• TABLE OF CONTENTS
HIDE
 Title Page
 Table of Contents
 Lecture 1. Characteristics of cohesive...
 Lecture 2. Settling, desposition...
 Lecture 3. Erosion
 Lecture 4. Resuspension by...
 Lecture 5. Vertical structure of...
 Lecture 6. Sedimentation probl...
 References Lectures 1-6






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 88/007
Title: Estuarine and coastal cohesive sediment transport
CITATION DOWNLOADS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00076152/00001
 Material Information
Title: Estuarine and coastal cohesive sediment transport notes for overhead slides
Series Title: UFLCOEL
Physical Description: 1 v. in various pagings : ill. ; 28 cm.
Language: English
Creator: Mehta, A. J ( Ashish Jayant ), 1944-
University of Florida -- Coastal and Oceanographic Engineering Dept
He hai da xue (Nanjing, Jiangsu Sheng, China)
Publisher: Coastal and Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1988?
 Subjects
Subject: Sediment transport   ( lcsh )
Sedimentation and deposition   ( lcsh )
Coastal and Oceanographic Engineering thesis M.S
Coastal and Oceanographic Engineering -- Dissertations, Academic -- UF
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Includes bibliographical references.
Statement of Responsibility: by Ashish J. Mehta for Dept. of Ocean and Waterway Engineering, Hohai University, Nanjing, The People's Republic of China.
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: UF00076152
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 - 19899866

Downloads

This item has the following downloads:

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )

PDF ( PDF )


Table of Contents
    Title Page
        Title Page
    Table of Contents
        Table of Contents 1
        Table of Contents 2
    Lecture 1. Characteristics of cohesive sediments
        Page 1
        Page 2
        Page 3
        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
    Lecture 2. Settling, desposition and bed formation
        Page 1
        Page 2
        Page 3
        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
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
    Lecture 3. Erosion
        Page 1
        Page 2
        Page 3
        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
        Page 19
        Page 20
        Page 21
        Page 22
    Lecture 4. Resuspension by waves
        Page 1
        Page 2
        Page 3
        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
    Lecture 5. Vertical structure of concentration profile
        Page 1
        Page 2
        Page 3
        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
        Page 19
        Page 20
    Lecture 6. Sedimentation problems
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
    References Lectures 1-6
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
Full Text






ESTUARINE AND COASTAL COHESIVE SEDIMENT TRANSPORT

NOTES FOR OVERHEAD SLIDES


Ashish J. Mehta


for


Department of Ocean and Waterway Engineering

Hohai University, Nanjing

The People's Republic of China





























Coastal and Oceanographic Engineering Department

University of Florida

Gainesville, Florida


L









TABLE OF CONTENTS


LECTURE

1 CHARACTERISTICS OF COHESIVE SEDIMENTS.............

1 SIGNIFICANCE ..................... .............

2 MUDDY COASTS ..................................

3 ESTUARIES.....................................

4 SEDIMENT CHARACTERIZATION.....................

2 SETTLING, DEPOSITION AND BED FORMATION.............

1 SIGNIFICANCE ...................................

2 SETTLING ................ ......... ... ........

3 SETTLING VELOCITY.............................

4 PARTICLE SORTING BY DEPOSITION.................

5 RATE OF DEPOSITION .... .....................

6 BED FORMATION .................................

3 EROSION...........................................

1 SIGNIFICANCE ..................................

2 RATE OF EROSION................................

3 SHEAR STRENGTH AND DENSITY....................

4 A PRACTICAL EROSION RELATIONSHIP...............

5 ENTRAINMENT.............. .....................

6 ORDER OF AGGREGATION AND TRANSPORT .............

4 RESUSPENSION BY WAVES .......................... ..

1 SIGNIFICANCE. .................................

2 BACKGROUND ....................................

3 DYNAMICS OF MUD-WATER SYSTEM ...................


PAGE

1-1

1-1

1-5

1-6

1-13

2-1

2-1

2-5

2-7

2-13

2-15

2-20

3-1

3-1

3-4

3-14

3-15

3-18

3-20

4-1

4-1

4-4

4-9










LECTURE PAGE

5 VERTICAL STRUCTURE OF CONCENTRATION PROFILE....... 5-1

1 SIGNIFICANCE ............. ................ .. 5-1

2 "HIGH" VERSUS "LOW" CONCENTRATIONS............. 5-3

3 VERTICAL STRUCTURE OF CONCENTRATION............ 5-6

4 COHESIVE BED BOUNDARY ......................... 5-7

5 HORIZONTAL TRANSPORT OF FLUID MUD.............. 5-8

6 LUTOCLINE EVOLUTION DEPOSITION.............. 5-11

7 LUTOCLINE EVOLUTION EROSION/DEPOSITION...... 5-12

8 FLUID MUD RHEOLOGY ............................. 5-18

6 SEDIMENTATION PROBLEMS.......................... 6-1

1 SIGNIFICANCE.................................. 6-1

2 CONCENTRATION/DENSITY MEASUREMENT............. 6-2

3 BASIN SEDIMENTATION........................... 6-6

4 PIER SLIP SEDIMENTATION BY TURBIDITY CURRENT... 6-11

REFERENCES

LECTURE 1 ................... ................. ......... ........ A-1

LECTURE 2..... ..... .. ....... ............................ .. A-2

LECTURE 3................................................... A-5

LECTURE 4................................................... A-7

LECTURE 5................................................. A-8

LECTURE 6.................................. ...... ......... A-10


iii









LECTURE 1
CHARACTERISTICS OF COHESIVE SEDIMENTS
1. SIGNIFICANCE

* Sedimentation in navigation channels and harbors.

* .Coastal and estuarine erosion.

* Pollutant loading water quality.


TABLE 1.


Costs to Maintain Channels and Harbors of Major Ports


in the United States by Dredging, and 1978
Tonnage


Trade, by


Annual Average
Port Depth Maintenance Cost 1978 Tonnage
(in feet) (in thousands)
Louisiana
Calcasieu River & Pass 40 $ 7,336.1 13,563,000
New Orleans 40 16,661.9 77,231,400
Baton Rouge 40 18,297.5 123,937,800

Maryland
Baltimore Harbor & 42 2,477.6 37,074,600
Channel

New York
Hudson River, Albany 32 1,907.5 10,440,500
New York-New Jersey 45 12,905.7 119,317,600

Source: U.S. Senate (1981)


TABLE 2. Annual Cost Per Cubic Yard Transferred


Entrance Study Period Cos ($
Ponce de Leon Inlet 1974-1977 2.61
Sebastian Inlet 1962-1977 0.83
Jupiter Inlet 1966-1977 0.61
Lake Worth Inlet 1967/68-1975/76 0.77
S. Lake Worth Inlet 1967/68-1975/76 0.76
Boca Raton Inlet 1972/73-1975/76 0.77
Hillsboro Inlet 1966-1975/76 0.97
Mexico Beach Inlet 1976 0.41
East Pass 1970-1976 0.75
Perdido Pass 1974 1.34


(in 1977 dollars)




consider ~ $1
per cubic yard
on the average
(1977).


