Title: Depositional behavior of cohesive sediments
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Title: Depositional behavior of cohesive sediments
Physical Description: xxii, 276 leaves. : illus. ; 28 cm.
Language: English
Creator: Mehta, Ashish Jayant
Publication Date: 1973
Copyright Date: 1973
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Subject: Sedimentation and deposition   ( lcsh )
Civil and Coastal Engineering thesis Ph. D   ( lcsh )
Dissertations, Academic -- Civil and Coastal Engineering -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
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Thesis: Thesis -- University of Florida.
Bibliography: Bibliography: leaves 272-275.
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00097584
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: alephbibnum - 000580671
oclc - 14071996
notis - ADA8776

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DEPOSITIONAL BEHAVIOR
OF
COHESIVE SEDIMENTS












By


ASHISH JAYANT MEHTA


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA
1973










ACKNOWLEDGMENT


The author wishes to express his sincere appreciation to

Dr. E. Partheniades, Chairman of his Supervisory Committee, for his

guidance and encouragement throughout the period during which the

present study was conducted. The author would like to thank the other

members of his committee: Dr. R. G. Dean and Dr. B. A. Christensen of

the Department of Civil and Coastal Engineering, and Dr. G. M. Griffin

of the Department of Geology, for their helpful suggestions and

assistance in clarifying various aspects of the subject matter.

Thanks are due to Professors R. P. Hoyer and Roger Nava of

the University of Zulia in Maracaibo, Venezuela, for their assistance

in providing sediment samples from the Maracaibo Channel. Sincere

thanks are also due to Dr. R. B. Krone of the Department of Civil

Engineering, University of California at Davis, for his help in

providing sediment samples from the San Francisco Bay.

Thanks go to the staff of Coastal Engineering Laboratory and

Mr. Peter Bush for help in installing the basic equipment. The

author would like to thank Mr. Bruce Ripy for doing the mineralogical

analysis of the sediments and Mr. Shailesh Bhende for drafting the

figures. Mrs. Karen Walker's patience in typing the dissertation is

especially acknowledged.

The author's deepest appreciation goes to his wife, Chetana,

without whose presence and support he would not have been able to

undertake the present work.

The present study has been conducted as a part of a major

research project entitled "Deposition of Fine Sediments in Turbulent











Flows," supported currently by the National Science Foundation under

Grant No. GK-31259. This support is sincerely and gratefully

acknowledged.


iii







TABLE OF CONTENTS



ACKNOWLEDGMENT..............................................

LIST OF FIGURES.............................................

NOMENCLATURE................................................

ABSTRACT.....................................................

CHAPTERS:

1. INTRODUCTION.......................................

1.1 Problem of Deposition.........................

1.2 Approaches to the Problem.....................

1.3 Nature of Fine Sediments......................

1.4 Present Study..................................

2. SCOPE OF PRESENT INVESTIGATION.....................

2.1 Properties of Fine Cohesive Sediments.........

2.1.1 Classification.........................

2.1.2 Composition..............................

2.1.3 Structural Aspects ....................

2.1.4 Interparticle Forces...................

2.1.5 The Double Layer.......................

2.1.6 Flocculation...........................

2.1.7 Cation Exchange Capacity...............

2.1.8 Origin and Occurrence of Clays.........

2.2 Review of Basic Investigations................

2.2.1 Erosion...............................

2.2.2 Deposition...............................

2.3 Objectives of Present Investigation...........








TABLE OF CONTENTS (Continued)


Page

3. EXPERIMENTAL EQUIPMENT AND PROCEDURE ............... 41

3.1 Experimental Equipment ........................ 41

3.1.1 Basic Apparatus........................ 41

3.1.2 Accessory Equipment.................... 49

3.1.3 Sedimentary Material................... 62

3.2 Experimental Procedure........................ 69

3.2.1 Calibration of Speed Controllers....... 69

3.2.2 Determination of Operational Speeds.... 70

3.2.3 Calibration of Equipment for Shear
Stress Measurements.................... 78

3.2.4 Calibration of Velocity Probes.......... 8

3.2.5 Preparation of Sediment Suspension..... 92

3.2.6 Sample Extraction and Concentration
Measurement.............................. 94

3.2.7 Procedure for Deposition Tests......... 95

4. RESULTS OF INVESTIGATION........................... 97

4.1 Preliminary Measurements ...................... 97

4.1.1 Indirect Bed Shear Stress Measurement.. 97

4.1.2 Direct Bed Shear Stress Measurement.... 100

4.1.3 Velocity Profiles..................... 102

4.2 Deposition Measurements ....................... 108

4.2.1 Degree of Deposition................... 108

4.2.2 Deposition Rates....................... 126

4.2.3 Comparison with Results of Other
Investigations......................... 172

4.2.4 Depth-Concentration Profiles........... 186









TABLE OF CONTENTS (Continued)


Page

4.3 Discussion of Results......................... 195

4.3.1 Near-bed Processes..................... 195

4.3.2 Nature of Equilibrium Concentration.... 204

4.3.3 Settling Velocities.................... 212

5. CONCLUSIONS AND RECOMMENDATIONS.................... 226

5.1 Summary and Conclusions....................... 226

5.2 Recommendations for Further Research.......... 232

APPENDICES .................................................. 238

A. BED DEPTH MEASUREMENT............................... 239

B. METHOD OF LEAST SQUARES FOR LINEAR RELATIONSHIPS
ON LOGARITHMIC-NORMAL PLOTS ........................ 243

C. ANALYSIS OF MARACAIBO SEDIMENT .................... 248

D. ANALYTIC FORMULATION OF DEPOSITIONAL PROCESS........ 256

E. APPLICATION OF RESULTS............................ 266

REFERENCES .................................................. 272

BIOGRAPHICAL SKETCH ......................................... 276









LIST OF FIGURES


Figure Pag

2.2.1 Depth-averaged Velocity u Versus Bed Shear Stress
Tb from Measurements of Partheniades ............... 30

3.1.1 Schematic Views of Annular Channel................ 42

3.1.2 Schematic Views of Annular Ring..................... 43

3.1.3 Schematic View of Annular Ring and Channel Assembly 45

3.1.4 Top View of Ring and Channel Assembly.............. 46

3.1.5 Steel Turntable.................. ................... 46

3.1.6 Height Adjustment Mechanism Including Radial Arm
and Blade Connections............................. 48

3.1.7 Support for Annular Plexiglass False Bottom......... 51

3.1.8 Brackets for Static Calibrations of Shear Stresses
on False Bottom and on Ring........................ 57

3.1.9 Annular Channel and Ring Assembly.................. 58

3.1.10 (a) Annular Channel with Ring in Operational
Position
(b) Annular False Bottom on Supports.............. 59

3.1.11 (a) Motors Driving Inner and Outer Shafts
(b) Housing for Experimental Equipment............ 60

3.1.12 Arrangement of Experimental Equipment............... 61

3.1.13 Particle Size Distributions of Fine Cohesive
Sediments.......................................... 63

3.1.14 X-ray Diffraction Pattern for Kaolinite for
Bulk Sample......................................... 64

3.1.15 X-ray Diffraction Pattern for Bay Mud for Less
than 62 Micron Fraction ............................ 67

3.1.16 X-ray Diffraction Pattern for Bay Mud for Less
than 2 Micron Fraction ............................... 68

3.2.1 Speed Calibration Curves for Ring and Channel...... 71

3.2.2 Secondary Cells in Ring-Channel System............. 72







LIST OF FIGURES (Continued)


Figure Page

3.2.3 Operational Speeds for Ring and Channel............. 79

3.2.4 (a) Location of Strain Gages
(b) Circuit for Strain Measurement................ 81

3.2.5 Schematic Representation of Resultant Moment on
Ring as Well as False Bottom....................... 84

3.2.6 Static Calibration of Ring.......................... 85

3.2.7 (a) Bending of Blade Supporting False Bottom
(b) Circuit for Measurement of Strain Produced
by Shear Stress on False Bottom............... 87

3.2.8 Static Calibration of False Bottom................. 89

3.2.9 Calibration Curves for 10 mm Velocity Probe......... 90

3.2.10 Calibration Curve for 4 mm Velocity Probe........... 93

4.1.1 (a) Ring Shear Stress T Versus Differential
r
Linear Velocity AV for Ring Only Rotating
(b) Ring Shear Stress T Versus Differential
Linear Velocity AV for Ring and Channel
Rotating Simultaneously ...................... 98

4.1.2 Direct and Indirect Measurement of Bed Shear Stress
Tb Versus Differential Linear Velocity AV.......... 101

4.1.3 Velocity Profiles for 6-1/4 in. Depth.............. 103

4.1.4 Velocity Profiles for 9 in. Depth ................. 104

4.1.5 Near-bed Velocity Profiles.......................... 106

4.1.6 Bed Shear Stress Tb as Function of Depth-
averaged Velocity u ............................... 109

4.2.1 Ratio C/C of Instantaneous to Initial Suspended
o
Concentration Versus Time t for Kaolinite in
Distilled Water.................................... 110

4.2.2 Ratio of Equilibrium to Initial Concentration
C q/C Versus Bed Shear Stress T .......r.......... 112
eq o b
4.2.3 Relative Equilibrium Concentration C in Percent
Against Bed Shear Stress Parameter Tb I.......... 113


viii






LIST OF FIGURES (Continued)


Figure Page

4.2.4 Relative Equilibrium Concentration C in Percent
eq
Versus Tb 1 for Three Different Suspensions...... 116

4.2.5 Relative Equilibrium Concentration Ceq in Percent
Against Bed Shear Stress Parameter
(Tb 1)/(Tb 1)50 ..................... ......... 117
*
4.2.6 Relationships Between Tbmin' (Tb 1)50 and rb50'.' 119

4.2.7 Relationships Between (r 1)50 Tbmin and Cation
Exchange Capacity (CEC) .......................... 123

4.2.8 Relationships Between (T 1)50 Tbmin and Cation
Exchange Capacity (CEC) ..................... ......... 125

4.2.9 Fraction of Depositable Sediment Concentration C
Deposited at Time t, in Percent, Versus Time
Parameter t/t50, for Kaolinite in Distilled Water.. 127

4.2.10 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 128

4.2.11 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 129

4.2.12 C in Percent Versus t/t0 for Kaolinite in
Distilled Water.................................... 130

4.2.13 C in Percent Versus t/t for Kaolinite in
Distilled Water................................... 131

4.2.14 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 132

4.2.15 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 133

4.2.16 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 134

4.2.17 C in Percent Versus t/thO for Kaolinite in
Distilled Water.................................... 135

4.2.18 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 136

4.2.19 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 137







LIST OF FIGURES (Continued)


Figure Pag(

4.2.20 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 138

4.2.21 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 139

4.2.22 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 140

4.2.23 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 141

4.2.24 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 142

4.2.25 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 143

4.2.26 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 144

4.2.27 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 145

4.2.28 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 149
*
4.2.29 C in Percent Versus t/t50 for Kaolinite in
Distilled Water.................................... 150

4.2.30 Fraction of Depositable Sediment Concentration
*
C Deposited at Time t, in Percent, Versus Time
t for Kaolinite in Distilled Water.................. 151

4.2.31 C in Percent Versus Time t for Kaolinite in
Distilled Water.................................... 152
*
4.2.32 C in Percent Versus Time t for Kaolinite in
Distilled Water.................................... 153
*
4.2.33 Log t5jand o2 Versus Tb for Kaolinite in Distilled
Water.............................................. 157

4.2.34 Log t50and 02 Versus Tb for Kaolinite in Distilled
Water.............................................. 158

4.2.35 Log t50 and 02 Versus Tb for Kaolinite in Distilled
Water.............................................. 159








LIST OF FIGURES (Continued)


Figure Page

4.2.36 Log t50and a2 Versus Tb for Kaolinite in Distilled
Water.......................................... ..... 160

4.2.37 Log t50and 02 Versus Tb for Kaolinite in Distilled
Water..... ....................................... 161

4.2.38 Log t50and 02 Versus Tb for Kaolinite in Distilled
Water............................................... 162

4.2.39 Fraction of Depositable Sediment Concentration
C Deposited at Time t, in Percent, Versus Time
Parameter t/t50 for Kaolinite in Salt Water......... 166

4.2.40 C in Percent Versus t/t50 for Kaolinite in
Salt Water......................................... 167

4.2.41 C in Percent Versus t/t50 for Kaolinite in
Salt Water......................................... 168

4.2.42 C in Percent Versus t/t50 for Kaolinite in
Salt Water......... ... .............. ............. 169

4.2.43 Log t50and 02 Versus Tb for Kaolinite in Salt Water 171

4.2.44 Fraction of Depositable Sediment Concentration C
Deposited at Time t, in Percent, Versus Time
Parameter t/t50 for Maracaibo Sediment............. 173

4.2.45 C in Percent Versus t/t50 for Maracaibo Sediment.. 174

4.2.46 C in Percent Versus t/t50 for Maracaibo Sediment.. 175

4.2.47 C in Percent Versus t/t50 for Maracaibo Sediment.. 176
*
4.2.48 Log t50 and o2 Versus Tb for Maracaibo Sediment..... 177
*
4.2.49 Fraction of Depositable Sediment Concentration C
Deposited at Time t, in Percent, Versus Time
Parameter t/t50 for Bay Mud........................ 179

