Citation
Laboratory experiments on cohesive soil bed fluidization by water waves

Material Information

Title:
Laboratory experiments on cohesive soil bed fluidization by water waves
Series Title:
UFLCOEL
Creator:
Feng, Jingzhi ( Dissertant )
Mehta, Ashish J. ( Thesis advisor )
Dean, Robert G. ( Reviewer )
Moudgil, Brij M. ( Reviewer )
McVay, Michael C. ( Reviewer )
University of Florida -- Coastal and Oceanographic Engineering Dept
Place of Publication:
Gainesville, Fla.
Publisher:
Coastal & Oceanographic Engineering Dept., University of Florida
Publication Date:
Copyright Date:
1992
Language:
English
Physical Description:
xvi, 109 leaves : ill., photos ; 28 cm.

Subjects

Subjects / Keywords:
Coastal and Oceanographic Engineering thesis M.S ( local )
Dissertations, Academic -- UF -- Coastal and Oceanographic Engineering ( local )

Notes

Abstract:
The mechanism by which fluid mud is formed by water wave motion over coastal and estuarine 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. This study investigated water wave-induced fluidization of cohesive soil beds composed of a 50/50 (by weight) mixture of a commercial attapulgite and a kaolinite in a laboratory flume. 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 previously developed hydrodynamic wave-mud interaction model of the two-layered water-mud system was employed to study the nature and the degree of wave dissipation, in terms of energy dissipation rate, during the bed fluidization process. By evaluating the mud rheological properties separately, a mud viscosity model was developed, which was then used in conjunction with the wave-mud interaction model to obtain an effective sheared thickness of the bed resulting from wave action. This thickness, considered to be a representative of the fluidized mud thickness, was compared with the latter obtained from pressure measurements. Also, through this wave-mud model the relationship between the rate of fluidization and the rate of wave energy dissipation during fluidization was examined. In general, for a given wave frequency, a larger wave fluidized the bed at a faster rate and to a greater depth than a smaller one. Furthermore, increased bed consolidation time decreased the rate of fluidization due to increased mud rigidity. The rate of bed fluidization was typically greater at the beginning of wave action and decreased with time. Eventually this rate approached zero, while in some cases the wave energy dissipation rate approached a constant value, which increased with wave height. As the fluidization rate approached zero, there appeared to occur an equilibrium value of the bed elevation, and hence a fluid mud thickness, for a given wave condition. During the fluidization process the bed apparently lost its structural integrity by loss of the effective stress through a build-up of the excess pore water pressure. After wave action ceased, the bed structure exhibited recovery by dissipation of the excess pore water pressure. Further studies will be required in which the hydrodynamic model must be improved via a more realistic description of mud rheology and relaxation of the shallow water assumption, and better pressure data must be obtained than in the present study. Nevertheless, this investigation has been instructive in demonstrating relationships between the degree of mud fluidization, wave energy dissipation and bed consolidation time, and thus offers insight into an important mechanism by which coastal and estuarine muds are eroded by wave action. xvi
Abstract:
ocean waves, fluidization, rheology
Thesis:
Thesis, M.S., Engineering
Funding:
This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.

Downloads

This item has the following downloads:


Full Text
UFL/COEL-92/005

LABORATORY EXPERIMENTS ON COHESIVE SOIL BED FLUIDIZATION BY WATER WAVES

Jingzhi Feng

Thesis

1992




LABORATORY EXPERIMENTS ON COHESIVE SOIL BED FLUIDIZATION BY WATER WAVES
By
JINGZHI FENG

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF MASTER OF SCIENCE
UNIVERSITY OF FLORIDA

1992




ACKNOWLED GEMENTS

I would like to express my gratitude to my supervisor and committee chairman, Professor Ashish J. Mehta, for his continuous guidance, encouragement and financial support during my studies in the Department of Coastal and Oceanographic Engineering at the University of Florida. I would also like to express my appreciation to Professors Robert G. Dean, Brij M. Moudgil and Michael C. McVay for serving on my committee, for their comments relative to this work and for their patience in reviewing this thesis. Many thanks are due to Dr. David G. Bloomquist of the Civil Engineering Department for providing the necessary equipment for pressure measurements, to Allen Teeter of WES for his technical help during the course of this study, and to Dr. David Williams and Dr. Rhodri Williams of University College, Swansea, UK, for their helpful suggestions during the initial phase of the fluidization experiments.
Gratitude must also be extended to the staff of the Coastal Engineering Laboratory, especially Sydney Schofield and Chuck Broward, for their cooperatiofi and assistance in the experiments. The support of fellow students, especially Feng Jiang, Jung Lee, Noshir Tarapore and Shoulian Zhu, as well as my friend Shujun Jiang, is also highly appreciated.
Finally, I would like to thank my parents for their constant encouragement and support in all my endeavors.




TABLE OF CONTENTS
ACKNOWLEDGEMENTS..................................1ii
LIST OF FIGURES.......................................v
LIST OF TABLES....................................... viii
LIST OF SYMBOLS.......................................x
ABSTRACT........................................... xv
CHAPTERS
1 IINTRODUCTION......................................1I
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




4 ESTIMATIONS OF FLUID MUD THICKNESS AND WAVE ENERGY DISSIPATION .. .... ... . ...... ....... . . ...... 53

4.1 Introduction ...................
4.2 Effective Sheared Mud Thickness ........
4.3 Wave Energy Dissipation Rate ..........
5 MUD BED FLUIDIZATION EXPERIMENTS .
5.1 Test Conditions ....................
5.2 Flume Data ......................
5.2.1 Wave Time-series ..............
5.2.2 Wave Spectra ................
5.2.3 Water/mud Interface ............
5.2.4 Density Measurement ...........
5.2.5 Total and Pore Water Pressures .
5.2.6 Bottom Pressure Gauge Data, Test #9 5.2.7 Rms Pressure Amplitudes, Test #9 .
5.2.8 Pressure Recovery after End of Test..
6 EXPERIMENTAL DATA ANALYSIS ........

. . . . . 61

. . . . . . 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 Rate100

7 CONCLUSIONS ............
7.1 Conclusions ............
7.2 Significance of the Study . BIBLIOGRAPHY .............
BIOGRAPHICAL SKETCH .....

. . . . . . . . . . . 104
. . . . . . . . . . . 104
. . . . . . . . . . . 105
. . . . . . . . . . . 107
. . . . . . . . . . . 109




LIST OF FIGURES
2.1 Schematic of water column with a muddy bottom in terms of vertical
profiles of sediment density and velocity, and vertical sediment fluxes . 6 2.2 Soil mass subjected to stress loading . . . . . . . . . 8
2.3 Definition sketch of soil stress terminology . . . . . . . . 9
2.4 Fluidization process of a soil bed at a given elevation . . . . . 10
2.5 Influence of waves on shear resistance to erosion of kaolinite beds in flumes 11
3.1 SEM of dry agglomerates of attapulgite. Scale 1cm = 10rpm . . . 18
3.2 SEM of dry agglomerates of bentonite. Scale 1cm = 10pm . . . 18
3.3 SEM of dry agglomerates of kaolinite. Scale 1cm = 10pm . . . . 19
3.4 Shear stress, a, versus shear rate, -, (K,A,B) . . . . . . . 22
3.5 Shear stress, a, versus shear rate, 4, (AK,BK,AB) . . . . . . 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, (BK,BKS,AK,AKS,AB,ABS) . 25
3.8 Viscosity, p, versus shear rate, (K,KS,A,AS,B,BS) ............26
3.9 Viscosity, p, versus shear rate, 4, (BK,BKSAK,AKS,AB,ABS) . . 27
3.10 Calibration curves for the wave gauges . . . . . . . . . 35
3.11 Calibration curve for the current meter . . . . . . . . . 35
3.12 Calibration curves for the total pressure gauges . . . . . . 38
3.13 Calibration curves for the pore pressure gauges . . . . . . 39
3.14 Dynamic response of pressure gauges, and comparison with results from
the linear wave theory: gauge elevations ranging from 0 to 4.9 cm . 40




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 3.18 Wave flume elevation profile and instrument locations ............. 44
3.19 Examples of wave time-series (depth=20cm, period=1.0s) 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=20cm; average wave height ranging from 6.4
to 9.1 cm, period ranging from 1 to 2 sec ....................... 48
3.22 Horizontal velocity profiles: comparison between experimental data (rms
amplitudes) and linear wave theory (peorid T=.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
5.5 Examples of density profiles, Test #9. Dashed line indicates interfacial
elevation ........ .................................... 69
5.6 Wave-averaged total and pore water pressures, Test #9 ............ 71
5.7 Total pressure at the bottom of the flume, Test #9 ... ........... 72
5.8 Root-mean square pore water pressure amplitudes, Test #9 ...... ... 74
5.9 Root-mean square total pressure amplitudes, Test #9 ............. 75
6.1 Effective sheared mud thickness, d, Tests #1 through #3 ........ ... 80
6.2 Effective sheared mud thickness, d, Tests #4 through #7 ........ ... 81




6.3 Effective sheared mud thickness, d, Tests #8 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 #8 through #11. 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, variations with time: Test #8 ................ 89
6.9 Effective stress, variations with time: Test #9 ................. 90
6.10 Effective stress, a, variations with time: Test #10 ................ 91
6.11 Effective stress, variations with time: Test #11 ................ 92
6.12 Bed elevation, water/mud interface, and fluidized mud thickness in Tests
#8 through #11 ....... ............................... 95
6.13 Fluidized mud thickness, di, variations with time .... ............ 96
6.14 Bed fluidization rate, OHb/Ot, versus time ..... ................ 99
6.15 Comparison between fluidized mud thickness, d1, 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, OHblOt, versus wave energy dissipation rate, ED, tests
#9 and #10. Dashed lines indicate exptrapolations .............. 103