Source: Jones and Mehta (1977)


1-1














































Fig. 1. Worldwide distribution of muddy coasts.
Source: Wells (1981)
ALASKA DISTRICT.GROUP A 0 2 MILLION CU YD
OTHERS-NEGLIGIBLE 0
PACIFIC OCEAN DIVISION GROUP A 02 MILLION CU YD
GROUP 80 1 MILLION CU YD
OTHERS-NEGLIGIBLE A


TOTAL QUANTITIES
GROUPS (ALL DISTRICTS)
A MUD CLAY. SILT. TOPSOIL. SHALE 786
B SILTANDSANDMIXED 975
C SAND GRAVEL. SHELL 364
D ORGANIC MUCK. SLEDGE. PEAT.
MUNICIPAL INDUSTRIAL WASTE 05
E MIXED 8.7


VALUES INDICATE ACTUAL QUANTITIES
IN MILLIONS OF CU YD


608


TOTAL DREDGING BY CE
DISTRICT (CU YDI
25 TO 60 MILLION
0 TO 25 MILLION



Fig. 2. Characteristics of materials dredged by the U.S. Army
Corps of Engineers.
Source: Pequegnat et. al. (1978)


1-2


E la

D
i









TABLE 3. Ocean Dumping in the U.S. in 1983.


Amount
Waste Type (103 tons)

Dredged material 65,160
Industrial wastes 304.5
Sewage sludge 8,312
Construction debrisa 0
Solid waste 0
Explosivesa 0
Wood incin. 31
Chemical incin.a 0
Total 73807.5
aWhile no materials in this
category were dumped in 1983,
they have been in prior years.
Source: National Research Council (1985)


TABLE 4. Regional Distribution of Disposal Volumes and Sites


Total Volume Ocean Dumped (106m3)

1976 1977 1978 1979
Atlantic 18 11 17 12
Gulf 24 10 15 36
Pacific 8 11 8 8
Total 50 32 40 56

Number of Active Dumpsites

1976 1977 1978 1979
Atlantic 28 20 23 20
Gulf 20 18 23 16
Pacific 24 25 21 14
Total 72 63 67 50


Source: Kamlet (1983)





1-3










TABLE 5. Design Depths for Underkeel Clearance of Maximum-Draft
Vessels
umber of vessels
Maximsu draft Required Required Project depth transits, drafts
vessel using channel depth, channel depth, of channel exceeding U0.. Total veesel
Channel channel in 1980 PIANC/lAPI* U.S. rule of thumb (controlling depth) rule of thumb* transit

Delaware River 40 44 45 42 (38.7) 439 12,408
Nortolk Harbor 45 50 50 45 (45) 300 64,481
Hmpton Roads 47 52 52 45 (45) 453 00,245
Noble 40 44 45 42 (39) 202 31,286
Calcasieu River 40 44 45 40 (40) 144 31,613
Houston 40 44 45 40 (30) 1,088 48,82
Galveston 41 45 46 42 (38) 817 16,855
Oakland 39 43 44 35 (33) 655 6,043
San Francisco 52 57 57 55 (52.6) 4 ,123
Columbia River, Lt er 44 51 49 48 (40-47 ) 0 6,002




*10% of ship's draft; 15% for areas subject to long or strong
swells (Applied in table only to Columbia River)
**Ship's draft +5 ft, without estimate for pitching and rolling
aDepending on side of channel, inside or outside

Source: National Research Council (1983)
WATER
REFERENCE LEVEL


ADMISSABLE DRAFT



S VERTICAL MOTION
GRO* (SWELL AND SQUAT)
GRO s ---------- VE-'---
UNDERKEEL CLEARANCE NET UNDERKE L CLEA'RNCE
t__NOMINAL'CHANNEL BED LEVEL f

SOUNDING ACCURACY

SEDIMENTATION BETWEEN DREDGINGS

TOLERANCE FOR DREDGING
Fig. 3. Conventional net underkeel clearance calculation,
definitions from PIANC.
Source: National Research Council (1983)

U.S. Rule of thumb: Minimum design depth = draft + squat (3
ft) + rolling and pitching allowance (estimate) + clearance
(2 ft for soft bottom; 3 ft for rocky or hard bottom).


1-4








2. MUDDY COASTS


CURRENT


CuMENT+ WAVES


\WAVE S


SEA


Fig. 4. Muddy shoreline environment




WATE


(open coast and

-0-0 e- "D


estuary).


l-


4*
c
c '


4 4 V. *


Fig. 5. Characteristics of wave motion over mud.



* l. WtvE "PWPl& (Cner5 j di&Sipch'o
2. OD MY\OT0 Di ow (bed weoeLen\i n)
3.RESOSPEWuS tIol(e:ck on 4loU stY


1-5


re)


L









* Waves provide an efficient mechanism to fluidize the bed but
not for entraining the fluidized material into the upper
water column.
TABLE 6. Muddy Coast Physical Parameters for Louisiana, Surinam
and Korea


Mudshoal dimension Fluid mud

Tidal Wave Bulk Particle
Location range energy Alongshore Offshore Thickness density size
(m) (km) (km) (m) (g/cm3) (pm)



Louisiana 0.5 Low- 1-5 0.5-3 0.2-1.5 1.15-1.30 3-5
moderate

Surinam 2 Moderate 10-20 10-20 0.5-2.0 1.03-1.30 0.5-1

Korea 5-9 High 1-30 5-50 0.1-3.0 1.20-1.30 6-11


Source: Wells (1983)


3. ESTUARIES


J, 141- 14 / Y) X- / 4/-89


-'. "wi~ -2 mn C~c


I-
,v Cc-rcL *4 /.'

^r\-)


0.6 3


Di 0.4 .36


a. Q2
00.08
S0.02 0006 0.002
U. O 25 50 75 100 125 150
CONCENTRATION, Co(rg/.)
Fig. 6. Concentration histogram northern Florida.
Source: Mehta and Maa (1985)


1-6


"rsc,;,OeO-









* Sediment transport in Florida is mainly episodic no useful
long-term applicable relationship between astronomical tidal
currents and suspension concentration can be obtained.
4''___ __l-- --- --l----"-1

GLOUCEST








NEWPTORT T/l

/ ,.,U-l,,, AVONMOUTH H30
it "I' 3W


Fig. 7. Severn estuary, UK.