4.2.50 C in Percent Versus t/t50 for Bay Mud.............. 180

4.2.51 Log t50and o2 Versus Tb for Bay Mud ............... 182

4.2.52 Fraction of Depositable Sediment Concentration C
Deposited at Time t, in Percent, Versus Time
Parameter t/t50 for Three Different Suspensions.... 183








LIST OF FIGURES (Continued)


Figure Page

4.2.53 Suspended Sediment Concentration C Versus Time t
for Three Different Suspensions.................... 184

4.2.54 Depth-Concentration Profiles Versus Time t for 2
Kaolinite in Distilled Water for Tb=2.95(dynes/cm ) 187

4.2.55 Depth-Concentration Profiles Versus Time t for 2
Kaolinite in Distilled Water for Tb=1.10(dynes/cm ) 189

4.2.56 Depth-Concentration Profiles at Equilibrium
Concentration ...................................... 192

4.2.57 Depth-Concentration Profile at Equilibrium
Concentration....................................... 193

4.3.1 Near-bed Effect of Shear Stress on Flocs............ 199

4.3.2 Probabilities of Erosion and Deposition for
Cohesive Sediments................................. 201

4.3.3 Finite Control Volume for Sediment Continuity in
Annular Channel...................................... 214

4.3.4 Apparent Settling Velocity W' Versus Time t
s
for Kaolinite in Distilled Water.................... 219

4.3.5 Apparent Settling Velocity W' Versus Time t
s
for Kaolinite in Distilled Water.................... 220

4.3.6 Apparent Settling Velocity W' Versus Time t
s
for Four Different Suspensions..................... 221

A.1 Measurement of Sediment Bed Depth Across Channel
Width .............................................. 240

A.2 Mean Bed Depth Versus Initial Concentration C ..... 241
o
C.1 Geographic Location of Maracaibo Channel........... 249

C.2 Particle Size Distributions of Sediment Samples
from Maracaibo Channel ............................. 250

C.3 X-ray Diffraction Pattern for Maracaibo
Sediment for Less than 62 Micron Fraction.......... 253

C.4 X-ray Diffraction Pattern for Maracaibo
Sediment for Less than 2 Micron Fraction........... 254









LIST OF FIGURES (Continued)

Figure Page

D.1 Sediment Continuity for an Elemental Volume......... 257

E.1 Periods of Erosion and Deposition in a Tidal Cycle. 267


xiii









NOMENCLATURE


a elevation of lowest sample tap

a' empirical coefficient in the exponential relation between

W' and time
s
A cross-section of idealized estuary

Sngstrbm unit

A area of ring as well as false bottom

A coefficient in the exponential solution for T

b annular channel width

B width of idealized estuary

C instantaneous suspended sediment concentration either with

respect to time of deposition or with respect to time scale

of turbulence

C' fluctuating component of sediment concentration

C1 constant of integration

C time-averaged component of sediment concentration

C suspended sediment concentration at y a

CD drag coefficient for drag exerted on a settling floc

CL lift coefficient

CR reference concentration in measurements of Etter and Hoyer

C initial suspended sediment concentration

C drag coefficient in near-bed zone

C equilibrium concentration
eq
C fraction of depositable concentration deposited at time t
**
C fraction of depositable concentration in suspension at time t
** **
C1 value of C at time t

C relative equilibrium concentration
eq







**
C degree of deposition
eq
d depth of flow measured from channel bottom

d' depth of flow measured from bed surface

d floc diameter
s
DL dispersion coefficient

f(Tb) function of Tb

F gage factor

F" cohesive force at sediment bed

g acceleration due to gravity

k coefficient of frictional resistance

k1 depth from channel bottom to y = C

k2 coefficient relating depth-averaged concentration to near-

bed concentration

k bed roughness
s
K dimensionless parameter in relation between W and d
s s

K empirical coefficient in Krone's measurement

K2 coefficient in Krone's measurements

K coefficient in measurements of Etter and Hoyer

basal order of diffraction

b near-bed zone thickness

L instantaneous lift force

L' fluctuating component of lift force

L time-averaged component of lift force

L length of an element before application of stress

L lower limit for fluctuation of L

L upper limit for fluctuation of L

m empirical coefficient in the exponential relation between

W and time
s








m' coefficient in hypergeometric equation

M mean of a normal distribution

n number of data points or estuarial segments

n' coefficient in hypergeometric equation

p pressure in fluid

p cumulative probability

Pi pressure at inner wall of annular channel

P2 pressure at outer wall of annular channel

p probability of erosion

pd probability of deposition
P probability

P cumulative probability for normal distribution

P measured cumulative probability

P computed cumulative probability for normal distribution

q' coefficient in hypergeometric equation

r radial distance

r' radius of largest idealized spherical floc

rl radius of the inner wall of annular channel

r2 radius of the outer wall of annular channel

R resistance

R source or sink term

Rd sink term in diffusion equation

Re source term in diffusion equation

t time after beginning of deposition

t50 geometric mean of the plot of C versus t

tl value of time beyond which W' decreases exponentially with
sti
time








T upper integral limit in the logarithmic-normal distribution

of C versus t/tO5

T1 tidal period

T t-dependent solution of diffusion equation

u flow velocity corresponding to x or 6 coordinate

U* friction velocity

u' fluctuating component of u

u time-mean component of u

u depth-averaged flow velocity

u velocity measured by propeller probe
p
ut instantaneous velocity above a floe

v flow velocity in y direction

v' fluctuating component of v

v time-mean component of v

w dummy variable

W buoyant weight of floc

W metric weight

W terminal settling velocity of floe

W' apparent settling velocity of floe
s
x coordinate in the direction of flow

x' independent variable in hypergeometric equation

x" logarithmic-normally distributed variable

x"0 geometric mean of x"

x normally distributed variable

y vertical coordinate

Yo virtual origin of logarithmic velocity profile


xvii









Ya upper integral limit in the logarithmic-normal distribution
*
of Ceq versus (rb 1)

Ym a particular value of y coordinate
Y y-dependent solution of diffusion equation

z coordinate transverse to the flow



Greek Letters

a constant of integration

a coefficient relating Ib to d

a" area shape factor

a2 volume shape factor

a3 coefficient in the expression for W'
S

y specific weight of water

Y6 specific weight of floc

6 laminar boundary layer thickness

A dimensionless laminar boundary layer thickness

AL change in the element of length L

AM small increment in M

Ap pressure difference p2 p1 between outer and inner walls

of annular channel

Ar difference in radii r2 rl between outer and inner walls

of annular channel

AR small change in resistance R
Ar' thickness of floc surface roughness
At small time interval

AV linear differential velocity between ring and channel

Ax control volume dimension in flow direction


xviii









Ao small increment in o

Vertical eddy diffusivity independent of y

C eddy diffusivity in x direction

C eddy diffusivity in y direction

z eddy diffusivity in z direction

n ratio of L' to L

n' water surface elevation in idealized estuary

nd limit of n for probability of deposition

ne limit of n for probability of erosion

o angular polar coordinate

K Karman constant

U micron

v kinematic viscosity of water

C finite control volume boundary elevation above bed surface

P density of water

p' density of suspension

o standard deviation of a logarithmic-normal distribution

o' applied stress

01 standard deviation of the logarithmic-normal relationship
*
between Ceq and (T 1)

02 standard deviation of logarithmic-normal relationship

between C and t

T shear stress at the boundary of the laminar flow field in

Krone's experiments

Tb mean bed shear stress

Tbi instantaneous bed shear stress



xix









Tbe critical shear stress for erosion in experiments of

Partheniades

Tbf bed shear stress measured by false bottom

Tbmax maximum bed shear stress corresponding to near-complete

suspension of sediment

Tbmin minimum bed shear stress below which entire suspended

sediment eventually deposits

Tbf bed shear stress measured by velocity probe

T dimensionless bed shear stress Tb/bmin
b b bmin
T critical bed shear stress for deposition according to Krone

Tch mean shear stress on channel boundaries

Ti local instantaneous shear stress

max floc shear strength

T ring shear stress

(rb )50 geometric mean of the logarithmic-normal relationship
*
between Ceq and (Tb 1)

)(n) frequency distribution

I flow velocity in z direction

m' fluctuating component of w

w time-mean component of w

S angular velocity

Q angular velocity of ring or channel

Pm angular velocity at y = ym
m











Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy



DEPOSITIONAL BEHAVIOR
OF
COHESIVE SEDIMENTS


By


Ashish Jayant Mehta

March, 1973

Chairman: Professor Emmanuel Partheniades
Major Department: Civil and Coastal Engineering


The depositional properties of flocculated fine cohesive

sediments in a turbulent flow field have been investigated. The

experiments have been conducted in a special apparatus consisting of

a system of an annular channel containing the sediment suspension, and

an annular ring positioned within the channel, and in contact with

the water surface. A simultaneous rotation of the two components

in opposite directions and at properly selected speeds eliminates the

secondary currents and generates a uniform turbulent flow field free

from any floc-disrupting elements.

For a given suspension and flow condition, the time-concentration

relationship indicates an initial period of deposition, after which the

suspended sediment concentration reaches a steady state value, Ceq,

defined as equilibrium concentration. It is found that the ratio

C = C /C where C is the sediment concentration at the beginning

of deposition, varies solely with the bed sheer stress, Tb. This










** *
variation of Ceq with Tb' and consequently of C = 1 Ceq defined

as the degree of deposition, is according to a logarithmic-normal

law. It is further found that the degree of deposition, for any given

suspension, is characterized by the minimum bed shear stress, Tbmin'

below which C is zero, i.e., below which the entire amount of initially
eq
suspended sediment eventually deposits. Finally, it is shown that

when the ambient water quality is constant, the cation exchange

capacity of the sediment, which is representative of the physico-

chemical properties of the sediment, correlates with Tbmin' and

therefore ultimately characterizes the degree of deposition.

A law describing the rates of deposition has been obtained.

This law gives the deposited fraction of the depositable portion of

the sediment as a logarithmic-normal function of time. For a given

suspension, the standard deviation and the mean of this functional

relationship are found to depend on the bed shear stress Tb, depth of

flow, and initial concentration, C Using a sediment continuity
o
principle, it is further shown that the apparent settling velocities

of the flocs also depend on the same parameters.

Reanalyzed data on the deposition of sediments from the

San Francisco Bay and the Maracaibo estuary in Venezuela indicate a

good agreement with the results derived from measurements in the

annular apparatus.


xxii









CHAPTER 1

INTRODUCTION


1.1 Problem of Deposition


In recent years the investigation of fundamental laws

governing the transport of fine cohesive sediments has been

emphasized, as a result of the need to control erosion and

shoaling of such material in rivers, canals, harbors and navigable

waterways. Shoaling due to deposition of fine grained sediments is espe-

cially an important problem in estuaries and estuarine channels,

where the presence of relatively high salinity and low flow velocities

results in the settlement of flocculated sediments carried by the flow.

The sediment may be derived from upstream river sources, or it may be

brought into the estuary from the ocean entrance by upstream saline

currents near the channel bottom (Partheniades, 1971).

When the sediment load is heavy, dredging becomes a necessary

albeit expensive operation. For example, the dredging maintenance of

harbors and navigable channels within the San Francisco Bay alone

amounts to an annual expenditure of more than two million dollars

(Krone, 1962). According to the Corps of Engineers, U. S. Army

(1963), the total volume of sediment dredged annually from major

harbors and tidal waterways in the United States is well over fifty

million cubic yards at a total cost well in excess of thirteen million

dollars. The maintenance of major estuarial waterways in other

countries amounts to similar figures in terms of sediment volume and

expenditure. For instance, about thirteen million cubic yards of wet












mud aredredged annually from the navigable channel in the Maracaibo

estuary in Venezuela at a cost exceeding five million dollars

(Partheniades, 1966), and an estimated volume of three million cubic

yards is dredged from the Thames River estuary in England (Partheniades,

1964).

Often, the presence of fine sediments in flows has a beneficial

rather than an adverse effect. For example, according to the Task

Committee on Preparation of Sediment Manual, Committee on Sedimentation

of the Hydraulics Division (1972), fine sediment carried in some

irrigation water is beneficial in sealing the canal or lateral, and if

carried through the canal, may contribute to the improvement of the

fertility of the croplands. For instance in countries like India,

sediments rich in organic matter derived from river floods have

maintained the productive fertility of the fields for centuries. It is

noteworthy that in such a situation, the problem is one of keeping the

sediment from shoaling, even at the lowest flow velocities, so that

the canals themselves do not get clogged, and yet are able to carry the

sediment through.

Recently, Krone (1966) has shown that suspended sediment

affects the growth of certain photosensitive algae in estuaries. He

found that the growth of these algae is inhibited by insufficient light

penetration. Thus, water free of sediment permits a different pattern

of light absorption in water, and will produce a different environment

for algae, than the same estuary carrying a suspended sediment load.

For this problem, therefore, the control of suspended sediment load

is of considerable interest.












1.2 Approaches to the Problem


In contrast to the more basic approach pursued in recent

times, earlier studies since early nineteenth century, which were

based on a large number of field and laboratory measurements, attempted

to derive empirical expressions related to the erosion and deposition

of sediments for designing of stable channels. These studies have

been well summarized by Leliavsky (1959). The obvious disadvantages of

using such expressions is that they provide no information on the

mechanics of the physical processes involved, and therefore are of a

limited utility, since they can only be used for conditions similar

to the ones on which they themselves are based.