LIST OF TABLES

3.1 Chemical composition of kaolinite ..................... 15
3.2 Chemical composition of bentonite ...... .................... 15
3.3 Chemical composition of attapulgite (palygorskite) ... ........... 15
3.4 Chemical composition of tap water ...... .................... 15
3.5 Size distribution of kaolinite ...... ........................ 16
3.6 Size distribution of bentonite .............................. 17
3.7 Size distribution of attapulgite ............................ 17
3.8 Selected muds (days and day mixtures) for theological tests ...... ... 20
3.9 Parameters for the Sisko power-law model for viscosity ............ 30
3.10 Shearing time effect on shear stress ...... .................... 31
3.11 Upper Bingham yield stress ...... ........................ 32
3.12 Rheological parameters for power-law given by Equation 3.4 ...... ... 34
3.13 Wave conditions for the charaterization tests ................... 46
3.14 Wave reflection coefficient, k ............................. 50
5.1 Summary of test conditions ............................... 63
5.2 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., j and p ......... .................................. 83
6.4 Representative values of the wave energy dissipation rate, ED ........ 88
6.5 Effective stress, a', at the beginning and end of Test #9 ............ 91




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




LIST OF SYMBOLS

A Normalized surface wave amplitude at x = 0 A, Coefficient of the cosine term of wave amplitude at gauge #1 A2 Coefficient of the cosine term of wave amplitude at gauge #2 A Horizontal projection of the contact area between soil particles along the
cutting surface
At Total horizontal projection of the cutting surface for the soil mass considered A, Horizontal projection of the portion of the cutting surface which passes
through the water phase
ao Surface wave amplitude at x = 0 al Amplitude of incident wave aR Amplitude of reflected wave a. Surface wave amplitude at a distance x B1 Coefficient of the sine term of wave amplitude at gauge #1 B2 Coefficient of the sine term of wave amplitude at gauge #2 C Wave celerity over the mud bottom Co Wave celerity over the rigid bottom c Constant parameter in the Sisko power-law model for viscosity c1 Constant parameter in Cross equation (Equation 3.1) D Square error (variance) of viscosity between model and experiment;
Particle diameter
d Model calculated effective sheared mud thickness




d1 Experimentally determined fluidized mud thickness
d, Equilibrium value of d
E0 Initial wave energy
Fr Froude number
g Acceleration due to gravity
H Wave height
H1 Water column thickness
H2 Mud layer thickness
'lb Bed elevation H#1 Upstream wave height H#2 Downstream wave height Hour Wave height where the current meter was located H2 Mud thickness normalized by upper water column thickness, H1
h Water depth over rigid bottom
k Wave number
k1 Surface wave attenuation (decay) coefficient over mud bed from model
kiep Surface wave attenuation (decay) coefficient over mud bed from experiment ki, Surface wave attenuation (decay) coefficient over rigid bottom k, wave reflection coefficient
k: Normalized wave number
k, Normalized surface wave attenuation (decay) coefficient
L Wave length
Al Distance between the two wave gauges
m Parameter in the water-mud interaction model




n Exponent in the Sisko power-law model for viscosity
N Number of data points
P time-mean (over wave period) pressure
Ph Hydrostatic pressure
Pi measured pressure
Pp, Pore water pressure PrrMS Root-mean square (rms) pressure p Constant parameter in Cross equation (Equation 3.1)
Re Reynolds number
r Normalized density jump across the mud/water interface
T Wave period
t Time
u Current velocity under a wave
u1 Wave-induced horizontal velocity in the water column
u2 Wave-induced horizontal velocity in the mud layer
U2s Wave-induced horizontal velocity at the mud surface u, Measured horizontal velocity
Ur Velocity amplitude in Figure 2.1
U Root-mean square (rms) horizontal velocity
ii Time-mean (over wave period) horizontal velocity
tF2 Normalized wave-induced horizontal velocity in the mud layer ut3 Normalized value of U2s Au Excess pore water pressure
x Horizontal distance from the wave maker




i Normalized horizontal distance
Ax Distance between wave gauge #2 and current meter z Vertical distance from bottom z Normalized vertical distance from bottom 4/ Shear rate
y., Average shear rate in mud layer ED Time-mean (over wave period) rate of energy dissipation ED1 Time-mean rate of energy dissipation due to horizontal velocity gradient ED2 Time-mean rate of energy dissipation due to vertical velocity gradient ED. Equilibrium value of ED EI Phase angle of incident wave
-R Phase angle of reflected wave T Surface elevation of incident wave 77R Surface elevation of reflected wave p Apparent viscosity P0 Asymptotic viscosity at low shear rates p~, Asymptotic viscosity at high shear rates v Kinematic viscosity of mud Pt Viscosity of the mud obtained from the experiment p Fluid density PI Water density p2 Mud density a Total stress; wave angular frequency a* Actual intergranular stress




or Effective stress 0B Upper Bingham yield shear stress 0I Phase of incident wave OR Phase of reflected wave X Mud layer thickness normalized by wave-induced boundary layer r Parameter in the water-mud interaction model




Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science LABORATORY EXPERIMENTS ON COHESIVE SOIL BED FLUIDIZATION BY WATER WAVES
By
JINGZHI FENG
August 1992
Chairman: Dr. A.J. Mehta
Major Department: Coastal and Oceanographic Engineering
The mechanism by which fluid mud is formed by water wave motion over coastal and estuarine cohesive soil beds is of evident interest in understanding and interpreting the inicrofabric of flow-deposited fine sediments in shallow waters, and hence the erodibility of muddy beds due to hydrodynamic forcing. This study investigated water wave-induced fluidization of cohesive soil beds composed of a 50/50 (by weight) mixture of a commercial attapulgite and a kaolinite in a laboratory flume. 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 previously developed hydrodynamic wave-mud interaction model of the two-layered water-mud system was employed to study the nature and the degree of wave dissipation, in terms of energy dissipation rate, during the bed fluidization process. By evaluating the mud rheological properties separately, a mud viscosity model was developed, which was then used in conjunction with the wave-mud interaction model to obtain an effective sheared thickness of the bed resulting from wave action. This thickness, considered to be a representative of the fluidized mud thickness, was compared with the latter obtained from pressure measurements. Also, through this wave-mud model the relationship between the rate of fluidization and the rate of wave energy dissipation during fluidization was examined.




In general, for a given wave frequency, a larger wave fluidized the bed at a faster rate and to a greater depth than a smaller one. Furthermore, increased bed consolidation time decreased the rate of fluidization due to increased mud rigidity. The rate of bed fluidization was typically greater at the beginning of wave action and decreased with time. Eventually this rate approached zero, while in some cases the wave energy dissipation rate approached a constant value, which increased with wave height. As the fluidization rate approached zero, there appeared to occur an equilibrium value of the bed elevation, and hence a fluid mud thickness, for a given wave condition. During the fluidization process the bed apparently lost its structural integrity by loss of the effective stress through a build-up of the excess pore water pressure. After wave action ceased, the bed structure exhibited recovery by dissipation of the excess pore water pressure.
Further studies will be required in which the hydrodynamic model must be improved via a more realistic description of mud theology and relaxation of the shallow water assumption, and better pressure data must be obtained than in the present study. Nevertheless, this investigation has been instructive in demonstrating relationships between the degree of mud fluidization, wave energy dissipation and bed consolidation time, and thus offers insight into an important mechanism by which coastal and estuarine muds axe eroded by wave action.




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 niicrofabric 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 i nter- relationship between soil mechanical changes and wave energy input, and to understand the bed fluidization process through these changes under loading by progressive, non-breaking water waves.
Unlike the boundary of soil beds composed of cohesionless material (e.g., sand), the cohesive soil bed boundary is often poorly defined, as it is not evident, e.g., from 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 particle-supported structured matrix, hence a measurable shear strength. On the other hand, fluidized mud is a suspension which by definition is essentially fluid-supported. Parker




2
(1986) noted ambiguities when lead lines, echo-sounders or nuclear transmission or 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 g/cm 3, while Krone (1962) used a density range of 1.011.11 g/cm 3 to define fluid mud. Wells (1983) specified a density range of 1.03-1.30 g/cm3, Nichols (1985), 1.003-1.20 g/cm 3, and Kendrick and Derbyshire (1985) 1.12-1.25 g/cm 3 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 wa's limited to using commercial clays whose theological properties
could be relatively easily characterized.
2. Waves were restricted to regular (monochromatic), I Hz progressive and non-breaking
type, whUe 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, u, (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 g1-1, 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




FP Ur Mobile
Suspension
C Entrainment
_ I -Fluid Mud
FludiatonFormation Deforming Bed
Stati ona ry Bed
Consolidation
Figure 2.1: Schematic of water column with a muddy bottom in terms of vertical profiles of sediment density and velocity, and vertical sediment fluxes mud composition, concentration, and the rate of shearing.
The fluid mud zone is of particular practical importance because this mud can be easily entrained and thereby substantially contribute to turbidity even under relatively low energy inputs, due to its high concentration and very weak internal structure (Ross, 1988). Fluid mud also plays a significant role in absorbing and dissipating turbulent kinetic energy, which can cause a transition from a typically visco-elastic response to a more viscous shear flow behavior. Depending on the time-history of the applied interracial 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 lutocine) or the fluid mud/bed interface. Under an oscillatory loading, e.g. water waves, the zero velocity elevation can extend well below the fluid mud/bed interface due to viscoelastic deformations in the cohesive soil bed.
There are three flux-related processes which define the sediment concentration profile: erosion, deposition, and bed consolidation. For cohesive sediments, however, such terms




