• TABLE OF CONTENTS
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 Front Cover
 Report documentation page
 Title Page
 Abstract
 Table of Contents
 Part I. Relationship between the...
 Part II. In-situ rheometry for...
 Bibliography
 Appendix: Solution for V/V(0)






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 92/015
Title: Laboratory experiments on cohesive soil bed fluidizatino by water waves
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 Material Information
Title: Laboratory experiments on cohesive soil bed fluidizatino by water waves
Series Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 92/015
Physical Description: Book
Creator: Feng, Jingzhi
Mehta, Ashish J.
Williams, David J. A.
Williams, P. Rhodri
Publisher: Coastal and Oceanographic Engineering Department, University of Florida
Publication Date: 1992
 Subjects
Subject: Rheology
Fluid mechanics
Fluidization
Mud
 Notes
Abstract: Part I. Relationships between the rate of bed fluidization and the rate of wave energy dissipation, by Jingzhi Feng and Ashish J. Mehta and Part II. In-situ rheometry for determining the dynamic response of bed, by David J.A. Williams and P. Rhodri Williams.
 Record Information
Bibliographic ID: UF00079947
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.

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Table of Contents
    Front Cover
        Front Cover
    Report documentation page
        Unnumbered ( 2 )
        Unnumbered ( 3 )
    Title Page
        Page i
    Abstract
        Page ii
        Page iii
    Table of Contents
        Page iv
        Page v
        Page vi
    Part I. Relationship between the rate of bed fluidization and the rate of wave energy dissipation
        Part I - i
        Part I. List of figures
            Part I - ii
            Part I - iii
            Part I - iv
        Part I. List of tables
            Part I - vi
            Part I - vii
        Introduction
            Part 1 - 1
            Part 1 - 2
            Part 1 - 3
            Part 1 - 4
        Study background and methodology
            Part 1 - 5
            Part 1 - 6
            Part 1 - 7
            Part 1 - 8
            Part 1 - 9
            Part 1 - 10
            Part 1 - 11
            Part 1 - 12
            Part 1 - 13
        Preliminary experiments
            Part 1 - 14
            Part 1 - 15
            Part 1 - 16
            Part 1 - 17
            Part 1 - 18
            Part 1 - 19
            Part 1 - 20
            Part 1 - 21
            Part 1 - 22
            Part 1 - 23
            Part 1 - 24
            Part 1 - 25
            Part 1 - 26
            Part 1 - 27
            Part 1 - 28
            Part 1 - 29
            Part 1 - 30
            Part 1 - 31
            Part 1 - 32
            Part 1 - 33
            Part 1 - 34
            Part 1 - 35
            Part 1 - 36
            Part 1 - 37
            Part 1 - 38
            Part 1 - 39
            Part 1 - 40
            Part 1 - 41
            Part 1 - 42
            Part 1 - 43
            Part 1 - 44
            Part 1 - 45
            Part 1 - 46
            Part 1 - 47
            Part 1 - 48
            Part 1 - 49
            Part 1 - 50
            Part 1 - 51
            Part 1 - 52
            Part 1 - 53
            Part 1 - 54
            Part 1 - 55
            Part 1 - 56
            Part 1 - 57
            Part 1 - 58
            Part 1 - 59
            Part 1 - 60
        Mud bed fluidization experiments
            Part 1 - 61
            Part 1 - 62
            Part 1 - 63
            Part 1 - 64
            Part 1 - 65
            Part 1 - 66
            Part 1 - 67
            Part 1 - 68
            Part 1 - 69
            Part 1 - 70
            Part 1 - 71
            Part 1 - 72
            Part 1 - 73
            Part 1 - 74
            Part 1 - 75
            Part 1 - 76
            Part 1 - 77
            Part 1 - 78
            Part 1 - 79
            Part 1 - 80
            Part 1 - 81
            Part 1 - 82
            Part 1 - 83
            Part 1 - 84
            Part 1 - 85
            Part 1 - 86
            Part 1 - 87
            Part 1 - 88
            Part 1 - 89
            Part 1 - 90
            Part 1 - 91
            Part 1 - 92
            Part 1 - 93
            Part 1 - 94
            Part 1 - 95
            Part 1 - 96
            Part 1 - 97
            Part 1 - 98
            Part 1 - 99
            Part 1 - 100
            Part 1 - 101
            Part 1 - 102
            Part 1 - 103
        Conclusions
            Part 1 - 104
            Part 1 - 105
            Part 1 - 106
            Part 1 - 107
            Part 1 - 108
    Part II. In-situ rheometry for determining the dynamic response of bed
        Part 1 - 109
        List of figures
            Part 1 - 110
        List of Tables
            Part 1 - 111
        Introduction
            Part 1 - 112
            Part 1 - 113
        Rheometry
            Part 1 - 114
            Part 1 - 115
            Part 1 - 116
            Part 1 - 117
        Theoretical bases
            Part 1 - 118
            Part 1 - 119
            Part 1 - 120
            Part 1 - 121
            Part 1 - 122
        Experimental considerations
            Part 1 - 123
            Part 1 - 124
            Part 1 - 125
            Part 1 - 126
        Flume experiments
            Part 1 - 127
            Part 1 - 128
            Part 1 - 129
        Analysis and discussion
            Part 1 - 130
            Part 1 - 131
            Part 1 - 132
            Part 1 - 133
            Part 1 - 134
    Bibliography
        Part 1 - 135
    Appendix: Solution for V/V(0)
        Part 1 - 136
Full Text




UFL/COEL-92/015


LABORATORY EXPERIMENTS ON COHESIVE SOIL
BED FLUIDIZATION BY WATER WAVES



PART I: RELATIONSHIP BETWEEN THE RATE OF BED
FLUIDIZATION AND THE RATE OF WAVE ENERGY DISSIPATION

by

Jingzhi Feng and Ashish J. Mehta

PART II: IN-SITU RHEOMETRY FOR DETERMINING THE
DYNAMIC RESPONSE OF BED

by

David J.A. Williams and P. Rhodri Williams


December, 1992






REPORT DOCUMENTATION PAGE
1. Report No. 2. 3. Recipiat 'a Aceeaioan o.


4. Title anod Subtitle 5. Report Date
LABORATORY EXPERIMENTS ON COHESIVE SOIL BED December, 1992
FLUIDIZATION BY WATER WAVES: PARTS I AND II 6.

7. Author(s) 8. Perforlai Organization Report No.
PART I: Jingzhi Feng and Ashish J. Mehta
PART II: David J.A. Williams and P. Rhodri Williams UFL/COEL-92/015
9. Perforing Organization a e and Address 10. Project/Taak/tork Unit Mo.
Coastal and Oceanographic Engineering Department
University of Florida
336 Weil Hall 11. Cotrace or Grant No.
3 DACW39-90-K-0010
Gainesville, FL 32611 DACW39-9
13. Type of Report
12. Sponsoring Organization lase and Address
U.S. Army Engineer Waterways Experiment Station Final
3909 Halls Ferry Road
Vicksburg, MS 39180-6199
14.
15. Supplmentary NoMt
PART I: RELATIONSHIP BETWEEN THE RATE OF BED FLUIDIZATION AND THE RATE OF WAVE ENERGY
DISSIPATION
PART II: IN-SITU RHEOMETRY FOR DETERMINING THE DYNAMIC RESPONSE OF BED
16. Abstract

A series of preliminary laboratory flume experiments were carried out to examine the time-dependent
behavior of a cohesive soil bed subjected to progressive, monochromatic waves. The bed was an aqueous,
50/50 (by weight) mixture of a kaolinite and an attapulgite placed in a plexiglass trench. The nominal bed
thickness was 16 cm with density ranging from 1170 to 1380 kg/m3, and water above was 16 to 20 cm
deep. Waves of design height ranging from 2 to 8 cm and a nominal frequency of 1 Hz were run for
durations up to 2970 min. Part I of this report describes experiments meant to examine the rate at which
the bed became fluidized, and its relation to the rate of wave energy dissipation. Part II gives results on
in-situ rheometry used to track the associated changes in bed rigidity.
Temporal and spatial changes of the effective stress were measured during the course of wave action,
and from these changes the bed fluidization rate was calculated. A wave-mud interaction model developed
in a companion study was employed to calculate the rate of wave energy dissipation. The dependence of
the rate of fluidization on the rate of energy dissipation was then explored.
Fluidization, which seemingly proceeded down from the bed surface, occurred as a result of the loss
of structural integrity of the soil matrix through a buildup of the excess pore pressure and the associated

17. Origiaator's Key Words 1I. Availability Statmet
Cohesive sediments Resuspension
Energy dissipation Rheology
Fluidization Rheometry
Fluid mud Water waves
Pore pressures
19. U. S. Security as of the ReportCl of Thi Page 21. o. of Page 22. Price
Unclassified Unclassified 148








loss of effective stress. The rate of fluidization was typically greater at the beginning of wave action and
apparently approached zero with time. This trend coincided with the approach of the rate of energy
dissipation to a constant value. In general it was also observed that, for a given wave frequency, the larger
the wave height the faster the rate of fluidization and thicker the fluid mud layer formed. On the other
hand, increasing the time of bed consolidation prior to wave action decreased the fluidization rate due to
greater bed rigidity. Upon cessation of wave action structural recovery followed.
Dynamic rigidity was measured by specially designed, in situ shearometers placed in the bed at
appropriate elevations to determine the time-dependence of the storage and loss moduli, G' and G", of
the viscoelastic clay mixture under 1 Hz waves. As the inter-particle bonds of the space-filling, bed
material matrix weakened, the shear propagation velocity decreased measurably. Consequently, G'

decreased and G" increased as a transition from dynamically more elastic to more viscous response
occurred. These preliminary experiments have demonstrated the validity of the particular rheometric
technique used, and the critical need for synchronous, in-situ measurements of pore pressures and moduli
characterizing bed rheology in studies on mud fluidization.
This study was supported by WES contract DACW39-90-K-0010.



















LABORATORY EXPERIMENTS ON COHESIVE SOIL BED FLUIDIZATION BY
WATER WAVES


PART I: RELATIONSHIP BETWEEN THE RATE OF BED FLUIDIZATION AND
THE RATE OF WAVE ENERGY DISSIPATION

By

Jingzhi Feng and Ashish J. Mehta


PART II: IN-SITU RHEOMETRY FOR DETERMINING THE DYNAMIC RESPONSE
OF BED



By


David J.A. Williams and P. Rhodri Williams















SYNOPSIS


A series of preliminary laboratory flume experiments were carried out to examine

the time-dependent behavior of a cohesive soil bed subjected to progressive, monochromatic

waves. The bed was an aqueous, 50/50 (by weight) mixture of a kaolinite and an attapulgite

placed in a plexiglass trench. The nominal bed thickness was 16 cm with density ranging

from 1170 to 1380 kg/m3, and water above was 16 to 20 cm deep. Waves of design height

ranging from 2 to 8 cm and a nominal frequency of 1 Hz were run for durations up to 2970

min. Part I of this report describes experiments meant to examine the rate at which the

bed became fluidized, and its relation to the rate of wave energy dissipation. Part II gives

results on in-situ rheometry used to track the associated changes in bed rigidity.

Temporal and spatial changes of the effective stress were measured during the course of

wave action, and from these changes the bed fluidization rate was calculated. A wave-mud

interaction model developed in a companion study was employed to calculate the rate of

wave energy dissipation. The dependence of the rate of fluidization on the rate of energy

dissipation was then explored.

Fluidization, which seemingly proceeded down from the bed surface, occurred as a result

of the loss of structural integrity of the soil matrix through a buildup of the excess pore

pressure and the associated loss of effective stress. The rate of fluidization was typically

greater at the beginning of wave action and apparently approached zero with time. This

trend coincided with the approach of the rate of energy dissipation to a constant value. In

general it was also observed that, for a given wave frequency, the larger the wave height the

faster the rate of fluidization and thicker the fluid mud layer formed. On the other hand,

increasing the time of bed consolidation prior to wave action decreased the fluidization rate

due to greater bed rigidity. Upon cessation of wave action structural recovery followed.


I








Dynamic rigidity was measured by specially designed, in situ shearometers placed in

the bed at appropriate elevations to determine the time-dependence of the storage and loss

moduli, G' and G", of the viscoelastic clay mixture under 1 Hz waves. As the inter-particle

bonds of the space-filling, bed material matrix weakened, the shear propagation velocity

decreased measurably. Consequently, G' decreased and G" increased as a transition from

dynamically more elastic to more viscous response occurred. These preliminary experiments

have demonstrated the validity of the particular rheometric technique used, and the critical

need for synchronous, in-situ measurements of pore pressures and moduli. characterizing

bed rheology in studies on mud fluidization.

This study was supported by WES contract DACW39-90-K-0010.









TABLE OF CONTENTS


SY N OPSIS . . . . .. . . . . . ii
PART I: RELATIONSHIP BETWEEN THE RATE OF BED FLUIDIZATION AND THE
RATE OF WAVE ENERGY DISSIPATION
LIST OF FIGURES .................................... ii
LIST OF TABLES .................................... v
CHAPTER
1 INTRODUCTION ........ .... ... ..... .............. 1
1.1 Brief Background ... ................... .... .... .... 1
1.2 Objectives and Scope ........ .... ............... .... 2
1.3 Outline of Presentation ........ ...... ...... .. ........ 4
2 STUDY BACKGROUND AND METHODOLOGY ................ 5
2.1 Fluid Mud Definition ................................ 5
2.2 Definition of Fluidization ............................ 7
2.3 Wave-induced Fluidization ............................ 10
2.4 Tasks .......................... ........... 11
3 PRELIMINARY EXPERIMENTS ........ ....... ......... 14
3.1 Sediment and Fluid Characterization ............ .... ..... 14
3.2 Rheological Experiments ...................... ...... 19
3.2.1 Influence of Shear Rate ..... ............... .... 21
3.2.2 Influence of Shearing Time ... ...... .... ...... 30
3.2.3 Upper Bingham Yield Stress ...................... 31
3.2.4 Gelling ........... ........ .............. 32
3.2.5 Summary .. ....... ........... ........... 32
3.3 Instrumentation ........ .... ...... ........ ....... 33
3.3.1 Wave Gauges ...... ...... .......... ........ .. 33
3.3.2 Current Meter .. .... ....... ..... ........... 34
3.3.3 Pressure Transducers ... ........... ..... ......... 36
3.3.4 Data Acquisition System .... ........ .. ....... 37
3.4 Flume Characterization Tests ... ...................... .. 37
3.4.1 Test Conditions .. ............................ 43
3.4.2 W ave Spectra ............................... 46
3.4.3 Wave Reflection Estimation . . . ... . 46
3.4.4 Current Velocity .... ... ....... ........ .. .. 50


I









4 ESTIMATIONS OF FLUID MUD THICKNESS AND WAVE ENERGY DISSIPA-
TIO N . .. . . . . . . . . 53
4.1 Introduction ..................... .............. 53
4.2 Effective Sheared Mud Thickness ................. ...... .. 53
4.3 Wave Energy Dissipation Rate ........................ 58
5 MUD BED FLUIDIZATION EXPERIMENTS ..................... 61
5.1 Test Conditions .................... .............. 61
5.2 Flume Data ..................... ............... 63
5.2.1 Wave Time-series ............................. 63
5.2.2 Wave Spectra ............................... 64
5.2.3 Water/mud Interface ........................... 64
5.2.4 Density Measurement ................... .... 64
5.2.5 Total and Pore Water Pressures . . . .. .. 68
5.2.6 Bottom Pressure Gauge Data, Text # 9 . . . .... 70
5.2.7 Rms Pressure Amplitudes, Test #9 . . . .... 72
5.2.8 Pressure Recovery after End of Test . . . ... 73
6 EXPERIMENTAL DATA ANALYSIS ........................ 76
6.1 Introduction .. ................. ........... ........ 76
6.2 Wave-Mud Interaction Model Results . . . .. ... 76
6.2.1 Wave Regime: Test Versus Model Conditions . . .... 76
6.2.2 Effective Sheared Mud Thickness . . . .. .. 77
6.2.3 Wave Energy Dissipation ........................ 79
6.3 Flume Test Results ................... .............. 88
6.3.1 Effective Stress ............................. 88
6.3.2 Fluidized Mud Thickness ........................ 93
6.3.3 Rate of Fluidization .... ........... ..... ..... 94
6.4 Comparison between Model Results and Experiments . . .... 98
6.4.1 Fluidized mud thickness, df, and Effective sheared mud thickness, d 98
6.4.2 Fluidization Rate as a Function of Wave Energy Dissipation Rate .100
7 CONCLUSIONS ................... ............... 104
7.1 Conclusions ................... .............. 104
7.2 Significance of the Study ................... .......... 105
BIBLIOGRAPHY ................... ................. 107











PART II: IN-SITU RHEOMETRY FOR DETERMINING THE DYNAMIC RESPONSE

OF BED


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

LIST OF TABLES ..................

