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Laboratory experiments on cohesive soil bed fluidizatino by water waves

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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
Creator:
Feng, Jingzhi
Mehta, Ashish J.
Williams, David J. A.
Williams, P. Rhodri
Place of Publication:
Gainesville, FL
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Coastal and Oceanographic Engineering Department, University of Florida
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Subjects / Keywords:
Rheology
Fluid mechanics
Fluidization
Mud

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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.

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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. Reort n. 2.3. Recipient -a Accessaion n.
4. TItle and Subtitle 5. Report Data LABORATORY EXPERIMENTS ON COHESIVE SOIL BED December, 1992 FLUIDIZATION BY WATER WAVES: PARTS I AND 11I6
7. Anthor(e) S. 1'erfnzming organization Report gon. PART I: Jingzhi Feng and Ashish J. Mehta F/OL901 PART II: David J.A. Williams and P. Rhodri WilliamsULCEL9/1
9. Peufoxuing Organization Jarn and Address 10. Project/Taktiork Unit No.
Coastal and Oceanographic Engineering Department University of Florida1.CotatrCesN. 336 Weil Hall 11.C trac or Grnt No Gainesville, FL 32611DCW99--Ol
____________________________________________________________ 13. Type of Report 12. Sponsoring organization emo and AddressFia U.S. Army Engineer Waterways Experiment StationFia 3909 Halls Ferry Road
Vicksburg, MS 39180-6199_______________14.
15. Supplementary Notes
PART I: RELATIONSHIP BETWEEN THE RATE OF BED FLUIDIZATION'AND THE RATE OF WAVE ENERGY
DISSIPATION
PART II: IN-SITU RHEOI4ETRY FOR DETERMINING THE DYNAMIC RESPONSE OF BED 16. Abstract
A series of preliminary laboratory flume experiments were carried out to examine the time-depend ent 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/in3, 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. originator's Key Words 1a. Availability Statmsest
Cohesive sediments Resuspension Energy dissipation Rheology Fluidization Rheometry Fluid mud Water waves Pore pressures
19. U. S. security ciaseif. of the Report 120. U. s. Secure ty Claseif. of This Page 21.N.oPae 2.Prc
Unclassified I Unclassified 148 fPae 122 1rc




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-OO 10.




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/in3 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.

ii




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-0O1O.

i




TABLE OF CONTENTS

SYNOPSIS................................................ i
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 Wave Spectra .. .. .. .. ... ... ... ... ... ... .... ..46
3.4.3 Wave Reflection Estimation .. .. .. .. ... ... ... .... ....46
3.4.4 Current Velocity .. .. .. ... ... ... ... ... ... ... ...50

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4 ESTIMATIONS OF FLUID MUD THICKNESS AND WAVE ENERGY DISSIPATION................................................... 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

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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 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 Modi 6.3 Concluding Remarks...............
BIBLIOGRAPHY......................
APPENDIX: SOLUTION FOR V/V(0)........

el Parameters

vi

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




PART I: RELATIONSHIP BETWEEN THE RATE OF BED FLUIDIZATION AND
THE RATE OF WAVE ENERGY DISSIPATION By
Jingzhi Feng and Ashish J. Melita




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 flexes 6 2.9 Soil mass subjected to stress loading.. .. .. .. .. ... ... ... ....
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 lcaolinite beds in flumes 11 3.1 SEM of dry agglomerates of attapulgite. Scale 1cm = 10im .. .. ...18 3.2 SEM of dry agglomerates of bentonite. Scale 1cmn= 10jzm .. .. .. ...18
3.3 SEMI of dry agglomerates of kaolinite. Scale 1cm = l01im. .. .. .. ...19
3.4 Shear stress, a, versus shear rate, 4,(K,A,B) .. .. .. .. ... .. ...22
3.5 Shear stress, o-, versus shear rate, 4,(AK,BKAB). .. .. .. .. .....23
3.6 Shear stress, a, versus shear rate, 4,(K,KSA,AS,B,BS) .. .. .. .. ...24
3.7 Shear stress, a, versus shear rate, 4,(BKBKS,AK,AKS,AB,ABS) . 25 3.8 Viscosity, M, versus shear rate, 4,(K,KS,AAS,B,BS). .. .. .. .....26
3.9 Viscosity, y~, versus shear rate, 4,(BK,BKSAKKS,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




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"'
amplifier .. .. .. .. .. ... ... ... ... ... .... ... ... ..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 3.13 Wave flume elevation profile and instrument locations .. .. .. .. ....44
3.19 Examples of wave time-series (depth=2Ocm, period=1.Os) for flume characterization 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=2Ocm; 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.Os). .. .. .. ... ..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 Wave spectra, Test #9. .. .. .. ... ... ... ... ... ... ....67
5.4 Time-variation of water-mud interface along the flume, Test #9 . .. 68
55 Examples of density profiles, Test #- 9. Dashed line indicates interfacial
elevation .. .. .. .. .. ... ... ... ... ... .... ... .. ...69
5.6 Wave-averaged total and pore water pressures, Test #9 .. .. .. .. ..
5.7 Total pressure at the bottom of the flume, Test #9. .. .. .. ... ..
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

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6.3 Effective sheared mud thickness, d, Tests #3rl through #11. .. .. ....82 6.4 Wave dissipation rate, ED, 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 #'1 through #1.Design wave heights are from Table 5.1. .. .. .. .. .. .... ... ... ...86
6.7 ED ki and a, 2 versus time: Tests #9...............87
6.8 Effective stress, d, variations with time: Test #TO8.. .. .. .. ... ...89
6.9 Effective stress, a~, variations with time: Test #Tl9 .. .. .. .. ... ....90
6.10 Effective stress, d, variations with time: Test #10. .. .. .. ... ...91
6.11 Effective stress, d, variations with time: Test #7111. .. .. .. .... ..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, M9I6/D, 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/lat, versus wave energy dissipation rate, ED, tests
#9 and #10. Dashed lines indicate exptrapolations. .. .. ... .....103

iv




LIST OF TABLES
3.1 Chemical composition of kaolinite. .. .. .. .. ... .... ... ....15
3.2 Chemical composition of bentonite .. .. .. .. .... ... ... ...15
3.3 Chemical composition of attapulgite (palygaorskite). .. .. ... .....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 (clays and clay mixtures) for rheological 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 W~vave reflection coefficient, k .. .. .. .. .. .. .. ... ... .. ..50
5.1 Summary of test conditions .. .. .. .. .. ... ... ... ... .....63
5.2 Wave 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/Ia.. .. .. .. ... ... ... ... ... ... ... ... ...83
6.4 Representative values of the wave energy dissipation rate, -D .........88
6.5 Effective stress, d', at the beginning and end of Test #9. .. .. .. ....91

v




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

Ai

I




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 rheological 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 understanding 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 potentially 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 c hanges and wave energy input, and to understand the bed fluidization process through the~e 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 echosounder 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 partidle-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

