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A LABORATORY STUDY OF FINE SEDIMENT RESUSPENSION BY WAVES
By
EDGAR EDUARDO CERVANTES
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
1987
ACKNOWLEDGEMENTS
I would like to express my heartfelt thanks to my advisor and supervisory committee
chairman, Dr. Ashish J. Mehta, Associate Professor, for his guidance and support through-
out my study at the University of Florida. My thanks are also extended to Dr. Donald
M. Sheppard, Professor, and Dr. James T. Kirby, Assistant Professor, for serving on my
committee and for their encouragement and advice.
My sincere thanks go to my research partner and friend, Mr. Mark A.Ross, for his
personal encouragement and technical assistance in all aspects of this research. Special
thanks are extended to Dr. Chung-Po Lin for spending his time answering endless questions.
Finally, I would like to thank my wife, Maria Isabel, for her love, support, patience,
and understanding during this new phase of my. life.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ......
. . . . . ii
LIST OF TABLES
.. v
LIST OF FIGURES .................. .................. vi
LIST OF SYMBOLS .. ........... ........................ viii
ABSTRACT ............. ............ ............... x
CHAPTERS
1 INTRODUCTION ............. ..... ....... ......... 1
1.1 Significance of the Study ... .......... ................ 1
1.2 Resuspension of Cohesive Sediment Beds .. .... .. ............ 2
1.3 Objective .... ........... ............... ....... 3
1.4 Outline of Upcoming Chapters ... ....... ............... 3
2 BACKGROUND AND THEORETICAL FORMULATION ............ 4
2.1 Introduction .......... ... .... ..... ........ ..... 4
2.2 Previous Studies ..... .. .. .......... ............. 4
2.3 Problem Formulation ... .... .... .. ... ... .......... 10
2.3.1 Time-variation of Concentration .................... 10
2.3.2 Steady State Value of ........ ........ ........ 17
3 EXPERIMENTAL SET-UP ............................. 19
3.1 Introduction ........ ..... ... .......... ......... 19
3.2 Wave Flume .......... ... ..... ........ .......... 19
3.3 Instrumentation ........ ... ...... ... .. .... ....... 22
3.3.1 Suspended Sediment Sampling ..... ................... 22
3.3.2 W ave Gauges ...............................
3.3.3 Bed Sampler ..............
3.4 Sediment ....................
3.5 Procedure ....................
3.5.1 Preliminary Test Procedure . .
3.5.2 Test Procedure .............
3.6 Other Experiments ...............
3.7 Summary of Tests Conditions . . .
4 RESULTS ......................
4.1 Introduction ...................
4.2 Suspended Sediment Concentration Profiles
4.3 The 6 Function .................
4.4 Time-variation of Concentration . .
4.5 Steady State Value of f ............
4.6 Influence of the Settling Velocity on the Time-
5 SUMMARY AND CONCLUSIONS .......
APPENDICES
SETTLING VELOCITY ..............
BIBLIOGRAPHY .................. .
BIOGRAPHICAL SKETCH . . . .
......
......
. . .
......
......
-variation
......
. . . 22
. . . 22
. . . 24
. . .. 24
. . . 24
. . . 25
. . . 26
. . . 27
. . . 26
.......... 27
.......... 27
. . . 27
.......... 27
. . 33
. . 43
' Concentration 45
. . . 4
LIST OF TABLES
Test Conditions ................. ... ............. 26
Summary of Test Results .......................... 40
LIST OF FIGURES
2.1 Suspended Solids and Bed Shear Stress for a Wave Resuspension Test
(After Alishahi and Krone, 1964). . . . ... .... 5
2.2 Wave Flume and Suspended Sediment Sampler (After Thimakorn, 1980). 7
2.3 Regional Distribution of Vertical Distribution Factor, E, and Settled
Mud Deposits for a) Spring Tide and b) Neap Tide in the Severn Estuary,
United Kingdom (After Kirby, 1986). . . . . 9
2.4 Vertical Concentration Field under Waves . . . ... 11
2.5 Typical Time-variation of Suspended Sediment Concentration. . 14
2.6 Schematic Variation of f with Time. . . . . ... 15
2.7 Time-variation of f Components. . . . ..... 16
3.1 Wave Flume and Mud Bed Configuration for Test C-1 (not Drawn to
Scale) . . . . . . . . .. 20
3.2 Wave Flume and Mud Bed Configuration for Test C-2 (not Drawn to
Scale) . . . . . . . . .. 21
3.3 Suspended Sediment Sampler . . . . .... 23
4.1 Suspended Sediment Concentration Profiles for Test C-1 at Station C. 28
4.2 Suspended Sediment Concentration Profiles for Test C-2 (T=1 sec.) at
Station C.................... .............. 29
4.3 A-variation with t for Tests C-l, C-2 (T=1 sec.), and C-2 (T=2 sec.). 31
4.4 4-variation with t for Tests T-1 and T-2. . . . .... 32
4.5 Normalized Suspended Sediment Concentration as a Function of the
Normalized Duration for Test C-. . . . ..... 34
4.6 Normalized Suspended Sediment Concentration as a Function of the
Normalized Duration for Test C-2 (T=2 sec.). . . . ... 35
4.7 Normalized Suspended Sediment Concentration as a Function of the
Normalized Duration for Test C-2 (T=1 sec.). . . .... 36
4.8 Normalized Suspended Sediment Concentration as a Function of the
Normalized Duration for Test M ....................... .37
4.9 Normalized Suspended Sediment Concentration as a Function of the
Normalized Duration for Test T-1. ................... .. 38
4.10 Normalized Suspended Sediment Concentration as a Function of the
Normalized Duration for Tests Y-1 and Y-2 . ......... 39
4.11 Schematic Plot of Time-Concentration Relationship. . . .... 41
4.12 fo versus Bed Shear Stress, Tb. . . . ..... . .. 44
4.13 Settling Velocity Effects on Suspended Sediment Concentration by Chang-
ing L. ................... ................ 46
4.14 Settling Velocity Effects on Suspended Sediment Concentration by Chang-
ing a ................... ................ 47
A.1 Settling Velocity against Concentration for Tampa Bay Mud...... .. 51
LIST OF SYMBOLS
C Suspended sediment concentration
C Depth-averaged concentration
C Depth-and wave period-averaged suspended sediment concentration
C Normalized concentration
Co Reference suspended sediment concentration
Cb Suspended sediment concentration at reference level z = zo
Cbf Final steady state suspended sediment concentration near the bed
C, Steady state suspended sediment concentration
Dab Molecular diffusion coefficient
E Vertical turbidity distribution factor
fw Wave friction factor
H Wave height
h Water depth
K Dimensionless coefficient
L Constant coefficient
m Empirical constant
T Wave period
t Time
t Normalized time
u Velocity in the z-direction
Ub Bottom wave induced velocity
w Velocity in the z-direction
W, Settling velocity of the particles or flocs
W,, Settling velocity evaluated at reference level z = zo
x Horizontal position coordinate
z Vertical elevation coordinate
zo Reference level
a Constant coefficient
6 Ratio of the concentration at reference level z = zo to the depth-averaged
concentration
Po Steady state value of f
ft Empirical coefficient
Pm Maximum value of P
6 Normalized f
81 Empirical coefficient
82 Empirical coefficient
Eo Diffusion coefficient at reference level zo
es Turbulent diffusion coefficient in the x- direction
ex Turbulent diffusion coefficient in the z- direction
A Wavelength
r1 Water surface elevation
7' Water surface elevation measured from the bottom
p Density of the fluid
8 Normalized time
TI Bed shear stress
r, Bed shear strength
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
A LABORATORY STUDY OF FINE SEDIMENT RESUSPENSION BY WAVES
By
EDGAR EDUARDO CERVANTES
August 1987
Chairman: Dr. Ashish J. Mehta
Major Department: Coastal and Oceanographic Engineering
Resuspension or erosion is a key factor in the cycling of fine cohesive sediment in
estuaries. The focus of the present study was to study the behavior of wave-resuspended
flocculated fine sediment beds by examining the time-response of the suspended sediment
concentration. Erosion tests were conducted in a flume using mud from Tampa Bay, Florida.
