In the upper reaches of estuaries, where the salinities
are typically less than 10 ppt for at least the latter stages of ebb
flow and first part of flood, and in situations where high stormwater
runoff significantly lowers the salinity over the entire water depth,
the aggregate structure, and hence the transport processes become
dependent upon the salinity level. Figure 1.6 shows the variation in
the vertical salinity profile with time measured in the upper reaches of
the Savannah River estuary at the same station as the suspended sediment
concentration-time profile shown in Fig. 1.3. As shown, the salinities
are less than 10 ppt for the entire measurement period. The effect of
stormwater runoff from a short duration, high intensity storm on the
salinity (chloride concentration) at the mouth of a Pacific ocean
estuary is observed in Fig. 1.7, which shows field measurements as well
as predictions from a water quality model developed by Orlob et al.
(1967). It is apparent that the effects of salinity variation must be
taken into account when the sedimentary regime in any estuary is being
investigated.
1.3.2. Predictive Modeling
Prediction of the fate of sorbed pollutants or the frequency and
quantity of dredging required to maintain navigable depths in a channel
or harbor can be accomplished by modeling the movement of fine sediments
1n the water body of concern. It becomes necessary to simulate the
various transport processes, I.e. erosion, convective and diffusive
transport, deposition and consolidation, and the physical factors, e.g.
movement of water and dissolved salt, that govern these processes. The
movement of suspended sediment, water and salt are highly interrelated,
as is evident upon examination of Fig. 1.8 which defines possible
-16-
-------
30
25
t 15
1 .0
tn
• 0.3 m
a 0.6 m
» 1.2 m
» 2.4 m
I 4.9 m
• 7.6 m
• Surface
15 16 17 18 19 20 21 22 23 24
9/24/68 TIME (Hours)
34 5
9/25/68
Fig. 1.6 Time and Depth Variation of Salinity in Savannah
River Estuary (after Krone, 1972).
Field Meosurements
Model Simulation
12 A.M. 12 P.M. 12 A.M. 12 P.M. 12 A.M. 12 P.M. 12 A.M. 12 RM. 12
TIME (Hours)
Fig. 1.7 Time Variation of Chloride Concentration in a Pacific
Ocean Estuary Due to Stormwater Runoff (after Orlob
eital.., 1967).
-17-
-------
Rigid
bound-
ries
Rapid
Medi urn
radual
Large
Bulk flow
tidal
propagation
Motion of
dissolved
salt
Channel
geometry
and
LargeVroughness
Rapid
Medi urn
Velocity field.
Internal water
circulation.
Bed shear
Erosion
and
deposition
Rapid
Medium
Gradual
Large
Vert.mixin
processes.
Internal
shear
Forces
induced by
density
radients
Motion of
suspended
mud
Gradual *
Medi urn
Coagulati
and
sett! i ngi/Medi um/properties
Very Gradual
Small
Gradual
Medium
Fig. 1.8 Interactions of Tidal and Estuarial Sediment Transport
Processes (after Owen, 1977).
-18-
-------
Interactions between these constituents 1n an estuary. The forces which
control tidal motions are given In triangles, the movements of the
water, salt and sediment are depicted 1n rectangles, and secondary
processes and factors which influence the movements of water, salt and
sediment are given in circles. Two scales are given between each of the
Interacting processes. The top one indicates the speed, i.e. time-
scale, of the interaction, while the bottom one indicates the magnitude
of the Interaction. Not surprisingly, theoretical descriptions of the
major processes and interactions involved in the motion of water,
sediment and salt are still far from complete.
Physical and mathematical models or combinations ("hybrid
approach") of these two types are the types of models available for use
in predicting cohesive sediment movement in a water body. Physical
scale models have been only partially successful due to lack of an
appropriate model sediment as well as due to poor model reproduction of
estuarial mixing processes and internal shear stresses (Owen, 1977).
Mathematical models, however, have been generally more successful in
reproducing, with some degree of accuracy, the movement of cohesive
sediments in estuarial waters. The modeling philosophy 1s delineated
below.
To mathematically model the motion of the three main constituents
in an estuarine environment the three-dimensional forms of the
conservation of momentum and mass equations for the water and the
conservation of mass equations for the dissolved salt, suspended
sediment and pollutant, if present, must be solved numerically.
However, due to the current high cost of solving such three-dimensional,
coupled, partial differential equations, only a few three-dimensional
models exist (Liu and Leendertse, 1978). The common procedure has been
to spatially Integrate these equations, laterally and/or vertically, in
order to reduce them to their two- or one-dimensional forms. Two-
dimensional vertical (I.e. laterally Integrated) fine sediment transport
models have been developed by O'Connor (1971), Odd and Owen (1972),
AMathural Jt_.al_. (1977) and others. Two-dimensional horizontal (i.e.
vertically integrated) models have been developed by among others April
and Brett (1975) and Ariathurai .et__al_. (1977). The horizontal length
scales relative to the transport of-estuarial sediment typically are one
-19-
-------
to three orders of magnitude greater than the vertical length scales.
As a consequence, and because horizontal transport distances are usually
of primary interest in ascertaining the magnitude of sedimentation or
the fate of sorbed pollutants, it is in most cases not unreasonable to
use vertically integrated transport equations for modeling purposes.
However, even using the two-dimensional forms of the governing
equations, some eight to ten coupled equations must be solved to
completely model the depth-averaged motion of water, sediment and
salt. As a result, the modeling of water and salt movement is commonly
performed separately from the sediment transport modeling. For example,
a two-dimensional hydrodynamic model, which solves the coupled momentum
and (water and dissolved salt) continuity equations, would be used to
model the movement of water and salt. Then a two-dimensional fine
sediment transport model would be used to predict the motion of sediment
using the results from the hydrodynamic model. This is the modeling
approach that has been used in this study, with all research and
development concerned with the two-dimensional vertically integrated
modeling of fine sediment transport.
None of the fine sediment transport models listed above has the
capability of determining the effect of salinity variation (e.g. in the
mixing zone between fresh and sea water in estuaries) on the processes
of erosion and deposition of cohesive sediments in a turbulent flow
field, since the empirical laws used in the models for these transport
processes were derived using empirical evidence from laboratory
experiments conducted in natural or artificial sea water. In addition,
the empirical laws of erosion and deposition cannot be considered to be
"the state-of-the-art" even for sea water, as a considerable number of
laboratory experimental tests conducted since these laws were proposed,
including some during this study, have revealed new evidence on the
erosional and depositional behavior of cohesive sediments.
1.3.3. Objectives and Scope of Investigation
The study described herein had the following five main objectives:
1) Conduct a comprehensive review of the existing laws on the erosion
and deposition of fine, cohesive sediments.
-20-
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2) Determine the effects of salinity on the rates of erosion of flow-
deposited cohesive sediment beds under turbulent flows.
3) Determine the effects of salinity on the deposition rates under
turbulent flows.
4) Upgrade an existing "state-of-the-art" two-dimensional, vertically
integrated mathematical model of cohesive sediment transport by
Improving upon this model's capability of predicting the erosion and
deposition of cohesive sediments in estuaries.
5) Demonstrate the utility of the improved transport model in
simulating the erosion and deposition of cohesive sediments and the
effect of salinity on these transport processes.
Research conducted to accomplish these objectives was directed
towards obtaining an improved understanding and quantitative description
of the erosion (resuspension) and deposition of fine sediments under
turbulent flows. This was achieved by experimental investigations on:
1) the erosive behavior of flow-deposited (I.e. stratified) cohesive
sediment beds, and 2) the effect of salinity on the rates of erosion and
deposition. The results from these investigations, in the form of
empirical erosion and deposition functions and an improved schematiza-
tion of flow-deposited beds, were Incorporated into the selected
cohesive sediment transport model. The fifth objective given above was
accomplished by using the modified model to: 1) simulate laboratory
erosion and deposition experiments, and 2) demonstrate the effect of
salinity on the rates of erosion and deposition of cohesive sediments in
both laboratory experiments and in a 10 km long hypothetical canal. The
following format is used to present the results.
In Chapter II, the improved cohesive sediment transport model is
described in detail. First, the governing equations for sediment
transport in an estuarial environment are developed in Section 2.1. In
Section 2.2, the numerical technique for solving the governing equations
is described. A description of the selected transport model and the
modifications made to this model are given in Sections 2.3 and 2.4,
respectively. The new bed schematization and new erosion and deposition
algorithms developed and incorporated into the transport model are
described in detail in Sections 2.5, 2.6 and 2.7, respectively. In
Section 2.8, the effects of- salinity on the-physico-chemical properties
-21-
-------
and estuarial transport processes of cohesive sediments are discussed.
Also presented 1n this section are the results from laboratory erosion
and deposition experiments, in which the effects of salinity on these
two processes were studied, and a description of the method used to
incorporate these effects into the transport model. The stability
characteristics of the improved model are discussed in Section 2.9, and
the limitations of the modeling approach used are discussed in Section
2.10. Lastly, possible applications of the improved model to water
quality and sedimentation management problems are given in Section 2.11.
In Chapter III, the results from the simulations of laboratory
erosion and deposition experiments using the improved model are
presented. The effects of salinity on selected laboratory experiments
and on the transport processes in the hypothetical canal are as well
demonstrated and presented therein.
In Chapter IV, important conclusions from this study and
recommendations for future research are stated.
In Appendix A, a flow chart of the model is presented. In Appendix
B, a user's manual for the model is given. Lastly, in Appendix C, a
discussion of the various physico-chemical factors that should be
characterized in any study of the erosive behavior of cohesive sediments
is given.
-22-
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II. MODELING CONSIDERATIONS
2.1. Significance of Important Physical Factors 1n Estuarial Transport
Prior to discussing the governing equations for the convective and
diffusive transport of suspended fine sediments, the significance of the
important factors controlling the hydrodynamic and sedimentary regimes
in an estuary is discussed.
As implied in Section 1.1, the hydrodynamic regime in an estuary is
governed by the interaction between the following seven factors: fresh
water flow, astronomical tides, wind-generated surface waves, surface
(i.e. wind) stresses, Coriolls force, the geometry of the water body and
the roughness characteristics of the sedimentary material composing the
bed (Dyer, 1973). Incorporated in geometry is the shape and the
bathymetry of the estuary. The geometry and bed roughness interact with
the driving forces - the first five factors - to control the pattern of
water motion (1n particular the shear stress and turbulence structure
near the bed), frictional resistance, tidal damping and the degree of
tidal reflections (Ippen, 1966).
The magnitude of the tidal flow relative to the fresh water inflow
governs, to a large extent, the intensity of vertical mixing of the
lower high density layer with the upper less dense layer. There exists
in all estuaries a horizontal, i.e. longitudinal, salinity profile which
decreases from the mouth to the upper reaches of the estuary. Such
profiles have been measured in numerous estuaries world-wide. A few
examples are: Cumbarjua Canal, Goa, India during the dry season, i.e.
October through June (Fig. 2.1); the San Francisco Bay and Sacramento-
San Joaquin Delta (Fig. 2.2); the Pamlico River estuary, North Carolina
(F1g. 2.3); and the Yangtze River Estuary, China (Fig. 2.4). As noted
1n Section 1.1, the existence of a longitudinal salinity gradient, or
baroclinic force, implies that there could be a gravity driven upstream
transport of a high density sediment suspension in the lower portion of
the water column (Officer, 1981; Mehta and Hayter, 1981).
Winds affect the hydrodynamic regime and mixing in an estuary by
generating a surface shear stress and waves. The surface stress is
capable of generating a surface current (whose magnitude will be
approximately three percent of the wind speed at 9.1 m elevation
-23-
-------
o.
-------
200
o>
~ 16.0
ro
in
i
tr
h-
2
LU
O
o
O
UJ
Q
•o
o
c
o>
1
O
Jl
128.8
152.9
DISTANCE FROM GOLDEN GATE (km)
Fig. 2.2 Variation in Chloride Concentration in San Francisco Bay and Sacramento-
San Joaquin Delta-September 1955 (after Orlob e_t al_., 1967).
-------
a.
a.
NM^
CO
>•
H
Z
_J
01
16
12
8
I
I
I
0 7.4 22.2 37.1 51.9
DISTANCE DOWNSTREAM (km)
66.7
Fig. 2.3 Salinity of the Surface Waters of the Pamlico River
Estuary as a Function of the Distance from the Railroad
Bridge at Washington, N.C. (after Edzwald e_t ajL,1974).
40
Q_
O.
co
20
Q =33000 cms
Q=45500cms -
-20 0 20 40 60
DISTANCE SEAWARD FROM JIANG ZHEN DCNG(km)
Fig. 2.4 Computed Longitudinal Salinity Profile 1n the Yangtze
River Estuary as a Function of the Distance Downstream
from Jiang Zhen Dong for Two River Discharges: Q =
33000 cms and 45500 cms (after Huang e£ aj_., 1980),
-26-
-------
(Hughes, 1956)) and a superelevation of the water surface along a land
boundary located at the downwind end of the estuary (Ippen, 1966). The
latter effect causes a vertical circulation cell, with landward flow at
the surface and a reversed seaward flow along the bottom. This
phenomenon as well increases the degree of vertical mixing.
Along the banks and in shallow areas, surface gravity waves induced
by the wind are capable of eroding bottom sediments. Since a tidal
current of sufficient strength to transport (but not necessarily to
erode the sediment by itself) suspended sediment is generally present,
this material is convected and dispersed both longitudinally with the
main tidal flow and sometimes laterally with secondary currents towards
the deeper sections of the estuary. Wave action and in particular wave
breaking substantially increase the intensity of surficial turbulence
and mixing.
The Coriolis force, caused by the earth's rotation, has both a
radial (horizontal) and a tangential (vertical) component. The latter
is generally negligible as it is linearly proportional to the vertical
component of the flow velocity, which is typically an order of magnitude
smaller than the horizontal velocity components. The magnitude of the
radial component depends upon the size of the water body. Most extra-
tropical estuaries are relatively large and therefore the effect of this
force on the hydrodynamic regime is measurable. Estuarial hydrodynamics
are described in extensive detail in such texts as Ippen (1966), Barnes
and Green (1971), Dyer (1973), Officer (1976) and Fischer et__al_. (1979).
As noted in Section 1.1, the sedimentary regime in an estuary is
controlled by the hydrodynamics, the chemical composition of the fluid
and the physico-chemical properties of the cohesive sediment. These
factors affect the following processes which cohesive sediments
typically are subjected to in such a water body: erosion, convection,
diffusion, coagulation, aggregation, settling, deposition and
consolidation of the deposited bed. These processes are briefly
described below, following a definition of a clay suspension.
A "solution" of clay in a medium consists of a homogeneous
dispersion of very small kinetic units, I.e. particles (van Olphen,
1963). when the Stokes diameter of the clay solution is less than 2 ^m,
the clay dispersion is usually referred to as a sol. The Stokes
-27-
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diameter of an arbitrarily shaped particle is determined by equating the
particle's settling velocity with Stokes law for spherical particles and
solving for the "equivalent spherical diameter" (Stokes diameter). When
this diameter is greater that 2 ^, the dispersion is called a
suspension. However, through use, the term suspension has become
synonymous with dispersion, and thus a clay suspension refers to both
sol and suspension.
Erosion of cohesive soils occurs whenever the shear stress induced
by fluid flow over the bed is great enough to break the electro-chemical
Inter-particle bonds (Partheniades, 1965; Paaswell, 1973). When this
happens, erosion takes place by the removal of individual sediment
particles and/or floes. This type of erosion is time dependent and is
defined as surface erosion or resuspension. In contrast, another type
of erosion occurs more or less instantaneously by the removal or
entrainment of relatively large pieces of soil. This process is
referred to as mass erosion or redispersion and occurs when the flow-
induced shear stresses on the bed exceed the soil bulk strength along
some deep seated plane.
Once eroded from the bed, the sediment is transported entirely as
suspended load (not as bed load) by the estuarial flow. Such transport
is the result of three processes: 1) convection - the sediment is
assumed to be transported at the speed of the local mean flow, 2)
turbulent diffusion - driven by spatial suspended sediment concentration
gradients; the material is diffused laterally across the width of the
flow channel, vertically over the depth of flow and longitudinally in
the direction of the transport, and 3) longitudinal dispersion - the
suspended sediment is as well dispersed in the flow direction by spatial
velocity gradients (Ippen, 1966).
Coagulation of suspended particles depends upon 1nter-part1c1e
collision and inter-particle cohesion after collision. The former
process occurs by: 1) Brownian motion of the suspended particles, 2)
effects of internal shear or velocity gradients within the fluid, and 3)
differential settling of the suspended particles or floes (Edzward et_
al., 1974; Krone, 1973; Hunt, 1980). A description of these collision
mechanisms is given 1n Section 2.8.4. Cohesion or particle
destabilizatlnn of cohesive sediments occurs in- an estuary because of
-28-
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the altered chemical environment found there. In fresh water, most clay
particles are in a stabilized or dispersed state because the repulsive
electro-chemical surface forces between the particles prevent them from
adhering to one another upon collision. In the increasingly saline
conditions encountered moving seaward in estuaries, the repulsive forces
are suppressed and clay particles coagulate to form floes. A systematic
"build up" of floes as occurs in estuaries is defined as aggregation.
An aggregate is considered to be the structural unit formed by the
joining of floes. The rate and degree of aggregation are two important
factors which govern the transport of fine sediments in estuaries.
Factors, besides the water chemistry and the magnitude of the surface
forces, known to govern coagulation and aggregation include sediment
size grading, mineralogical composition, particle density, organic
content and the suspended sediment concentration (i.e. availability) of
the sedimentary material, the water temperature, height through which
the floes have settled, and the turbulence intensity of the suspending
flow (Owen, 1971).
Given the mechanisms which influence the rate of aggregation in an
estuary, the order of aggregation, which characterizes the packing
arrangement, density and shear strength of aggregates, is determined by
the following factors: 1) sediment type, 2) fluid composition, 3) local
shear field, and 4) concentration of particles or floes available for
aggregation.
Primary or 0-order floes are highly packed arrangements of
elementary particles, with each floe consisting of perhaps as many as a
million particles. Typical values of the void ratio (volume of pore
water divided by volume of solids) have been estimated to be on the
order of 1.2. This is equivalent to a porosity of 0.55, which is a more
"open" structure than commonly occurs in cohesionless sediments (Krone,
1963). Continued aggregation under favorable shear gradients can result
In the formation of first or higher order aggregates composed of loosely
packed arrays of 0-order floes. Each succeeding order consists of
aggregates of lower density and lower shear strength. Experimental
observations (Krone, 1963; 1978) tend to Indicate the following
approximate relationship between the aggregate shear strength, ts, and
aggregate density, Pa, for many (although not all) sediments
-29-
-------
V «
-------
F1g. 2.5, the sediment sample has two possible orders of aggregation.
Krone (1963) postulated that each segment is related to a particular
volume fraction and therefore to a different manner in which the same
sediment can aggregate, i.e. different order of aggregation. Thus, for
the suspensions of the first four sediments listed in Table 2.1, three
different linear segments were obtained on the Theological diagrams,
while for Bay mud, six segments, and therefore six orders of aggregation
were found. This indicates that Bay mud can aggregate in three more
ways than the other four sediments, and further suggests that the Bay
sediment is more cohesive than the others. Also observed in this table
is the very rapid decrease in the shear strengths and somewhat less
rapid decrease in densities with increasing order of aggregation. These
trends indicate that as the order of aggregation increases, the inter-
aggregate pore volume increases and the strength of these aggregates
decreases because of limited bonding area between the lower order
aggregates (Krone, 1978).
22
. 20
o
2
Q 18
16
_j
1 I*
12
Change of Symbol indicates Mixing
H= 24.3 cm
T=22.7°C
Sediment Concentration
O.II2g/cucm
20 40 60 80 100 120 140 160 180
OUTER CYLINDER ROTATION,rpm
Fig. 2.5 A Plot of Raw Viscometer Data Obtained from the
U.S. Army Corps of Engineers Philadelphia Oistrict
Sample (after Krone, 1963).
-------
Table 2.1
Properties of Sediment Aggregates (after Krone, 1963)
Sediment Order of
Sample Aggregation
Brunswick
Harbor
Wilmington
District
Gulf port
Channel
White River
(salt)
San Francisco
Bay
0
1
2
3
0
1
2
3
0
1
2
3
0
1
2
3
0
1
2
3
4
5
6
CEC . Density
(meq/100 gm) pjKg/m3)
a
38 1164
1090
1067
1056
32 1250
1132
1093
1074
49 1205
1106
1078
1065
60 1212
1109
1079
. 1065
34 1269 .
1179
1137
1113
1098
1087
1079
Shear Strength
ts(N/m2)
3.40
0.41
0.12
0.062
2.10
0.94
0.26
0.12
4.60
0.69
0.47
0.18
4.90
0.68
0.47
0.19
2.20
0.39
0.14
0.14 .
0.082
0.036
0.020
-32-
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The settling rate of coagulated sediment particles depends on, in
part, the size and the density of the aggregates and as such is a
function of the process of coagulation and aggregation (Owen, 1970).
Therefore the factors which govern these two processes also effect the
settling rate of the resulting aggregates. As noted in Section 1.1, the
settling velocities of aggregates can be several orders of magnitude
larger than those of individual clay particles (Bellessort, 1973).
Deposition of aggregates occurs relatively quickly during slack
water. Deposition also occurs in slowly moving and/or decelerating
flows, as was observed (see Fig. 1.3) in the Savannah River estuary
during the second half of flood and ebb flows (Krone, 1972). Under such
conditions only those aggregates with shear strengths of sufficient
magnitude to withstand the highly disruptive shear stresses in the near
bed region will actually deposit and adhere to the bed. Thus,
deposition is governed by the bed shear stresses, turbulence structure
above the bed, type of sediment, depth of flow, suspension concentration
and the ionic constitution of the suspending fluid (Mehta and
Partheniades, 1973). An important conclusion derived from laboratory
erosion and deposition experiments using a wide range of cohesive
sediments under steady flow conditions was that under these conditions
the two processes do not occur simultaneously as they do in cohesion!ess
sediment transport (Mehta and Partheniades, 1975; 1979).
A flow-deposited bed of cohesive sediment aggregates possesses a
vertical bulk density and shear (i.e. yield) strength profile which
changes in time primarily due to consolidation. Secondary causes are
thixotropy (see Section 2.5.1) and associated physico-chemical changes
affecting inter-particle forces. Consolidation, caused by the
gravitational force (overburden) of overlying deposited aggregates which
crushes and thereby decreases the order of aggregation of underlying
sediment, is known to occur in three phases (Migniot, 1968). During the
first phase the bed consolidates quickly as the water in the bed moves
upward through the interstices of the bed material. This phase has been
found to last up to approximately 10 hours for cohesive sediments (Owen,
1977). During the second phase, which can last up to about 500 hours,
water is expelled from the bed by percolation. The rate of
consolidation during the third phase is even slower and the length of
-33-
-------
time it takes for a cohesive sediment bed to reach Its final, fully
consolidated state depends upon the nature of the sedimentary material
comprising the bed and the chemical composition (i.e. ionic
concentrations) of the bed pore water (Owen, 1977). The average values
of the bed bulk density and shear strength Increase and their vertical
profiles change during each of these three phases. Consideration of the
consolidation process is essential in modeling the erosive behavior of
such beds because of the following two factors: 1) the susceptibility to
erosion of a consolidating bed decreases with time due to the continual
increase in shear strength, and 2) the vertical profile of the shear
strength determines the level to which a bed will erode when subjected
to excess shear, i.e. an applied bed shear stress in excess of the shear
strength of the bed surface.
2.2. Governing Equations
2.2.1. Convection-Diffusion Transport Equation
A right-handed Cartesian coordinate system 1s used (Fig. 2.6). The
positive x-axis 1s coincident with the longitudinal axis of the estuary
and points downstream. The coordinate system origin is located at some
datum below the bed level. The positive z-ax1s is the vertical
dimension and points upward. The y-axis defines lateral distances and
points from right to left.
v Water Surface
Upstream
Downstream
lateral axis of
water body
* longitudinal axis of
water body
•Datum
F1g. 2.6 Coordinate System.
-34-
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The principle of conservation of mass describes the convective and
diffusive transport of suspended sediment in a turbulent flow field. In
this law the time-rate of change of mass of sediment 1n a stationary
control volume is equated to the spatial rate of change of mass due to
convection by an external flow field plus the spatial rate of change of
mass due to diffusion. Specifically for a binary sediment-water system
the EuleMan law of mass conservation is given as
•§•+ v(
-------
The diffusive flux term in Eq. 2.2 is that due to molecular
diffusion, which by Pick's law is
where E^ = coefficient of molecular diffusion, and p =• density of the
sediment -water system. For low suspension concentrations the density
may be assumed to be spatially and temporally invariant. Substituting
Eqs. 2.3 and 2.4, including the constant density assumption, into Eq.
2.2 yields
|f + 7k j. (C + u } ^. + C — §. + JL
at * u ax + v ay * ^w * "s' az ^ az ax
- -
32 - ax M ax ay
in which the continuity equation (•• + |^ + -^ = 0) for an incompressible
ox ay oz '
fluid has been applied. The period T must satisfy the following
criteria: 1) it must be large enough so that the time averages of u',
v1, w1 and c1 over T are approximately zero, and 2)-it must be small
enough that the variations of u, v, w and c are changed with respect to
time (MacArthur, 1979).
The Reynolds analogy is used to relate the turbulent diffusive flux
terms such as u'c1 to the mean concentration gradients, e.g. aC/dx,
as follows:
-36-
-------
where Ey, E and E are the turbulent diffusion coefficients in the x-,
* y z
y- and z-direct1ons, respectively. Substituting Eq. 2.7 into Eq. 2.6
gives
at ax ay az az s az ax l x ax'
A. (E |£) . |_(EZ |£) . |_(EM |L) . A_(EM |
Eq. 2.10 is obtained by Integrating this equation over the depth of
flow. Performing this integration and assuming that: 1) Ws is constant
-37-
-------
over the depth (i.e. aWs/dz - 0), 2) the fluid mass density is constant
and 3) the concentration flux ITc* (where u" and c" are the deviations
of u and C over the depth of flow about their respective depth-averaged
values, u and c) is equal to -KxdC/3X by the Reynolds analogy, gives the
following form of the depth-averaged convection-diffusion equation for
sediment transport: .
where 0 * E + K is the effective turbulent diffusion tensor with K a
dispersion tensor introduced through use of the Reynolds analogy in the
third assumption above. The tensor 0, with components Ox and 0 ,
accounts for both turbulent diffusion and dispersion due to spatial
velocity gradients. The source/sink term in this equation can be
expressed as
dC
dt
+
dC
dt
(2.12)
where
from the
dC
dt « dc
is the rate of sediment addition (i.e. source) due to erosion
€5 jp
bed, and §~ is the rate of sediment removal (I.e. sink) due
dt u . Af>\ dc
to deposition of sediment. Expressions for -^\ and ^r
dtIe at
respectively in Sections 2.6 and 2.7.
are given
2.2.2. Initial and Boundary Conditions
In order to solve Eq. 2.11 for the depth-averaged suspended
sediment concentrations at specified points in the flow field the
following boundary and initial conditions are required:
1. Free surface Boundary condition: There can be no net rate of
transport across the free surface. This condition may be expressed
mathematically as
^ - °x £>"x * ny * ° (2a3)
where nx and ny are the x and y components, respectively, of the
unit normal vector to the free surface.