The desirability of relating sediment transport to flow

parameters and sediment characteristics has led to fundamental studies

on the hydrodynamic interaction of flow and sediment, mainly in the

past three decades. Based on phenomenological theories of turbulence,

semitheoretical expressions have been developed, supplemented by

some experimentally estimated "universal" constants. One of the well-

known and widely accepted theories is the bed load function theory

formulated by Einstein (1950). For such theories, although a dependence

on empirical data is unavoidable because of the complexity of sediment

transport, the fundamental functional relationships between the

variables involved are based on the laws of mechanics, the empirical

information being used only for the evaluation of certain constants in

these relationships. Unfortunately, the applicability of these theories

is generally limited to granular cohensionless beds consisting of sand

and gravel, and for alluvial channels in equilibrium.











1.3 Nature of Fine Sediments

The predominant constituents of fine cohesive sediments are silt

and clay, with particles ranging in size from a minute fraction of a

micron up to several microns. In contrast to a cohesionless or coarse

sediment, a basic characteristic of a fine sediment is that the effect

of interparticle physicochemical forces is much more important in

controlling its hydrodynamic behavior than the submerged weights of

its individual particles. Some of these forces are attractive, while

others are of a repulsive nature. Their resultant effect is either

repulsive or attractive depending on the types of ions adsorbed on the

particle surface and also on the ions in the ambient aquatic medium.

When the net forces are repulsive, the particles remain in a dispersed

or peptized state (van Olphen, 1963), so that the finer particles may

indefinitely remain in a state of suspension either due to a slight

turbulence, or even due to Brownian motion. On the other hand, when

the net interparticle forces are attractive, the particles tend to

aggregate themselves into flocs, whose dimensions, and consequently

settling velocities, often are orders of magnitude higher than those

of the individual particles. This phenomenon of flocculation is the

primary cause of shoaling in estuaries (Partheniades, 1971). An

investigation of the depositional behavior of fine cohesive sediment is

essentially therefore a study of the settling properties of sediment

flocs.

In a flocculated suspension, where a floc rather than an

individual particle is the settling unit, the floc size distribution is

contingent not only upon the physicochemical properties of the sediment,












but also on the flow conditions themselves. This is the main cause of

the relatively much more complex depositional behavior of cohesive

sediments as compared to that of cohesionless sediments. This fact often

has not been recognized by some investigators. For example, Owen (1971)

attempted to observe the effect of turbulence on the settling velocities

of suspended floes, from samples of flocculated suspensions collected

in a special instrument at various locations in the Thames estuary.

The collecting apparatus essentially consisted of a tube pivotted near

its center, and so balanced that it could remain horizontal in water

and hang vertically in air. Samples were collected by automatically

closing the ends of the tube while in water. It was then pulled out

of water and the settling velocities were measured in the vertically held

tube by the conventional method of sample withdrawal at various times.

Owen found that the settling velocities thus obtained were up to ten

times greater than if the same suspension were tested in the laboratory

by standard methods. The results of tests using such an instrument

however are questionable, since the floc characteristics strongly

depend on the flow conditions. Therefore observing the settling of

flocs under quiescent conditions in the tube, even almost immediately

after they have been removed from the turbulent flow field, is not

likely to produce comparable results.

The dearth of sufficient knowledge on the settling behavior

of flocs of fine cohesive sediments has been a limiting factor in its

application to transport processes. For example, Gole, Tarapore and

Brahme (1971) have developed an interesting method for predicting the

siltation load in harbor channels, based on a sediment continuity











principle. However, it is noteworthy that since the continuity equation

involves the settling velocities of flocs, and since these were not

known as functions of the flow parameters, they had to be computed for

quiescent conditions, and for certain estimates of the floc diameter.

Such approximations often tend to attenuate the validity of the results.

Shubinski and Krone (1970) have proposed a commendable matt

matical model to predict suspended sediment concentrations in

estuarine systems. In the model, they have used an empirical law of

deposition derived from measurements by Krone (1962). Results of the

present experimental analysis have indicated, however, that Krone's

measurements may have a limited applicability. The work of Harrison

and Owen (1971), in which an expression for computing the rate of

siltation in a channel across an estuary is developed, is also limited

by the use of the same law of deposition obtained by Krone.


1.4 Present Study

In a deposition study, it is necessary to identify both the

flow variables as well as the physicochemical parameters that determine

the behavior of cohesive sediments. Using a given type of fine sediment

in a water of given quality, the physicochemical properties of the

sediment suspension may be kept constant, so that the depositional

behavior of the sediment can be related to identifiable flow variables.

Then, using different sediment types, and also varying the water

quality, these flow variables can be correlated with parameters that

represent the physicochemical properties of the various suspensions

tested. A study of this nature is described and discussed in the











present experimental work, which utilizes a specially designed annular

rotating channel to measure the rates of deposition of various

cohesive sediment suspensions. The subject matter is presented in the

following sequence.

Chapter 2 begins with background information on the physico-

chemical and mineralogical aspects of fine sediments. There, the

important process of flocculation is also discussed. Previous investiga-

tions on erosion and deposition are next described, and lastly, the

objectives of the present investigation are stated.

In Chapter 3, the annular rotating apparatus is described along

with accessory equipment, followed by procedures for the measurements

and calibration of the equipment.

In Chapter 4, the results of the investigation are described

and discussed in detail. Comparison with measurements of other

investigations is also included therein.

Chapter 5 summarizes the conclusions derived from the results.

Some suggestions for related future research are also presented.

Finally, in Appendices A through E, material which is

supplementary to the main subject matter is included.











CHAPTER 2

SCOPE OF PRESENT INVESTIGATION


2.1 Properties of Fine Cohesive Sediments


2.1.1 Classification

Fine cohesive sediment particles essentially have high specific

surface areas (surface area per unit weight) in comparison with the

relatively larger cohesionless particles such as sand, and tend to

exhibit cohesion, or tendency to stick together, by virtue of the

physicochemical surface forces which exist between them. For example,

a quartz sphere of 1 mm diameter has a specific surface area of nearly

0.0023 m2/gm, whereas van Olphen (1963) has calculated the specific

surface area of a sodium substituted montmorillonite to be approximately

750 m2/gm. As a consequence of these large specific surface areas,

the physicochemical forces acting on the fine particle surfaces are

often orders of magnitude higher than the gravitational forces, as

indicated by Terzaghi and Peck (1967). If, for instance, a cube of

quartz with a volume of 1 cm were subdivided into smaller ones with

sides of 1 micron, then the ratio of gravitational force to the
-4
physicochemical force would decrease by a factor of 10 These

surface forces therefore largely determine many of the properties of

the fine sediments.

The nature of these physicochemical forces depends on many

factors, important among which are particle size, shape, and the

crystal-chemical nature of the material itself. As a result, any

classification of a fine sediment in terms of one of these factors

alone is not sufficient to describe all the properties of the sediment.











The most common method of classification used by engineers and

geologists is based on particle size, and although by no means completely

descriptive, it is adequate for a preliminary or a general description.

In Fig. 3.1.13, the size distributions of the three different

types of cohesive sediments shown are classified according to the M.I.T.

system of classification (Terzaghi and Peck, 1967). In general,

particles in silt and clay size range are expected to exhibit cohesion,

with the degree of cohesion depending among other factors, on the type

of the sedimentary material.


2.1.2 Composition

A cohesive sediment may be termed clay material, which according

to Grim (1968) is "any fine grained, natural, earthy argillaceous

material." Clay material itself contains clay minerals and non-clay

minerals. While the non-clay minerals include substances such as

calcite, dolomite, large flakes of mica, pyrite, feldspar, gibbsite

and others, the term clay minerals refers specifically to a certain

small number of hydrous aluminum silicates called clays in general, which

are largely present in size fractions smaller than 1 or 2 microns. Now

in the M.I.T. classification, the size range less than 2 microns is

referred to as clay fraction. However, from a mineralogical point of

view, this size range contains both clay minerals as well as non-

clay minerals, the latter also being present in sizes less than 2

microns. For example, many clay materials contain extremely fine iron

oxide or hydroxide, which acts as a pigment.

In addition to clay and non-clay minerals, clay materials often










contain varying amounts of organic matter. In general, organic matter

occurs in clay materials in several ways. For instance, it may be

present as discrete particles of wood, leaf matter, spores, etc.

It may also be present as organic molecules on the surface of the clay

mineral particles, or it may be intercalated between layers of clay

minerals. The discrete particles may be present in any size from

large visible chunks, to particles of colloidal size which act as

pigments. These pigments often tend to impart a greyish or black

appearance to the sediment.

Clay materials often contain water-soluble salts, such as

chlorides and sulfates of alkalies and alkaline earths, which may

have been entrained at the time of accumulation, or may have developed

subsequently as a consequence of geological weathering and other altera-

tion processes. Exchangeable cations and anions are also present on the

clay particle surfaces in an adsorbed state.

In addition to the above, cohesive sediments dredged from rivers

and estuaries may contain small and large shells, woody remains, a

host of industrial and other pollutants, and different kinds of

bacteria and other forms of organisms.


2.1.3 Structural Aspects


Essentially, clay minerals are hydrous silicates of aluminum

and/or iron and magnesium. Structurally, there are two fundamental

building units for the crystalline clay structure (Grim, 1968).

One is a silica tetrahedral unit. It consists of four oxygens

in a tetrahedral configuration enclosing a silicon atom. The tetrahedra










are combined in a sheet structure so that the oxygens of the bases of

the tetrahedra are in a common plane, and each oxygen is shared by

two tetrahedra.

The second is an octahedral unit. It consists of four oxygen

atoms plus two hydroxyl (OH) groups in an octahedral configuration

enclosing an aluminum, iron or magnesium cation. The octahedral units

are combined into a sheet structure with each anion shared by two units.

The sheet may be viewed as two layers of densely packed oxygens and/or

hydroxyls, with the cation in octahedral coordination.

The above two units combine to give several types of clay

minerals, of which three basic types important to the present

investigation are described below.

a. Kaolinite: Its structural unit is composed of an aluminum

octahedral layer with a superimposed inverted tetrahedral layer such

that the tips of the tetrahedra and one of the hydroxyl layers of the

octahedral sheet form a common plane. Successive structural units are

held together by van der Waals attractive forces. Inasmuch as the

individual units are nearly neutral electrically, it is difficult for

water molecules or cations to penetrate between the units. Kaolinite

particles have plate-like forms with well-defined hexagonal boundaries.

b. Montmorillonite: The structural unit is made up of two

tetrahedral layers with their tips pointing towards each other, and

with an octahedral sheet in between. The oxygens of the tetrahedral

tips are shared with the oxygens of the octahedral layer, so that the

three layers form a single structural unit. Part of the silicon of

the tetrahedral layer is typically replaced by aluminum or other cations

of lower valence, and also, part of the aluminum of the octahedral layer is











typically substituted by magnesium. As a consequence, the unit assumes a net

negative charge, which results in the attraction of exchangeable cations

(exchange cations) between the units. The ion-dipole bond that results

holds the negative dipolar units together but rather weakly; therefore,

water molecules dipoless) can penetrate between the units in addition

to the exchangeable cations, leading to the well-known swelling

properties characteristic of montmorillonite.

Electron micrographs of montmorillonite show broad undulating

mosaic sheets that when disturbed and dispersed break easily into

irregular fluffy masses of extremely small often flake-like particles.

c. Illite: The structural unit is similar to that of mont-

morillonite, except that there is a significantly greater substitution

of silicon by lower valence cations, especially aluminum. This

substitution leaves a net negative charge deficiency within the

structural lattice that is considerably greater than montmorillonite.

This charge is almost always compensated by the potassium ion, which

fits into the structural cavity of the oxygen rings almost perfectly.

This ion is relatively firmly intercalated in the basal planes

between the units, forming a bond that resists the intrusion of

water molecules and other exchangeable ions between the units. As

a result, the mineral does not swell measurably.

Electron micrographs of illite show small, poorly defined flakes

commonly grouped together in irregular aggregates.

Some of the clay minerals not mentioned above include dickite,

nacrite and anauxite, which are similar to kaolinite. It

should be noted that montmorillonite is in fact a name given to the











most important member of a group of clay minerals referred to lately

by the name of smectites (Grim, 1968). Two other important members

are nontronite (iron substituted) and saponite (magnesium substituted).

Illite has several polymorphic forms. Halloysite, chlorite and vermicu-

lite are also relatively important clay minerals. They are essentially

made up of the same two basic tetrahedral and octahedral units. Sepiolite,

palygorskite and attapulgite minerals are fibrous in nature and are

structurally distinct from the above described minerals. They are also

relatively less abundant. Finally, in nature one finds a range of

certain mixed layer minerals which consist of ordered to disordered

stacks comprised of two or more of the above described minerals

together.