CHAPTER

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

1.1 Preamble ...................

1.2 Investigation .................

2 RHEOMETRY ...................

2.1 In-situ Rheometry ..............

2.2 Shear Wave Rig ................

2.3 Ancillary Equipment .............

2.4 Signal Processing and Data Analysis ....

3 THEORETICAL BASIS .............

3.1 Definitions of G' and G" ............

3.2 Shear Wave Velocity Determination ...

3.3 Voigt and Maxwell Models ..........

4 EXPERIMENTAL CONSIDERATIONS ....

4.1 M materials ...................

4.2 In-situ Rheometry ..............

4.3 Shear Wave Velocities ............

5 FLUME EXPERIMENTS ............

5.1 Initial Condition ...............

5.2 Preliminary Tests with 20 mm Water Waves

5.3 Tests with 40 mm Water Waves .......

5.4 Tests with 20 mm Water Waves .......

6 ANALYSIS AND DISCUSSION .........

6.1 Shear Wave Velocity .............

6.2 Temporal Response of Bed in Terms of Mod

6.3 Concluding Remarks .............

BIBLIOGRAPHY ...................

APPENDIX: SOLUTION FOR V/V(0) .......


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el Parameters.

.........

.........

.. .


I


. . . . . .

..................



























PART I: RELATIONSHIP BETWEEN THE RATE OF BED FLUIDIZATION AND
THE RATE OF WAVE ENERGY DISSIPATION







By







Jingzhi Feng and Ashish J. Mehta















LIST OF FIGURES


2.1 Schematic of water column with a muddy bottom in terms of vertical
profiles of sediment density and velocity, and vertical sediment fluxes .. 6

2.2 Soil mass subjected to stress loading . . . . 8

2.3 Definition sketch of soil stress terminology . . . . 9

2.4 Fluidization process of a soil bed at a given elevation . ... 10

2.5 Influence of waves on shear resistance to erosion of kaolinite beds in flumes 11

3.1 SEM of dry agglomerates of attapulgite. Scale 1cm = 10m . 18

3.2 SEM of dry agglomerates of bentonite. Scale 1cm = 10pm ...... .. 18

3.3 SEM of dry agglomerates of kaolinite. Scale 1cm = 10im . ... 19

3.4 Shear stress, a, versus shear rate, 4, (K,A,B) . . ..... 22

3.5 Shear stress, oa, versus shear rate, 4, (AK,BK,AB) . . .... 23

3.6 Shear stress, a, versus shear rate, 4, (K,KS,A,AS,B,BS) . . 24

3.7 Shear stress, a, versus shear rate, 4, (BK,BKS,AK,AKS,AB,ABS) 25

3.3 Viscosity, p, versus shear rate, 4, (K,KS,A,AS,B,BS) . . .. 26

3.9 Viscosity, /, versus shear rate, 4, (BK,BKS,AK,AKS,AB,ABS) . 27

3.10 Calibration curves for the wave gauges . . . ..... 35

3.11 Calibration curve for the current meter . . . ..... 35

3.12 Calibration curves for the total pressure gauges . . ... 38

3.13 Calibration curves for the pore pressure gauges . . .... 39

3.14 Dynamic response of pressure gauges, and comparison with results from
the linear wave theory: gauge elevations ranging from 0 to 4.9 cm 40




ii










3.15 Dynamic response of pressure gauges, and comparison with results from
the linear wave theory: gauge elevations ranging from 7.5 to 14 cm 41

3.16 Example of instrument drift, in pore pressure measurement, with old
and new amplifiers. Gauge #2 was connected to the "new" amplifier.
Comparison is made with gauge #3 response connected to the "old"
am plifier . .. .. .. ...... .. . . .......... 42

3.17 Example of instrument drift, pore pressure gauge #1, Time range over
which most of the pressure data were obtained is indicated. ...... 42

3.18 Wave flume elevation profile and instrument locations .......... 44

3.19 Examples of wave time-series (depth=20cm, period=1.0s) for flume char-
acterization tests with a false bottom . . . .... 45

3.20 Wave spectra, water depth=20cm; average wave height ranging from 3.9
to 4.6 cm, period ranging from 1 to 2 sec. . . . .... 47

3.21 Wave spectra, water depth=20cm; average wave height ranging from 6.4
to 9.1 cm, period ranging from 1 to 2 sec. . . . .... 48

3.22 Horizontal velocity profiles: comparison between experimental data (rms
amplitudes) and linear wave theory (peorid T=1.0s) . . ... 52

4.1 Two-layered water-fluid mud system subjected to progressive wave action 54

4.2 Diagram of calculation process for effective sheared mud thickness, d 57

5.1 Sketch of flume profile in the fluidization experiment . ... 62

5.2 Wave time-series, Test #9 ......................... 65

5.3 W ave spectra, Test #9 ................... ........ 67

5.4 Time-variation of water-mud interface along the flume, Test #9 . 68

5.5 Examples of density profiles, Test #9. Dashed line indicates interfacial
elevation ... ..... .......... ..... . .......... 69

5.6 Wave-averaged total and pore water pressures, Test #9 . . 71

5.7 Total pressure at the bottom of the flume, Test #9 . . 72

5.8 Root-mean square pore water pressure amplitudes, Test #9 ..... .. 74

5.9 Root-mean square total pressure amplitudes, Test #9 . ... 75

6.1 Effective sheared mud thickness, d, Tests #1 through #3 . ... 80

6.2 Effective sheared mud thickness, d, Tests #4 through #7 . ... 81


i










6.3 Effective sheared mud thickness, d, Tests #8 through #11 ...... .. 82

6.4 Wave dissipation rate, sD, versus time: Tests #1 through #3 . 84

6.5 Wave dissipation rate, ED, versus time: Tests #4 through #7. Design
wave heights are from Table 5.1 . . ... . ....... 85

6.6 Wave dissipation rate, eD, versus time: Tests #8 through #11. Design
wave heights are from Table 5.1 . . . ..... . 86

6.7 ED, k, and a,2 versus time: Tests #9 ................... 87

6.8 Effective stress, a, variations with time: Test 8 . . .. 89

6.9 Effective stress, a, variations with time: Test #9 . . .. 90

6.10 Effective stress, a, variations with time: Test 10 . . ... 91

6.11 Effective stress, ', variations with time: Test #11 . . ... 92

6.12 Bed elevation, water/mud interface, and fluidized mud thickness in Tests
#8 through #11 ................... ........... 95

6.13 Fluidized mud thickness, df, variations with time . . ... 96

6.14 Bed fluidization rate, 9Hi/9t, versus time ................ 99

6.15 Comparison between fluidized mud thickness, df, and effective sheared
mud thickness, d ................... ............ 101

6.16 Wave energy dissipation rate, ED, versus time for tests #9 and #10. .102

6.17 Fluidization rate, a9Hb/9t, versus wave energy dissipation rate, ED, tests
#9 and #10. Dashed lines indicate exptrapolations . . ... 103
















LIST OF TABLES




3.1 Chemical composition of kaolinite . . . ..... 15

3.2 Chemical composition of bentonite . . . ...... 15

3.3 Chemical composition of attapulgite (palygorskite) . . ... 15

3.4 Chemical composition of tap water . . . ...... 15

3.5 Size distribution of kaolinite . . . ... ........ .. 16

3.6 Size distribution of bentonite . . . ... ...... .. 17

3.7 Size distribution of attapulgite . . . ... ..... .. 17

3.8 Selected muds (days and clay mixtures) for theological tests . 20

3.9 Parameters for the Sisko power-law model for viscosity . ... 30

3.10 Shearing time effect on shear stress . . . ...... 31

3.11 Upper Bingham yield stress ........................ 32

3.12 Rheological parameters for power-law given by Equation 3.4 . 34

3.13 Wave conditions for the charaterization tests ... . .... 46

3.14 Wave reflection coefficient, k . . . . . 50

5.1 Summary of test conditions ................... ...... 63

5.2 W ave heights, Test #9 .......................... 64

6.1 Parameters for determining the water wave condition . ... 77

6.2 Input parameters for calculating the effective sheared mud thickness .. 79

6.3 Values of the (representative) constant effective sheared mud thickness,
d,, and /. ................... .................. 83

6.4 Representative values of the wave energy dissipation rate, ED, ..... 88

6.5 Effective stress, ', at the beginning and end of Test #9 . ... 91










6.6 Bed elevation and fluidized mud thickness at different times . 97
















CHAPTER 1
INTRODUCTION



1.1 Brief Background

The interaction between unsteady flows and very soft muddy bottoms, a key process

in governing coastal and estuarine cohesive sediment transport, is not well understood at

present. What is quite well known, however, is that oscillatory water motion, by "shaking"

and "pumping," generates fluid mud which is a high concentration near-bed slurry having

non-Newtonian theological properties. This mud therefore becomes potentially available

for transport by uni-directional currents. The precise mechanism by which fluid mud is

formed by water wave motion over cohesive soil beds is of evident interest in understand-

ing and interpreting the microfabric of flow-deposited fine sediments in shallow waters, and

hence the erodibility of muddy beds due to hydrodynamic forcing. Results from preliminary

laboratory tests in a wave flume by Ross (1988), using known soil mechanical principles,

indicated that the fluidization process is perhaps even more significant in generating po-

tentially transportable sediment than previously realized. It was therefore decided in the

present study to extend this work of Ross to examine the inter-relationship between soil

mechanical changes and wave energy input, and to understand the bed fluidization process

through these changes under loading by progressive, non-breaking water waves.

Unlike the boundary of soil beds composed of cohesionless material (e.g., sand), the

cohesive soil bed boundary is often poorly defined, as it is not evident, e.g., from echo-

sounder data, at what depth the near-bed suspension ends and the soil bed begins. The

marine cohesive soil bed is primarily composed of flocculated, fine-grained sediment with

a particle-supported structured matrix, hence a measurable shear strength. On the other

hand, fluidized mud is a suspension which by definition is essentially fluid-supported. Parker









2
(1986) noted ambiguities when lead lines, echo-sounders or nuclear transmission or back-

catter gauges were used to identify the cohesive soil bed boundary below a fluid-supported,

high concentration sediment slurry.

Many investigators have identified fluid mud slurry in terms of a range of bulk density

of the sediment-fluid mixture. For example, Inglis and Allen (1957) defined fluid mud by

the density range of 1.03-1.30 g/cm3, while Krone (1962) used a density range of 1.01-

1.11 g/cm3 to define fluid mud. Wells (1983) specified a density range of 1.03-1.30 g/cm3,

Nichols (1985), 1.003-1.20 g/cm3, and Kendrick and Derbyshire (1985) 1.12-1.25 g/cm3 as

fluid mud. These ranges are not congruent in general. In fact, to provide a quantitative

definition for fluid mud based on a discrete density range is not possible because the effect

is not simply dependent on the density, but also on the flow condition and the sediment

properties. Thus, Ross et al. (1987) noted that due to the dynamic nature of the cohesive

bed boundary which responds significantly to hydrodynamic forcing, e.g., waves, the density

of the suspension by itself cannot be used either to identify the cohesive bed boundary or

the fluid mud layer which occurs immediately above this boundary. The fluidization of the

cohesive soil bed, accompanied by measurable degradation in soil geotechnical properties,

should in fact be quantified by measuring soil pressures since the bed is characterized by

the occurrence of a measurable effective stress, while the overlying fluid has practically none

(Ross et al., 1987). Therefore the zero effective stress plane defines the bed surface. Given

these soil characteristics, and the desire to better understand the fluidization process under

wave action, the following objectives and scope were set for the ensuing work.

1.2 Objectives and Scope

At the outset it is necessary to mention again the work of Ross (1988), who conducted

flume tests using a Kaolinite estuarine sediment to study wave-induced cohesive soil bed

fluidization. Total and pore water pressures were measured to obtain the effective stress,

which in turn was used for tracking bed elevation change during the fluidization process,

and fluid mud thickness determined from the bed elevation change. However, in his work









3
the wave dissipation rate during fluidization was not calculated; therefore the possibility

of a dependence of the bed fluidization rate on the rate of wave energy dissipation could

not be explored. Given this limitation of Ross's work, the objectives of this study were to

simultaneously evaluate the effective stress response (via soil pressure measurement), and

wave dissipative characteristics (through a hydrodynamic wave-mud interaction model),

and from these to explore the relationship between the process of mud fluidization and

wave energy input for selected cohesive soil beds subjected to progressive wave action in

a laboratory flume. By way of this approach, several fundamental issues related to the

manner in which the cohesive bed fluidizes were chosen to be examined. Specifically the

following aspects were considered:

1. To measure total and pore pressure profiles in the mud as a function of time under

different wave conditions, as well as the corresponding damping characteristics of the

surface waves.

2. To measure changes in the effective stress within the mud, and to investigate the

definition of the cohesive bed boundary based on tracking the zero (or near-zero)

effective stress level.

3. To determine if any tangible relationship exists between the rate of the bed fluidiza-

tion, bed consolidation time and the rate of wave energy dissipation.

4. To compare the measured fluidized layer thickness and the calculated effective sheared

mud thickness (a chosen measure of fluid mud thickness) from a two layered hydro-

dynamic wave-mud interaction model.

To meet the above objectives, the scope of this research was selected to be as follows:

1. The investigation was limited to using commercial clays whose theological properties

could be relatively easily characterized.

2. Waves were restricted to regular (monochromatic), 1 Hz progressive and non-breaking

type, while wave heights ranged from 2 to 8 cm.









4
3. Mud bed thickness was limited to 10 -20 cm. The water level was maintained to be

35 cm above the flume bottom in all cases.

4. Different consolidation periods, from one to ten days, for the mud beds were selected,

the tests been limited to self-weight consolidation.

5. Tap water was used, and a 50/50 (by weight) mixture of attapulgite and kaolinite was

used to prepare the bed for the fluidization tests.


1.3 Outline of Presentation

Chapter 2 reviews the definition and theory of fluidization of mud, and also gives the

approach to this study. All preliminary experiments, including auxiliary tests involving on

the theological properties of selected muds, instrument calibration tests and flume charac-

terization tests are presented in Chapter 3. The selected two-layered hydrodynamic wave-

mud interaction model for calculating the rate of wave energy dissipation and the effective

thickness of fluidized mud are described in Chapter 4. Chapter 5 presents the fluidization

experiments including test conditions, wave data, total and pore water pressure data, eleva-

tions of water/mud interface, and mud density measurements. Data analysis and results are

presented and discussed in Chapter 6. Chapter 7 concludes the presentation of the entire

investigation.
















CHAPTER 2
STUDY BACKGROUND AND METHODOLOGY



2.1 Fluid Mud Definition

As mentioned in Chapter 1, many investigators have identified fluid mud in terms of

a range of bulk density of the sediment-fluid mixture. Since fluid mud properties depend

on the physico-chemical properties of this mixture and the hydrodynamic settling, a unique

density range cannot be defined appropriately on theoretical grounds, hence a definition

that accounts for the dynamical effects can significantly assist in estimating, for example,

the rate of advective mud transport.

It has been suggested that the fluid mud density range be preferably examined in con-

junction with the corresponding horizontal velocity field (Ross et al., 1987). Figure 2.1

shows the various layered regimes resulting from cohesive bed response to waves, defined

by the profiles of instantaneous vertical density (or concentration) and velocity amplitude,

Ur, (Mehta, 1989). The density profile has been idealized by indicating only two significant

concentration gradients that categorize the water-mud system into three zones. The top

zone, which is above the upper gradient, is a mobile, relatively low concentration suspen-

sion, which may be less than 1 gl-', but can exceed 2-3 gl-1 during extreme energy events

(Ross & Mehta, 1989). This suspension is practically a Newtonian fluid. The lower gradient

defines the cohesive bed within which there is sufficient interparticle contact to result in a

finite, measurable effective stress. Between the two concentration gradients there occurs a

relatively high concentration layer (e.g., up to 200 g1-1) as fluid mud. As noted in Chap-

ter 1 it is essentially a fluid-supported slurry with non-Newtonian theological properties,

typically appearing to conform to a pseudoplastic (shear thinning) or dilatant (shear thick-

ening) description with respect to the stress-rate of strain relationship, depending upon













_MWL


Mobile
SSuspension


Q Entrainment
A .Lutocline Settling
u Fluid Mud


Fluidization
FuidizatiFormation Deforming Bed

Cn iatio Stationary Bed
Consolidation


Figure 2.1: Schematic of water column with a muddy bottom in terms of vertical profiles
of sediment density and velocity, and vertical sediment fluxes

mud composition, concentration, and the rate of shearing.