7
as erosion and deposition are not always easily defined in an unequivocal sense. Thus, for example, fluidization of the cohesive soil bed and entrainment of fluid mud due to hydrodynamic forcing may both be thought of as erosion-type processes, while gravitational settling of sediment onto the lutocline (water-mud interface), as well as formation of the bed by dewatering of fluid mud, can be considered to be deposition-type phenomena (Mehta, 1989). These processes are shown in Figure 2.1.
2.2 Definition of Fluidization
Because of the different responses of the solid and the liquid phases to stress loading, it is necessary to consider each phase independently. The liquid phase is incompressible; under a differential compressive stress, however, it flows because a liquid, by definition, is not capable of resisting a shear load. Ultimately, the solid phase controls the resistance to compression and shear.
Consider a saturated soil mass cut along its surface, as shown in Figure 2.2, subjected to an applied average normal stress, a. Imagine that the soil mass is cut along a surface so that a free-body diagram could be drawn. Suppose that this surface is approximately horizontal, but is wavy, so that it always passes between particles rather than through particles, as shown in the figure. Then the surface will pass through areas of solid-to-solid contact, and through void spaces filled with water. Let At be the total horizontal projection of the cutting surface for the soil mass considered, 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, + Pp,1A,, (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 = AC + Pr,, (2.2)




S
I

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
, + PP (2.3)
As noted by Perloff and Baron (1976), the product of orA, must approach a finite limit corresponding to a constant intergranular force, even though a is very large and A, is very small. In fact, the first term on the right side of Equation 2.3 must be some measure of the average stress carried by the soil skeleton. It is called effective stress, df, defined by 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
- (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, Au, which is the difference between actual pore water pressure, P., and the hydrostatic pressure, Ph. Under dynamic




9
Water Surface
Mobile Suspension
0
w
> =0Fluid Mud
Flid Bed Surface
a.u a,
PRESSURE
Figure 2.3: Definition sketch of soil stress terminology conditions, if the sum of excess pore pressure, Au, and the hydrostatic pressure, Ph, approa.hes the total stress, o, i.e., Au + Ph -- ar, 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, o, is equal to the hydrostatic pressure, Ph, within the suspension. Inthe fluid mud layer ar increases much more rapidly with depth due to higher sediment concentration, while the effective stress, ao; 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, Ppw in the bed is equal to the hydrostatic pressure Ph, i.e. Au = 0 (assuming this to be the initial condition). Then




CnY
LUI A U
(n Ph
0
0 TIME
Figure 2.4: Fluidization process of a soil bed at a given elevation
under dynamic loading the excess pore water pressure, A u. builds up and the effective stress o'reduces gradually. When the pore water pressure Pp,, equals the total pressure a*, the bed at this elevation is fluidized.
2.3 Wave-induced Fluidization
Surface waves and other highly oscillatory currents have a particularly pronounced influence on erosion in comparison with uni-directional currents. Because of the increased inertial forces associated with a local change in linear momentum, the net entrainment force is much greater than with turbulent uni-directional flows (Ross, 1988). Also noteworthy is the effect that bed 'shaking' and 'pumping' can have under highly oscillatory flows. '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
c" 0.4
0 Without Waves (Parchure, 1984) LLw With Waves (Maa, 1986)
z
Cr
Cn 0.2
(I Wave
Effect
0 I
0 5 10 15
LUI
BED CONSOLIDATION PERIOD (Days) Figure 2.5: Influence of waves on shear resistance to erosion of kaolinite beds in flumes effect of waves on the resistance to erosion is highlighted for beds of kaolinite of different consolidation periods in laboratory flumes. Erosion shear strengths representative of the top, thin bed layer in the upper curve were obtained by Parchure (1984) in the absence of waves. Representative values of bed shear resistance under waves corresponding to the lower curve were obtained by Maa (1986). The mean wave height during the wave experiments was 3.7 cm and the period was 1.6 sec. This example suggests that the fluid mud generating potential of waves can be a critical factor in eroding the cohesive soil bed, particularly in shallow water bodies. On the other hand, tidal current tends to serve as the main agent for advecting fluidized mud.
In the following section, the tasks carried out to meet the objectives of the present study mentioned in Section 1.2 are enumerated.
2.4 Tasks
The main experiments were carried out in a wave flume in the Coastal Engineering Laboratory of the University of Florida. The tasks were as follows:
1. Three types of clays, an attapulgite (palygorskite), a bentonite and a kaolinite, which
together covered a wide range of cohesive properties. were initially selected for characterizing their rheological properties including viscosity and the upper Bingham yield




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 capacitance gauges within the test section of the flume were used to monitor
the wave amplitudes. Bulk density profiles of the deposit during wave action were
measured vertically with a Paar (model 2000) density meter.
7. The hydrodynamic wave-mud interaction model was used to calculate the effective
sheared mud thickness, and the wave energy dissipation rate.




13
8. The effective sheared mud thickness from the hydrodynamic model was compared with
the fluidized mud thickness obtained from the flume pressure measurements. Also, the relationship between the rate of wave energy dissipation and the rate of fluidization
was investigated.




CHAPTER 3
PRELIMINARY EXPERIMENTS
3.1 Sediment and Fluid Characterization
Three types of commercially available clays: a kaolinite, a bentonite. and an 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).




Table 3.1: Chemical composition of kaolinite
Si02 46.5% MgO 0.16%
A1203 37.62% Na20 0.02%
Fe203 0.51% K20 0.40%
TiO2 0.36% SO3 0.21%
P205 0.19% V205 < 0.001%]
CaO 0.25%

Table 3.2: Chemical composition of bentonite
SiO2 63.02% A1203 21.08%
Fe203 3.25% FeO 0.35%
MgO 2.67% Na20 & K20 2.57%
CaO 0.65% H20 5.64%
Trace Elements 0.72%
Table 3.3: Chemical composition of attapulgite (palygorskite)

SiO2 55.2% A1203 9.67%
Na20 0.10% K20 0.10%
Fe203 2.32% FeO 0.19%
MgO 8.92% CaO 1.65%
H20 10.03% NH20 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




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 CAPA 700 ), and allowed to gradually settle down to the bottom. Particle concentration and fall velocities were determined with an X-ray, which could be converted to Stokes equivalent diameters. The median particle sizes of kaolinite, attapulgite, and bentonite were 1.10pm, 0.86pm, and 1.01pum, respectively. Scanning Electron Microscope (SEM) photographs of the three types of clays, as dry agglomerates, are shown in Figures 3.1, 3.2 and 3.3.

Table 3.5: Size distribution of kaolinite
D(pm) Percent size distribution(%) Cumulative size distribution(%)
5.00< 0.0 0.0
5.00-3.20 0.0 0.0
3.20-3.00 2.9 2.9
3.00-2.80 4.0 6.9
2.80-2.60 2.6 9.5
2.60-2.40 4.1 13.6
2.40-2.20 4.0 17.6
2.20-2.00 6.0 23.6
2.00-1.80 5.7 29.3
1.80-1.60 6.2 35.5
1.60-1.40 5.5 41.0
1.40-1.20 6.2 47.2
1.20-1.00 5.8 53.0
1.00-0.80 5.0 58.0
0.80-1.60 10.4 68.4
0.60-0.40 11.2 79.6
0.40-0.20 13.6 93.2
0.20-0.00 6.8 100.0




Table 3.6: Size distribution of bentonite

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

Table 3.7: Size distribution of attapulgite

D(jpm) 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
0.20-0.00 1.2 100.0




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

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




Figure 3.3: SEM of dry agglomerates of kaolinite. Scale 0.5cm = 10jsm
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 I 1.05
BS bentonite + 0.5 % salt 1.03
A attapulgite 1.10
AS attapulgite + 0.5 % salt i 1.08
BK kaolinite + bentonite | 1.16
BKS kaolinite + bentonite + 0.5 % salt 1 1.16
AB attapulgite + bentonite 1.05
ABS attapulgite + bentonite + 0.5 % salt i 1.05 AK attapulgite + kaolinite i 1.19
AKS attapulgite + kaolinite + 0.5 % salt F 1.19

The samples were set aside for about two weeks to attain equilibration between the solid and the liquid phases in terms of ion exchange. The equipment used was the Brookfield viscometer (model LVT), in which a rotating bob is immersed in a beaker of mud. The bob can rotate at selected fixed speeds, giving a shear rate range of 0.125 to 12.5 Hz. The torque generated can be read from a meter, to which the shear stress is directly proportional. In each test the shear rate was increased in steps, with a fixed time interval, e.g., 10 mins (or 10 cycles of the bob rotation) between the change of shear rate. and then decreased gradually back to the starting point. For the pure muds, i.e., A, B. K, cycles of bob rotation were used, and for the composite ones and muds with salt, i.e., KS. BS, AS, BK, BKS, AB, ABS, AK, AKS, the time of application of a shear rate in mins was used. For each type of mud the test was repeated several times with different time intervals including 5 mins, 10 mins, and 20 mins (or 5 cycles, 10 cycles, and 20 cycles ) to examine the time-dependent behavior of the materials.