Source: Kirby (1986)


1-7


1




























DISTANCE FROM GASPER SHOALS (kilometers)


Fig. 9. Depth-mean salinity and suspended sediment concentration
in the Hooghly river, India.
Source: Mehta and Hayter (1981)


-1.0 0.0
ulul (m 2S2)


Fig. 10. Flow-sediment hysteresis
a flood and an ebb.
(Courtesy: Prof. Keith Dye


in the Humber river, UK, during


1-8










* The rate of horizontal mass transport of sediment is


F = uca


where


a = flow area
u = horizontal flow velocity
c = sediment concentration



u + U

Tidal Tidal
mean


u A


cross-sectional
mean


deviation


Similarly


U = UA + Ud


Therefore


u = UA + Ud + UA + Ud


Similarly


c = CA + cd + CA + Cd
Ad A d


and


a= A+A


1-9


u d










* We want to calculate the tidal mean flux (uca)A, where A
denotes averaging over the cross-section. Omitting second
order terms (Dyer, 1986)


ucA

Eulerian
Transport


AU *C
A A
Stokes
Transport


Lagrangian advection
Lagrangian advection


+ AC.AUA + A-UACA + AUACA
A A A A A A


Terms arising from phase
differences between u, c and a.
Referred to as tidal pumping
(result mainly from erosion and deposition)


A(UdCd)A


due to vertical
gravitational
circulation

L___________


+ A(UdCd)A


lag effects due
to sediment response
to velocity variation
at different levels
__ L '


shear terms


London
Bridge


............ Low Water Line
== Shipping Channel
Areos of Accretion of Mud


Scale
0 1 2 3 4 5 Miles


Fig. 11. The Thames River, UK.


1-10









* Thames River UK (Dyer, 1978)


Flux (kgs-l)(+ve downstream)


-25
-186
895
103


470


Upstream
No


pumping important
residual circulation due
to salinity not all that
important


Ocean


Dispersed -- Loss
Riverborne-- Mixture of new Riverborme
Sediment-- Particles and returning 1 1
...i.... o r o- f Aggregates. Aggregates
-' portion of Agg' collect fine particles
SDiffuse upward I
fand Circulat


- Higher conc. low bed -
shear and consolidation
during slack produce shoals


Region of fresh and
salt water mixing and
enhanced shearing


Fig. 12. Schematic diagram showing transport and shoaling process
of fine sediments in estuary.
Source: Krone (1972)


Suspension in Transport


De n
Deposition Redispersion


Resuspension


Fig. 13. Schematic representation of the physical states of fine
sediment in estuarial mixing zone.
Source: Mehta et al (1982)


1-11


Term

1
2
3-5
6

7










CONCENTRATION, c or VELOCITY, u




A--C U
Moble
Suspension

ENTRAINMENT C

Lutodine
7 FLUIDIZATION SETTLING Moble
Fluid Mud

FORMATION Cohesive
Bed
CONSOLIDATION |


Fig. 14. Vertical structure of
concentration due to
current (general case).


A
U






- Lutocline


MWL


Mobile
Suspension


CONCENTRATION, c or VELOCITY, u


Mobile
Suspension


CONSOLIDATION


Fig. 15. Vertical structure of
concentration due to
current (a restrictive
definition).




Bed deformation by
oscillatory loading leads
to degradation of bed
properties and subsequent
fluidization.


Deforming Bed

Stationary Bed


Fig. 16. Vertical structure of
concentration under waves.


1-12









4. SEDIMENT CHARACTERIZATION


Curve for
erosion
entrainmentt
function) for
grain size less
than 0.06 mmn
is ill-defined.
In fact a unique
relationship
does not exist
for fine
(cohesive)
material.


Fig. 17.

Source :


DIMENSIONLESS GRAIN SIZE, dgr

Relationship between entrainment
function and dimensionless grain size.
Ackers (1972)


1/3
( fg s 2
Yv


v = fluid viscosity
d = particle diameter


* A bed-load function of the type applicable to sand transport
is not definable when cohesion is measurable.

* Unlike in the case of sand transport, the structure (vertical
variation in properties) of cohesive bed plays a key role in
governing transport.


1-13


GD

o

I-
L2

z


cr
UJ


0.01


dgr = d






.0C 00-9
ga


SO /C~-4~


ii------- CQo Ft/c ____-0__

,C o'6/ o N


* C ao f& # &# rc OF' r 4Wd
I-- nre-c S r- e


* 5 5P,*. 5't sC-, 7P&C C.r -A, 7'


C A ----'A/lA/,


* ^i-*y Co*Yes-/y^


.* VJ X' 0 V' S* J JO/ v -0


/Y,,P6 (


dqC4po r/ 4#7


7y:' -w AP / /rg


DOUBLE-LAYER REPULSION
AT THREE DIFFERENT ELECTROLYTE
CONCENTRATIONS


GO
0 0









van der wools
ATTRACTION


I I
Grl
GI





L
Gi

0u


GO


0
D (D (

i
0 (


Diffused
S Double Layer


Fig. 18.


Repulsive and attractive
energy as a function of
particle separation at
three electrolyte con-
centrations.


Fig. 19. The clay micelle.


1-14


/ A0fto


m
m


.- .1 A#$"










TABLE 7. Critical Cation Concentrations and Corresponding
Salinity for Potential Aggregation in Sea Water

Total Cation
Clay Type Concentration Salinity
(me/liter) (g/liter)

Kaolinite 1.0 0.6
Illite 2.0 1.1
Montmorillonite 4.3 2.4

Source: Ariathurai (1974)


U, I I II I,


-lo0


0.01 0.I 1.0 10
dj (microns)


Fig. 20.





Source:


Third order aggregate
of a flocculated fine
sediment. The aggregate
is composed of zero (C).
First (B) and second
(A) order aggregates.
Krone (1963)


Fig. 21. Comparison of col-
lision functions for
Brownian motion,
shear and differential
settling.
Source: Hunt (1980)


0 Aggregation due to flow shearing is typically the most
important mechanism for inter-particle collision leading to
cohesion.


1-15


SI p p


100 1000









TABLE 8. Properties of Brunswick Harbor Aggregates

Order of Density, pf Shear Strength, Ts
Aggregation (g/cm3 ) (N/m2)

0 1.164 3.40
1 1.090 0.41
3 1.067 0.12
4 1.056 0.062

Source: Krone (1963)

* Above analysis is based on rheologic (stress vs. rate of
strain) data. In a very approximate way the relationship is

Tsa(pf- 1)n


'Flocculation Factor

Wf
wf
F -
wd


W = floc settling
velocity
Wd = individual
particle
settling
velocity (from
Stokes' law).

Cohesion is
negligible for
particles > ~ 20
microns.