Five additional experimental results, from three different investigations, were also analyzed.
The suspended sediment concentration profiles showed the existence of a high concen-
tration layer near the bed, and the attainment of a steady state concentration after a long
time on the order of hours. The time-variation of the ratio between the concentration
near the bed and the depth-averaged concentration, P, was reproduced by an empirical
relationship. The trend of the time-variation of the depth-averaged suspended sediment
concentration was found to follow a theoretical relationship based on the mass transport
equation, using the empirical 6 function as well as a relationship between the sediment
settling velocity and concentration. The agreement between data and computed results
was found to be acceptable. Mass erosion, settling, and surface erosion were identified as
the dominant processes during the time-variation of the concentration. The coefficient ,o
defining the 6 function was found to increase with increasing values of the bed shear stress.
Values of 6 at the steady state, computed theoretically and from experimental results, were
found to have the same order of magnitude. It was found that the time-variation of the
suspended sediment concentration is affected in a significant way by changing the settling
velocity.
CHAPTER 1
INTRODUCTION
1.1 Significance of the Study
The rapid development of harbors, the construction of navigation channels, reclamation
of land, and the growth of centers of population and industry along the estuarine banks
and muddy coastal zones, together with concern for the protection of the environment, has
increased the interest in understanding fine, cohesive sediment transport mechanics. The
tendency of cohesive sediments to deposit in navigation channels, basins such as harbors
and marinas, and behind pilings placed in water, makes it necessary to accurately estimate
the volume of material to be dredged in order to maintain minimum navigable depths, and
to predict the consequences of new construction or dredging. Mud banks can be found near
many coastlines of the world, from the equator to the frozen latitudes of the Arctic. These
mud beds occur in the intertidal and subtidal zones of major rivers, which are the source of
the sediment found in the mud banks. Good examples are the Mississippi and the Amazon
rivers which supply mud to the shorelines of Louisiana and French Guiana, respectively
(Wells, 1983).
Increasing the suspended load via resuspension, and therefore the turbidity, reduces
light penetration in the water column and may result in a reduction in the production of
phytoplankton, which is the first step in the marine food chain. Resuspension may modify
the water quality by the release of chemicals, pore water and nutrients, as well as provide
a transporting mechanism for dissolved and suspended pollutants (Nichols, 1986).
The two main agents for the transport of mud in these areas are currents and waves.
While currents both resuspend and advect the suspended material, the role of waves is
mainly to resuspend the sediment which may then be transported by currents. This lab-
2
oratory study was mainly concerned with the erosion behavior of mud beds subjected to
waves. The main issue examined were the physical factors which influence the time-rate of
change of the suspended sediment concentration during the resuspension process.
1.2 Resuspension of Cohesive Sediment Beds
Cohesive sediment consists primarily of silt and clay, with particles of sizes less than 60
microns. Muds may in addition include organic matter, biogenous detritus, waste materials
and sometimes small quantities of very fine sand. A significant characteristic of cohesive
sediments is that the forces between cohesive particles are dominated by physico-chemical
properties and, in general, are orders of magnitude stronger than the gravity force due to
the submerged weight. Additionally, the presence of minimum amounts of ionic constituents
such as salt (1-3 parts per thousand) causes the particles to flocculate and form much larger
aggregates when brought together by collisions in turbulent shear flow. Each aggregate may
contain thousands or even millions of elementary particles, which suggests that the studies
of erosional and depositional properties of cohesive materials should be made primarily
using these aggregated flocs rather than the individual particles.
Two modes of cohesive sediment erosion have been identified: 1) surface erosion, which
takes place by the removal of individual sediment particles or aggregates from the bed
surface, and 2) mass erosion, which is characterized by the removal of relatively large pieces,
or even a whole layer, of bed sediment. Unlike surface erosion, which is time dependent and
slow, mass erosion occurs rapidly.
Based on examinations of laboratory procedures, cohesive beds can be divided into two
classes (Parchure and Mehta, 1985): 1) Uniform beds, which possess approximately uniform
properties (e.g. density and shear strength) throughout the bed. This type of a bed results
from pouring a thick slurry of sediment and fluid in the flume, or by remodeling a previously
formed bed. 2) Stratified or nonuniform beds, in which the properties vary with depth.
These are formed by allowing suspended sediment to settle under low flow velocities or
under quiescent conditions. After deposition the bed undergoes gelling and consolidation,
3
which cause physical and chemical changes in the bed structure by dewatering and by
breaking and rearrangement of the aggregates. Gelling is complete within a few hours. For
relatively thin beds, the consolidation process can last from a few days to one or two weeks,
and the final thickness of the bed depends upon the initial sediment mass and the type
of sediment (Parchure and Mehta, 1985).All the laboratory tests (conducted and analyzed
from other investigations) for the present study were for cohesive beds belonging to the
second class.
1.3 Objective
The main objective of the present investigation was to study the resuspended sediment
behavior of soft (non-uniform) cohesive sediment beds under waves, and to determine the
most significant physical factors governing their behavior. Specifically, the time-response of
concentration of suspended sediment generated by monochromatic, non-breaking progres-
sive waves was studied. The tests were conducted in a flume at the Coastal Engineering
Laboratory of the University of Florida. This objective was met through the following tasks:
1) Beds composed of a natural mud were subjected to waves for several hours, and the re-
sulting suspended sediment concentration profiles were measured. 2) The time-response of
the depth-averaged concentration was examined via the vertical sediment mass transport
equation. 3) Data from three other experimental investigations, one of these using uni-
directional flows, were also analyzed in order to derive more general conclusions concerning
the applicability of the selected approach using the mass transport equation.
1.4 Outline of Upcoming Chapters
Chapter 2, in its first part, briefly reviews the relevant investigations on wave erosion
of cohesive beds. In the second part of this chapter the theoretical formulation of the
problem is presented. Chapter 3 describes the experimental apparatus, procedure, and
tests conditions. In Chapter 4, the results of the investigation are presented and discussed
in detail. Finally, Chapter 5 contains conclusions derived from the results.
CHAPTER 2
BACKGROUND AND THEORETICAL FORMULATION.
2.1 Introduction
In the first part of the chapter a review of previous studies on wave erosion is presented.
The second part is devoted to the theoretical formulation of the problem necessary for
interpretation of the results.
2.2 Previous Studies
Alishahi and Krone (1964) carried out one of the first experiments on the resuspension
of cohesive sediment by wind- generated waves. The sediment used for these experiments
was taken from Mare Island Strait, which is a part of the San Francisco Bay system. Two
experiments were conducted in a 18 m long wind-wave flume provided with a centrifugal fan.