1




2
(1986) noted ambiguities when lead lines, echo-sounders or nuclear transmission or backcatter 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 9/cm3, while Krone (1962) used a density range of 1.011.11 g/cm3 to define fluid mud. Wells (1983) specified a density range of 1.03-1.30 g/cm 3, Nichols (1985), 1.003-1.20 9/cmn3 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 fluidization, 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 hydrodynamic 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 rheological 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 rheological properties of selected muds, instrument calibration tests and flume characterization tests are presented in Chapter 3. The selected two-layered hydrodynamic wavemud 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, elevations 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 conjunction 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, Urn (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 suspension, which may be less than 1 g1-', but can exceed 2-3 g1-1 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 Chapter 1 it is essentially a fluid-supported slurry with non-Newtonian rheological properties, typically Appearing to conform to a pseudoplastic (shear thinning) or dilatant (shear thickening) description with respect to the stress-rate of strain relationship, depending upon

5




6

Suspension
utcinen Settling
Luoln- Fluid Mud
FiudiatonFormation Deforming Bed
Static o na ryBed
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 lutodine (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, A. 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*A, + PpA, (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 C a ~ + P W (2.2)




8

Figure 2.2: Soil mass subjected to stress loading For soils A, is very small, approaching zero (Sowers, 1979). Therefore, A,, approaches At, and o, must be very large. Thus
= +A P (2.3) As noted by Perloff and Baron (1976), the product of oA, must approach a finite limit corresponding to a constant intergranular force, even though o-* 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, d', defined by d= 0 A, (2.4)
At
Hence by measuring the total stress a and pore water pressure Pp,,, the effective stress at a point can be obtained from
d --P" (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 d' --+ 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, A~u, which is the difference between actual pore water pressure, P~w, and the hydrostatic 'pressure, Ph. Under dynamic




0

9
Water Surface .
Mobile Suspension
Fluid Mud Surface (Lutacine)
Ph Bed
*u W'

PRESSURE
Figure 2.3: Definition sketch of soil stress terminology conditions, if the sum of excess pore pressure, Au, and the hydrostatic pressure, P, approaches the total stress, a, i.e., Au + 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, PP., at a given elevation, leading ultimately to bed fluidization, e.g. by wave action. At first, Pp,, in the bed is equal to the hyd4rostatic pressure Ph, i.e. Au = 0 (assuming this to be the initial condition). Then




10

0 TIME
Figure 2.4: Fluidization process of a soil bed at a given elevation
under dynamic loading the excess pore water pressure, A u, builds up and the effective stress d-reduces gradually. When the pore water pressure PP,, equals the total pressure o-, 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. 'Shaking' 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




11

z0.4
0 Without waves (Parchure, 1984)
W. With Waves (Maa, 1986)
C.)
(n0.2
I7 wave
Effect
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 fluidlized 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 (paiygorskite), a bentonite and a kaolinite, which
together covered a wide range of cohesive properties, were initially selected for characterizing their rheological properties including viscosity and the upper Bingham yield




12
stress, and their time-dependent changes, before conducting the flume tests on fluidization.
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 hydrodynamic 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 kaolinite, 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 capad-tance 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 attapulgite, 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 purchased 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).

14




15
Table 3.1: Chemical composition of kaolinite
SSiO2 46.5% MgO 0.16% A 1203 37.62% Na2O 0.02% Fe2O3 0.51% K20 0.40% TiO2 0.36% S03 0.21% P205 0.19% V205 < 0.001%
GadtO 0.25% _______ I

Table 3.2: Chemical composition of bentonite
SiO2 63.02% A1203 21.08% Fe203 3.25% FeO 0.35% MgO 2.67% Na2O & K20 2.57% GaO 0.65% H20 5.64% Trace Elements 0.72% __________ I

Table 3.3: Chemical composition of attapulgite (palygorskite)

SiO2 -55.2% A12O3 9.67% Na2O 0.10% K20 0.10% F62O3 2.32% FeO 0.19% MgO 8.92%- GaO 1.65% H20 10.03% 1NH120 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




16

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 suspension 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 GAPA 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/.tm, 0.86pum, and 1.01pim, respectively. Scanning Electron M1icroscope (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 68.4 060-0.40 11.2 79.6 0.40-020 13.6 93.2
0.20-0.00 6.810.

i




17

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 2.2G-2.00 3.0 18.6 2.00-1.80 4.9 23.5 1.80-1.60 5.3 28.8 1.6G-1.40 8.1 36.9 1.4-1. 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 1.00-0.80 17.4 54.9 0.80-1.60 25.5 80.4 0.60--0.40 12.3 92.7 0.40-0.20 6.1 98.8 E0.20-0.00 1.2 100.0




18

Figure 3.1: SEM of dry agglomerates of attapulgite. Scale 1cm 10AsM Figure 3.2: 5PM of dry agglomerates of benton-ite. Scale 1cm lO0im




19

Figure 3.3: SEM of dry agglomerates of kaolinite. Scale 0.5cm l0kim
3.2 Rheological Experiments
The rheological 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 rheological 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 1.1I9 AKS attapulgite + kaolinite + 0.5 % salt 1.1 9

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 inins (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 shearthickening 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 Y 1/-1 = (c14)" (3.1) where yo and y... 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




10.0

12.0

14I.0

10.0 12.0 111.0

4.0 6.0 8.0
SHEAR RATE (HZ)

10.0 12.0

Figure 3.4: Shear stress, a, versus shear rate, j5, (K,A,B)

22

70.0 60.0 so.0o 110.0

20.0 10.0

cc (0
Cr) U)
(0

0.0

2.0

RK
E 0-e10 M INS

20.0
18.0 16.0 111.0
12.0
10.0
8.0 6.0 11.0
2.0 0.0

41.0

4.0

6.0

6.0

8.0

8.0

BK
e e E) 5MINS ..------ .----- 10 MINS
*----*----*20 MINS

).0

2.0

100.0C 90.0 80. 0 70.0 60.0 50.0 110. 0 30. 0
20.0 10.0 0.0

0.0

2.0

AB
0 E 10 CYCLES

111.0




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)