The fluid mud zone is of particular practical importance because this mud can be

easily entrained and thereby substantially contribute to turbidity even under relatively

low energy inputs, due to its high concentration and very weak internal structure (Ross,

1988). Fluid mud also plays a significant role in absorbing and dissipating turbulent kinetic

energy, which can cause a transition from a typically visco-elastic response to a more viscous

shear flow behavior. Depending on the time-history of the applied interfacial shear stress

above the fluid mud layer, a finite depth limit of horizontal mobilization corresponding to

a momentum diffusion layer within the fluid mud layer occurs. This limit defines the zero

velocity interface which generally exists in the fluid mud layer but is not bounded by either

the mobile suspension/fluid mud interface (or lutocline) or the fluid mud/bed interface.

Under an oscillatory loading, e.g. water waves, the zero velocity elevation can extend well

below the fluid mud/bed interface due to viscoelastic deformations in the cohesive soil bed.

There are three flux-related processes which define the sediment concentration profile:

erosion, deposition, and bed consolidation. For cohesive sediments, however, such terms








7
as erosion and deposition are not always easily defined in an unequivocal sense. Thus,

for example, fluidization of the cohesive soil bed and entrainment of fluid mud due to

hydrodynamic forcing may both be thought of as erosion-type processes, while gravitational

settling of sediment onto the lutocline (water-mud interface), as well as formation of the bed

by dewatering of fluid mud, can be considered to be deposition-type phenomena (Mehta,

1989). These processes are shown in Figure 2.1.

2.2 Definition of Fluidization

Because of the different responses of the solid and the liquid phases to stress loading,

it is necessary to consider each phase independently. The liquid phase is incompressible;

under a differential compressive stress, however, it flows because a liquid, by definition, is

not capable of resisting a shear load. Ultimately, the solid phase controls the resistance to

compression and shear.

Consider a saturated soil mass cut along its surface, as shown in Figure 2.2, subjected to

an applied average normal stress, a. Imagine that the soil mass is cut along a surface so that

a free-body diagram could be drawn. Suppose that this surface is approximately horizontal,

but is wavy, so that it always passes between particles rather than through particles, as

shown in the figure. Then the surface will pass through areas of solid-to-solid contact,

and through void spaces filled with water. Let At be the total horizontal projection of the

cutting surface for the soil mass considered, Ac the horizontal projection of the contact area

between the solids lying in the cutting surface, and A, be the horizontal projection of the

portion of the cutting surface which passes through water. Then, by the requirement of the

force balance in the vertical direction,


aAt = a*Ac + P,,A, (2.1)

where a* is the actual intergranular stress at points of contact, and Pp, is the pressure in

the water, i.e., pore water pressure. Or

A A,
a = a* + Pp (2.2)
At PwAt












'\ I I I II I 1 I I t








'-Arl


Figure 2.2: Soil mass subjected to stress loading

For soils Ac is very small, approaching zero (Sowers, 1979). Therefore, A., approaches At,

and o' must be very large. Thus

a = (' + Pp (2.3)

As noted by Perloff and Baron (1976), the product of o'Ac must approach a finite limit

corresponding to a constant intergranular force, even though a* is very large and A, is very

small. In fact, the first term on the right side of Equation 2.3 must be some measure of the

average stress carried by the soil skeleton. It is called effective stress, ~', defined by


At

Hence by measuring the total stress a and pore water pressure Ppu,, the effective stress at

a point can be obtained from

a= ( Pp (2.5)

which governs the mechanical behavior of soil. For example, a reduction in the effective

stress can lead to a reduction in the soil strength and possibly the critical shear stress for

erosion. Eventually if a' -- 0, there is no contact between the soil particles and a zone of

instability and potential failure is created.

Another important parameter is the excess pore pressure, Au, which is the difference

between actual pore water pressure, Pp,, and the hydrostatic pressure, Ph. Under dynamic














Water Surface



Mobile Suspension
Ph=
0
I- Fluid Mud Surface (Lutocllne)
> = 0 Fluid Mud
LU ___Bed Surface





u,



PRESSURE

Figure 2.3: Definition sketch of soil stress terminology


conditions, if the sum of excess pore pressure, Au, and the hydrostatic pressure, Ph, ap-

proaches the total stress, a, i.e., An + Ph -- a, fluidization occurs (Ross, 1988). Figure 2.3

is an idealized sketch of the stress profile corresponding to three-layered cohesive sediment

concentration profile (see Figure 2.1). In the upper mobile suspension layer the total stress,

a, is equal to the hydrostatic pressure, Ph, within the suspension. In,the fluid mud layer

a increases much more rapidly with depth due to higher sediment concentration, while the

effective stress, a, is still zero. Finally, in the cohesive bed, structural integrity due to closely

packed flocs results in a skeletal framework which partially self-supports the soil medium.

The pore water pressure, Pp,, in the bed is equal to the hydrostatic pressure, Ph, plus the

excess pore water pressure, Au, which represents the component of the bed material not

supported by the porous solid matrix.

Figure 2.4 shows the time changes of the pore water pressure, Ppw, at a given elevation,

leading ultimately to bed fluidization, e.g. by wave action. At first, Pp, in the bed is equal

to the hydrostatic pressure Ph, i.e. Au = 0 (assuming this to be the initial condition). Then

















( y/ /pw

f --------Ph



0 "-
0 TIME


Figure 2.4: Fluidization process of a soil bed at a given elevation

under dynamic loading the excess pore water pressure, Au, builds up and the effective stress

-'reduces gradually. When the pore water pressure Pp, equals the total pressure a-, the bed

at this elevation is fluidized.

2.3 Wave-induced Fluidization

Surface waves and other highly oscillatory currents have a particularly pronounced

influence on erosion in comparison with uni-directional currents. Because of the increased

inertial forces associated with a local change in linear momentum, the net entrainment force

is much greater than with turbulent uni-directional flows (Ross, 1988). Also noteworthy is

the effect that bed 'shaking' and 'pumping' can have under highly oscillatory flows. 'Shak-

ing' or bed vibrations occur because of the oscilatory bed shear stress which is transmitted

elastically (while at the same time damped) down through the bed. 'Pumping' occurs from

oscillatory normal fluid pressure which, given the low permeability of cohesive soils, can lead

to internal pore pressure build up and liquefaction (Ross, 1988). These effects can cause

the dissipation of the effective stress in mud layers depending on the bed characteristics,

thereby leading to mass erosion and fluid mud formation.

The example given in Figure 2.5 shows that resistance to bed erosion under waves was

lower than that for a corresponding bed subjected to steady shear flow (Mehta, 1989). The










r 0.4
o Without Waves (Parchure, 1984)
WL With Waves (Maa, 1986)
Z
.) 0
(n 0.2
3 Wave
Effect



0 0
0 5 10 15

BED CONSOLIDATION PERIOD (Days)
Figure 2.5: Influence of waves on shear resistance to erosion of kaolinite beds in flumes

effect of waves on the resistance to erosion is highlighted for beds of kaolinite of different

consolidation periods in laboratory flumes. Erosion shear strengths representative of the

top, thin bed layer in the upper curve were obtained by Parchure (1984) in the absence of

waves. Representative values of bed shear resistance under waves corresponding to the lower

curve were obtained by Maa (1986). The mean wave height during the wave experiments

was 3.7 cm and the period was 1.6 sec. This example suggests that the fluid mud generating

potential of waves can be a critical factor in eroding the cohesive soil bed, particularly in

shallow water bodies. On the other hand, tidal current tends to serve as the main agent for

advecting fluidized mud.

In the following section, the tasks carried out to meet the objectives of the present

study mentioned in Section 1.2 are enumerated.

2.4 Tasks

The main experiments were carried out in a wave flume in the Coastal Engineering

Laboratory of the University of Florida. The tasks were as follows:


1. Three types of clays, an attapulgite (palygorskite), a bentonite and a kaolinite, which

together covered a wide range of cohesive properties, were initially selected for charac-

terizing their theological properties including viscosity and the upper Bingham yield


I









12
stress, and their time-dependent changes, before conducting the flume tests on flu-

idization.

2. A constitutive power-law model for the viscosity of the selected muds, fitted by the

experimental data, was developed and used in a previously developed two-layered hy-

drodynamic wave-mud interaction model (Jiang & Mehta, 1991) to calculate the wave

energy dissipation rate and the effective sheared mud thickness (defined in Chapter

4), a model-calculated representative of the fluidized mud thickness.

3. A composite mud, prepared from a 50/50 (by weight) mixture of attapulgite and kaoli-

nite, was used to prepare the cohesive soil bed for the mud fluidization experiments.

This bed had a "medium" degree of the resistance to shear stress, and was much

more dissipative, and more realistic, compared with the mud which Ross (1988) used

previously.

4. Wave flume characterization tests were conducted before the mud was introduced to

determine the optimal operational domain for the flume specified by the wave height,

period, and the water depth within which the waves were well behaved.

5. Pairs of total and pore pressure gauges were deployed at different elevations below the

mud surface in a vertical array, and one additional total pressure gauge was mounted

at the bottom of the flume for accurately determining the total load at the bottom.

With these gauges the soil mechanical change during wave action was monitored.

6. Two capacitance gauges within the test section of the flume were used to monitor

the wave amplitudes. Bulk density profiles of the deposit during wave action were

measured vertically with a Paar (model 2000) density meter.

7. The hydrodynamic wave-mud interaction model was used to calculate the effective

sheared mud thickness, and the wave energy dissipation rate.









13
8. The effective sheared mud thickness from the hydrodynamic model was compared with

the fluidized mud thickness obtained from the flume pressure measurements. Also, the

relationship between the rate of wave energy dissipation and the rate of fluidization

was investigated.
















CHAPTER 3
PRELIMINARY EXPERIMENTS



3.1 Sediment and Fluid Characterization

Three types of commercially available clays: a kaolinite, a bentonite, and an atta-

pulgite, which together cover a wide range of cohesive properties, were initially selected.

Kaolinite (pulverized kaolin), a light beige-colored power, was purchased from the EPK

Division of Feldspar Corporation in Edgar, Florida. The Cation Exchange Capacity (CEC)

of the kaolinite given by the supplier is 5.2-6.5 milliequivalents per 100 grams. Bentonite

was obtained from the American Colloid Company in Arlington Heights, Illinois. It is a

sodium montmorillonite, its commercial name is Volclay and is light gray in color. Its CEC

is about 105 milliequivalents per 100 grams. Attapulgite, of greenish-white color, was pur-

chased from Floridin in Quincy, Florida. It is also called palygorskite, and its CEC is 28

milliequivalents per 100 grams as given by the supplier. Tables 3.1 through 3.3 give the

chemical compositions of the three clays (given by the suppliers).

Table 3.4 gives the results of chemical analysis of the tap water used to prepare mud,

whose pH value was 8 and conductivity 0.284 milimhos. This analysis was conducted in the

Material Science Department of the University of Florida. The procedure was as follows:

firstly, an element survey of both the tap water and double-distilled water was performed,

which determined the ions in tap water. Secondly, standard solutions of these ions contained

in the tap water were made, and the tap water was analyzed against the standard solutions

to determine the concentrations of the ions by an emission spectrometer (Plasma II).









15




Table 3.1: Chemical composition of kaolinite

SiO2 46.5% MgO 0.16%
A1203 37.62% NazO 0.02%
Fe20O 0.51% K20 0.40%
TiO2 0.36% SO3 0.21%
P205 0.19% V205 < 0.001%
CaO 0.25%


Table 3.2: Chemical composition of bentonite

SiO2 63.02% A1203 21.08%
Fe20s 3.25% FeO 0.35%
MgO 2.67% Na20 & K20 2.57%
CaO 0.65% H20 5.64%
Trace Elements 0.72%


Table 3.3: Chemical composition of attapulgite (palygorskite)


SiO2 55.2% A1203 9.67%
Na20 0.10% K20 0.10%
Fe203 2.32% FeO 0.19%
MgO 8.92% CaO 1.65%
H20 10.03% NH2O- 9.48%


Table 3.4: Chemical composition of tap water


Si
Al
Fe
Ca
Mg
Na
Total Salts


11.4 ppm
1.2 ppm
0.2 ppm
24.4 ppm
16.2 ppm
9.6 ppm
278 ppm


I














The particle size distributions of kaolinite, attapulgite, and bentonite are given shown in

Tables 3.5, 3.6 and 3.7. The procedure for determination was: firstly, a particular suspen-

sion was prepared at about 0.5% by weight concentration, and run for at least 15 minutes

in a sonic dismembrater (Fisher, model 300) to breakdown any agglomerates. Secondly,

the suspension was analyzed in a particle size distribution analyser Horiba (model CAPA

700 ), and allowed to gradually settle down to the bottom. Particle concentration and fall

velocities were determined with an X-ray, which could be converted to Stokes equivalent

diameters. The median particle sizes of kaolinite, attapulgite, and bentonite were 1.10/lm,

0.86pm, and 1.01/pm, respectively. Scanning Electron Microscope (SEM) photographs of

the three types of clays, as dry agglomerates, are shown in Figures 3.1, 3.2 and 3.3.


Table 3.5: Size distribution of kaolinite

D(pm) Percent size distribution(%) Cumulative size distribution(%)
5.00< 0.0 0.0
5.00-3.20 0.0 0.0
3.20-3.00 2.9 2.9
3.00-2.80 4.0 6.9
2.80-2.60 2.6 9.5
2.60-2.40 4.1 13.6
2.40-2.20 4.0 17.6
2.20-2.00 6.0 23.6
2.00-1.80 5.7 29.3
1.80-1.60 6.2 35.5
1.60-1.40 5.5 41.0
1.40-1.20 6.2 47.2
1.20-1.00 5.8 53.0
1.00-0.80 5.0 58.0
0.80-1.60 10.4 68.4
0.60-0.40 11.2 79.6
0.40-0.20 13.6 93.2
0.20-0.00 6.8 100.0


i

















Table 3.6: Size distribution of bentonite


Table 3.7: Size distribution of attapulgite


D(pm) Percent size distribution(%) Cumulative size distribution(%)
3.00< 5.9 5.9
3.00-2.80 1.9 7.8
2.80-2.60 2.3 10.1
2.60-2.40 2.5 12.6
2.40-2.20 3.0 15.6
2.20-2.00 3.0 18.6
2.00-1.80 4.9 23.5
1.80-1.60 5.3 28.8
1.60-1.40 8.1 36.9
1.40-1.20 4.5 41.4
1.20-1.00 9.3 50.7
1.00-0.80 9.1 59.8
0.80-1.60 11.4 71.2
0.60-0.40 11.2 82.4
0.40-0.20 11.5 93.3
0.20-0.00 6.1 100.0


D(pm) Percent size distribution(%) Cumulative size distribution(%)
2.00< 11.8 11.8
2.00-1.80 4.1 15.9
1.80-1.60 4.9 20.8
1.60-1.40 5.3 26.1
1.40-1.20 5.6 31.7
1.20-1.00 5.8 37.5
11.00-0.80 17.4 54.9
0.80-1.60 25.5 80.4
i0.60-0.40 12.3 92.7
0.40-0.20 6.1 98.8
0.20-0.00 1.2 100.0



































Figure 3.1: SEM of dry agglomerates of attapulgite. Scale 1cm = 10jLm


Figure 3.2: SEM of dry agglomerates of bentonite. Scale 1cm = 10Im

































Figure 3.3: SEM of dry agglomerates of kaolinite. Scale 0.5cm = 10im


3.2 Rheological Experiments

The theological properties of mud, including viscosity and the upper Bingham yield

stress, and their time-dependent changes, are very important in ultimately controlling soft

muddy bottom erosion, wave energy dissipation, and mud transportation along coasts and

in estuaries. In the present study, the viscosity and the upper Bingham yield stress of

several types of muds (clay-water mixtures) were measured to determine which ones could

be selected for the wave-induced fluidization experiments. Also through these measurements

a mud viscosity model was developed, which was then used in the two-layered hydrodynamic

wave-mud interaction model as described in Chapter 4.

Each mud sample was prepared by adding tap water to the clay, or a mixture of two

clays, and mixing the material for 5 to 20 minutes and adjusting the amount of water to

the desired density which was selected to approximate those of typical soft natural muds.

Composite muds were made by adding any two of equally weighted clays together. One-half







20

percent salt, which is about the critical salinity value for coagulating clays in sea water,

was added in each of six samples, while no salt was added in six other samples of the same

compositions. Thus as shown in Table 3.8 a total of twelve mud samples were prepared in

this way.