The mud beds were 1.2 m in length and located at the downstream side of the flume. The
bed consolidation times were 38 hrs and 148 hrs for the first and second tests, respectively.
The average thickness of the beds was 1 cm. Suspended sediment samples, which gave the
depth-averaged concentration, were taken along the flume at intervals of 5 to 10 minutes.
Figure 2.1 shows the results obtained from the first experiment. From the tests the authors
demonstrated the existence of a critical wave induced shear stress necessary to suspend the
material at the bed surface, below which negligible erosion occurred, until the 4th hour as
seen in Figure 2.1. The authors also pointed out that there was a sudden loosening of
the bed and direct movement of sediment into suspension", which was responsible for the
increase of the suspended sediment concentration, as can be seen after 4.5 hrs in Figure 2.1.
Krone (1966) pointed out the significance of wave-suspended sediments in the transport
and deposition of fine sediment in the San Francisco Bay. He found that after the sediment
II
V) E
3
tnO C
-J'
ZCD
z C
0
TIME AFTER START OF EXPERIMENT(hrs)
Figure 2.1 Suspended Solids and Bed Shear Stress for a Wave Resuspension Test (After Alishahi and Krone, 1964).
6
enters the system during the winter river flows, they settle in the upper bay. Wind generated
waves, during the summer, resuspend the fine material which is transported by tidal and
wind driven currents throughout the system and eventually to the ocean.
Anderson (1972) investigated the effect of small amplitude waves on resuspending co-
hesive sediment in the Great Bay estuarine system of New Hampshire. Field experiments
were carried out in order to take tidal readings, wind speed and direction, wave height, and
suspended sediment water samples. He found a linear relationship between the wave height
(independent variable) and suspended sediment (dependent variable) at flood tide. For the
ebb tide such a relationship was not found. He also found that resuspension decreased as
the water depth increased at a given wave height. He concluded that resuspension by
small amplitude waves is an important process that introduces suspended sediment into the
estuarine water column".
Thimakorn (1980) performed a series of laboratory experiments in order to investigate
the resuspension of fine sediment by water waves. The sediment used was a clayey material
taken from Samut Sakhon River mouth, Thailand. The tests were carried out in a flume with
dimensions of 40 cm width, 60 cm depth, and 45 m length with a paddle type wave generator
at the upper end, see Figure 2.2. The mud bed was formed by uniformly distributing
the mud sample, previously rinsed with fresh water, over the length of the channel, and
allowing it to settle for two weeks. After this consolidation period the bed thickness was
2.5 cm. Thimakorn collected water samples at nine elevations at one location and the
suspended sediment concentration of the samples was obtained using a photo-transistor
sediment meter.
Thimakorn found a linear relationship between the bottom wave-induced velocity (Ub)
and the final, steady state concentration at the bed (Cbf). Thimakorn further found that the
maximum value of the normalized concentration, /m, which is the ratio of the concentration
at the bed to the depth-averaged concentration, can be related to the bed shear stress, rb,.
He concluded that during the erosion process a layer of suspension in the vicinity of the bed,
0.45m
T
0.60
i
---- 45m ---in
Figure 2.2: Wave Flume and Suspended Sediment Sampler. (After Thimakorn, 1980)
8
and another layer in the upper part of the wave-flow field, can be identified. Also identified
were the parameters of the acting forces including bed shear stress and the wave-induced
velocity, which affect the concentration field.
Maa (1986) investigated the influence of water waves on fine sediment beds. He devel-
oped a 2-D hydrodynamic numerical model to evaluate the bed shear stress at the mud-
water interface. The model computed velocity profiles, pressure, shear stress, and wave
attenuation coefficient for given non-breaking, regular, propagating waves. Laboratory ex-
periments were carried out in a wave flume to verify the model, and to study wave induced
erosion. The sediments used were a commercial kaolinite and an estuarine mud taken from
Cedar Key, Florida. With respect to the sediment concentration, Maa pointed out that
the concentration profiles are characterized by an upper layer (80% of the water column)
with relatively low concentrations and a high density lower layer near the bed. He also
concluded that the most significant features of the wave erosion process are bed softening
and fluid-mud (in the lower layer) generating capacity of waves.
Kirby (1986) and co-workers conducted an extensive study on suspended fine sediment
in the Severn estuary, United Kingdom. The regional distribution of mobile (horizontally
moving) and stationary (without horizontal movement) suspensions, mixing and settling
behavior of the sediment were studied. An important observation was that the erosion and
deposition potentials could be predicted by knowing the magnitude, variation, and distri-
bution of the vertical turbidity distribution factor, E, defined as the tidal mean ratio of the
suspended concentration at the bed to the depth-averaged concentration. The definitions of
E and #,r of Thimakorn (1980) are qualitatively similar; they differ from each other mainly
in the time scale used for averaging. E is tide averaged while #m is a wave averaged quan-
tity. Kirby noted that areas with high values of E would suggest regions where deposition
is likely, and areas with low E are likely to have erosion or non-deposition. Figure 2.3 shows
the distribution of E and that of the settled mud deposits. The highest values of E are
observed to coincide with locations of settled mud.
N 0 5 10
30' b 3* w
r K 110
2 20
20 / 2
2 Aeas of settled
-0 Contours of E
-S,
Neap Tide&
s30' b 3
Figure 2.3: Regional Distribution of Vertical Distribution Factor, E, and Settled Mud
Deposits for a) Spring Tide and b) Neap Tide in the Severn Estuary, United Kingdom
(After Kirby, 1986).
10
2.3 Problem Formulation
2.3.1 Time-variation of Concentration
The vertical concentration field under waves is shown schematically in Figure 2.4, where
Cb is the concentration at reference level z = zo, above the bed at z '= 0, )7 is the
instantaneous water surface elevation, h is the still water depth, H is the wave height,
C(z, t) is the instantaneous suspended sediment concentration, and C is the depth-averaged
concentration.
The two-dimensional turbulent mass transport equation may be expressed as
ac ac ac awC a c a ac
+ u- + = DABVC + -(eO + -a(-) (2.1)
Where u, w are the instantaneous fluid velocities in the z, and z directions, respectively,
W, is the settling velocity of the particles or flocs, DAB is the molecular diffusion coefficient
and cs and e, are the turbulent- diffusion coefficients in the z and z directions, respectively.
The two-dimensional equation of continuity for an incompressible fluid may be written
as
a- + a = 0 (2.2)
Tx az
After neglecting the molecular-diffusion coefficient and adding equation (2.2) (after
multiplying by C) to equation (2.1), the resulting equation becomes
aC auC awC 8W,C a ac a ac
+ --+ a( = X -) + (exz-) (2.3)
Depth-averaging equation (2.3) between zo and vr' = h+r and using Leibnitz rule yields
a a ra' an'I at'
(' zo)C + (f. uCdz) + C In, (w I,, t -
+W.C I,0 -WC ,' -wC IO = e dz + (e, ) i, -( ) 1 (2.4)
where the depth-averaged concentration, C, is defined as
S= ( C dz (2.5)
(17' -zo) .,
11
SWLL.
z \
=Z0
Z=O ._ ,
Figure 2.4: Vertical Concentration Field under Waves
h
12
Using the free surface kinematic boundary condition (w B u = 0) Ij, and
assuming the vertical velocity, w, at zo to be equal to zero, and that
auC 8wC a8 a 8 C
<< and T ) << (- (2.6)
jz az ,z 8) < z z(
The first of the above assumptions essentially implies at the same time that A- < --.