DomiO m moyf rmc0nlm- M an m',Cron

Fig. 22. Effect of particle size
on flocculation.
Source: Migniot (1968)


1-16








PRINCIPAL FACTORS CONTROLLING

EROSION OF SATURATED
COHESIVE SEDIMENT BEDS
HYDRODYNAMIC FACTORS (Erosive Force)
BED SHEAR Flow Characteristics
BED SHEAR
Bed -Fluid Interface


BED AND FLUID PROPERTIES (Resistive Force)

IM C IClay Mineral Type) lon Exchange Capacity
SEDIMENT COMPOSITION Clay Percentage by Weight
Organic Matter
Mono-and Divalent Cations Concentrations Conductivity
PORE FLUID Relative Abundance of SAR (Na'CadMg")
COMPOSITION Mono- and Divalent Cation
Temperature
pH
Salinity (NaCI,CaCI2,MgC 2)
ERODING FLUID Temperature
COMPOSITION pH
Cementing Agents (Iron Oxide,etc)


BED STRUCTURE Stress History Dited Bed
Deposited Bed

Fig. 23. Schematic representation of factors controlling erosion.
Source: Mehta (1981)

Many muds are pseudo- .,,
plastics. Some can be
approximated as Bingham
plastic. \






Fig. 24. Stress-rate of ) /\
strain curves.


1-17 5t~ptR










LECTURE 2
SETTLING, DEPOSITION AND BED FORMATION
1. SIGNIFICANCE

Shoaling in navigation channels, harbors and basins.
Formation of deltas, spatial gradation of bed material.
o Growth of wetlands and mud flats.
o Scavenging (removal) of dissolved and particulate
pollutants from the water column by sorption and subsequent
burial.




S Gu Yi /
Hai Yan Xian YueTin Wang )
HaiYon/Xion ang YueTing Paon _n/
'\.^


Xie Jia
Tang


Fig. la.

Courtesy:


Historic accretion along the southern bank of Hangzhou
bay, China.
Prof. H. Wang

PROJECT DEPTH 35' UNLESS OTHERWISE
SPECIFIED
l o DREDGED 1 TIME EACH YEAR
O DREDGED 2 TIMES EACH YEAR
O DREDGED 3 TIMES EACH YEAR
E AREAS TO BE DREDGED
S\ EXISTING DEPTH BELOW M.L.W.


900 O So 90
Fig. lb. Areas dredged around Navy pier and slips at Charleston, SC.
Source: Hoffman (1982)


L








Bar front:lnterbedded sands
a silts; climbing ripples,
parallel laminations,
lenticulor laminations,
burrowing 8 contorted
bedding

Distal bar:lnterbedded silts;
clays and sands; ripple and
parallel laminations;
lenticular laminations;
burrowing a contorted
bedding


Prodelto: Clays with thin
interbedded silts; parallel
laminations, burrows,shell
inclusions and contorted
bedding


SEDIMENT TEXTURE I8
SEDIMENTARY STRUCTURES


Boa B^




n r b r S oai
loster




Fr Fvi

gal

s Lake c





,-i-r/a clafie~~.Y1:~9~,-~Pontc m _La t


Maa~o
PO A ta d, Il
Fe I^.


Channel. Poorly sorted sand
and silt,medium bedded,
cut and fill, scour face
Crevasse splays 5 natural
levees: Sands, silts, cloys,
peats, root burrows,
climbing ripples, lenticular
lamination
Subaqueous levee: Silts,with
interbedded sandi 8 clays,
climbing ripples; parallel
laminations


Bar back: Poorly sorted
sands 8 silts; cut and fill;
small-scale trough cross
bedding




Bar crest: Well sorted sands;
planar laminations,
tangential cross bedding:
small-scale cross laminations








ia,
Pu rvi


md zt






ass
'C j^C^?^^h~7
irv^a/Tfoi-^'~
p^:^;/J^^4^^^rfd


S
Breaion






ran fasle


Merr

istom-










I. k
L'i





SPPI






(orthP.
DELTA
t heastf
Olsl/afdl


ShpSrehiL' "'Souti estP.


M E X I C 0



E 91" F Longitude West 90 of Greenwich G 89"


Fig. 3. Mississippi delta and
Atchafalaya bay,
Louisiana


DISTAL BAR




20


PRODELTA


Fig. 2. Delta model based
on Mississippi
Source: Wright and
Coleman (1974)


2-2


g~t^^
***A *c SA/^


. .. % .. .


-- -^~~ Y-*PL -an~


_I


f.t.>.i>'gg-T.ifi<.i^jijh?ri,?'.i8nKa';a


if


n


I









* A complex set of flow and sediment related conditions leads
to bed lamination. Lamination produced under flowing water
is influenced by factors different than those under quiescent
conditions. In a flowing fluid, the vertical profile of the
mean flow velocity, the structure of turbulence, type of
sediment and its initial concentration are important.



* Lamination in the prototype environment is strongly
influenced by tides, storm conditions and runoff. Layering
occurs under variable conditions imposed by deposition,
erosion and consolidation.


10 ------


-~0'-


Fig. 4. Lamination in bottom
core sample,
Elezabeth River,
Virginia. Depths are
in centimeters.
Courtesy: Prof.
M. Nichols


Fig. 5. Lamination resulting
from flow in a flume
with diatomic
particles.
Source: Berthault (1986).


I


25 ^^^^^






























2 4 6 8 10 12
RELATIVE SEA LEVEL RISE (mm/yr)

Fig. 6. Rate of marsh accretion
versus rate of sea level
rise.
Source: Stevenson et al (1986)



A positive correlation is
observed between the heavy
metals and the amount of fine-
grained particles expressed by
the percentage of particles less
than 16 microns in diameter.

Since clay-sized particles
preferentially sorb pollutants,
the latter are extracted from
the water column and settle in
the bed material. Deposition in
this sense has a beneficial
role.


)ne likely reason for higher
'ate of accretion than sea level
ise is that in some cases
!ompaction effects are not
properly accounted for. Marshes
.n Louisiana are accreting at a
power rate than sea level due to
insufficient supply of sediment.


0.24


020



6.16-

0.12-


0.08


0.04-


0.0 L
O
0


I I I




I0


S15
I


' I i

Zn








PCr


Pb







* I i


20 40 60 80 100


%< 16.Lm
Fig. 7. Variation of sorbed
metals with particle
size.
Source: Salomons and Mook
(1977)


2-4


0.281 '


r










2. SETTLING


Characterization
by appearance


Analysis
approach


Increasing
concentration

Dilute Concentrated Soft settling Consolidated
suspension suspension mud sea- bed


Fluid mechanics: Continuum mechanics:
Classical non-Newtonian, two phase skeletal
fluid pseudo plastic, framework, soil
mechanics two phase mechanics approach


Fig. 8. Transition from dilute suspension to consolidated
(settled) bed.
Source: Sills and Elder (1986)

* Settling under turbulent conditions as opposed to quiescent
environment is complicated by continuing aggregation due to
local shear gradients and upward diffusive flux related to
turbulence intensities.