Table 3.8: Selected muds (clays and clay mixtures) for theological tests

Symbol Components Density (g/l)
K kaolinite 1.30
KS kaolinite + 0.5 % salt 1.30
B bentonite 1.05
BS bentonite + 0.5 % salt 1.03
A attapulgite 1.10
AS attapulgite + 0.5 % salt 1.08
BK kaolinite + bentonite 1.16
BKS kaolinite + bentonite + 0.5 % salt 1.16
AB attapulgite + bentonite 1.05
ABS attapulgite + bentonite + 0.5 % salt 1.05
AK attapulgite + kaolinite 1.19
AKS attapulgite + kaolinite + 0.5 % salt 1.19


The samples were set aside for about two weeks to attain equilibration between the solid

and the liquid phases in terms of ion exchange. The equipment used was the Brookfield

viscometer (model LVT), in which a rotating bob is immersed in a beaker of mud. The bob

can rotate at selected fixed speeds, giving a shear rate range of 0.125 to 12.5 Hz. The torque

generated can be read from a meter, to which the shear stress is directly proportional. In

each test the shear rate was increased in steps, with a fixed time interval, e.g., 10 mins (or 10

cycles of the bob rotation) between the change of shear rate, and then decreased gradually

back to the starting point. For the pure muds, i.e., A, B, K, cycles of bob rotation were

used, and for the composite ones and muds with salt, i.e., KS, BS, AS, BK, BKS, AB, ABS,

AK, AKS, the time of application of a shear rate in mins was used. For each type of mud

the test was repeated several times with different time intervals including 5 mins, 10 mins,

and 20 mins (or 5 cycles, 10 cycles, and 20 cycles ) to examine the time-dependent behavior

of the materials.








21
The viscosity of muds can be significantly affected by such variables as the shear rate,

temperature, pressure and the time of shearing. Here the shear rate and the shearing

duration (time or cycles) are considered to be the most relevant influences on viscosity.

Figures 3.4 and 3.5 show the experimental flow curves, plotted as shear stress versus

shear rate. For comparison between different materials, the curves corresponding to muds

subjected to the same shearing time of 10 mins (or 10 cycles) are shown in Figures 3.6 and

3.7, showing the relationship between shear stress and shear rate, where the arrows indicate

the direction of the rising and falling flow curves. The corresponding curves of viscosity

(obtained by dividing shear stress by shear rate using the rising curves) versus shear rate

are plotted in Figures 3.8 and 3.9.

3.2.1 Influence of Shear Rate

The experimental data points, which are represented by point markers in Figures 3.8

and 3.9, indicate that all the materials, except attapulgite, generally exhibit a shear-thinning

behavior, i.e., the viscosity decreases as the shear rate increases. While attapulgite at

low shear rates shows a shear-thinning behavior, at higher shear rates it exhibits shear-

thickening behavior and then reverts to shear-thinning as the shear rate is increased to even

higher values. In the case of Figure 3.8(e),(f), for example, it can be seen that the viscosity

of attapulgite decreases up to a shear rate of 2 Hz, then increases as the shear rate increases

from 2 Hz to 6 Hz, and finally decreases again as the shear rate continues to increase beyond

6 Hz, when the sample is subjected to a shearing duration of 20 mins (or 20 cycles) at each

step.

General power-law equations that predict the shape of the curves representing the

variation of viscosity with shear rate typically need at least four parameters. One such

relation is the Cross (1965) equation given by

Yo A
S-1 = (c1 )P (3.1)
PI IPoo
where 0o and too refer to the asymptotic values of the viscosity at very low and very

high shear rates, respectively, cl is a constant parameter having dimensions of time, p is a













70.0

60.0

50.0

40.0

30.0

20.0

10.0


2.0 4.0 6.0 8.0 10.0


12.0 14.0


-






BK

E O 5S MINS
S------------------ 105 MINS
......"... ...- 10 MINS

----6-------' 20 MINS
.0 2.0 I I I
.0 2.0 '4.0 6.0 8.0 10.0 12.0


0.0 2.0 4.0 6.0 8.0


SHEAR RATE (HZ)


10.0 12.0 14.0


Figure 3.4: Shear stress, a, versus shear rate, j, (K,A,B)


20.0
18.0
16.0
111.0

12.0
10.0

8.0
6.0
1.0
2.0

0.0


11.0











70.0

60.0

50.0

40.0

30.0

20.0

10.0


2.0 4.0 6.0 8.0 10.0


20.0

18.0

16.0
14.0

12.0

10.0

8.0

6.0

4.0
2.0

0.0


2.0 4.0 6.0 8.0 10.0


100.0

90.0

80.0
70.0

60.0

50.0

40.0

30.0 RB

20.0 e 9

10.0

0.0 I I I
0.0 2.0 4.0 6.0 8.0 10.0


12.0 14.0


12.0 14.0


12.0 14.0


SHEAR RATE (HZ)


Figure 3.5: Shear stress, a, versus shear rate, 4, (AK,BK,AB)


I





































0.0 2.0 1.0 1.0 8.0 10.0 12.0 I1.O

SHEAR RATE IHZ)

KAOLINITE, SALT

25.0.


2.0 '.0 8.0 8.0 10.0 12.0

SHEAR RATE IHZ)

KAOLINITE, NO SALT


0.0 2.0 4.0 8.0 8.0 10.0 12.0 14.O

SHEAR RATE (HZ)

BENTONITE, SALT


cr
60.0





30.0
c'c-
I -



S 20o.0 10 CYCLES







BENTONITE, NO SALT
E


0.0
I3.0 0.0 2.0 '1.0 6.0 8.0 10.0 12.0

SHEAR RFOTE (HZ)

BENTONITE, NO SALT


0.0 2.0 4.0 6.0 8.0

SHEAR RATE

ATTnPULGITE,


cr
60.0
')
U")
Ui 60.0



a:
n 0.0


-- 0.0
r.0 0.0
tLo 20.0


0.0
34.0 0.0


10.0 12.0 14.0

(HZ)

SALT


2.0 4.0 6.0 8.0 10.0 12.0 14.0

SHEAR RATE I(Z)

ATTAPULGITE.NO SALT


Figure 3.6: Shear stress, a, versus shear rate, 4, (K,KS,A,AS,BI,HS)


S 10 CYCLES


0.0 L
0.
o.


0





































0.0 2.0 4.0 6.0 8.0 10.0 12.0 1

SHEAR RATE 1HZ)

BK SALT










0
B



0






10 MINS


0.0 2.0 4.0 6.0 6.0 10.0 12.0 14.0

SHEAR RATE IHZ)

BK, NO SALT


r 50.0.
aL

(n) 0.0
U)
IUj
cn
I- 30.0


S20.0
U 10 HINS
') IO.1.



4.0 0.0 2.0 q.0 6.0 8.0 10.0 12.0 11.0

SHEAR RATE IHZ)

K t+ SALT

70.0


60.0 0


a.
5n 10.0

L
(n

i- 30.0


ar 20.0
W u 10 MINS
)r


0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

SHEAR RATE (HZ)

AK ,NO SALT


0.0 2.0 4.0 f.0 8.0 10.0 12.0 14.0

SHEAR RATE IHZI

AB SnLT




^0 F




0
0


0
o



J 10 MINS

u

0.0 2.0 4.0 6.0 8.0 10.0 12.0 IV.0

SHEAR RATE lHZ)

AB NO SALT


Figure 3.7: Shear stress, a, versus shear rate, 4, (BK,BKS,AK,AKS,AB,ABS)




















25.0

S,
20.0
r


- 15.0
I--
o 10.0
u

> 5.0


0.0
0.0


90.0

80.0

n 70.0
cr
a. 60.0

. 50.0
I--
40.0

U 30.0

> 20.0

10.0

0.0
0


.0


SHEAR RATE (HZ)

KAOLINITE, NO SALT


cn
a-


1-

10 MINS
ci




2.0 q.0 6.0 8.0 10.0 12.0 14.0

SHEAR RATE (HZ)

BENTONITE, SALT


100.
90.0

80.0

70.0

60.0

50.0

40.0

30.0

20.0

10.0

0.0
0.


u -


ou.u
U,
S50.0
a.

>- 40.0
I-
, 30.0

'l 20.0

10.0

0.0


SHEAR RATE (HZ)

BENTONITE, NO SALT


2.0 4.0 6.0 8.0

SHEAR RATE

ATTAPULGITE,


10.0 12.0 1

IHZ)

SALT


0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

SHEAR RATE (HZ)

ATTAPULGITE,NO SALT


Figure 3.8: Viscosity, p, versus shear rate, 4, (K,KS,A,AS,B,BS)


30.0


2.0 4.0 6.0 8.0 10.0

SHEAR RATE (HZ)

KAOLINITE, SALT


C


E










20 MINS


^S )-- 0 ____ _


60.0


50.0

40.0
s o.o

a.

- 30.0
a-

0 20.0
S0.
> 10.0


F







20 CYCLES




_o0
Q)O


m


.-- 1 A


it


r-


0




































SHEAR RATE (HZ)
BK SALT


B








10 MINS


2.0 4.0 6.0 8.0
SHEAR RATE

BK NO SALT


10.0 12.0 14.0
(HZ)


90.0

80.0

70.0

60.0

50.0


90.0

80.0

70.0

60.0

50.0

40.0

30.0

20.0

10.0

0.0
0.


25.0


20.0
n-

. 15.0


10.0
Sl0O
(-)

> 5.0


0.0
0


2.0 4.0 6.0 8.0 10.0 12.0 14.0

SHEAR RATE (HZ)

AK SALT


SHEAR RATE (HZ)

AK NO SALT


150.

135.

120.1

105.
90.0
75.0

60.0

45.0

30.0

15.0
0.0
0


SHEAR RATE (HZ)

AB SALT


.0


2.0 4.0 6.0 8.0
SHEAR RATE

AB ,NO SALT


10.0 12.0 14.0
(HZ)


Figure 3.9: Viscosity, p, versus shear rate, 4, (BK,BKS,AK,AKS,AB,ABS)


0.0

30.0

20.0

10.0

0.0 -
0.0


140.(

120.1

S100.
aoo.

S80.0

- 60.0

S40.0

20.0

0.0
0.


.0


0
D








10 MINS


F9--
F








.10 MINS


hh


,.u c








28

dimensionless constant, p is the apparent viscosity and 4 is the shear rate.

In all the studied cases, p < y0, hence the above equation can be simplified as

110 = (cil)" (3.2)
P Poo

which can be further written as

S= o + (3.3)

or

ti = Poo + c "-1 (3.4)

Equation 3.4 is referred to as the Sisko (1958) model, where pjo is the constant viscosity

at the limit of high (theoretically infinite) shear rate, c is a measure of the consistency

of material, and n is a parameter that indicates whether the material is shear-thinning or

shear-thickening, that is, when n > 1 the material exhibits shear-thickening, otherwise it

possesses a shear-thinning behavior.

To solve for the three parameters, po, c and n, the least squares method was used for

fitting the curves obtained from Equation 3.4 to the experimental data. For this method it

is required that the viscosity difference between the model (Equation 3.4) and data, D, be

minimized, that is,
N
D = "(Ai /)2 = minimum (3.5)
i=1
or
N
D = (i, poo c"n-1)2 = minimum (3.6)
i=1
where A/ is viscosity of the mud obtained from the experiment, and N is the number of

data points.

Setting
OD
=0 (3.7)

OD
= 0 (3.8)

OD
0 (3.9)
On











Equations 3.5 and 3.6 can be expressed as

N
S- c n-1) = 0 (3.10)
i=1

therefore
N
n{- -1 P c"-1)} = 0 (3.11)
i=1
hence
N
{c-in-1 log 4(A Po c"-1)} = 0 (3.12)
i=1
In this way, ,oo, c and n can be determined from the three equations above. The results are

given in Table 3.9. In all cases, n < 1, and that the data point of attapulgite near the shear

rate of 6 Hz was conveniently removed when fitting the model. Therefore, all the materials

(except of course attapulgite over a certain shear rate range) are observed to exhibit shear-

thinning behavior. The greater the departure of n from unity, the more pronounced the

shear-thinning behavior of the material. The higher the value of c, the more viscous the

mud (Wilkinson, 1960). The upper limit of viscosity, po, represents resistance to flow in

the limit of a very high shear rate. It can be seen that attapulgite has the highest value of

Ioo among the three types of cays, up to 5 to 6 Pa.s. Kaolinite and bentonite have lower

/z. values, about 2 Pa.s. For the composite materials, AB has a high /zo of 4.3 Pa.s, ABS

has as high as 7 Pa.s because of the coagulating effect of adding salt. While BK has a low

value of /zo, about 0.6 Pa.s, salt also increases /oo (of BKS) to a comparatively high value

of 4.7 Pa.s.

Generally, salinity does increase the coagulating tendency of clays (Parchure, 1984),

which in turn increases the viscosity. However, salt does not greatly affect the viscosity of

kaolinite due to its somewhat anomalous properties. For example, kaolinite flocculates more

readily in distilled water than in salt water, although the nature of flocculation is different

in the two cases (Parchure, 1984).


I












Table 3.9: Parameters for the Sisko power-law model for viscosity

Mud p o (Pa.s) c n
K 2.10 7.08 0.106
KS 2.06 3.31 0.117
B 0.41 48.68 0.207
BS 2.46 28.26 -0.009
A 6.34 6.86 -1.0
AS 5.00 11.54 0.038
BK 0.61 12.29 -0.057
BKS 4.69 20.60 -0.114
AB 4.28 45.2 0.002
ABS 7.06 45.07 -0.039
AK 4.44 0.76 -1.083
AKS 3.35 8.02 0.059


3.2.2 Influence of Shearing Time

For a given shear rate, the corresponding shear stress, and hence the viscosity, can

either increase or decrease with time of shearing. This type of behavior is either called,

respectively, "thixotropy," which usually occurs in circumstances where the material is

shear-thinning, or "anti-thixotropy," which is usually associated with shear-thickening be-

havior. As an illustration of the generally thixotropic influence of shearing time on shear

stress, Figures 3.4, 3.5, and Table 3.10 give the shear stresses at different times at the

selected shear rate of 6 Hz. It can be seen that shearing time had the greatest effect on

the viscosity of attapulgite and the smallest on kaolinite. Bentonite was in-between. For

the muds containing kaolinite, i.e., KS, BK, BKS, the effect of shearing time was also very

small, while for AS and BS this effect was relatively greater.


Time-dependent mud behavior leads to a hysteresis loop in the flow curves of shear

stress versus shear rate when the curves are plotted first for increasing and then decreasing

shear rate sequences. This behavior is observed in Figures 3.4, 3.5, 3.6, and 3.7, in which it

can be seen that all the materials more or less exhibit a hysterisis loop. When the material

is sheared, typically the structure progressively breaks down and the apparent viscosity













Table 3.10: Shearing time effect on shear stress

Symbol 5 cycles 10 cycles 15 cycles 20 cycles 25 cycles 30 cycles
K 19.4 17.9 17.7 18.8
B 74.3 69.9 61.8 66.8
A 25.0 90.9 25.7
5 mins 10 mins 15 mins 20 mins
KS 14.7 13.5 13.0
BS 46.7 39.2
AS 62.7 76.5
BK 14.4 13.9 13.5
BKS 53.3 50.5 56.7
AB 76.5
ABS 101.6
AK 23.8
AKS 35.9


decreases with time. The rate of breakdown of the structure during shearing at a given rate

depends on the number of linkages available for breaking and must therefore decrease with

time (Wilkinson, 1960). Also, during shearing asymmetric particles or molecules are better

aligned, i.e., instead of a random, intermingled state which exists when the material is at

rest, the major particle axes are brought in line with the direction of flow. The apparent

viscosity thus continues to decrease with increasing rate of shear until no further alignment

along the streamline is possible.

3.2.3 Upper Bingham Yield Stress

The upper Bingham yield stress, as, the stress that must be exceeded before flow starts,

can be determined from the plots of shear stress versus shear rate in Figures 3.6 and 3.7 by

drawing a line tangent to the upper range of shear rates (Wilkinson, 1960). The intersection

of this tangent with the stress axis gives aB. The results are presented in the Table 3.11.

This table shows that among the three types of clays, attapulgite has the highest upper

Bingham yield stress with 72 Pa, kaolinite has the lowest one with 10 Pa, and bentonite is

in-between with 50 Pa. The composite materials that contain kaolinite, i.e., AK, AKS, BK,

have very low upper Bingham yield stresses that are less than 10 Pa, except BKS, which


I












Table 3.11: Upper Bingham yield stress

sample K IKS B BS A AS BK BKS AB ABS AK AKS
-B (Pa) 15.0 9.5 50.0 36.0 66.0 72.0 10.0 39.0 58.0 88.0 0.0 4.0


has a relatively higher a0 of 39 Pa. The higher value of the upper Bingham yield stress

for BKS is likely to be due to the presence of salt, which in general promotes flocculation

of clays. Of the composite materials AB and ABS have the highest upper Bingham yield

stresses with values of 58 Pa and 88 Pa, respectively. ABS also has a higher value of aB

than AB presumably because of the effect of salt. Salt might increase the upper Bingham

yield stress of bentonite as well, although the upper yield stress of BS, 36 Pa, is less than

that of B, which is 50 Pa. Note that when BS was tested the density had to be reduced

from 1.05 gl~- to 1.03 gl-1 in order to keep the torque reading within the viscometer gauge

range.