2.1.4 Interparticle Forces


Two types of interparticle forces which are important in the

phenomenon of flocculation to be discussed in Section 2.1.6 are described

in the sequel.

a. van der Waals Forces: The attractive force between fine

particles is attributed to the van der Waals electrochemical attraction

forces between all atoms of one particle and all atoms of another

particle. The total attractive force between the particles is the

sum of the forces between all atom pairs, and the magnitude of this

total force depends on the size and shape of the particle, but does not

depend on the ambient water quality or its salt content (van Olphen,

1963). These forces are strong at short range, but fall inversely

with the seventh power of separation for small spheres, and with the

square or cube of the distance for parallel plates.










b. Electric Surface Forces: There are a number of attractive,

and particularly repulsive forces generated by electric charges on

the particles. The following two causes of the presence of these

charges are of interest.

Imperfections within the interior of the crystal lattice may

be the cause of a net positive or net negative lattice charge. More

commonly, as in clay suspensions in water, the net particle charge

is created by the preferential adsorption of certain specific ions

on the particle surface. The magnitude of the total charge on a

particle of course depends on the type of adsorbing material as well

as on the availability of certain ions in the ambient medium. Such

ions are called peptizing ions (van Olphen, 1963).


2.1.5 The Double Layer


Whatever the origin of the surface electric charges, any

charged particle in an ion containing aquatic medium will attract

ions of opposite charges called counter-ions, to compensate its own

electric charge. At the same time, the counter-ions tend to diffuse

away from the particle surface because of their thermal activity, since

such a diffusion takes place from a zone of high ionic concentration

to one of lower ionic concentration. Thus, a clay particle idealized

by a thin plate will be surrounded on either side by a diffused layer

of counter-ions, whose positions will be determined by the balance

between their electrostatic attraction and thermal activity. This

layer known as "double layer" and the particle together are electrically

neutral. This double layer significantly determines the properties

of clays in suspension.












2.1.6 Flocculation

Flocculation, or aggregation of fine sediments in saline waters,

is a well-known phenomenon. The importance of flocculation to estuarial

sediment transport lies in the associated changes in the character of

the suspended particles. These changes strongly affect the transport

of the suspended sediment itself.

Flocculation of sediment particles occurs as a result of

cohesion between particles brought sufficiently close together, and

for this to happen, particle collisions are essential. Collisions

themselves are caused by Brownian motion of the suspended particles,

by the shear flow and by the differential settling velocities of the

suspended particles or flocs (Krone, 1962). Now cohesion results from

the predominance of attractive van der Waals forces. These forces

are strong at short range, but as was mentioned in Section 2.1.4, they

decay rapidly with distance. Thus, whether colliding particles cohere

depends on whether the short range attractive forces dominate the

repulsive electric forces created by the double layer of counter-ions.

Ordinarily, when no salt is present, a sediment suspension remains in

a dispersed or peptized state because, under such a condition, the

influence of the repulsive forces extends beyond that at which the

attractive forces are significant. .In this case, the double layer of

counter-ions surrounding each particle is in a given state of equilibrium,

due to the attractive particle surface forces, and the opposing tendency

of the counter-ions to diffuse away from their high concentration near

the particle surface. However, when salt is added to the suspension,

the increase in the ambient medium of the concentration of ions with










charge of the same sign as that on the counter-ions, results in a

reduction in the diffusive tendency of the counter-ions, since this

tendency decreases with decreasing magnitude of the counter-ionic

concentration gradient. As a consequence, a new state of equilibrium

is established, with the double layer closer to the particle surface.

If the amount of salt added is sufficient, the thickness of the double

layer will be depressed to an extent such that the attractive forces

will prevail over a longer distance compared to the repulsive forces,

causing a cohesion of particles, when they are brought sufficiently

close together by collisions.

In estuarial waters, the kinds of dissolved salts present are

determined largely by the composition of ocean water, and only at high

river flows the composition of the river water is of significance.

Since the relative abundance of the constituent salts is nearly constant,

the variables affecting flocculation are the salt concentration and the

mineral type. For example, in the San Francisco Bay, where the minerals

appear to be well-mixed, flocculation of Bay mud depends only on

salinity (Krone, 1962).


2.1.7 Cation Exchange Capacity

Clay minerals have the property of adsorbing certain anions

and cations and retaining them in an exchangeable state, i.e., these

ions are exchangeable for other anions or cations by treatment with

such ions in a water solution. This exchange capacity is determined

under neutral conditions (pH 7) in terms of milliequivalents per

hundred grams of the clay mineral. Thus,for example, one equivalent











of Na expressed as Na20 would be a combining weight of 31, and 1 milli-

equivalent per hundred gram would be equal to 0.031% Na20 (Grim, 1968).

The cation exchange capacity (CEC) is an important property of

clay minerals, and in a cohesive sediment it is largely restricted to

the clay size fraction. As such it depends on the mineral type

and is independent of the ambient medium. There are three causes of

the CEC, which are discussed below.

a. Broken bonds around the edges of the clay-structural unit

give rise to unsatisfied charges, which are balanced by adsorbed

cations. These broken bonds tend to be on the edges rather than

cleavage planes of the particles, and they are the primary cause of

CEC in kaolinite and illite minerals.

b. Substitutions in the lattice structure result in unbalanced

charges. Exchangeable cations resulting from lattice substitutions

are found mostly on the basal cleavage planes of the clay minerals.

Thus, in smectites, for example, 80% of the CEC results from this cause.

c. The hydrogens of the exposed hydroxyls in the structure

may be replaced by exchangeable cations.

The CEC of a mineral strongly depends on its chemical pretreat-

ment. Particle size and temperature also affect the CEC. Such

materials as iron oxide and sulfur compounds tend to cover the sites to

be occupied by exchangeable ions and thereby reduce the CEC.


2.1.8 Origin and Occurrence of Clays

Clays are formed from rock-forming material by weathering and

other geological alteration processes. The type of clay formed depends











on the parent rock material, but also depends to a significant extent

on the conditions under which alteration takes place. Thus, for

example, an acidic environment is conducive to the formation of

kaolinite. Another important factor is the presence or absence of

certain ions. If, for instance, alkali, alkaline earths and calcium

are absent, kaolinite will be formed. This happens,for example,under

conditions of heavy rainfall and sufficient capacity for the soil to

allow a downward percolation of the water and the salts, thus leaching

the soil of ions. The presence of such ions as iron and magnesium

favors the formation of smectites, while if potassium is present,

illite is the result.

On the surface of earth, kaolinite, smectites, illites and

chlorites are abundant clay minerals, followed by halloysite and

vermiculite, while sepiolite, palygorskite and attapulgite minerals

are comparatively rare.


2.2 Review of Basic Investigations

2.2.1 Erosion


An extensive literature review of empirical measurements,

field studies and laboratory research on the erosion of cohesive soils

is made by Partheniades (1971). Only the basic research aspect, which

is within the scope of the present study, is briefly reviewed here.

Fundamental laboratory research has been concentrated on two

classes of cohesive soils, namely medium to high strength consolidated

clays, and soft cohesive soils ranging from freshly deposited mud to

low strength older deposits.











a. Erosion of consolidated and compacted clays: Dunn (1959)

tried to experimentally correlate the shear strength of different clays

measured with a vane shear test apparatus, and the measured critical

tractive force. This tractive force was created by a water jet

impinging on the bottom of a container, part of which was occupied by

the surface of a clay sample. The critical point was arbitrarily

defined as the shear stress which caused erosion to cloud the water

carried to the surface continuously.

Smerdon and Beasley (1959) tried to correlate the tractive

force at failure with plasticity index, dispersion ratio and mean

particle size, using an open flume. The point of bed failure was

arbitrarily defined as "the tractive force at which the bed material

was in general movement."

Moore and Masch (1962) and Epsey (1963) also attempted to

devise a small-scale testing apparatus for determining the scouring

resistance of cohesive soils. The first two investigators used a

method employing a submerged jet in a manner similar to that of Dunn.

Epsey used a system of rotating coaxial cylinders with the inner

stationary cylinder composed of the clay samples. Neither of these

two investigations showed conclusive results, and no correlations

with soil parameters were attempted. Erosion took place by the removal

of relatively large chunks of the sample.

In general, as indicated above, basic work on erosion has

concentrated on the correlation of some "critical" velocity or shear

stress, with the indices defining clay properties. Some of these

correlations are based on small-scale scour tests. The definitions of

critical shear stress and of the point of bed failure have been











arbitrary and based entirely on visual observation and judgment of the

experimentor. It is therefore difficult to utilize such information

to predict the stability of channels subject to high flow rates for

short time periods, or to predict the erosion depth of a channel at

constant flow rate during its expected life. Further, the effects of

suspended sediment concentration on erosion or the conditions under

which eroded material may redeposit were not studied by the above

investigators.

Grissinger (1966) studied the effects of bulk density, water

temperature, antecedent water, type and orientation of clay mineral,

aging and percent clay on erodibility under constant flow conditions.

Instead of an arbitrary critical shear stress, the determination of

erodibility was given in terms of mass erosion rates (Partheniades

and Paaswell, 1970). Grissinger found that all the above variables have an

effect on the erosion rates. This, in fact, points out the difficulty

in an arbitrary assignment of existing soil parameters as representative

indices for erosion studies. Indices such as percent clay, plasticity

index and dispersion ratio are in effect secondary indices which reflect

the primary physicochemical forces which essentially control the soil

properties.

b. Erosion of soft clay deposits: This research phase was

aimed at an understanding of the details of mechanical interaction

between the clay particles and water, the discovery of important flow

parameters and soil properties controlling the initiation and rates of

erosion, and the establishment of relationships between these properties

and parameters. These studies, coupled with similar investigations on

the depositional behavior of fine cohesive sediment suspensions, to be












discussed in Section 2.2.2 have thrown a considerable light on the

hydrodynamic interaction between fine sediments and turbulent

flows.

Partheniades (1965) conducted investigations on the erosion

and deposition of a cohesive sediment in an open flume with

recirculating water at ocean salinity and constant depth of flow.

The sediment used was composed of nearly equal amounts of silt and

clay, with traces of sand and some organic matter dredged from the

San Francisco Bay. This sediment, commonly known as Bay mud, is

described in Section 3.1.3. The original purpose of the study was to

investigate the influences of shear stress, suspended sediment

concentration and shear strength of the bed on erosion rates, and to

study in a more general way the deposition of the sediment at

different flow velocities. The depositional aspect is discussed in

Section 2.2.2.

Two types of beds were tested. The first was remolded at

field moisture of about 110%. The ultimate remolded shear strength

was about 20 psf, and the strength at yield point was about 11 psf.

The second bed was flocculated and deposited in the flume directly

from suspension at very low flow velocity. Two experimental series

were run on the first bed and one on the second. The ratio of strengths

of the dense to the flocculated bed measured by a special device, was

of the order of 100:1. The following important conclusions were

reached.

The minimum velocity or shear stress at which erosion was

first observed was about the same for both beds. The minimum scouring










shear stress was of the order of 0.0020 psf. For these two series,

the rates of erosion were found to be independent of the macroscopic

bed shear strength.

In all but one run, erosion took place by removal of

individual clay particles and clay clusters. This type of erosion

may be referred to as surface erosion. In contrast, the kind of

erosion that was observed by investigators in experiments described

previously in this section took place by removal of relatively large

chunks of the soil, and may be referred to as mass erosion. Mass

erosion occurs when the flow-induced forces on the bed cause

shear stresses which may exceed the soil strength along some plane

below the soil surface. Such a failure is of little practical signi-

ficance since it goes far beyond the desirable design stability

conditions.

The erosion rates depended strongly on the increase of

average bed shear stress past a threshold value. It was observed

that eroding shear stresses varied widely starting from 0.002 psf.

Partheniades therefore concluded that the term "critical" in fact

depends on the particular rate, which is why any designated critical

shear stress based on observed mass scouring may differ from observer

to observer even for the same soil.

During the process of erosion the time-concentration relation-

ship was linear, suggesting constant erosion rates independent of

suspended sediment concentration.

A mechanistic model was developed to explain the observed

erosion phenomena, and an expression, giving the erosion rates in terms










of known or measurable quantities representing the flow condition

and soil properties,was derived. This expression had as an under-

lying assumption the Gaussian or normal distribution of time varying

shear and lift forces. Christensen (1965) has pointed out that based

on experiments by El-Samni (1949) it appears that the instantaneous

velocity fluctuations rather than the shear stresses follow a normal

distribution. On the basis of this interpretation he rederived the

expression giving the erosion rate and presented it in a dimensionless

form.

An important conclusion derived from the above experiments is

that erosion of cohesive sediments is controlled by the bed shear

stress. Moreover, any designation of a shear stress as critical should

indicate either the stress at which erosion just begins, or the

stress that would cause a particular erosion rate, or the stress

that would be expected to cause a maximum estimated depth or erosion.

It was shown that the soil shear strength is not the only

-property governing erosion. For low strength clays, no definite

correlation has been found between strength and erodibility. For

medium to high strength clays, the resistance to erosion seems to

increase with increasing strength, although no well-defined empirical

relationship has been developed. As a large number of physicochemical

factors control erosion, attention should be paid to duplicate in a

model test the natural conditions as far as possible.


2.2.2 Deposition

It is pointed out in Appendix D, that as a result of the











complex behavior of depositing sediment flocs in a turbulent flow

field, the boundary conditions that are required to integrate the

sediment continuity equation are not known, and therefore an analytic

solution describing the rates of deposition is difficult to formulate.

As a consequence, studies on the depositional behavior of cohesive

sediments have mainly been of experimental nature.