-38-
-------
2. Bottom boundary condition: Eroded sediment material Is transported
in the vertical direction away from the bed by turbulent diffusion.
Deposited sediment becomes part of the bed. This condition is
expressed by Eq. 2.12.
3. Boundary condition at solid boundaries: At all solid boundaries of
the water body being modeled the normal transport flux is equal to
zero, i.e.
°x£ nx + °yf "y = ° <2-">
where, in this case, nx and n are the x and y components,
respectively, of the unit normal vector to the solid boundary.
4. Boundary condition at water boundaries: At each external water
boundary (EWB) either the depth-averaged suspended sediment
concentration must be a known function of time, F(t), for the time
period being modeled, i.e.
C(t)
EWB
F(t) (2.15)
or the zero normal flux condition (Eq. 2.14) must be used as the
boundary condition.
5. Initial condition: The Initial (i.e. at the start of the model
simulation) value of the suspension concentration at each node must
be known.
In addition, the flow depth and the two horizontal velocity
components must be specified at each node for the time period of model
simulation.
2.2.3. Solution of Governing Equation
The finite element method has been used to solve the governing
equation (Eq. 2.11). This method is a numerical analysis technique for
obtaining approximate solutions of differential equations. The
discretization procedures used reduce the equation to be solved to one
with a finite number of dependent variables by dividing the solution
domain into a number of elements and by expressing the dependent
variable in terms of approximating interpolation (i.e. shape) functions
within each element. The values of the dependent variable at node
-39-
-------
points are used to define the interpolation functions. Node points are
usually located on the boundaries of elements and are used to define the
connection between adjacent elements. The number and location of the
node points must be chosen such that continuity of the dependent
variable across common boundaries of adjacent elements is achieved
(Zienkiewicz, 1971). The behavior of the dependent variable within each
element is defined by the values of the dependent variable at the nodes
and the Interpolating function. A detailed description of the method 1s
presented by Zienkiewicz (1971).
This method is preferred over the finite difference method because
derivative boundary conditions do not require special treatment in the
finite element method as they do in the former. In addition, the finite
element method is generally more numerically stable than the finite
difference method. It is a particularly advantageous method to use in
estuarial transport problems because of the ability to use arbitrarily
shaped elements.
Isoparametric quadrilateral and/or triangular elements may be used
in which a quadratic functional approximation is used to describe both
the intra-element spatial variation of the geometry and suspended
sediment concentration. Therefore, the elements may have curved sides.
The Galerkin weighted residual method is used to solve Eq. 2.11 for
the nodal sediment concentrations. As described earlier, the dependent
variable, C, is approximated as the following function of the unknown
nodal point values, C-j:
. 1-n
C, - I N.C, (2.16)
J 1»1 1
where Cj = approximate sediment concentration at any location inside the
jth element, fy = quadratic shape function at the 1th node, and n »
number of nodes forming the jth element. The value of n 1s equal to 8
and 6, respectively, for isoparametric quadrilateral and triangular
elements. Substituting the approximate concentration C Into Eq. 2.11
gives
at dx dy
where r(x,y) » residual resulting from the use of c.
-40-
-------
In order for C to satisfy all the stipulated boundary conditions,
the sum of the normal concentration fluxes from adjacent elements and
any source or sink must be equal to zero on all internal and external
boundaries in the solution domain. This condition may be expressed
mathematically as (Ariathurai and Krone, 1976):
q1 * qi + q1 3 ° 1 = 1""»NL (2<18)
where
q^ * outward normal flux from one element
qT = Inward normal flux from adjacent element
q? =» normal flux from source/sink on the ith boundary
NL = number of element interfaces and external boundaries
Application of the Galerkin weighted residual method to Eq. 2,17
and the residual which results from the use of C in Eq. 2.18 requires
that the summation of the weighted residuals over the solution domain
vanish when the weighting factors are the nodal interpolation
functions. This procedure results in a set of simultaneous equations.
The necessary boundary conditions are Included and the equation set is
solved for the nodal values of the suspended sediment concentrations.
The transient problem is solved using the Crank-Nicholson scheme.
Details of the solution technique for solving Eq. 2.11 are given by
Ariathurai (1974) and Ariathurai et^. (1977).
2.3. Description of Selected Transport Model
The fine sediment transport model selected for use and
modification, i.e. Incorporation of the results from this study is
SEDIMENT III developed by Ariathurai _e£_al.. (1977). This model was
selected because at the beginning of this study it was a "state-of-the-
art" mathematical model of estuarial fine sediment transport. .SEDIMENT
III is a time varying two-dimensional finite element model that is
capable of predicting the horizontal and temporal variations in the
depth-averaged suspended concentrations of cohesive sediments and bed
surface elevations 1n an estuary, coastal waterway or river. In
addition, It can be used to predict the steady-state or unsteady
transport of any conservative substance (e.g. salt) or non-conservative
-41-
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constituent if the reaction rates are known. The model describes the
convective and diffusive transport of suspended or dissolved
constituents, the settling, deposition (i.e. sink) and erosion (I.e.
source) of cohesive sediments to and from the bed respectively, and
consolidation of the bed due to continuing deposition.
The model uses experimentally developed empirical expressions for:
1) rates of surface and mass erosion, 2) rate of deposition and 3)
settling velocities of coagulated particles as a function of the
suspended sediment concentration, thus accounting for the time-varying
coagulation and aggregation of fine sediment particles. The effective
turbulent diffusion coefficients in the two horizontal dimensions are
required input in order to predict the diffusive transport of the
constituent being modeled. The sediment bed is considered to be
composed of a specified number of layers, each of which 1s characterized
by an experimentally determined thickness, average bulk density, average
shear strength, and average erodibility rate constant. The
consolidation of the bed due to crushing of underlying sediment by new
sediment deposits, i.e. increased overburden pressures, is accounted for
by increasing the average bulk density and shear stength of each bed
layer.
At each time-step the average bed shear stress induced by the
turbulent flow velocity of the suspending fluid 1s calculated for each
grid element. Then the amount of fine sediment either deposited onto or
resuspended from the bed in each element during the previous time-step
is determined. The concentrations of suspended fine sediment at the
next time-step are then computed for every node point. The new bed
elevation at each element is determined by adding or subtracting the
thickness of sediment deposited to or resuspended from, respectively,
the bed profile that existed during the previous time-step. Lastly,
consolidation of the previous bed profile is simulated using the method
described above.
2.4. Model Modifications
Newly developed bed schematizatlon model as well as mass erosion,
surface erosion and deposition algorithms and the effect of salinity on
the rates of surface erosion and deposition, described in Sections 2.5,
-42-
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2.6, 2.7 and 2.8, respectively, were coded in FORTRAN and integrated
Into SEDIMENT III. The modified version of the model is referred to as
SEDIMENT IIIA. Each of these algorithms was thoroughly tested to insure
that no errors occur in the operation of the program.
In addition to these algorithms, the following additions and/or
modifications were made to SEDIMENT III:
1) The mean water temperature is read 1n and the kinematic viscosity, v
(1n m2/s) is calculated using the following equation:
v= 1.701721xlO~6.exp(-0.025109.T) (2.19)
w
where Tw is the water temperature in degrees Celcius. This equation
was determined, with data obtained from Bolz and Tuve (1976), using
least squares linear regression analysis, with the coefficient of
determination r2 = 0.9935. This coefficient indicates how closely
Eq. 2.19 fits the actual data. The value of r2 can vary between 0
and 1» and the closer r2 is to 1, the better the fit. As indicated
by the given r2 value, a good agreement was obtained.
2) The salinity field is read in to the model as nodal values (i.e. the
value of the suspending fluid salinity at each node is read in at
every designated time-step). The nodal salinity values are used in
evaluating the settling velocity and the deposition rate at every
node. Elemental average salinity values are calculated and then
used to adjust the bed shear strength of the top new deposit layer
(1f such exists) and in calculating the total dry mass of sediment
deposited per element for the time-steps and elements at which
deposition occurs.
3) The density of the suspending fluid (In kg/m3) is calculated at .each
node as a function of the mean water temperature and nodal salinity
value using the following equation (Wilson and Bradley, 1968):
pw - 1000.0.(0.702 + 100.0-(17.5273 * 0.1101.TW-0.000639.TW
-0.039986.S-0.000107.T.S)(5881.913 + 37.592-T
W
-0.34395.TW + 2.2524.S)" ) (2.20)
-43-
-------
Incorporating, in addition, the effect of the suspended sediment on the
local fluid density gives (MacArthur, 1979)
where pef^ w =» effective local fluid density « f(T,S,C), and p^ is given
by Eq. 2.20. At each time-step where nodal salinity values change, new
nodal values of p^ and peff,w are calculated. At each time-step where
nodal concentrations change, new nodal values of peff w are determined.
The values of peff w are used to calculate the nodal values of the bed
shear stress ifo, while the values of p^ are used in determining the
nodal values of the dry bed density, pp, which are used in the erosion
and deposition algorithms.
In the following section, the fine sediment bed schematlzation
developed during the course of this study is described. This
description is preceded by a general discussion on the nature (i.e.
structure) of these beds as revealed in several laboratory
Investigations. .
2.5. Fine Sediment Bed
2.5.1. Introductory Note
As noted 1n Section 1.1, surflcial layers of estuarlal beds,
typically composed of flow-deposited fine, cohesive sediments, occur in
three different states: stationary suspensions, partially consolidated
(or consolidating) beds and settled (or fully consolidated) beds.
Stationary suspensions, also referred to as new deposits, are defined by
Parker and Lee (1979) as assemblages of high concentrations of sediment
particles that are supported jointly by the water and the developing
skeletal soil framework. These suspensions, which result from the
settling of suspended aggregates during periods of deposition (e.g. the
period immediately preceding as well as during slack water) and adhesion
to the existing bed surface, tend to have a high water content
(therefore low bulk density) and a very low, but measureable, shear
strength, tc, that must be at least as high as the bed shear, T^, which
existed during the deposition period (Mehta et__aj ., 1982a). Thus, they
exhibit a definite non-Newtonian rheology. Krone (1963) found that, in
-44-
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addition to the bed shear, the structure (or framework) of these
suspensions depends on the aggregate order in the following manner: if
the aggregates settle onto the bed without being broken up by the bed
shear, the surfidal layers of these new deposits will be composed of an
aggregate network whose order is one higher than that of the individual
settling aggregates; therefore, these layers will have lower bulk
densities and shear strengths than those of the aggregates which form
them.
Whether or not entrainment of these deposits, also referred to as
redispersion (Parker and Kirby, 1977) and mass erosion (Paaswell, 1973),
occurs during periods of erosion (e.g. typically the period following
slack water) depends upon the mechanical shear strength (i.e. stability)
of this aggregate network. That portion which remains on the bed
undergoes: 1) consolidation, due to overburden pressure resulting from
the weight of the overlying sediment which crushes the aggregate network
below, and 2) thixotropic effects, defined as the slow rearrangement of
deposited aggregates attributed to internal energy and unbalanced
internal stresses (Mitchell, 1961), both of which reduce the order of
aggregation of the sub-surface bed layers. This.implies that the bed
becomes stratified with respect to bulk density and shear strength, with
both properties typically increasing monotonically with depth, at least
under laboratory conditions (Mehta^t_jU, 1982a). Differential
settling caused by sorting processes is another cause of stratified bed
formation.
Continued consolidation results in the formation of settled mud,
defined by Parker and Lee (1979) as "assemblages of particles
predominantly supported by the effective contact stresses between
particles as well as any excess pore water pressure." This portion of
the bed has a lower water content, a lower order of aggregation, and a
higher shear strength and therefore is better able to resist high bed
shear stresses.
In this study the primary characteristic used to distinguish
between a stationary suspension and a partially consolidated or settled
bed is the mode of failure that occurs when the bed surface is subjected
to an excess shear stress (i.e. ^ > TC). As stated previously,
stationary suspensions undergo redispersion while partially consolidated
-45-
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and/or settled beds undergo resuspenslon (Parker and Kirby, 1977) or
surface erosion (Paaswell, 1973). Both erosion processes are discussed
in Section 2.6.1.
The nature of the bulk density and shear strength profiles
typically found in flow-deposited cohesive sediment beds has been
revealed in laboratory tests, among others, by Richards jet^jJl,. (1974),
Owen (1975), Thorn and Parsons (1980), Parchure (1980), Bain (1981) and
Oixit (1982). A review of this subject has been made by Parchure (1980)
and Oixit (1982); only a synopsis is given here.
Figure 2.7 shows the dimensionless relationship found using
reanalyzed data of Owen (1975) and Thorn and Parsons (1980) for
consolidation periods, t 48 hours (Fig. 2.8a) which gave c -'
0.794 and 5 = 0.288. However, the data for t ZCP» TC(Z) continues to increase but at a greatly decreased
rate (Fig. 2.9). The influence of such a -sc(z) profile on the erosion
rate is discussed in the following section. Figure 2.10 shows a tc(z)
profile found by Oixit (1982). From the tests conducted by 01x1t, the
following two observations may be made: 1) such a tc(z) profile was not
found in five out of nine experiments, and 2) the sediment beds used by
Dixit were up to six times thicker than those used by Parchure.
Therefore, the TC(Z) profiles measured by Oixit are naturally more
representative of estuarine beds, and as such it is believed that until
further studies are conducted, no definitive statement regarding the
precise nature of T (z) profiles in cohesive sediment beds can be made.
-46-
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1.0
0.5
O.I
005
Tdc H />
(hr) (cm) (g/cm3)
• >48 436 0.204
x 48 25.41 0.151
o 48 25.41 0.208
* 48 25.41 0.172
02
0.5
p/p
1.0
2.0
Fig. 2.7 z/H vs. p/p for Avonmouth, Brisbane and
Grangemouth Muds (after Dixit, 1982).
1.0
0.1
Consolidation Period
(hrs)
• 48
o 72
o 96
• 144
• 240
1.0
1.0
0.1
Consolidation Period
(hrs)
o 2
o 5
• II
• 24
O.I
P/P
1.0
0.3
Fig. 2.8 z/H vs. p/p for Consolidation Periods (a) Less than
48 Hours and (b) Greater than 48 Hours (after Dixit,
1982).
-47-
-------
O.I
0.2
6
E
UJ
o
<
u.
CC
UJ
h-
Z
20
40
Expt. 17
T. =0.05 N/m2
d
Td = 24 hrs
Tch=0.2!N/m2
Expt. 18
Td=O.OI5N/m2
Td =40 hrs
Expt. 19
Td= ON/m2
Td = l35hrs
Tch= 0.34 N/m2
BED 5HEAR STRENGTH (N/m2)
Fig. 2.9 Bed Shear Strength Observed as a Function of Depth
(after Parchure, 1980).
-48-
-------
0.8-
Tc(N/m2)
0.2
0.4
Fig. 2.10 Variation of Critical Bed Shear Strength, T , with Depth
(after Oixit, 1982). c
Thorn and Parsons (1980) found the following relationship between
TC and pj, the dry sediment density at the bed surface, for three
different natural muds:
TC = aj pspl (2.23)
where 01 » 5.42xlO~6 and 0i = 2.28, provided the units of TC are N/m2
and the units of ps are kg/m3. In an earlier study, however, these
researchers observed no strong correlation between -cc and ps for
Grangemouth mud (Thorn and Parsons, 1977). Dixit (1982) concurred with
their earlier findings as he observed no relationship between these two
soil properties for at least the upper bed layers. However, for the
lower bed layers, where •% does not increase as rapidly, there may be a
higher degree of correlation, as suggested by the following. Bain
(1981) found a relationship between the bed voids ratio (which is
-49-
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related to the bed density.) and •% at relatively high shear stress (^ >
0.5 N/m2) for Mersey and Grangemouth muds. The high shear stresses used
by Bain suggests that this relationship was for lower, more consolidated
bed layers, where such high TC values exist.
In addition to being formed by deposition from flowing water,
sediment beds may be formed artificially, i.e. placed beds. Such beds
include those that are remolded and/or compacted after placement 1n a
test apparatus (Mehta and Partheniades, 1979). A basic difference
between these two types of beds 1s their stress history (I.e. the
conditions under which they are formed and the time allowed for
consolidation). The stress history of a bed largely dictates the degree
and the rate of failure that will occur when subjected to an excess
shear stress. In these beds, the shear strength and bulk density
profiles show much less significant stratification over the depth of the
bed than in flow-deposited beds (Mehta Jt..al_.» 1982a).
2.5.2. Bed Schematization '
To facilitate the modeling of changes 1n the bed surface elevation
due to erosion and deposition processes, the bed 1s treated in the
following manner: 1) it is discretlzed into a number of layers, or
strata, and 2) the bed propert1es» e.g. thickness, are assumed to be
spatially (in the x-y plane) invariant within each element, but not so
from element to element, 1n order to account for Inter-element spatial
variances in shoaling and/or scouring patterns. These two factors are
expounded upon below.
The bed in each element is considered to be composed of the
following two sections: 1) the original, settled (consolidated) bed that
is present at the start of the modeling, and 2) new deposits located on
top of the original bed, that result from deposition during the
modeling. Each of these two sections is divided into a number of layers
in order to specify the actual shear strength and bulk density profiles
in the model. The new deposit bed section is subdivided into two sub-
sections, the top referred to as unconsolidated new deposit (UNO) layers
and the bottom as partially consolidated new deposit (CND) layers (Fig.
2.11). The former sub-section, i.e. the one corresponding to a
stationary suspension, is considered to undergo mass erosion while the
-50-
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Unconsoiidoted
New Deposit
(UNO)
Partially ($
Consolidated vo
New Deposit 7=s
(CND)
©
(2)
©
, TUNO
TUNO
TUNO
f,(TLAYM(D)
,2
,3
© TCND,I (TLAY(D)
© TCND,2
®
@
©
©
TCND,
TCNO
To,.
T0,2
3
,4
(THICKO(D)
© T0,3
© T0|4
New Deposits
--
Original Bed
Fig. 2.11 Bed Schematization used in SEDIMENT IIIA.
BED SHEAR STRENGTH, TC (N/ m2)
).0 . 0.2 0.4
Linear
Approximation
o - Node
NLAYTM=5
Fig. 2.12 Hypothetical Shear Strength Profile Illustrating
Determination of Bed Layers Thicknesses.
-51-
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latter, i.e. the partially consolidated bed, undergoes surface erosion
when subjected to an excess shear stress. The original bed as well
undergoes surface erosion. The number of layers indicated in Fig. ?..ll
for each of the three bed sections are not fixed, as each section can be
assigned any given number of layers. The following bed-related model
input parameters are required:
1) The bed shear strength profile 1n the UNO. 'This can be ascertained
from laboratory erosion tests using samples of the sediment from the
water body being modeled (see Appendix B, Section 8.3).
2) The number of UNO layers (NLAYTM) and the thickness of each layer
(TLAYM(I), 1*1,NLAYTM) . These parameters must be determined using
the shear strength profile. For example, Fig. 2.12 shows a
hypothetical TC(Z) profile and illustrates that this bed section
must be divided such that the variation of tc within each layer is
approximately linear. The ^ values at the NLAYTM+1 nodes need to
be read into the model.
3) The bulk density values at the NLAYTM+1 nodes as well need to be
determined. The pa(z) profile may be determined using a laboratory
freeze-drying method (appropriately modified for field samples,
where necessary) described by Parchure (1980), the pumping method
described by Thorn and Parsons (1977). or through use of a gamma-ray
nuclear transmission densitometer (Whitmarsh, 1971).
4) The same parameters for the CND layers and the original, settled bed
layers must be read, with the original bed parameters read in for
each element (where an original bed exists). The parameters read in
for the UNO and CNO layers are assumed to be constants for all
elements.
5) A stationary suspension present on top of the original bed at the
start of the modeling is simulated in the model by reading in the
dry mass per unit bed area of stationary suspension samples obtained
from every element (where such exists).
Included 1n Appendix 8 is a brief description of how these various
bed properties can be determined through the use of a field data
collection program and a laboratory testing program. Other parameters
characterizing the rate of surface erosion that each layer undergoes
when subjected to an excess shear must be evaluated as well; these are
discussed in Section 2.7.2.
-52-
-------
The following procedure was developed for forming the new deposit
bed layer(s) which result from stationary suspensions initially present
Ofl top of the original bed and/or formed during the modeling.
The dry sediment mass per unit bed area per element, MQ, read in
initially if a stationary suspension exists in any given element, or
formed during modeling (as determined by the deposition algorithm) is
used in conjunction with the UNO and CNO properties to solve iteratively
for the thickness of bed formed by MQ for each element where Mg > 0.
This thickness, AT, depends on the bulk density profile, p8(z), for the
UNO and CNO layers. The bulk density profile is converted to the dry
sediment density profile, PQ(Z), using the following formula:
t \ B " PW I? 5,4%
^ 3 PS - pw ' ps {2'24)
As in the case of the PB profile, the PQ profile is discretized, and the
variation between the nodal values (i.e. within each layer) is assumed
to be linear. The thickness AT is determined using the following
relationship:
4>
/ f^(z)-zdz
(2.25)
where 4 = AT ± 0.02AT. If AT is greater than TLAYM(l) (see F1g. 2.11)
then more than one layer of UNO is added. The assumed linear variation
of PQ within each layer is used in the above equation. When or if the
UNO layers are filled, the same procedure is used to fill up the CNO
layers below the UNO layers. The bottom CND layer can never fill up;
therefore, continuing deposition is accounted for by increasing the
thickness of this layer, while the thicknesses of the overlying UNO and
CND layers remain the same. As a result, the thickness of the bottom
CNO layer, I.e. TLAY(NLAYT) is not specified in the input data. This
particular filling sequence was used in order to account for the
consolidation of the sediment bed due to overburden pressure by virtue
of the increasing -^ and pg values with bed depth.
In the next section, a discussion on the erosive behavior of fine
sediment beds is given, followed by a description of the erosion
algorithm.
-------
2.6. Erosion of Fine Sediment Beds
2.6.1. Introductory Note
Of interest in this study are the erosion (resuspension)
characteristics of saturated, flow-deposited fine sediment beds. A
number of laboratory investigations were carried out in the sixties and
early seventies in order to determine the rate of resuspension, c,
defined as the mass of sediment eroded per unit surface area unit time,
as a function of the bed shear stress in steady, turbulent flows. An
important conclusion from these tests was that the usual soil indices
such as liquid or plastic limit do not adequately describe the erosive
behavior of these soils (Mehta, 1981). For example, Partheniades (1962)
concluded that the bed shear strength as measured by standard tests,
e.g. the direct-shear test (Terzaghi and Peck, 1960), has no direct
relationship with the soil's resistance to erosion, which is essentially
governed by the strength of the inter-particle and inter-aggregate bonds
between the deposited sediment material. Shown 1n Table 2.2 are the
various physico-chemical factors known to govern the erosive properties
of these beds. These factors must be specified to properly characterize
the erosive behavior. The hydrodynamic factors define the erosive
forces while the bed and fluid physico-chemical properties determine the
resistivity of .the bed to erosion.
The erosive forces, characterized by the flow-Induced instantaneous
bed shear stress, are determined by the flow characteristics and the
surface roughness of the fluid-bed Interface. The sediment composition,
pore and eroding fluid compositions and the structure of the flow-
deposited bed at the onset of erosion must be determined in order to
properly define the erosion resistance of the bed. Sediment composition
is specified by the grain size distribution of the bed material (I.e.
weight fraction of clays, silts)» the type of clay minerals present, and
the amount and type of organic matter. The CEC can be used to
characterize the clay mineral type. Arulanandan j!t_jal_. (1973) and
Alizadeh (1974) have attempted to characterize clay composition using
the apparent dielectric constant measured at selected frequencies. Each
clay tested appeared to have a characteristic value of a "dielectric
dispersion" parameter determined from these measurements. The
-54-
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Table 2.2
BED SHEAR STRESS
Principal Factors Controlling Erosion of
Saturated Cohesive Sediment Beds
HYDRODYNAMIC FACTORS (Erosive Force)
/-Flow Characteristics
^-Bed -Fluid Interface
BED AND FLUID PROPERTIES (Resistive Force)
SEDIMENT COMPOSITION
-Clay Mineral Type] Ion Exchange Capacity
-Clay Percentage by Weight
•Organic Matter
PORE FLUID
COMPOSITION
^Ml
MOB
MM
•Mono-ond Divalent Cations Concentrations | Conductivity
.Relative Abundance of \ CAR UNat,Ca1t,Mo*t)
Mono-and Divalent Cations/ SAR v ' ' y
^Temperature
N—nH
ERODING FUJID
COMPOSITION
—4
•MM
•MM
Salinity (NaCI.CaCI 2, MgCI 2)
•Temperature
•pH
•Cementing Agents (Iron Oxide, etc)
BED STRUCTURE
(Placed Bed
Deposited Bed
-55-
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dielectric dispersion has been defined as the amount of decrease in the
apparent dielectric constant with frequency (Alizadeh, 1974).
The composition of the pore and eroding fluid are specified by the
temperature, pH, total amount of salts and the type and abundance of
ions present, principally CT", Na"1", Ca*2 and Mg*2. Cementing aqents
such as iron oxide can significantly increase the resistance of a
sediment bed to erosion. Measurement of the electrical conductivity is
used to determine the total salt concentration, whereas the
concentration of Na^ relative to that of Ca + Mg 1s characterized by
the sodium adsorption ratio (SAR), defined as:
[ (Ca „*)]•/' '
where the cation concentrations are in mil 11 equivalents per liter
(Arulanandan, 1975). The effect of SAR on the rate of erosion is
discussed in Section 2.8.3* The physico-chemical aspects pertaining to
the aforementioned factors have been summarized by Sargunam et al .