23

70.0 60. 0 50.0 40.0 30.0a
20.0a 10.0

0r
Ui
Lo

0.0

0.0

2.0

A K
e e 10 MINS

20.0 18.0 16.0 14t. 0
12.0
10.0 8.0 6.0
4.0 2.0 0.0

0.0

cc a,
cc
cx 0
U) U)
U) cc
U,

BK
e E --eS MINS .1----- .---- 1 10 MINS
*-.--*-.--*20 MINS

2.0

4.0

4.0

4.0

6.0

6.0

6.0

8.0

8.0

8.0

10.0

10.0

10.0

100.0 90.0 80.0 70.0 60.0 50.0 40.0 30.0
20.0 10.0 0.0
0

.0

2.0

AB
-' ~~ in ha. un

p

& IIIJ




a: a
cc U) U')

0.0 2.0 IL.0 a .0 8.0 10.0 32.0 14.0
SHEAR RATE (HZ)
KAOLINITE, SALT

10 CYCLES
0.0
0.0 2.0 '3.0 6.0 8.0 30.0 32.0 14.0
SHEAR RATE (HZ)
IiPOLINITE, NO SALT

a:
0~
U)
U)
Lii

c1

U)
a: a:
Lii
E
U)

3S5*0 30.0 25.0 20.0 35.0 30.0 5.0 0.0

10 MINS

a:
a
cc U)
Lo

0.0 2.0 1.0 5.0 8.0 30.0 32.0 34.0
SHEAR RATE (HiZ)
BENrONITE, SALT

90.0H 80.00 70.0 60.0 50.0 0 40. G 30.0
i..L 10 CYCLES

30.0

0 0.0 2.0 '3.0 6.0 8.0 30.0
SHEAR ROTE UHZ)
BENTONITE, NO SA

Ea:
U') V)
U-1 cc I-
to
CC
a: Lii
m
Lo

00 60.0U 70.0 60.0 $0. 0 .10.0
50.0 20.0 10.0 o.0n

320. 300. 50.0

0.0 2.0 4.0 6.0 8.0 10.0 1 2. 0 14.0
SHEAR RATE (HZ)
nTTAPULGITE, SALT

60.014

'40.0a 20.0

12.0 14.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
SHEAR RATE M1Z)
LT ATTRPULGITE.NO SAlLT

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

r10 MIN

20.0
aS.0
30.0 5.0

U)

0.0

DI
20 MINS

20.0

B

U)
to cci
a:
3-

F

0 ~20 CCLES




70.0.

0.0 2.0 It. 0 0.0 0.0 10.0 12.01
SHEAR RATE (HZ)
BK SALT

cc
L
4.0

cc L
U-)
(U) U)
cc
a:

0.0 2.0 q1.0 6.0 8.0 10.0 12.0 14.0
SHEAR RATE (HZ)
BK, NO SALT

60.0 50.0 'l0.0 30.0 20.0
10. 0.0

60.0 50.0

cc
0
Lo IUJ 114
CC
1-

0.0 2.0 q1.0 6.0 8.0 W0.0 12.0 14.0
SHEAR RATE (HZ)
Kt A SALT

30.0
20.0-

000.0 2.0 '1.0 68..0 8 ..0 1 0.0 1 2.0
SHEAR RATE (HZ)
AK .NO SALT

cc
0.
W) Cc cci
a:J kn

14.0

120.
100.

00.0 60.0

10MINS

c
I10 t~ IN S

0.0 20 4.0 6 .0 8 .0 10.0 12.0 14.0
SHEAR RATE IIIZ)
AB SALT

90.0 80.0 70.0 60.0 s0.0 '10.0 30.0 20.'U

0.0 2.0 '1.0 8.0 8.0 10.0 12.0 14.0
SHEAR RATE lHZ)
AB NO SALT

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

60.0 50.*0 %10.0 30.0 20.0 l0.d

a:
tU)
(r) uLJ cc
I.
U)J
En

20. 0.0

U

0.0
20.

E
5 M1111

15.0 10.0

V)
(n
Ii.J
a:

B
10 MINS

10 MI0

ci'

F
10 fIMS

0




0.0 2

30.0
25.0 20.0 15.0 10.0 5.0 0.0 0
60.0.

90.0 80.0 S70. 0

a.
C)
U

.0

U.,
ci
a-
I
U)
0 Li
U,

~.0 4.0 6.0 8.0 10.0 12.0 14.0
SHEAR RATE (HZ)
KAOLINITE, NO SALT

cr

LI10 MINS (9C 0D

100. 90.0 80.0 70.0 60.0 50.0 '10.0 30. 0
20.0
10.0 0.0
0.

60.0 50.0 40.01 30.0
20.0 10.0
-0
0.0
100.(90.0 80.0 70.0 60.0 50.0 40. 0 30.0
20.0
10.0 0.0
0.0

2.0 4.0a 6.0 8.0
SHEAR RATE ATTAPULGI TE.

10.0 12.0 1 (H Z) SALT

1.0

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

U.,
cr
a
10 MINS
U
2.0 4.0 6.0 8.0 10.0 12._0 14.0
SHEAR RATE (HZ) BENrONITE, SALT
U
(n
2.0 40 6.0 8.0 0.0 1.01 .
SHEAR RTE (HZ
BENTOITE. O SAL

2.0 4.0 6.0 8.0 10.0 12.0 1'
SHEAR RATE (HZ) KAOLINITE, SALT

F
20 CYCLES
Q0 (D

C

.0

E
20M MINS

50. 0 c 40.0 ~-30.0
020.0 1 0.0

B
10 CYCLES

fl-I I

0.0 2.0 4.0 6.0 8.0 10.0 12.0 24.0
SHEAR RATE (HZ)
ATTAPULGITENO SALT

80.0 70.0 60.0 50.0 40.0 30.0
20.0
10.0 0.0

.-- 1 A

a




2. 0 ti.0 6.0 8. 0
SHEAR RATE
BK SALT

10.0 12.0 n1 (H Z)

U)
a:
U

90.0 80.0 70.0 60.0 50.0 40. 0 30.0
20.0 10.0 0.0
0.

2.0 4.0 6.0 8.0
SHEAR RATE
AK SALT

90.0 80.0 S70.0
cr
n~60.0 >.50.0
ci30.0
20.0

10.0 12.0 14.0 (H Z)

10 LINS

0.0 2.0

AB

4.0 6.0 8.0 10.0 12.0 14.0 SHEAR RATE (HZ)
SALT

25.0 20.0 0.15.0 10.0
U
> 5.0

2.0 4.0 6.0 8.0 10.0 12.0 14.0
SHEAR RATE (HZ) BK NO SALT

0.0
0

nt, w~ U.., W.U SHEAR RATE (HZ) AK NO SALT

9'.U

a
U

1.0

150.( 135.(
120.(
105.t 90.0 75.0 60.0 45.0 30. 0 15.0 0.0
0.