Then, equation (2.4) yields
S[(' zo) ] + (W,C) Io + e, ,, = 0 (2.7)
where the net vertical flux at the free surface (EzaT + WC) j'r, has been set equal to zero.
Averaging each term of equation (2.7) over several wave periods gives
aC aC
(h zo) - + (W,) Iz +(e6, ) Io= 0 (2.8)
where the symbol ~ stands for wave period average.
Introducing a coefficient, P, such that
(W.&) Io= X(TW ) (2.9)
and substituting equation (2.9) into equation (2.8) gives
(h- z) t + w, I + (ezz) 10o = 0 (2.10)
The settling velocity can be expressed as a function of concentration as (see appendix)
W. = W.( )L (2.11)
Co
where W,, and Co are reference settling velocity and suspended sediment concentration,
respectively, and L is an empirical constant. In choosing equation (2.11) for the present
purpose, the hindered settling effect, whereby W, actually decreases with C at high con-
centrations, has been ignored for simplicity of problem treatment.
Substituting equation (2.11) into equation (2.10) yields
( ac W, -L+1 aC
(h- z,) t +( )C + (E-z) I,= 0 (2.12)
at c~ O
13
Based on experimental results, the time-variation of the suspended sediment concen-
tration is found to be qualitatively similar to that shown in Figure 2.5, where a steady state
concentration, C,, is reached after a long period of time.
Experiments in laboratory flumes under wave-induced oscillating flows (Thimakorn,1980)
indicate a time-variation of P which is qualitatively similar to that shown in Figure 2.6,
where f, after an initial increase, reaches a maximum and later a constant value, /o. From
these results, / can be shown to follow the empirical relationship
P = o(1 e-t) + p/te-'t (2.13)
where P/ and 61 are empirical coefficients. In equation (2.13) the first term on the right
hand side is an exponential function which reaches a constant value, /o, after a long time,
see curve A in Figure 2.7. The second term is a function with a shape qualitatively similar
to the log-normal distribution, see curve B in Figure 2.7. The addition of these two terms
will result in a curve as the one shown in Figure 2.6.
Based on Figure 2.5 and equation (2.13), after a long time
a = 0 = C, = fo (2.14)
Applying these conditions to equation (2.12) then gives
/ c = C- a( ) I (2.15)
Substituting equation (2.15) into equation (2.12) gives
aC W,+ -_L+1 Wo -L+1
((h ) ) o( )-C, = 0 (2.16)
Selecting a dimensionless concentration
S= (2.17)
c,
and dimensionless time
S tw, (2.18)
h-zo
Figure 2.5: Typical Time-variation of Suspended Sediment Concentration.
TIME
Figure 2.6: Schematic Variation of / with Time.
Figure 2.7: Time-variation of P Components.
17
and substituting equations (2.17) and (2.18) into equation (2.16) yields
a + ( )( Ao) = 0 (2.19)
which is the desired mass transport equation.
2.3.2 Steady State Value of P
As pointed out (see equation (2.13) and Figure 2.6), the 6 function reaches a constant
value, Po, after a long time. This steady state value of f, as obtained from equation (2.13) is
an empirical constant. However, #o may also be evaluated from theoretical considerations,
as noted below.
For the steady state condition, applying the assumptions given in equation (2.6) and
considering settling as the only significant vertical movement in the flume, equation (2.3)
is reduced to
ac
WC + e- = 0 (2.20)
where the diffusion coefficient, e,, can be expressed as (Kennedy and Locher, 1972)
ez = Co(. )m (2.21)
zo
In equation (2.21), m is an empirical constant and eo is the diffusion coefficient at the
reference level zo. There appears to be no general agreement in the literature regarding
the variation of e. with respect to z. However, for oscillating flows, the observation of a
constant diffusion coefficient seems to be common as noted by Maa (1986). Therefore, for
the present investigation m was simply assumed to be equal to zero, which corresponds to
a constant e,. Additionally, the expression for e, under wave action was chosen as (Muir
Wood and Fleming, 1981)
KHX
ez =K (2.22)
where K is a dimensionless coefficient equal to 2.8 x 10-5, and H, A, and T are the wave
height, wavelength, and wave period, respectively.
Integrating equation (2.20) yields
W, (z- zo)
C e e (2.23)
where Cb is the concentration at the reference level zo and the settling velocity, W,, has
been considered to be independent of the suspended sediment concentration.
Depth averaging, equation (2.23) may be written
Wh Wz0
C _-A I -
C-= e e e ez (2.24)
WIzo
where A = e ez and h is the water depth.
If the settling velocity is assumed to be independent of the concentration, equation (2.9)
is reduced to
f = (2.25)
Then equation (2.24) can be expressed as
1
S= Wh W,zo (2.26)
h (e ez e e )
Equation (2.19), which describes the time-variation of the depth-averaged concentra-
tion, will be solved numerically and compared with experimental results obtained from the
laboratory tests. Equation (2.26) will be used to compute a theoretical value of f8 and
compare it with the one obtained by using equation (2.25) for test C-2.
CHAPTER 3
EXPERIMENTAL SET-UP
3.1 Introduction
The wave resuspension experiments were conducted at the Coastal Engineering Labo-
ratory of the University of Florida. This chapter describes the test facilities, instruments
and experimental procedures used. Two laboratory tests were carried out using mud taken
from Tampa Bay, Florida, as bed sediment. Additionally, five other laboratory data sets,
from three different investigations, were analyzed. Two of the five tests used kaolinite as bed
material and the remaining three used samples taken from Samut Sakhon River, Thailand,
in two cases, and one from Amelia River, Florida.
3.2 Wave Flume
The experiments were conducted in a plexiglass flume. Minor modifications were made
to the flume, which was originally designed for other purposes. The flume dimensions were:
length 20 m, width 48.5 cm, and height 45 cm. In order to generate regular progressive
waves, a plunging- type wavemaker was set at the upstream end of the flume. The wave
height and the period were adjusted by a D.C; motor controller. In order to hold the mud
bed, a trench was formed using a false bottom made of plexiglass. The trench bed length
was 8 m with slopes of 1 in 2 for the first experiment (C-1), see Figure 3.1. For the second
test (C-2), a bed length of 11.1 m with slope of 1 in 15 at the upstream end and of 1 in 18
at the downstream end was used, as shown in Figure 3.2.
Impermeable sloped beaches, with plastic doormat material at the top, were installed
at the upstream and downstream ends of the flume in order to damp water level fluctuations
produced by the wavemaker and to reduce wave reflection.
O Suspension Sampling Station
* Wave Gauge Location
S= 14.3 x = 12.3
8 @*
S= 9.2
@
z = 6.5
.
2 = 4.0
SWave maker
x = 13.3 x = b.3
Bed Sampling Station x
2=0
Dimensions in meters
Figure 3.1: Wave Flume and Mud Bed Configuration for Test C-1. (not Drawn to Scale)
O Suspension Sampling Station
* Wave Gauge Location
x = 14.2 x = 12.3 x = 9.2
@ @* @*
x = 6.5 x = 4.6
@6* (*
* Wave maker
x = 15.4 Bed Sampler Station x = 4.3 x
z=0
Dimensions in meters
Figure 3.2: Wave Flume and Mud Bed Configuration for Test C-2. (not Drawn to Scale)
22
3.3 Instrumentation
3.3.1 Suspended Sediment Sampling
Suspended sediment concentration was determined by gravimetric analysis of liquid
samples withdrawn at five locations (A, B, C,D, E) along the flume as shown in Figures 3.1
and 3.2. At each location, one sample was taken at five different vertical distances from the
mud bed using samplers of the type shown in Figure 3.3. All the samples were taken along
the center line of the flume. They were collected into 105 ml capacity plastic cups with
tight-fitting lids. The sample volume was approximately 50 ml. It should be pointed out
that any likely interference produced over the bed by the sampler was considered negligible.