(1973), Kandiah (1974), Arulanandan .et^jiT.. (1975) and Arlathurai and
Arulanandan (1978). The effect of the bed structure, specifically the
vertical bulk density and shear strength profiles, on the rate of
erosion is discussed by Lambermont and Lebon (1978) and Mehta et al _.
(1982a).
Several different types of relationships between the rate of
erosion, e, and the time-mean value of the flow-induced bed shear
stress, tb, have been reported for non-stratified beds. These include
statistical -mechanical models (Partheniades, 1965; Christensen, 1965), a
rate process model (Paaswell, 1973; Kelly and Gularte, 1981) and
empirical relationships (Ariathurai and Arulanandan, 1978). These
relationships typically have the following general form (Mehta, 1981):
ij.T^."*^) (2.27)
where TL ,tv,...,n. are parameters that specify the bed resistivity.
The surface erosion rate, e,.1s related to the time-rate of change
of the suspension concentration, dC/dt, and to the time-rate of change
of the depth of erosion, z, with respect to the original bed surface
elevation, by the following expressions:
-56-
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dC 1
dz
(2.28)
(2.29)
where d - flow depth and PQ(Z) « dry bed density profile.
Figure 2.13 shows the general nature of laboratory determined
relationships, found by, among others, Parthenlades (1962) and
ChMstensen and Das (1973) for placed beds. Shown in F1gs. 2.14 and
2.15 are examples of this relationship, which may be expressed as
ech
(2.30)
where M * slope, and the subscript ch refers to a "characteristic" value
(Mehta, 1981; Hunt, 1981). For -^ < t^, M = Mi and for -c > TCH, M-
M2. Thus, Eq. 2.30 has the general form e = e(TK*Tch'eCh» MI* M*^ as in
Eq. 2.27. The parameter T , determined by extrapolation of the M2 line
to the e = 0 axis, has been interpreted to be the critical shear stress
for erosion (Partheniades, 1962; Gularte, 1978). Values of ech> t^,
MI and Ma are largely determined by the physico-chemical factors given
in Table 2.2.
o»
"o
o
'55
'C
0
Bed shear stress T
F1g. 2.13 Typical Laboratory Determined Rei«:ionship
between Surface Erosion Rate e and Time-mean
Bed Shear Stress T (aftp- "u
-------
0.02
o
O)
in
I
w£ 0.01
^
en
vu
0
~TIIIIIIT
Christensen and Das (1973)
grundite
TCH=0.853 N/m2
^=0.006 gm/m -sec
0
i i ii i
0.2
0.4 0.6
T(N/m2)
0.8
0.02
o
0>
CM
E o.oi
^>*
E
o»
Ml
0
Partheniades(l962)
San Francisco Bay mud
1.0
i.2
Fig. 2.14
Example of Relationship between Surface
Erosion Rate e and Bed Shear Stress T.
Data of Christensen and Das (1973) for
Grundite (after Mehta, 1981),
0 I 2
r (N/m2)
Fig. 2.15 C-T Data of Partheniades
(1962), Series I and II
(after Mehta, 1981).
-------
Ariathurai and Arulanandan (1978) found the same general
relationship for remolded beds as given In Eq. 2.30, but with Ml * M2.
Thus, Eq. 2.30 becomes
.-t-
Tcr
where M' « M»t . Figure 2.16 gives an example of this relationship,
with a1 =:1/M'.
Figure 2.17 shows the measured variation of C with time typically
found by several investigators (Partheniades, 1962, iienca and
Partheniades, 1979; Mehta _et__al_., 1982a) in laboratory resiupension
tests with flow-deposited (stratified) beds under a constant applied
•t* As observed, dC/dt is high Initially, decreases monotonically with
time and appears to approach zero. The value of -c at the depth of
C
erosion at which dC/dt, and therefore e becomes essentially zero has
been interpreted to be equal to v (Mehta Jt__aU, 1982a). This
interpretation is based on the hypothesis that erosion continues as long
as -t > t , i.e. the excess sK.^r stress tv-tc > °» Erosion is arrested
at the bed level at which T-T = 0. This interpretation, coupled with
b c
measurement of pg(z) and the variation of C with t can result in an
empirical relationship for the rate of erosi-m of stratified beds.
Resuspension experiments with deposited (stratified) beds were
performed by Parchure (1980) in a rotating annul«r flume anu by Dixlt
(1982) 1n a recirculating straight flume. The objective of these
experiments was to determine the effect of varying bed shear strength
with depth below the initial bed surface on the rate of surface erosion
under a flow-induced shear stress. A description of the experimental
procedures and results from these experiments has been given by Parchure
(1980), Dixit (1982) and Mehta et__al_. (1982a). A synopsis is given
here.
The annular flume used in these experiments had the following
dimensions: 0.20 m wide, 0.46 m deep and 0.76 m mean radius. The flume
consisted of three main components: 1) a rotating circular channel which
held the sediment-water mixture, 2) an annular ring with '•he same mean
radius as the channel, and 3) a steel frame and r1»«-*-ric ,,,u;.ors. The
ring, positioned 1n contact with the water efface, and channel could be
-59-
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2.0
1.5
1.0
0.5-
0
Ariothurai and Arulanandan(l978)
30%illite
o 9.5°c
' • I8°c
A 23°c
* 42°c
0
0.5
1.0
1.5
2.0
• ' Tcr
Fig. 2.16 Dimensionless e-t Relationship Based on Results of
Ariathurai and Arulanandan (1978) (after Mehta, 1981),
Tb= Q.207 N/rrf
2 4
6 8 10 12 14 16 18 20 22 24
TIME (Hours)
F1g.
2.17 Relative Suspended Sediment Concentration versus
Time for a Stratified Bed at Bed Shear Stress
T530.207 N/m2 (after Mehta and Partheniades,
1979).
-60-
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rotated simultaneously in opposite directions in order to achieve a
uniform turbulent shear field in the channel, and to minimize the
effects of rotation-induced radial secondary currents. This design and
operational procedure eliminated the presence of aggregate-disrupting
elements such as circulatory pump blades. The required bed shear stress
was attained by adjustment of the rotational speeds of the channel and
the ring. Four taps, located on the oute* channel wall, were used to
obtain suspended sediment samples from the channel.
The redrculating flume was 18 m long, 0.6 m wide and 0.9 m deep
with an underflow-type control gate at the downstream end. One side of
the flume was made of glass panels to allow visual observacions. The
diameter of the return pipe was 0.2 m.
A commercial grade kaollnite with a CEC of approximately 9 meq/100
gm was used in these experiments. Tap water, with a total salt
concentration of 0.28 ppt, pH = 8.5 and SAR = 0.012, was used in the
recirculating flume, while tap water plus commercially available sodium
chloride at 35 ppt concentration, pH = 8.1 and SAR » 12.0 was used in
the annular flume. The kaolin,re was equilibrated with the fluid used
for at least two weeks prior to the tests. The equilibration time is an
important factor that can affect the rate of erosion'due to the
possibility of concentration gradients of ioric constituents between the
solid and the liquid phases, or between the pore fluid and the eroding
fluid, 1n the sediment-water system if the time allowed for
equilibration is insufficient (Mehta, 1981).
The resuspension test methodology is depicted in Fig. 2.18.
Specifically, this figure shows how the bed shear was varied over the
course of each experiment. In Phase I the sediment-water mixture with
sediment concentration Co was mixed at a high shear stress, IR, for a
period Tm. The shear stress -cm must be greater than TK , the maximum
bed shear stress at which deposition of suspended sediment occurs. In
Phase II the bed shear was lowered in steps, to t. for T , then
to -r. for T. and finally to zero shear stress for a period Tejc.
During this phase the sediment settled out of suspension, forming a bed
which began to consolidate. As indicated in Fig. 2.18, the first two
phases define the pre-erosion stress history of • -aa. in Phase III,
the shear stress was increased as shown in aiscretized (one-hour) steps,
-61-
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cr>
1N3
in
I
CO
"8
CO
•h-
• Phase I
m
Tm -4—Td, -4*-
•Tdc
Pre-Erosion Stress History
4-fTsH
Resuspension
•*Time
Fig. 2.18 Schematic Representation of the Selected Methodology for the Variation of the Applied Bed
Shear Stress During Bed Preparation and Resuspension Tests (after Mehta £t aU, 1982).
-------
i.e. TI 3 T2 - ...T.j (» 1 hour), and resuspenslon of the deposited
material occurred.
The following parameters were held constant in most of the
experiments in each flume: C0, T^, Tm, T. , T. , -t. , T. and T^. Shown
in F1g. 2.19 are typical values for these parameters and the measured
variation of suspended sediment concentration with time for a test 1n
tap water. The parameter AT* , which may !>e referred to as the
normalized incremental bed shear stress, 1s defined as (^i-^)/"^
where -^ 1s the bed shear stress, -c^, during ith time-step.
In steps i » 1,...,5 in this figure it is apparent that the
suspension concentration approaches a constant value duriny the latter
stages of each time-step, i.e. dC/dt-»0, while for steps i = 6 and 7 no
appreciable decrease 1n dC/dt occurs over the one hour periods. This
difference in the concentration-time profiles is represented in a
different manner in Fig. 2.20, which shows the suspension concentration
at the end of step i, C(T^), plotted against t^ for three different
tests 1n the recirculating flume. The value of Tcn, a characteristic
shear stress (similar to one wfined previously for tests with placed
beds) is determined as shown for each test. It is apparent that
dC(Tj)/dt is higher for ^ > Tch than for T^ < .Tch. The significance of
this observation is better appreciated when zch, wnere zch is
the depth below the initial bed surface at which TC = TC^ (Mehta et al .,
1982a).
The following empirical relationship between ei and T^-TC(Z) was
derived from these experiments
t2-32'
where eoj and «i are empirical coefficients. Figures 2.21 and 2.22 show
this relationship for tests 1n tap water and salt water respectively.
This relationship is analogous to the rate expression which results from
a heuristic interpretation of the rate process theory TOI chemical
reactions (Mehta ^^K, 1982a). Christen&en anj ".- {ia/^), Paaswell
(1973) and Kelly and Gularte (1981) have ur^-a rate process theory in
-63-
-------
e
o>
o
z
o
§
tr
uu
u
I
o
en
z
UJ
Q.
CO
3.50
ELAPSED TIME T (hrs)
4.50 5.50 6.50
0.00
0.00
1.00 2.00 100
ELAPSED TIME T (hrs)
4.00
F1g. 2.19 Variation of Suspension Concentration with Time for T. =48
Hours (after Dixit, 1982).
-64-
-------
8
_ 6
w.
a>
«•—
o»
- 4
H=~
O
- C0s44.lgm/liter
h =30.5 cm
_ Tm=0.9 N/m2
Tm=24hrs
Tft =0-0.050N/m2
TdisTdc
0 hrs
h Tdc=24-I35hrs
Tj =
Symbol
c ch
(hrs)(N/m2)
24 0.21
40 0.29
135 0.34
0.2
0.4
(N/m2)
0.6
Fig. 2.20 C(T-j) versus TI for Three Values of Tdc, Using
Kaolinite 1n Salt Water (after Kehta et a_l_., 1932a)
-65-
-------
2.5
2.0
JS
vw
1.5
1.0
05
Series 4
T* 24 hr
0
*
a
7
Time
Step
i
1
2
3
4
5
Tb^
0.037
0.060
0.086
0.129
0.188
<* <
(a
5.6
150
IOB
12.1
ll.i
cm*2fnin"'j
0
0
1
1
I
,38
.80
.30
.21
.53
0.5
1.0
1.5
2.0
2.5
rc
Fig. 2.21 Normalized Rate of Erosion, e}/eoi» versus Normalized Excess
Shear Stress, (Ti"tc(z)}/TC(z), Using Kaolinite in Tap Water
(after Mehta et al.., 1982).
-66-
-------
2.0
1.5
"V 1.0
0.5
Q
Series 3
Tdc*40hr
Time
Step
i
,
o
a
A
1
2
3
4
5
(Nm-2)
0.100
0.120
0.145
0.175
0.210
tgcm^min"4)
5.S
5.5
5.5
5.5
8.4
0.04
0.25
0.30
0.27
0.22
0.5
1.0 1.5 2.0 2.5
Fig. 2.22 Normalized Rate of Erosion, e-j/epi, versus
Normalized Excess Shear Stress, (V /T-(Z))/TC(Z),
Using Kaolinite in Salt Water (after ,'ehta et al.,
1982). r
-67-
-------
explaining the erosional behavior of cohesive sediment beds. By
analogy, e^ is a quantitative measure of the work done by ^ on the
system, i.e. the bed, and e^ and a^/tc(z) are measures of the system's
internal energy, i.e. bed resistance to an applied external force.
An important conclusion reached from the above experiments was that
new deposits should be treated separately from settled, consolidated
beds (Mehta et_j»]_., 1982a). The rate of surface erosion of new deposits
may be evaluated using Eq. 2.32, while the erosion rate for settled beds
may be suitably determined using Eq. 2.31, in which e varies linearly
with the normalized excess shear stress. The reasons for this
differentiation in determining e are twofold: 1) typical tc and pg
profiles in settled beds vary less significantly with depth than in new
deposits, and may even be nearly invariant. Therefore, the value
of (TV/TC) - 1 * At*, will be relatively small. For small values
of AIL, the exponential function in Eq. 2.32 can be approximated
by «•(! + A-cJ, which represents the first two terms in the Taylor
series expansion of exp(a(A-O). For sma^ values of A* » i.e-
AIL « 1, both expressions for e vary linearly with £ Thus, the
variation of e with depth in settled beds can be just as accurately and
more simply determined using Eq. 2.31. 2) the laboratory resuspension
tests (briefly described in Appendix 8) required to evaluate the
coefficients SQ and o for each CND layer can not be practically or
easily performed using vertical sections of the original settled bed
(obtained from cores). A simpler laboratory test has been described by
Ariathurai and Arunlanandan (1978) to evaluate the variability of M with
depth. This procedure is briefly noted in Appendix B.
2.6.2. Erosion Algorithm
A description of the mass erosion algorithm^ contained in
Subroutine MASERO in SEDIMENT IIIA, followed by that for the surface
erosion algorithm, contained in Subroutine SURERO, are given below. In
both algorithms, the rate of erosion is calculated on an element by
element basis. '
A portion of the unconsolldated new deposit (UKO), when present,
will mass erode (redisperse) when -c^ is greater than the surface shear
strength of the UNO, i.e. t (z=0). The thickness of the UNO that fails
-68-
-------
totally and is instantly redispersed is equal to zw, where z# = bed
depth at which t (z) = -c . The value of z^ is determined from the
linearly varying T (z) profile 1n each UNO layer. The value of z^ may
be greater than the thickness of the top layer, TLAYM(l), in which case
more than one layer is redispersed. The dry mass of sediment that is
redispersed, MQ, 1s calculated according to
(2,33)
where MQ has units of Kg/m2 and is considered to b t!~.e mass eroded over
one time-step At. The contribution to the source term in the governing
equation (Eq. 2.11) caused by mass erosion is given by Eq. 2.33 divided
by the product of the average element water depth and the time-step
At. New UNO layer(s) thicknesses and -^(z), pg(z) and pn(z) profiles
are calculated at each time-step when mass erosion occurs by subtracting
z* and resetting TC(z=0), PB(Z=O) and pn,(z=0) equal to the respective
initial values at z * z^. If z^ 1s calculated to be greater than the
thickness of the entire UNO, *hen all of this sediment is redispersed.
For both the mass and surface erosion algorithms, erosion is
considered to occur only during accelerating flows, i.e. Th(t+At) > Tu(t),
Thus, -^(t+At) may be greater than TC(Z=O), no erosion will occur
if t. (t) > rU+At). This stipulation for the occurrence of erosion,
and an analogous one for deposition as will be Discussed 11, the
following section, is based on an interpretation of the typically
observed Eulerian time-concentration variation in an estuarial
environment. For example, F1g. 1.3 shows a time-concentration profile
from the Savannah River estuary (Krone, 1972). Also indicated is the
observed correlation between accelerating flows-and Increasing
suspension concentration and between decelerating flows and decreasing
suspension concentration. Laboratory evidence (Mehta and Partheniades,
1975; Partheniades, 1977; Mehta _et_jJl_., 1982a) suggests that under
accelerating flows, erosion occurs without redepositlon of the eroded
sediment. Likewise, during decelerating flows, sediment deposits
without reentrainment of the deposit. During periods <*. steady flows,
erosion or deposition may occur. These two process"*; will r.ot, however,
occur simultaneously even in this case. The ,nitial condition at the
-69-
-------
inception of the steady flow period will determine whether erosion or
deposition will occur. If the antecedent phase was one of deceleration,
deposition will continue under the steady flow condition. If the
antecedent phase was one of acceleration, the sediment will continue to
erode under the steady flow condition. In both cases, however,
relatively short transient periods of simultaneous erosion and
deposition sometimes do tend to occur (Yeh, 1979). For estuarlal
modeling purposes, however, these periods may be Ignored without
introducing any significant errors.
Surface erosion of consolidating new deposits (CND) occurs when: 1)
the entire UNO has been redispersed, 2) -^(t+At) > ^(t) and 3)
T. (t+At) > T (2=0), where z=0 is now at the flu1d-CND interface. The
surface erosion rate expression (Eq. 2.32) found by Mehta jet_ jl_. (I982a)
is used to determine the thickness of the CND, z#, that is resuspended
during a time-step, At. The following iterative procedure is used to
calculate z^ during any given time-step.
The average erosion rate, "e, for the period At 1s calculated as:
I(t+&t) -i (e(t) + e(t+At)) . (2.34)
1n which
Th(t+At)
e(UAt) = e0(l)exp|>(l)(-2 —-I)] (2.35)
*c
where eo(l) and ot(l) are the average empirical coefficients for the
first (i.e. top) CND layer, and
*c3 2 Wz-0>+ i
As a first guess, z^ 1s set equal to TLAY(l) • z^ (see F1g. 2.11). A
new value of z*, designated zw , is calculated according to:
z* « e«At. -S- (2.37)
2 PD
where dfi is the elemental average flow depth, and p_ 1s the average dry
bed density over the first bed depth z# . Then the following parameter
is evaluated;
-70-
-------
(2-38)
If AX < 0.02, then z^ 1s taken to be the depth of bed eroded during
this time-step. If AX * 0.02, then yet another new value of
z*, designated z^ , 1s calculated using the following equation:
(2-39'
where Xj * pg-z* /(e»At«de), with ^ and I determined using zw » z
Using z# , the entire procedure, i.e. Eqs. 2.34 through 2.39, is
repeated until the chosen error criterion, i.e. AX < 0.02, is
satisfied. As in the mass erosion routine, new CNO layer thickness (es)
and TC(Z), PD(Z) and p.j(z) profiles are determined. As before, z^ may
be greater than the thickness of the top layer. Laboratory tests
required to evaluate tAz), po(z), and the average values of EQ and a
C.o w
for each CNO layer are described in Appendix 8.
Once the entire new deposu bed section has been eroded, the
original consolidated bed, if any exists, will undergo surface erosion
when the following two conditions exist: 1) tu(t+At) > tb(t) and
2) tu(t+At) > -c (z=0), where z=0 is now at the top of the original
•bed. The surface erosion rate expression (Eq. 2.31) given by Ariathurai
and Arulanandan (1978) is used to evaluate the tnickness, z^,, of the
original bed that is eroded each time-step. The iterative procedure
used for the CND 1s again used to solve for zw, with only the expression
for e being different. Equation 2.34 becomes
1) (2.40)
where H(l) is the credibility constant for the. first layer.
The contribution to the source term in Eq. 2.11 caused by surface
erosion is given by Eq. 2.34, with Eq. 2.35 used for the consolidating
bed section and Eq. 2.40 used for the original consolidated bed section,
divided by the average element water depth.
-71-
-------
In the following section, the depositional behavior of cohesive
sediments is summarized, followed by a description of the deposition
algorithm.
2.7. Deposition of Fine Sediment
2.7.1. Introductory Note
Deposition has been defined to occur when tjj is not high enough to
resuspend sediment material that settles onto and bonds with the bed
surface. This process, therefore, involves two other processes,
settling and bonding, i.e. cohesion. Laboratory studies on the deposi-
tional behavior of cohesive sediment in steady turbulent flows have been
conducted by, among others, Krone (1962), Rosillon and Volkenborn
(1964), Partheniades (1965), Partheniades _et_jl_. (1966), Mlgniot (1968).
Lee (1974), Mehta and Partheniades (1975) and Mehta et^. (1982b). The
results from these and other studies on the settling rates of cohesive
sediments pertinent to the deposition model described in Section 2.7.2.
are summarized below.
In laboratory flumes, the depositional behavior is usually
investigated by allowing sediment suspended in a flume at a high shear
stress to deposit by reducing the shear stress. Since the sediment
concentration gradient in the direction of flow is usually small, the
observed time-rate of change of the depth-averaged concentration, C, is
due to the deposition of suspended material. The conservation of
sediment mass can be expressed as
where t =» time, d = flow depth, W$(c) =» sediment settling velocity as a
function of C, and p
-------
Pd = 1-TT (2'42)
cd
where t^ » critical shear stress for deposition, above which no
deposition occurs. Therefore, p t... The value of -ccd was found to be equal to
0.06 N/m2 for the Bay mud with C < 0.3 g/1. Krone found that when C <
0.3 g/1, Us was Independent of C. In this case, integration of Eq. 2.41
gives:
^Llt] (2.43)
where CQ is the initial suspended sediment concentration. Thus,
according to this equation all the suspended sediment will eventually
deposit when ^ < T ..
For 0.3 g/1 < C < 10 g/1 and for C > 10 g/1, logarithmic laws of
the following form were derived:
log C -K^log(t) +.Constant (2.44)
where K was found to be a function of d and p^. Krone attributed the
variation of the depositional properties with suspension concentration
to different forms of settling. Various forms of settling of coagulated
fine sediment are discussed later in this section.
Partheniades (1965) conducted deposition tests in an open, flow
recirculating flume using Bay mud. He noted that for flows above a
certain critical bed shear, the suspended sediment concentration, after
an initial period of rapid deposition, approached a constant value,
which he referred to as an equilibrium concentration, Ceq. The ratio
Ceq/C0 = C was found to be a constant for given flow conditions,
regardless of the value of CQ. Whereas for flow velocities even
slightly less than this critical value, all the sediment eventually
deposited.
Partheniades _et_j»K (1966) conducted deposition experiments in a
rotating annular flume (similar to the one at the University of Florida,
but with mean diameter of 0.82 m and 0.19 m wide) ** the rkssachusetts
-73-
-------
Institute of Technology using a commercial grade kaolinite. Based upon
these experiments It was concluded the Ceq represents the amount of
sediment that, having settled to the near bed region, cannot withstand
the high shear stresses present there (due to insufficiently strong
Inter-particle bonds) and are broken up and resuspended. In addition,
Ceq in the fine sediment deposition tests appears not to be the result
of an interchange betweer^ suspended and bed material as it is for
cohesionless sediment, because, if such *ere the case, Ceq would not be
dependent on C0. Therefore, it follows that Ce_ does not represent the
maximum sediment carrying capacity of the flow, as it does in the case
of cohesionless sediment, but instead may be considered to be the steady
state concentration (Mehta and Partheniades, 1973).
As noted by Mehta and Partheniades (1975), Krone did not observe
Cen in his tests because most of them were conducted at t^ < t .,
wherein C would be expected to be equal to zero. It is apparent that
the definition of p^ must be extended to include bed shear stresses
greater than tcd»
Mehta and Partheniades (1975) investigated the deposttlonal
properties of a commercial grade kaolinite in distilled water and in
salt water at seawater salinity (35 ppt) 1n the rotating annular flume
facility at the University of Florida. Figure 2.23 shows typical
suspended sediment concentration-time plots found in these tests. It is
evident that a steady state concentration was reached 1n each test and
that for bed shears above approximately 0.16 N/m2, the value of Ceq was
greater than zero and in fact increased monotonically with increasing
*'
Figure 2.24 shows the ratio C = C /CQ plotted against -q, for all
the tests with kaolinite in distilled water. Two important conclusions
are obtained from this figure: 1.) C is a constant for a given ^ (and
type of sediment) and is not a function of depth, d, or CQ, and 2) for
tK < TW , C =0. The first conclusion 1s based on the observation
^ bmin eq
that the data points for all the different flow conditions are almost
randomly scattered about a "best fit" line. The minimum bed shear,
IL_. , observed in Fig. 2.24 is the same as the TC(J value defined by
"mm
Krone (1962), and the critical bed shear obtained by Partheniades
(1965). As observed in this figure, -t . was found to be approximately
0.18 N/m2 for kaolinite in distilled water.
-74-
-------
i
^j
en
10
Kiwi
F1g.
2.23 Ratio C/C0 versus Time t for Kaollnite 1n Distilled Water (after Hehta
and Partheniades, 1975).
Fig. 2.24 Ratio Ceq/C0 versus Bed Shear Stress TJ, (after Mehta and Partheniades, 1975).
-------
In Fig. 2.25 the data of Fig. 2.24 are plotted on log-normal
* * *
coordinates as C in percent against vl, where tu * tw/it . The
eq ODD onrin
straight line through the data points gives the following relationship
between these two dimensionless parameters:
C*q*| (1 + «rf(k)) (2.45)
with
(2.46)
where
-------
•vl
•>!
I
001
*
Fig. 2.25 Relative Steady State Concentration Ceq in Percent Against Bed Shear Stress
Parameter T£-! (after Mehta and Partheniades, 1975).
-------
and where C * (C0-C)/(C0-Ceq) represents the fraction of the
deposltable sediment, C0-Ceq, deposited at any given time t, 02 is tne
standard deviation of the log-normal relationship, and ts_ is the
geometric mean (i.e. the time at which C* =» 50%). Figure 2.26 shows a
comparison between some typical depositional data for kaollnlte 1n
distilled water and the log-normal relationship given by Eq. 2.48. This
relationship was found to hold for all values of tj*(» tb/Tb ) greater
than approximately 0.25, with the exception that for very high C0 values
(around 20-25 g/1) with T£ < 1, an acceptable agreement with the
measured data was not obtained. Good agreement was as well obtained
between Eq. 2.48 and the data sets mentioned previously 1n this section.