3.2.4 Gelling

Gelling is a special case of flocculation. It can result instead of flocculation when

electrolytes are added to certain moderately concentrated soils. A gel is a homogeneous-

looking system displaying some rigidity and elasticity. When gelling occurs, its effect is

manifested in the flow curve of shear stress versus shear rate. Thus at the beginning,

starting with a very low shear rate, the stress decreases when the shear rate increases due

to the breakdown of the gel. Thereafter, the stress goes up as the shear rate continues to

increase. Attapulgite and bentonite exhibit measurable gelling behavior, especially when

salt is added. Gelling also occurred in AB, ABS, BKS. See examples in Figure 3.6 (c), (e)

and (f), as well as in Figure 3.7 (d), (e) and (f).

3.2.5 Summary

Table 3.12 gives a summary of the properties of the materials that have been studied,

where rB of ABS refers to the value corresponding to 5 mins shearing duration. The










following observations are noteworthy:


1. All the selected materials exhibited shear-thinning, although attapulgite behaved as

a shear-thickening material somewhere in the shear rate range from 2.5 to 6.0 Hz.


2. For both the viscosity and the upper Bingham yield stress, kaolinite had the lowest

values among the three types of clays, attapulgite the highest, and bentonite was

in-between. The composite materials that contained kaolinite had relatively low vis-

cosities and low upper Bingham yield stresses, while the attapulgite and bentonite

composite had higher values.


3. Salt had a measurable effect in increasing the viscosity of bentonite as well as the

composites that contained bentonite. Salt increased the upper limit viscosity, uoo, of

B by 500%, BK by 660%, and AB by 65%. It increased the upper Bingham yield

stress of BK by 290% and AB by 50%. Salt did not significantly change the viscosity

of kaolinite and attapulgite. It decreased both po, and as of kaolinite by less than

10%. Finally, salt decreased t/ and increased aB of attapulgite by less than 10%.


4. Of the three types of clays, time or duration of shearing had the greatest effect on

attapulgite, the smallest on kaolinite, and bentonite was in-between. Thus attapulgite

had the highest thixotropy.


5. Attapulgite and bentonite were influenced by gelling, especially when salt was added.

The gelling effect also appeared in AB, ABS, BKS. Kaolinite did not exhibit this

effect.



3.3 Instrumentation

3.3.1 Wave Gauges

Two capacitance-type gauges were installed in the flume to monitor the required surface

wave information. Calibration of the two gauges was conducted in situ by increasing the


I












Table 3.12: Rheological parameters for power-law given by Equation 3.4

Mud time Density OaB oo c n
(g/1) (Pa) (Pa.s)
K 10 cycles 1.30 15.0 2.1 7.08 0.106
K+0.5% S 10 mins 1.30 9.5 2.06 3.31 0.117
B 10 cycles 1.05 50.0 0.41 48.68 0.207
B+0.5% S 10 mins 1.03 36.0 2.46 28.26 -0.009
A 20 cycles 1.10 66.0 6.34 6.86 -1.0
A+0.5% S 20 mins 1.10 72.0 5.00 11.54 0.038
B+K 10 mins 1.16 10.0 0.61 12.29 -0.057
B+K+0.5% S 10 mins 1.16 39.0 4.69 20.6 -0.114
A+B 10 mins 1.05 58.0 4.28 45.2 0.002
A+B+0.5% S 10 mins 1.05 88.0 7.06 45.07 -0.039
A+K 10 mins 1.19 0.0 4.44 0.76 -1.083
A+K+0.5% S 10 mins 1.19 4.0 3.35 8.02 0.059


water level in steps of 1 to 2 cm, while the gauges were held in fixed positions. The linear

least squares method was used to obtain a regression equation. Results of calibration are

shown in Figure 3.10. Water level variation was recorded by a data acquisition system

briefly described later in this chapter. The sampling frequency was 40 Hz for 0.5-sec wave

and 20 Hz for 1 to 2-sec waves.

3.3.2 Current Meter

An electromagnetic Marsh-McBirney current meter (model 523) was used to measure

the horizontal velocities in the water column. Calibration of the current meter is shown

in Figure 3.11, which was conducted in a V-notched weir flume in the Civil Engineering

Department. The current meter had two restrictions. Firstly, the probe could not be placed

close to the water-air or water-bed interface due to the drastic change in material (medium)

density and conductivity associated with the electromagnetic field, which resulted in an

unrealistic output. Secondly, the meter generated strong interference with other instruments

which meant that only the current meter could be used at a given time. Thus other data

had to be collected during separate time windows. The sampling frequency for the current

meter data was the same as the wave gauges.

















60.0

57.5 -

55.0

52.5

50.0

L7.5

45.0

42.5

U0.0 -

37.5

35.0
1000 1250


1500 1750 2000 2250 2500 2750 3000 3250 3500

BITS


Figure 3.10: Calibration curves for the wave gauges


40.0

35.0

30.0

25.0 -

20.0

15.0

10.0

5.0

0.0
-0.20 -0.18 -0.16 -0.14 -0.12 -0.10 -0.08 -0.06 -0.04 -0.02 0.00

VOLTAGE (V)


Figure 3.11: Calibration curve for the current meter











3.3.3 Pressure Transducers

Six pairs of total and pore pressure transducers were flush-mounted on the side wall of

the flume at different elevations for quantifying the effective stress at different elevations.

One additional total pressure transducer was installed at the flume bottom to check the

weight of the column. The elevations of the 6 paired-transducers from the flume bottom

were: 14cm(#1), 12cm(#2), 9.5cm(#3), 7.5cm(#4), 5.1 cm (#5), and 3.1cm(#6) for the

pore pressure gauges, and 14cm(#5), 11.9cm(#7), 9.5cm(#1), 4.9cm(#3), 2.6 cm(#2), and

Ocm(#6) for the total pressure gauges. The pore pressure transducers were Druck model

PDCR 810, each covered with a water-saturated porous stone. Each gauge was fitted with a

specially designed 300x signal amplifier. Four of the total pressure transducers were Druck

model PDCR135/A/F, and the remaining three were Druck model PDCR 81, each fitted

with 200x signal amplifiers. The gauges were checked in a calibration cylinder filled with

water to the desired depth. The cylinder was graded with a 1 mm scale. Calibration curves

for the 13 pressure transducers are shown in Figures 3.12 and 3.13. The sampling frequency

during the fluidization experiments was 20 Hz, sampling duration was 30 sec for each record.

The pressure gauges were then tested under dynamic loading by subjecting them to a

1 sec period, about 5cm high wave in the flume. Measured pressures were compared with

results from the linear wave theory with respect to amplitudes, as shown in Figures 3.14

and 3.15. The comparison shows that the experimental data agreed reasonably well with

theory, thus indicating that the temporal response of the pressure transducers to dynamic

wave loading were of acceptable quality. Phase lags appeared between the pressures from the

theory and the measurements as observed in the figures, caused by the distance between the

wave gauge and pressure gauges. The wave gauge was located approximately 0.6m upstream

from the pressure gauges, so that the peak value of the pressure from theory was ahead of

those from measurement. Between the pore and total pressure gauges there also was a small

distance, plus there was the lag effect of the porous stone in the pore pressure sensor that

also possibly delayed its response to the wave loading in a measurable way. These factors


I









37
also caused the peak values of pore pressure to lag behind total pressure.

All the gauges worked properly over short time scales, but when tested in still water

over longer times, e.g., a day, a drift in the measurement appeared, an example of which is

shown in Figure 3.17. It can be observed that during the first approximately seven hours the

drift was typically more significant than at later times, so that in the fluidization experiment

measurements were made after the gauges were turned on for about 7 hours. After that

the measuring system became relatively stable, and most of the measurements were made

within the next 9 hr period to minimize the drift.

In order to find out where the drift problem came from, a different, more reliable

amplifier (Omega, model DMD 465) was used in a drift test to compare gauge response

with the responses of the gauges used throughout the experiments. This drift test was also

conducted in still water, and the new amplifier was used together with pore pressure gauge

#2. A set of results is shown in Figure 3.16. It appears that the drift problem may not have

been from the amplifier, since both the curves in the figure show similar trends in drift. The

data acquisition system, or the gauges themselves might have caused this problem. Note

that the accuracy of the pressure gauges stated by the suppliers was 68 Pa.

3.3.4 Data Acquisition System

In the test setup, two channels were required for wave information and thirteen for the

pressure gauges. All the time-series data were collected by a Multitech personal computer

via a digitizing interface card. The interface card had 16 channels for analog to digital (A/D)

conversion. The A/D conversion could be triggered by Global Lab software command, The

computer sampled digitized data at selected sampling intervals and stored the data into

disk files. The computer scanned at 20 Hz frequency for 1 to 2 sec waves, and 40 Hz for 0.5

sec waves. Record lengths were 30 sec for pressure gauges and 1 min for wave gauges.

3.4 Flume Characterization Tests

The dimensions of the plexiglass laboratory flume were: length 20 m, width 46 cm, and

height 45 cm. A programmable wave maker, which covered a large portion of the water








































0.0 0.3 0.6 0.9

VOLTAGE IV)


0.5 1.0 1.5 2.0 2.5

VOLTAGE (V)


Figure 3.12: Calibration curves for the total pressure gauges


j





















8.0
--- GAUGE *1
7.0 -.----- ----- GRUGE *2
--------- GAUGE m3
6.0

5.0




3.0

2.0

1.0

0.0
-1.0 -0.5 0.0 0.5 1.0 1.5

VOLTAGE


-1.0 -0.5 0.0 0.5 1.0 1.5

VOLTAGE (V)


2.0 2.5 3.0


2.0 2.5 3.0


Figure 3.13: Calibration curves for the pore pressure gauges


i I





















2.75

2.65
-- THEORY OCM

2.55

2.45 W J ---TOTAL OCM




2.25
2.0 7.0 12.0 17.0 22.0
2.40

C3 2.30 THEORY 3.1CM
0.

2.20 :. ; --- PORE 3.ICM
LJ
2.10 II ----- TOTAL 2.6CM

) 2.00 -
-I
cc
O 1.90 I l I I
2.0 7.0 12.0 17.0 22.0
2.25

2.15
S---- THEORY 4.9CM
2.05 "! ri





1.75
1.75 II------*------- j---------TOTAL--.9C

2.0 7.0 12.0 17.0 22.0

TIME (SEC)







Figure 3.14: Dynamic response of pressure gauges, and comparison with results from the
linear wave theory: gauge elevations ranging from 0 to 4.9 cm













2.00

1.90

1.80 --- THEOR 7.5CM

1.70 ...---- PORE 7.5CH

1.50

1.50 ------------------------------
2.0 7.0 12.0 17.0 22.0
1.75

1.65 A- I -- THEORY 9.5CH

1.55 ------ .PORE 9.5CH
CE: 1 i i --- TOTAL 9.5CM
1 ..

1.35 -

S1.50
S1.25 I








1.20 I I ------------------ ---- --T-L--1.
2.0 7.0 12.0 17.0 22.0

1.25
S1.o -- THEORY 12CM
: ..... ...v":.:

1.30 12CM

10.95 ; TOTAL 19C

1.10








1.00.75 I I
2.0 7.0 12.0 17.0 22.0
1.25

1.15 \ i ; i THEORY 11CM

1.05 f j PORE 14CM

0.95 tTOTL 111CM

0.85

0.75 -------
2.0 7.0 12.0 17.0 22.0

TIME (SEC)




Figure 3.15: Dynamic response of pressure gauges, and comparison with results from the
linear wave theory: gauge elevations ranging from 7.5 to 14 cm


I














2.3000


0-2.


1500 h


2.1000 '
0.0



-2.5500 -


LLj 2.5000


u 2.4500
LJ

C-2.4000
0.0


50.0 100.0 150.0
TIME (MIN)


Figure 3.16: Example of instrument drift, in pore pressure measurement, with old and new
amplifiers. Gauge #2 was connected to the "new" amplifier. Comparison is made with
gauge #3 response connected to the "old" amplifier


200 400 600
TIME (MIN)


800 1000 1200 1900 1600


Figure 3.17: Example of instrument drift, pore pressure gauge #1, Time range over which
most of the pressure data were obtained is indicated.


PORE PRESSURE E NEW PFIE
PORE PRESSURE GARGE =2. NEW AMPLIFIER lr -


50.0 100.0 150.0 2


00.0


200.0


0.0


-0.1


-0.2

I.
-- -0.3

w0.1
-O0


I .-.. -~
I I


I I
3r


2500s


2000









43

column and moved in the piston-type manner, was installed at one end of the flume to

generate regular (monochromatic) waves. The wave height and period could be adjusted by

a DC motor controller. An impermeable, 1 in 4 sloped beach covered with astroturf, a type

of plastic wire mesh about 1 cm thick, was installed at the end behind the wave maker to

damp out water level fluctuations caused there by the wave maker. At the downstream end

of the flume, a plexiglass board was installed to provide a 1 in 20 sloped beach. Astroturf

was also placed on top of this beach for reduction of wave reflection. In the test section, a

trench, from x=6.1 m to 13.3 m (Figure 3.18), with a height of 14 cm and side slopes of

1 in 12, was formed to hold the sediment. Here x is the distance measured from the wave

maker as shown in Figure 3.18.

Before the mud fluidization experiments were carried out in the flume, wave perfor-

mance in the flume, without mud, was examined in order to characterize flume hydrody-

namics and to define the domain of flume operation for the next phase of the work. For

this purpose a false bottom made of plywood was introduced to cover up the trench, as

shown in Figure 3.18. The data obtained were used to determine the optimal ranges of the

wave height, wave period and water depth within which the waves seemed reasonably well

behaved, and the ranges over which significant higher harmonics occurred. In the charac-

terization test, two wave gauges and a current meter were used to record wave heights and

horizontal current velocities, respectively. As shown in Figure 3.18, one gauge was set up at

the upstream end of the test section, and the other was approximately in the middle. The

distance between the two gauges was 5 m.

3.4.1 Test Conditions

Two water depths, 15 and 20 cm, were selected for this experiment. For each depth

two wave heights were chosen, and the periods were 0.5s, 1.0s, 1.5s and 2.0s. A total of 15

tests were conducted, as noted in Table 3.13. Examples of 1 sec wave time-series at 20 cm

water depth are shown in Figures 3.19, where H refers to wave height.


I





















Current Meter Wave Gauge #2 Wave Gauge #1 Wave Maker
(x = 14.7 m) (x =10 m) (x = 5 m) (x = 0)




:20.o Water False Bottom 1

Mudiur 3.18: Trench lvatio rofie



Figure 3.18: Wave flul=,n elevation p)rofihe anld insStrimienlI t loh altionsS




















I--g-
U 6.0


2.0
0.0
L -2.0
-I
L -4.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0
Z TIME (SEC) H=7.8 CM GAUGE #1
U 6.0
S14.0
2.0
I-
c 0.0
S-2.0 -
-J
LUJ -4.O I
0.0 5.0 10.0 15.0 20.0 25.0 30.0
TIME (SEC) H=L.62 CM GAUGE #1
U 6.0 C
Z 4.0
2.0
I 0.0
LJ -2.0
-J
LU I.O 1
0.0 5.0 10.0 15.0 20.0 25.0 30.0
TIME (SEC) H=7.6 CM GRUGE #2
U 14.0
z
i 2.0

0.0
CC
L -2.0
-J
Ll 4.0 1 I
0.0 5.0 10.0 15.0 20.0 25.0 30.0
TIME (SEC) H=L4.5 CM GRUGE #2






Figure 3.19: Examples of wave time-series (depth=20cm, period=1.0s) for flume character-
ization tests with a false bottom









46


Table 3.13: Wave conditions for the charaterization tests

Depth (cm) Period T(sec) Wave height H(cm)
gauge #1 gauge #2
15 0.5 2.7 2.3
15 0.5 4.2 3.7
15 1.0 2.3 2.3
15 1.0 5.0 4.8
15 1.5 2.7 2.5
15 1.5 5.0 4.9
15 2.0 2.7 2.4
15 2.0 4.9 4.2
20 0.5 3.1 2.7
20 1.0 4.6 4.3
20 1.0 7.8 7.6
20 1.5 4.4 4.5
20 1.5 9.1 9.2
20 2.0 4.3 3.9
20 2.0 8.4 6.4


3.4.2 Wave Spectra

The wave spectrum for each wave condition was obtained from the time-series. Some

examples of spectra given in Figures 3.20 and 3.21 indicate that among all the selected

frequencies, 1 Hz waves had the highest fundamental harmonic, and comparatively very

small higher harmonics. For the same water depth and wave height, a second harmonic

wave appeared as the wave period increased. When the wave period .was increased to 2

seconds, the wave became visually non-linear, and there were two or even three dominant

wave components. For the same depth and wave period, when the wave height increased,

the second harmonic became more pronounced. Also for the same wave height and period,

the deeper the water, the lesser was the magnitude of the second harmonic.