21
The viscosity of muds can be significantly affected by such variables as the shear rate, temperature, pressure and the time of shearing. Here the shear rate and the shearing duration (time or cycles) are considered to be the most relevant influences on viscosity. Figures 3.4 and 3.5 show the experimental flow curves, plotted as shear stress versus shear rate. For comparison between different materials, the curves corresponding to muds subjected to the same shearing time of 10 mins (or 10 cycles) are shown in Figures 3.6 and 3.7, showing the relationship between shear stress and shear rate, where the arrows indicate the direction of the rising and falling flow curves. The corresponding curves of viscosity (obtained by dividing shear stress by shear rate using the rising curves) versus shear rate are plotted in Figures 3.8 and 3.9.
3.2.1 Influence of Shear Rate
The experimental data points, which are represented by point markers in Figures 3.8 and 3.9, indicate that all the materials, except attapulgite, generally exhibit a shear-thinning behavior, i.e., the viscosity decreases as the shear rate increases. While attapulgite at low shear rates shows a shear-thinning behavior, at higher shear rates it exhibits 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 /'o 4 (cI) (3.1)
As /00
where yo and p,,. refer to the asymptotic values of the viscosity at very low and very high shear rates, respectively, cl is a constant parameter having dimensions of time, p is a




70.0 60.0 50.0
40.0 30.0 20.0 10.0

2.0 4.0 6.0 8.0 10.0

12.0 14.0

20.0 18.0
16.0 11.0
12.0 10.0 8.0 6.0
4.0 2.0 0.0

10.0 12.0

0.0 2.0 4.0 6.0 8.0 10.0

12.0 14.0

SHERR RATE (HZ)

Figure 3.4: Shear stress, u, versus shear rate, -, (K,A,B)

- BK
- O O O 5 MINS
- -------- 4. ---- - 10 MINS
- -------)---- 20 MINS
I I I

14.0




70.0 60.0 50.0 40.0
30.0 20.0 10.0

2.0 4.0 6.0 8.0 10.0

2.0 4.0 6.0 8.0 10.0

2.0 4.0 6.0 8.0 10.0

12.0 14.0

12.0 14.0

12.0 14.0

SHEAR RATE (HZ)

Figure 3.5: Shear stress, a, versus shear rate, 9, (AK,BK,AB)

20.0 18.0 16.0
14.0 12.0 10.0
8.0 6.0 4.0
2.0
0.0
100.1 90.0 80.0
70.0 60.0 50.0 40.0
30.0 20.0 10.0 0.0




a: a:
L L
U/') IO.)
,- 10 MINS ,,
= 5.0
a: a:
0.0 el e
0.0 2.0 4.0 6.0 8.0 10.0 12.0 1.0N
SHEAR RATE (HZ)
KAOLINITE, SALT
25.0
n IB
20.0
1S.0
LIj Ui
cc
10.0(
a- 10 CYCLES c
o S .
O.O) , f*
I 0.0 I
0.0 2.0 I.0 a .0 0.0 10.0 12.0 1.0
SHEAR RATE IHZ)
KAOLINITE, NO SALT

90.0

0 .
.0 In
0 a
p
a a a:
0 10 MINS *
I) s e i l l i Lo
0.0 2.0 1.0 6.0 8.0 10.0 12.0 1.0
SHEAR RATE lIIZ)
BENTONITE, SALT
0
o )
U)
tii
I
0
0 1 L
a10 CYCLES aL.

0.0 2.0 1.0 6.0 8.0 10.0 12.0 11.0
SHEAR RATE (IMZ)
BENTONITE, NO SALT

do. U 70.0 60.0 50.0 40.0 30. d 20.0 20 H I US
10.04 0.0
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
SHEAR RATE 1HZ)
ATTAPULGITE, SALT 120.
00. F
60.0
qo. 0
20.0 QY 20 CYCLES
0.0
0.0 2.0 q.0 6.0 8.0 10.0 12.0 q14.0
5HEARl RATE IlIZ)
AITAPULGITENO SALT

Figure 3.6: Shear stress, a, versus shear rate, 4, (K,KS,A,AS,11,IIS)

I'




50.0 40.0 UT
Ld
30.0 cc
20.0
"r
10 iIINS a
0.0 to
lo.o 0***
0.0 2.0 4 0 6.0 6.0 10.0 12.0 14.0
SHiEAR RATE (HZ)
BK SALT 20.0
IS.0
a:
in
in
30.0 1li
a:

IIo 111115a:
ii
0.0 2.0 41.0 6.0 8.0 10.0 12.0 1.0
SHiEAR RATE ilIZl
BK, NO SALT

50.0
40.0 Lp
h )
ir
30.0 120.0 C
in
10 MINS us
r
10.4
lo o c
0.0 2.0 I.0 8.0 6.0 10.0 12.0 I9.0
SH4EAR RATE (IZ)
K + A SALT
0.0.

60.o0

0.0 2.0 6.0 6.0 8.0
SHEAR RATE
AK ,NO SALT

10.0 12.0
tHZ)

Ur"
C:
Iuj
in in
14.0

20.1

0.0 2.0 4.0 6.0 1.0 10.0 12.0 l1.0
SHIEAR RATE IIZI
AB SALT

2.0 %.0 6.0 0.0 10.0 12.0 l1.0
SHEAR AR IE 11Z) AB NO SALT

Figure 3.7: Shear stress, a, versus shear rate, 4, (lIK,BKS,AK,AKS,Al,AlS)

0
10 MINS




cr
10 MINS
o
U_)
00
2.0 4.0 6.0 8.0 10.0 12.0 14.0
SHEAR RATE (HZ) KAOLINITE, SALT
B
U)
ac
_.
10 CYCLES
i
2.0 4.0 6.0 8.0 10.0 12.0 14.0
SHEAR RATE (HZI
KAOLINITE, NO SALT

70.0 60.0 50.0
qo. 0
40.0 30.0
20.0
0.0
0.0
0.0

0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
SHEAR RATE IHZ)
BENTONITE, SALT
D

too100.
90.0 80.0 70.0 60.0 50.0
40.0
O.o 0
30.0
20.0
10.0 0.0
a.

a:
10 CYCLES
2.0 4.0 6.0 8.0 10.0 12.0 1.0
SHEAR RATE I(Z)
BENTONITE, NO SALT

.0

2.0 4.0 6.0 8.0
SHEAR RATE ATTAPULGITE.

10.0 12.0 14.0 IZ)
SALT

.0 4.0 6.0 8.0 10.0 12.0 14.0
SHEAR RATE (IZ)
ATTAPULGITENO SALT

Figure 3.8: Viscosity, it, versus shear rate, 4, (K,KS,A,AS,1I,IIS)

E
20 MINS
(D

40.0
ac
S30.0
0.0
-j 20.0 > (0.0
0.0
0.0

!

60.0 50.0




SHEAR RATE (HZ) BK SALT

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

90.0 00.0 70.0 60.0
50.0
40.0 30.0
20.0 10.0 0.0
0.
25.0

20.0 15.0
10.0
0
5.0

.0

2.0

a UU.V

90.0 80.0 v 70.0
cc
- 60.0 S50.0 40.0 30.0 > 20.0

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

10 MINS

U U

0.0 I
0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
SHEAR RATE (HZ)
AK NO SALT

c
10 IINS

0

2.0 4.0 6. 0 8.0
SHEAR RATE
AB SALT

10.0 12.0 14.0
IHZ)

12.0 14.0

SHEAR RATE (HZ) AB ,NO SALT

Figure 3.9: Viscosity, /I, versus shear rate, 4, (lK,IKS,AI(,AI(S,AII,AlS)

0.0 0.0

E
10 MINS




28
dimensionless constant, 1 is the apparent viscosity and 4 is the shear rate.
In all the studied cases, 1z Y0 (cl (3.2)
which can be further written as = 110 + P'- (3.3)
or
=a. + C+ c-' (3.4)
Equation 3.4 is referred to as the Sisko (1958) model, where o/1 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, POO, 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 = 11(i-/p)2 = minimum (3.5)
i=1
or
N
D = E(Ai p20 c n-1)2 = minimum (3.6)
i=1
where /i is viscosity of the mud obtained from the experiment, and N is the number of data points.
Setting
0/o 0 (3.7)
D
-7 =0 (3.8)
n -0 (3.9)
an




Equations 3.5 and 3.6 can be expressed as
' N
- c j"-) = 0 (3.10)
therefore
N
.- c4'-')} = 0 (3.11)
i=l1
hence
E{c -j log ( O- o c n-l)} = 0 (3.12)
In this way, pto, 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, joo, represents resistance to flow in the limit of a very high shear rate. It can be seen that attapulgite has the highest value of y,, among the three types of clays, up to 5 to 6 Pa.s. Kaolinite and bentonite have lower y,, values, about 2 Pa.s. For the composite materials, AB has a high it. 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 M, about 0.6 Pa.s, salt also increases po (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).




Table 3.9: Parameters for the Sisko power-law model for viscosity
I Mud po (Pa.s) c n
K 2.10 7.08 0.106
KS 2.06 3.31 0.117
B 0.41 48.68 0.207
BS 2.46 28.26 -0.009
A 6.34 6.86 -1.0
AS 5.00 11.54 0.038
BK 0.61 12.29 -0.057
BKS 4.69 20.60 -0.114
AB 4.28 45.2 0.002
ABS 7.06 45.07 -0.039
AK 4.44 0.76 -1.083
AKS 3.35 8.02 0.059

3.2.2 Influence of Shearing Time
For a given shear rate, the corresponding shear stress, and hence the viscosity, can either increase or decrease with time of shearing. This type of behavior is either called, respectively, "thixotropy," which usually occurs in circumstances where the material is shear-thinning, or "anti-thixotropy," which is usually associated with shear-thickening 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 kaolinite, i.e., KS, BK, BKS, the effect of shearing time was also very small, while for AS and BS this effect was relatively greater.
Time-dependent mud behavior leads to a hysteresis loop in the flow curves of shear stress versus shear rate when the curves are plotted first for increasing and then decreasing shear rate sequences. This behavior is observed in Figures 3.4, 3.5, 3.6, and 3.7, in which it can be seen that all the materials more or less exhibit a hysterisis loop. When the material is sheared, typically the structure progressively breaks down and the apparent viscosity