Taking the derivative of Eq. 2.48 with respect to time gives the
following expression for the rate of change of C with time:
dC* n 0.434 exp(*T /2) /2 5{)*
/2n 02
The standard deviation, aj, and the geometric mean, t50, were found
to be functions of r*,d, and C_, Shown 1n Figsi 2.27 and 2.28 are
D Q ;
examples of the relationship found between these parameters. The
following conclusions were arrived at from these and other similar plots
given by Mehta (1973): 1) for a specific value of T£, the deposition
rate was minimum. This ?* value was found to vary between 1 and 2 for
b
kaolinite in distilled water. The rate of deposition Increased
for •£ values both less than and higher than this specific value, but
not as significantly for higher values as for the lower values.
However, for t. > T. , no deposition of suspended sediment occured.
D ^max
For Bay mud in sea water, t. was determined to be 1.69 N/m2. 2)
+ brnax
for i-r, < 1, the rate of deposition Increased with an Increase 1n d,
while for t* > l, the effect of d on the deposition rate was minimal.
3) the deposition rate decreased with an increase in CQ. A possible
explanation for this last result is that C0 was in the hindered settling
range (explained below) where the settling velocity of suspended
sediment decreases with increasing concentatlon (Owen, 1970; Huang £t_
al_., 1980; Thorn, 1981).
As noted, the settling velocity of suspended fine sediment
particles has been found to be a function of, among other parameters,
-78-
-------
lO
I
005
50 i
Fig. 2.26 C In Percent versus t/t50 for Kaolinlte In Distilled Water (after Mehta
and Partheniades, 1975).
-------
1.5
1.0
o
*P \
0.0-5
0.0
-0.5,
0.5
1.0
1.5
2.0
2.5
3.0
Fig. 2,27 log t50 versus TJ, for Kaollnite in Distilled Water (after Mehta
and Partheniades, 1975).
1.5
t.O
0.5
Symbol Depth(m) C0(
-------
the suspension concentration (Krone, 1962). There appears to be at
least three types of settling: 1) no mutual interference, 2) mutual
interference and 3) hindered settling. For very low suspension
concentrations, on the order of 0.1-0.7 g/1, the aggregates or
elementary particles settle independently without much mutual
interference, and therefore the settling velocity is independent of C.
For concentrations between approximately 0.3 g/1 and 10-15 g/1, the
settling velocity increases with increasing concentration due to the
accompanying increase in inter-particle (floe) collisions, and therefore
increased mutual interference (Fig. 2.29). For concentrations higher
than 10-15 g/1, the settling velocity actually decreases with increasing
concentration (Figs. 2.30 and 2.31). At such high concentrations the
sediment suspension, referred to as fluid mud or mud cake (Bellessort,
1973), hinders the upward flux of water expelled by consolidation of the
lower suspension (Krone, 1962).
In the mutual interference range, Krone (1962) and Owen (1971) have
found the following empirical relationship between the median settling
velocity, W , and C:
Ws - KCn (2.51)
where K and n are empirical constants that depend on the sediment type
and the turbulence intensity of the suspending fluid. Krone found n to
be equal to 1.33 for Bay mud in laboratory experiments (see Fig. 2.29).
Owen (1971) studied the effect of turbulence on the settling
velocities of natural mud. No description of the sediment was reported,
except that it was collected in the River Thames near Oagenham,
England. A specially designed sampling instrument was used to collect
sediment samples during both a spring tide and a neap tide. This tube
collected undisturbed samples of suspended sediment in an estuarine
environment, and immediately thereafter the median settling velocity of
"natural aggregates" could be determined using the bottom withdrawal
method described by Owen (1970). The value of n determined using this
method was 1.1 and 2.2 for sediment collected during a spring and a neap
tide, respectively. The turbulence intensity dun-"; » spring tide is
greater than that during a neap tide, Owen therefore postulated that n
-81-
-------
, lao
o
- 8.0
(A
£
6.0
4.0
LU
>
O
S
_j
UJ
2.0
1.0
a o-8
0.6
• In Graduated Cylinder
a In Flume
L lili I
0.1 0.2 0.4 0.6 0.8 1.0 2.0
SUSPENDED SEDIMENT CONCENTRATION, aa/^)
Fig. 2.29 Settling Velocity, Ws, versus Suspended Sediment
Concentration, C, for San Francisco Bay Mud (after
Krone, 1962).
-82-
-------
Q
•5 3.0
B 2.0
o
I
to
1.0
Ill
I I
20 40 60
SUSPENDED CONCENTRATION, C(gA0)
F1g. 2.30 Settling Velocity, Ws, versus Suspended Sediment
Concentration, C, for Yangtze River Estuary Mud
(after Huang et aj_., 1980).
~Z 100.0
J 10.0
8 1-0
>
& O.I
0.01
P 0.001
Severn estuary mud
(saline water)
0.01 0.10 1.0 10.0 100.0
SUSPENDED SEDIMENT CONCENTRATION,
C
Fig. 2.31 Settling Velocity, Ws, versus Suspended Sediment
Concentration, C, for Severn P U'ary Mud (after
Thorn, 1981).
-83-
-------
was greater (and therefore W as well was greater) during the neap tide
because the lower level of turbulence did not cause significant breakage
of the aggregates; thus relatively large aggregates with higher settling
velocities were formed. During the spring tide the higher degree of
turbulence, and therefore greater internal shearing rates, did result 1n
breakage of a significant proportion of the aggregates. Thus, small
aqqreqates with lower settling rates, and therefore lower value of n,
were formed. Owen believed that the inter-particle collision rate was
significantly high during both tides and therefore did not consider it
very probable that the aggregate size would have been affected (I.e.
limited) by this factor. Owen also performed standard settling tests in
a one meter high bottom withdrawal tube using the same sediment samples
as above, and found that Ms varied linearly with C (i.e. n«1.0) for both
spring and neap tide samples and that the values of Ws were
approximately one order of magnitude smaller than the Ws values
determined with the aggregate collection tube. The latter result is
very significant in that it reveals the following apparent effect of
turbulence on the behavior (e.g. settling velocities) of sediment
aggregates: larger, stronger aggregates with corresponding higher
settling velocities are formed in a turbulent flow field than under
quiescent conditions primarily because of increased collision rates due
to high internal shearing rates (see also Section 2.8.4).
Migniot (1968) defined a "flocculatlon factor" F, given below, in
order to quantify the effect of the aggregation intensity on Ws:
Ws
(2.52)
where MS A ^s the median settling velocity of the aggregates and H^ is
the median settling velocity of the elementary sediment particles.
Bellessort (1973) reported that F varies with the grain size of the
elementary (i.e. def 1 occul ated) particles according to
F = a3-0"2p3 »%~P3 (2-53)
o
where 0 1s the mean diameter of the particles in microns (10" m), «3 «
250 and p3 =• 0.9, provided VI is measured in mm/s. Figure 2.32 shows
-84-
-------
MEAN DIAMETER (Microns)
a:
e
§
o
0.10
I
10
IU
in4
IU
io3
in2
in1
IU
i
•\
\
X
<
.1 i i i
» Marine Silt
o Estuary Silt
A River Silt
* Lake Silt
• Muds and Powders
\
;*>
V
\
* UF Test with
AtchafaloyaBayl
• Other Sediments
obtained by C-^'ati°n
S =30ppt
>.
fa
V»
A-
\
vlud
CQ '4.0-1 1.0 gtf
S *0.0ppt
i t i
3
u\
V
^%
j,
>v
V
.N
x^
r
10-4 IQ-2
VELOCITY (mm/s)
Fig. 2.32 Effect of Size and Settling Velocity of Elementary
Particles on the Coagulation Factor of Natural
Muds (after Sellessort, 1973).
-85-
-------
this effect of the particle size on F and Ws. for numerous sediment
samples at CQ » 10 g/1 and salinity S » 30 ppt. Also plotted in this
figure is the variation of F with 0 found by 01x1t et^jJL (1982) using
mud from Atchafalaya Bay, Louisiana. However, in these data C0 varied
from 1.2 to 11 g/1 as indicated and S=0.0 ppt. Another important
difference between the two data sets is that Bellessort measured VL
^A
under quiescent conditions* while Dixit jet^^aK measured this settling
velocity under turbulent flow in a flume. As observed, these data have
the same slope between F and 0 as given by Bellessort. This suggests
that, in general, F may be proportional to O"1'8, albeit with different
intercept values, for at least suspension concentrations with C0 * 1.2-
11 g/1 and 0 c2 (2.57)
where g02(ps/pw-l)/(18v) » M$ and pd is defined by Eq. 2.42.
Therefore, depending upon the value of C, the rate of deposition in
-86-
-------
Range I is given by Eqs. 2.54 - 2.57. These three expressions
for W' are based upon the experiment results of Krone (1962), Bellessort
(1973) and Owen (1971). Typical values for GI and Ca are 0.1-0.7 g/1
and 10-15 g/1 respectively. The value of a was found to be
approximately -0.6 using the settling velocities measured by Owen
(1970), Huang et__al_. (1980) and Thorn (1981). The values WSji, K, n and
Ci can vary widely, depending, among other factors, upon the particle
diameter, 0, the type of sediment and the salinity. These parameters
must be determined in laboratory settling tests using a sample of the,
sediment from the water body being modeled (further discussion of this
aspect is given in Appendix B, Section B.3).
For the intersection of TL , c i£ < •&* (where tu =
T>,C D T)max "max
•v /•*. )» designated as Range II, and the concentration range
Dmax T>mi n
C > C i the rate of deposition is determined using the log-normal
relationship (Mehta and Partheniades, 1975):
* -
where Ol- 0.49, Eqs. 2.45 - 2.47 and C* » (C0-C)/(C0-Ceq) have been
substituted into Eq. 2.50. The following expn
was determined by equating Eqs. 2.54 and 2.58:
substituted into Eq. 2.50. The following expression for W in Range II
k,d exp(-T2/2) Crt . (i*-l) 2,04
)1 )) (2-59>
min
where Ic2 s 0.434/(2/Zii). For tbC 1 for the following reason: the
phenomenon of hindered settling was not observed in the steady-state
deposition tests under turbulent flows performed by Mehta (1973) for
*
concentrations up to about 20 g/1. Evidently, the higher tb values that
Mehta used in his tests prevented the occurrence of this mode of
settling, inasmuch as Krone (1962) did observe hindered settling in his
tests which, in general, were conducted at lower values of T. .
Deposition tests with 0.25 < a using San Francisco Bay mud in sea
-87-
-------
water and kaollnite in distilled water revealed that for suspension
concentrations less than C^ 0.1-0.7 g/1, the exponential law given by
Eq. 2.54 was valid. Therefore, for C < CL 1n Range II, the rate of
deposition is given by Eqs. 2.54 and 2.55 with pd equal to the following
approximate expression:
"d3
f * * *
1 - tjj for tb c < -^ < 0.95 (2.60)
0.05 for •£ > 0.95 (2.61)
The lower limit of 0.05 was chosen for pd when T > 0.95 and C < Cj in
Range II so that deposition would be predicted to occur under these
*
conditions. Assuming that pCi in Range II.
* *
The parameter •& 1s defined to be the value of T. at which the
expression for W'(C) 1n Range I is equal to the same 1n Range II.
Thus, W (and therefore dC/dt) is a continuous function of the entire
deposition range (T* < 1). It is apparent that tw 1s n°* a
b(nax otc
constant, as it is a function of the depth-averaged concentration, C.
Solving for T. gives
* . r -- • ^x - (2.62)
2.7.3. Deposition Algorithm . . • ..
In SEDIMENT IIIA, deposition of suspended sediment occurs when, 1) ,;
the flow is decelerating, I.e. ^(t-t-At) < -^(t), and 2) when Tb(t+At) <. '
TU . When these two conditions are met at any node, the rate of
deposition is calculated as follows. The value of T* is evaluated
D,C
using Eq. 2.62. Inasmuch as the log-normal relationship was found not
to be suitable for ^ < 0.25, the minimum t£ value is set equal to
0.25. Therefore, Eqs. 2.54 - 2.57 are always used to calculate the
value of dC/dt for ^ < 0.25 < T£ c (Range I) while Eqs. 2.54-2.57 and
-88-
-------
2.60-2.61 are used for •t > -t with C o,c *•
for t* 1s 0.95; therefore, Eq. 2.58 is used to determine dC/dt for
0.95 >V < v < •£ (Range II) with OC,.
D*C D DfnftX
The amount of dry mass of sediment deposited per time-step per
element, Mp., is determined according to
Mjj-f-.At.ag (2.63)
where 3 - \ (d (t) + d(t+At)) and dC/dt is given by
c c 6 c
i (?r + ^r 1 (2.64)
in Range I
(2.65)
in Range II.
In. Eq. 2.65, e =• -jr (e(t) + e(t+At)), where 9 = C, t50, tb and o2.
Equation 2.65 was obtained by integration of Eq. 2.58 from t=0 to
t»&t. The thickness of the bed formed by MD 1s calculated in Subroutine
NEWBED using the procedure described in Section 2.5.2. The sink term 1n
the governing equation (Eq. 2.11) is given by Eq. 2.64 in Range I and
for C < Ci in Range II, and by Eq. 2.65 for C > Cl in Range II.
For unsteady flows, as occur in estuaries, the value of C Q, which
is the steady state value of the suspended sediment concentration found
in laboratory tests under steady flows, 1s assumed to be zero.
Nevertheless, the laboratory determined log-normal relationship for
dC/dt, as given by Eq. 2.65, is used for Range II in the deposition
algorithm for the following reasons. The time-step, At, used 1n
estuarlal sediment transport problems is typically of the order
-89-
-------
O.H50
-------
from the molecular arrangement of the oxygen and hydrogen atoms.
According to Grim (1962), the electrostatic field emanating from the
surface of a clay particle orients the polar water molecules In the
pores separating adjacent particles.
As noted In Section 2.1, Inter-particle forces consist of both
attractive and repulsive forces. The attractive forces present are the
London-van der Waals, and are due to the nearly Instantaneous
fluctuation of the d1poles which result from the electrostatic
attraction of the nucleus of one atom for the electron cloud of a
neighboring atom (Grimshaw, 1971). These electrical attractive forces
are weak, and are only significant when the interacting atoms are very
close together. However, they are strong enough to cause structural
build-up as they are additive between pairs of atoms. Thus, the total
attractive force between two clay particles is equal to the sum of the
attraction between all the atoms comprising both particles. This
additive effect results in a larger attractive force and to a smaller
decrease in this force with Increasing particle separation. Figure 2.33
shows qualitatively the relationship between the attractive energy Va
and the particle separation distance. Va is inversely.proportional to
the sixth power of the separation distance for two atoms and to the
second power for two spherical particles. The magnitude of Va decreases
with increasing temperature and is dependent upon the geometry and the
size of adjacent clay particles. Va has been found to be only slightly
dependent upon the salt concentration (i.e. salinity) of the medium (van
Olphen, 1963).
The repulsive forces in cohesive sediments are due to the repulsive
forces of the nuclei of adjacent atoms. The repulsion potential
increases in an exponential fashion with decreasing particle separation.
The magnitude of these forces is dependent upon the salinity, decreasing
with increasing salinity as shown in Fig. 2.33, where Vr is the
repulsive energy. This dependence of Vr on the salinity can best be
explained using the concept of the electrical double layer and the
surrounding diffuse layer, van Olphen (1963) states that the double
layer is composed of the net electrical charge of the elementary clay
particle and an equal quantity of Ionic charge of opposite sign located
in the medium near the particle surface. Thus, the net electrical
-91-
-------
Double-Layer Repulsion at
Three Different Electrolyte
Concentrations
van der waals
Attraction
F1g. 2.33 Repulsive and Attractive Energy as a Function of
Particle Separation at three Electrolyte Concentrations
(after van Olphen, 1963).
v,t
--Net Interaction
Energy
1! \
\^
'"!
'/.
'mm
F'article Seoaration
Fig. 2.34 Net Interaction Energy as a Function of Particle
Separation at High Electrolyte Concentration
(after van Olphen, 1963).
-92-
-------
charge is balanced In the surrounding medium. The ions of opposite
charge are called the counter-ions, i.e. cations. The counter-ion
concentration increases with decreasing distance from the particle
surface. This layer of counter-ions is referred to as the diffuse
layer. A clay particle and the associated double layer is referred to
as a clay micelle (Partheniades, 1971). When the salinity is increased,
the diffuse layer is compressed toward the particle surface (van Olphen,
1963). The higher the salinity, and as well the higher the valence of
the cations which compose the diffuse layer, the more this layer is
compressed and the greater the repulsive force is decreased.
With a high salinity, corresponding to a value approximately that
of seawater (35 ppt), the attractive forces become predominant at all
but extremely small particle separation distances. The interaction
potential, determined by summing Va and Vr, reflects this dominance, and
shows the highest attractive potential (primary minimum) at separation
distances on the order of 1 nm (10 m) (Parker, 1980). At distances
less than this the short range repulsive forces are predominant (van
Olphen, 1963). Figure 2.34 shows this net interaction potential as a
function of particle separation for high salinity. Thus, two clay
particles will adhere when they reach the separation distance at which
the primary minimum occurs. Oestabilization occurs at a maximum rate
due to the presence of attractive forces even at relatively great
distances.
For medium and low salinities, on the order of 10-15 ppt and 1-2
ppt respectively (Parker, 1980), repulsive forces are predominant at
separation distances of approximately 10 nm where a local repulsive
potential maximum occurs (Figs. 2.35 and 2.36). At distances closer
than this, these interaction potentials are similar to that for high
salinity. As indicated by these figures, the destabilization of two or
more particles would be expected to decrease for decreasing salinities
as a result of net repulsive forces existing at increasingly larger
distances (van Olphen, 1963). Nevertheless, clay particles are known to
become cohesive at salinities between 0.6 and 2.4 ppt (Ariathurai,
1974).
-93-
-------
——— Net Interaction
Energy
Particle Separation-
mm
F1g. 2.35 Net Interaction Energy as a Function of Particle
Separation at Intermediate Electrolyte Concentration
(after van Olphen, 1963).
— Net Interaction
Energy
Particle Separation
F1g. 2.36 Net Interaction Energy as a Function of Particle
Separation at low Electrolyte Concentration
(after van Olphen, 1963).
-94.
-------
2.8.2. Effect of Salinity on Bed Structure
For most cohesive soils the Inter-particle and 1nter-floc contact
is considered to be the only significant region between particles where
normal stresses and shear stresses can be transmitted (Mitchell et a!.,
1969). In particular, 1t seems very likely that the primary role of the
double-layer interaction and other physico-chemical forces is to control
the structure of the soil and to alter the transmitted stresses from
what they would be due to the applied flow-induced shear and overburden
normal stresses alone. Two factors that effect the structure of a
cohesive soil, swelling and permeability, and the effect salinity has on
these factors are discussed next.
The degree of swelling which occurs when a cohesive soil is
immersed in a fluid is influenced by factors such as the amount of clay,
shape and size of the soil particles, the salinity and the sodium
adsorption ratio (SAR) of the eroding and pore fluid, and the presence
of an Imposed load on the swelling areas (GMmshaw, 1971). Sargunam et
^1_. (1973) state that as the salinity of the eroding fluid decreases or
the SAR increases, the more surface clay particles will swell. This
swelling causes a weakening of the inter-particle attractive forces and
thus increases the susceptibility of the' soil to erosion. Increasing
the salinity of the eroding fluid causes a greater compression of the
diffuse layer, thereby reducing the repulsive forces of soil particles
which serves to limit the amount of swelling.
Sargunam Jt^^].. (1973) found that when the salinity of the eroding
fluid is greater than that of the pore fluid the yield strength of the
soil is greater and therefore the erosion potential is decreased. In
this case the osmotic pressure gradient across the fluid-bed interface
may result in deswelllng, or consolidation of the bed sediment
particles, which would cause an increase in the inter-particle bonding
forces and therefore lessen the susceptibility to erosion.
It is believed that while this phenomenon of swelling influences to
some degree the structure and hence the erosion potential of a cohesive
bed, it is not nearly as significant as the upward flux of pore water
due to gravitational forces in a consolidating mud.
Quirk and Schofield (1955) found that the degree of permeability of
clay soils depends upon the nature and the concentration of the cations
-95-
-------
present in both the eroding and pore fluids. In particular they found
that the permeability increased with an increase in the salinity of the
eroding fluid. Swelling and stabilization (i.e. decoagulation) are
generally considered to be the main reasons for changes in the
permeability. The former can cause either partial or total blockage of
soil pores which would result in a decrease in permeability.
Stabilization essentially occurs during swelling when the clay particles
have separated to the extent that the inter-particle repulsive forces
are dominant over the attractive forces. Since an increase in the
salinity of the eroding fluid serves to limit the amount of swelling
which occurs and thus restricts the amount of stabilization as well, an
increase in salinity would result in increased permeability. The
converse was found to occur as well since, as stated previously, a
decrease in the salinity of the eroding fluid causes an increase in the
degree of swelling and stabilization.
2.8.3. Effect of Salinity on Surface Erosion
Sherard ^t_^i.. (1972) have shown that the susceptibility of a
cohesive sediment bed to erosion depends on two factors: 1) the pore
fluid composition, as characterized by the SAR, and 2) the salinity of
the eroding fluid. It was found that as the eroding fluid salinity
decreases, soil resistivity to surface erosion decreases as well. These
results were verified by Arulatiandan ^_al_. (1975). In addition,
Sherard_et_^V. (1972) found that the erosion resistance decreased by
either the exchange of cations or a reduction of the valence of the
cations in the pore fluid. Kandiah (1974) and Arulanandan _et^jfl_. (1975)
confirmed these findings by showing that the erosion resistance
decreased and the rate of surface erosion increased with increasing SAR
(and therefore decreasing valency of the cations) of the pore fluid.
Figure 2.37 shows such a relationship between the SAR and the critical
shear stress tor erosion, which is a measure of soil resistance to
erosion (Alizadeh, 1974).
Experiments were conducted during this study to determine the
effect of the eroding fluid salinity on the rate of surface erosion.
The experiments were performed in the rotating annular flume described
previously using bottom sediment from Lake Francis, Nebraska. The
-96-
-------
CM
en
en
UJ
E
en
ir
UJ
en
_j
o
2.5
2.0
1.5
CONCENTRATION
• 0.250 N
o O.I25N
0.050N
0.005N
0 20 40 60 80
SODIUM ADSORPTION RATIO, SAR
100
F1g. 2.37 Critical Shear Stress versus SAR for Montmorillonitic
Soil (after Alizadeh, 1974).
-97-
-------
particle size distribution of this sediment, determined using a standard
hydrometer analysis (described in Appendix B), indicated that 50% of the
material was finer than 2pm (clay-sized particles) and 90% finer than
ZQysn. The organic content of the sediment was approximately 1.5%. X-
ray diffraction analysis showed that the sediment was predominantly
composed of smectite, illite, kaolinite and quartz. The cation exchange
capacity (CEC) of the sediment was found to be about 100 meq./lOO gm,
which indicates a higher percentage of smectite than the other two clay
minerals. Analysis of water from the lake indicated the presence of
Na+, K+, Ca+2, Mg+2, Al+3, Fe+3, CT, S04"2. These above cations and
anions would be expected to be present in the sediment as well. The
average pH of the lake water was 8.6. The sediment was repeatedly
washed in an attempt to remove these free salts so that their effect on
the sediment properties was minimized. The washing was performed by
immersing the sediment in delonized water, vigorously stirring the
sediment and water, allowing time for the sediment to settle out of
suspension by gravity, and then siphoning off the clear supernatant
water. This procedure was repeated at least three times.
Commercial grade sodium chloride dissolved 1n different proportions
in tap water constituted the eroding fluid in these experiments. The
manufacturers of the sodium chloride supplied the data given in Table
2.3 regarding the contents of the processed sodium chloride. The cation
concentrations in sea salt, also Included in this table, were obtained
from Bolz and Tuve (1976).
Table 2.3
Cation Concentrations in Processed
Sodium Chloride and Standard Sea Salt
Cation NaCl . " Sea Salt
Sodium 357460.pom 301720.ppm
Calcium, Magnesium 50. 47770.
Potassium 10. 10860.
Phosphate 1.0
Iron ' 0.5
-98-
-------
Tests were conducted for the following five salt concentrations: 0, 1,
2, 5 and 10 ppt by weight. However, as the concentrations of the three
most abundant cations, Na"1", Ca"1"2 and Mg , in the manufactured salt were
different from those in standard sea salt (see Table 2.3), the five
different eroding fluids used in these experiments were not exactly
equivalent to sea water at the various salinities. In spite of this,
useful qualitative and quantitative information was obtained regarding
the effect of varying dissolved salt (i.e. electrolyte) concentrations
on the erosive characteristic of the mud.
The experimental procedures used in these tests has been described
in Section 2.6.1. Suspended sediment concentration as a function of
time as well as the bed bulk density profile were measured. The values
of -1^, Tffl and T^ were 0,9 N/m2, 24 hours and 40 hours respectively (see
Fig. 2.18). The bed shear stress during resuspension ranged from 0.14
to 0.52 N/m2.
Figure 2.38 shows the bed bulk density profiles in a non-
dimensional form for each salt concentration. The bulk density
generally increases with increasing.salinity. These profiles were used
in conjunction with the concentration-time profiles for computing the
depths of erosion resulting from the different bed shears stresses.
Using the method described in Mehta ^t_^l_. (1982a) the bed shear
strength (or the critical shear stress for erosion), tc, as a function
of depth below the initial bed surface was determined for each salinity
(Fig. 2.39). Two trends are observed in this graph. First, TC
increased with depth in the upper part of the bed for all salinities (no
definite data could be obtained for the lower part of the bed, i.e. for
z > 0.5 cm, inasmuch as this portion of the bed did not erode during
these experiments). Second, tc Increased with Increasing salinity from
0 to 2 ppt; thereafter, for salinities up to 10 ppt, no measurable
increase in -cc occurred.
Rates of surface erosion, E, were calculated from the concentration-
time profiles in the following manner. Smooth curves were drawn through
the data points and values of concentration were read off these curves
at 0, 5, 15, 30 and 60 minutes after each change in the bed shear
stress. Values of dC/dt were determined using a backward difference
differentiating scheme. Values of e were calculated using Eq. 2.32.
-99-
-------
o
o
0|
O2
0.4
0.6
O.8
I I I
S*OPPT
C0= 68.86 yntl
h0= 4.45cm
i !•• r
= I.OPPT
= 66.60 gm/f
»= 3.81cm
S=2.0PPT
=76.0qm
= 3.81cm
10
0
O.2
0.4
0.6
0.8
1.0
20 30 0
IO 20
f>'Po
30
5 IO
S=IO PPT
55,82 gm/f
= 3.18cm
10
20 * 30
5 10
20
30
20
30
Fig. 2.38 Dimensionless Bed Density versus Bed Depth Profiles for Salinities of 0, 1, 2, 5
and 10 ppt.