Equipment used for the gravimetric analysis included a Millipore vacuum filtration
apparatus (flask, funnel, tubing, clamp, etc.), Millipore type HA 0.45 pm pore size filter
papers, drying oven, and a precision balance.
In addition to the concentration samplers, wave gauges were installed along the flume. A
data acquisition system was used to continuously register the data. The water temperature
was registered by visual readings. It was 25C for the first test and 19C for the second.
3.3.2 Wave Gauges
Four capacitance type wave gauges were installed along the flume centerline in order to
determine the mean wave height and period along the mud bed. The location of the wave
gauges for tests C-1 and C-2 is shown in Figures 3.1 and 3.2, respectively.
3.3.3 Bed Sampler
In order to determine the mud density, samples of 1 to 2 cm3 at predetermined elevations
were withdrawn at x = 9.2 m, see Figures 3.1 and 3.2, using a hypodermic syringe. The
dry density was obtained gravimetrically.
3.4 Sediment
The sediment used for all tests was a natural estuarine mud from Tampa Bay, Florida.
The mud was collected from the east side of the bay. The material was pumped from a
Pipe
CONCENTRATION
SAMPLER
Figure 3.3: Suspended Sediment Sampler
24
depth of about 6 m into two 200 liter drums on the boat's deck and transported to the
Coastal Engineering Laboratory. A hydrometer test indicated that the mud had a median
diameter of 2.5 pm and 38% of this material in size of silt and 60% in the range of clay.
Before using, the mud was processed as follows:
The mud was allowed to settle in the drums for about 4 days. Then, the overlaying
water was drained out and replaced by tap water. The drums, with the mixture of mud and
tap water, were shaken for about ten minutes in order to homogenize the mixture and the
material was then allowed to settle for another 4 days. This draining and remixing process
was repeated twice. It should be pointed out that although most of the salt was removed
from the sediment by the washing process, enough of it remained to flocculate the sediment.
The washed mud was pumped into a mixing tank before pumping it into the flume.
After the first test, the mud was transferred back to the mixing tank. Before the second
test, more mud, which was treated in the same way as the mud used in the first test, was
added to the material remaining after the first experiment.
3.5 Procedure
3.5.1 Preliminary Test Procedure
Before pumping the mud into the flume, two temporary partition walls were installed
at the two ends of the test section in order to prevent the mud from spreading out along
the entire length of the flume. The partition walls were removed one day before the tests.
The sediment was allowed to consolidate for five days for the first test and for three days
for the second. Tap water was used as the eroding fluid for both the tests.
3.5.2 Test Procedure
S Before the wavemaker was turned on, mud surface elevation and bed samples as well as
suspension samples were taken in order to obtain the initial conditions. The wavemaker was
then turned on to produce regular progressive waves. In the first test the wave loading was
\ maintained for 13.5 hours. In the second test the initial wave conditions were maintained
for 2.5 hours and then changed and maintained for 9 more hours. After 13.5 hours in the
25
first experiment and 11.5 hours in the second one, the wave generator was turned off and
the sediment was allowed to settle before pumping the material back into the mixing tank.
3.6 Other Experiments
As mentioned in section 3.1, data from five additional tests, collected from three inves-
tigations, were also analyzed in this investigation. This section describes the experimental
procedures used to carry out the above noted tests.
Maa (unpublished,1984) conducted a single experiment (M) of resuspension of fine
sediment in a recirculating flume, which was modified by installing a wave-generating paddle.
The flume dimension were: length 18.3 m, width 0.60 m, and depth 0.90 m. The water
depth was 0.17 cm with waves of 0.065 m height and a period of 1.9 sec. Suspended sediment
concentration was determined gravimetrically.
Two experimental data (T-1 and T-2) were taken from Thimakorn (1980). A description
of the experimental procedure was given in section 2-1.
Yeh (1979) conducted several laboratory experiments in order to investigate the resus-
pension properties of flow deposited cohesive sediment beds under a uni-directional turbu-
lent flow field. These experiments were carried out in an annular flume which consisted of
a rotating annular ring and an annular channel. Kaolinite and mud samples taken from
a marina near Fernandina Beach, Florida, were used as sediments. Salt water at ocean
salinity (3.5% by weight) and distilled water were employed as the eroding fluids. All the
tests were performed with the channel filled up to 30 cm and with mean bed sediment con-
centration of 4% by weight. Suspended sediment concentration samples were withdrawn at
different times by opening a valve located 22.2 cm above the bottom channel. The concen-
tration was obtained gravimetrically. Two data sets, one (Y-l) using kaolinite in salt water
with a bed shear stress of 0.23 N and the other (Y-2) using Fernandina mud in salt water
and a bed shear stress of 0.28 ;-, were analyzed in the present investigation in order to
compare the behavior of the time-variation of the suspended sediment concentration under
uni-directional flows with that under oscillating flows. It should be pointed out that the
uni- directional flow data of Yeh (1979) are compatible with a constant (depth-invariant)
diffusion coefficient as found for the annular flume by Mehta (1973).
3.7 Summary of Tests Conditions
Table 3-1 presents a summary of the conditions for the laboratory flume tests considered
in the present study.
Table 3.1: Test Conditions
Test Sediment Mean Bed Water Depth Temperature Wave Wave Test
Density height period duration
( ) (m) (CC) (m) (sec) (hours)
C-1 Mud 1.1 Fresh 0.16 25 0.06 1.0 13.5
0.03 2.0- 2.5
C-2 Mud 1.1 Fresh 0.18 19 0.03 2.0 2.5
0.07 1.0 9
M Mud 1.1 Fresh 0.17 0.07 1.9 7
T-1 Mud 1.7 Fresh 0.30 0.13 1.0 2
T-2 Mud 1.7 Fresh 0.30 0.09 1.5 2
Y-1 Kaolinite 1.1 Salt 0.27 23 200
Y-2 Mud 1.1 Salt 0.27 23 200
CHAPTER 4
RESULTS
4.1 Introduction
In this chapter, the erosion test results are presented and discussed. The concentration
profiles are analyzed. The time-variation of concentration computed from data is compared
with the results obtained by using equation (2.19). The coefficients fo, #1, and 61 are corre-
lated with the bed shear stress, ra. #o values, at steady state, are computed theoretically by
equation (2.26), and from data. The influence of the settling velocity on the time-variation
of concentration is investigated.
4.2 Suspended Sediment Concentration Profiles
Figures 4.1 and 4.2 show the suspended sediment concentration profiles for tests C-1 and
C-2, respectively, obtained at selected times at station C (Figures 3.1 and 3.2). These figures
clearly show the existence of a steep concentration gradient near the bed, which implies at
the same time the existence of a high concentration layer next to the bed. Additionally,
in both cases the attainment of a steady state is suggested by the occurrence of very close
concentration profiles at times 300 min and 360 min in test C-l and at times 475 min
and 535 min in test C-2. The concentration profiles in Figures 4.1 and 4.2 indicate a high
degree of density stratification due to sediment. The vertical gradient in density tends to
have a stabilizing effect on the flow, inhibiting vertical exchange processes. Dyer (1986) has
summarized the effects of density gradients on the flow field for uni-directional flows.