3.4.3 Wave Reflection Estimation

Goda and Suzuki (1976) developed an experimental technique for the resolution of

incident and reflected waves in continuous runs in the absence of multi-reflections of irregular

waves between the wave maker and a reflective (beach) structure. This method was used

in the present study to calculate the wave reflection coefficients, in order to assess the


















400
360
S320
u 280
z
5j 240

S200
(r
3 160
u_ 120
o- 80
(0
40
0
C


I-.




--
I--


Cu
ai


(n


A


GAUGE at












1.0 0.5 1.0 1.5 2.0 2.

FREQUENCY (HZ)


T=1.OSEC AVG.HT.=q.6CH


B


GAUGE #2











0.0 0.5 1.0 1.5 2.0 2.
FREQUENCY (HZ)

T=1.OSEC AVG.HT.=I.3CH


400
360
. 320
' 280

5L 290

-'200
160

(u-) 120
a0- 80
(n
40
0


I-

U,
C)
0 x
Cu
a U


a.
UJ
q-
(n)


C


GAUGE a1












1.0 0.5 1.0 1.5 2.0 2.

FREQUENCY(HZ)

T=1.5SEC RVG.HT.=q4.CM


0


GAUGE #2











).0 0.5 1.0 1.5 2.0 2.
FREQUENCY(HZ)

T=1.5SEC AVG.HT.=q.5CM


I-


zx



u
a: ~


C.
cn
UJ
0-
(2m


Sn
121
z

oX

cl
-i
Cr


2 U_
UJ
0
a-
(,


E


GAUGE al











,2.
).0 0.5 1.0 1.5 2.0 2.

FREQUENCY (HZ)

T=2.0SEC RVG.HT.=q.3CM


F


GAUGE "2











3.0 0.5 1.0 1.5 2.0 2.
FREQUENCY (HZ)

T=2.0SEC AVG.HT.=3.9CM


Figure 3.20: Wave spectra, water depth=20cm; average wave height ranging from 3.9 to 4.6
cm, period ranging from 1 to 2 sec.




















>-


z
U-
cor

a:


a-
tO
O '


I ui .


>- 100C
I-

z 800
uU)

j 600
c r
I- = 400
u 2

200
(n 200


120C
A
100%

800 GAUGE t
800


600


400

200

0
0.0 0.5 1.0 1.5 2.0 2.!

FREQUENCY(HZ)

T=1.OSEC AVG.HT=7.8CM

1200
B
1000

o80 GAUGE #2

600

400


200


0.0 0.5 1.0 1.5 2.0 2.!

FREQUENCY(HZ)

T=1.OSEC AVG.HT.=7.6CM


].0 0.5 1.0 1.5 2.0 2.5

FREQUENCY (HZ)

T=1.5SEC AVG.HT.=9.ICM


200
D
000

GAUGE *2
00

00



00
O0



0.0 0.5 1.0 1.5 2.0 2.5
FREQUENCY(HZ)

T=1.5SEC AVG.HT.=9.2CM


>-

I-s
z
hiU L
C3


1200

1000


800


600

E: 100
U- i^
ui
a-
^ 200

0


I "nr


>-
I--

z
in




UL
0'-
U
CL
(r


.0 0.5 1.0 1.5 2.0 2

FREQUENCY(HZ)

T=2.0SEC AVGH=8.4CH


F


GAUGE =2











.0 0.5 .. 0 .5 2.0 2.
FREQUENCY(HZ)

T=2.0SEC AVG.HT.=6.qCM


Figure 3.21: Wave spectra, water depth=20cm; average wave height ranging from 6.4 to 9.1
cm, period ranging from 1 to 2 sec.


C


GAUGE #1


I-


I
(-')

o

UJ
(-
cn


z


Ct


..r
lu
a-
(L


E


GAUGE #1










I I


,i C









49
progressive character of the waves. The principle is briefly, described next.

The incident wave and the reflected wave are described in the general forms of


71 = ai cos(kx at + si)

77R = aR cos(kx + at + ER) (3.13)

where 771 and rjR are the surface elevations of the incident and the reflected waves, re-

spectively, at is the amplitude of the incident wave and aR is that of reflected wave, k is

the wave number, 27r/L, with L the wavelength, a is the angular frequency, 27r/T, with

T the wave period, and EI and ER are the phase angles of the incident and the reflected

waves, respectively. The surface elevations must be recorded at two adjacent stations, xz

and X2=Xl + Al. The measured profiles of the composite waves, selecting the fundamental

frequency for analysis, are


7ri = (771 + 77R)z=zx = A1 cos at + B1 sin at

72 = (771 + rr)x=x2 = A cos at + B2 sin at (3.14)

where

A1 = a cos 0 + aR cos R

B1 = aI sin I aR sin OR

A2 = ai cos(kAl + 04) + aR cos(kAl + OR)

B2 = aI sin(kAl + 4) + aR sin(kAl + OR) (3.15)


0l = kxl + ei

OR = kl + ER (3.16)

Equation 3.15 can be solved to yield aj and aR according to

S/(A2 A1 cos kAl B1 sin kAl)2 + (B2 + A1 sin kAl B cos kAI)2
2 I sinkAl I


V(A2 A1 cos kAl + B1 sin kAl)2 + (B2 Ai sin kAl B1 cos kAl)2
2 1 sin kAl


(3.17)


aR =









50

Using Fourier analysis enables the estimation of the amplitudes A1, B1, A2 and B2 for the

fundamental frequency. The amplitudes of the incident and the reflected waves, aI and

aR, are then estimated from Equation 3.17. Table 3.14 gives the reflection coefficients,

kr = aR/al, for the two series experiments, with water depths of 15 and 20 cm. This table

shows that at a water depth of 20 cm and a frequency of 1 Hz, the wave reflection coefficient

was less than 0.3, which could be considered to mean that the waves under these conditions

were generally of the progressive type. For this reason as well as another sited previously, in

the fluidization experiments described in Chapter 5, the chosen wave frequency was 1 Hz.

The range of water depth was selected from 16 to 20 cm. The waves under these conditions

were found to be acceptably well behaved, even when the false bottom was removed and

the trench filled with mud.


Table 3.14: Wave reflection coefficient, kr

Depth (cm) Period (sec) Wave height(cm) kr
15 1.0 2.3 0.48
15 1.0 4.8 0.37
15 1.5 2.5 0.81
15 1.5 4.9 0.18
15 2.0 2.4 0.59
15 2.0 4.2 0.52
20 1.0 4.3 0.30
20 1.0 7.6 0.17
20 1.5 4.5 0.24
20 1.5 9.2 0.51
20 2.0 3.9 0.11
20 2.0 6.4 0.35


3.4.4 Current Velocity

For each selected wave condition the horizontal current velocity was measured at ele-

vations of 2.6 cm, 4.6 cm, 6.6 cm, 8.6 cm and 9.6 cm from the bottom of the flume. These

velocities were then compared with those calculated from the linear wave theory. Consid-

ering the 4.7 m distance between the current meter and wave gauge #2, it should be noted

that there was measurable wave dissipation over this distance, even in the absence of mud.


I









51
The mean wave decay coefficient, ki,, was found to be 0.02/m, as calculated from the wave

height recordings by gauges #1 and #2. The wave height where the current meter was

located, Hr,, would be

Hour = H#2e-kimx (3.18)

where H#2 is the wave height at gauge #2, and Az is the distance between gauge #2 and

the current meter. Here Ax=4.7 m.

The root-mean square (rms) velocity from the current velocity time-series is obtained

from

urms = (Ui i)2 (3.19)
i=1
where u, is the instantaneous velocity and ii is the time-mean velocity. According to the

linear wave theory (Dean & Dalrymple, 1984), the horizontal orbital current velocity under

a wave is
H,,ra cosh kz
u = h k cos(kx at) (3.20)
2 sinh kh

where H the wave height, a the angular frequency, k the wave number, h the water depth,

and z the elevation above the flume bottom. Thus urm amplitude can be calculated as

(van Rijn, 1985)
SHEra cosh kz
S= Hurcosh (3.21)
s 2 2 sinh kh

As shown by examples in Figure 3.22, at T=1 sec the measured velocities agreed well with

theory. At T=2 sec, the measured velocities (not shown) were about 50% larger than those

from theory, because the 2 sec wave was not quite linear. At T=1.5 sec the two results

did not agree well either for the same reason. The two curves in Figure 3.22 represent the

results from the theory. The solid curve includes wave dissipation, while the dashed one

does not, i.e., kim in Equation 3.18 is 0.02/m for calculating HE, for the solid curve and is

zero for the dashed curve.


I
















15.0


12.0 /


9.0


6.0


3.0 ,


0.0 i
0.0 5.0 10.0 15.0 20.0

VELOCITY (CM/SEC)

DEP=15CH H=3.1CM
20.0


16.0 -


12.0


8.0


4.0


0.0


25.0 30.0


15.0


12.0


9.0


6.0


3.0


0.0


E 20.C



I-
I-

uj




-J
uJ 4.0
Ui
-J
q .o
w.
..J


0.0 5.0 10.0 15.0 20.0 25.0 30.0

VELOCITY(CH/SEC)

DEP=20CH H=q.iCH


0.0 5.0 10.0 15.0 20.0

VELOCITT(CM/SEC)

DEP=15CH H=4.8CM


25.0 30.0


0.0 5.0 10.0 15.0 20.0 25.0 30.0

VELOCITY(CM/SEC)

DEP=20CH H=7.3CH
THEORY, CONSIDER DISSIPATION
.-.-- THEORY, WITHOUT DISSIPATION
EXPERIMENTAL DATA


Figure 3.22: Horizontal velocity profiles: comparison between experimental data (rms am-
plitudes) and linear wave theory (peorid T=1.Os)


1


I


I
















CHAPTER 4
ESTIMATIONS OF FLUID MUD THICKNESS AND WAVE ENERGY DISSIPATION



4.1 Introduction

A previously developed shallow water wave-mud interaction model (Jiang & Mehta,

1991) was used to calculate the rate of wave energy dissipation and an effective fluid mud

thickness during the fluidization process. This model considers a two-layered mud/water

system forced by a progressive, non-breaking surface wave of periodicity specified by fre-

quency o-, as depicted in Figure 4.1. In the upper water column of thickness H1, in which

the pressure and inertia forces are typically dominant in governing water motion and the

flow field is practically irrotational, sediment concentration usually tends to be quite low, so

that the suspension density, pi, is close to that of water which is considered to be inviscid.

The lower column is a homogeneous layer of fluid mud having a thickness of H2, density P2

and dynamic viscosity /. This last assumption of mud having fluid properties to begin with

is a noteworthy limitation of the simple model description chosen, some consequences of

which are discussed later. Likewise, the shallow water assumption proved to be yet another

limitation, since the data were obtained in the intermediate water range for practical rea-

sons. Finally, a third limitation arose from the fact that while the model assumed constant

properties (density, viscosity) in the mud layer. These properties varied with depth in the

experiments. Some horizontal variations, also ignored in the model, were significant as well,

e.g., the model surface elevation.

4.2 Effective Sheared Mud Thickness

The surface and interface variations about their respective mean values are 771(x, t) and

rh(x, t). The amplitude of a simple harmonic surface wave is assumed to be small enough


I











0 (XIt)


Hi P 2( x,.) Water




Z 2 2 Fiuid Mud

Bed


Figure 4.1: Two-layered water-fluid mud system subjected to progressive wave action

to conform to the linear theory, as also the response of the mud layer. Accordingly, the
relevant linear governing equations of motion and continuity can be written as:

upper layer:

+ g = 0 (4.1)


a(7 72) + H = 0 (4.2)
at (4.2)
lower layer:
u2 072 Oar 82U2
+ rg + (1 r)g = V (4.3)
aZ zu2. O
2dz + = 0 (4.4)

where ui(z, t), u2(x, t) are the wave-induced velocities, h = H2 + 77, r = (P2 P1)/P2 is the

normalized density jump, and v = ip/p is the kinematic viscosity of mud.

The following boundary conditions are imposed:

7i(0, t) = aocos at (4.5)

ui(o, t), u2(oo, z, t), 77(co,t), 2(cX, t) 0 (4.6)


u2(z, 0, t) = 0


(4.7)







55

du2(, H12, t)
92= 0 (4.8)
OZ

where ao(= H/2) is the surface wave amplitude at x = 0. Equation 4.5 specifies the surface

wave form, Equation 4.6 represents the fact that, due to viscous dissipation, all motion must

cease at an infinite distance, Equation 4.7 is the non-slip bottom boundary condition, and

Equation 4.8 states that because the upper layer fluid is inviscid, there can be no stress at

the interface.

Solutions (Jiang & Mehta, 1991) give the normalized wave number, k = kH1, which is

a complex valued function

k 1 + H2r [(1+ 2r)2 4rlH2r]1/2 1/2
_= }2r2 (4.9)
Fr 2rHl2 r

where

F = 1 tanh(mH2) (4.10)
=12- (4.10)
mH2
#H2 = H2/HI, m = (-iRe)1/2, Re = aH2/v is the wave Reynolds number and F, =

u(Hi/g)1/2 is the wave Froude number, a is the wave angular frequency.

The imaginary part of k, i.e., ki, is the wave attenuation (decay or damping) coefficient

with respect to the travel distance x, defined by


a, = aoexp(-k;x) (4.11)


where a, is the wave amplitude at any x. Also the normalized, horizontal wave-induced

velocity in a mud layer is given as

k k
12 = A {1 r( )2}{ cosh(mi) + tanh(mfi2) -
Fr
sinh(mi)} exp{i(ki t)} (4.12)


where i2 = u2/(uH1), A = ao/H1, i = z/H1, and x = x/H1.

As noted in Section 3.2.1 in Chapter 3, the dynamic viscosity of mud can be expressed

as


P = ,oo + C"n-1


(4.13)


I







56
where oo, c and n are constants for a given material, and 4 is the shear rate.

With the two recorded wave amplitudes ao (=H#1/2 at gauge #1) and a. (=H#2/2

at gauge #2) from the experiment, the wave dissipation coefficient, ki, could be calculated

from Equation 4.11. By equating this ki with the model result from Equation 4.9, the

viscosity, p, was determined. Then from Equation 4.13 a representative shear rate in the

mud layer corresponding to this viscosity, 4,, was calculated. Also, by substituting the

viscosity, p (or v = pI/p2), into Equation 4.12, an effective sheared mud thickness, d, was

obtained from the equation:
U-2s U2s 1aH
d= (4.14)

where u2, is the amplitude of u2 at the mud surface and us2 = u2./(auH) is the normalized

value of U2s. Note that this is a very approximate procedure, particularly because the

experiments were not conducted with a fully fluidized mud, as assumed in the model, and,

furthermore, the mud properties were assumed to be depth-invariant in the model, which

was not the case in the experiment. Nevertheless, the objective was to examine if d was

related in any way to the mud fluidization depth obtained from the pressure measurements,

as described in Chapter 5. The process for the calculation of d is illustrated in Figure 4.2,

in which jo is an initially selected value of gamnma required for iterative calculation of j,.

A physical implication of Equation 4.14 is that, assuming d < H2, u2 will be zero at

elevation z = H2 d. This requirement is not compatible with the fact that u2 in the model

is consistently equal to zero only at the flume bottom, i.e., z = 0. Thus the attempt to

calculate a fluidized mud thickness, d, within a layer of thickness H2 that is already a fluid,

by definition in the model, is an artifact meant only to experiment with the possibility of

evaluating the fluidization depth that is commensurate with the experimental data. This

attempt at developing correspondence between the model and the data is necessitated by

the fact that the mud in the flume was not in general a fluid, except in the upper elevations

when fluidization occurred by virtue of wave action.