-------
BED SHEAR STRENGTH, Tc (N/m2)
Fig. 2.39 Bed Shear Strength Profiles as a Function of Salinity.
The logarithm of the erosion rate was plotted against the average
normalized excess shear stress, i.e.
- T
)/TC,
where T is the
average shear strength of the bed layer that was eroded by the bed shear
stress nj. ^Qure 2.40 shows these plots for the 1 ppt salinity test.
The slope of each line, a, and the ordinate intercept, e , were
determined from each graph. The values of a and e plotted as a
o
function of depth for each salt concentration are given in Figs. 2.41
and 2.42 respectively.
Before evaluating these results it is appropriate to discuss the
parameters other than the salt concentration that varied from test to
test, in order to examine the possible significance of their variance on
the rate of erosion. The other uncontrolled parameters were the
temperature, pH and the SAR of the eroding fluid. The rotating annular
flume does not have the facility to maintain a constant water
temperature during the course of an experiment. As a result the
temperature typically varied 3° to 5°C over the seven to eight hour
duration. A temperature variation of this magnitude has been found to
-101-
-------
0.40
0.44
0.49
0.53
0.59
0;64
Fig. 2..40 Surface Erosion Rate e versus Normalized Excess Shear Stress
-102-
-------
I o.o
LJ
LL
LU
CD
Mw
s:
0.2
0.4
0.6
8
10
12
F1g. 2.41 Slope, a, Plotted Against Depth Below Bed Surface,
z, as a Function of Salinity.
_ 0.0
e
u
IM
cr
LJ
i
CD
02
0.4
o 0.6
SALINITY (PPT)
o
•
A
a
~0
2 I
5 V
10 J
it i i i i 11
i i i I i i i i
10'
-5
Sxlti"5 IO"4
SxlO"4 IO"3
€0 (kg/'m2 -min)
F1g. 2.42 Ordlnate Intercept, e , Plotted Against Depth
Below Bed Surface, z,°as a Function of Salinity.
5x10
.-3
^103-
-------
result in less than a 3% decrease In the bed shear strength (Kelly and
Gularte, 1981) and is considered to be insignificant. Likewise, over
the one per-cent salt concentration range used in these experiments the
variation in pH is considered to be not significant. However, due to
the relatively small quantitites of Ca*^ and Mg"1^ compared to that of
Na"1", the SAR values were rather large and increased significantly with
increasing salt concentration. For example, the SAR values varied from
110 to 349 as the salinity increased from 1 to 10 ppt. AHzadeh (1974)
showed that both the concentration of the electrolyte and the SAR are
important controlling factors in the process of coagulation.
Specifically he found that the effect of salt concentration gradually
decreases with increasing SAR. Thus, the varying SAR values are
considered to have had some, albeit unmeasured, effect on these
experiments.
Analysis of the variation in the bed density profiles with
salinity, shown in Fig. 2.38, revealed no discernable relationship. It
is felt that further investigations are necessary to determine 1f any
relationship exists between pg and the salt concentration of the eroding
fluid for a stratified fine sediment bed.
The bed shear strength profiles, shown in Fig. 2.39, were analyzed
by determining the weighted depth-averaged value (weighted with respect
to spacing, i.e. depthj between adjacent data points) of TC at the ^ve
different salt concentrations, S. The following relationship was found:
TC(S) » TC(S=0).(|- .S + 1) for 0 < S < 2
(2.67)
tc(S) = 2~cc(S*0) for S > 2
where S is in ppt. This relationship was incorporated Into Subroutine
NEWBED algorithm 1n the following manner. The discretlzed value of TTC
at the top of the uppermost new deposit bed layer is changed
instantaneously, i.e. during the same time-step, at every element where
the elemental average salinity value changes. For the second bed layer
the discretized TC value is not changed during the first time-step
during which the average value of salinity changes; it is changed at the
time-step during which the salinity changes for the second time.
-104-
-------
However, for this bed layer the new TC value is determined using Eq.
2.67 and the second preceding value of the salinity at that element.
This procedure is similarly repeated for the remaining new deposit bed
layers. This method of incorporating the effect of the salinity of the
eroding fluid on the bed shear strength profile was used in order to
account, at least partially, for the finite amount of time it takes for
denser (i.e. higher salinity) eroding fluid to diffuse downward into the
bed or for denser pore fluid to diffuse upward into the overlying
eroding fluid. The diffusion coefficients of C1~ and Ma* in Pacific red
clay and Lake Ontario sediment were experimentally determined to be of
the order of 10"5 - 10"6 cm2/sec at a temperature of 24°C (Li and
Gregory, 1974; Lerman and Weiler, 1970). These extremely small
diffusion coefficients indicate that rates of diffusion in
unconsolidated sediments are generally from one half to one twentieth of
the diffusion rates in the eroding fluid (Manheim, 1970).
For the first time-step the initial salinity value at each element
is used to determine the TC values in both the unconsoli dated and the
partially consolidated bed layers, while the salinity of the pore water
in the consolidated original bed layers, an input parameter in SEDIMENT
IIIA, is used to evaluate the TC values in this bed section. The TC
values of the fully consolidated bed layers are thereafter assumed to be
invariant with respect to the salinity of the eroding fluid. The
justification for this assumption is based on the observation that
dissolved silica concentrations in pore waters of Lakes Ontario, Erie
and Superior sediments were, in general, invariant with respect to depth
after the first 20 cm below the water-mud interface (Nriagu, 1978).
Therefore, the salinity of the eroding fluid would not be expected to
influence that of the pore fluid below the top 20 cm of the bed, which
clearly encompasses the consolidated bed section.
The values of a and e are seen in Figs. 2.41 and 2.42, to decrease
and increase, respectively, with Increasing salinity. However, Inasmuch
as these parameters are considered to be characteristic properties of
the sediment bed and as the effect of salinity on another bed property,
o
TC, which is as well estimated indirectly from measured data, has
already been incorporated into the model, it was not necessary to
consider the variation of a and eQ with salinity in the erosion
algorithm.
-105-
-------
2.8.4. Effect of Salinity on Coagulation
As noted in Section 2.1, when salt is added to water containing
suspended particles in the clay size range, and to a lesser degree in
the silt range, the coagulation characteristics of the sediment
particles are affected. This effect can be explained by briefly
reviewing the theory of coagulation.
In order for dispersed colloidal particles to coagulate and
possibly form comparatively large aggregates, two separate processes
must occur first; repeated collisions of the particles and cohesion of
the colliding particles. The size, strength and the density of the
resultant aggregates play an important role 1n characterizing the
transport of cohesive sediments under tidal conditions. Cohesion and
collision, discussed in detail by among others Kruyt (1952), Einstein
and Krone (1962), Krone (1962), Partheniades (1964), O'Melia (1972) and
Hunt (1980) are reviewed here.
As discussed 1n Section 2.8.1, cohesion of colloidal particles is
caused by the presence of net attractive electro-chemical surface forces
on the particles, the latter condition is promoted by increased
concentration of dissolved ions and/or increased ratio of multivalent to
monovalent ions, both of which serve to depress the double layer around
micelles and thus allow the attractive London-van der Waals and
coulombic forces to predominate (Krone, 1962). Since sea salt 1s a
mixture of salts, with monovalent sodium ions and divalent calcium and
magnesium ions prevalent in natural electrolytes, the effect of these
salts on cohesion is determined by the relative abundances of mainly
these three ions (see Table 2.3), the latter being indicated by the SAR
value. The relationship between the SAR and salinity is seen in Fig.
2.43. As noted in Section 2.1, the cation exchange capacity (CEC),
along with the salt concentration and SAR all serve'to determine the net
inter-particle force and thus the potential for micelles to become
cohesive (Ariathurai, 1974).
Kandiah (1974) found that the boundary between the dispersed and
coagulated states for the three main clay groups, kaolinlte, mite and
montmorillonite, varied with the SAR, total salt concentration and pH of
the solution (see F1gs. 2.44a, b, and c). The dashed lines in these
figures represent interpolated boundary curves for a pH range of 7.5 to
-106-
-------
I
l->
o
I I I I I I
60
0 20 40 60
SALINITY (meq/l)
Fig. 2.43 Variation of SAR with Salinity (Sea
Salt Concentrat1on)(after Ar1athura1,
1974).
o:
<
in
40
20
0
_ Coagulation at 43 meq
• pH4-5
A pH6.5-75
o pH 10-11
dispersed
coagulated J
I i II
0 20 40
TOTAL CATION CONC.(meq/l)
F1g. 2.44a Coagulation-Dispersion Boundary Curves
for Montmor1llon1te at three pH Ranges
(after Kandiah, 1974).
-------
OL
<
£/>
o
CD
I
Coagulation at
2 meq/ I
pH 4-5
pH 6.5-7.5
pH 10-II
cooguloted
I
(T
<
C/V
'0 20 40
TOTAL CATION CONC.(meq/l)
Coagulation at I meq/1
coagulated « pH 4-5
• pH'6.5-7-5
opHIO-ll
'O 2O 40
TOTAL CATION CONC.Cmeq/i)
Fig. 2.44b Coagulation-Dispersion Boundary
Curves for 111 He at three pH
Ranges (after Kandiah, 1974).
Fig. 2.44c Coagulation-Dispersion Boundary
Curves for Kaollnite at three pH
Ranges (after Kandiah,1974).
-------
8.5, which is the range found in sea water at all -salinities. It is
evident that the boundary between the dispersed and coagulated states
for these three clays are different. Kaolinite becomes cohesive at a
salinity of 0.6 ppt, illite at 1.1 ppt and montmorillonite at 2.4 ppt
(Ariathurai, 1974). Wh1tehouse^t__aU (1960) and Edzwald j£_al_. (1974)
reported that the cohesiveness of these micelles develops quickly at the
given salt concentrations, and that little increase in coagulation
occurs at higher concentrations, which implies that the micelles must
have attained the maximum degree of cohesion. The rapid development of
cohesion and the low salt concentrations at which the main clay types
become cohesive indicates that cohesion is primarily affected by
salinity variations near the landward end of an estuary where salinities
are less than about 3 ppt.
The above cohesion mechanism is referred to as salt flocculation.
There is another cohesion mechanism that operates in water between
micelles in the absence of salt, and hence it is termed non-salt
flocculation. However, in an estuary the conditions are conducive for
destabi 11 ration to be caused by salt flocculation (i.e. depression of
the diffuse double layer). Both types of destabilizing mechanisms are
reported in detail by Lambe (1953).
The collision frequency, I, for suspended sediment particles of
effective diameters d^ and dj is given by (Hunt, 1980):
I * p(d.,d.).dN .dN. (2.68)
I J * J
where p(d ,d.) =» collision function determined by the type mechanism
(discussed below), which has units of fluid volume per unit time, and
dfH » number of particles with sizes between di and dj+d(di) per unit
volume of the fluid.
There are three principal mechanisms of inter-particle collision in
suspension, and these influence the rate at which elementary sediment
particles coagulate. The first is due to Brownian motion resulting from
thermal motions of molecules of the suspending ambient medium. The
collision function corresponding to this mechanism is given by (Hunt,
1980):
-109-
-------
where k = Boltzmann constant, T^ = absolute temperature and ^ = dynamic
viscosity of the fluid. Generally, coagulation rates by this mechanism
are too slow to be significant in estuaries unless the suspended
sediment Concentration exceeds 10 g/1. Aggregates formed by this
mechanism are weak, with a lace-like structure, and are easily fractured
by shearing in the flow or are crushed easily when deposited (Krone,
1962).
The second mechanism is that due to internal shearing produced by
local velocity gradients 1n the fluid. Collision will occur 1f the
paths of the particle centers 1n the velocity gradient are displaced by
a distance which is less than the sum of their radii (referred to as the
collision radius, R-JJ, between the dj and dj size particles). The
collision function is given as
where G is the local shearing rate and R^ = ^i"1^,-. Aggregates produced
by this mechanism tend to be spherical, and. are relatively dense and
strong because only those bonds that are strong enough to resist the
internal shearing due to local velocity gradients can survive. The
frequency of collision is especially high in an estuarial mixing region
where a large number of suspended particles are found.
The third mechanism, differential sedimentation, results from the
fact that particles of different sizes have different settling
velocities. Thus a larger particle, due to its higher settling
velocity, will collide with smaller, more slowly settling particles
along its path and will have a tendency to "pick up" these particles on
its way down. The collision function is expressed as
«d» • f (Wi l'i- ! {2'71)
where v = kinematic viscosity of the fluid, ps = floe density and pw -
fluid density. This mechanism produces relatively weak aggregates and
contributes to the often observed rapid clarification of estuarial
waters at slack.
-110-
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All three mechanisms operate in an estuary, with internal shearing
and differential sedimentation generally being predominant in the water
column, excluding perhaps the high density near-bed layer, where
Brownian motion is likely to contribute significantly as a collision
mechanism. Then again, internal shearing is probably more important
than differential sedimentation during times excluding those near slack
water, when collision and coherence due to differential settling would
be expected to be the main mechanism controlling the rate of
coagulation.
Hunt (1980) compared the values of the three collision functions
(Eqs. 2.69 - 2.71) for collision of a di»l \sn size particle with varying
sizes, dj, of the colliding particle under the following conditions:
temperature 14°C, shearing rate G = 3 sec , and (p -p )/p = 0.02. The
. •. • •> W W
comparison is shown in Fig. 2.45 and reveals that each collision
mechanism is dominant over a certain particle size range. In this
example, Brownian motion is the dominant mechanism for particles less
than 1 \tnt internal shearing is dominant for particles between 1 and 100
iin, and differential sedimentation 1s dominant for particles greater
than 100 urn. Hunt states that the same ordering of the dominant
collision mechanisms with increasing dj would be achieved for collisions
with other d| sizes. Thus, the collision frequency is controlled not
only by the prevailing flow conditions and local suspension
concentration, but by the size of the colliding particles and/or floes
as well.
In summary, it is apparent that fine sediment transport in
estuaries is strongly influenced by the coagulation behavior of
dispersed sediment particles and by the properties (e.g. shear strength,
density and size) of the resulting floes and aggregates, which in turn
are controlled by the salinity field, velocity gradients and the
concentration of suspended sediments. In particular, the salinity of
the suspending fluid effects the process of coagulation in two ways: 1)
elementary clay particles become cohesive when the salinity is equal to
or greater than 1-3 ppt, and 2) the presence of high velocity gradients
1n the estuarine mixing zone increase the collision frequency between
dispersed particles and/or aggregates.
-Ill-
-------
UD
O
u
-------
2.8.5. Effect of Salinity on Deposition
The larger, stronger aggregates of natural muds formed 1n a saline
medium have been found to result 1n higher settling velocities (Krone,
1962; Owen, 1970) which, as apparent 1n Eq. 2.54, 1n turn result 1n
higher rates of deposition. Thus, the effect of salinity on the
deposition of fine sediments may be quantified 1n terms of a
relationship between salinity and the median settling velocity, Ws, of a
particular sediment.
Krone (1962) studied the effect of salinity and suspended sediment
concentration on Ws of fine sediment from Mare Island Strait in San
Francisco Bay. Hydrometer analysis showed that 60% by weight of this
sediment was in the clay size range (I.e. < 2\tn), with the remaining in
the silt size range. X-ray diffraction and differential thermal
analyses of the clay fraction revealed a large content of illite,
montmorillonite and kaolinite clay groups along with small quantities of
chlorite and quartz. The results from settling tests performed under
quiescent conditions 1n one-liter cylinders showed the effect of both
salinity and suspension concentration on MS (Fig. 2.46). The influence
of salinity on Ws is especially significant in the range 0-2 ppt,
particularly for the 1.0 and 0.53 g/1 suspension concentrations. This
result is expected considering the discussion presented 1n Section
2.8.4. One possible explanation for the apparent increasing Influence
of salinity on Ws with increasing suspension concentration, as shown in
this figure, is the following. As the suspension concentration
Increases, the number of collisions (by Brownian motion and differential
settling mechanisms in such an experiment) would likewise increase and
therefore promote the formation of larger aggregates with higher
settling velocities. The lowest order aggregate that could be formed
would be limited by the suspension concentration, so that even with an
increase in salinity (and therefore a corresponding increase in cohesive
forces), lower order aggregates with typically higher settling
velocities could not form due to the Insufficient concentration of
suspended particles.
Owen (1970) studied the variation of Ws of a natural mud with
salinity and suspension concentration. Approximately 55% of the mud was
in the clay size range, with the remainder in the silt range. It was
-113-
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revealed that the clay fraction was composed of, 1n order of abundance,
Ulite, kaoHnite, montmorillonlte and chlorite. These settling tests
were conducted 1n a two meter high bottom withdrawal settling tube.
The results of Owen's tests are shown in F1gs. 2.47 and 2.48.
These figures show that, 1n general, as the salinity and suspension
concentrations are Increased, Increased cohesion and Inter-particle
collision result In higher coagulation rates with accompanying higher
settling velocities. This trend corroborates that found by Krone
(1962), except that no "leveling off" of Ms aoove a certain salinity
value was found 1n these tests. The decrease 1n Ws above a given
salinity and concentration, as observed 1n both figures, usually
represents the onset of hindered settling. The effect of salinity on W$
1s seen to be diminished at suspension concentrations 1n the hindered
settling range.
Owen (1971) found a negligible effect of salinity on the settling
velocity of natural aggregates at two different locations 1n the Thames
River estuary. The salinities at the two sampling stations varied
between 6-10 ppt and 21-26 ppt, respectively. Evidently, the effect of
salinity on Ws at these salinities In a turbulent flow field was much
less than that under quiescent conditions (see F1g. 2.47). This implies
that the increased cohesion caused by the higher salinities was counter-
balanced by the high internal shear rates which cause the aggregates to
be broken apart.
Deposition tests were conducted at the University of Florida during
the reported study in order to further investigate the effect of both
salinity and bed shear stress on the settling rates of a natural mud.
The mud used in these tests was sediment from Lake Francis, Nebraska
(see Section 2.6.1 for a description of this sediment). The following
salt concentrations were utilized in these tests: 0, 1, 2, 5 10, 20 and
35 ppt. The tests were conducted in the previously described rotating
annular flume with a water depth of 0.31 m at values of the bed shear
stress, tb, during deposition equal to: 0.0, 0.015, 0.10, 0.20 and 0.30
N/rn2. The Initial concentration for these tests varied between 3.7 and
4.7 g/1. Before the start of each test, the sediment and water were
mixed for two hours at a shear stress of 0.90 N/m2. The shear stress
was then reduced to the appropriate •% value and samples of the
-114-
-------
in
e
o
§
Q
Ul
1.0
0.8
Oj6
0.4
0.2
0.1
OO8-
0.06
0.04
Q.02
Suspended Concentration ~
o 0,25
A 1.0
a 4.0
• 16.0
•> 32.0
i i i > t i
i.o 2.0 4o aoaoio; 20.
SAUNHY.S (PPT)
60. 60.100
Pig, 2.47 Effect of Salinity on Settlinf Velocity of Avonmouth Mud
(aft«? Owen,
-IIS*.
-------
CTl
I
100.0
50.0
2QO
IO.O
j 1 I | I I I I |
Settling Velocities in mm/s
I I
£83
0.2
0.5 1.0 2O 5.0 iQO 2aO
SUSPENDED SEDIMENT CONCENTRATION , C
50.0
100.0
Fig. 2.48 Effects of Salinity and Suspension Concentration on Settling Velocity of
Avonmouth Hud (after Owen, 1970).
-------
suspended sediment were collected from a tap located on the outer wall
of the flume at 0, 1, 2, 5, 10, 15, 20, 30 and 60 minutes after the
shear stress was reduced to tb« Subsequent samples were collected with
lower frequency. Each experiment was conducted for a period of 21
hours.
The measured suspension concentrations were plotted against time
for each experiment. Plots of C/CQ versus time for each t^ value at a
salt concentration of 5 ppt are shown 1n F1g. 2.49. The steady state
concentration, Ceq, for each deposition test was determined from a curve
drawn to represent the mean variation of the concentration with time, as
seen in this figure. The following observations were made: 1) for the
two lowest values of tb, I.e. tb = 0.0, and 0.015 N/m2, the
concentration decreased over the duration of the experiment for all salt
concentration values, Indicating that Ceq for these -CD values would have
been equal to zero 1f the experiment had been of longer duration. 2)
for n>:» 0.05, 0.1, 0.2 and 0.3 N/m2 the concentration decreased rapidly
during the first hour and Ceq was. reached more rapidly as the value of
tb Increased. 3) at the four lowest values of tb the effect of the salt
concentration on the deposition rate (i.e. concentration variation with
time) was appreciable. For the two highest 15 values the salt effect
was much less discernible. These results seem to indicate that at
relatively low values of tb cohesive forces are predominant whereas at
higher values the hydrodynamlc forces (i.e. disruptive internal shears)
are also significant. This explanation follows from the results
obtained by Owen (1970; 1971) and by Mehta and Partheniades (1975).
The ratio Ceq/C0 was plotted against tb values for all salt
concentrations (F1g. 2.50). Interpolation of the resulting plot yields
IL «• 0.035 N/m2. It 1s believed that even though additional data,
I.e. Cgq/Co against tb values, might result in a different value
of ibgript the two values would be reasonably close (probably within t
25%).
The settling velocity at the time when 501 of the depositable
sediment had deposited, i.e. tso, was determined for each experiment in
Range I in order to quantitatively evaluate the effect of salt
concentration, and possibly the bed shear stress, on the rate of
deposition. This particular value of the settling velocity, designated
-117-
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c/c,
I I I—I—1
S = 5 PPT
o 0.0
•• 0.015
0.05
0.10
a 0.20
• 0.30
0
8 10 12
TIME (Hours)
14 16 18 20
Fig. 2.49 Ratio .C/C .versus Time ;as a ..Function of ,the Bed Shear,
T> for Lake Francis Sediment with S=5 ppt.
0.8
0.6
*cf 04
0.2
SALINITY (PPT)
0.0
0.3
0.1 0.2
Th (N/m2)
O * _ U —- ! > - - ~
Fig. 2.50 Ratio C /C versus T. for Deposition Tests with
Lake FrlrtdS Sediment?
-118-
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as W , was chosen for this analysis because it can be shown to be more
representative of the deposition rates 1n the time Interval of interest
1n numerical simulation (see Section 2.7.3 for discussion of this
aspect) than either the mean or the median value. The analysis was
performed 1n the following manner for the experiments 1n Range I (I.e.
•^ * 0.0 and 0.015 N/m2). Equation 2.41 was Integrated and rearranged
to yield the given expression for MSS(J:
0*^50
<2-72>
where Cso « suspension concentration at time tso. Values of W
computed from Eq. 2.72 are shown 1n F1g. 2.51 superposed on Fig. 2.47,
with lines of equal shear stress drawn as indicated. The average value
of the initial concentration, C0, 1n these experiments was 4.2 g/1 . No
consistent trend between tb and visso (e.g. increasing Ws5Q
values with Increasing ^ values for all salt concentrations) 1s
apparent 1n F1g. 2.51. This observation suggests that WS5Q 1s Invariant
with respect to 15 in Range 1.
due to the limited data obtained, as well as the noted invariance
of WSSQ with respect to •*& for Range I, the values of WSSQ for the two
tjj values were averaged for each salt concentration. These average
values, W-0, are as well plotted against salt concentration in F1g.
2.51.. Such an averaging procedure was performed in order to further
investigate the effect of salt concentration on W .
A power curve relationship between W and the salinity, S, of the
following form was desired:
).Sm (2.73)
where Qs5(J (35.C) » KCn (K and n are defined 1n Section 2.7.1) and A and
m are empirical constants. It was proposed that when S was less than
0.1 ppt, its value would be set equal to 0.1, so that W.,. « (S<0.1,C)
would be greater than zero and in fact J
-------
<
Q
10
5
002
U F Data
Tb (N/m2)
• 0.0
* 0.015
Average Values
t t t.....t i i.i t
Owen's Data
Suspended Concentration
o
A
a
0.25 g//
1.0 g/^
4.0 g/P
16.0
32.0
i
i t t t t t
1.0 . 20 4.0 £08.010. 20.
SALINITY.S (PPT)
40. 60. 80.100.
Fig. 2.51 Effect of Salinity and Bed Shear Stress on Settling
Velocity of Lake Francis Sediment.
-120-
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gave the following values for A and m and the coefficient of
determination, r2: A » 0.57, m » 0.13 and r2 - 0.96. As Indicated by
this r2 value, a good agreement was obtained between Eq. 2.73 and the
data. This confirms that, at least for these experiments and the
analysis method employed, the effect of salt concentration on W 1n
Range I can be expressed by a power relationship of the form given In
Eq. 2.73.
The function given 1n Eq. 2.73 1s Incorporated Into the deposition
rate expressions for Range I and for C < Ci (which 1s the concentration
below which mutual Interference is negligible) 1n Range II as follows:
Equation 2.73 Is used to evaluate the settling velocity as a function of
the concentration of dissolved salt and suspended sediment. Based on
the variety of relationships found between W and C for several of
these experiments, the following general expressions for W in Range I
and for C < G! in Range II have been Incorporated Into SEDIMENT IIIA:
Ai'We .s""1 for C
-------
03
0.2
e
£ 0.10
J» 0.08
t 0.06
g 0.05
3 0.04
UJ
> OD3
o
~ 0.02
UJ
0.01
I 1 I
Tb =O.ON/m
S *0.ppt
i it
I I
"O.I 02 0.4 0.60.81.0 2.0
CONCENTRATION, C(g/-0
4.0
Fig. 2.52 Settling Velocity versus Suspension Concentration
for Deposition Test with Lake Francis Sediment.
0.6
0.4
cr
«
o
Tb*0.3N/m
O.I N/m* _
10 15 20 25
SALINITY, S (PPT)
30
Fig. 2.53 Variation of C with Salt Concentration, S, and
Bed Shear Stress, T. .
35
-122-
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and m2 are for C2 < C < C3 and A3 and m3 apply for C > C3; 1f C2 » C3,
then A2 « Ax and m2 » m^ The values of C3.
For the experiments 1n Range II (I.e. t^ » 0.05, 0.1, 0.2, and 0.3
N/m2) the following analysis was performed. Figure 2.53 shows the
*
relationship found between C and the salt concentration for the values
* eq
of -t > t. where C > 0. Based on the nature of the equal Tb curves
In this figure and taking Into consideration the limited number of
*
deposition tests performed at -^ > t , C 1s assumed to be Invariant
with respect to the salt concentration.