4.3 The f Function
The 6 function was defined previously in two different ways: 1) As the ratio of the
concentration at the reference level zo, Cb, to the depth-and wave-averaged concentration,
I I I I 1111 I
I I I I I 1I I 1
Mean Water Surface Elevation 30 cm
25 F
LEGEND TIME (min)
X 60
n 120
0 300
A 360
Initial Mud Bed
I I
Elevation at 11.5 cm
I I I I lll
I I I l rIi i' I
0.1 1 10
SUSPENDED SEDIMENT CONCENTRATION (Q)
Figure 4.1: Suspended Sediment Concentration Profiles for Test C-1 at Station C.
Me I Wate I SI I 31I I5
Mean Water Surface Elevation 31.5 cm
LEGEND TIME (min)
X 25
3 265
A 475
0 535
Initial Mud Bed Elevation 12.5 cm
*LU . W I I I1 1
0.1 1 10
SUSPENDED SEDIMENT CONCENTRATION ( )
Figure 4.2: Suspended Sediment Concentration Profiles for Test C-2 (T=1 sec.) at Station
C.
25 -
I I I 1111i I
20 .
15 F
..,. _
......
. I
30
C, see equation (2.9), and 2) By the empirical relationship expressed in equation (2.13).
The time-variation of f was examined through both methods as described in the following.
Suspended sediment concentration profiles were plotted for every station and time. Vi-
sual readings of the bed elevation were used to determine the bed location at every sampling
time. By knowing the concentration profile and the bed elevation, the concentration at any
level from the mud bed could be found. For tests C-1 and C-2 the reference elevation, zo,
was selected to be equal to 0.5 cm. This value corresponds to an elevation equal about 6%
of the flow depth, which is consistent with the usually recommended 5% (Dyer, 1986).
The values of the concentration at zo = 0.5 cm, Cb, at each station for a particular
time, were then spatially-averaged over the mud bed in order to obtain a representative
mean value of Cb for every sampling time. Concentrations obtained from the water samples
at selected times and locations were first depth-averaged over the water column and then
spatially-averaged over the mud bed. Then, with the values of bC and the depth-and wave-
averaged concentration, C, the values of f for a particular time were computed by using
the relationship
S= (C)L+ (4.1)
C
where equations (2.9) and (2.11) have been combined. f / (-3o i -\
The P values found from equation (4.1) were then plotted and equation (2.13) was
used in order to reproduce the trend of the experimental data. The values of the empirical
coefficients f1, and 61 were obtained by trial and error until the best fit with the data was
obtained. These coefficients can also be obtained by using a mathematical fitting procedure
involving a non-linear least squares regression.
In Figures 4.3 and 4.4, f = as a function of i = 6bt, based on equation (2.13) is
compared with the data from tests C-1, C-2 and T-l, T-2, respectively. Trend agreement
between the measurements and equation (2.13) appears to be reasonable. Although a steady
state was not fully reached during the first part of test C-2, the trend of the curve is clear.
For tests T-1 and T-2, Figure 4.4, the settling velocity was considered to be independent
K C-I
A C-2 (T1l SEC.)
n C-2 (T=2 SEC.)
C-2 (T=2 SEC.)
A W
NORMALIZED TIME ,i
Figure 4.3: 0-variation with 1 for Tests C-1, C-2 (T=l sec.), and C-2 (T=2 sec.).
o K T-1
o
a.
A T-2
0
O
( A
a M
o
= (1- e 61)+4 ie-
a
00oo ,'.oO 8.00 12.00 16.00 20.00 21.00 28.00
NORMALIZED TIME,i
Figure 4.4: /-variation with t for Tests T-1 and T-2.
33
of the suspended sediment concentration; therefore, L was set equal to zero. In this case
equation (4.1) becomes equal to equation (2.25).
At the beginning of the resuspension 6 rises rapidly, reaches a maximum, and then
approaches unity. This behavior may be explained by referring to the high concentration
layer near the bed with concentration Cb. The initial rise of P implies a high rate of storage
of suspended sediment mass in this layer. This storage occurs because the rate at which
the sediment enters the high concentration layer by bed erosion is greater than the rate at
which the sediment is entrained upward from the high concentration layer. With time, the
rate of erosion decreases as the shear strength of the soft, non-uniform bed increases and
the supply of sediment from the bed decreases. This increase in shear strength is due to the
fact that as the bed is scoured, the flow encounters lower bed layers of increasing density
and shear strength (Parchure and Mehta, 1985). Erosion stops eventually, when the shear
stress, rb, equals the shear strength, r,, and 6 attains a constant value, o,, at steady state.
4.4 Time-variation of Concentration
The time-variation of suspended sediment concentration may be obtained in two differ-
ent ways: 1) By solving equation (2.19) and 2) from experimental data.
Equation (2.19) with initial condition of 6 = 0 at 8 = 0 was solved numerically, after
including the empirical coefficients (Po, 1P, 61) defining 8 obtained as noted in section 4.3,
and compared with the experimental data. It was assumed that bed scour and associated
change in water depth did not alter the bed shear stress significantly. Also the effect of
suspended sediment concentration on the bed shear stress was assumed to be negligible.
In Figures 4.5 through 4.10, the normalized suspended concentration, C, as a function
of the normalized duration, 8, are compared with the experimental data. The oscillating
flow tests are shown in Figures 4.5 through 4.9. For test T-2, noted in section 4.3, the
time-variation of the suspended sediment concentration was not reported. The steady flow
tests Y-1 and Y-2 are shown in Figure 4.10.
The agreement between data and equation (2.19) may be considered to be acceptable for
0C
--:- r -----------
',0
z
Do
I--
z
LO
c:-
ho
8-
CD
0oa 20.00 0.00o 60.00 8b.00oo t10o.00o 120.00 10.00o
NORM. DURATION ,e
Figure 4.5: Normalized Suspended Sediment Concentration as a Function of the Normalized Duration for Test C-1.
Figure 4.5: Normalized Suspended Sediment Concentration as a Function of the Normalized Duration for Test C-l.
O
0
Do
I-.-0
CC
Zo
zUC
z
0
8-
o
0
Z
o
r'-
So00 20.00 40.00 60.00 80.00 100.00 120.00 140.00
NORM. DURATION,e
Figure 4.6: Normalized Suspended Sediment Concentration as a Function of the Normalized Duration for Test C-2 (T=2 sec.).
0
CM1
*o.
Z
0
0a
CE
I-
()
U
Z
0-
M M
3- n-i
ro
.0oo
20.00
ub0.00
60.00 80.00 100.00 120.00
NORM. DURRTION,e
Figure 4.7: Normalized Suspended Sediment Concentration as a Function of the Normalized
Duration for Test C-2 (T=1 sec.).
'
01
CD
0
-~f r*iH-i m -. -
CA
-I
60.00
NORM.
Figure 4.8: Normalized Suspended Sediment Concentration as a Function of the Normalized
Duration for Test M.
C3 C
a m- ^--
I n
El El
Y m n
I I I I I I 1 I
20.00 0.00 60.00.00 800 100.00 120.00 140.00 160.00
NORM. DURATION ,e
Figure 4.9: Normalized Suspended Sediment Concentration as a Function of the Normalized
Duration for Test T-1.