Early experimental studies connected with a systematic

investigation of the depositional behavior were performed in recircula-

ting open flumes. Krone (1962) conducted an important series of

experiments on the measurement of deposition rates of Bay mud from

the San Francisco Bay, described in Section 3.1.3. He used a 100 ft.

long and 3 ft. wide flume, and essentially correlated his results

with the bed shear stress.

For sediment concentrations less than 300 ppm, his measurements

indicated an exponential decrease in the suspended concentration with

time, which he explained in the following manner: Since his measure-

ments were made at relatively low flow velocities at which all the

sediment eventually deposits, he assumed that under these conditions,

the particle-bed collision frequency is independent of the flow

velocity. Considering pd as the probability of a particle or a floc

sticking to the bed, continuity for the amount of sediment may be

expressed as


dC c Pd Ws (2.2-1)
dt d

where C is the suspended sediment concentration at time t, d is the

total depth of flow, and W is the near-bed settling velocity of the
s











particles, so that W C is the flux of the particles approaching the

bed. Then, assuming W to be independent of C and t, integration of
s

Eq. (2.2-1) yields


C = exp dW t (2.2-2)



where C is the concentration at t = 0. According to Krone, pd depends

on the bed shear stress Tb' and can be expressed as

bb

d 1 (2.2-3)
c


where T is the critical shear stress above which no particle can

stick to the bed; this is by virtue of T being that shear stress

above which no deposition can take place, while at lower stresses,

all sediment must eventually deposit. From experimental measurements

below 300 ppm, T = 0.6 dynes/cm and W 6.6 x 104 cm/sec. were
c s
obtained.

For concentrations between 300 ppm and 10000 ppm, a logarithmic

relationship was derived:


log C = K2 log t + constant (2.2-4)


where K2 was found to be approximated by the expression



K = --- 1 -(2.2-5)
c

2
For this concentration range, T was found to be equal to 0.78 dynes/cm.
This higher value of for higher concentrations as compared to those
This higher value of T for higher concentrations as compared to those
c











below 300 ppm was mainly attributed to the observation that at higher

concentrations, larger flocs are formed due to the greater number of

interparticle collisions.

For high concentrations in excess of 10000 ppm, Krone found

the relationship

log C = K1 log t + constant (2.2-6)


which is similar to Eq. (2.2-4) and where K is an empirical coeffi-

cient.

The different depositional behaviorsin the three concentration

ranges were attributed to three modes of settling. For very low

concentrations, i.e., less than about 300 ppm, the particles or the

flocs settle more or less independently, without any significant

mutual interference. For intermediate concentrations between 300 ppm

and 10000 ppm there is an increasing amount of interference due to

increased interparticle collisions, with the result that larger flocs

are able to form, causing a faster rate of deposition. Finally for

concentrations above 10000 ppm the suspension assumes a form of a

continuous network called "fluid mud," with water escaping upward

between the network spaces due to settling. This type of settling

is called "hindered settling," and Krone suggested that this type of

settling is the cause of lower deposition rates at very high sediment

concentrations.

Krone made a deposition test in which he labeled part of the

sediment with radioactive gold-198, and observed that the labeled

sediment showed a higher deposition rate than the total sediment;












from which he concluded that during deposition, an interchange between

suspended and deposited sediment takes place. This conclusion has been

contradicted by Partheniades (1962).

Inasmuch as the floc size is controlled by the local shear

within the flow, Krone conducted an experiment using two concentric

cylinders to determine a relationship between floc size and shear

stress, under laminar conditions. The shearing rates were varied by

inserting stationary cylinders of diameters ranging from 0.5 cm to

2.25 cm inside an outer cylinder of 5.8 cm diameter, which rotated at

a speed of 28 rpm. Now internal shearing can both promote floc growth

and limit its size, since up to a certain limit, interparticle colli-

sions have the dominating effect of increasing floc size, while above

that limit, shear may exceed the shear strength of the flocs and

begin disrupting them. Krone therefore reasoned that the flocs should

approach a maximum limiting size under each condition of sustained

shearing. The floc size was determined by taking photographs with

the help of a strobe light. The results of the experiments showed

an inverse relationship between the maximum floc diameter and shear
2
stress at the inner cylinder down to a shear stress of 0.06 dynes/cm2

Below this limit, the floc size increased rapidly with decreasing

shear stress. This inverse relationship agrees with a theoretically

derived expression


r'= [-1 (r')Tma] (2.2-7)


where r'is the radius of the largest idealized spherical floc and T is

the shear at the boundary of the laminar shear field. The terms Ar' and











T refer to the thickness of the floc surface roughness and to the
max
floc shear strength, respectively, which are assumed to be properties

of the sediment only. Krone assumed a value of 2 microns for Ar and

2
calculated the shear strength of the Bay mud flocs as 2.7 dynes/cm2

The deposition tests of Partheniades (1965) on the Bay mud

were adjunct to his erosion studies described in the previous section.

He nevertheless made some important observations. In a given test,

after each velocity reduction a sudden concentration drop occurred,

whereas at constant flow conditions, after a period of relatively

rapid deposition, the suspended sediment eventually approached an

apparent "equilibrium value." It was noted that two deposition

runs, one of high and one of low initial concentration, resulted in

nearly the same ratio of the apparent "equilibrium concentration"

to initial concentration Co, at the beginning of the run. From

this observation he concluded that for a given flow condition, a

constant proportion of the total suspended cohesive material (silt

and clay) is always carried in suspension. This implies that the

equilibrium concentration is due to the amount of material available

of a size equal to or less than the maximum size the flow can support,

and that it does not represent the total sediment carrying capacity

of the flow.

Partheniades also observed in his deposition tests that by

reducing the flow velocity from 0.81 to 0.58 ft/sec, negligible

deposition took place. However, by reducing the velocity further

from 0.58 to 0.47 ft./sec, the suspended sediment concentration

decreased from 5500 ppm to a very low value, and it appeared that if












given sufficient time, all the remaining suspended material would

settle out. He estimated the "critical" velocity below which all the

sediment must eventually deposit to be approximately 0.50 ft./sec.

Since this velocity was lower than the observed minimum scouring

velocity of 0.70 to 0.80 ft./sec for the same material, he reasoned

that for the range of concentrations studied, simultaneous erosion

and deposition did not take place, i.e., interchange between the bed

particles and suspended particles did not occur.

It is interesting to obtain an approximate estimate of the

critical shear stress corresponding to the critical velocity of 0.50

ft./sec obtained by Partheniades, and to compare it with T of

Krone's measurements, which also essentially is the critical shear

stress for complete sediment deposition. Partheniades made several

measurements of mean flow velocities and corresponding bed shear

stresses; the latter being computed from the slope of the energy

grade line, which in turn was obtained by measuring the downstream

drop in the water surface elevation in the flume. The measurements

are plotted in Fig. 2.2.1, which nearly fall on a straight line on

a log-log plot, with a slope of 1.94. When the same data points are

plotted on a Moody friction factor diagram for pipes (which involves

multiplying the hydraulic radius of the flume by a factor of 4 to

obtain the corresponding equivalent pipe diameter), all except two

points consistently fall in the near-fully rough to fully

rough flow regime, and they indicate an average bed roughness

of 0.0015 ft. This observation is also consistent with the near

square law which describes the straight line of Fig. 2.2.1. When





























"E


CO
. 0





rc-






0.I




0.1 t I 10
0.5
Um (ft./sec)

Fig. 2.2.1. Depth-averaged Velocity u Versus Bed Shear
Stress Tb from Measurements of Parcheniades.
I












this straight line is extrapolated to lower shear stresses, the

value of the critical shear stress at the critical velocity of 0.50
2
ft./sec is observed to be 0.65 dynes/cm2. This value is consistent
2
with Krone's 0.60-0.78 dynes/cm2. Now as noted, Partheniades

observed that the minimum scouring velocities were of the order

of 0.70 to 0.80 ft./sec, which are significantly higher than the

critical velocity of 0.50 ft./sec for the complete deposition of

the same sediment in suspension. Based on these scouring velocities,

the corresponding critical shear stresses for erosion are observed
2
from Fig. 2.2.1 to be 1.25 to 1.65 dynes/cm2. Hence, the ratios of

the critical stress for erosion to that for deposition are 1.92

and 2.54, respectively.

It is noteworthy that since Krone's deposition measurements

were carried at shear stresses below the critical shear stress for

deposition, he did not observe the phenomenon associated with the

equilibrium concentration in his experiments.

Etter and Hoyer (Partheniades, Kennedy, Etter and Hoyer,

1966) conducted deposition experiments in salt water at the University

of Zulia in Maracaibo, Venezuela. The sediment, referred here as

Maracaibo sediment, came from the Bay of Tablazo, and is described in

Section 3.1.3. Four runs were conducted in which the suspended

sediment attained a concentration of less than 300 ppm. In all cases,

an exponential decrease of the suspended concentration was observed

for data below 200 to 300 ppm, but not for higher concentrations. They

obtained the relationship










C- = exp[-Kt] (2.2-8)
CR

where CR is not the initial concentration of the run, but rather is

a reference concentration corresponding to the time at which the

straight line slope -K begins on the plot. Etter and Hoyer were unable

to correlate the exponent K with the bed shear stress.

Rosillon and Volkenborn (1964) also studied the depositional

behavior of the Maracaibo sediment. They noted that the deposition

rates varied significantly with depth. Also, they found that increasing

the initial concentration increased the rate of deposition throughout

a given run. In two of their runs, the suspended sediment concentration

apparently reached an equilibrium value. An examination of their

data, however, reveals that many of their runs were not carried out for

long enough periods to determine whether equilibrium concentrations

would be attained, and this fact limited the possibility of a systematic

analysis of their measurements.

In addition to the deposition runs, they studied the deposition

of the sediment in still water of varying salinity. In determining the

effect of salinity on a sediment with an initial concentration of 3000

ppm, they observed that flocculation of the sediment particles

increases with increasing salinity up to nearly 15000 ppm, above

which salinity has no further effect on flocculation. This observa-

tion is in agreement with that of Krone (1962).

The various studies described above were able to isolate some

of the important factors affecting the depositional behavior of cohesive

sediments. These are bed shear stress and turbulent structure











above the bed, type of sediment and ionic constitution of the

ambient water including salinity, depth of flow, and the initial

sediment concentration. The geometry of the flume and the return

pipes are also significant insofar as they influence flocculation

through the effect of local shear stresses. However, since the

number of variables involved is large, none of the above investigations

can be considered as exhaustive in terms of analyzing the effects

of each of these variables over wide ranges of values. One of the

causes of a dearth of experimental data is due to the long time

periods required to complete a deposition run. In many cases, even

after several hundred hours of operation, complete deposition was

not achieved, even at relatively low flow velocities. This problem

is characteristic of straight flumes, in which the process of

deposition is slow as a result of the suspended sediment having to pass

through the return pipes. The high shears acting in these pipes by

virtue of their relatively small cross-sections causes a disruption

of the sediment flocs into smaller units, so that when this sediment

reappears at the upstream end of the flume, it is completely

resuspended and with relatively smaller floc sizes, with the result

that deposition of the sediment is retarded. Often two other limiting

factors in the operation of straight flumes are the rather narrow

range of possible flow rates, and the relatively large amount of

total sediment required to run the experiments.

In order to overcome the difficulties inherent in a straight

flume, a special apparatus was designed at M.I.T. Its main components

were an annular channel with inner and outer diameters of 28-3/8 in.











and 36 in., respectively, for containing the sediment suspension,

and an annular ring positioned within the channel and in contact

with the water surface. A simultaneous rotation of the ring and

channel in opposite directions generated a turbulent flow field.

The advantages of this apparatus in comparison with a conventional

straight flume are as follows: (1) The flow is uniform at every

section, and is free from any floc-disrupting elements such as pump

blades, return pipes and diffusers. (2) The apparatus can be

instrumented so that the average shear stresses acting on the ring

and on the channel boundaries can be readily evaluated. (3) The

equipment permits a quick and precise variation of the flow parameters

over a wide range of values. (4) Due to its relatively small

volume, a large number of tests with different fluids, sediment types

and concentrations can be performed inexpensively, and in much shorter

periods of time as compared to a straight flume. (5) The entire

apparatus occupies a relatively small area.

The effect of rotation-induced secondary currents on the

uniformity of deposition was practically eliminated by properly

adjusting the speeds of the ring and channel for a uniform sediment

deposition across the width of the channel. For these particular

speeds, the bed shear stress distribution across the channel width

was found to be almost uniform (Partheniades, Cross and Ayora, 1968).

The details of the instrument and its operation are described by

Partheniades et al. (1966) and Etter et al. (1968). A commercial

kaolinite clay was used as the sediment with a grain size distribution

from a fraction of a micron up to nearly fifty microns. Inasmuch as











the experiments were concentrated on the role of flow variables in

deposition, the type of sediment and the ambient water quality were

kept constant. The results of the investigation are summarized below.

1. For a given flow confining geometry, sediment type and

flow conditions, the suspended sediment concentration reaches, after

a period of relatively rapid deposition, a constant value Ceq defined

previously as equilibrium concentration. This equilibrium concentra-

tion is a constant fraction of the initial concentration Co; i.e.,

the ratio Ceq/Co is independent of Co and is a function of the flow

conditions only. This implies that each flow can maintain in suspension

a constant percentage of a given initial amount of sediment.