In Range II, the effect of salt concentration of the deposition
rate was evaluated 1n the following manner. The value of dC/dt at t*tso
was determined for each experiment. Substituting t»tso into Eq. 2.50
gives the following expression for the rate of deposition at tso:
.r -0.434 C fl-C* )
dC . - Ql e
-------
where 8 * 10.78, f * -0.33 and r2 » 0.93 when S < 0.1 ppt, its value is
set equal to 0.1 ppt.
The effect of salinity on the deposition rate expression for C >_Ci
in Range II was incorporated by substituting Eq. 2.77 Into Eq, 2.50.
The resulting value of the time-rate of change of concentration, dC/dt,
will decrease raonotonically at any given time with decreasing salt
concentration, while at the same time, the expression for C given by
Eq, 2.48 still approaches 0 as t*«. This methodology of incorporating
the effect of salinity requires that the values of tso and g^ used in
Eq. 2.50, be evaluated at a salinity of 35 ppt.
2,9. Convergence and ^Stability of the Numerical Scheme
The accuracy of the numerical scheme used in SEDIMENT IIIA, which
is the same as that used in SEDIMENT III, has been investigated in
detail by Ariathurai (1974) and Ariathural Jt_jl. (1977). These authors
reported.that rapid convergence to the exact analytical solutions was
achieved for the numerical formulation for the one-dimensional,
transient heat conduction problem with and without radiation, the one-
dimensional, for the steady-state and transient convection-diffusion
problem, and for the two-dimensional Laplace equation. -
The results from these convergence tests also indicated that the
combination of the unconditionally stable finite element formulation
used to solve the spatial problem and the unconditionally stable Crank-
Nicholson finite difference formulation used to solve the temporal
problem is as well unconditionally stable. However, these tests
revealed that instabilities might still occur when the Peclet numbers
(ratio of convection to diffusion, i.e. uL/Dx, where u * flow velocity,
Dx =« diffusion coefficient and L = system longitudinal dimension) become
either too large (greater than =• 100) or too small (less than « 10 ).
For too large Peclet numbers, smaller time-steps must be used to improve
the accuracy of the numerical scheme (Ariathurai _et_jU, 1977). Too
small Peclet numbers rarely ever occur for typical flow conditions in
estuaries, and therefore associated roundoff errors, which can lead to
instabilities, should never be a problem in modeling such systems.
However, spurious results caused by roundoff errors were encountered 1n
simulating laboratory depositlonal experiments with SEDIMENT IIIA. This
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problem was eliminated by using double precision arithmetic in the
model. No Instability problems were encountered 1n modeling a prototype
system using single precision arithmetic.
2.10. Model Limitations
A two-dimensional, vertically Integrated model such as SEDIMENT
IIIA can strictly be applied to only estuaries, harbors and basins (such
as marinas) where the horizontal dimensions of the water body are at
least one order of magnitude greater than the vertical dimension.
Applications to partially mixed water bodies or especially to highly
stratified water bodies should be made when only rough estimates of some
sedimentary process (e.g. shoaling rate) are required.
Currently the model has the capability of simulating the movement
of only one constituent (e.g. cohesive sediment, water temperature, or
algae, provided the source/sink expressions for a nonconservative
constituent are known). It 1s possible, however, to modify the model so
that any number of constituents may be incorporated.
Probably the main "limitation" of a model arises from three
sources: 1) insufficient data, 2) poor quality of data and 3)
limitations of the hydrodynamic modeling. The first two sources are
attributable to the fact that, owing mainly to time and cost
considerations, all the bathymetric, hydraulic and sedimentary data
required for use in such a model are rarely, if ever, measured and/or
collected in the body of water being modeled. In addition, the quality
of the data is often questionable. Data requirements and the field
collection and laboratory testing programs required to obtain these data
are briefly described 1n Appendix 8.
The third source is itself often the result of the first two,
inasmuch as progress has been achieved in the past two decades in
modeling estuarial hydrodynamics (Leendertse, ^t^jiU, 1967; King et al.,
1973; Liu and Leendertse, 1978).
The Importance of experience in effectively using the model cannot
be over emphasized. Experience gained through knowledge of the physical
systems being modeled and repeated applications of the model will
enhance the user's ability to choose the proper values of the various
parameters, e.g. time-step size and diffusion coefficients. The user
-125-
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will also gain the ability to anticipate the effect of changing the
value of a particular parameter by a certain percentage on the model
solution (i.e. model sensitivity).
2.11. Model Applicability
2,11.1. Water Quality Problems
The model can be used to assist in the performance of the following
water quality related computational tasks:
1.) Assessment of the disposition of dissolved and sorbed pollutants,
possibly either transported to an estuary or harbor by stormwater
runoff or released into these water bodies by nearby industries,
and their effect on the receiving waters and the aquatic ecosystem
therein, when linked with a particulate contaminant transport
model that contains a sorption submodel (Onishi and Wise, 1979).
2.) Prediction of the effect of reduced sediment inflows to estuaries,
caused by upstream water storage and subsequent use,, to ascertain
the degree of waste water management required to control estuarial
water pollution.
3.) Prediction of the limitation of sunlight penetration in estuarial
waters resulting from high turbidity levels which, 1n turn, are
caused by high concentrations of suspended sediment. This reduced
light penetration can cause the algae multiplication rate to
decrease significantly, and thus effect the entire aquatic
ecosystem.
2.11.2 Sedimentation Management Problems
The model can be used as a tool to help solve the following
sedimentation problems:
1.) Prediction of the movement of dredged material released in open
waters in order to estimate the effect of the disposal at a given
location in the water body on the shoaling rates elsewhere, and in
particular in the dredged area.
2.) Selection of harbor sites in estuaries and bays where shoaling is
minimized.
3.) Prediction of changes in the sedimentary regime that may occur as
a result of a proposed change or development of an estuary or
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harbor, such as the dredging of new navigation channels and the
possible change 1n the salinity field (e.g. further Inland
Intrusion) caused by the proposed change.
4.) Estimation of shoaling rates and maintenance dredging requirements
1n areas of very low flow such as marinas, harbors and docks, and
recommendation of means by which shoaling rates might be minimized
In these areas.
5.) Prediction of the spatial (primarily -longitudinal) variance 1n the
shoaling and/or scouring rates, caused by varying flow conditions
and salinities, along the entire reach of an estuary.
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III. SIMULATION OF FINE SEDIMENT TRANSPORT PROCESSES
3.1. Introductory Note
In this chapter the results of model simulations of laboratory
erosion and deposition tests and sediment transport in a hypothetical
prototype canal are presented. The purpose 1s two-fold: 1) to show the
capability of the model 1n predicting cohesive sediment transport
processes by comparing measured and predicted results, and 2) to show
the effect salinity has on these same processes.
3.2. Simulation of Laboratory Erosion Test
A resuspenslon test (Expt. 17) performed by Parchure (1980) 1n the
previously described annular flume was simulated. The result 1s shown
1n F1g. 3.1. Good agreement 1s observed between measurement and
prediction for the first six hours of the experiment. The deviation at
6.5, 7.5 and 8.5 hours 1s attributable to the fact that the results for
the last three hours in this experiment did not conform precisely to the
empirical surface erosion rate expression given by Eq. 2.32. The
sediment and suspending fluid used in the resuspenslon test were,
respectively, kaolinlte and water with a 35 ppt concentration of
commercial grade sodium chloride (see Section 2.8.4 for a description of
this artificial sea water). The bed shear strength profile for Expt.
17, shown in F1g. 2.9, was used 1n this simulation. The initial, I.e.
background, concentration at the start of the test was 0.32 g/1. The
rapid Increase in suspension concentration (up to 0.60 g/1) at the start
of the test was simulated as mass erosion. The remainder of the bed was
simulated to undergo surface erosion, with the rate of erosion
determined using Eq. 2.32.
The effect of salinity on the bed shear strength (described in
Section 2.8.4) and hence on the rate of surface erosion, is shown 1n
Fig. 3.2. In this figure, the results of simulations of the same
resuspenslon test at salinities of 0 and 1 ppt have been superposed on
the simulation at a salinity of 35 ppt. The suspension concentration
became a constant (8.2 g/1) for the S » ~0 and 1 ppt simulations when
the entire bed was resuspended. As indicated by Eq. 2.67, the effect of
salinity on the bed shear strength was found to be Invariant above a
-128-
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9.0
eo-
~ T.O
o»
6.0
TIME (Hrs)
5.0 6.0 7.0 8.0
2
LU
5.0
8 4.0-
g 3.0
CL
2.0
1.0
0.0
Mod«f
• Measurement
iao
'OO 1.0 20 3.0 40 5.0
TfMC (Hrs)
Fig. 3.1 Caspar1son of Predicted and Measured Suspension
Concentrations versus time for a Resuspenslon
Experiment.
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Limit due to Erosion
of Entire
S*-Op»t Sslppt
2JOO 4.00 6XK) 8.00 10.00
TlME(Hrs)
Fig. 3.2 Demonstration of the Effect of Salinity on tnt Resuspension
Rates of a Flow-Deposited Kaolinite Bed.
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salinity of 2 ppt. The increase in suspension concentration at a given
time with decreasing salinity (below 2 ppt) is a result of the
decreasing bed shear strength and therefore increasing rate of surface
erosion. Therefore, In the upper-most reaches of an estuary, where
salinities are typically less than 2 ppt during at least the latter
stages of an ebb tide and the first stages of the subsequent flood tide,
the sediment bed would be simulated to undergo a higher rate of surface
erosion when subjected to an excess bed shear stress in an accelerating
flow in comparison with a bed in the middle and lower reaches where the
salinities are generally higher than 2 ppt. In regions where the
salinity is in excess of 2 ppt, the influence of salinity upon erosion
appears to be negligible.
3.3. Simulation of Laboratory Deposition Tests
Three laboratory deposition tests performed by Mehta (1973) and one
performed during the course of this study were simulated. Figures 3.3 -
3.6 show that good agreement was obtained between the measurement and
prediction. The sediment used 1n the deposition test shown in F1g. 3.3
was Lake Francis, Nebraska, sediment in tap water, while the sediment in
the other three tests was kaollnlte in distilled water. The hydraulic
and sedimentary conditions for each test are specified in these
* .*
figures. The values of tb In these four tes'ts, I.e. T. = 0.0, 0.9, 1.41
and 2.70, cover both depositlonal ranges (I.e. Range I and II, defined
in Section 2.7.2).
*
The effect of salinity on the deposition rates for the •« a 0.0
test with Lake Francis sediment 1s shown in Fig. 3.3. The rate of
deposition, as reflected by the decrease 1n suspension concentration
with time, increases slightly with increasing salinity of the suspending
fluid (see Section 2.8.5 for discussion and development of the
quantitative effect of salinity on deposition rates of natural muds).
Based on these results alone, a higher shoaling rate may be expected
near the mouth of an estuary where, typically, salinities close to that
of the sea (i.e. 30 - 35 ppt) occur. Likewise, lower shoaling rates may
be expected near the upland end of the estuary where salinities less
than 10 ppt are common over an entire tidal cycle (see Fig. 1.6).
However, the effect of turbulent shearing rates in the fluid on the
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O.I
G08
0Q0
S» Oppt
S=2ppt
Tb =
C0 =3.
d = 0.305m
I i II II I
I I
2.
4. 6.
TIME (Hrst
8.
JO.
Fig-. 3.3 Cowparfson of Predicted and Measured Deposition Rates for
Lake Francis Sediment at a Salinity of 0.0 ppt, and
Demonstration of the Effect of Salinity on the Deposition
Rate.
-132-
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CO
I
80
60
T - ,
C0=5.37g/f
d = 0.229m
T = O.I62N/m2
t50=2.82sec
CT2=0.67
Measurement
•
Model Simula lion
50 JOO 200
0.2 0.6 IX) 2.0
DJMEN SIGNLESS TIME
Fig. 3.4 Comparison of Predicted and Hsawrgd Variation of C Versus (t/t50)
Kaoltnlte 1n Distilled Water with t? = 0.^0.
D
5QO
for
-------
I
_J
co
I
O
UJ
2
5
99
96
95
90-
80-
60
40
20
\0
5
a
0.05 O.I
CU= I.OOSg/tf
C& 0.452
d =0.152m
Tb=0.254N/m
Tf 1.41
%cf 228 sec
_L
Measurement
Model Simulation
0.2 0.5 1.0 2.0
DIMENSIONLESS TIME (t
5.0 10.0 20.0 50.0
Fig. 3.5 Comparison of Predicted and Measured Variation of C versus (t/t50) '°2 for
Kaollnlte In Distilled Water with rf = 1.41.
D
-------
CO
tn
8
o
o
uj .£
fc«.
o
8
J
5
g
UJ
C*= 0.78
d =0.229 m
Measurement
•
Model Simulation
0.05
0.2 0.5 1.0 2.0
OlMENStQNUSS TIME
50O
Fig. 3.6 Comparison of Predicted and Measured Variation of C versus (t/t50) '°2 for
KaoHntte 1n Distilled Water with T£ - 2.70.
-------
aggregation of the sediment, and therefore on the rate of deposition,
must not be Ignored. This effect can often be the dominating factor
controlling the rate of shoaling 1n a given reach of the estuary.
3.4. Simulation of Sedimentation Processes 1n a Prototype Canal
The dimensions of a 10 km long hypothetical canal are shown in Fig.
3.7. The canal was divided Into nine elements and 48 nodes, with the
length of elements 1-3 equal to 833 m and that of elements 4-9 equal
to 1250 m. The canal was assumed to have a uniform bottom roughness, as
quantified by a Manning's coefficient of 0.02, which Is a reasonable
value for a straight natural waterway with a muddy bottom. The depth
and the mean velocity at nodes 1, 2 and 3 were taken to be 5.0 m and 0.5
m/s respectively. The velocities and water depths at nodes 4-48 were
evaluated using the conservation of energy and mass equations for an
open channel. The total drop 1n the water depth over the 10 km distance
due to frlctlonal resistance and the gradual enlargement In width at
element 5 was determined to be 0.16 m. The Initial suspension
concentration 1n the canal was .taken to be 0.0 g/1. The following
boundary conditions were used: nodes 1, 2 and 3: C(t) - 0, and nodes 46,
47 and 48: aC(t)/ax « 0. The upstream (I.e. nodes 1, 2 and 3) boundary
condition states that no suspended sediment was transported Into the
canal from upstream sources, while the downstream (I.e. nodes 46, 47 and
48) boundary condition stipulates that the longitudinal flux of
suspended sediment across the downstream boundary was zero. In elements
1 - 4, an Initial, partially consolidated sediment bed of 0.37 m 1n
thickness was assumed to exist, while 1n elements 5 - 9, no Initial bed
was present.
Erosion of the Initial sediment bed occurred In elements 1-4,
while deposition of the sediment suspended 1n the first four elements
occurred In elements 5-9. The suspension concentration-time record
for elements 4 and 5 are shown 1n F1gs. 3.8 and 3.9 for salinities of 0,
1, 20 and 35 ppt. As evidenced by the over three-fold decrease 1n
concentration between F1g. 3.8 and 3.9, a high percentage of the
suspended sediment deposited 1n element 5. Also observed in these two
figures is a reduction in sediment suspended with Increase In
salinity. This observation follows from the previously described effect
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-------
I • NODE NUMBER
CD ELEMENT NUMBER
3
50m 2
1
5 §
CD
7
10 I
®
12
1469
» 15 18 2p 22
(3)
17
1 14
S>
22
6 19 21
V
2
X
27
X
8 3O 33 35 39 40 4
32
37
26 29 31 34 3
«
42.
* 3» 4
> 45 41
47.
1 44 -4
1
l(
'
X)m
te
, 833*n, 633m ,833 TI250 m ,125pm , 1250 in ,1260m ,1280m ,1250m
10000 m
Fig. 3.7 Plan View of 10 km Hypothetical Canal.
-------
s
ce
70-
ao-
&
5
o
UJ
a
ui
Q.
V)
\ II I I
Element 4
Salinity(ppt)
0
l -•——
10
35
8 12 16 20
TIME (Mrs)
. 3.8 Predicted Concentration-time Record for Element
4 in 10 km Canal.
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-------
1.75
*-%
^
2 1:3
I
z
Ul
o
UJ
± Q75-
o
UJ
-------
of salinity on the rate of surface erosion. Also apparent is the small
effect of salinity on the rates of deposition. This result 1s not
surprising considering the fact that salinity was found from laboratory
deposition tests to only slightly Influence these rates.
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IV. SUMMARY. CONCLUSIONS AND RECOMMENDATIONS
4.1. Summary and Conclusions
The following are the main observations from this study:
1. Modeling the movement of cohesive sediments in order to predict the
fate of pollutants Introduced Into an estuary 1s Important, because
a significant fraction of many pollutants, e.g. heavy metals,
radioactive elements, organic substances, 1s typically transported
sorbed to these sediments rather than 1n the non-sorbed state.
2. Modeling the transport of cohesive sediments in an estuary requires
a knowledge of Its geometry, the flow and salinity fields, the
coagulation, settling and depositional characteristics of the
sediment, the structure (I.e. bed shear strength and bed density
profiles) of the sediment bed at several different locations in the
estuary, and the erosional characteristics of these beds when
subjected to an excess bed shear stress.
3. SEDIMENT III, a two-dimensional, depth-averaged cohesive sediment
transport mathematical model was upgraded by Improving upon Us
capability of predicting the erosion and deposition of cohesive
sediments in an estuarial environment, and by Incorporating the
effect of salinity on these two transport processes. The new model
1s referred to as SEDIMENT IIIA.
4. Deposited estuarlar. occur 1n three different stages of
consolidation: unconsolldated, partially consolidated and settled
(fully consolidated). Unconsolidated deposits, sometimes referred
to as stationary suspensions, possess a very high water content and
low shear strength and are redispersed, or mass eroded, when
o
subjected to an excess bed shear stress (I.e. when the bed shear
stress 1s greater than the shear strength of the exposed bed
surface). Partially consolidated deposits have a somewhat lower
water content and higher shear strength and are resuspended
aggregate by aggregate, I.e. undergo surface erosion, when subjected
to an excess shear stress. Settled, or fully consolidated beds
possess a much lower water content, a much higher shear strength and
as well are resuspended aggregate by aggregate when subjected to an
excess shear. The shear strength and the density of partially
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consolidated beds were shown by laboratory tests to Increase with
depth, z, below the water-bed interface, and as such are vertically
stratified. Both stationary suspensions and partially consolidated
beds undergo consolidation due to overburden pressure, with the bed
shear strength increasing with time of consolidation. The bed
density as well was found to increase with consolidation time up to
240 hours. In settled beds, the shear strength and the density
profiles exhibit relatively uniform properties over the depth.
The sediment bed schematization incorporated into the model allows
for the above-mentioned three bed sections, and divides each section
into a characteristic number of layers. Within each layer, the bed
shear strength and density are assumed to vary in a linear manner
with depth. The number of layers as well as the shear strength and
the density profiles in each section must be determined from
laboratory resuspension tests.
Flow-deposited beds should be used in these laboratory tests. In
forming such a bed in a flume the pre-erosion stress history
(determined by the shear stress during mixing, the period of mixing,
the shear stress during deposition and the periods of deposition and
consolidation), has a significant effect on the resulting bed
structure. The methodology depicted in Fig. 2.18 and described by
Mehta jt__aJL (1982a) may be used in investigating the resuspension
potential of flow-deposited unconsolidated and partially
consolidated beds. Resuspension tests performed during this study
with beds of kaolinite and.sediment from Lake Francis, Nebraska,
showed that the rate of surface erosion of partially consolidated
beds varied exponentially with the excess bed shear stress (Eq.
2.32). The empirical relationship given by Eq. 2.32 is analogous to
the rate expression which results from a heuristic interpretation of
rate process theory for chemical reactions. The rate of surface
erosion of settled beds has been found to vary linearly with the
excess shear stress (Eq. 2.31).
The erosion algorithm incorporated into the model simulates the mass
erosion of unconsolidated stationary suspensions by instantly
redispersing the thickness, of bed above the level (I.e. depth below
the bed surface) at which the bed shear stress is equal to the bed
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shear strength. The average rate of surface erosion of the
partially consolidated bed layers over one time-step At 1s given by
Eqs. 2.34 and 2.35. The average rate of surface erosion of settled
bed layers 1s given by Eqs. 2.34 and 2.40. In the latter two cases,
the thickness of bed eroded per time-step 1s determined using an
Iteration routine. Erosion Is simulated to occur only when the bed
shear stress, ib» Is greater than the shear strength of the bed
surface and only when the flow 1s accelerating, I.e.
8. The settling velocity of the sediment 1s a function, among other
parameters, of the suspension concentration, C. For concentrations
less than C. « 0.1 - 0.7 g/1 the sediment particles settle
Independently without much mutual Interference, and therefore the
settling velocity 1s Independent of C. In the range Ci < C <
C2 * 10 - 15 g/1, the settling rate 1s proportional to Cn with n >
0, due to mutual Interference. In the range C > C2, the settling
velocity decreases with Increasing concentration due to hindered
settling.
9. The deposition algorithm Integrates the concepts proposed by various
Investigators and represents a unified model of this process.
Deposition 1s predicted to occur only 1n decelerating flows,
I.e. T (t+At) < -^(t), when the bed shear stress, •%, 1s less than
the maximum value at which deposition can occur, -t . For -c^ <
•a, c (Range I), where -n, c Is the value of th at which the
*+ 9 V* L/y I* U
deposition rate In Range I 1s equal to that in Range II (defined
below), and for C < Ci for all values of IL < TU , the rate of
deposition, dC/dt, 1s determined using the exponential law given by
Eq. 2.54. For the Intersection of tb.c < % < *w (Range II) and
for C > C it the deposition rate 1s given by the log-normal
expression (Eq. 2.58). The mass of sediment deposited per time-step
1s evaluated by averaging dC/dt at times t and t+At in Range I and
for C < Ci 1n Range II, as given by Eq. 2.64, while in Range II, the
log-normal relationship 1s Integrated over this time period, as
given by Eq. 2.65. The thickness of the bed formed by this
deposited mass 1s determined using the properties of the
unconsolldated and partially consolidated bed sections. As
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deposition continues, first the unconsolldated layers are filled up,
followed by the partially consolidated layers. This filling
sequence has been used in order to account for consolidation of the
bed due to overburden pressure by virtue of the increasing shear
strength and density with bed thickness.
10. The salinity of the eroding fluid, S, had the following effect on
the resuspension rates of partially consolidated beds using Lake
Francis sediment. Between a salinity of ~Q and 2 ppt, the bed shear
strength, as determined Indirectly from analysis of resuspension
tests conducted at salinities between ~0 and 10 ppt, was found to
double in value, in a linear manner, between S =» «0 and 2 ppt, and
thereafter, i.e. for S > 2 ppt, was found to remain practically
constant. Therefore, the erosion potential for a cohesive sediment
bed with S » -0 ppt is approximately twice that for the same bed
with S >2 ppt.
11. Increasing the salinity of the suspending fluid increases slightly
the settling velocities, and hence the rates of deposition of a
natural mud. Deposition tests were performed with Lake Francis
sediment at salinities of -0, 1, 2, 5, 10, 20 and 35 ppt and for bed
shear stress of 0.0, 0.015, 0.05, 0.10, 0,20 and 0.30 N/m2. For the
deposition tests in Range I, the settling velocity was found to
Increase at a rate proportional to S , and was practically
Invariant with respect to shear stress. For the tests in Range II,
the effect of salinity on the deposition rate is given by Eqs. 2.75
and 2.77, and was approximately the same as that in Range I.
12. Simulation of various sediment problems using the model showed that
the numerical scheme 1s stable for all conditions. The accuracy of
the solution is affected when the Peclet number, which is the ratio
of convection to diffusion, becomes too large (greater than 102) or
to small (less than lO"3).
13. The model was used to simulate a laboratory resuspension test and
four laboratory deposition tests. Reasonably good agreement between
the predicted and measured results was obtained in each of these
cases. The 'effect of salinity on both the resuspension test and one
of the deposition tests revealed that, as expected, the rates of
resuspension and deposition decreased and Increased, respectively,
-144-
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with Increasing salinity. Sedimentation processes In a 10 km
hypothetical canal, 1n which both erosion and deposition of sediment
occurred, were also simulated at three different salinities to show
the effect of salinity under typical prototype conditions. The
effect of salinity in this simulation was less apparent than in the
case of the laboratory tests because of the simultaneous occurrence
of erosion, convection, diffusion and deposition along the canal.
4.2. Recommendations for Future Research
The reported study was primarily concerned with Improving the
capability of an existing fine sediment transport model to. simulate the
erosion and deposition of fine, cohesive sediments in estuaries. The
processes of turbulent diffusion of suspended sediment and the
consolidation of a bed were not addressed. To further upgrade the
model, an Investigation of the latter two processes is recommended.
Specific objectives of such a research could be the following:
1. Conduct a comprehensive review on the turbulent diffusion and
dispersion of non-conservative suspended matter 1n estuarial flows.
2. Develop and Incorporate a diffusion algorithm In order to account
for the effect of local flow conditions and sediment properties on
the diffusion processes. In this algorithm, the components of the
turbulent dispersion coefficient in the horizontal dimensions, x and
y, should be calculated as functions of the longitudinal (I.e. in
the direction of the local flow) and transverse dispersion
coefficients and the angle between the flow and the positive x-
axis. Diffusion caused by the local velocity distribution and
turbulent, Ficklan diffusion processes should be combined and
represented by these effective turbulent dispersion coefficients.
3. Conduct a comprehensive review on the consolidation of cohesive
sediments.
4. Develop and Incorporate a consolidation algorithm in order to
account for the Increase 1n the bed bulk density and shear strength
and the decrease in bed thickness with time due to primary
consolidation. Only consolidation, I.e. crushing, of underlying
sediment material by new deposits during the bed formation process
1s currently considered. A complete consolidation algorithm 1s a
useful component of an estuarial fine sediment transport model in
-145-
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order to account for changes in the bed's structural propertiese and
hence Us erosion potential, over relatively long periods of time
(i.e. of the order of one month and longer).
-146-
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Sedimentology, Vol. 11, 1968, pp. 105-144.
Terzaghi, K., and Peck, R. B., Soil Mechanics 1n Engineering Practice,
John WHey and Sons, New York, isoo. !