1200-

Pressure plotted obove Settling test in a 2 m column
hydrostatic using an estuarine silty clay

80- o Total stress (Combwich mud). Effective
E x Pore pressure stress is the difference
E between total stress
(pressure) and pore
0 pressure. Level (~ 500 mm)
oo- below which effective stress
is significant is the
cohesive bed boundary.


1.1 12 0-2 04 0-6 0-8 10
Density Mg/rn3 Pressure kN/m2
Been? Initial density 1-09 Mg/m3 A hour profile

Fig. 9. Development of effective
stress at 4.75 hr.
Source: Sills and Elder (1986)


2-5






20 min


1600 Density profiles measured by x-
ray transmission technique, a
non-intrusive approach. Measure-
3 hr ment accuracy is 0.01 gcm-3.
Spatial resolution better than 2
mm. Fate of interface (lutocline)
with time is observed. Note that
1200 4hr l5min at 20 min the profile is nearly
uniform with a density of 1.09
gcm-3(Mgm-3), which is equiva-
E lent to a concentration of
E 140 gL-1.

E 6hr 30 min



24 hr

S79hr 4 \ hours

6 hr
3hr
Lines of constant density

24 hr o 1-00 Mg/m'
a 1.09 Mg/m3
79hr 1600 + 1.13 Mg/m3
a 1.16 Mg/m3
v 1.20 Mg/m3
20min -- 10

1.0 1.1 1.2 1-3
Fresh water
Density Mg/m3 1200 F
Suspension
Fig. 10. Time-change of density E
profile in 2 m column.
Source: Sills and Elder (1986) S 10B 107
I 800
A transition from suspension to
structural phase occurs between
concentrations of 140 and -13
204 gL-1 (1.09 to 1.13 gL-1). 0Density step change
.1-09- Density step change
Type of sediment and initial 4 116
concentration influence this11
transition. Also the degree of
flocculation.
120

2 4 6 8 10
Time hrs


Fig. 11. Density changes in
the first 10 hours.
Source: Sills and Elder (1986)










Characterization
by pore water
pressure and total
vertical stress


Transition by
concentration or
density for Combwich
mud


Pore water pressure equals Pore water pressure less
total vertical stress. total vertical stress.
SUSPENSION PHASE STRUCTURED PHASE


I I I I
0 100 200 300

Only Can be either Structured phase
suspension suspension or only. Suspension
found structured phase not possible


I I I I I I
10 105 1-1 115 12


Concentration
g/I





Density
(fresh water)
Mg/m3


Fig. 12. Schematic of transition from suspension to structured
phase.
Source: Sills and Elder (1986)

3. SETTLING VELOCITY


Stokes Law


2y- y
W = gd (s
s 18v
TABLE 1. Primary Particle and Aggregate Diameters and Settling Vel


= kinematic viscosity
= diameter
= unit wt. of particle
= unit wt. of water


Source: Mehta et al. (1987)

o While Stokes velocity decreases rapidly with particle size,
-the aggregate settling velocity as well as diameter retain
the same order of magnitude as a consequence of increasing
aggregation with decreasing particle size.


2-7










o In general, Ws varies with concentration, C. For C < ~ 100
mgL-1, Ws is independent of C due to free settling.

SThe curve illustrates two
000 =0.513 important regimes Flocculation
Ws=k" C =1.29 settling and hindered settling.
S10.0 o=.6m/s_ In flocculation settling Ws
=4.00 increases with C. Hindered
3 settling implies decreasing W,
1.0- with C. The relationship for
flocculation settling was
0 *originally proposed by Krone
0.1 (1962). The relationship for
/ P \ hindered settling is based on
S0.01- W =Wso(-k2C) the work of Richardson and Zaki.


0.0 ,0
Q001 0.10 1.0 10.0 100.0
-CONCENTRA-nON,C(g/.) _

Fig. 13. Ws against C for data
from Severn (UK)
obtained by Thorn
(1981).
Source: Mehta (1986)

In Situ Settling Velocity Data:

o In the flocculation settling range, values of k1 and n can
differ greatly, particularly kl, between prototype and
laboratory measurement. Collision frequency in the
prototype is principally determined by local shear
gradients. k1 can be an order of magnitude higher in the
field. In situ measurement techniques are therefore
required.
Pivot line -- -.-Spring unit


Rubber sock' Conio grip Sttotr Rotor
(shown closed) Assembled unit Stabilizing ring
In--------.Om I-----------
51m I.D. erspex tube Block keyed to rotor

Guide blocks/
Sampling (inner) tube

89mm O.D. perspex tube
nr ------------------F -- --------------U-
1L-- ----------*-- L1----------- -----y
Supporting (outer) tube
Fig. 14. Field sampling instrument.
Source: Burt (1986)










The Owen tube is essentially a 1 m long perspex tube of 50
mm internal diameter. It is initially open at both ends
and is lowered, usually from a boat, into the water where
it is suspended horizontally in line with the flow at the
depth where sample is desired. After a short time, when
flow through the tube has been established the ends of the
tube are closed off and the tube containing the sample is
raised to the working deck. The tube is designed so that
as it is lifted out of the water it automatically swings to
the vertical position. At this precise time a stopwatch is
started and the settling test is begun.

One test gives just one point
for W50 (by weight) for one
initial concentration. However
since both Ws and C change with
Suspended concentration 920mg/1 /time at each elevation, it is
Salinity 17.2 gl/1
so Temperature 20'c feasible to obtain a complete
SSetting tube height ,0m Ws-C relationship from a single
'/ test. This latter approach, due
60.e
o-- ----------- ----------- wso to McLaughlin (1959) has been
S./ further improved by Ross (1988).
301
10
20
10
o01 o1 1o 10o 00oo
Settling velocity mmlis)


Fig. 14. Settling velocity
distribution obtained 1o- 0
from Owen tube or
settling column test.
Source: Burt (1986) E

Slope and intercept (n and kl)
of the settling velocity-
concentration curve in the 01
flocculation settling range are
strongly dependent on sediment
type and rates of shearing in
the water column.

0-o 0
10 100 1000
Concentration (ppm)
Fig. 15. Ws-C data from five
estuaries.
Source: Burt (1986)

In the hindered settling range, laboratory column may be
used to simulate prototype behavior because flow shearing
is less important in this case. Settling is controlled by
the rate of upward escape of interstitial water.


2-9










Settling Velocity by Removal Rate Concept:


aC 32C + a
at 2 s az
a2

e Initial and boundary conditions are
(1) at t=0, C = f(z) when 0 < z < h (where h = depth of
flow) is a known function.
(2) as t+-, C = A, an equilibrium value,
(3) no transport across the surface, i.e.