Table 3.10: Shearing time effect on shear stress
Symbol 5 cycles 10 cycles 15 cycles 20 cycles 25 cycles 30 cycles
K 19.4 17.9 17.7 18.8
B 74.3 69.9 61.8 66.8
A 25.0 90.9 25.7
5 mins 10 mins 15 mins 20 mins KS 14.7 13.5 13.0
BS 46.7 39.2
AS 62.7 76.5
BK 14.4 13.9 13.5
BKS 53.3 50.5 56.7
AB 76.5
ABS 101.6
AK 23.8
AKS 35.9

decreases with time. The rate of breakdown of the structure during shearing at a given rate depends on the number of linkages available for breaking and must therefore decrease with time (Wilkinson, 1960). Also, during shearing asymmetric particles or molecules are better aligned, i.e., instead of a random, intermingled state which exists when the material is at rest, the major particle axes are brought in line with the direction of flow. The apparent viscosity thus continues to decrease with increasing rate of shear until no further alignment along the streamline is possible.
3.2.3 Upper Bingham Yield Stress
The upper Bingham yield stress, o-B, the stress that must be exceeded before flow starts, can be determined from the plots of shear stress versus shear rate in Figures 3.6 and 3.7 by drawing a line tangent to the upper range of shear rates (Wilkinson, 1960). The intersection of this tangent with the stress axis gives aB. The results are presented in the Table 3.11. This table shows that among the three types of clays, attapulgite has the highest upper Bingham yield stress with 72 Pa, kaolinite has the lowest one with 10 Pa, and bentonite is in-between with 50 Pa. The composite materials that contain kaolinite, i.e., AK, AKS, BK, have very low upper Bingham yield stresses that are less than 10 Pa, except BKS, which




Table 3.11: Upper Bingham yield stress
sampleI K IKS B BS IA AS BK IBKS AB ABS AK AKS
'B (Pa) 15.0 9.5 50.0 36.0 66.0 72.0 10.0 39.0 58.0 88.0 0.0 4.0
has a relatively higher aB of 39 Pa. The higher value of the upper Bingham yield stress for BKS is likely to be due to the presence of salt, which in general promotes flocculation of clays. Of the composite materials AB and ABS have the highest upper Bingham yield stresses with values of 58 Pa and 88 Pa, respectively. ABS also has a higher value of aB than AB presumably because of the effect of salt. Salt might increase the upper Bingham yield stress of bentonite as well, although the upper yield stress of BS, 36 Pa, is less than that of B, which is 50 Pa. Note that when BS was tested the density had to be reduced from 1.05 g1-1 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 toincrease. Attapulgite and bentonite exhibit measurable gelling behavior, especially when salt is added. Gelling also occurred in AB, ABS, BKS. See examples in Figure 3.6 (c), (e) and (f), as well as in Figure 3.7 (d), (e) and (f).
3.2.5 Summary
Table 3.12 gives a summary of the properties of the materials that have been studied, where rB of ABS refers to the value corresponding to 5 mins shearing duration. The




following observations are noteworthy:
1. All the selected materials exhibited shear-thinning, although attapulgite behaved as
a shear-thickening material somewhere in the shear rate range from 2.5 to 6.0 Hz.
2. For both the viscosity and the upper Bingham yield stress, kaolinite had the lowest
values among the three types of clays, attapulgite the highest, and bentonite was in-between. The composite materials that contained kaolinite had relatively low 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, it, of B by 500%, BK by 660%, and AB by 65%. It increased the upper Bingham yield stress of BK by 290% and AB by 50%. Salt did not significantly change the viscosity of kaolinite and attapulgite. It decreased both it and aB of kaolinite by less than
10%. Finally, salt decreased joo 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




Table 3.12: Rheological parameters for power-law given by Equation 3.4
Mud time Density aB A00 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 10 mins 1.19 4.0 3.35 8.02 0.059

water level in steps of 1 to 2 cm, while the gauges were held in fixed positions. The linear least squares method was used to obtain a regression equation. Results of calibration are shown in Figure 3.10. Water level variation was recorded by a data acquisition system briefly described later in this chapter. The sampling frequency was 40 Hz for 0.5-sec wave and 20 Hz for 1 to 2-sec waves.
3.3.2 Current Meter
An electromagnetic Marsh-McBirney current meter (model 523) was used to measure the horizontal velocities in the water column. Calibration of the current meter is shown in Figure 3.11, which was conducted in a V-notched weir flume in the Civil Engineering Department. The current meter had two restrictions. Firstly, the probe could not be placed close to the water-air or water-bed interface due to the drastic change in material (medium) density and conductivity associated with the electromagnetic field, which resulted in an unrealistic output. Secondly, the meter generated strong interference with other instruments which meant that only the current meter could be used at a given time. Thus other data had to be collected during separate time windows. The sampling frequency for the current meter data was the same as the wave gauges.




60.0 57.5
55.0 52.5 S 50.0
47.5 '5.0 L12. 5 237.5
35.0
1000 1250

1500 1750 2000 2250 2500 2750 3000 3250 3500
BITS

Figure 3.10: Calibration curves for the wave gauges

40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0
0.0 1 I
-0.20 -0.18 -0.16 -0.14 -0.12 -0.10 -0.08 -0.06 -0.04 -0.02 0.00
VOLTAGE (V

Figure 3.11: Calibration curve for the current meter




3.3.3 Pressure Transducers
Six pairs of total and pore pressure transducers were flush-mounted on the side wall of the flume at different elevations for quantifying the effective stress at different elevations. One additional total pressure transducer was installed at the flume bottom to check the weight of the column. The elevations of the 6 paired-transducers from the flume bottom were: 14cm(#l), 12cm(#2), 9.5cm(#3), 7.5cm(#4), 5.1 cm (#5), and 3.lcm(#6) for the pore pressure gauges, and 14cm(#5), 11.9cm(#7), 9.5cm(#1), 4.9cm(#3), 2.6 cm(#2), and Ocm(#6) for the total pressure gauges. The pore pressure transducers were Druck model PDCR 810, each covered with a water-saturated porous stone. Each gauge was fitted with a specially designed 300x signal amplifier. Four of the total pressure transducers were Druck model PDCR135/A/F, and the remaining three were Druck model PDCR 81, each fitted with 200x signal amplifiers. The gauges were checked in a calibration cylinder filled with water to the desired depth. The cylinder was graded with a 1 mm scale. Calibration curves for the 13 pressure transducers are shown in Figures 3.12 and 3.13. The sampling frequency during the fluidization experiments was 20 Hz, sampling duration was 30 sec for each record.
The pressure gauges were then tested under dynamic loading by subjecting them to a 1 sec period, about 5cm high wave in the flume. Measured pressures were compared with results from the linear wave theory with respect to amplitudes, as shown in Figures 3.14 and 3.15. The comparison shows that the experimental data agreed reasonably well with theory, thus indicating that the temporal response of the pressure transducers to dynamic wave loading were of acceptable quality. Phase lags appeared between the pressures from the theory and the measurements as observed in the figures, caused by the distance between the wave gauge and pressure gauges. The wave gauge was located approximately 0.6m upstream from the pressure gauges, so that the peak value of the pressure from theory was ahead of those from measurement. Between the pore and total pressure gauges there also was a small distance, plus there was the lag effect of the porous stone in the pore pressure sensor that also possibly delayed its response to the wave loading in a measurable way. These factors




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




0.0 0.3 0.6 0.9
VOLTAGE (V)

0.5 1.0 1.5
VOLTAGE

Figure 3.12: Calibration curves for the total pressure gauges

0.0




-1.0 -0.5 0.0 0.5 1.0 1.5
VOLTAGE

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

2.0 2.S 3.0

2.0 2.5 3.0

Figure 3.13: Calibration curves for the pore pressure gauges




2.75
2.65
THEORY OCM
2.55
2.1.5 LI i --! 1TOTAL OCM
2.3S
2.25 I
2.0 7.0 12.0 17.0 22.0
2.0
CC 2.30 --- THEORY 3.1CM
2.20 ------- PORE 3.1CM
a- 2.10 *: / 1 -- TOTRL 2.6CM
( 2.00
LLJ
O.- 1.90 I II
2.0 7.0 12.0 17.0 22.0
2.25
2.15
---THEORT 4.9CH
2.05.
----TOTAL 4.9CM
1.85 L *.
1.75I I
2.0 7.0 12.0 17.0 22.0
TIME (SEC)
Figure 3.14: Dynamic response of pressure gauges, and comparison with results from the linear wave theory: gauge elevations ranging from 0 to 4.9 cm




2.00
1.90
1.80 -THEORT 7.5CH
1.70 ------ PORE 7.50
1.50I
2.0 7.0 12.0 17.0 22.0
1.75
1.65 L -- THEORY 9.SCM
. 5 ------ PORE 9.5CM
C S 15 .---- TOTAL 9.5CM
1.35
I I
LLJ
1.25
2.0 7.0 12.0 17.0 22.0
U" 1.50
U.
C 1.40 -- THEOR 12CM
1.30 PORE 12CM
1.20 ----- TOTAL 11.9CH
1.10
2.0 7.0 12.0 17.0 22.0
1.25
1.15 A --- THEORY I4CM
1.05 ....... PORE 14CM
0.95 ----- TOTAL 14CM
0.85 0.75
2.0 7.0 12.0 17.0 22.0
TIME (SEC]
Figure 3.15: Dynamic response of pressure gauges, and comparison with results from the linear wave theory: gauge elevations ranging from 7.5 to 14 cm




2.3000
S2.2500
---2.2000
S2. 1500
2. 1000
0.0

50.0 100.0 150.0

5500

2.5000
u
2.4500
0-2.4000
0.

PORE PRESSURE GARGE =3. OLD IMP'PLIFIER
-fi

0

50.0

100.0 TIME (MINI

150.0

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

0.0 -0. 1
S-0.2
'- -0.3

200 400 600
TIME (MIN)

800 1000 1200 1q00 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.

200.0

200.0


I ..~. ~.
I -~
I I




43
column and moved in the piston-type manner, was installed at one end of the flume to generate regular (monochromatic) waves. The wave height and period could be adjusted by a DC motor controller. An impermeable, 1 in 4 sloped beach covered with astroturf, a type of plastic wire mesh about 1 cm thick, was installed at the end behind the wave maker to damp out water level fluctuations caused there by the wave maker. At the downstream end of the flume, a plexiglass board was installed to provide a 1 in 20 sloped beach. Astroturf was also placed on top of this beach for reduction of wave reflection. In the test section, a trench, from x=6.1 m to 13.3 m. (Figure 3.18), with a height of 14 cm. and side slopes of 1 in 12, was formed to hold the sediment. Here x is the distance measured from the wave maker as shown in Figure 3.18.
Before the mud fluidization experiments were carried out in the flume, wave 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.