.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,AII,AIIS)

90.0.

80. 0 70.0
zn
c60.0
-50.0
q- 0. 0 O30.0
-.20.0

10.0[0.

10.0 0.0

r

C
10 MINS

E
10 LMINS

140.(
120.(
S100
-80.0
!Z 60.0
()
C
C-U 40. 0
20.0
0.0
0,

10 MINS

.0

-10 MHINS ID

F

a

0

0




28
dimensionless constant, M is the apparent viscosity and 4 is the shear rate.
In all the studied cases, y 110 -= (cif)' (3.2)
which can be further written as 1=1oo+ AcO) (3.3) or
+ (3.4) Equation 3.4 is referred to as the Sisko, (1958) model, where pi, 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, IL, 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 A Zf )2 = minimum (3.5) or
N
D = (ji-p., cn-1)2 = minimum (3.6) where A2j is viscosity of the mud obtained from the experiment, and N is the number of data points.
Setting
0D (3.7) OD- (3.8) 5- (3.9)




29

Equations 3.5 and 3.6 can be expressed as
N
-.a Cn-)= 0 (3.10)
therefore
N
n-1c"1) 0 (3.11) hence
E{c-3n-1 log 4(ft, IL_ 1~)} = 0 (3.12) i=1
In this way,ju,,, 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 shearthinning 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, represents resistance to flow in the limit of a very high shear rate. It can be seen that attapulgite has the highest value of IL, among the three types of clays, 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 Y" 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 1,O, about 0.6 Pa.s, salt also increases y,,o (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).




30

Table 3.9: Parameters for the Sisko power-law model for viscosity
Mud a,, (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 0J.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 behavior. 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 lcaolinite, 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




31

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, OB, 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 cYB. 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




32

Table 3.11: Upper Bingham yield stress
Sample I K I KSI B BS A jAS IBK I BKS IAB I ABS IAKAKI
_o-B (Pa) 115.0 19.5 50.0 36.0 66.0 72.0 110.0 139.0 158.0 1_88.0 10.0 14.0 1
has a relatively higher oB of 39 Pa. The higher value of the upper Binghiam 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 gh to 1.03 g1-1 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 homogeneouslooking 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




33

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 viscosities 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, jof 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 P,, and a.B of kaolinite by less than
10%. Finally, salt decreased tt. 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




34

Table 3.12: Rheological parameters for power-law given by Equation 3.4
Mud time Density U'B go c n
___________ _______ (g/l) (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 110 mins 11.19 4.0 3.35 8.02 10.059

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-Mcflirney 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.




35

1000 1250 1500 1750 2000 2250 B IT S

2500 2750 3000 3250 3500

Figure 3.10: Calibration curves for the wave gauges

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

Figure 3.11: Calibration curve for the current meter

L:)
z
-LJ LUJ LUJ

60.0 57.5 SS.0
52.5
50.0
47. 5 45* 0
42.5 40. 0 37.5 35 0

.GUGE al
.. . .. .. G A G E

U) LUI LO
U
-j
LUJ

LbO. 0 35.0 30.0
25.0 20.0 15.0 10.0
5.0

0.0




36

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 p aired- transducers from the flume bottom were: l4cm(#1), l2cm(#2), 9.5cm(#3), 7.5cm(#4), 5.1 cm (#5), and 3.lcm(#6) for the pore pressure gauges, and l4cm(#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




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 measurment 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




38

8.0 7.0 6.0 5.0
1.0 3.0
2.0 1.0 0.0
8.0 7.0 6.0 5.0 4.0 3.0
2.0 1.0 0.0

1.0

0.6
VOJLTAGE (V)

1.5
VOL TAGE

Figure 3.12: Calibration curves for the total pressure gauges

GAUGE a I GAUGE .2 GAUGE n3 GAUGE m4

0.0

0.3

0.9

- 0.-- GAUGE .5
- ----*-----GAUGE .6
-e-------GAUGE *7

1.2

0.0

0.5

2.0

(V)

2.5

3.0




39

8.0 7.0 6.0 5.0
14.0 3.0
2.0
1.0 0.0
8.0 7.0 6.0 5.0 41.0 3.0
2.0
1.0 0.0

-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

A GAUGE # I .---GAUGE '2 e--GAUGE m3

a
cc :D
U
cc
:D co
LU

-1.0 -0.5 0.0 0.5 1.0 1.5
VOLTAGE (V)

~-GAUGE *4 ----GAUGE *5
S--GAUGE *6




40

2.75 2.6S 2.55
2.145 2.35
2.25 2. 40

0E
U-)
(I.)
-IJ cc
Q-

2.30
2.20 2.10
2.00 1.90
2.25 2.15
2.05 1.95 1.85 1.75

2.0

2.0

7.0

7.0

12.0

12.0

17.0

17.0

THEORY 0CM
~ j~~ j 0 .1~ ~ .-TOTAL 0CM

*1'. jj jf ~ -- TOTAL 4. 9CM

a
.0
.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.

-THEORY 3.1CM I, ~ .PORE 3.1CM ~ 'K .,...'ji~.;~I.TOTAL 2.6CM

22

17.0

12.0

7.0

2.0

22

22




41

2.00
1.90
1.80 -THEORY 7.5CM
1.70
1.0 2. 0 7.0 12 .0 17.0 22.0
1.75
1.65 AA. T1~- HEORY 9.5CM 1.55. .~ ~PORE 9.SCM CrZI/~ --TOTAL 9.5CM
1.35 I
u J .2
D2.0 7.0 12.0 17.0 22.0
U- 1.50
LuJ
CC 1.0 ~ THE. OR 12CM
1.30
1.10
1.0 2.0 7.0 12.0 17.0 22.0
1.25
-THORE 14CM
1.05 .
0.9 .. ~ : : J ~J TOTL 14CM
0.85
0.75S
O.S 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




42

50.0

100.0 TIME (M IN)

150.0

00.0

200.0

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)

800 100 1200 1400 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.

2.3000

C.. 2.

2.

- PORE PRESSURE GRRGE =z2. NEW RMPL[FIER

1500 h-

2. 1000
0.
C- 2.50

50.0 100.0 150.0 2

0,,PORE PRESSURE GARCE u,3, OLD RHMPLIFIER

Loi 2.S4000
C-2.'4000
0.