2. The ratio Ceq/C for various depths depends on the bed

shear stress, according to a logarithmic-normal relationship

(Partheniades, Cross and Ayora, 1968). For the particular sediment

and geometry of the annular channel, this relationship was found to

be


C 6logiP
C h
Ceq logA. 1 exp(- -. [logAP 1.76412 d(logtP ) (2.2-9)
C 0 .49/7f 04


where

4 0.834
AP = log(2.38 x 104 x T83 65) (2.2-10)
Id b

in which the average bed shear stress Tb is expressed in psf.

3. The initiation and rates of erosion of cohesive sediments

have also been found to depend strongly on the bed shear stress, as

observed by Partheniades (1965). Moreover, the stresses at which










erosion begins for a given sediment are considerably higher than the

stresses at which the same sediment is suspension deposits entirely.

This observation is in complete agreement with field observations in

irrigation canals (Partheniades and Paaswell, 1970).

4. The conclusions cited so far reveal that the

aspects related to the erosion and deposition of cohesive sediments

are different from those of a coarse sediment. The constancy of

the relative equilibrium concentration C /C for constant flow
eq o
conditions is a fundamental depositional characteristic of cohesive

sediments. It has been well established that in flows over a movable

cohesionless bed there is a simultaneous deposition and erosion of

particles. A constant concentration of sediment in such flows is

attained when the number of particles eroded is equal to the number

of particles deposited per unit bed area, per unit time. If the

suspended load is suddenly increased by an additional amount of

sediment of similar composition to the one already in suspension,

the concentration will eventually drop to its original equilibrium

value, and the fluxes of erosion and deposition will again become

equal. The constant value of C q/C independent of C in the case

of fine sediments suggests that interchange of bed and suspended

material does not take place. Such an interchange is also excluded

by virtue of conclusion 3. Moreover, experiments in the rotating

channel in which the suspended sediment at equilibrium concentration

was gradually flushed out have directly confirmed this conclusion

(Partheniades, Cross and Ayora, 1968). The constant equilibrium

concentration of sediments in suspension does not therefore represent











the level of saturation of the sediment-carrying capacity of the flow.

It rather appears to represent the fraction of the sediment with weak

enough interparticle bonds, such that the settling flocs of that

part of the sediment cannot resist the high disruptive shear stresses

near the bed. The part of sediment which can form floes large enough

to settle on the bed and with sufficiently strong bonds to resist

breaking and resuspension, deposits permanently without being

resuspended.

5. The ratio C e/C ceases to be a unique function of the
eq o
average bed shear stress for any speed combination other than the one

resulting in a uniform deposition. This suggests that the rotation-

induced unbalanced secondary currents in the annular channel also

control the equilibrium concentration.

6. Mechanical analysis has revealed that at equilibrium

concentration, the suspended sediment contains the entire particle

size range of the original sediment (Partheniades et al., 1966). From

this observation, it has been concluded that the degree of flocculation

and the strength of the interparticle bonds play a dominant role

in the deposition process rather than the particle size, and that

there is little correlation between the particle size and the

intensity of interparticle forces.

7. Limited data from experiments showed that the deposition

rates are also strongly controlled by the bed shear stress. The

following two tentative expressions were developed for the instan-

taneous concentration C by two different approaches (Partheniades,

Cross and Ayora, 1968):











C C f(Tb)t-2.14 10-6 -1.84 (2.2-11)
o b b

and


C C
o0 -- = -0.592 + 0.135 log C + 0.455 log t (2.2-12)
C C o
o eq

where t is in minutes and Tb is in psf, and f(Tb) is a function of Tb.

Differentiating Eq. (2.2-12) with respect to time, the following

equation for the rate of deposition is obtained:


dC 0.198 -eq (2.2-13)
dt t o C


In Eq. (2.2-13) the effect of the shear stress Tb exists implicitly

through C /C .
eq o

2.3 Objectives of Present Investigation


In the preceding section it was noted that the annular rotating

apparatus used at M.I.T. was a convenient and efficient means to

study, under controlled conditions, the depositional behavior of

fine cohesive sediments. A similar apparatus, described in Section

3.1 was therefore used in the present investigation, with the

following specific objectives.

1. A study of the effects of flow parameters on the rates of

deposition of flocculated sediments under turbulent flow conditions,

and derivation of quantitative relationships describing these effects.

Limited measurements at M.I.T. discussed in the previous section had

indicated that the bed shear stress, flow depth and the initial

sediment concentration were some of the important variables involved.












2. Verify and generalize the logarithmic-normal law relating

the equilibrium concentration to the bed shear stress as determined

by the M.I.T. experiments.

3. Inasmuch as accurate values of the bed shear stresses

are required, it was decided to measure them with the help of a false

annular channel bottom. This false bottom would be instrumented

so that it would directly measure the stresses acting on it.

Velocity profiles would also be measured to supplement these shear

stress measurements.

4. Once objectives 1 and 2 were met, it would then be possible

to test more than one sediment,and thereby investigate the effects

of the physicochemical properties of the sediments on the depositional

behavior. Particular attention would be given to obtaining suitable

and readily measurable parameters representing the physicochemical

properties of the sediments, and relating the hydrodynamic behavior

of a sediment in terms of these parameters.

5. A comparison of the experimental laws describing the

depositional behavior with results of earlier investigations

described in the previous section. A comparison with the data

obtained in straight flumes would especially reflect on the merit of

using the special annular rotating apparatus for testing cohesive

sediment suspensions.

6. To attempt to elucidate the nature of the depositional

process, in terms of a physical model. Since the behavior of sediment

flocs is rather complex by virtue of their dependence both on the

hydrodynamic as well as physicochemical forces, such a model would







40



essentially have to be based on certain simplifying assumptions

related to sediment continuity, the nature of the physicochemical

forces, the physical boundary conditions and the structure of

turbulence.











CHAPTER 3

EXPERIMENTAL EQUIPMENT AND PROCEDURE


3.1 Experimental Equipment

3.1.1 Basic Apparatus

The components of the basic experimental equipment, consisting

essentially of a system of a rotating ring and an annular channel

are described in the following paragraphs. It is similar in

principle to the one designed by Partheniades et al. (1966) at

M.I.T., but is of twice the size (in linear dimensions) of the

latter. The components are:

a. An annular channel, shown in Fig. 3.1.1, which'is 8 in.

wide, 18 in. deep and 30 in. in mean radius, and is made of 3/8 in.

thick fiberglass. Four 3 x 2 in. plexiglass windows are provided

every 90 in the lower part of its outer wall for visual observation.

Lateral rigidity is provided by top and bottom horizontal flanges

as well as by vertical stiffeners, also made of 3/8 in. thick

fiberglass. The interior of the channel is smooth, without any

obstructions that might impede the flow, and is coated with a white

oil based paint.

b. An annular 1/4 in. thick plexiglass ring of the same mean

radius as the channel, but with a slightly smaller width of 7-3/4 in.,

described in Fig. 3.1.2. The ring can be positioned within the

channel, at any given height, with a clearance of 1/8 in. between

its edges and the channel walls, so that it can rotate freely while

in contact with the water surface. A plexiglass reinforcing member















HORIZONTAL
FLANGES








VERTICAL
STIFFENERS


3x 2in. PLEXIGLASS
WINDOWS EVERY 90


Fig. 3.1.1. Schematic Views of Annular Channel.





























REINFORCING MEMBERS


CROSS-SECTION QQ ENLARGED



Fig. 3.1.2. Schematic Views of Annular Ring.


_t ~I
r










has been glued at the center of the ring, forming a T-shaped cross-

section, to minimize deflection between the supports.

c. Two concentric steel shafts, as depicted in the schematic

diagram of the entire assembly, shown in Fig. 3.1.3. The 3 in.

diameter hollow outer shaft, which rotates the channel, is supported

by the two indicated 1/2 in. thick, 18 in. equilateral triangular

plates, through ball bearings. The 1 in. diameter inner shaft,

which supports and turns the ring, is also supported by ball bearings,

inside the hollow outer shaft.

d. A steel turntable, made essentially from octagonally

positioned I-beams, with a circular plate in the middle, as shown

in Fig. 3.1.5. The turntable is attached to the outer shaft, and

the channel is bolted to the turntable, with a 5/8 in. chip board

in between for a uniform support.

e. A ring support made of four 29-1/2 in. long, 2 in. wide

and 1/4 in. thick radial steel arms shown in Fig. 3.1.3 as well as

in Fig. 3.1.4, which is a top view of the assembly, showing some

essential details. The arms themselves are attached to the 1 in.

diameter inner shaft by an arrangement indicated in detail in

Fig. 3.1.6. The ring is suspended from the radial arms by four

20-1/2 in. long, 3 in. wide and 0.025 in. thick flexible stainless

steel blades, through clamping fixtures also indicated in Fig. 3.1.6.

The lower end of each blade is rigidly bolted to the ring and to the

plexiglass reinforcing member attached to the ring by two aluminum

plates and angle brackets.


























TOP HORIZONTAL SUPPORT BEAM

TRIANGULAR / L-SHAPED
STEEL PLATE (------ STEEL ANGLE
B EARNING FOR ARM SUPPORTING
HEIGHT INNER SHAFTTHE RING
ADJUST ENT SHAFT
MEANS S NG BUSH STRAIN GAGES
BLOCK ASSEMy/ RING SUSPENDING
REFILLING WELL I BLADE

INNER SHAFT REFILLING FUNNEL

FIBERGLASS CHANNEL
r-F | FIBERGLASS STIFFENER
CHIP BDARD PLEXI NGLASS S A ST TAP


SAMPLE BOTTLE



COLLECTOR SPESON TRIANGULAR TURNTABLE
PLATES
SUPPORTING
SUPP OUTER SHAFT -------- OUTER SHAFT
SUPPORT BEAMS

SUPPORTING LEG

TRIANGULAR
STEEL CORNER I T 7


DRIVING MOTORS


Fig. 3.1.3. Schematic View of Annular Ring and
Channel Assembly.






































INNER SHAFT
Fig. 3.1.4. Top View of Ring and Channel Assembly.


AMERICAN STANDARD
BEAM
3"X2 "NOMINAL SIZE
5.7 LB./FT.


CIRCULAR PLATE UNEQUAL LEG ANGLE
DIAMETER 24" I/ 4 IX
THICKNESS <


Fig. 3.1.5. Steel Turn-table.











f. A vertical height adjustment mechanism as shown in

Fig. 3.1.6. This mechanism is designed with coarse and fine adjust-

ment devices, to position the ring to touch the water surface for

any given depth of flow. It consists of two components, the first

of which is a steel collar fitting closely to the inner shaft. The

collar slides on the shaft to the desired height, and is locked into

position by a set screw which fits into countersunk cavities, spaced

1 in. apart vertically on the inner shaft. The collar is thus used

for a coarse adjustment. The second, outer component, is attached

to the four radial steel arms, and is threaded onto the steel collar.

A lock nut, which also threads over the inner collar, is used to

lock the outer component in any position, and is used for a fine

height adjustment.

g. The support structure shown in Fig. 3.1.3. It is made

from 3 x 3 in. square steel beams. These beams are hollow, with

1/4 in. thick walls. The three legs of the structure are placed

120" apart. The legs are securely bolted to the concrete floor, to

provide the necessary rigidity to the structure. This support

structure holds the outer hollow shaft through the triangular plates

and ball bearings mentioned previously. Two horizontal support

frames, each made of three 3 x 3 in. square and 34 in. long beams

radially placed 1200 apart as indicated in Fig. 3.1.4, and located

at heights of 24 in. and 48 in. from the floor, are welded at the

center to the triangular plates. 1/4 in. thick, triangular steel

corners with base lengths of 14 in. are used to weld the frame

beams and the legs together. One of the legs is extended to a total









































ARM CONNECTION









005 _BLADE

CLAMPING
FIXTURE





BLADE
,RADIAL 3"WIDE
ARM SUPPORTING
THE RING


Fig. 3.1.6. Height Adjustment Mechanism Including
Radial Arm and Blade Connections.










height of 150 in., and a horizontal 37 in. long 3 x 3 in. steel

beam is connected to it at the top by bolts through two 1/4 in.

thick and 28 in. base length triangular steel plates. This

horizontal beam is used to hold the inner shaft in place through an

L-shaped steel angle and a bearing, as indicated at the top of

Fig. 3.1.3.


3.1.2 Accessory Equipment

Auxiliary equipment attached to the basic system described

in Section 3.1.1, as well as special equipment used in the experimental

work, is described in this section.

a. Four SR-4 type FAP-50-12-S9 temperature compensated strain

gages, each with 120 ohm resistance and 2.1 gage factor were attached

two on each side, of one of the blades supporting the ring, 1-1/2 in.

below the top of the blade, for the measurement of the shear stress

transmitted by the ring to the flow. For specifications and

instructions for the use of these strain gages, refer to Strain

Gage Bulletin (1967). A B.L.H. Portable Digital Strain Indicator

Model 120C was used to measure the strain directly in a digital

microinches per inch readout. For specifications on the indicator,

see Strain Instruments Catalog (1968). The circuit diagram and

procedure for the measurements is given in Section 3.2.3.