C ac
z=h


= WsCh


(4) at equilibrium (t+-), the rate of floc rupture and
reentrainment equals the rate of deposition at the bed
z=0, i.e.


SC
z=0


= -W C= 0= -WA
stz
t-o


* The solution is (Dobbins, 1943)


-W ze
s =
C = Ae


-0.5 W ze1 1 -(a2 + 0.25 W2 C )t
s I n s CY
e Cnn
n=l


where


2
2 a
n
2
w W
a2n + s2) h + s
4e


h
f [f(z)
0


-1
-W ze1
- A e


0.5 Wz-
0.5 w ze
s


Z = cos
n


W
a z + s sin a z
n 2ca n
n


and al, a2,...an are the successive real positive roots of the
transcendental formula

Wh
s
ha 2c
2 cot h a h
Wh ha
s
2c


2-10


Cn =


Z dz
n









Camp (1943) adapted the above solution to an open channel-
type settling basin under the following two conditions: 1) there
is negligible scour, i.e. A=0, and 2) the initial concentration
is independent of z, i.e. f(z) and Co. A removal ratio r was
defined as the fraction of the incoming suspended sediment which
is deposited. The value of r is found from (Brown, 1949)


r = s)i
(qs )i
"i51


Ws WsL
= f(U*
^us Uh


(qs)e = amount of sediment
of given particle
size in the
effluent
(q )i = amount of sediment
of given particle
size in the
influent
u* = friction velocity
U = mean flow velocity
in the basin


00 0.02 005 0.1 Q2 0.5 I 2 5 10

Ws / u*


Fig. 16. Removal ratio, r, as
of Wg/u* and WgL/Uh.
Source: Brown (1949)


a function


Application for settling velocity estimate. Deposition
data from a 100 m long flume (Dixit et al., 1982).

Sediment discharge, q, at any section is

h
q = b J C(z)u(z)dz
0


where b = flume width.


2-11












U
% 70 Series I
E Time: 15 min

0 *

I- \


z50




0 I I I I I I i
S I10 20 30 40 50 60 70 80
DISTANCE ALONG FLUME (m)


Fig. 17. Sediment kaolinitee) discharge, q, as a function of
distance along 100 m Flume. Series 1, 15 min after
test initiation.
Source: Dixit et al. (1982)

Sediment discharge variation in the above figure may be
considered to occur under a steady state condition.

Calculation of Ws (for the 12.2 m 24.4 m reach) is as
follows:

Discharge Q = 0.007 m3s-1
Width of flume b = 0.23 m
Depth of flow h = 0.152 cm
Mean velocity U = Q/hb = 0.2 ms-1
Length of reach L = 12.2 m
Manning's coefficient n = 0.022
Hydraulic radius Rh = 0.0655 m
Friction velocity u = 0.0217 ms-1 (Manning formula)
qsi = 59.5 gs-1 (from Fig. 17)
qse = 56.0 gs-1 (from Fig. 17)
r = 0.059
Ws/u* = 46.1 Ws
WL/Uh = 401.3 Ws
By trial and error iteration, Fig. 16 yields Ws =
0.0148 ms-1


2-12









0-5-
0o (14)


03

0.1
a Based on reanalysis of previous
012 data, Hayter (1983) obtained the
10 Krone(9) %S0o following relationship
0-08
0-0e Ws(S,C) = AWs(35,C)Sm
E o04- 530 C = suspension concentration
X2 002o- 220 12 S = Salinity
n 2, A,m = empirical coefficients
35 = 35 ppt salinity
9- Allersma (1)


08
07-
0-6-

0-4 -
03 -

0500
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28
Salinity (ppt) -
Fig. 18. Effect of salinity on
settling velocity at
different sediment
concentrations.
Studies of Krone
(1962), Allersma et
al. (1967) and Owen
(1970).
Source: Burt (1986).

4. PARTICLE SORTING BY DEPOSITION

Particle population in suspension at any instant and
.. is.. -, spatial location is typically a
mixture of dispersed and
/ Motno iloe coagulated flocculatedd) units of
SKoIni,- \ highly variable sizes, shapes and
uat Mica densities (when flocculated). An
i. ". outcome is sorting of deposited
/. material by size, by mineralogical
composition etc.
1006040 20 1086 4 2 I1A4.4 .2 .1
PARTICLE DIAMETER (.m)
Fig. 19. Relative frequency
distributions of
component mineral sizes
discharged by the
Amazon.
Source: Gibbs (1977)


2-13







PARTICLE DIAMETER (rm)


Trends similar to these have
also been observed with distance
offshore. Physical size
segregation produced a
corresponding clay mineral
segregation because clay
minerals have different sizes
and different cohesion.


DISTANCE FROM RIVER MOUTH (km)
Fig. 20. Spatial variation of
clay mineral composi-
tion (%) of bottom
sediment with along-
shore distance from
the Amazon mouth.
Source: Gibbs (1977)

* Size analysis by a coulter counter. Modal (corresponding to
the peak) rather than mean sizes were used. Kranck (1975)
found an empirical relationship between the modal size of the
original flocculated sample and that of the deflocculated
sample:


log(grain mode) = a+Blog (Floc mode)
a = 0.528 Size in microns
= 1.235
6rF


g 1.6
a.
1.2

,0.8
I-


I 2 4 8 16 32 64 125
DIAMETER (im)
Fig. 21. Concentration-particle
size relationship of a
settling suspension of
a natural sample in sea
water after successive
time period in hours.
Source: Kranck (1975)


W
z
0
u


0

0.22
0.87

03 S
-- fi


I 2 4 8 16 32 64 125
DIAMETER (.Lm)


Fig. 22. Concentration-
particle size
relationship of a
settling suspension
of inorganic defloc-
culated sample in sea
water after succes-
ive time period in
hours.
Source: Kranck (1975)


2-14


04










60- Data in Figs. 21, 22, 23 are
a22-0.87 based on sample from Murray
SHarbor, Northumberland Strait.
z 34-1 The size distribution of grains
U settled between successive times
a:20 shows a pattern of decreasing
a. diameter due to sorting.