0.0
-0.31
-0.14

I .- -~
I I
I I 3d
I ___________________________

2500 2000

0




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 mn (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 performance in the flume, without mud, was examined in order to characterize flume hydrodynamics 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 characterization 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= 47 ) x= 0 )(x = 5m) (x O) Asr:20 Water------------- False Bottom 12
Figure 3.18: W~ave II ine e levationt profile and iuustrua uuent I.locations




45

LU
LiJ
I
ciJ
LU
CD
U
LU
LiJ
I
LUj
-J
LU

6.0
4i.0
2.0 0.0
-2.0
-4.0
0.
6.0
Lt.0
2.0 0.0
-2.0
-4. 0
0.
6.0 4.0 2.0 0.0
-2.0
-4.0
0.
14.0 2.0 0.0
-2.0

10.0 (SEC)

10.0 (SEC)

5.0 10.0 TIME (SEC)

5.0
TIME

10.0 (SEC)

15.0 20.0 25.0 H=7.8 CM GAUGE #1

15.0 20.0 25.0 H=4l.62 CM GRUGE #1

1S.0 20.0
H=7.6 CM GAUGE

15.0
H=4l.5 CM

20.0 GAUGE

25.0

25.0

Figure 3.19: Examples of wave time-series (depth=2Ocm, period=1.Os) for flume characterization tests with a false bottom

0

I I I I

30.0

B

I I ffi~

5.0
TIME

0

5.0
TIME

-4.0

30

C

0

30

.0
I.0

I
0.0

0

0

3'

I I -




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




A
GAUGE at
1.0 0.5 1.0 I.S 2.0 2
FREQUENCY (HZ)

400 360
~2 320 S280
z
Uj 240
S200 3r 60 (-_~ 120
o.80
40
0

400 360
S 320
280
LL O240 xJ'~ 200 a:r160
(-) 120 0- 80
40 0

U

T=1.05EC RVG.HT.=q.6C1

0.0 0.5 1.0 1.5 2.0
FREQUENCY (HZ)

If
U
U,

2.5

T=1.OSEC RVG.HT.=LI.3CM

q00 360 320
280 240 200 160
120 80
40
0

C
GAUGE a1
.0 0.5 1.0 1.5 2.0 2
FREQUENCY (HZ)

T=1.5SEC RVG.HT.=.IC
0
GAUGE #2
L.

0.0

0.5 1.0 1.5 2.0
FREQUENCY (HZ)

z
Cu
cc
a:

.5

z
LiU,
a
( E

2.5

T=I.5SEC FVG.HT.=q.SCM

400 360 320
280
2M
200
160
120
80
40
0

400 360 320
280
240 200
160
120 80 40
a

E
GAUGE at
FREQUENCY (HZ) 2. T=2.OSEC AVG.HT.=4.3C1

0.0

05 1.0 3.5 2.0 FREQUENCY (HZ)

T=2.OSEC RVG.31T.=3.9CM

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

.5

GAUGE #2

z
LU
Cu
I
i

400 360 320
280 240 200
160
120 80
40
0

F
GAUGE a2

-1

.5




1204-I u

GAUGE I1
.0 0.5 1.0 1.5 2.0
FREOUENCYr(HZ)
T=1.QSEC RVG.HT=7.BCM

300C UU)
6 00 orX I-- = 400
(n 200

.5

U, L F: A
cc
(n

0.0 0.5 1.0 3.5 2.0 2.5
FREQUENCY (HZ)
T=1.OSEC RVG.HT.=7.6CM

0

0

z 800 hU)
(M 600
q: x
E400
to 200
0
C

1200
10000
800 -GAUGE u2 600
400
200
0
0.0 0.5 1.0 1.5 2.0a 2.5
FREQUENCY (HZ)
T=I.5SEC RVG.HTl.=9.2CM

z
hiU L C3

1200~ 1000 800

_jX600
400 Li
LO200

i ,nr

3000
-)
z 800 'xi
-J 600
-. 400
S 200
0

.0 0.5 1.0 1.5 2.0
FREQUENCY (HZ)
T=2.OSEC AVGH=8.LlCt

.5

F
GAUGE #2
0 0.5 13j.0 3.5 2 .0 2 .5 FREQUENCY (HZ)
T=2.OSEC AVG.HT.=6.IICM

Figure 3.21: Wave spectra, water deptli=2Ocm; average wave height ranging from 6.4 to 9.1 cm, period ranging from I to 2 sec.

.0 0.5 1.0 1.5 2.0 2.5
FREQUENCY (HZ)
T=1.5SEC AVG.HT.=9.IC1

C
GAUGE #1

E
GAUGE #I
I I

B
GAUGE 42

z
Cr
a
I(2

120C~ 1000 S00 600 400
200

coo

Idull

0
I

0

I




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 771 = ai cos(kx -at + i)
7R= aR cos(kx +at + FR) (3.13) where 771 and 7Rjj are the surface elevations of the incident and the reflected waves, respectively, aj 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 E~I and ER are the phase angles of the incident and the reflected waves, respectively. The surface elevations must be recorded at two adjacent stations, x, and X2=Xl + Al. The measured profiles of the composite waves, selecting the fundamental frequency for analysis, are
71 = (771 + 77R)x=xi A, cos at + B, sin at 72= (771 + 77r)X=X2 =A2 COS at + B2 sin at (3.14) where
A, = al COS 01+ aR COSqOR
B1 = aj sin01 aR sin OR
A2 = aj cos(kAl + 01) + aR cos(kAl + OkR) 1B2 = aj sin(kAl + 0b1) + aR sin(kAl + OR) (3.15)
01= kl+
OR= kxl +ER (3.16) Equation 3.15 can be solved to yield ai and ajR according to
ai /A2- A, cos kiM B, sin kAI)2 + AB + A, sin kiM Bcos kAI)2 2IsinkiMI

V(A2 A, cos kAl + B, sin kAl)II + (B2 A, sin kAl B, cos A2
2 1 sin~ IM

(3.17)

aR =




50
Using Fourier analysis enables the estimation of the amplitudes A,, BI, A2 and B2 for the fundamental frequency. The amplitudes of the incident and the reflected waves, aj and aR, are then estimated from Equation 3.17. Table 3.14 gives the reflection coefficients, k,. = 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, k, Depth (cm) Period (sec) Wave height(cm) k,.
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 elevations 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. Considering the 4.7 mn 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, kim, was found to be 0.02/rn, as calculated from the wave height recordings by gauges #1 and #2. The wave height where the current meter was located, Hfcu,, would be
H.,_r = H#2e-kimAx (3.18) where H#2 is the wave height at gauge #2, and A~x 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 N (Ui ii)2 (3.19) where ui 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 cosh kz cos(kx at) (3.20) U 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 urms amplitude can be calculated as (van Rijn, 1985)
_rs V2_Hu,.acosh kz (3.21) Urs-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/rn for calculating Hu for the solid curve and is zero for the dashed curve.