The electrical connection between the gages and the indicator

had to pass through a set of four copper slip rings and carbon brush

blocks shown in Fig. 3.1.3. These were designed at the Coastal

Engineering Laboratory, and were able to function well, as long as

the ring surfaces were periodically cleaned of carbon deposits.










b. An annular false bottom was designed for a direct measure-

ment of the bed shear stress. It is made of 1/8 in. thick plexiglass,

and has the same dimensions as the annular ring, i.e., it has a mean

radius of 30 in. and a width of 7-3/4 in. Fig. 3.1.7 shows a schematic

representation of the false bottom and plexiglass support used to

position the former in the channel. Three such supports were designed

and positioned every 120 in the channel, between plexiglass blocks

glued on the channel bottom, with one of the supports instrumented

with strain gages for shear measurement. Stiffeners are attached

below the false bottom to keep it from flexing. Essentially, the

false bottom is held in place by three 3-3/4 in. long and 2 in. wide

blades made from a 0.004 in. stainless steel shim material. These

blades are securely clamped between the false bottom and the support

base by the indicated fixtures. The elevation of the false bottom

is 5 in. above the channel bottom. Since plexiglass is slightly

denser than water, with a specific gravity of 1.05, to avoid buckling

of the blades due to the submerged weight of the false bottom, six

6-1/2 x 5 in. pieces of 1/2 in. thick styrofoam were glued under-

neath the false bottom to provide a sufficient upward buoyant

force to balance its submerged weight. To adjust the number and

size of the styrofoam pieces, the false bottom was placed in a

large tank containing water, and styrofoam pieces of various sizes

were introduced underneath the false bottom until it became almost

neutrally buoyant.

The bed shear is measured by the bending strain produced in

two SR-4 type FAP-50-12-S9 temperature compensated strain gages,



















































TRIANGULAR


Fig. 3.1.7. Support for Annular Plexiglass False Bottom.











one on each side, on one of the blades, as shown in Fig. 3.1.7. The

bending of the blade itself is due to the shear exerted on the false

bottom by the flow above. In order to stop the flow below the false

bottom, three vertical plexiglass partitions were positioned, half

way between each support and below the false bottom. Stops shown

in Fig. 3.1.7 are provided to keep the blades from bending more than

3/4 in. from its mean position either way, so that the elastic limit

of the shim material is not exceeded. Since the strain gages were

operating underwater, a thorough waterproofing was required. This

was achieved by coating the gages with Dow Corning 3140 RTV Coating.

Even on the two blades on which gages were not installed, the same

coating was applied similarly to keep the bending characteristics of

the three blades as similar as possible. Silicone grease was

additionally applied on the blades for further protection against

penetration by water.

c. Sampling equipment for sediment concentration includes

four sample taps, at mean elevations of 1-9/16, 5, 8-3/4 and 12-1/8

in. from the bottom of the channel. Vinyl tubes attached to the

taps lead to four 250 ml polyethylene sample bottles placed on a

plexiglass stand attached below the chip board supporting the

channel, as shown in Fig. 3.1.3. Due to the convenient locations

of the taps and the bottles, it was possible to withdraw samples

from the taps, as well as remove and replace the sample bottles

while the channel was in motion.

A Millipore filtration apparatus was used for collecting

the sediment from the samples taken through the taps. The equipment










consists of a Millipore vacuum-pressure pump, which provides a vacuum

up to 27 in. Hg, a Pyrex filter holder with a stainless steel screen,

a 1 liter capacity filtering flask, a 10 ml pipette, and type HA

MF-Millipore filters with a mean pore size of 0.45 micron.

The pore size of 0.45 micron is about twice the diameter of

the upper limit of a fine or colloidal clay particle, as given by the

M.I.T. classification system, which is in the neighborhood of 0.20

micron, as indicated by Terzaghi and Peck (1967). Since clay particles

always appear in a flocculated state in the samples, even the

colloid-sized particles, if present, will be retained on the filter.

Water lost due to sample withdrawals was replaced through a

refilling funnel shown in Fig. 3.1.3. A refilling well,also shown in

Fig. 3.1.3, was designed for replenishing water lost by evaporation

during long periods of several hours between sample withdrawals. The

funnel over the well was filled with water, and it was allowed to

drip into the well at a rate adjusted by trial and error to be equal

to the mean rate of evaporation. Since the well is connected to the

channel by a rubber tubing, water lost from the channel was thus

replenished. It was later found, however, that under the controlled

temperature conditions in the room where the experiments were conducted,

evaporation of water was not sufficient to warrant the use of the

well.

d. In order to thoroughly mix the sediment with water before

introducing it into the channel, a Hamilton Beach mixer with a large

glass bowl was employed. Another mixer was constructed in the labora-

tory for mixing the sediment within the channel. This mixer consists










basically of a steel rod with three blades for mixing at one end, and

with the other end attached to an electric drill gun which rotates

the rod at a high speed. The mixer can be clamped on to the frame

of the ring-channel assembly such that it can continue mixing while

the channel is rotating. This way, a thorough mixing of all the

sediment is achieved.

e. A Kent Miniflow Velocity Kit was used to measure

velocities in the channel. This kit contains a D.C. velocity indicator

with two 10 mm propeller probes, Nos. 265-3 and 265-4, together

covering a range of velocity from 2 cm/sec to 300 cm/sec. An

additional 4 mm probe with a velocity range from 1 in./sec to 30 in./sec

was used to measure velocities close to the bottom surface.

f. Two Louis Allis 1 Hp forward and reverse motors were

used to drive the ring and channel, separately. The attached

tachometers are electrically connected to two Louis Allis Saber 3100

controllers for adjusting the speeds of the ring and the channel.

Pulleys of 5-1/4 in. diameter on the inner and outer shafts are

connected to those on the motors by belts, as shown in Fig. 3.1.3.

g. A 1 KHz square wave generator was designed for the

measurement of bed shear stress through the false bottom. The out-

put of the measured values was read on a Triplett Auto Polarity Micro

Power V-O-M Model 602 on which A.C. voltage as low as 0.01 volt

can be read on a linear scale.

h. A CL-277 B Soiltest hydrometer was purchased for measuring

the particle size distributions of the various cohesive sediments.

It has a specific gravity range of 0.995 to 1.038 with divisions of

0.001.









i. A drain and a polyethylene suspension collecting bottle

are provided for collecting large quantities of the sediment suspension,

while the channel is in motion. This is done in order that the

particle size distribution of that portion of the sediment which is in

suspension may be determined. The drain itself consists of two con-

centric steel pipes with the inner 1 in. O.D. pipe sealed at the upper

end, and with two 1/2 in. diameter holes in its side, 1 in. below the

upper end. The lower end of the inner pipe is connected to a vinyl

tubing, the other end of which goes into the suspension collector.

The inner pipe closely fits inside the outer pipe, but slides freely

with the help of silicone grease. This way, water-tightness is

maintained. Ordinarily, the top of the inner pipe stays flush with

the channel bottom, so that no water can go through the drain. If a

collection of the suspension is required, the inner pipe can be

pushed upward, causing the suspension to flow through the two side

holes into the collector. Pulling it back to the original position

stops the flow. In this way, any required amount of suspension can

be collected.

j. For the static calibration of the ring and the false bottom,

as described in Section 3.2.3, two special types of plexiglass

brackets were designed. These can be clamped on to the channel flanges.

Pulleys are provided on these brackets, so that metric weights on

small metallic pans can be hung from these pulleys, using nylon

threads, with one of their ends attached to the pan and the other to

the ring or the false bottom. In this way, torques of known values can

be applied. The bracket used for the static calibration of the false









bottom is shown on the left of Fig. 3.1.8, while on the right, the

one used for the calibration of the ring is shown.

Fig. 3.1.9 is a photograph of the complete annular channel and

ring assembly. The air conditioner at the top right of the picture

was used to control the room temperature, and maintain it at approxi-

mately 20'C. Below the air conditioner, one of the two Louis Allis

Saber 3100 speed controllers is visible. On the assembly itself, the

channel, its flanges and windows, ring arms and blades, supporting

structure, driving motors, refilling funnel, sample taps and bottles

and the drain and suspension collector are visible. At the top of

the inner shaft, four slip rings can be observed.

Fig. 3.1.10(a) shows a closer view of the channel with the

ring in operational position. Part of the refilling well also can be

observed. In Fig. 3.1.10(b), the plexiglass false bottom is shown

on four roller type supports. This arrangement was found inadequate

because it could not keep the false bottom from flexing, nor could

it prevent it from displacing vertically, due to the hydrodynamic

lift exerted on it by the flow. As a result, the arrangement was

changed to that described earlier in this section.

Fig. 3.1.11(a) shows the driving motors, pulleys and belts.

The motor on the right drives the inner shaft, while the one almost

perpendicular to the photograph is connected to the outer shaft.

Fig. 3;l.11(b) shows the building that housed the experimental

equipment. It has now been extended to include other additional

experimental facilities.

Fig. 3.1.12 shows a schematic plan view of the arrangement of

experimental equipment within the building shown in Fig. 3.1.11(b).









CHANNEL
FLANGE


WEIGHING PAN


ATTACHED TO
FALSE BOTTOM


Fig. 3.1.8. Brackets for Static Calibrations of Shear Stresses on False Bottom
and on Ring.

























































Fig. 3.1.9. Annular Channel and Ring Assembly.






































(a) (b)


Fig. 3.1.10. (a) Annular Channel with Ring in Operational Position
(b) Annular False Bottom on Supports.



































(a) (b)

Fig. 3.1.11. (a) Motors Driving Inner and Outer Shafts
(b) Housing for Experimental Equipment.



































PLUG I "

SPACE FOR
MINIMUM HEIGHT o
ANNULAR ROTATING MINIMUM HEIGH o
OF ROOM II'
APPARATUS



0
0
EQUIPMENT

PLUG CABINETS PLUG



16




Fig. 3.1.12. Arrangement of Experimental Equipment.









3.1.3 Sedimentary Material

a. Kaolinite: The kaolinite clay used in the deposition

experiments was supplied by R. T. Vanderbilt Company of New York.

Part of the following information on the clay is taken from the

Technical Data Sheet (1970) provided by the company.

The trade name for the particular kaolinite clay used is

Peerless No. 2. It is a light cream-colored secondary kaolin which

is non-abrasive and non-alkaline, is compatible with commonly used

wetting and dispersing agents, and it immediately flocculates in

distilled water. It is mined in Bath, South Carolina by Dixie Clay

Company, by the open pit method. The clay is air dried in sheds and

passed through a rotary kiln. It is ground in a Raymond mill and air

separated. Table 3.1.1 gives its chemical composition.



TABLE 3.1.1


Loss on
Constituent SiO Al203 Fe2 03 TiO2 Ca MgO Na20 K20 Ignition

% by Weight 44.99 39.95 0.34 0.73 trace trace 0.12 0.10 13.82





Fig. 3.1.13 shows the particle size distribution as measured

by Partheniades et al. (1966). It is observed that 66% by weight of

the material is in the clay size range, and 34% in the silt range.

X-ray diffraction pattern with copper (Cu) Ka radiation of the

bulk material is shown in Fig. 3.1.14. Since a sediment slide was used,

the basal (00) reflections are intense. The material appears to
















% coarse medium fine course medium fine course medium fine

100 .-- -i -- -- --- -";- o ^ -- -- --- --- - -"-- -----" ----
1-00 _

90_ t__ -__ ___

so .3




60 -



50 I- -'_

o Portheniodes et ol. (Koolinite)

2 Krone (Boy mud)
,o ---I-------- \ ---------- -- -- ----,--- --
20
o Rosillon and Volkenborn (Morocaibo Sediment)



200 000 10to10 I 0.I


DIAMETER (microns)

Fig. 3.1.13. Particle Size Distributions for Three Types of Fine Cohesive
Sediments.


r-



,r
Lj
3:



w
U-


CLAY


SAND


__v














I ',. I I


Kaolinite
Bulk sample
Sediment slide


0
z







LL
U


U.
0
LL-


I-



I-


I I" I ' I


S I I I I I I I I I I


40' 35


25' 20
DIFFRACTION ANGLE


Fig. 3.1.14. X-ray Diffraction Pattern for Kaolinite for Bulk Sample.


Koolinite
(0021
3.50 A











Kaolln4to

Koolinite 4.36
-- lllts 4.17~ 4,46 A
2.30 3.34 A Illte
2.50 A (002)
I2.A6 4.90 A


ITT- -_-_--_~_-


1 1 1 1 1 1 1 1 1 1 1 1 l i


oIlnlte
001)
16 A
























Illlte
(001)
9.o A


I . . I . 1 . .












consist almost entirely of kaolinite with a very small amount of

illite, as indicated by the peak intensities.

The cation exchange capacity of the material was found to be

77 milliequivalents per hundred grams of the material. This high

value is not representative of the CEC of kaolinite, which should be

approximately in the range of 3 to 15 milliequivalents per hundred

grams, according to Grim (1968). Even after almost complete salt

removal from the material, as checked by the silver nitrate test,

similar high values of the CEC were obtained. This high value is

therefore attributed to a possible chemical pretreatment of the

commercial material, which could significantly alter its CEC (Grim,

1968). Such a pretreatment would also account for the tendency of

the material to flocculate even in distilled water.

For the material free of sodium chloride, a pH of 5.1 was

determined, indicating an acidic nature.

b. Bay mud: Part of the following description of the Bay

mud, dredged from the Mare Island Strait of San Francisco Bay, is

obtained from studies by Krone (1962).