O
0
Oo
CE
z
LLo
(0
C-,
ZO
00
o
~3
Z
oC
CC
0
Y T-2
A T-2
to
40.00 80.00 120.00 160.00 200.00 2012.00 280.00
NORM. DURATION ,exo1
Figure 4.10: Normalized Suspended Sediment Concentration as a Function of the Normal-
ized Duration for Tests Y-1 and Y-2.
40
tests C-l, C-2 (T=1 sec), Y-l, and M. Tests T-1 and Y-2 showed somewhat less satisfactory
agreement, but equation (2.19) is indicative of the data trend. A coefficient 62 = 0.11 was
added to the last term of equation (2.13), which became -61St2, in order to improve the
agreement of Y-2 with equation (2.19). 62 = 1 was selected for all the other eases. For Y-2,
the use of 62 = 1 resulted in a large discrepancy between data and equation (2.19). Table
4-1 gives the tests analyzed and the empirical coefficients found. In this table the bed shear
stress for tests C-l, C-2, and M was computed by using the following equation
rb = fpfwUb (4.2)
2
where p is the density of the fluid, Ub is the maximum horizontal velocity near the bottom,
which can be evaluated using the linear wave theory, and f, is the wave friction factor. A
chart to evaluate f, can be found in Kamphuis (1975).
Table 4.1: Summary of Test Results
Test -r (;) C () () S6 (;e)
C-1 0.43 1.55 18.5 4.5 x 10- 5.5 x 10-
C-2 0.32 0.40 50.0 2.2 x 10- 9.0 x 10-4
(T=2 sec)______
C-2 0.50 0.90 48;0 6.0 x 10- 5.0 x 10-
(T=1 sec)
M 0.42 1.55 1.9 1.5 x 10- 1.3 x 10-3
T-1 0.17 13.6 3.2 4.0 x 10- 6.5 x 10-
T-2 0.12 12.5 1.1 6.0 x 10- 1.1 x 10-
Y-1 0.23 10.2 6.0 2.0 x 10- 1.7 x 10-
Y-2 0.28 2.4 1.2 9.0 x 102 5.9
For tests T-1 and T-2 the bed shear stress was computed from Thimakorn (1980). The
bed shear stresses for tests Y-1 and Y-2 were reported by Yeh (1979).
The time-variation of suspended sediment concentration in all the tests, except Y-2, is
found to be qualitatively similar to that shown in Figure 4.11 (Yeh,1979). In this figure
three different phases are noticed. The first period (P-I) is dominated by mass erosion,
0 Cs
0
z
o
I I
Z I
SI I
o I
O
0 1 I
Mass -- Settling --- ----- Surface Erosion Dominant
Erosion Dominant
Dominant I
I I
0 ta tb TIME,t
-IP-14-- P-ll P-Ill
Figure 4.11: Schematic Plot of Time-Concentration Relationship.
42
which takes place by removal of relatively large pieces, or even a whole layer, of sediment
within a short period. Referring to Figures 4.5 through 4.10, in all the tests the suspended
sediment concentration was observed to increase very rapidly within the first few seconds or
minutes; thus this period is hardly seen in the tests analyzed. Mass erosion occurs initially
due to the effects of inertia associated with flow start-up which generates an initial higher
shear stress, and also because the surficial layer at the bed typically possesses a low shear
strength.
During the second period (P-II), between times to and tb in Figure 4.11, the observed
change of the concentration is the result of two different processes: 1) surface erosion, which
is characterized by the removal of individual sediment particles or aggregates at the bed
surface, and 2) settling of some of the mass eroded during the first period. During the
process of mass erosion, large pieces of suspended bed material are subsequently broken up
by the turbulent shear flow into flocs of different strengths and settling velocities. Some of
these flocs will remain in suspension because of the small size, but the larger and stronger
ones will deposit because the shear stress is not high enough to break them up and keep
them in suspension. During the first part of the second period, the rate of settling of the
flocs is higher than the rate of surface erosion, thus producing a decrease in the suspended
sediment concentration until a temporary balance is reached at the lowest part of the curve.
Then surface erosion becomes dominant and the suspended sediment concentration increases
again until a steady state is attained (P-III). The behavior of the components A and B in
Figure 2.7 are also indicative of these trends. The A component is related to mass erosion
and settling while the B component is related to surface erosion.
A noteworthy feature of the time-variation of concentration is that the same behav-
ior is observed in tests under steady as well as under wave-induced oscillating flows, which
suggests that, at least qualitatively, it is apparently not very important to know what mech-
anism produces the shear stress in order to know the behavior of the suspended sediment
concentration.
43
An attempt to correlate the coefficient Pj, to the principal factor characterizing bed
erodibility, the bed shear stress was carried out. In Figure 4.12 the value of Po has been
plotted against the bed shear stress, rb, for the tests C-1, M, C-2 (T=1 sec), T-2, and T-1.
In this figure, fto seems to show a tendency to increase with increasing values of rb. The
scatter in the data could be due to the different kinds of sediment used in the experiments.
Additionally, the use of directly measured, bed shear stress instead of values of rb computed
using the linear wave theory, may reduce the scatter in the data. Also a more clear trend
would be expected to occur when the same sediment is used in the erosion tests under
different wave loads.
An increase in the bed shear stress implies a higher amount of suspended sediment
entering the high concentration layer near the bed and, therefore, higher values of f8o; see
section 4.3. At the same time, a high value of #o and suspended sediment would suggest a
higher potential for deposition. Conversely, low values of Po would imply a low depositional
potential, which agrees with the field observations made by Kirby (1986). The coefficients
Pi and 61, which are related to mass erosion, as noted previously, depend on the time-rate
of change of the bed shear stress in addition to its magnitude.
4.5 Steady State Value of f
As mentioned in section 2.3.2, &o may be found from experimental data using equation
(2.25) or by using analytically obtained equation (2.26). In both cases the settling velocity
has been assumed to be independent of the concentration. Po values computed through
equation (2.25) are given in Table 4.1.
3o, using equation (2.26), was computed for tests C-2. The diffusion coefficient, eV,
obtained from equation (2.22) was found to be equal to 2.3 x 10-6 I. The constant value
of the settling velocity, W,, was chosen to be equal to 0.02 ,, which corresponds to L = 0
in equation A.1 in the appendix. The analytical value of Po was computed to be equal to 14,
using a value of W = 0.87 cm-1 computed with the values of W, and e, noted above, while
a value of 16 was found from experimental results. Thus, there is a good agreement between
a value of 16 was found from experimental results. Thus, there is a good agreement between
I .
100
10
1
BED SHEAR STRESS 7b N
Figure 4.12: So versus Bed Shear Stress, 7r.
LEGEND
O C-1
A M
SC 2(T = Isec)
D T-2
T T-1
45
the analytical value of o, and the one obtained by using data. This means that the 8, value
can be estimated, at least in its order of magnitude, from theoretical considerations.
4.6 Influence of the Settling Velocity on the Time- variation of Concentration
In this section, the effect of the settling velocity on the suspended sediment concen-
tration is briefly investigated. In the derivation of equation (2.19), the settling velocity
was assumed to be dependent on the suspended sediment concentration and to conform to
equation (2.11).