57












input: o, poo, c, n, H1, H2, pi, P2, a, H#', H#2, Al




S= f(7, c, n, oo); Eq. 4.13



Iki = Im(k); Eq. 4.9 kie, = f(H#, H#2, Al); Eq. 4.11




I k kiexp \< 0.01

no yes


S 2, = f(k, H2,f, a); Eq. 4.12





d = f(U2l,,jI); Eq. 4.14









Figure 4.2: Diagram of calculation process for effective sheared mud thickness, d






58
4.3 Wave Energy Dissipation Rate

The wave-mean rate of energy dissipation with respect to time, ED, is given by (Dean
& Dalrymple, 1984):
rHi+H2 u u u, w Ou
ED = p [2( )2 + (- + )2]dz (4.15)

where the overbar indicates wave-mean value. Note that since the water layer is assumed to
be inviscid, wave dissipation in this layer is theoretically zero. The integration was therefore
carried out only over the mud layer of thickness H2. For the two-dimensional shallow water
model, the vertical velocity, w, is ignored. Thus Equation 4.15 can be simplified as:

ED = p2V [2(o)2 + ( )2]dz (4.16)

or, dividing eD into two terms:

ED = ED1 + ED2 (4.17)

ED1 = P2v 2( 2)2dz (4.18)
Jo ao
ED2 = P2V ( )dz (4.19)

Physically, ED1 and ED2 are the wave-mean rates of energy dissipation due to the horizontal
and vertical velocity gradients, respectively. Equation 4.12 gives:

u = (ik)t2 (4.20)

and
2 aT2 k k 21
= a- = oA {1 r( )2 -msinh(mi) + mtanh(mi) cosh(mi)} exp i(ki t)
z OZ FT2r Fr
(4.21)
Therefore, the time-averaged values of ('~ )2, (%2)2 are:

(u)2 = -22( )' { r( )2}2 1 cosh(mi) + tanh(mf2) sinh(mi)}2 (4.22)

and
22 1 2 Ak2 k 2 tanh2(mH2)-1
( 2 = ma(_) {1 r(-) }2{ 2(
+z 2 Fc2 F, 2
tanh2(m12) + 1 cosh(2mi) tanh(ml2) sinh(2m/)} (4.23)
+ 2








Therefore

1 2 9u2 2 QU
ED1 = 2p2V o2)2dz = 22V HI( 2)2dj
Ak k
= 2p2vHIzC2( )2{1 r(-)2

3 1 2 tanh(mHt()
{3 2 -i2 tanh2(m ) + tanh(m2)[cosh(m2) 1]
2 2 m
tnh(mH) [cosh(2m2) 1 -- sinh(mH2)
2m m
1 + tanh2(mH2)
+ 4m sinh(2mH2)} (4.24)

and

fD2 = P2V H2(F~ )2dz (4.25)
1 AO Z
=1 vHlm2a2( )2{1 r( k)2}2
72- Fr
tanh2(mHi2) 1 1+ tanh2(mH2)
2 H2 + sinh(2mH2)
2 4m
tanh(mHi2)[cosh(2mH2) 1]}
2m

Introducing

x = H2( )1/2 (4.26)
2v
the normalized mud layer thickness, where (2v/a)1/2 is the thickness of the laminar wave-

induced (mud) boundary layer (Jiang & Mehta, 1991), Equations 4.24 and 4.26 can therefore

be further written as:

ED1= F2 f222-2 ) ({1 R( 2 2
1 r T Fr
3 1 2HJ2tanh(V X)
S2 -2 tanh(v X) + 22[cosh(v-x) 1]

12 tanh(VX--2i) 2112
Stanh( [cosh(2V--2X) 1] sinh(v/--X)
2 f-2iX 2-X-2
I + tanh2( -' X)
-+H2aX sinh(2--2ix)} (4.27)

and

Eoa (1 -i)2 k 2
ED2 = ( 1 -( )2)2
2 1-r F, F,






60
S1 t (anhV(2 /- 'X)
{ [tanh2(v2) 1] + 21 + taih' sinh(2/-2iX)
2 4J-- x
[tanh(tn(v ) 4V)x
-12 tnh[cosh(2V--2 x) 1]} (4.28)
2-2X

where Eo = 0.5plgag is the initial energy (at wave gauge #1). For any set of conditions in

the flume, Equations 4.17, 4.27 and 4.28 can be used to calculate ED.

As an alternative to the above approach, the same dissipation rate can also be obtained

via the following procedure:
dE
ED = dt (4.29)

The wave energy, E, is obtained from


E = pligax2 (4.30)

where

a. = aoexp(-kiejx) (4.31)

is the surface wave amplitude at any x, and


x = Ct (4.32)

and (Jiang & Mehta, 1991)

C = Co-r (4.33)
kr
with Co = VgHi being the wave celerity in shallow water over the rigid bottom and kr

being the normalized wave number from Equation 4.9. Therefore, Equation 4.29 can be

further written as:

ED = Pr ga kiexp (4.34)
kr
Where g is the acceleration due to gravity; H1 is the water column thickness, pi is water

density and ki is the surface wave attenuation (decay) coefficient over mud bed obtained

from the fluidization experiment. This approach, which was especially suitable for analyzing

the data obtained in this study, was used for calculation of the energy dissipation rate in

Chapter 6.














CHAPTER 5
MUD BED FLUIDIZATION EXPERIMENTS



5.1 Test Conditions

Originally, three composite sediments (AK, BK, and AB) were selected as muds for the

fluidization experiment, based on the theological data presented in Chapter 3. However,

time limitations permitted testing of only one composite, i.e., AK. This mud was mixed

with the help of a compressed air jet in a 1.2m diameter and 1.4m high aluminum tank with

a protective cover lid for two days before placement into the flume. The selected initial mud

density was approximately 1.2 gl-1.

In all the tests, water level in the flume was maintained at 35 cm, and wave period close

to 1 sec. The only change in the experimental conditions was with the respect to the wave

height. In different tests, the bed was subjected to wave heights ranging from 2 cm to 8 cm

for selected durations. In addition to the wave height, total and pore water pressures, bed

density profile (vertical), visual bed elevation, and water temperature were also recorded

during the tests.

The flume setup is shown in elevation view in Figure 5.1. Eleven sets of tests were

conducted. Except for test #1 in which the wave height was increased in steps without

interruption, in all the other tests the wave height was kept constant at the wave maker

throughout the fluidization process. Depending on the wave conditions, tests were run

continuously for 6 hours to over one day. In tests #1 through #7 pressures were recorded

but had to be discarded for want of accuracy due to a significant mean drift (see Section

3.3.3, Chapter 3) that was recorded by most pressure gauges. From test #8 onwards, the

pressure measuring system was turned on at least at least 6 hrs before data collections, in

order to minimize the drift problem. Table 5.1 summarizes the test conditions, including the


I















1II)It!1O (IX- IIo!Wuz)!piIU aill IJOJ(Id alliifl Jo (plalys :t- 01121d.



(UI L'O = x) (w 6*8 = x)
ainss8Jd Allsuea




-ro alemM oar

(o=x) (mw9gL = x) (mvuL=x)
JO)JeWJ OA13M t# e6neE) BALM Z# o1ne9 GAIM










Table 5.1: Summary of test conditions

Test Consolidation Average initial Design wave Frequency Duration Temp.
No. time (hrs) bed thickness(cm) height (cm) (Hz) (min) OC
15.6 2 1.06 130 19
15.3 4 1.06 30 19
1 20 15.2 5 1.06 50 19
14.5 7.7 1.06 45 19
2 15 13.9 2 1.06 135 20
3 15 13.7 3 1.06 290 20
4 160 18.3 4 1.06 2970 17
5 140 17.0 6 1.04 770 16
6 160 17.0 7.5 1.04 350 15
7 150 17.6 5 1.06 380 17
8 240 17.5 4 1.06 460 19
9 65 16.6 5 1.06 450 20
10 85 16.4 8 1.06 385 21
11 90 16.4 3 1.06 1700 20



bed consolidation time, average initial bed thickness, design wave height (at the beginning

of the mud trench), wave frequency, experimental duration, and mean water temperature.

.As observed, the water temperature remained fairly constant through the entire test series.

Note that sediment densities were measured within mud only, not in the water column.

This is because during the experiments, entrainment of mud into the water column was

comparatively small. For example, Maa (1986) using the same flume found that the max-

imum sediment concentration in the water column was on the order of 0.05 to 0.5g/l only.

5.2 Flume Data

The complete set of experimental data from test #9 is given as an example here.

5.2.1 Wave Time-series

Wave heights at different times from test #9 are given in Table 5.2, and examples of

the wave time-series are shown in Figure 5.2, where time refers to the beginning of the test.

It can be observed that the wave height decreased with respect to both time and traveling

distance, which in general suggests that the rate of wave energy dissipation changed during

the course of the bed fluidization process. This issue is discussed later in Section 6.2.3.















Table 5.2: Wave heights, Test #9

Time(mins) H#l(cm) H#2(cm)
4 5.0 3.4
8 5.2 3.0
11 5.1 2.8
14 5.1 2.5
18 5.2 2.4
24 5.2 2.1
28 5.1 2.0
36 5.1 1.9
43 5.1 1.9
50 5.1 1.9
59 5.1 1.8
71 5.0 1.8
80 5.0 1.7
90 4.9 1.8
102 4.9 1.6
115 4.9 1.6
135 4.8 1.7
150 4.8 1.6
165 4.7 1.5
180 4.7 1.6
195 4.7 1.7
210 4.7 1.7
230 4.6 1.6
250 4.6 1.6
265 4.6 1.6
285 4.6 1.7
300 4.5 1.7
320 4.5 1.5
340 4.5 1.6
360 4.4 1.6
380 4.4 1.6
400 4.4 1.6
420 4.3 1.5
450 4.3 1.5
























5.0 10.0 15.0 20.0 25.0
TIME (SEC) 71 MINUTES GAUGE Il


0











0


5.0
TIME


10.0
(SEC)


15.0
71 MINUTES


20.0
GAUGE


25.0
#*2


5.0 10.0 15.0 20.0 25.0
TIME(SEC) 210 MINUTES GAUGE =2


Figure 5.2: Wave time-series, Test #9


2.0

0.0

-2.0

-4.0
0.1


4.0

2.0

0.0

-2.0

-4.0
0.


4.0

2.0

0.0

-2.0


30.0


5.0 10.0 15.0 20.0 25.0
TIME(SEC) 210 MINUTES GAUGE *1


-4.0 '
0.(


4.0

2.0

0.0

-2.0

-4.0
0.


30.0


c

AAMAWWVWVVWWVWWC


I I


0


30.0


0

NVWVAAMAVVANV\"


0


30.0











5.2.2 Wave Spectra

Wave spectra from test#9 are shown in Figure 5.3, where time represents test duration

from the beginning. These spectra highlight the dissipation of wave energy during the test.

At 71 mins the wave energy density decrease between the two gauges was 76 cm2s, while at

210 mins and 360 mins the decrease was about 70 cm2s, which is consistent with the trend

in the wave energy dissipation rate, ED discussed in Section 6.2.3, Figure 6.6 (b).

5.2.3 Water/mud Interface

During wave action mud was initially observed to be transported downstream, due to the

non-linear effect of the waves, especially due to net mass transport, which resulted in a slope

(set-up) with interfacial elevation increasing in the downstream direction. Subsequently,

under the opposing effects of mass transport and hydrostatic force due to the slope, the

interfacial profile appeared to approach an equilibrium shape. Later on, however, when the

upper part of the bed became fluidized, the top mud layer moved back again slightly. This

phenomenon is seen from Figure 5.4 and the water/mud interface change in the density

profiles presented in Section 5.2.4. After each test was conducted, recovery of the effective

stress (described later in Section 6.3.1, Chapter 6), dewatering and gelling, all combined

to cause the residual slope to become rapidly static. Even after some days no measurable

change in the slope could be observed visually.

5.2.4 Density Measurement

Examples of mud density profiles during test #9 are shown in Figure 5.5. These profiles

indicate the generally stratified nature of the bed throughout the test. However, a change

in bed density due to the fluidization could not be identified clearly from this test or others,

an observation that is in agreement with that of Ross (1988). A part of the difficulty lies

in the low accuracy of the measurements which were made at discrete elevations. However,

since there was very little entrainment of mud into the water column, and since the bed did

not dilute to any significant elevation during fluidization, a significant density change could

not have been expected in these tests.




















_ 120

z
LU 90



C 60
u ,
UJ
a- 30
(n


FREQUENCY(HZ)

AVG.HT.=5.0CM 71 MINUTES


1.0


20

I--
IS
cn

a: O


ou
uj 5
0-
0n


0.5 1.0 1.5 2.0 2.5


FREQUENCY (HZ)

AVG.HT.=1.8CM 71 MINUTES


12'
0n
z
U 90
oX
-iX
a 360
ea
3U
a. 30
(n


A


GAUGE al











1.0 0.5 1.0 1.5 2.0 2,


FREQUENCY (HZ)

AVG.HT.=4.7CM 210 MINUTES

20
D

i-
GAUGE #2 n
z




ou
L55








.0 0.5 1.0 1.5 2.0 2.5
j 10

a:
L 5




.0 0.5 1.0 1.5 2.0 2.5
FREQUENCY (HZ)

AVG.HT.=1.7CM 210 MINUTES


S 121

z
U 90
a:

6 60
c-J.
u
a. 30
01


Figure 5.3: Wave spectra, Test #9


C


GAUGE 1











0.0 0.5 1.0 1.5 2.0 2.


,5


E


GAUGE al











0.0 0.5 1.0 1.5 2.0 2.5
FREQUENCT(HZ)

AVG.HT.=q.l4CM 360 MINUTES


F


GAUGE #2











0.0 0.5 1.0 1.5 2.0 2.5

FREQUENCY (HZ)

AVG.HT.=1.6CM 360 MINUTES


B


GAUGE n2










__A ^ ..


20

>-
15







U 5
a
0.
(H


0
0


(







68







22.0


20.0 ^ .


18. Gauges
2o O ....... Total Pressure

0 .............. 0 MINS

------------0 MINS ........
16.0 -


u., 14'.0' ------ 210 MINS
-J
SLJ ----300 MINS
12.0


10.0
15.0 14.0 13.0 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0

DISTANCE (m)



Figure 5.4: Time-variation of water-mud interface along the flume, Test #9


5.2.5 Total and Pore Water Pressures

Wave-averaged total and pore water pressures are shown in Figure 5.6. As indicated in

Section 3.3.3, the total pressure gauge elevations did not match precisely with those of the

pore pressure gauges, hence interpolation had to be used to calculate the value of the total

pressure at exactly the same level at which the corresponding paired pore pressure gauge

was located.

At the beginning, when wave action was started, the pore water pressure at a given

elevation was equal to the corresponding hydrostatic pressure. Then under wave action an

excess pore water pressure generally developed. In those cases in which the pore pressure

curve intersected the total pressure curve, fluidization was considered to have occurred in
i


















18.0
I6.0 100 MINS
I - - -


1.00 1.05 1.10
DENSITY


1.15 1.20
(G/CMx3)


1.00 1.05 1.10 1.15 1.20 1.25
DENSITY (G/CMx3)


18.0[380 -INS
,s.o 3-80 -MINS_ _


1.00 1.05 1.10 1.15 1.20 1.25
DENSITY (G/CMx3)


Figure 5.5: Examples of density profiles, Test #9. Dashed line indicates interfacial elevation


320 MINS









70
accordance with Figure 2.4. Note that the total pressure was also obtained independently

from the density profiles, and these had to be used to "calibrate" for the total pressures

in cases where the gauge data exhibited significant drift problems. Problems of instrument

related drift noted in Section 3.3.3 (Chapter 3) are apparent in most cases in Figure 5.6.

Drift generally caused both types of pressures to change over a time-scale that was much

larger than the wave period, thus compromising the accuracy of determining the time at

which fluidization occurred. The pore pressure data points at 14cm elevation dropped

below the hydrostatic value which is unrealistic, and suggests a serious instrument problem.

Note that with the exception of the gauge pair at 14cm elevation, all the gauges showed a

response that suggested a drift that seem to cause the pressure to rise for the first 100-150

mins followed by a drop. This uniform behavior suggests that the drift problem may have

been, at least in part, associated with the data acquisition system excluding the gauges

themselves.

At this point it is worth considering the range of variation in total pressure that would

have resulted from a change in the interfacial elevation during the course of the test. Refer-

ring to the time-variation of water-mud interface in Figure 5.4, at the pressure gauge site

the maximum change of the mud surface elevation during test # 9 was about 5mm, which

corresponded to 10 Pa pressure change, which was less than the accuracy of the pressure

gauge (68Pa). On the other hand, the pressure measurement, for example at the 5.1cm

elevation, indicated a difference of 90 pa. This difference was therefore attributed primarily

to the drift problem.