Differential thermal analysis (DTA) and X-ray diffraction

measurements of the sediment show that the predominant clay mineral

constituent is montmorillonite, followed by illite, kaolinite,

halloysite and chlorite. Among the non-clay materials, quartz,

organic matter and iron flocs are present. Some structural iron is

also present, due to the replacement of aluminum by iron in illite.










Suspended, or recently deposited, Bay mud has a light brown

color, while sediment from a depth of a few centimeters below the

surface has a color ranging from light grey to black. When a

sample of wet dredged sediment was placed in a large glass cylinder

and thoroughly stirred in water, a color change from dark grey to

brown took place. When allowed to stand, the color slowly changed

back to greenish grey and finally back to dark grey. These color

changes take place due to the following reasons: in the dark grey

sediment iron is present as ferrous sulfide. When stirred, ferrous

sulfide is easily oxidized, due to aeration, to ferric hydroxide,

which imparts a brownish color to the sediment. If allowed to stand,

bacterial reduction first changes ferric iron to ferrous iron which

is greenish, and then finally back to ferrous sulfide.

Particle size distribution of the Bay mud is shown in

Fig. 3.1.13. It is seen that 60% by weight of the sediment is in the

clay range, and the remaining in silt range. Comparison with the

curve for kaolinite shows that there is relatively more silt in Bay

mud than in kaolinite.

Fig. 3.1.15 shows an X-ray diffraction pattern of a sediment

slide of the less than 62 micron fraction (silt and clay) of the Bay

mud. The pattern confirms Krone's observations, with an additional

peak for orthoclase feldspar at 3.19 R.

In Fig. 3.1.16, the pattern corresponds to a less than 2 micron

fraction (clay) of a sediment slide treated with ethylene glycol,

which has shifted the montmorillonite peak to 17 R. A chlorite (001)

peak at 14.2 X is therefore observed clearly.





















Bay mud
Less than 624 sample
Sediment slide


rKootnzIs Ki /
tchlh tlt J II r
Orthoclost I.53
Chlorlt5 3 .19 O urt 0
2.544 4,274
KooC5ll te .

Ouo t 2.56A
Irtz 1.82$ uortz,
V2.13




55" 50' 45' 40' 35' 30" 25' 2 15' 10' 51
DIFFRACTION ANGLE


Fig. 3.1.15. X-ray Diffraction Pattern for Bay Mud for Less than 62 Micron
Fraction.












a (001)
y 17.0o
0 Boy mud
z Less than 2p sample Chlorile
o (001)
S Ethylene Glycol treated 14.2(
1- 14.?
S Sediment slide

cr

0 Illite
hI
- fKaolinite (001)
< (001) 9.8
t Chlorite oo
eLL Ii(002)
3lt Chlorlte 7.14

{0 Koolinite}
;> Chlorite J
3.56 A Illite
(002)
z 4.93A4









40 35 30 250 20 15 100 5
DIFFRACTION ANGLE

Fig. 3.1.16. X-ray Diffraction Pattern for Bay Mud for Less than 2 Micron
Fraction.











The cation exchange capacity was found to be 24 milliequivalents

per hundred grams of the material, and this value is in agreement with

values ranging from 18.7 to 30 milliequivalents per hundred grams

obtained by Krone (1957).

c. Maracaibo Sediment: The Maracaibo sediment was not

studied for its depositional behavior in the annular channel. However,

results of Rosillon and Volkenborn (1964), who used the sediment in

depositional studies carried out in a straight flume, have been

reanalyzed and compared with those using kaolinite and Bay mud in

Section 4.2.3. For that reason, three samples of the sediment from

the Inner Maracaibo Channel were analyzed in the Geology Department of

the University of Florida, for their particle size distribution, clay

mineral and non-clay mineral content and the cation exchange capacity.

This analysis is included in Appendix C.

Fig. 3.1.13 shows the particle size distribution of the

sediment used by Rosillon and Volkenborn. Approximately 7% by

weight of the material is fine sand, 53% is silt and 40% is in the clay

range.


3.2 Experimental Procedure

3.2.1 Calibration of Speed Controllers

The Louis Allis Saber 3100 speed controllers required

calibration, since the meters provided on them did not read the

speeds of the ring and the channel directly in rpm. Calibration was

therefore carried out by actual rpm measurements for the ring and the

channel using a stopwatch, for given different settings on the meters.











Fig. 3.2.1 shows the calibration curves for the ring and the

channel.


3.2.2 Determination of Operational Speeds

The rotational motion of the channel and the ring induces a

secondary motion in the radial direction, in addition to the main

flow in the tangential direction. The following explanation for the

mechanism which generates this secondary motion is taken from the

report by Partheniades et al. (1966), in which the same phenomenon

occurring in the smaller annular channel used at M.I.T. is described.

Consider the ring-channel system sealed off and filled with

water completely, with a hydrostatic pressure distribution, i.e., at

the ring = 0, as indicated in Fig. 3.2.2(a). Now consider a simul-

taneous rotation of the ring and the channel at the same angular speed

Q. After a sufficient length of time, at steady state, a rigid

body rotation will be established. The tangential velocity u at

any point with a radius r is then given by


u = Or (3.2-1)


and from the equation of motion in the r-direction (Bird, Stewart and

Lightfoot, 1960) one obtains

S u2 2
1 r2 (3.2-2)
p Dr r


where p is the density of water. Or, expressing the pressure gradient

as a total derivative














4


22


20 -


18-


16
16 RING


14 -
E

12
z

0-









CONTROLLER METER READING
wF
w
. 8


6


4





0
0 10 20 30 40 50 60 70 80

CONTROLLER METER READING

Fig. 3.2.1. Speed Calibration Curves for Ring and Channel.


















IA


(c)



j j _
U \


Fig. 3.2.2.


CHANNEL





,-SECONDARY
CURRENT
CELL


Secondary Cells in Ring-Channel System
(a) Solid Body Rotation
(b) Ring Only Rotating
(c) Channel Only Rotating
(d)' Ring and Channel Rotating at Operational
Speeds.


e


n










= pro2 (3.2-3)
dr

Integrating Eq. (3.2-3) gives

2 2
p= 2 + C1 (3.2-4)


where C1 is a constant. The pressure difference Ap between the outside

and inside walls becomes

2
P2 = p2 P l (r2 r2) (3.2-5)


Now the y-component of the equation of motion gives



S= pg (3.2-6)
ay

which implies a hydrostatic pressure distribution. In the case of

solid body rotation, there is no secondary flow, since at any

cylindrical surface (corresponding to r const.), the velocity u is

constant at any level, so that the centrifugal force on every fluid

element is exactly counter-balanced by the net pressure force acting

on the element.

Now with reference to the notation of Fig. 3.2.2, the following

cases arise:

Case a: Ring only rotating with an angular velocity l In this

case, f varies from Qo at the ring to zero at the channel bottom. The

pressure difference between the outside and inside wall is the same

according to Eq. (3.2-5) for any elevation, since the pressure varies










hydrostatically with depth. This pressure difference corresponds to

a speed Qm at y = ym, such that


= prO2 (3.2-7)
dr m

Now for ym < yd d, n > Qm and



S< prt2 (3.2-8)
dr
or

dp < prQ2dr (3.2-9)


Hence the existing pressure is not adequate to balance the centrifugal

force, and as a result the fluid particles move radially outward. For

0 < y < y 2 < m and


dp > prn2dr (3.2-10)


which means that there is an excess of pressure force over the centri-

fugal force, which causes the fluid particles to move radially inward.

The resultant effect of these two situations above and below y = y

is that a counterclockwise secondary circulatory motion is set up

in the channel, as shown in Fig. 3.2.2(b).

Case b: Channel only rotating with an angular speed o By a similar

argument as in case a, it can easily be shown that in this situation,

a clockwise secondary current is set up, as indicated in Fig. 3.2.2(c).

Secondary currents such as those described above also occur

in pipes and flumes, when bends are present. Schlichting (1968) dis-

cusses secondary flows in pipes of circular as well as non-circular










cross sections. In describing flow through a curved circular pipe,

he indicates that a secondary flow arises because of the fact that

particles near the flow axis which have higher velocities are acted

upon by a larger centrifugal force than the slower particles near the

walls. This leads to a secondary current directed outward in the

center, and inward, toward the center of curvature, near the wall.

Secondary currents are also present in straight flumes, where

the velocities at the corners are comparatively very large, which is

because the fluid flows towards the corner, along the bisectrix of

the angle, and then outward in both directions. Thus the secondary

flows continuously transport momentum from the middle region to the

corners, and generate high velocities there. Such flows are

undesirable because they tend to complicate a nearly two-dimensional

flow pattern into a three-dimensional one, which is difficult to

interpreted analytically.

In order to minimize the effect of secondary currents on the

uniformity of sediment deposition across the width of the channel,

the ring and the channel are rotated simultaneously in opposite

directions. This motion sets up two circulatory currents in opposite

directions, since both near the ring and near the channel bottom,

the fluid particles tend to move outward, as shown in Fig. 3.2.2(d).

Now if the speed of the ring is sufficiently higher than that of the

channel, the vertical momentum of the downcoming particles could be

high enough to build adequate pressure, in order to compensate the

excess centrifugal force near the bottom, and thus eliminate the









secondary circulation there. Then, a fairly uniform deposition of

suspended sediment could be expected to take place. The ring, which

has a smaller area of contact with the water surface than the channel,

would apparently have to rotate faster than the channel, to produce

a secondary circulation cell of the magnitude equal to that produced

by the channel. Correspondingly, as the distance between the ring

and the channel bottom, i.e., the depth, increases, the relative

speed of the ring would have to become greater with respect to that

of the channel.

In order to determine the ratio of speeds at which the effect

of the secondary current is minimized, plastic beads of 3/8 in. mean

diameter, and of 1.04 specific gravity were introduced to simulate

sediment motion. These beads, very close to the specific gravity of

water, were easily moved by the induced shear flow at the bottom, and

were extremely sensitive to the secondary currents. Rotating the ring

alone caused the beads to move toward the inside wall of the channel,

as predicted by the current pattern of Fig. 3.2.2(b). Similarly,

rotating only the channel moved the beads toward the outside wall,

as predicted by the current pattern of Fig. 3.2.2(c). Thus the

presence of two secondary cells of currents cancelling each other at

the bottom could be detected when various ratios of the ring and

channel speeds caused the beads to remain at the center of the channel.

This position of the beads was then chosen as the criterion for

minimum secondary current effect.

For a more refined measurement of the ring-channel speed

ratios corresponding to minimum secondary current effect, kaolinite










sediment itself was introduced into the channel. Since preliminary

values of these ratios were already available from the tests using

beads, in a given test, the ring and channel were rotated at speeds

corresponding to a known ratio, and after several hours during which

the initially suspended sediment was allowed to deposit, the system

was gently brought to a stop. Then after any remaining small fraction

of the total sediment settled out, thus freeing the water of any

turbidity, the sediment bed depth across the width of the channel was

measured. This was done with the help of a point gage with vernier scale.

If these measurements showed that the bed was too thick near the inner

wall of the channel, the test was carried out again with a slightly lower

ring speed. On the other hand, if the bed was found to be too thick near

the outer wall of the channel, the test was performed with a slightly

higher ring speed. This way, by trial and error adjustments, it was

possible to accurately determine the ring-channel speed ratios corres-

ponding to a uniform sediment deposition across the width of the channel.

Bed depth measurements are discussed in Appendix A. After several measure-

ments at various ring-channel speed ratios, or speed combinations,

and at different flow depths, it was found that in measurements

using beads, the ring was rotating faster than the required speed

for a uniform sediment deposition, and that in all cases its speed

had to be reduced by 9.5%. This discrepancy between the values

obtained by using beads and those obtained using the sediment is

attributed to the fact that while the mean radius of the beads is

3/16 in., the effective mean radius of the sediment flocs is probably

not more than a few hundred microns. Therefore, since the relative














strengths of the secondary currents due to the ring and the channel

are expected to vary with the distance from the bottom of the channel,

the beads, with their relatively large size, are acted upon by

secondary currents of different strengths than those acting on the

comparatively small sediment flocs. This results in a difference

between the ratios of ring-channel speeds for a minimal secondary

effect,which requires the beads on the one hand and the sediment on

the other to remain uniformly distributed. Essentially therefore,

the beads were too large for accurately simulating sediment motion.

The ring-channel speed combination is herein referred to as

"operational speed." Fig. 3.2.3 shows the operational speeds for

flow depths ranging from 2 in. to 14 in. The measurements corres-

ponding to the slowest operational speeds correspond to a channel

speed of 1.35 rpm. Below this value, it was difficult to move the

beads with the prevailing shear stresses. The straight line corres-

ponding to depth d = 0 in. is of course the one for which the ring

and channel speeds are equal, since at zero depth, both of them have

the same area of contact. Also, it is clearly observed that as pointed

out earlier, as the depth increases for a constant channel speed,

the ring has to be rotated with increasing speed to maintain a minimal

secondary flow effect. In all the experiments, the plot of Fig. 3.2.3

was used to obtain the ring speed, for a given channel speed and depth

of flow.


3.2.3 Calibration of Equipment for Shear Stress Measurements


For the determination of the bed shear stress in the channel,




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