I




15.0
12.0 9.0 6.0 3.0 0.0
0
20.0
16.0
12.0
8.0
4.0 0.0

0.0 5.0 10.0
VELOCITY
OEP=2OCM

I-j LU

25.0 30.0

1.5.0 20.0 25.0 30.0 (CH/SEC) H'q. '1CM

15.0
12.0
9.0 6.0 3.0 0.0

E20.C
S16.0
12. I
8j .0 Ui
-J

0.0

0.0 5.0 10.0 15.0 20.0
VELOCITY (CN/SEC)
DEP=15CM H=4.8CM

0.0 5.0 10.0 15.0 20.0
VELOCITY (CM/SEC)
OEP=20CN H-=7.3CH
-THEORY, CONSIDER
.----THEORY. WITHOUT
EXPERIMENTAL DATA

25.0 30.0

25.0

:30.0

D ISS IPAT ION DISSIPATION

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

experimental dlata (rins am-

: AL

C

.0 5.0 10.0 15.0 20.0
VELOCITY (Ctl/SEC)
DEP=15CM H=3.ICM

B

- 0

C;'




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 frequency 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, P1, 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 14. 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 reasons. 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 mh(x, t). The amplitude of a simple harmonic surface wave is assumed to be small enough

53

I




54

0T(XIt)
Hi 111112( X.) Water
Z H2 P2 Fi uid 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:
Ou1 + '97 =0(41
a71- 772) + HI au1 (4.2) at a
lower layer:
aU2 _77 art, a2U2
1 U z+ (4.4) where ul(x, t), u2(X, t) are the wave-induced velocities, h H2 + 772, r =(P2 -P1)/P2 is the normalized density jump, and V = ji/P2 is the kinematic viscosity of mud. The following boundary conditions are imposed: i11(0, t) = ao cos at (4.5) U1i(00,t), U2 (00, z7 t), 771(00,t), t2 (X,t) --+ 0 (4.6)

U2 (X,0, t) = 0(4)

I

(4.7)




55
'9U2(XH27t) =- (4.8)
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 =kHj, which is a complex valued function
k 1 + ft2r [( + #2r)2 4rHi2r]1/21/12(49
where
F 1 -tanh(mH2) (4.10) Mff2
_#2 = H2/H1, m = (-iRe)'/2 ,Re -aHl/z1v 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= ao exp (- kix) (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
1F2 = A+{-1 (-) } f{I cosh(mi) + tanh(MHi2)
-Fr
sinh(mi)} expf i(ki T)} (4.12) where ti2 = U2/(uH1), A =ao/IHi, i = z/Hl, and i = x/HI.
As noted in Section 3.2.1 in Chapter 3, the dynamic viscosity of mud can be expressed as

Pt = 1Loo + -

(4.13)




56
where pc 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, it, 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, p1 (or v = pU/P2), into Equation 4.12, an effective sheared mud thickness, d, was obtained from the equation:
d = -. -.H (4.14) where U2, is the amplitude Of U2 at the mud surface and u52 = u25,/(uHi) 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 'io is an initially selected value of garhma required for iterative calculation of 1,,.
A physical implication of Equation 4.14 is that, assuming d < Hf2, 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 HJ2 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

L input: o, IIo, c, n, HI, H2, PI, P2, 6, H#'j., H#

P

1. Eq) 41

k= Im(k); Eq. 4.9J

kiezp = f(H#I, H#2, Al); Eq. 4.1

ki- kiexp 1< 0.01
Iyes

I j2 (k, H 2 ); Eq. 4.12

d = fAU2s, j.); Eq. 4.14

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

75

L

no




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):
ED = A I +1 [2( OU)2 + ( O + -)2]dz (4.15) JO lox O9x Oz
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 =P21-' H2 2(o2) +(U22]d (4.16) or, dividing EDl into two terms: ED = ED1 + ED2 (4.17) ED1 = 2 2( 2 )2dz (4.18) =D P2V 0 5 O z (4.19) Physically, ED, and ED2 are the wave-mean rates of energy dissipation due to the horizontal and vertical velocity gradients, respectively. Equation 4.12 gives: aU2 a 12 (.0
-~=u- = C(ik)t2(.0
and
(7u -- _r 011 A r 2{ sinh(mi) + m tanh(m.F) cosh~mi)} exp i~tki f
z T~ 2 'Fr~
(4.21)
Therefore, the time-averaged values of (8ua')2, (%il )2 are:
1 U2 2 'j2A { r(k {2} l cosh(mi) + tanh(MHl2) sinh(Mi)} 2 (4.22) and
OtU2)2 =1 202Ak)2f r k 22tanh2 (mH2)_=z 2 F'2 Fl-r- 2 taih 2 (M112) + 1 cosh(2mi) tanh(mH!2) sinh(2m/:0} (4.23) +2




59

Therefore
ED1= 22V Ox22d 2P2V] HI Ox22d
- 2( A(')21 k( )2. 3{ff2 !1i2 tah2 (MI) + 2 tanh(mH2) [cosh(mff2) 1]
2 2 m
tanh(mH2) [cosh(2mff2) 1]--2 sinh(mB'2) 2m m
1 + tanh 2(mH2)
+ 4m -sinh(2mH2)) (4.24) and
fD 2V HU( 2)2dZ (4.25)
1 P2vHlm2 a 2(k)21 r( k)2 2}2 tanh 2 (M12) 1 + tanh 2 (m12)
2 H2+- 4m sin.h(2m]H2)
-M tanh(m112)[cosh(2mH2) 1]} Introducing
x = H2( )1/2 (4.26) the normalized mud layer thickness, where (2v/a,)1/2 is the thickness of the laminar waveinduced (mud) boundary layer (Jiang &Mehta, 1991), Equations 4.24 and 4.26 can therefore be further written as: e~=Eo F2.ff22X2 (){1 -R(k2} 1 r T,. Fr. 3- 1 2I2tn(VV-r(.- ~
-2 2 tah 2X 12 ahV2X cosv-z2X) 1]
{-2 -2 Vanh2(C2i X
.12 tanh(VyC-2x) 2HI
-y [cosh(2vfW-2X) 1] ; sinhV'2iX
-H2 1 + tan2i ~X) sinh(2VC-2X)} (4.27) and
E0o (1-_ i)2k )2 D 2- l-r F, {lr(,