Current Meter (x = 14.7 m)

Wave Gauge #2
(x = 10 m)

Wave Gauge #1
(x = 5 m)

Wave Maker
(x = 0)

- -- -- - --- -FI -t-n-

Figure 3.18: Wave flintn elevation profile andi instrumient locations

p's tv

Mud Trench A-,A




J 6.0 Z 4.0
- 2.0 CE 0.0
LJ -2.0 ..J
LJ -4.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0
TIME (SEC) H=7.8 CM GAUGE #I
J 6.0 B Z 4.0 S2.0 CC 0.0 L -2.0
-J
UJ I I I
-4.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0
TIME (SEC) H=4.62 CM GAUGE *I
L 6.0 Z 4.0 CD
S2.0
0.0
CY
LLuJ -2.0 UJ -4.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0
TIME (SEC) H=7.6 CM GAUGE =2
i) 4.0
z
c 2.0 0.0
L -2.0
_J
iLi -4.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0
TIME (SEC) H='4.5 CM GAUGE #2
Figure 3.19: Examples of wave time-series (depth=20cm, period=l.Os) for flume characterization tests with a false bottom




Table 3.13: Wave conditions for the charaterization tests
Depth (cm) Period T(sec) Wave height H(cm) gauge #1 gauge #4-2
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




ui
C
or
N
q:
U
(n

400 360
S320
a; 280
z
uj (f 240
ox
200
._j x 0
x 160
u 120 a- 80
(n
40 0
.5 a

A
GAUGE 1
1.0 0.5 1.0 1.5 2.0 2
FREQUENCY (HZ)
T=1.OSEC RVG.IIT.=4.6CH
B
GAUGE u2
1.0 0.5 1.0 1.5 2.0 2
FREQUENCY (HZ)

T=1.05EC AVG.HT.=q.3CM

C
GAUGE 1
'.0 0.5 1.0 1.5 2.0 2,
FREQUENCY (HZ)
T=1.5SEC AVG.IIT.=q.qCHM

0
GAUGE .2
0.0 0.5 1.0 1.5 2.0 2,
FREQUENCY (HZ)
T=I.5SEC AVG.HT.=tI.5CHM

I
i cr
I
u
0

0

z
Li ILl CE'3 a
(n

E
GAUGE 1
.0 0.5 1.0 1.5 2.0 2.
FREQUENCY (IZ)
T=2.0SEC AVG.IIT.=1.3CM

400 360 320
280
240 200 160
120 80 40
0
0.0

0.5 1.0 1.5 2.0 FREQUENCY (HZ)

T=2.05EC RVG.HT.=3.9CM

Figure 3.20: Wave spectra, water depth=20cm; average wave height ranging from :1.9 to .1.6 cm, period ranging from I to 2 sec.

I
z
I.I LJin U C3
-j
LLJ
a.
(n

400 360
- 320
280
z
0 o 240
200 cx 160 u J 120 lLzJ
(. 80 In
0

F
GAUGE u2




.0 0.5 1.0 1.5 2.0
FREQUENCY (HZ)
T=I.OSEC AVG.HT=7.8CN

B
GAUGE #2
I

0.5 1.0 1.5

U.
z
C3 X

ccH
LU
a
(n

1200 1000 800
600 100

luut )-- IVUL I-
- 800
C3XI
S600
a
9 200

2.0 2.5

FREQUENCY (HZ)

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

0.5 1.0

FREQUENCY (HZ)
T=1.5SEC AVG.HT.=9.1CM
0
GAUGE #2
.. I .1

0.0 0.5 1.0 1.5

)- 100(1
I-
Z 800
" L
S600
c x
: -oo
2: 400
200
0
.5 0

t

C
GAUGE I
1.5 2.0 2

E
GAUGE It
i I .

1.5 2.0 2

FREQUENCY (HiZ)
T=2.OSEC AVGH=8.'ICl
1200

>- IOUI i-
U)
z 6000
6800
IL c X CC
-: 400
U
a_ 2 (n 200

2.0 2.5

FREQUENCY (HZ)

T=I.5SEC AVG.HT.=9.2CM

F
GAUGE =2
a .1
.0 0.5 1.0 1.5 2.0 2.5
FREQUENCY (HZ)
T=2.05EC AVG.HT.=6.LICM

Figure 3.21: Wave spectra, water depth=20cmn; average wave height ranging from 6.-1 to 9.1 cmi, period ranging from I to 2 sec.

1200,

A
GAUGE l 1
, .

)-IOOC
: 800
J
S600
C
0 x 00
OS 0 L00
O 200

ia.nn

.0 0.5 1.0

01

- 100 I-
S 800 o V
600
a: qO
- 1100 L)
ii
(
5 200

I

n

a

I

'""'

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 = at cos(kz at + -I)
iJR = aR cos(kx + at + ER) (3.13)
where ,71 and 7R are the surface elevations of the incident and the reflected waves, respectively, ai is the amplitude of the incident wave and an is that of reflected wave, k is the wave number, 2r/L, with L the wavelength, a is the angular frequency, 27r/T, with T the wave period, and EJ and ER are the phase angles of the incident and the reflected waves, respectively. The surface elevations must be recorded at two adjacent stations, x1 and zX2=Xl + Al. The measured profiles of the composite waves, selecting the fundamental frequency for analysis, are
1 = (,71 + 7Rn)x=x = A1 cos at + B1 sin at T2 = (771+ r)z=z2 = A2cos at+ B2sinat (3.14)
where
A1 = a cos 4 +aR cos R
B1 = a sin I aR sin OR
A2 = aI cos(kAl + i) + aR cos(kAl + ORn) B2 = ai sin(kAl + OI) + aR sin(kAl + OR) (3.15)
Or = kzxi +I
R = kxl + R (3.16)
Equation 3.15 can be solved to yield aj and an according to
j/(A2 A cos kAld B1 sin kAI)2 + (B2 + A, sin kiAl B1 cos kAl)2
a=2 1 sinkAl I

/(A2 A, cos kAl + BI sin kAl)2 + (B2 A, sin kAl B1 cos kAl)2
2 sin kAl I

(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/ar, 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 m distance between the current meter and wave gauge #2, it should be noted that there was measurable wave dissipation over this distance, even in the absence of mud.




51
The mean wave decay coefficient, kim, was found to be 0.02/m, as calculated from the wave height recordings by gauges #1 and #2. The wave height where the current meter was located, Ho,,, would be
H., = H#2e-km' (3.18)
where H#2 is the wave height at gauge #2, and Ax is the distance between gauge #2 and the current meter. Here Ax=4.7 m.
The root-mean square (rms) velocity from the current velocity time-series is obtained from
urms = (ui i)2 (3.19)
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
HC ua cosh kz cos(kx t) (3.20)
2 sinh kh
where H the wave height, a the angular frequency, k the wave number, h the water depth, and z the elevation above the flume bottom. Thus Urms amplitude can be calculated as (van Rijn, 1985)
Vf H, ro cosh kz (3.21)
Urms = 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., ki,-m in Equation 3.18 is 0.02/m for calculating Hc,r for the solid curve and is zero for the dashed curve.




15.0
12.0
9 0 I
6.0
3.0
0.0
0.0 5.0 10.0 15.0 20.0
VELOCITY (CM/SEC)
DEP=ISCH H=3.1CHM

25.0 30.0

15.0 12.0 9.0 6.0 3.0
0.0
0.0 5.0 10.0 15.0 20.0
VELOCITT(CM/SEC)
DEP=ISCH H=q.8CH

0.0 5.0 10.0 15.0 20.0 25.0 30.0
VELOCITY(CIM/SEC)
DEP=20CH H=R.4CHM

0.0 5.0 10.0 15.0 20.0 25.0 30.0
VELOCITY (CH/SEC)
DEP=20CH f=7.3CH
THEORY. CONSIDER DISSIPATION
----- THEORY. WITHOUT DISSIPATION
EXPERIMENTAL DATA

Figure 3.22: Horizontal velocity profiles: comparison between experimental data (rms aimplitudes) and linear wave theory (peorid T= l.0s)

25.0 30.0




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 ai, 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, pl, 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 J. 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 7,(x, t) and m(x, t). The amplitude of a simple harmonic surface wave is assumed to be small enough




H Water
zT1 X""2 p
z H2 2 Fluid 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 :he mud layer. Accordingly, the relevant linear governing equations of motion and continuity can be written as:
upper layer:
-- + g = 0 (4.1)
at az
8(i- i2) 1
a(77- H = 0 (4.2)
at Ox
lower layer:
Ou2 872 1 a2u2
-+ rg + (I r)g- - (4.3)
t ox ax az2
SMdz +- = 0 (4.4)
where ul(z, t), u2(z, t) are the wave-induced velocities, A = H2 + l72, r = (p2 Pl)/P2 is the normalized density jump, and v = A/p, is the kinematic "iscosity of mud. The following boundary conditions are imposed:
7(0, t) = ao cos ui(co, t), u2(oo, z, t), ti(oC,t), r2(-0, t) -+* 0 (4.6)

u2(X, 0, t) = 0

(4.7)