Thorn, M. F. C., and Parsons, J. G., "Properties of Grangemouth Mud,"
Report No. EX781, Hydraul1cs Research Station, Wallingford, England,
July, 1977.
Thorn, M. F. C., and Parsons, J. G., "Erosion of Cohesive Sediments in
Estuaries: An Engineering Guide," Proc. Third International Symposium
on Dredging Technology, Paper Fl, March, 1980.
Thorn, M. F. C., "Physical Processes of Slltation in Tidal Channels,"
Proc. Hydraulic Modelling Applied to Maritime Engineering Problems,
ICE, London, 1981, pp. 47-55. ~~:
Tubman, M. VI., and Suhayda, J. N., "Wave Action and Bottom Movement 1n
Fine Sediments," Proc. Fifteenth Coastal Engineering Conference,
Honolulu, 1977, pp. 1168-1183.!
Vanderborght, J.' P., Wollast, R., and 8111 en, G., "Kinetic Models of
Olagenesis 1n Disturbed Sediments, Part 2: Nitrogen Diagenesis,"
limnology and Oceanography, Vol. 22, No. 5, September, 1977, pp. 794-
803.
-159-
-------
van Olphen, H.. An Introduction to Clay Colloid Chemistry. Intersdence
Publishers, New York, 1963.
Veltman, M., "Disposal of Contaminated Estuarlal Sediment," First
International Conference on Cohesive Sediments, ChurchillCollege,
Cambridge, England, 1979.
Vincent, 8., Bljsterbosch, 8. H., and Lyklema, J., "Competitive
Adsorption of Ions and Neutral Molecules 1n the Stern Layer on Silver
Iodide and Us Effect on Colloid Stability," Journal of Colloid
Interface Science, Vol. 37, 1971.
Weckmann, 0., "Sediment Management at a Coastal Marina," M.E. Thesis,
University of Florida, Gainesville, 1979.
Whltehouse, U. G., Jeffrey, L. M., and Oebbrecht, J. 0., "Differential
Settling Tendencies of Clay Minerals in Saline Waters," Proc. Seventh
National Conference on Clays and Clay Minerals, 1960, pp. 1-79.
Whitmarsh, R. B., "Precise Sediment Density by Gamma-Ray Attenuation
Alone," Journal of Sedimentary Petrology, Vol. 41, 1971, pp. 882-883.
Wilson, W., and Bradley, D., "Specific Volume of Sea Water as a Function
of Temperature, Pressure and Salinity," Deep-Sea Research, Vol. 15,
1968, pp. 355-363.
Yeh, H. Y., "Resuspension Properties of Flow Deposited Cohesive Sediment
Beds." M.S. Thesis, University of Florida, Gainesville. 1979.
Zeichner, G. R., and Schowalter, W. R., "Use of Trajectory Analysis to
Study Stability of Colloidal Dispersion in Flow Fields," Journal of
the American Institute of Chemical Engineering, Vol. 23, No. 3,197>.
Zienklewicz, 0. C., The Finite Element Method in Engineering Science,
McGraw-Hill, London, 1971.
-160-
-------
APPENDIX A
Model Flow Chart of SEDIMENT IIIA
-161-
-------
FLOW CHART OF SEDIMENT IIIA
START
READ I/O
FILE NUMBERS
READ NSTOP,
JOB TITLE
READ JOB
CONTROL
PARAMETERS
READ NODAL
CONNECTIONS
COORDINATES,
-162-
-------
[READ TRANSIENT
INPUT DATA
READ ELEMENT
NUMBERS FOR WHICH
TIME HISTORY IS TO BE
PRINTED OUT
INITIALIZE
NECESSARY
ARRAYS
READ AVERAGE
WATER TEMP
AND INITIAL
SALINITIES
SEDIMENT PROBLEM-
INITIALIZE BED
PROPERTIES
STEADY-STATE
AND
UNSTEADY
PROBLEMS
CALL SPROP-
READ SEDIMENT
PROPERTIES
-163-
-------
i
CALL DIFCQF-
READ INITIAL
VALUES OF
DIFFUSION-COEFS.
CALL INPUTV-
READ INITIAL
VALUES OF FLOW
VELOCITIES
YES
NO
CALL INCONC-
READ INITIAL
CONCENTRATION
VALUES
STEADY-STATE
PROBLEM
'READ ELEVATION
OF BED SURFACE
AT EACH NODE
NO
UNSTEADY STATE
PROBLEM
-164-
-------
CALL DEPTHS-
READ FLOW
DEPTH AT
EACH NODE
CALL SHPFNS
AND TSHAPE-
FORM SHAPE
FUNCTIONS
NO
YES
CALL SHEAR-
CALCULATE
BED SHEARS
CALL DENSTY-
ELEMENTAL BED SHEAR
STRENGTHS AND BULK
DENSITIES CALCULATED
AS A FUNCTION OF
ELEMENTAL SALINITY
VALUES
CALL SETVEL-
READ/CALCULATE
NODAL SETTLING
VELOCITIES
-,66-
-------
CALL BED-
READ INITIAL
BED PROFILE AND
PROPERTIES
CALL INPUTC-
READ CONCENTRATION
BOUNDARY CONDITIONS
CALL DRYNOD-
DETERMINES WHICH
NODES AND
ELEMENTS ARE DRY
CALL LOAD-
NUMBER OF EQUATIONS
IN THE SYSTEM COEF.
MATRIX AND BANDWIDTH
DETERMINED
CALL LOADX-
NUM8ER OF EQUATIONS
IN THE SYSTEM COEF.
MATRIX AND BANDWIDTH
DETERMINED
PRINT INITIAL
CONDITIONS AND
SEDIMENT PROPERTIES
-------
STEADY-STATE
PROBLEM
UNSTEADY AND
SEDIMENT
PROBLEMS
CALL FRONT-
NODE SOURCE
TERMS ADDED,
GLOBAL COEF.
MATRIX FORMED
AND SOLVED
BY FRONTAL
ELIMINATION
ROUTINE USING
FULL PIVOTING
CALL FANDS-
NODE SOURCE TERMS
ARE ADDED INTO
SYSTEM LOAD
MATRIX, GLOBAL
COEF. MATRIX FORMED!
AND IS SOLVED
BY GAUSSIAN
ELIMINATION
CALL DEPSN-
DEPOSITION
RATES
CALCULATED
CALL SURERO-
SURFACE
EROSION
RATES
CALCULATED
NO
CALL OUTPUT-
PRINT CONCS.
/^
\
r
CALL OUTTES-
COMPARE WITH
EXACT SOL.
CALL ELSTIF-
ELEMENT STIFFNESS
ARRAYS FOR FIRST
TIME STEP FORMED
-167-
-------
MAIN TIME LOOP
DO N-2.NTTS
CHANGE TIME STEP
DEPENDING ON
VALUE OF NPMA(N)
DEPENDING ON INPUT
CODES, READ NEW
PARAMETERS FOR
THIS TIME STEP
YES
NO
CALL DENSTY-
SET NEW
SALINITIES
YES
X
:(N)\ NO
*/
CALL DIFCOF-
SET NEW
DIFFUSION COEFS.
NO
CALL SETVEL-
SET NEW
SETT. VELOCITIES
YES
-168-
-------
YES
NO
CALL INPUTV-
SET NEW
VELOCITIES
YES
NO
CALL DEPTHS-
SET NEW
FLOW DEPTHS
YES
NO
CALL DRYNOD
YES
CALL LOADX
NO
CALL INPUTC-
SET NEW
BOUNDARY
'CONDITIONS
YES
12
NO
-169-
CALL SHEAR
-------
CALL DEPSN
CALL MftSERO-
HASS EROSION
RATES CALCULATED
CALL SURERO
CALL FANDS
CALL NEWBED-
FORM THE NEW BED
CAUSED BY
DEPOSITION
CALL TIMHIS-
OUTPUT FOR THIS
TIME STEP SAVED
-170-
-------
CALL OUTPUT-
ONCS,AND SEDIMENT
DATA PRINTED OUT
CALL OUHES-
EXACT SOLUTION
PRINT TIME
HISTORY OF FLOW
AND SEDIMENTATION
-171-
-------
APPENDIX B
User's Manual
-172-
-------
B.I. Data Required for Model Use
SET A JOB CONTROL CARDS
CARD A.I
(1315)
1-5
6-10
11-15
16-20
21-25
26-30
31-35
36-40
41-45
46-50
51-55
56-60
61-65
IN
LP
INC
IND
INE
INF
ING
INH
INI
INB
INS
INSS
ISOLV
I/O file numbers and equation solver used
General Input file number (default 5)
Output file number (default 6)
Initial concentrations
Diffusion coefficients
Node point bottom elevations (Initial)
Node point flow velocities
Settling velocities
Fl ow depths
Finite element grid geometry data
Boundary conditions
Salinities
New nodal salinities
0 - use band solver (Subroutine FANDS)
1 - use front solver (Subroutine FRONTS)
CARD A.2 (II, 19A4) Job stop and title
1 : NSTOP 0 - continue
1 - end of job
2-78 : TITLE
CARD A.3 (1615)
Job title
Job Control Parameters, Input Codes, and
Problem Options
1-5 : NOPT Type of Problem
1 - steady state transport problem
2 - unsteady transport problem
3 - sediment transport problem
6-10 : ICOOE Output control for non-sediment problems
0 - standard output
1 - compares with analytic solution
calculated in Subroutine EXACT
11-15 : NTTS Number of time steps
16-20 : IVEL Determines Initial velocity field. I.e., at
time step #1 (for unsteady problems only)
1 - X S Y velocities set equal to constants
CONXV and CONYV read 1n Subroutine INPUTV
2 - each nodal velocity read 1n from Input
file INF
3 - velocity computed using user supplied
routine 1n Subroutine INPUTV
-173-
-------
21-25 : IELEV Elevation of bottom above a given datum at
node points
0 - all elevations set equal to 0.0.
1 - read each value read in from file number
INE
26-30 : IOIF1 Initial diffusion coefficient values at each
node.
1 - 0 'and Ov are set equal to constants read
in Subroutine OIFCOF
2 - Nodal diffusion coefficients are read in
from file number INO
3 - Diffusion coefficients are calculated
using user supplied procedure.
31-35 : IBED Initial bed profile
0 - no sediment present on bed
1 - bed profile read in Subroutine 8EO
36-40 : ISET Initial settling velocity at each node
1 - set to a constant read in Subroutine
SETVEL
2 - each settling velocity is read in from
file number ING
3 - settling velocities are computed from
model in Subroutine SETVEL
41-45 t IOEP Initial depths of flow at each node
1 - set to constant read in Subroutine DEPTHS
2 - read in from file number INH
3 - computed according to user supplied
procedure in Subroutine DEPTHS
46-50 : ICONC Initial suspended sediment concentrations
1 - set to constant
2 - read in from file number INC
3 - computed according to user supplied
procedure in Subroutine INCQNC
51-55 : INBC Boundary Conditions
1 - each value read in from file number IN8
2 - computed in Subroutine INPUTC using user
supplied routine
5S-60 : IDRY Code to indicate dry node (i.e. negative flow
depth) problem
0 - no dry nodes will occur
1 - possible dry nodes
61-65 : IPL Number of nodes where concentration-time
plots are to be generated using plot routine
in Subroutine PLOTR
-174-
-------
SET 6 HESH DATA
These data are read from file unit INI
CARD B.I (215)
1-5 : NE Number of elements 1n system
6-10 .: NP Number of nodes 1n system
CARD B.2 et.seq.(8I5/)
1-5 : NOP(I.K) Nodal connections counterclockwise (8 per
card for quadrilateral element)
CARD B.3 et.seq.(4(2F8.4/))
6-15 : CORD(J.l) X-coordinate (meters)
16-25 : CORD(J,2) Y-coordinate (meters)
SET C TRANSIENT PROBLEM INPUT
CARD C.I (3F10.5)
1-10 : TETA "Implicitness factor" for Crank-Nicholson
time-marching scheme
0, - explicit
1. - implicit
11-20 : DT Time step size - sees
21-30 : TIM(l) Starting time - sees
CARD C.2 et.seq.(80Il) Code to change time step
l.etc : NPMA(I) The value of NPMA at each time determines 1f
the time step will be changed
0 - no change
l"f double time step
2 - halve time step
for I-1,...,NTTS
f
CARD C.3 et.seq.(SOIl) Code for new Boundary conditions
l.etc : IFF(I.l) Determines 1f there are new boundary
conditions
0 - no change 1n boundary conditions
1 - each value read 1n from cards
2 - computed in Subroutine INPUTC using user
supplied procedure
3 - each value read in from file number 1KB
-175-
-------
CARD C.4 et.seq.(80Il)
l.etc : IFF(I,2)
CARD C.5 et.seq.(SOIl)
l.etc : IVCOO(I)
CARD C.6 et.seq.(SOIl)
l.etc : IDIF(I)
CARD C.7 et.seq.(80Il)
l.etc : IDEPC(I)
CARD C.8 et.seq.(SOIl)
l.etc : ISALC(I)
Output control
0 - no output
1 - sedimentation data only
2 - concentrations only
3 - concentrations and sediment transport
data
5 - comparison with analytic solution 1n
Subroutine EXACT
New velocities
Same as IVEL but for each time step
0 - no new velocities
1 - X & Y velocities set equal to constants
CONXV and CONYV read 1n Subroutine INPUTV
2 - each nodal velocity read in from input
file INF
3 - velocity computed using user supplied
routine 1n Subroutine INPUTV
New diffusion coefficients
Same as IOIF
0 - no new diffusion coefficients
1 - Ox and 0 are set equal to constants read
1n Subroutine DIFCOF
2 - nodal diffusion coefficients are read in
from file number INO
3 - diffusion coefficients are calculated
using user supplied procedure
New depths of flow
Same as IOEP
0 - no new depths
1 - set to constant read in Subroutine DEPTHS
2 - read 1n from file number INK
3 - computed according to user supplied
procedure in Subroutine DEPTHS
New Salinities
0 - no new salinities
1 - set to a constant read in Subroutine
DENSTY
2 - new salinities at specified nodes are
read In Subroutine DENSTY
3 - new salinities for all nodes are read in
Subroutine DENSTY
-176-
-------
CARD C.9 et.seq.(80Il) Only for sediment problems NOPT«3
l.etc : ISVS(I) New settling velocities. Same as ISET
0 - no new settling velocities
1 - set to a constant read in Subroutine
SETVEL
2 - each settling velocity is read in from
file number JNG
3 - settling velocities are computed from
model in Subroutine SETVEL
CARD C.10
1-5
6-10
etc
SET 0
(1615)
: NHIS number of elements that time history
required for (maximum 6)
: NELH Element numbers
WATER AND SEDIMENT PROPERTIES
is
Read in Subroutine DENSTY
CARD 0.1 (F1Q.5,I10) Water Parameters
1-10 : TMP Average Water Temperature (°C)
11-20 : IS Determines how initial salinities are read in
0 - constant salinity for all nodes
1 - salinity for each node is read in
If IS = 0:
CARD 0.2 (F10.5) Constant Salinity
1-10 : SW Value of constant salinity read in'- ppt
If IS - 1:
CARD 0.2 et.seq.(7F10.5) Nodal Salinity Values
1-10 : SAL(I) Salinity value for I— node - ppt
Read in Subroutine SPROP for sediment problems (NOPT«3)
CARD 0.3 (4F10.5) Settling Velocity Parameters
1-10 : CRCN*Ci See Equations for Ws below - kg/m3
11-20 : CRCN2=C2 See Equations for Ws below - kg/m3
21-30 : CRCN3=C3 See Equations for Ws below - kg/m3
31-40 : GAC Density of sediment mineral - kg/m3
-177-
-------
CARD 0.4 (6F10.5)
1-10
11-20
21-30
31-40
41-50
51-60
AA»AJ
AB-A2
AC-Aj
8
F
AL
CARD 0.5 (2E10.3)
1-10
11-20
WS1=
0
si
CARD D.6 (2F10.5)
1-10 :
11-20 : EXPN2=n|
CARD 0.7 (3F10.5)
1-10
11-20
21-30
EXPMl-mj
EXPM2*m2
EXPM3«m,
CARD 0.8 (2E10.3)
1-10
11-20
WSK2-K2
See Equations for Ws below
See Equations for Ws below
See Equations for Ws below
See Equations for Ws below
See Equations for Ws below
See Equations for Ws below
See Equations for Ws below - m/s
Equivalent Sediment Particle Diameter at tso - m
See Equations for Ws below
See Equations for Ws below
See Equations for Ws below
See Equations for Ws below
See Equations for Ws below
See Equations for Ws below - m/s
See Equations for Ws below - m/s
NOTE: For RANGE I (0 <*<•&. ) and C < C, in Range II
# * * " o»C' A
max
W. • AA*WS1*(SAL)**EXPM1 for C < CRCN1 where SAL = salinity
If (SAL < 0.1 ppt)SAL - 0.1 ppt
Ws - AA*WSK1*C**EXPN1*(SAL)**EXPM1 for CRCN1 < C < CRCN2
ws-
AB*WSK2*C**EXPN2*(SAL)**EXPM2 for CRCN2 < C < CRCN3
Ws - AC*G*D**2*(GAC/GAW-1)*250*(C/CRCN3-1)**AL*(SAL)**EXPM3/
(18*v*0**1.8) for C > CRCN3
If there is only one Ws = KCn relationship between C * CRCN1 and
the concentration at wftich hindered settling begins, set CRCN3 -
CRCN2 1n CARD 0.3.
NOTE: For C > G! in Range II
T-AL0610((TM/T50)*B*(SAL)**F)**(1./SIS2)
-178-
-------
CARD 0.9 (2110, 2F10.5) Properties of new deposits
1-10 : NLAYTM
11-20 : NLAYT
21-30 : TAUMIN
Number-of layers formed by unconsblidated new
deposits (UNO)
Number of layers formed by partially
consolidated new deposits (CND)
-H/m
and
31-40 : TAUMAX
Parameters characterizing functional relationship between -el
10g10(t50) and 02 at a salinity of 35 ppt. D
CARD D.10 (5F10.5)
See Equations for 02 below
See Equations for 0% below
See Equations for a? below
See Equations for 0% below
See Equations for
-------
CARD 0.13 et.$eq.(8F10.5)
1-10 : TLAYM(I) Thickness of unconsolidated new deposit
layers - m
for I - 1.....NLAYTM
CARD 0.14 et.seq.(4(2F10.5)) Shear strength and bulk density for
partially consolidated new deposit layers. NLAYT+1 pairs of
values are read 1n starting at top of these layers and
proceeding downward.
1-10 : SS(I) Bed Shear Strength 5 N/m*
11-20 : GB(I) Bulk density - kg/m3
for I * 1 NlAYT+1
CARD D.15 et.seq.(2(3F10.5)) Thickness, e and a values for each
partially consolidated new deposit layer.
1-10 : TLAY(I) Layer thickness - m
(Set TLAY/NLAYT) » 0.0)
11-20 : EPSLOH(I) . - kg/mz/s
21-30 : ALFA(I) a - dimension!ess
for I » 1,...,NLAYT
Note: The properties read 1n on CARDS D.12-0.15 are determined from
laboratory experiments (see Section B.3 for a description of
these experiments). These are the properties assigned to new
deposits If/when deposition occurs during model simulation or
Initially 1f new deposits (I.e. fluid mud) are present on top of
the consolidated original bed, as specified 1n SET K.
SET E INITIAL DIFFUSION COEFFICIENTS
The form of Input 1s set by value of IDIF.
IDIF « 1 Diffusion coefficients are set to constant values.
CARD E.I (2F10.5)
1-10 : COIFX X-d1ffus1on coefficient - mf/sec
11-20 : CDIFY Y-dlffuslon coefficient - nr/sec
IDIF - 2 Diffusion coefficients are read in node by node.
CARD E.2 et.seq.(3(I5,2F10.5)
1-5 : IT(J) Node number
6-15 : TEMP(l.J) X-diffus1on coefficient - m^/sec
16-25 : TEMP(2,J) Y-d1ffusion coefficient - mz/sec
Reading stops for IT(J) < 0
-180-
-------
ID IF * 3 Diffusion coefficients computed analytically using user
supplied procedure.
SET F INITIAL VELOCITY FIELD
The velocity components at each node must be specified. The value of
IVEL determines type of input. This input only for unsteady problems.
All reads are from file number INF
IVEL « 1 Velocities are set to constant values.
Read from file unit INF
CARD F.I (2F10.5)
1-10 : CONXV X-veloclty - m/sec
11-20 : CONYV Y-velocity - m/sec
IVEL = 2 Each nodal velocity component read in.
CARD F.2 (4(2510.5)) Must be read in order for all NP nodes.
1-10 : XVEL(J.l) X-velocity at node J - m/sec
11-20 : XVEL(0,2) Y-velocity at node J - m/sec
IVEL * 3 User supplied procedure in Subroutine INPUTV is used to
calculate nodal velocities.
For NOPT « 2 or 3; .
SET G INITIAL CONCENTRATION FIELD
The initial concentration at each node, must be specified for all
unsteady problems. The type of input is determined by the value of
ICONC.
Read from file unit INC
ICONC = 1 Initial concentration set to a constant at all nodes.
CARD G.I (F10.5)
1-10 : CVSX Concentration - kg/m3
ICONC * 2 Read in for each node .
CARD G.1 et.seq.(4(I10,F10.5))
1-10 : IT(J) Node number ,
11-20 : TEMP(J) Concentration - kg/m3
Reading stops for IT(J) <0
ICONC * 3 Compute concentrations at each node using user supplied
model in Subroutine INCONC.
-------
For NOPT - 3 (Sediment Problems);
SET H INITIAL BED ELEVATION
ONl
\
If IELEV*0» the Initial bed elevation, with respect to some datum, at
each node 1s read in.
Read from file unit INE
CARD H.I et.seq.(8F10.5) j
1-10 : EL£V(I) Bed elevation for node I - m
I - 1.....NP
SET.I INITIAL DEPTHS OF FLOW
Depths of flow at each node are read 1n depending on the value of IDEP.
Read from file unit INH.
IDEP » 0 All depths set to 1. by default
IDEP ° 1 All nodal depths set to constant
CARD I.l(FlO.B) Constant value of depth
1-10 : CDEP Depth of flow - m
IDEP « 2 Read node point depths from file INH.
CARD 1.2 (4(I10,F10.5))
1-10 : IT(0) Node Point Number
11-20 : TEMP(J) Depth of flow - m
Stops reading 1f IT(J) < 0.
IDEP • 3 Compute depths from user supplied procedure in Subroutine
DEPTHS.
For NOPT * 3;
SET_J INITIAL SETTLING VELOCITIES
The Initial settling velocities at each node point must be read 1n. The
form of input is determined by the value of ISET.
Read from file unit INS
ISET • 1 All settling velocities are set to constant
-182-
-------
CARD J.I (F10.5)
1-10 : CVSX Settling velocity - m/sec
ISET = 2
CARD J.2 et.seq.(4(110, F10.5))
1-10 : IT(J) Node number
.11-20 : TEMP(J) Settling velocity - m/sec
Stops reading if IT(J) < 0.
ISET * 3
Settling velocity model, for which parameters were read in in SET 0, is
used to compute each nodal settling velocity.
For NOPT * 3:
SET K ORIGINAL BED PROFILE
Read in only if IBED (Card A.3) is not zero. Otherwise the default bed
condition will be a clean bed.
CARD K.I et.seq,(315,F10.5) for each element
1-5 : NN Element number
6-10 : NLA Number of layers of consolidated original bed
11-15 : NM If NM » 0, bed properties are read 1n for
each element. If NM*0, constant values are
read in and used for all elements.
16-25 : GWA Average density of pore water in original bed
- kg/m3
CARD K.2 et.seq.(2F10.5) Shear strength and bulk density for
consolidated original bed layers. NLA+1 pairs of values are
read in starting at the top layer and proceeding downward.
The first values are for the top of the original bed.
1-10 : SSTO(NN.L) Bed shear strength = N/m2
11-20 : GBO(NN.L) Bulk density - kg/nr
For L » 1,...,NLA+1
CARD K.3 et.seq.(F10.5.E10.3) Thickness and value of M for each
consolidated bed layer
1-10 : THICKO(NN.I) Thickness of Ith layer - m
11-20 : EPSLNO(NN.I) M value of WTTayer - kg/m2/s
for M,.M,NIA
-183-
-------
Note: CARDS K.I, K.2 and K.3 are repeated for NN*1 ,...,NE when NM»0.
When NM*0, these cards are read 1n only once.
If stationary suspension 1s present on top of original bed, set NN=-10
at the end of the above set (i.e. CARDS K.I, K.2 and K.3). For NN=-10,
read the following cards.
CARD K.4 et.seq. (3(110, F10. 5)) for each element
1-10 : IT(J) Element number
11-20 : TEMP(J) Dry mass per unit area of fluid mud (soft
sediment) on top of consolidated original
bed - kg/m2.
Reading stops when IT(J) < 0.
SET I BOUNDARY CONDITIONS
For any problem, concentration boundary conditions must be specified at
least at one node. At all external boundaries that have no
cencentration specified, the normal diffusive flux is defaulted to
zero. Type of input is determined by value of INBC. File number for
input is INB.
1 Read node number and specified boundary condition from cards
CARD L.I (2(I10,F10.5))
1-10 : IT(0) Node number
11-20 : TEMP(J) Specified concentration - kg/m3
for 0*1,..., NP
INBC = 2 Concentration computed according to user supplied procedure in
. Subroutine INPUTC
INBC « 3 Read node number and specified boundary condition from file
- INB.
CARD L.2 (3(I10,F10.5))
1-10 : IT(J) Node Number
11-20 : TEMP(J) Specified concentration - kg/m3
for J-1.....NP
SET M New Salinities
Type of input is determined by value of ISALC(J), for J-2,...,NTTS.
-184-
-------
1SALC(J)»1.
CARD M.I (F10.5)
1-10 : SW Constant salinity value read 1n - ppt
ISALC(J)*2. File number for Input is INSS
CARD M.2 (3(I10,F10.5)) Salinities for specified nodes
1-10 : IT(J) Node number
11-20 : TEMP(J) New salinity at node J - ppt
ISALC(J)"3. File number for Input is INSS
Card M.3 (7F10.5) New salinities for all nodes.
1-10 : SAL(J) Salinity at Jth node.
DYNAMIC INPUT
The same subroutines that read initial values are used to read changes
in these values during a dynamic run. The Input code arrays 1n SET C
tell the program if any new values should be read 1n at each time
step. Note that the starting time 1$ timestep 1. The order of reading
each set of data is given below. If the code is zero no Input of that
parameter will be expected. If 1t 1s non-zero the value of the code
will determine the type of Input.