60
2 2X 1] + ft21 + taiih ('a)sinh(2,/-2X)
2 4,tan2(v-1x 4V X
-12 an~r-2i)[cosh(2Vf-2iX) 1]} (4.28) where E0 = O.5p~gao 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 EDAs an alternative to the above approach, the same dissipation rate can also be obtained via the following procedure: ED = ~(4.29) The wave energy, E, is obtained from E = pigax2 (4.30) where
a. aoexp(-kj,:xx) (4.31) is the surface wave amplitude at any x, and X =Ct (4.32) and (Jiang & Mehta, 1991) C=cFr (4.33) with C0 = Vrg-Hi being the wave celerity in shallow water over the rigid bottom and k being the normalized wave number from Equation 4.9. Therefore, Equation 4.29 can be further written as:
ED = vg9-rpiga 2kiexp (4.34) Where g is the acceleration due to gravity; H, 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 rheological 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 g1-'.
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

61




Wave Gauge #2 Wave Gauge #1 Wave Maker
(x =12.2 m) (x =7.5 m) (x 0)
Density Pressure
(x =8.9 m) (x = 8.1 m)
Figure 5.1: Sketch of flume pr~ofile in the fluidizationi experiment




63

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) 00 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
82 17.5 4 1.06 460 19
9 65 16.6 5 1.06 450 20
10 85 16.4 8 1.06 385 2
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 maximum 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. Th is issue is discussed later in Section 6.2.3.




64

Table 5.2: Wave heights, Test #9
Time(mins) H#i(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




65

5.0
TIME

10.0 (SEC)

2.0
0.0
-2.0
-4.0
0.I
4.0
2.0 0.0
-2.0
-4l. 0
0.
41.0
2.0 0.0
-2.0

5.0
TIME

10.0 (SE C)

30.0

15.0 20.0 25.0 71 MINUTES GAUGE #1

30.0

15.0 20.0 25.0 210 MINUTES GAUGE *21

15.0
71 MINUTES

20.0 GAUGE

30.0

25.0 #2

30.0

5.0 10.0 15.0 20.0 25.0 TIME(SEC) 210 MINUTES GAUGE t2

Figure 5.2: Wave time-series, Test #9

A

0

5.0 10.0 T IME (SEC)

B

0

C

I I

0

-4.0
4.0
2.0 0.0
-2.0
-4. 0
0.I

D

0




66

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 cm 2 while at 210 inins 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.




GAUGE al

0

0

120
z
o: X CC 60 LU a- 30
(n

0

.5

C
GAUGE al
0.0 0.5 1.0 1.5 2.0 2.

12
z
a: 60 a-X LU
a._ 30
0

0

FREQUENCY (HZ)
AVG.H-T.=5.OCM 71 MINUTES

'.0

FREQUENCY (HZ)
AVG.IIT.=4.7CM 210 MINUTES

20
is (1
z
LU0Lo
N10
LU 5
(1(1

0.5 1.0 1.5 2.0 2.5

FREQUENCY (HZ)
AVG.HT.=1.8CM 71 MINUTES

0
0

I.0

FREQUENCY (HZ)
AVG.1IT.=I.LCM 360 MINUTES

20
is
z
LU01
-j 10
LLJ (L
0

0

0.5 1.0 1.5 2.0 2.5

FREQUENCY (HZ)
AVG.IIT.=t.7CM 210 MINUTES
Figure 5.3: Wave spectra, Test #9

0.0 0.5 1.0 1.5 2.0
FREQUENCY (HZ)

2.5

AVG.IIT.=1.6CM 360 MINUTES

120
z
C:) cc 60 LU
a.. 30
01

'5

E
GAUGE al
nA nl q in I r- nf

B
GAUGE n2

20
15 U0
(\ 10
LU 5
a
In

0
0

0
GAUGE #2

F
GAUGE #2

ISO

ISO

ISO




68

22.0

20. 0 r

LUJ LUJ

18.0 16.0 14. 0
12.0

10U.U
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 (in)
Figure 5.4: Time-vaxiation of water-mud interface along the flume, Test #
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 grauge 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

Total Pressure Gauges 0i MINS
-------------- -40 M N
--- ---120 MI.

-1 1 INS

I I I

I I




69

DENS ITY

z
-j
wU

1.15 1.20 (G/CM)(3)

i6.0
12.0 10.0 8.0 6.0 '1.0 2.0

18.0 16.0 1'1.0 12.0 10.0 8.0 6.0 q1.0 2.0

1.25

1.00 2.05 1.10 1.15 1.20 1.25
DENSITY (G/CMxB3

1.00 1.05 1.10 1.15 1.20 1.25
DENSITY (G/CMmB3)

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

18.0.

100 MINS

.320 .MINS--- - - ----

16.0 q~.0 12.0 10.0 6.0 6.0 '1.0 2.0 0.0

z

-LJ

380 MINS

0 0

0 0




'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. Referring 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
0._ 2.55
c:
:D 2.45 (-I
LiJ 2.80 a
2.75
2.65 3. 15 3. 10
3.05 3.00
2.90
3.140
3.35
3.25 3.20 3. 10
0

300
TIME (MIN)

500

Figure 5.6: Wave-averaged total and pore water pressures, Test #9

71

LEVEL-14CM
E) PORE PRESSURE
-4 TOTAL PRESSURE 8l FROM DENSITT
LEVEL-12CM LEVEL=9. 5CM LEVEL=7. SCM
LEVEL=5. 1CM LEVEL=3. 1CM

100

200

400

600




72

4.00
CL 3.80 LUJ 3.60
U3.40 - FROM GAUGE
LUJ
El FROM DENSITY
C 3.20
3.00 10 0 20 0 30 0 40 0 50 10 600 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 nns, 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
p11. TV E1. P)2 (5.1) where Pi is the instantaneous pressure, Pis the time-mean pressure, and N is the numer 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




73

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 iluidizaton 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




74

I -~

90.0

60.0I

30. 0

a so 100 ISO 200 250 300 350
TIME (MIN)

120.0,r

90. 0 60.0 30. 0

400 '150 So0 550

0 s0 100 I50 200 250 300 350 400 450 S00 550
TIME (MIN)

Figure 5.8: Root-mean square pore water pressure amplitudes, Test #9

LUj U-,
LO

---14CM
W*- 12CM
-0-9.SCH

LU
LU
:D

A~- 7.5SCM

-0D--- 3. ICM

I I I I I-

n

A
Ac .