55
Ou2(z,H2,t)
0z = 0 (4.8)
O~z
where ao(= H/2) is the surface wave amplitude at z = 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 kH, which is a complex valued function
k 1 + IH2r [(1 + H2r)2 4rT2r]1/2 11/2 (4.9)
Fr_ 2rH2r
where
r=- 1 tanh(mH2) (4.10)
m /=t1 -(4.10)
mH2
112 = H2/Hl, m = (-iRe)1/2, Re = aH4/v is the wave Reynolds number and F, = o(Hl/g)1/2 is the wave Froude number, a is the wave angular frequency.
The imaginary part of k, i.e., ki, is the wave attenuation (decay or damping) coefficient with respect to the travel distance x, defined by
a = aoexp(-k;x) (4.11)
where a. is the wave amplitude at any z. Also the normalized, horizontal wave-induced velocity in a mud layer is given as
112 = A-{1 r(-)'}{1 cosh(mi) + tanh(mf!2)
sinh(mi)} exp{i(ki T)} (4.12)
where ti2 = u2/(aH1), A = ao/H1, ,i = z/H1I, and :i = x/H1.
As noted in Section 3.2.1 in Chapter 3, the dynamic viscosity of mud can be expressed as

P = Poo + cn4-

(4.13)




56
where ,ic, c and n are constants for a given material, and j' is the shear rate.
With the two recorded wave amplitudes a0 (=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, was calculated. Also, by substituting the viscosity, Ui (or v = Ap2), into Equation 4.12, an effective sheared mud thickness, d, was obtained from the equation:
d- =2 u3 (4.14)
where U2, is the amplitude Of U2 at the mud surface and ui-2 = U2,/(orHi) 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 1io is an initially selected value of garitma required for iterative calculation of !..
A physical implication of Equation 4.14 is that, assuming d < H2, U2 will be zero at elevation z = H2 d. This requirement is not compatible with the fact that U2 in the model is consistently equal to zero only at the flume bottom, i.e., z = 0. Thus the attempt to calculate a fluidized mud thickness, d, within a layer of thickness H2 that is already a fluid, by definition in the model, is an artifact meant only to experiment with the possibility of evaluating the fluidization depth that is commensurate with the experimental data. This attempt at developing correspondence between the model and the data is necessitated by the fact that the mud in the flume was not in general a fluid, except in the upper elevations when fluidization occurred by virtue of wave action.




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




58
4.3 Wave Energy Dissipation Rate The wave-mean rate of energy dissipation with respect to time, ED, is given by (Dean & Dalrymple, 1984):
i+H2 Bu Ow bu
ED = P H [2(L)2 + (- + )2]dz (4.15)
Jo 9X 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 = P2V oH2 [2( )2 + ( )2)]dz (4.16)
or, dividing eD into two terms: ED = ED1 + ED2 (4.17)
ED1 = P2V f2 2( U )2dz (4.18)
H2 U
ED2= P2V 0H z )2dz (4.19)
Physically, ED1 and ED2 are the wave-mean rates of energy dissipation due to the horizontal and vertical velocity gradients, respectively. Equation 4.12 gives: Bu2 Bu'2
= a-- = (ik)u2 (4.20)
and
U= = aA 0 {1i r( )k 2}{-msinh(mi) + mtanh(mi) cosh(mi)} exp i(k F)
OZ- -a =Z F2 r() mz(4.21)
Therefore, the time-averaged values of (8 )2, (. Z)2 are:
( )= 1a2'(2( )2{l- r(i )2} {1 cosh(mZ) + tanh(ml72) sinh(m7)}2 (4.22) and
'U22 1 22Ak2 tanh2(m 2) -1
(--)2= -m "(-) {1-r(-)2}2{
Sz 2 F 2
tanh (mHl2) + 1
+ 2 cosh(2mi) tanh(mH2) sinh(2m.)} (4.23)




Therefore
/H2 22 8E2
ED1 = 2p2Z] ( )2dz = 2P2V H,()d
= 2p2 2HA()21- r(
r F
3- 1 tah(/])2 tanh(mHt2)
{3 -H2tanh2(mH2) + 2tanh(m [cosh(mH2)- 1]
2 2 m
tanh(mH2) 2
m [cosh(2mH2) 11 - sinh(mH2)
2m m
1 + tanh(m[2)
+ 4m sinh(2mf2)} (4.24)
4m
and
ED2 = P2v H2( aU)2dz (4.25)
1
1 tanh(mH2)[cosh(2mH2)- 1]} 2m
Introducing
x = H2(0 )1/2 (4.26)
2v
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:
Eo 2- 2 2( ,k 411 Rk 2)2 ED1 = EaF,2 2 X k){ R()
1 r F Fr
3- 1- 221
- 12-2tanh 2 tanh((-x)X) vhx r-- 1]
{ H2 + E tosntv- X)
2 X
H2 tanh(V'O2X) 2H2
2 X [cosh(2V/-RYX) 1] v- sinh(v/-7X)
+ 1 + tanh2(v-iX) sinh(2y/-C X)} (4.27)
and
ED2 Eoa(1 i)2( )2 k){21
2 1-r F Fr,




60
2 1 2+_anh(_)
{H[tanh ( 2X) 1] + I21 + tanh2( X) sinh(2V0x)
2 4V-X
-H / a x cosh(2v-0x) 1]} (4.28)
22
where Eo = 0.5pigag is the initial energy (at wave gauge #1). For any set of conditions in the flume, Equations 4.17, 4.27 and 4.28 can be used to calculate ED*
As an alternative to the above approach, the same dissipation rate can also be obtained via the following procedure: dE
ED = dt (4.29)
The wave energy, E, is obtained from E = pigax2 (4.30)
where
a. = aoexp(-kierzpx) (4.31)
is the surface wave amplitude at any x, and x = Ct (4.32)
and (Jiang & Mehta, 1991)
F
C = CO (4.33)
k,.
with Co = fMH being the wave celerity in shallow water over the rigid bottom and k-r being the normalized wave number from Equation 4.9. Therefore, Equation 4.29 can be further written as:
ED plga kep (4.34)
Where g is the acceleration due to gravity; H1 is the water column thickness, Pl 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 glh1.
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




Wave Gauge #2 Wave Gauge #1 Wave Maker
(x = 12.2 m) (x = 7.5 m) (x = 0)
1:20 Water \o
M 7Jd Tre n-ch- ,4 -
Density Pressure
(x = 8.9 m) (x = 8.1 m)
Figure 5.1: Sketch of Ila.me profile ill the fluidization experiment




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) 0C_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
5140 17.0 6 1.04 1 770 16
6 160 17.0 7.5 1.04 350 15
7150 17.6 5 1.06 380 17
8 240 17.5 4 1.06 460 19
9 65 16.6 5 1.06 450 20
10 85 16.4 8 1.06 1 385 21
ll 90 16.4 3 1.06 1700 2

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, Mlaa (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. This issue is discussed later in Section 6.2.3.




Table 5.2: Wave heights, Test #9
Time(mins) H#x(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
1 300 4.5 1.7
320 4.5 1.5
340 4.5 1.6
i 360 4.4 1.6
1 380 4.4 1.6
1 400 4.4 1.6
420 4.3 1.5
450 4.3 1.5




5.0 10.0 15.0 20.0 25.0
TIME (SEC) 71 MINUTES GAUGE -t

5.0 10.0 15.0 20.0 25.0
TIME(SEC) 210 MINUTES GAUGE #1

5.0 10.0
TIME(SEC) 71

15.0 20.0 MINUTES GAUGE

25.0 u2

5.0 10.0 15.0 20.0 25.0
TIME(SEC) 210 MINUTES GAUGE n2

Figure 5.2: Wave time-series, Test #9

0
0
0

30.0

4.0 2.0 0.0
-2.0

-4.0
0.
4.0
2.0 0.0
-2.0
-4.0
0.
4.0
2.0 0.0
-2.0

0.
4.0 2.0 0.0
-2.0
-4.0
0.

C
1II II

0.0 0.0

0

0

0

30.0

30

3




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.s, while at 210 mins and 360 mins the decrease was about 70 cm 2s, 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.




150 .

GAUGE #

120 U-)
z
N .-ix
cc 60
L 3 a_. 30 Un)

0

0.0 0.5 1.0 1.5 2.0 2.5
FREQUENCY (HZ)
RVG.HT.=5.0CM 71 MINUTES

U.U U0.5 1.0

20
1-5
u I
z
-1 10 a:
cc
Li-i 5
OL
(n)

1.5 2.0 2.5

FREQUENCY (IHZ)
AVG.IIT.=1.BCM 71 MINUTES

12(
Iii 90
0 x
z
x60
(J3 (L 30 U-)

FREQUENCT (HZ)
AVG.IIT.=q.7CM 210 MINUTES 20
0
Or
GAUGE "2 15
m
10
CLL (n 0
0.0 0.5 1.0 1.5 2.0 2.5
FREQUENCY (HZ)
AVG.IIT.=1.7CM 210 MINUTES

E
GAUGE 1
1.0 0.5 1.0 1.5 2.0 2.5
FREQUENCY (HZ)
AVG.IIT.=q.QICM 360 MINUTES

FREQUENCY (IZ)
AVG. HT.=1.6CM 360 MINUTES

Figure 5.3: Wave spectra, Test #9

- 120
z
S 90 to g
-r
60
3 JL LJ
a- 30 U-n

C
GAUGE a
n A r IA I c i n

B
GAUGE *2
J '" *

20
I-
- Is
105
z
C3
u
5
0

150




68
22.0
20.0
Total Pressure
18.0 Gauges
0M MINS
..................
20 MINS .... :>
m 04. o-------- 210 MINS
-J _300 MINS
12.0 7
10.0
15.C 14.0 13.C 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0
DISTANCE (m)
Figure 5.4: Time-variation of water-mud interface along the flume, Test 4E9
5.2.5 Total and Pore Water Pressures
Wave-averaged total and pore water pressures are shown in Figure 5.6. As indicated in Section 3.3.3, the total pressure gauge elevations did not match precisely with those of the pore pressure gauges, hence interpolation had to be used to calculate the value of the total pressure at exactly the same level at which the corresponding paired pore pressure gauge was located.
At the beginning, when wave action was started, the pore water pressure at a given elevation was equal to the corresponding hydrostatic pressure. Then under wave action an excess pore water pressure generally developed. In those cases in which the pore pressure curve intersected the total pressure curve, fluidization was considered to have occurred in