5.2.6 Bottom Pressure Gauge Data, Test #9

Figure 5.7 shows the total pressure at the bottom of the flume during test #9. This plot

shows that at first the total pressure decreased (from 3.73 kPa to 3.7 kPa, i.e., 30 Pa) for

about 40 minutes, then increased slightly. This change suggests mud advection movement

due to wave action. When waves just began, mud moved in the downstream direction

because of the non-linear effects of waves, thus causing a set-up in the flume as noted in














2.20

1.90

1.60

1.30

1.00


2.32

2.29

2.26

2.23

2.20
2.65

2.60
CE
0. 2.55

2.50
a:
:) 2.45
(n
(n
L 2.80
Cc
a-
2.75

2.70

2.65
3.15

3. 10

3.05

3.00

2.95

2.90
3.40
3.35
3.30
3.25
3.20
3.15
3. 10
0


Figure 5.6: Wave-averaged total and pore water pressures, Test #9


LEVEL=5. 1CM









LEVEL=3.1CM







100 200 300 400 500 60

TIME (MIN)













4.00


L 3.80 -

J 3.60

U)
u( 3.40 FROM GAUGE
LLJ
(" E FROM DENSITY
C-
3.20 -


3.00 --
0 100 200 300 400 500 600
TIME (MIN)


Figure 5.7: Total pressure at the bottom of the flume, Test #9


Section 5.2.3. When the top of the bed was fluidized, which thus became a suspension, the

mud moved back again to level out the bed surface.

This result from the total pressure measurement was very consistent in the first 200

mins, with the phenomenon shown in Figure 5.4 in Section 5.2.3. which shows that the

pressure data dropped in the first 40 mins, then started to increase slightly. However, after

200 mins, it dropped again.

5.2.7 Rms Pressure Amplitudes, Test #9

Root-mean square (rms) amplitude pressure is obtained from


p1 = .( P)2 (5.1)
i=1

where Pi is the instantaneous pressure, P is the time-mean pressure, and N is the number

of data points. Rms amplitudes of pore and total pressure data are shown in Figures 5.8

and 5.9. For both the total and pore pressures there was a trend of increasing amplitudes

initially in the first approximately 30 mins, especially at the top three levels. This increase

was an indication of the wave-induced movement been transmitted relatively rapidly into the

bed. Later on as the bed began to fluidize, which dissipated more wave energy, the pressure


I











amplitudes decreased accordingly. The largest decrease in pressure amplitude occurred at

about the same time when the wave energy dissiapation rate was highest (see Figure 6.16).

The decreasing of the rms amplitudes can reflect increasing the wave energy dissipation

during the bed fluidization process. Such a decrease was more rapid initially, as further

noted in Section 6.2.3.

Combining the data in Figure 5.8 and 5.9 with those in Table 5.2 it can be concluded

that as the wave height decreased with time, the rms amplitudes of pore and total pressure

also decreased with time, especially for the top three (elevations of 14cm, 12cm, and 9.5cm)

pressure data. Apparently, the pressure amplitudes decreased only slightly after fluidization

occurred (the elevations and times when fluidizaton occurred are given in Table 6.6, Section

3.2 of Chapter 6). Finally, it can be concluded that the amplitudes in the lower levels of mud

layer had smaller values than at higher elevations, presumably because the wave amplitude

decreased as the dynamic pressure was transmitted and dissipated downwards into the bed.

5.2.8 Pressure Recovery after End of Test

In test #9, pressure data were obtained after wave action ceased. The corresponding

effective stresses are calculated and discussed in Section 6.3.1.


I













































50 100 150 200 250 300 350 400 450 500 550

TIME (MIN)


50 100 150 200 250 300 350

TIME (MIN)


400 450 500 550


Figure 5.8: Root-mean square pore water pressure amplitudes, Test #9


30.0
0


120.0.


90.0






60.0






30.0
0


--A- 7.5CM





S--- -- 5.1CM


-0-- 3.1CM


I I I1 I I____________


l @ I I # m ,


i



















120.0





90.0

LLJ
uCL


IL 60.0
a-




30.0
0


I I I I I I I I I
50 100 150 200 250 300 350 400 450 500 550 600

TIME (MIN)


Figure 5.9: Root-mean square total pressure amplitudes, Test #9


50 100 150 200 250 300 350 400 450 500 550 600

TIME (MIN)


120.0r


90.0 -


60.0


30.0
0


-t- 4.9CM


.--*-- 2.6CM


-a, *,,*~~ .-

~~K"~^gE "*. .~


-- 0O.OCM
















CHAPTER 6
EXPERIMENTAL DATA ANALYSIS



6.1 Introduction

In this chapter, results are presented, based on the wave-mud interaction (introduced in

Chapter 4), which were applied to calculate the effective sheared thickness, d, as a possible

representative of the fluidized mud layer thickness, as well as the rate of energy dissipation,

ED (also from Chapter 4). The pressure data are then analysed to determine the fluidized

mud thickness, df, and the rate of fluidization. The two types of thicknesses, d and df, are

then compared, and the relationship between the rate of fluidization and the rate of wave

energy dissipation, ED, is examined.

6.2 Wave-Mud Interaction Model Results

6.2.1 Wave Regime: Test Versus Model Conditions

As noted in Chapter 4, the wave-mud interaction model is based on the shallow water

assumption, i.e., HI/L < 0.05, where L is the wave length,which was obtained from the

linear wave dispersion equation (assuming rigid bed condition):


L= -T2 tanh 2H (6.1)
27 L

The range 0.05 < H1/L < 0.5 is the transition condition from the shallow water to deep

water. Table 6.1 presents the values of Hi/L for the present experiments. As observed the

test condition was not really shallow water according to this classification. There are two

different types of effects on the model-based results due to shallow water assumption. Firstly,

in the shallow water model the particle horizontal velocity is assumed to be uniform in the z

direction in the water column. When waves are not in the shallow water regime this velocity

decreases downwards from the water surface, so that near the bottom of the water column












Table 6.1: Parameters for determining the water wave condition

Test # H1 L H1/L
(cm) (m)
1 19.4 1.11 0.17
2 21.1 1.13 0.19
3 21.3 1.14 0.19
4 16.7 1.05 0.16
5 18.0 1.11 0.16
6 18.0 1.11 0.16
7 17.4 1.07 0.16
8 17.5 1.07 0.16
9 18.4 1.09 0.17
10 18.6 1.09 0.17
11 18.6 1.09 0.17


the particle movement is smaller than that at the surface. Thus the velocity at the bottom

of the water column (at the mud surface) was overpredicted by the model. Consequently

the model also overpredicts the degree of the bed fluidization in this sense. On the other

hand, however, the shallow water model assumes the particle vertical acceleration to be

equal to zero, which was not quite the case. The vertical movement of the water particle at

the bottom of the water column would contribute to the wave energy transmission down to

the mud layer, thus enhancing bed fluidization. Therefore from this point of view the model

underestimates the degree of bed fluidization. These two factors therefore have opposing

effects on fluidization, hence the overall influence of the shallow water assumption in reality

depends on which of the two factors is dominant. The limited scope and data in this study

prevented a quantitative evaluation of these two factors on the observed fluidization process.

6.2.2 Effective Sheared Mud Thickness

As a possible representative of the fluidized mud layer thickness, the effective sheared

thickness of the bed, d, within which (fluid) mud was sheared by the wave, was calculated

according to the diagram presented in Figure 4.2. Results are shown in Figures 6.1, 6.2,

and 6.3, where the marker points represent experimental data, and the solid lines are

obtained from least squares polynomial fit using these data. The procedure for calculating









78
d, notes in Chapter 4, is repeated here for convenience:

1. Select an initial value of the shear rate, o, to calculate viscosity, i/, by the power-law

equation for viscosity, i.e., by Equation 4.13 (M = Poo + c o).

2. Use the viscosity thus obtained to calculate k from Equation 4.9. The imaginary part

of k, i.e., ki, is the wave damping coefficient.


3. With the recorded wave heights at the two gauges, the measured wave damping co-

efficient, kiexp, can be obtained from H#2 = H#iezp(-kiexpAl), via Equation 4.11,

where H#1 is the wave height at gauge #1 and H#2 the height at gauge #2.


4. When ki obtained from step 2 "matches" ki,,p obtained from step 3 by iterating for

4, i.e., | (kiEq.4.11 kiEq.4.9) < 0.01 j, the selected 4 is assumed to be right, or a new

4 is chosen for Equation 4.13 and the above procedure repeated until ki and kiejp

match.

One example of the calculation for test #9 is given here. The input parameters are:

oo = 4.44Pa.s, c = 0.76, n = -1.083, water density, pl = Ig/cm3, mud density, P2 =

1.17g/cm3 (representative depth-mean value), distance between two gauges Al = 5.3m,

average bed thickness within the test section, H2 = 16.7cm, water column depth, HI =

35 H2 = 18.3cm, a = 27r/T = 6.28Hz, H#i = 5.0cm and H#2 = 1.8cm. An iterated

value of the shear rate 4 = 0.01Hz was selected to be used in Equation 4.13 to obtain the

dynamic viscosity ip = 611Pa.s, which in turn was used in Equation 4.9 to calculate the

wave dissipation coefficient ki that agreed with the one from experimental data obtained

from Equation 4.11. The wave-induced horizontal velocity in the mud layer (surface) was

determined by Equation 4.12, which together with Equation 4.14 gave the effective sheared

thickness d = 6.6cm.

Table 6.2 gives the input parameters for all the tests. The wave heights H#1 and

H#2, and the test section-average mud thickness H2 changed with time, i.e., they were not

constant within each test. Therefore these parameters are not given in the table. Note


I












Table 6.2: Input parameters for calculating the effective sheared mud thickness

Test # ,oo c n P2 c
(Pa.s) (g/cm3) (rad/sec)
1 4.44 0.76 -1.083 1.19 6.28
2 4.44 0.76 -1.083 1.19 6.28
3 4.44 0.76 -1.083 1.19 6.28
4 4.44 0.76 -1.083 1.17 6.28
5 4.44 0.76 -1.083 1.17 6.28
6 4.44 0.76 -1.083 1.17 6.28
7 4.44 0.76 -1.083 1.17 6.28
8 4.44 0.76 -1.083 1.17 6.28
9 4.44 0.76 -1.083 1.18 6.28
10 4.44 0.76 -1.083 1.19 6.28
11 4.44 0.54 -0.68 1.18 6.28



that in test #11 the parameters c and n had to be changed, Since under small waves bed

deformation was limited to a small upper portion of the bed, and the bed density of that

portion was much less than the depth-average density used otherwise, so that the viscosity

of that layer was lower than that based on the depth-mean density. Based on this concept, c

was reduced (from 0.76 to 0.54) and n (from -1.083 to -0.68) was increased. These reduced

values corresponding a density p2 = 1.12g/cm3. The wave frequency used was selected

throughout to be 1 Hz (6.28 rad/sec) in the model, which was not exactly equal to those

given in Table 5.1, but was acceptably close.

It can be seen from Figures 6.1, 6.2 and 6.3 that, in general, the larger the wave

height the thicker the effective sheared thickness, d, and that initially it generally increased

relatively rapidly and eventually approached some constant value, d,, under a given set

of flume conditions. In general, values of d, also increased with the wave height, and the

results for the eleven tests are shown in Table 6.3.

6.2.3 Wave Energy Dissipation

Wave energy dissipation per unit of time, eD, was determined from Equation 4.34.

Figures 6.4, 6.5 and 6.6 present eD as a function of time for all the tests. These figures

show that typically ED was relatively small in the beginning, then increased gradually under
















5 cm 7.7 cm
-- 2 cm -- 4 cm '- 1 o-ls a




0 Model Output /

Polynomial Fit

TEST =1

50 100 150 200 250 300


20 40 60 80 10

C









TEST v3
1--- i----i_________


TIME (MIN)


Figure 6.1: Effective sheared mud thickness, d, Tests #1 through #3


14.0

12.0

10.0

8.0

6.0

4.0

2.0


0.4




Z 0.2
03
= 0.2
ro l
X --


E


03 1.0
-J
Z

0.5
I
H:


S

S


TEST =2














2.
U 10.(
CD
4) 8.0
Z 6.0

, 4.0

S2.0

0.0


0
11 n


10.0
CO
On 8.0
UJ
Z 6.0

S4.0

- 2.0

0.0

11.7

S9.8
CO)
1) 7.8
z 5.9

3.9

- 2.0


11.7

9.8

7.8

5.9

3.9

2.0

0.0
0


2500


2000


1000


1500


3000


0 100 200 300 400 500 600


0
0 C







TEST #6


100 200 300 400 50



D






TEST #7
TEST 7

-- I I I I


300
TIME (MIN)


Figure 6.2: Effective sheared mud thickness, d, Tests #4 through #7


R






TEST =4

_ II I I I


B






TEST #5

I I I I I I


I 0 fn


0













6.0

!5.0 R

n, 4.o0
LU 0 0 9 0 --
Z 3.0
U E0
2.0
7-
1.0 TEST n8

0.0 1
0 100 200 300 400 500

S9.8
U
S7.8 B

Cn qc 0 E ......
c,)
s S.9 -E E) ooEc E

U 3.9

S2.0 TEST #9

0.0 1
0 100 200 300 400 500

13.7
U 11.7 OE)
9.8 -gE-OOQOO O
C
U7 7.8
z
5.9
3.9
2.0 TEST t10

0.0
0 100 200 300 400 500
S6.0

s5.0
c-)
CO 4.0

Z 3.0 '- -.0

2.0

--1.0 TEST all

0.0 ( I
0 200 400 600 800 1000 1200 1400 1600 1800

TIME (MIN)



Figure 6.3: Effective sheared mud thickness, d, Tests #8 through #11


I













Table 6.3: Values of the (representative) constant effective sheared mud thickness, d,, 7
and L


Test No. d, p
(cm) s-1 or Hz (Pa.s)
1 9.4 0.043 425
2 0.2 0.017 2634
3 0.7 0.035 680
4 4.9 0.032 728
5 6.6 0.032 770
6 7.8 0.034 662
7 6.8 0.034 670
8 3.6 0.032 750
9 6.1 0.036 630
10 9.2 0.037 575
11 2.8 0.036 600


the wave action to a maximum value, and decreased again to approach some constant value,

EDs. The respective values of ED, for the tests are given in Table 6.4, although since in some

tests ED did not quite reach the constant value eDs, the final experimental value of ED has

been reported instead. As seen from Equation 4.34, the magnitude of ED is controlled by

two primary factors, the wave amplitude (squared), a,2, and the wave decay coefficient, ki,

which have been plotted as functions of time for test #9 in Figure 6.7 for further discussion.

At the beginning of wave action, the bed had greater rigidity, ki was comparatively small

(although much higher than the representative value 0.02 s-1, that can be derived from

the flume charaterization tests using a false rigid bottom described in Section 3.4), and

although the wave amplitude was higher, the product of ki and a.,2 was still comparatively

small. As the fluidization process went on, there was more fluid mud involved in the energy

dissipation process, and ki increased rapidly, which in turn increased ED eventhough a.,

decreased. Thus more wave energy dissipation occurred when the fluidized mud thickness

increased, but there was apparently a limit to it corresponding to a constant value, as the

fluid mud thickness approached a constant value as well.



















4.0000



3.0000



2.0000



1.0000



0.0000
0
0.0400


0.0300
C))

0.0200
1Z-
z

U 0.0100
r-

0.0000
Z 0
S0.2000
I-

0. 1500
C.r)
(n

00.1000



0.0500



0.0000
0


Figure 6.4: Wave dissipation rate, ED, versus time: Tests #1 through #3


5 cm 7.7 cm A
-2 cm ------4 cm ~---
-0


-0




TEST l1


50 100 150 200 250 30C


B

E)

0





TEST =2, DESIGN WV.HT=2 CM


20 40 60 80 10(


C
0
-E)
-0








TEST #3, DESIGN WV.HT=3 CM


50 100 150 20C
TIME (MIN)


I











1.0000

0.8000

0.6000

0.4000

0.2000

0.0000
0
2.0000


1.5000
Co)

: 1.0000
Z
0.5000
LULJ
I-
S0.0000
Cc 0
z3.0000

-2.5000
I--
CE
2.0000

0-)1.5000

1.0000

0.5000

0.0000
0


e0


e0


TEST *7,


0 E


S 0)


DESIGN WV.HT=5


I 1 I 1 I-- I I
50 100 150 200 250 300 350 400
TIME (MIN)


Figure 6.5: Wave dissipation rate, ED, versus time: Tests #4 through
heights are from Table 5.1


#7. Design wave


TEST -, DESIGN WV.HT= CM

TEST *t4, DESIGN WV.HT=4 CM

I I I I I


3000


2500


2000


1500


1000


B


00e 00 E e E0 e e0
0




TEST #5, DESIGN WV.HT=6 CM

I I I I 1 I I
100 200 300 400 500 600 700 80C
0 00 C




0 0



TEST #6, DESIGN WV.HT=7.5 CM


50 100 150 200 250 300 350 40(


eeooe


1.2000

0.9000 -

0.6000

0.3000


0.0000
0


I


I




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