75

-0- 14CM
0s 9.5SCM s0 100 150 200 250 300 350 400 450O 500 550 600 T IME (MIN)

I -1 1 1 1 1J 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

120.0,r

a~

90.0

IL! 60.0 0r
30. 0
0

120. Or

90.0 I-

LuJ :D Vr)
0L_

60.0

0- 14. 9CM

.-*-2.6CM

k o o N e0 0 ~ I

OD'- 0.0OCM

30.0
a




1~~

CHAPTER 6
EXPERIMENTAL DATA ANALYSIS
6.1 Introduction
In this chapter, results axe presented, based on the wave-mud interaction (introduced in Chapter 4), wh-ich 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., 11/L < 0.05, where L is the wave length,which was obtained from the linear wave dispersion equation (assuming rigid bed condition): L = LT 2tanh 2rfk (6.1) 2ir 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 HilL 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

76




77

Table 6.1: Parameters for determining the water wave condition
Test # H1 L Hj/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, 4o, to calculate viscosity, it, by the power-law
equation for viscosity, i.e., by Equation 4.13 (M = iPoc, + 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 coefficient, ki.p can be obtained from H#2 = H#iexp(-kieAl), via Equation 4.11,
where H1 is the wave height at gauge #1 and H#2 the height at gauge #2.
4. When ki obtained from step 2 "matches" ki., obtained from step 3 by iterating for
4i.e., I (kiEq.4.11 kiEq.4.9) < 0.011j, the selected 4 is assumed to be right, or a new 4is chosen for Equation 4.13 and the above procedure repeated until ki and kj.
match.
One example of the calculation for test #9 is given here. The input parameters are:
P = 4.44Pa.s, c = 0.76, n = -1.083, water density, pi = lg/cm mud density, P2=
1.179/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, H, 35 H2 = 18.3cm, a* 27r/T = 6.28Hz, H#1 = 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 it = 6llPa.s, which in turn was used in Equation 4.9 to calculate the wave dissipation coefficient k, 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




79

Table 6.2: Input parameters for calculating the effective sheared mud thickness Test # pr,,. c n P2a
_____(Pa.s) (g/cm') (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




s0

20

s0
TIME (MIN)

Figure 6.1: Effective sheared mud thickness, d, Tests #1 through #3

80

1'4.0 12. 0 10.0 8.0 6.0
4.*0 2.0

z

cm ~ 5cm 7.7 cma
a Model Output 0
-Polynomial Fit ... .. .......T E ST I1

0

0.0 0.5

ISO

200

250

EC., 4 C.)
Z 0.2 =0.1

300

100

'aO

b

S
S

TEST =2

0

0.0 2.0

80

100

-f
z
0.

0.0

C

s0

100

ISO

a

0




81

2500

2000

1000

500

1500

0 100 200 300 400 500 600

700

B
0D
E) III

0 C
TEST #6

400

80

s0

300

200

100

200 300
TIME (MIN)

400

s0

10.0 CO) tjn 8.0
Lu Z 6.0
i
-4.0
I-2.0
0.0
11.7
29.8
V')
(n) 7.8 uiJ z .
Li I.3.9
I-2.0

Figure 6.2: Effective sheared mud thickness, d, Tests #4 through #7

10.( CO~ 8.0
uLJ
Z6.0 ,~4.0
1-2.0
0.0

0
t nl

T EST a41

3000

0
0
0

0.0

Li zr

0

11.7 9.8 7.8 5.9 3.9
2.0 0.0
0

D
TEST #7

100

I

0




82

6.0
~5.0 (.fn 4.0 LU
Z 3.0
S2.0 i-1.0
0.0
-'9.8
- 7.8
CO)
LU 5.9 U~ 3.9
h.. 2.0

0 200 1400 600 800 1000 TIME (MIN)

1200

1400 1600 1800

Figure 6.3: Effective slieared mud thickness, d, Tests #8 through #11

R

TEST u89
100 200 300 400 50(
TEST #91
100 200 300 400 500

0.0

0

LU
z U-

13.7 11.7
9.8 7.8 5.9 3.9
2.0
0.0

0

-2 6.0 U 5.0
U-) 4.0
LUJ
Z 3.0 U
2.0 I 1.0

D

0.0

............... ''I'll". .... ........ E )
TEST I I




83

Table 6.3: Values of the (representative) constant effective sheared mud thickness, d., and IL

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 0

the wave action to a maximum value, and decreased again to approach some constant value, ED,. 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 ED8, 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., 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, k1 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.




84

4.0000 3.0000 2. 0000
1 .0000 0.0000
0
0.0400 0.0300 20.0200
z
LU 0.0 100 0.0000 z 0 C0. 2000 2:0. 1500o (n
00.1000 0. 0500 0.0000
0

so

100
TIME (M IN)

150

200

Figure 6.4: Wave dissipation rate, ED, versus time: Tests #1 through #3

A

-~~------2~~~ cm*j4---4ccm 7.7 cm
2 cm o-4 -40

TEST ni

0

50 100 150 200 250 30C
B
TEST #2, DESIGN NV.HT=2 CM
20 40 s0 80 boc
c
TEST #3, DESIGN klV.HT=3 CM

I




85

I1.0000 0. 8000 0. 6000 0.11000
0. 2000 0. 0000
0
2. 0000
1. 5000
z
0. 5000
LUJ
E:0.* 0000 z 3. 0000 ED .50
-2.000 CE
2.0000 0. 0000 0.5000
0

D

EbDeEOEOE

0)0E

E) E

0) 0

0) 0)

0

0)

TEST #*7,

DESIGN WV.HT=5

I - - I
S0 100 150 200 250 300 350 400
TIME WIN)

Figure 6.5: Wave dissipation rate, ED, versus time: Tests #4 through heights are from Table 5.1

#7. Design wave

A
TEST #'4, DESIGN WV.HT='4 CM

3000

2500

2000

1500

1000

500

B
00 0 E) EP 000e E
TEST i#5, DESIGN kV.HT=6 CM
100 200 300 1100 500 600 700 so
0) 0
TEST *#6, DESIGN WV.HT=7.5 CM

1. 2000

I

350

so 100 150 200 250 300

0. 9000 r 0.6000 F 0. 3000 I-

0.0000
0

C M

I

400