• TABLE OF CONTENTS
HIDE
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 List of symbols
 Abstract
 Introduction
 Background and theoretical...
 Environmental set-up
 Results
 Summary and conclusions
 Settling velocity
 Bibliography (p.52 missing)






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 87/010
Title: A laboratory study of fine sediment resuspension by waves
CITATION PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00076162/00001
 Material Information
Title: A laboratory study of fine sediment resuspension by waves
Series Title: UFLCOEL
Physical Description: xi, 54 leaves : ill., (1 col.) ; 28 cm.
Language: English
Creator: Cervantes, Edgar Eduardo, 1956-
University of Florida -- Coastal and Oceanographic Engineering Laboratory
Publication Date: 1987
 Subjects
Subject: Suspended sediments -- Mathematical models   ( lcsh )
Beach erosion -- Mathematical models   ( lcsh )
Sedimentation and deposition   ( lcsh )
Sediment transport   ( lcsh )
Coastal and Oceanographic Engineering thesis M.S
Coastal and Oceanographic Engineering -- Dissertations, Academic -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (M.S.)--University of Florida, 1987.
Bibliography: Includes bibliographical references (leaves 52-53).
Statement of Responsibility: by Edgar Eduardo Cervantes.
General Note: Typescript.
General Note: Vita.
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
Bibliographic ID: UF00076162
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: oclc - 17886139

Table of Contents
    Title Page
        Title Page
    Acknowledgement
        Acknowledgement
    Table of Contents
        Table of Contents 1
        Table of Contents 2
    List of Tables
        List of Tables
    List of Figures
        List of Figures 1
        List of Figures 2
    List of symbols
        Unnumbered ( 8 )
        Unnumbered ( 9 )
    Abstract
        Abstract 1
        Abstract 2
    Introduction
        Page 1
        Page 2
        Page 3
    Background and theoretical formulation
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
    Environmental set-up
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
    Results
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
    Summary and conclusions
        Page 48
        Page 49
    Settling velocity
        Page 50
        Page 51
    Bibliography (p.52 missing)
        Page 53
Full Text


















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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