In Figure 4.13, solutions to equation (2.19) are plotted for three different values of the
exponent L, with constant values of fo = 9.3, #1 = 4.6x10-2 sec-1, 61 = 6.5x10-4 sec-1
and C, = 1.6 f. The values of L chosen for this figure range from that corresponding to a
constant settling velocity (L = 0), up to a value of L = 2, which is higher than the maximum
reported, L = 1.37, by Burt (1986). The increase of L causes a lowering of the trough of
the curve and a decrease in the time to reach the steady state. A high value of L implies a
high value of W, and, therefore, a high downward mass flux. A larger downward mass flux
will balance the upward entrainment sooner than a smaller downward flux. Although, the
variation of a (see appendix) causes similar effects as the changes in L, these are much less
significant, as can be seen in Figure 4.14.
46
o
cc
L=2
uo
0=
z
S/\
o
00 20.00 40.00 60.00 80.00 100.00 120.00
NORM. DURRTION,e
Figure 4.13: Settling Velocity Effects on Suspended Sediment Concentration by Changing
L.
47
o
(u
= 0.002
0
z
CDC
0
9: = 00 0.
gN
roj
0
.O00 20.00 I0.00 60.00 80.00 100.00 120.00
NORM. DURATION ,e
Figure 4.14: Settling Velocity Effects on Suspended Sediment Concentration by Changing
CHAPTER 5
SUMMARY AND CONCLUSIONS
Due to the rapid development of human activities along the estuarine banks as well as
along muddy coastal zones, together with concern for the protection of the environment,
there is a need to understand fine, cohesive sediment transport processes. Among these
processes, resuspension plays a key role in the cycling of cohesive sediments, as well as
in biological productivity and in the chemical reactivity of estuaries. Unlike the erosion
behavior of cohesionless sediments, the influence of waves on the erosion of fine sediments is
not well known. In order to study the time-response of resuspended sediment concentration
of soft, cohesive sediment beds by waves, laboratory experiments were carried out in a
wave flume using mud samples from Tampa Bay, Florida as the bed sediment and tap
water as the eroding fluid. Additionally, five other laboratory data sets from three different
investigations were analyzed. Important conclusions derived from the results are as follows.
Suspended sediment concentration profiles showed the existence of a strong concentra-
tion gradient near to the mud bed and, therefore, the occurrence of a high concentration
layer of about 0.5 to 3 cm in thickness. Furthermore, a steady state with respect to the
concentration profile was observed to occur after a long (several hours) time.
The time-variation of f, defined as the ratio between the concentration at the reference
(near-bed) level, Cb, to the depth-averaged concentration, C, was found to rise rapidly at
the beginning, then reach a maximum, and finally approach a lower, constant value,o > 1.
This trend was found to be reproduced by the empirical relationship 6 = 3o(1 e-t) +
flte-61i, where 61, and 61 are empirical coefficients.
The trend of the time-variation of the depth-averaged suspended sediment concentration
could be reproduced by using equation (2.19) representing vertical mass transport due to
49
upward diffusion and downward gravitational settling. The agreement between data and
equation (2.19) was found to be acceptable in most cases. It was observed that the time-
concentration relationship is governed by three different physical processes. Initially the
dominant process is relatively rapid mass erosion. During the subsequent period, surface
erosion and settling of some of the mass eroded during the initial period are the dominant
processes. Finally, surface erosion is dominant in the last period at the end of which the
concentration attains a constant, steady state value.
The time-variation of the suspended sediment concentration under uni-directional flows
was found to follow the same mass transport-determined relationship (equation (2.19)) as
the one for oscillating flows, suggesting that, at least qualitatively, the behavior of the
suspended sediment concentration can be evaluated in the same way regardless of whether
the flow is oscillating or uni-directional.
The Po coefficient defining the f function was found to increase with increasing values
of the bed shear stress, which in turn implies higher values of P with higher bed shear stress.
High values of 6 imply high amounts of suspended sediment and, therefore, high depositional
potential as well. Lower 6 values, by contrast, would suggest low depositional potential.
These observations are in agreement with the field observations made by Kirby(1986).
The steady state value of 6, i.e. Po, computed from theoretical considerations was
found to be in reasonable agreement with the one obtained from experimental results. This
implies that &o may be estimated, at least approximately, from theory.
The settling velocity strongly affects the time-response of concentration. Thus, for
instance, an increase in the value of the settling velocity will mean a reduction in the
time to reach steady state. This is because of correspondingly higher downward mass flux
of sediment and a shorter time required to balance the upward flux of sediment due to
diffusion.
APPENDIX
SETTLING VELOCITY
The settling velocity of suspended cohesive sediment is function of, among other param-
eters, the suspended sediment concentration. Krone (1962) and Owen (1971) found that
the median settling velocity and the suspended sediment concentration follow the empirical
relationship
W, = aCC (A.1)
where a and L are empirical constants that depend on the sediment type and the turbulence
intensity of the flow. For the present investigation, the diffusion coefficient was found to be
on the order of 10-~ _, which is about the same as the kinematic viscosity of water, which
normally implies viscous flow or, in the present case a flow in the transitional range.
In order to investigate the variation of the settling velocity with the suspended sediment
concentration, several quiescent settling column tests were performed to estimate the me-
dian settling velocity of Tampa Bay mud at various concentrations. The experimental and
calculation procedures used here are described in detail by Lott (1986). In Figure A.1, the
values of the median (by weight) settling velocity obtained from the tests has been plotted
against the corresponding concentration. Using the least squares method to obtain the best
fit through the experimental points, the values of a and L are found to be W, = 0.02 C0386,
where C is in units of f and W, is in 1.
By taking a reference settling velocity, W,,, and its corresponding concentration, Co,
such that W,, = a CL, equation (A.1) can be expressed as
W, = W.o ( ) (A.2)
Sand C were taken equal to 0.02 and respectively,in the present study.
W,, and C. were taken equal to 0.02 SM and 1.1 ^, respectively,in the present study.
51
1 S ill I I I I f I
S0.1
0.01
1 10 100
CONCENTRATION (
Figure A.1: Settling Velocity against Concentration for Tampa Bay Mud.
Muir Wood, A. M., and Fleming, C. A., Coastal Hydraulics, Second Edition, John Wiley
and Sons, Inc., New York, 1981.
Nichols, M. M., "Effects of Fine Sediment Resuspension in Estuaries," Estuarine Cohesive
Sediment Dynamics, A. J. Mehta ed., Springer-Verlag, Berlin, Federal Republic
of Germany, 1986, pp. 5-42.
Owen, B. A., "The Effect of Turbulence on the Settling Velocities of Silt Flocs,"
Proceedings of 14th Congress of the IAHR, Vol. 4, Paris, France, 1971, pp. 27-
32.
Parchure, T. M., and Mehta, A. J., "Erosion of Soft Cohesive Sediment Deposits," Journal
of Hydraulic Engineering, ASCE, Vol. 111. No. 10, 1985, pp. 1308-1326.
Thimakorn, P., "An Experiment of Clay Suspension under Water Waves," Proceedings
of the 17th Coastal Engineering Conference, ASCE, Vol. 3, 1980, pp. 2894-2906.
Wells J. T., "Dynamics of Coastal Fluid Muds in Low-, Moderate-, and High-tide-
range Environments," Canadian Journal of Fisheries and Aquatic Sciences, Vol.
40, Supplement No. 1, 1983, pp. 130-142.
Yeh, H.-Y., Resuspension Properties of Flow Deposited Cohesive Sediment Beds, M.S.
Thesis, University of Florida, Gainesville, Florida, 1979.
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