I 2 4 8 16 32 64
DIAMETER (, m)

Fig. 23. Size distributions of
grains settled out of
suspension between
successive time inter-
vals shown in Fig. 22.
Source: Kranck (1975)

5. RATE OF DEPOSITION


tb -zcu;Cf=Co Tb = bed shear stress
o/ Co = initial concentration
O CCf = final concentration
Co cl and rcM define the range of
M >b > C =C critical stress for deposition,
cm b cl' f f Tc.

o
oz C1 b;Cf=O


TIME


Fig. 24. Typical time-
concentration relation-
ship during deposition.
Source: Mehta and Lott (1987)
Uniform
2 Sediment
0/ Deposition law for uniform
Sediment was proposed by Krone
(1962). At low concentrations
the time-decay is exponential
z NonUnonrm according to that law.
0- Sediment


S cl tCM
S BED SHEAR STRESS, b
Fig. 25. Dependence of Cf on Tb
for uniform and non-
uniform sediments.
Source: Mehta and Lott (1987)


2-15







N i N fc wci WsI n(Tcm/rcd)
N r 1 Wsi In (W'S rMm
Non-uniform: C (WsI)exp[--t;m TW /


Uniform: C exp r-(c- )


Tcm= TcM in Fig. 24; Tcd = Tcl in Fig. 24. h is flow
depth. Wsmin and Wsmax define the range of W. Ws
is divided into settling velocity classes, i. #(Wsi) is the
frequency distribution of Ws. Expression reduces to that
for uniform sediment for a single class.



GCiAItJ Sz.e PVSTR, I80ro o0U

T 7 .


^Awo


coA se I AeuuJ% I


R WC


ScLT


costase seas Roe


I _MNa I I _I-


* huroveker aGlylsts
o cornmrdc<-l oaervcw5
I Ii


N0


_________ I I I i.I


6O.ooo00 mvm


CrI.T .,J


1)t S -


i.AmeTlT7in.


G. bc r -I I

S5Pee tonr

stecuy stde


0.001


0.00


oDI


Fig. 26. Kaolinite size distribution in suspension,
finally at steady state.
Source: Partheniades et al. (1966)


initially and


e Particle sorting during deposition is characteristics of
non-uniform sediments. Kaolinite, which is relatively
weakly cohesive, is sorted in this way.


2-16


U .


SA.. I I T C JW


! *' I Nt -4*


0 --d


V1


'


CJtY











<(= *
|fli Q0r)


0 \w cLW Fvo ,,-- W.L*/ C J.5=


Basic relationships used
are:

Ws = klCn
TcCa Wsm
The second relationship is
an assumed one. It has not
been verified directly. Only
^ indirect verification has
| C- T -. ST S (1987).
c TICtAC STRe-ess






S/Fl










1Fig. 27. Inter-relationships between distributions of Ws, Co and
Tc used to derive deposition rate expression for non-
uniform sediment.
Source: Mehta and Lott (1987)
t Cl^ T a^








f >urce: ehta and Lott (1987)


2-17








jim ^-P [^
L settling velodtotl d IstribL-I'*o0
Lrti+icc d sCvress 0dissri b4-',on
in tiwic conce\+rac-ron dcistrib u+i'ovn


AhP ( Tea) AER


=> dr -L-.- L -P


dm/dt is the time-rate of change of suspended sediment mass
during deposition.
The non-uniform law may be applied to deposition data from
the annular rotating flume.



35-

30 Distribution obtained by
Yeh (1979) in a settling
25- column. Validity of this
distribution to
20o- deposition under
2 1 turbulent flow is
5 assumed. Note that Ws1
*is is treated as a
calibration parameter.


W. [ (W -W,,)] x 0 n(misec)


Fig. 28.





Source:


Settling velocity
histogram representing
discretized frequency
distribution relative to
minimum settling
velocity, Ws1, for non-
dispersed kaolinite.
Mehta and Lott (1987)


2-18


OeiATLD -rO (WS)


S(CcO)










There is no longitudinal
concentration gradient in
this flume. dC/dt is there-
fore entirely due to depo-
sition since longitudinal
dispersion is absent.


Fig. 29. Annular rotating
flume.
Source: Mehta (1973)




Comparison between data and
Eq. 12 of Mehta and Lott
(non-uniform law)
illustrates the need to
"split" the sediment into
different size or, better,
settling velocity classes.
"Settlable" fractions
deposit while the remainder
remain in suspension at a
given applied bed shear
stress.


6 8
TIME, t (hr)


Fig. 30. Time-concentration
relationship during
kaolinite deposition.
Source: Mehta and Lott (1987)


2-19










6. BED FORMATION

o A complex process involving a combination of settling and
consolidation and associated physico-chemical changes
involving electro-chemical inter-particle bonds and internal
energy of the bed matrix.
Effect of overburden typically leads to the development of a
stratified matrix.
One-dimensional (vertical) theory has been used to examine
linked sedimentation and consolidation.












SPESWHITE FINE CHINA CLAY This clay is a pure, mined
Test 2, e o103 Kaolin. e is void ratio =
4- Vv(V- Vv); V = total volume,
c Vv = total volume of solids. e
8 --culated -= initial value of e.
o Measured
12

E 16----

p 0 0 300 400 500 60
24


32 V -e<30

36-
0 100 200 300 400 500 600 700
Time, (min)





Fig. 31. Sedimentation/consoli-
dation of Speswhite
fine china clay.
Source: Schiffman et al. (1986)

* Better understanding the transition from suspension to the bed
(with a structured phase) is critical for accurate modeling of
estuarine cohesive sediment transport.


2-20










H = bed thickness
' b = depth below bed surface
p(z) = dry density of bed
p = depth-mean bed density
0.8 0 MEASURED
PREDICTED Layered bed model used for
S simulation. The bed is divided
S0.- into three sections:
unconsolidated stationary
N suspension, partially
consolidated bed and settled
S0.4 (fully consolidated) bed.
0 Empirical algorithm for
consolidation accounts for self-
0.2 weight consolidation.



0 0.4 0.8 1.2 1.6 2.0

P/P
p(Z,) (Kg/ms)

Fig. 32. Comparison between 50 300 250 0 250 400 / 5350 500
laboratory measured and 0.0 1 I
model-simulated bed
density profiles.
Source: Hayter (1986) 0.2



Tdc = consolidation period 0.4

Instantaneous deposition amounts
were at 0 hr, 48 hr and 72 hr 0.6
were 83.5 kg/m2. At Tdc = 24 hr 2
the bed is 0.61 m thick, while E T,24hr.
at 240 hr the thickness is N
0.77 m. 0.8 T.


'1.0 T,-48hr.


1.2
Tdac72hr.
I I I I l l I I I

Fig. 32. Predicted bed density
profiles for multiple
periods of deposition
as a function of Tdc.
Source: Hayter (1986)


2-21










Profiles after 24, 48 and 72
hrs. 10 m high and 0.092 m dia.
settling column. Each deposition
4 liters of suspension at
26.3 gL-1 solids contents.
0.22 2-5.81
0-20 -
S018 concentration
in
06 kg m-3x 10-2.
c 0.14 1-5-81
S2-loyers
24 hrs ofter dep.


0 "08 1 layer
S0-06
0.04 -
0.02
0.00 I I I I I I
0 1 2 3 4 0 1 2 3 4 5 0 1 2 3 4 5
density profiles under
multiple deposition.
Source: Burt and Parker (1984)

Notice similarities between data of Fig. 34 and simulation
in Fig. 33.