DESCRIPTION COHE ARRAY INPUT CARD SET
Salinities ISALC(J) SET H
Diffusion Coefficients IDIF(J) SET E
*Settl1ng Velocities ISVS(J) SET J
Velocities IVCOO(J) SET F
Depths of Flow IDEPC(O) SET I
Concentration B.C. IFF(J.l) SET L
• ' • • *
*only for sediment problems
B.2. Description of Field Data Collection Program
In this section a description of the field data collection program
to obtain the data requirements of the model 1s summarized. The data
collection program required for modeling the hydrodynamic regime 1n an
estuary is rather well-known, and will not be discussed.
The first Item that must be considered is the time period over
which data will be collected for eventual use in the model. This will
be contingent upon the desired results from the modeling effort. In
tidal bodies of water, data should be collected over a minimum of 15
hours (assuming the tide is semi -diurnal) over a minimum of three
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different tidal cycles: spring, mean and neap. It would be more
desirable to have the data collection period span at least one week,
starting, for example, on a spring tide and finishing at the subsequent
neap tide. The next consideration is how many data sampling stations
{ there should be and where they should be located in order to adequately
monitor the spatial variations of the concentration of the suspended
sediments. Stations should be located at all exterior water boundaries
(cross-sections) of the estuarial system to be modeled. The width of
the.Boundary cross-section and the lateral variability of the depth
should be considered when deciding upon the minimum number of stations
to be located laterally across such a boundary. For example, stations
should definitely be located at predominant features such as navigation
channels. Additional stations must be located at all interior
confluences and bifurcations, and at as many other interior locations as
possible. It is recognized that the length of the data collection
period and the number of stations are often less than desired due to
economic and logistical considerations.
A. Topographic and hydrographic surveys of the system to be modeled
must be obtained at the outset. A sonar fathometer may be used to
perform the latter survey in those areas which historically have
not experienced any significant shoaling. However, in areas where
shoaling has been a problem, a gamma-ray transmission densitometer
may be used.. This instrument obtains in situ measurements of the
sediment bulk density profile, which, in high shoaling areas where
stationary suspensions (i.e. new deposits) are typically present,
can be used to determine the thickness of this suspension and the
location (i.e. vertical elevation with respect to datum) of the top
of the settled (consolidated) original bed. The location of the
top of the settled bed is defined in Section 8.3. Representative
publications on gamma-ray densitometers and their use in obtaining
In situ bulk density measurements Include Preiss (1968, 1969), Rose
and Roney (1971) and Hirst et_ji_L (1975). A description of the
methods available today to perform hydrographic surveying 1n
estuaries is given by Ingham (1975) and Dyer (1979).
8. Before the data collection period begins, two or three 10-12 cm
diameter cores should be collected at each sampling station. Each
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core should have a minimum length of approximately 2 m. Fixed
piston tube corers (Ginsburg and Lloyd, 1956) or vlbracorers
(Kirby, 1972; Finkelstein and Prlns, 1981) may be used. The cores
should contain both new deposits, if present, and consolidated bed
sections. In addition, at least 200 liters of water should be
collected during a peak flood flow.
C. At each station the location of the top of the consolidated bed
with respect to a geodetic or tidal vertical datum must be
determined using the method mentioned above. Then at the start of
the data collection period the water temperature, electrical
conductivity (or salinity) and concentration of suspended sediments
should be measured at each of the sampling stations. These
measurements should be made at a minimum of three depths over the
vertical: one-half meter below the water surface, mid-depth and
one-half meter above the bottom (I.e. top of consolidated bed).
For locations where the water depth 1s greater than about 3.5
meters, measurements should be made at additional depths over the
vertical. Both the measurement and analysis of water temperature
and electrical conductivity data are discussed by Dyer (1979). The
concentration of suspended sediments in a known volume of water can
be determined gravimetrically. Several water sampling devices such
as water bottles (N10 bottle), shipboard pump systems (Crickmore
and Aked, 1975) and sediment traps (Delft Bottle) are available. A
description of these and more water sampling devices, various
filtration procedures, as well as other methods for determination
of suspension concentrations (e.g. optical methods, remote sensing)
is given by Dyer.(1979)..
0. The parameters listed in the previous paragraph should be measured
at least once every one-half-hour for the duration of the
collection period at each of the sampling stations.
8.3. Description of Laboratory Sediment Testing
The following physico-chemical sediment and fluid properties need
to be determined using the collected cores and water:
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A. Properties of Undisturbed Sediment Cores
The gamma-ray densitometer may be used to determine the bulk
sediment density profile in the undisturbed cores still in the liner
tubes as soon after the cores are obtained as possible. A description
of this procedure is given by Whitmarsh (1971) and Kirby and Parker
(1974). If this instrument is not available, the freeze-drying
procedure used by Parchure (1980) and Dixit (1982) or the pumping method
used by Thorn and Parsons (1977) may be used to determine the bulk
density profile. The pumping method consists of removing by suction a
thin layer, e»g. 3 cm, from the top of the core. This procedure is
repeated, layer, by layer and each layer is analyzed to determine the
mean bulk density.
8. Properties of Consolidated (Original) Bed
The bulk density and bed shear strength profiles and the erosion
rate constant for each layer need to be determined for one of the cores
from each station. The number of layers and the thickness of each are
determined from the nature of the bed shear strength profile (Section
2.6). The erosion rate constant for each layer and the shear strength
profile can be determined, for example, in the rotating cylinder
credibility testing apparatus described by Sargunam et_jil_. (1973). In
order to use this apparatus, the core sample must be trimmed. The
portion of each core that is sufficiently consolidated such that it can
be trimmed and tested in the erosion apparatus is defined to be the
consolidated bed. The thickness of this portion defines the location of
the top of the settled bed. Soft, unconsolidated portions of each core
are assumed to be new deposits.
C. Properties of Stationary Suspensions (New'Deposits)
For cores with soft, unconsolidated sediment on top of the
consolidated (settled) portion, the following method must be used to
estimate the credibility characteristics of such new deposits. The new
deposit samples from the cores at all the stations should be mixed and
subjected to laboratory erosion and deposition tests (described by
Parchure (1980), Mehta and Partheniades (1973) and in Sections 2.6, 2.7
and 2.8) to determine: the settling velocity as a function of suspension
concentration and salinity (see Section 2.8.5), minimum and maximum
-------
depositional shear stresses, g. and ^ (Section 2.7), variation
of t/0 and * 2 '*itn tne bfid shear stress, 5D (Section 2.7), the number of
characteristic unconsoildated new deposit layers and the thickness, bulk
density and shear strength profile of each layer (Section 2.5), the
number of characteristic partially consolidated new deposit layers and
the thickness, bulk density, shear strength and the sediment parameters
eQ and a of each layer (Sections 2.5 and 2.6). The variation of the
bulk density and shear strength profiles with salinity should also be
determined by performing the erosion tests at the following salinities:
0, 1, 2, 5, 10, 20 and 35 ppt.
D. Fluid Composition
Samples of the pore fluid in the consolidated bed portion of one
core from each station should be collected. The pH, total salt
concentration, and concentrations of ions such as Ma*, Ca+2, Mg+2, K+,
Fe*3 and Cl~ should be determined for both the pore fluid samples and a
sample of the suspending fluid.
E. Composition and Cation Exchange Capacity of the Sediment
The sediment contained in the consolidated bed portion of one core
from each collection station should be thoroughly mixed so that a
spatially homogeneous sample is obtained* For each so-prepared sample a
standard hydrometer analysis should be conducted to determine the
sediment particle size distribution and thereby the percentage by weight
of clay, silt and fine to coarse sand in each sample. In preparing the-
samples for this analysis, the sediment should not be initially air-
dried (to obtain the dry weight of the material used in the test), as it
has been found that dried, sediment will not completely redisperse when
the dispersing agent is added (Krone, 1962). For this reason, the total
dry weight of the sample should be obtained from another portion of the
sample, and the corresponding value for the test sample-calculated
assuming that both portions have the same water content. The percentage
by'weight of organic matter should be determined through use of a method
such as the Walkley-Black test (Allison, 1965). In addition, X-ray
diffraction analysis of the bulk sample, and < 2 um unglycolated and
glycolated portions should be conducted in order to determine the
predominant clay and non-clay mineral constituents. The cation exchange
capacity roust be determined for each sample.
-------
APPENDIX C
Characterization of Factors
Involved in the Study of Erosion of
Fine Sediments
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1. Introduction
The properties and behavior of cohesive sediments have been found
to be quite different from those of non-cohesive sediments. Various
researchers have attempted to understand these characteristics through
laboratory experiments using a variety of apparatuses, techniques and
measurements. This research revealed that conventional parameters from
the field of soil mechanics, such as bulk density, vane shear strength,
liquid limit, plastic limit, etc. are not adequate for a fundamental
understanding. It has been shown that mineralogy of clays, chemistry of
water, and structure of the bed are important factors in the study of
erosion of cohesive sediment beds. In addition to obvious parameters
such as particle size, water content, void ratio, etc., new parameters
such as sodium adsorption ratio, dielectric constant and the cation
exchange capacity have been added and their influence clearly
demonstrated. However, due to the inadequate available knowledge on
this subject during the early stages of the research effort, some of the
parameters found to be important by one research worker were not
measured by other researchers and vice versa. This has posed the
following difficulties .in comparing and evaluating the results of
different research workers:
i) There is no consistency in the selection of parameters or indices
used to characterize the sediment, the bed structure or the
erosion process.
ii) Contradicting conclusions are offered, e.g. on the correlation of
bed density to the bed shear strength.
iii) Different notions prevail in describing the "critical" shear
stress.
iv) Size of the experimental apparatus, duration of tests and the
range of magnitudes of parameters have a wide variation.
v) Different views exist on the interpretation of data, e.g. on the
existence of a steady-state concentration and the exchange of
material between the bed and the water column.
The purpose of this appendix is to reveal the diversity of physico-
chemical parameters measured and experimental methods employed by
researchers fn investigating the erosive behavior of cohesive
sediments. This diversity greatly enhances the complexity of this
subject matter and makes the task of comparing the results of different
studies a difficult one*
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2. Procedure Followed for Laboratory Studies
The following procedure is generally adopted for laboratory
studies:
1) A sediment of Interest is selected. This may be a pure clay
mineral, a mixture of clay minerals, or a mixture of clay and
non-clay minerals. The sediment 1s described with the use of
certain characterizing Indices.
ii) Pore and eroding fluids of interest are selected and
characterized.
iii) A sediment bed is formed in the laboratory apparatus and is
characterized by suitable parameters. Several parameters/indices
are used to determine the effect of the pore and eroding fluid on
the structure of the bed. The bed formation/erosion processes
which occur in the field are shown 1n Fig. 1.4 whereas the
laboratory schematization of these processes is shown in Fig.
2.18.
iv) Erosion of bed is not directly measured. It is usually estimated
from the analysis of relevant data, such as change in suspension
concentration as a function of time, collected during the course
of the experiment. This approach is schematically depicted in
Fig. C.I.
3. Description of the Diversity in Laboratory Studies
Since there are few well-established parameters or indices to
characterize cohesive sediments, the fluid, bed structure or the rate of
erosion, a high degree of diversity exists in laboratory studies on each
of these factors. However, these studies can, in general, be classified
into one of the following seven categories:
1) Characterization of Sediment
2) Characterization of Pore Fluid and Eroding Fluid
3) Characterization of Bed Structure
4) Characterization of Coagulation and Settling
5) Characterization of ErodibiHty Index
6) Bed Shear Stress
7) Measure of Erosion
A list of parameters identified in each of the above seven areas is
given under Tables A through G. Each table is followed by references to
typical studies related to each parameter given in the table. These
references are listed in the same order and denoted by the same serial
number as the parameters, and are prefixed by the alphabet corresponding
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In "Bed
Pore Fluid
(Characterized by B*)
Bed Structure
(Characterized by C*)
Erodibility Index .
(Characterized by E*)
Erosion Rate
(Characterized by G*)
Sediment
(Characterized by A*)
Formation of Bed
(See Fig. 2.18)
Application of
Bed Shear Stress
(Characterized by F*)
In Suspension
Eroding Fluid
(Characterized by B*)
Coagulation and
and Settling
(Characterized by 0*)
*See Tables A, B, C* 0,
E, F, 6 for explanation
Fig. C.I: Diagramatic Representation of the Steps in the Study of Erosion
Rates of Fine Sediments.
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to the table. This tabulation has been carried out in order to organize
the large number of research topics on the erosive behavior of cohesive
sediments into a few relatively well-defined categories.
TABLE A: Characterization of Sediment
1. Type of Material
A. Clay Minerals
i) Clay mineral alone
ii) Mixture of clay minerals in varying proportions
iii) Mixture of clay-mineral and non-clayimineral, both in
the fine sediment range
B. Soils, Muds and Clay Material
i) Mixture of cohesive and non-cohesive {such as sand)
sediments
ii) Mixture of clay material and organic matter or organic
compounds
iii) Sediments from natural environment (unclassified)
iv) Sediments from natural environment (classified according
to Soil Classification System)
C. Non-sediment Fine Materials
2. Nature of Clay Structure
A. Electrical forces acting between particles
i) Net Energy of Attraction
it) Double Layer Thickness
8. Particle arrangement or fabric consisting of texture and
particle orientation
3. Particle Size Distribution
A. Median Diameter
8. Effective Size
C. Uniformity Coefficient
0. Curvature Coefficient
4. Cation Exchange Capacity
5. Exchangeable Sodium Percentage
6, Sodium Adsorption Ratio of Clay .
7. Dielectric Constant
8. Silica-sesquioxide Ratio
9. Chemical Composition
10. Specific Gravity
11. Hydration or Adsorbed Water
12. Antecedent Water
13. Aging
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Illustrative References for TABLE A
A.I. Type of Material
A.I.A. Clay Minerals and Mixtures
1. Kaolinite
Wt, Mohtmorillonite
»','# '.\V\r.n flour
if 0. II Mt.<-
flour
4. 40% Kaolinite
+60% Silica flour
,5. Grundite: 50% Illite + 50% Silt
6. English Kaolinite (finer than
Georgia Kaolinite (between 2\in and 8pm)
7. Sand-clay lamination
A. 1 . B . Soi 1 s , Muds and Cl ay Materi al
1. Iredell Sandy Clay Loam
Davidson Clay '
Putnam Soils
Bentonite
2. San Francisco Bay Mud
(Predominantly Montmorillonite and Illite)
3. Fernandina Bay Mud
4. Boston Blue Clay
5. Lake Francis Sediment
6. Lake Erie Sediment
7. Grangemouth Mud
8. Avonmouth Mud
9. Norwegian Marine Clays
10. Soils within the Australian Environment
11. Taylor Marl
12. Yolo Loam (Montmorillonite, Kaolinite,
Mica and Vermiculite)
13. Mare Island Strait Sediment
14. Belawan Mud
Taunton River Spoil
Thames River Spoil
Christensen S Das (1973)
Mehta & Partheniades (1973)
Yen (1979)
Parchure (1980)
Alizaden (1974)
Alizadeh (1974)
Alizaden (1974)
Christensen & Das (1973)
Raudkivi & Hutchison
(1974)
Terwindt et^VL (1968)
Lutz (1934)
Partheniades (1962)
Krone (1962)
Yen (1979)
Lambe (1958)
Parchure Jt_jj_. (1981)
Fukuda (1978)
Lee (1979)
Thorn & Parsons (1977)
Owen (1975)
Bjerrum (1954)
Aitchison (1956)
Espey (1963)
Arulanandan (1975)
Krone (1962)
Thorn A.Parsons (19flO)
Gularte et al. (1977)
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A.l.C. Non-Sediment Fine Minerals
1. Polyvinyl chloride
2. Silver iodide
A.2. Nature of Clay Structure
A.2.A. Electrical Forces
1. Bed shear strength as a function of
net energy of attraction
A.2.8. Particle Arrangement
1. Fabric of consolidated kaolinite
Particle orientation in clays
Fabric changes in kaolin
Structure of compacted clay
2.
3.
4.
5.
Importance of structure to the engineering
behavior of clay
6. Structure of compacted soils
7. Structure of clay
A.3. Particle Size Distribution
A.4. Cation Exchange Capacity
A.5. Exchangeable Sodium Percentage
A.6. Sodium Adsorption Ratio
A.7. Dielectric Constant
A.8. Silica-sesquioxide Ratio
A.9. Mineral Composition
A.10. Specific Gravity
A.11. Adsorbed Water
A.12. Antecedent Water
A.13. Aging
TABLE 8:
Bibeau X Matijevic (1973)
Vincent et._aU (1971)
Kandiah (1974)
Martin (1965)
Morgenstern & Tchalenko (1967)
McConnachi (1974)
Lambe (1958)
Mitchell (1956)
Pacey (1956)
Casagrande (1932)
Kranck (1981)
Kandiah (1974)
Kandiah (1974)
Gardner et__a_U (1959)
Kandiah (1974)
Kandiah (1974)
Alizadeh (1974)
Middleton (1930)
Bennett (1926)
Gibbs (1977)
Kranck (1981)
Lambe (1958)
Martin (1960)
Grissinger (1966)
Grissinger (1966)
Characterization of Pore Fluid
1. Type of Fluid
A. Distilled Water
B. double Distil led/Redistil led/Conductivity Water
C. Oeionized Water
0. Distilled Deionized Water
E. Reconstituted Water
F. Fresh Water
-------
G. Salt Water
H. Fluid other than Water
?. './»». iorr. and/or Anions Constitutinq Electrolyte, as represented by:
A. '.dl init.y of Fluid
B. Uilorinity of Fluid
C. Electrical Conductivity
0. Sodium Adsorption Ratio of the Fluid
E. Concentration of Electrolyte
F. Activity of Solute
G. Ion Valence
H. Anion Adsorption
I. Hydration Radius
3. pH
*
4. Temperature ' ••• .
5. Other chemicals
Illustrative References for TABLE B
B.I. Type of Fluid .
1. Salt Water
2. Distilled Water
3. Fresh Water
4. Reconstituted Water .
5. Distilled Oeionized Water
6. 0.1 M Solution of NaNoj
7. Carbon Tetrachloride
8.2. Electrolyte Ions
1. Electrolyte Concentration
2. Ion Valence
3. Dielectric Constant
4. Conductivity
5. Sodium Adsorption Ratio
6. Hydration Radius
7. Chlorinity
8. Salinity
8.3. pH :
B.4. Temperature
Partheniades (1962)
Mehta (1973)
Fukuda (1978)
Sheng and Lick (1979)
Parchure et_^i.. (1981)
Raudkivi & Hutchison (1974)
Raudkivi & Hutchison (1974)
Liou (1970)
Lambe (1958)
Gardner ^jj_. (1959)
Lambe (1958)
Lambe (1958)
Alizadeh (1974)
Kandiah (1974)
Miqniot (1968)
Kandiah (1974)
Lambe (1958)
Whitehouse_et.jl_. (1958)
Gularte (1978)
Kandiah (1974) ,
Lambe (1958)
Gularte (1978)
Christensen & Das (1973)
-------
8.5. Other Chemicals
Alkali Phosphates
Michaels (1957)
TABLE C: Characterization of Red Structure
Type of Bed: a) Placed (Remolded) Bed
b) Deposited Bed
c) Compacted Bed
Physical Properties
1. Water Content, also called
Moisture Content
2. Degree of Saturation
3. Swelling
4. Permeability, also called
Hydraulic Conductivity
5. Porosity
6. Void Ratio
7. Dry Density
8. Relative Density
9. Unit Weight, also called
Bulk Unit Weight
10. Dry Unit Weight which
is the same as Dry Density
11. Saturated Unit Weight
12. . Submerged Unit Weight
13. Volumetric Soil Solution
Content
14. Solids Volume Fraction
15. Water Volume Fraction
16i Equilibration Time/Aging
Soil Indices
1. Liquid Limit
2. Plastic Limit
3. Shrinkage Limit
4. Plasticity Index
5. Liquidity Index
6. Unconfined Compression
Strength
7. Consistency
8. Relative Consistency
9. Sensitivity
10. Thixotropy
11. Activity of Clay
12. Compressibility Coefficient
13. Compression Index
14. Group Index
15. Oiffusivity
16. Rate of Wetting Front Advance
17. Oilatancy
18. Dry Strength
19. Toughness
Used for
field
identification"
of soils
Illustrative References for TABLE C
Physical Properti es
1. Water Content
2. Solids Volume Fraction
3. Water Volume Fraction
4. Hydraulic Conductivity
5. Volumetric Soil Solution Ratio
6. Bed Density
7. Swelling
8. Aging
Lee (1979)
Kandiah (1974)
Kandiah (1974)
Dane0 & Klute (1977)
Dane & Klute (1977)
Thorn & Parsons (1980)
Kandiah (1974)
Grissinger (1966)
Soil
1. Density, Liquid Limit
2. Vane Shear Strength, Plasticity Index
3. Plasticity Index
..-rigs-
Carlson & Enger (1962)
Dunn (1959)
Smerdon & 8easly (1959)
-------
4. Shear Strength, Angle of Repose,
Specific 'Weights- of Fluid and
Particle Size
5. Unconfined Compression Strength
6. Oiffusivity of Water in Soil
7. Rate of Wetting Front Advance
Sundborg (1956)
Flaxman (1963)
Gardner et_±\_. (19&9)
Christenson & Ferguson (1966)
TABLE D; Characterization of Coagulation and Settling
.1. Settling Rate of sediment-water interface
2. Settling Velocity
3. Microscopic Observation
4. Change in the Order of Aggregation
5. Change in Permeability of Suspension
6. Degree of Coagulation
.11lustrative References for TABLE n
0.1. Settling Rate of Interface
D.2. Settling Velocity
0.3* Microscopic Observations
D.4. Order of Aggregation
0.5. Permea bi Ti ty of Su spension
D.6. Degree of Coagulation
Thorn & Parsons (1977)
Whitehouse etjil_. (1960)
Bowles (1969)
Krone (1978)
tutz (1934) r
Harris etal. (1966)
TABLE E: Erodibility Index
1. For Sediment Bed
A. Critical Shear Stress for surface erosion
B. Bulk Shear Strength/Vane Shear Strength
C. Floe Shear Strength at surface
0. Critical Shear Stress at which the rate of erosion changes from
"low" to "high"
E. Characteristic Shear Stress
F. Change in Concentraton of Suspension as a Function of Time
G. Dispersion Ratio
H. Erosion Ratio
I. Steady State Concentration
J. Limiting Flow Velocity
K. Erosion Factor
L. Erosion Index
-------
2. For Sediment Suspension (Colloid): Rheologic Properties
A. Bingham Shear Stress
8. Dynamic Viscosity of Fluid
C. Kinematic Viscosity of fluid
0. Viscosity of sediment suspension
E. Zeta Potential
Illustrative References for TABLE E
E.I. Erodibility Index for Sediment Beds
1. Critical Shear Stress
2. Bulk Shear Strentgh
3. Floe Shear Strength
4. Critical Shear Stress for Erosion Rate
5. Characteristic Shear Strength
6. Dispersion Ratio
7. Erosion Ratio
8. Limiting Flow Velocity
9. Erosion Index/Erosion Factor
E.2. Rheological Properties of Colloids
1. Rheological Properties of Estuarial
Sediments
2. Suspensions of Rigid Particles
3. Measurement of Bingham Shear Strength
of a Deep Marine Sediment
4. Viscosity
5. Zeta Potential
6. Particle Growth Rate
7. Colloidal Dispersion
Kandiah (1974)
Krone (1962)
Partheniades (1962)
Krone (1962)
Espey (1963)
Parchure (1980)
Middleton (1930)
Middleton (1930)
Miller (1960)
Dash (1968)
Krone (1963)
Jeffrey and Acrives (1976)
Das (1970)
Krone (1962)
Kandiah (1974)
Sugimoto (1978)
Zeichner and
: Schowalter (1977)
TABLE F: Bed Shear Stress
1. Method
A. Unidirectional flow in laboratory flume or in rotating cylinder
apparatus
B. Jet impinging on cohesive sediment bed.
C. Wave induced bed shear stress
2. Measure
A. Velocity of Flow
8. Velocity of Jet
C. Bed Shear Stress (tb)
0. Series of Bed Shear Stressas (t.
o
-200-
V'"\
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E. Shear Stress Ratio:
n-1
F. Excess Shear:
- T,.
G. Normalized Excess Bed Shear Stress (At)
Vc
ex
H. Equilibrium Bed Shear Stress, Tgq "" "c
Illustrative References for TABLE F
F.I. Method
1. Unidirectional flow in straight flume
2. Unidirectional flow in rotating circular
channel
3. Unidirectional flow in rotating cylinder
4- Submerged verti cal jet
. 5.';Wave induced shear
Krone (1962)
Yen (1979)
Espey (1963)
Moore & Masch (1962)
Tubman & Suh ayda '(1977)
F.2. Measure • '' '..;'
1. Velocity of .flow
2. Velocity of jet
3. Shear Stress Ratio
4. Excess Shear
5. Equilibrium Bed Shear
6. Series of Bed Shear Stresses
7. Normalized Excess Bed Shear Stress
B. Bed Shear Stress
TABLE G: Measure of Erosion
Type of Erosion
A. Surface Erosion
i) Flocculated Particles
ii) Deflocculated Particles
Mass Erosion ,
i) Flocculated Particles
ii) Oeflocculated Particles
B
Krone,(1962)
Dunn .(1959)
Parchure (1980) '
Thorn S Parsons (1977)
Thorn X Parsons (1977)
Parchure (19SO)
Thorn & Parsons (1980)
Parchure (1980)
Krone (1962)
Parthenfades (1962)
Yen (1979)
-20T-
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2. Method Used to Determine Erosion Rate
A. The rate of change of:
1) Suspension concentration (dC/dt)
11) bed elevation (dz/dt)
111) weight of sediment in bed (dw/dt)
8. Time required to reach Steady State Concentration (Cea)
C. Equilibrium depth of scour H
Illustrative References for TABL'E G
G.I. Type of Erosion
Surface Erosion Partheniades (1962)
Mass Erosion Yeh (1979)
G.2. Method Used to determine Erosion Rate
dC/dt . . . Partheniades (1962)
dz/dt ''••-..,. Thorn & Parsons (1977)
dw/dt <.' .-... Espey (1963)
where, C = concentration of sediment in suspension
z a elevation of sediment bed
w « weight of sediment in the bed
t "time
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