18.0
10. T0 MINS 16.0 100 MINS 11.0 12.0 10.0 8.0 6.0 1.0 2.0 0.0
1.00 1.05 1.10
DENSITY

1.15s 1.20 1.25
(G/CMw3)

1.00 1.05 1.10 1.15 1.20 1.25
DENSITY (G/CMM3)

18.0 16.0 380 MINS 1q.0 12.0 10.0 8.0 6.0
2.0 0.0
1.00 1.Os 1.10 1.15 1.20 1
DENSITY (G/CM)3)

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

320 MINS




70
accordance with Figure 2.4. Note that the total pressure was also obtained independently from the density profiles, and these had to be used to "'calibrate" for the total pressures in cases where the gauge data exhibited significant drift problems. Problems of instrument related drift noted in Section 3.3.3 (Chapter 3) are apparent in most cases in Figure 5.6. Drift generally caused both types of pressures to change over a time-scale that was much larger than the wave period, thus compromising the accuracy of determining the time at which fluidization occurred. The pore pressure data points at 14cm elevation dropped below the hydrostatic value which is unrealistic, and suggests a serious instrument problem. Note that with the exception of the gauge pair at 14cm elevation, all the gauges showed a response that suggested a drift that seem to cause the pressure to rise for the first 100-150 mins followed by a drop. This uniform behavior suggests that the drift problem may have been, at least in part, associated with the data acquisition system excluding the gauges themselves.
At this point it is worth considering the range of variation in total pressure that would have resulted from a change in the interfacial elevation during the course of the test. 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 LEVEL=I4CM
1.90 E) PORE PRESSURE
1.60 -1 TOTAL PRESSURE
1.30 E FROM DENSITY
1.00
2.32 LEVEL=12CM
2.29 2.26
2.23 2.20 2.65
LEVEL=9.5CM
2.60
oL 2.55
2.50 LIJ
2.45
n ~LEVEL=7.SCM
LU 2.80
CL
2.75

2.70
2.65
3.15 3.10
3.05 3. 00
2.95
2.90 3.40 3.35
3.30 3.25
3.20
3.15
3.10
0

LEVEL=5. 1CM LEVEL=3.1CM t100oo 200 300 400 500 60
TIME (MIN)

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




4.00
r_ 3.80 "- 3.60
V1) 3.'40 -1 FROM GAUGE
LJ
El FROM DENSITY
C
3.20
3.00 I
0 100 200 300 '400 Soo 600
TIME (MIN)
Figure 5.7: Total pressure at the bottom of the flume, Test #9
Section 5.2.3. When the top of the bed was fluidized, which thus became a suspension, the mud moved back again to level out the bed surface.
This result from the total pressure measurement was very consistent in the first 200 mins, with the phenomenon shown in Figure 5.4 in Section 5.2.3. which shows that the pressure data dropped in the first 40 mins, then started to increase slightly. However, after 200 mins, it dropped again.
5.2.7 Rms Pressure Amplitudes. Test #9
Root-mean square (rms) amplitude pressure is obtained from
Pm3 = ( P)2 (5.1)
where Pi is the instantaneous pressure, P is 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.S 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




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 fluidizaton occurred are given in Table 6.6, Section 3.2 of Chapter 6). Finally, it can be concluded that the amplitudes in the lower levels of mud layer had smaller values than at higher elevations, presumably because the wave amplitude decreased as the dynamic pressure was transmitted and dissipated downwards into the bed.
5.2.8 Pressure Recovery after End of Test
In test #9, pressure data were obtained after wave action ceased. The corresponding effective stresses are calculated and discussed in Section 6.3.1.




120.0
:
U-)
Li 60.0 a
30.0
0
120.0

50 100 150 200 250
TIME

300 350 (MIN)

400 450 500 550

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

50 100 150 200 250 300 350 400 450 500 550
TIME (M IN)

90.0 60.0 30.0
0

S7.5CM
- 5 ICM
-0--- 3. ICM
I I I Ili




120.0
90.0
Cr
r-0
LUJ 60.0
0.
30.0
0

50 100 150 200 250 300 350 q00 450 500 550 600
TIME (MIN)

Figure 5.9: Root-mean square total pressure amplitudes, Test #9

50 100 150 200 250 300 350 400 450 500 550 600 TIME (MIN)

CI
0 90.0
LU
U-) L- 60.0
CC

30.0
0




CHAPTER 6
EXPERIMENTAL DATA ANALYSIS
6.1 Introduction
In this chapter, results are presented, based on the wave-mud interaction (introduced in Chapter 4), which were applied to calculate the effective sheared thickness, d, as a possible representative of the fluidized mud layer thickness, as well as the rate of energy dissipation, ED (also from Chapter 4). The pressure data are then analysed to determine the fluidized mud thickness, df, and the rate of fluidization. The two types of thicknesses, d and df, are then compared, and the relationship between the rate of fluidization and the rate of wave energy dissipation, ED, is examined.
6.2 Wave-Mud Interaction Model Results
6.2.1 Wave Regime: Test Versus Model Conditions
As noted in Chapter 4, the wave-mud interaction model is based on the shallow water assumption, i.e., H1/L < 0.05, where L is the wave length,which was obtained from the linear wave dispersion equation (assuming rigid bed condition): L = gT2 tanh 2rHj (6.1)
27r 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 H1/L for the present experiments. As observed the test condition was not really shallow water according to this classification. There are two different types of effects on the model-based results due to shallow water assumption. Firstly, in the shallow water model the particle horizontal velocity is assumed to be uniform in the z direction in the water column. When waves are not in the shallow water regime this velocity decreases downwards from the water surface, so that near the bottom of the water column




Table 6.1: Parameters for determining the water wave condition
Test # HI L H1/L
__ _(cm) (in)
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, "0, to calculate viscosity, /1, by the power-law
equation for viscosity, i.e., by Equation 4.13 (I = a,, + 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, kiexip, can be obtained from H#2 = H#1ezp(-kie.,pAl), via Equation 4.11,
where H#1 is the wave height at gauge #1 and H#2 the height at gauge #2.
4. When ki obtained from step 2 "matches" ki, ep obtained from step 3 by iterating for
- ,i.e., I (kiEq.4.11 kiEq.4.9) < 0.01 1, the selected -, is assumed to be right, or a new is chosen for Equation 4.13 and the above procedure repeated until ki and ki p
match.
One example of the calculation for test #9 is given here. The input parameters are: = 4.44Pa.s, c = 0.76, n = -1.083, water density, p, = lg/cm3, mud density, P2 = 1.17g/cm3 (representative depth-mean value), distance between two gauges Al = 5.3m, average bed thickness within the test section, H2 = 16.7cm, water column depth, H, = 35 H2 = 18.3cm, a = 2r/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 i.t = 611Pa.s, which in turn was used in Equation 4.9 to calculate the wave dissipation coefficient ki that agreed with the one from experimental data obtained from Equation 4.11. The wave-induced horizontal velocity in the mud layer (surface) was determined by Equation 4.12, which together with Equation 4.14 gave the effective sheared thickness d = 6.6cm.
Table 6.2 gives the input parameters for all the tests. The wave heights H#1 and H#2, and the test section-average mud thickness H2 changed with time, i.e., they were not constant within each test. Therefore these parameters are not given in the table. Note




Table 6.2: Input parameters for calculating the effective sheared mud thickness Test # Poo, c n fill
I____ (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 J 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




1I.0
5 cm 7.7 cm
12.0 2 cm 4 cmm
100 A e

0 Mcdel Output
- Polynomial Fit
- TEST :1

50 100 150 200 250 30C
b
e
DE)) TEST a2
' 0

so
TIME (MIN)

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

0.0 2.0
E
U 1.0
lii
Z O.
z I00
0.0

.

-




3000

100 200 300 400
TIME (MINI

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

- 12.I
(f)
c 8.0 U0
Z 6.0
4.0 2.0
0.0

12 0

TT
TEST aE
100 5 2 0

0

o.
U 10. C')
(f 8.0 Z 6.0
4.. 0
-- 2.0

B
E)o E)) lz
- ~
) ee ee
0TEST 5
TEST =5
I II II

0.0

100 200 300 400 500 600

11.7
9.8 7.8 5.9 3.9
2.0

S11.7
U
9.8
Cr)
C 7.8 LLJ
z 5.9
U)
S3.9
S2.0

0.0
0

0

0

1000

1500

2000

2500

700 800




6.0
5.0
CO
U-) u-r 4.0
0.0
0
-' 9.8
7.8
Co
O") L.J 5.9
z U 3.9
S2.0
0.0
0
13.7 11.7 C) 9.8 U)
LU 7.8
z
5.9
3.9
2.0 0.0
0

400 600 800 1000 1200 1400
TIME (MIN)

1600 1800

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

TS
TEST ::8

100 200 300 400 51

5.0 Cr)
() 4.0 z 3.0 S2.0 l- .0

D
-TEST I I
I -- I- f

0 200




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

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 ED,, 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, k1, which have been plotted as functions of time for test #9 in Figure 6.7 for further discussion. At the beginning of wave action, the bed had greater rigidity, ki was comparatively small (although much higher than the representative value 0.02 s-1, that can be derived from the flume charaterization tests using a false rigid bottom described in Section 3.4), and although the wave amplitude was higher, the product of ki and a, .2 was still comparatively small. As the fluidization process went on, there was more fluid mud involved in the energy dissipation process, and ki increased rapidly, which in turn increased ED eventhough a_decreased. Thus more wave energy dissipation occurred when the fluidized mud thickness increased, but there was apparently a limit to it corresponding to a constant value, as the fluid mud thickness approached a constant value as well.

Test No. d,
______(cm) s-1 or Hz (Pas)
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 1750
9 6.1 0E03 630
10 9.2 0.037 575
11 2.8 0.036 600