Consolidation plays a significant role in controlling
sediment erodibility. Thin (~ few cm thickness) beds gel
and consolidate fairly rapidly in the first one or two days
after deposition, thereby increasing erosion resistance.




Given a sufficiently
(- weeks) long time, a
uniform settled bed
results.








Fig. 34. Increasing
erosion shear
strength of bed
with time.

N OIv2-22
2-22









Note the step-like structure
after 1 day. This is due to a
change of the structure of the
aggregates at that level. After
8 days the step is gone and the
bed is much more uniform.


D.1


0.5


2.0


BED SHEAR STRENGTH, Ts (N/m2)

Q2 03 0.4 0.5


0.6


Fig. 35. Kaolinte bed shear
strength profile
after 1 day and 8
days of consolida-
tion.
Source: Parchure and Mehta
(1985)


* While bed density profile also exhibits a similar
progression with time, the bed shear strength is only
approximately related to density.


2-23










LECTURE 3

EROSION


1. SIGNIFICANCE


Loss of valuable land.
Shifting of navigable channels.
Recycling of chemical constituents.


* In terms of its aerial extent erosion is sometimes a more
localized phenomenon than deposition. Coastal erosion can
however extend for long distances. Erosion combined with
compaction can be drastic Isles Dernieres in Mississippi.


Fig. 1. Shoreline changes at the Isles Dernieres, Mississippi,
1853-1978.
Source: Penland et al (1985)


3-1






t


Uncertainty of
channel position
and heavy dredging
needs has resulted
in under-
utilization of the
oil terminal at
Haldia.


Fig. 2. Channel shifting in the
Hooghly river near the
port of Haldia.
Source: McDowell and O'Connor
(1977)




Waves can be quite important in
bank erosion which is
quantitatively not a well
understood phenomenon.


Fig. 3. Bank erosion of Hooghly
river near Barrackpore.
Top of bank is 4m above
water level.
Source: McDowell and O'Connor
(1977)


3-2


I.'-. ~c~~aa~--L~















Exchange of sediment between
the bed and the water column
is enhanced by waves during
dry summer months. This causes
sediment deposited in the
Delta during winter flows to
move through San Pablo Bay
into central S.F. Bay.


Fig. 4. San Francisco Bay system.


SUSPENDED SEDIMENT

IN 01 01100111
1WITN AQUATIC
AVE DISPOSAL
SUSPIRSIOM
T-lllr T Nl T o ITrrn s

NEW ANlUAL DEPOSIT


/ //// / // //////
PREVIOUSLY DEPOSITED
StDIMENTS


01.18 AVM.
DELTA OUTFLOW

TRIBUTARY
OuTFLOW


TO LANO DISPOSAL


Very fine-grained
material is
transported to the
ocean by erosion.
Water depths
actually increased
in south S. F. Bay
during 1923-50,
partly due to sea
level rise.


Fig. 5. Average annual sediment
transport rates in S. F.
Bay. Values in million
cubic yards.
Source: Krone (1979)


3-3


4A83 MET
OUTFLOW TO
OCEAN PLUS
ocus rus ^_
I0. t FROM
0.ROS IO OF
So. SF. IAY








TABLE 1. Average annual sediment accumulation
rates (106yds3yr-1)

Area 1897-1922 1923-1950
(26 years) (28 years)

Suisun & Grizzly Bays & -0.66 -0.17
Carquinez Straits
San Pablo Bay 2.31 0.62
North San Francisco Bay 2.59 3.80
Loss of Water Volume 4.24 4.25
Volume of Sealevel Rise 1.29 1.29
TOTAL 5.5 5.5
South San Francisco Bay
Loss of Water Volume -1.96 -1.96
Volume of Sealevel Rise 1.07 1.07
TOTAL -0.91 -0.91

Source: Krone (1979)

2. RATE OF EROSION
A unique, operational definition of cohesive bed is not yet
available. Therefore, identification of a plane at which
erosion flux condition must be considered can be a difficult
task, particularly in the high concentration, fluid mud
environment.






r \ fCTPRAIMMENT

.4TOCL.ME Z II15 U5P6S.SON







LOGARtTH o01 CONCEmT-AtI-

Fig. 6. Definition of erosion versus entrainment.
Fig. 6. Definition of erosion versus entrainment.


3-4










RA'S OF E'NTR~INMT-J.

- eilv 1eric c harLc-reis+ics oC5
\al+h in4er-a-Ce C-+ ZA


i~-e- C~4,cA.&c I


4uluids


Cins3bi I it / evA+rrwmen+


t~RTE OF EROSION


vS+4e ST j dep'
\;CLU twrtd dep4+h)


* Entrainment behavior of fluid muds is not well understood at
present although similarities with salt water entrainment
behavior have been recognized.

* At present an "adjusted" erosion rate expression is the usual
option, i.e. to use the erosion rate expression (with rate
a T- T ) after calibration of the free coefficients to
account for entrainment of fluid mud.

* In very low concentration environments, e.g. Florida, the
interface between bed and suspension is characterized by a
drastic change in concentration. For such conditions the
erosion rate expression is quite suitable for application.


3-5


dP%-1:


Aim
arL





SoME ERosioN RT sE EkFsg&IoDMS


PA..TH EN I -EFS


( tr tz)


[1-


CMLSTEN4SEh (CLs)

0ADIA-H (1974);


E iotjC, ]S -


S ep(- /2)
-(A /?Z-)-A


-(b.lo+(&l.O./33?
^f ep(-,yw2) ad)
0


A-ULAVANbAN (q7+")


LibeRoNT- A*N D
LezBbN (C178))
NON- UNLtFcR eS:
K, ok 6: (tq1 42)
YeHl (lq7'); PUKUDA
AJD LICK (lqOD)
Tik3kw A40D iefsw*s
(^^o)

PMA- U((trI4)


TDAS (q973);


if


e pL X c--s 2.
6 = dC+ (0-e)


f- t(exp- A )

= dzz)[- E (2]
=/ e- p. _/(-z s
S ,-,,


3-6


C-.4ISTETSFE ANJD


kRADK vi
(uLt.A.,T


A-D HIUTCH soj (1174);


(^2
( ^
orsS


.= o(3


z)]


exp C.c (--









0O SHEAR STRENGTH
zs I do4& Non-uniform bed shear strength
SN I t *Yt increasing with time. Strength
0 at the surface does not change
o3 because there is no
3 overburden. At t + profile
T becomes nearly uniform.
I-
a t
0







Fig. 7. Increasingly uniform bed
shear strength profile
with time.
Beds formed by deposition from suspension are usually non-
uniform (water content > 100%). Uniformity increases with
time.
Beds formed by pouring a pre-prepared slurry (water content
< 100%) are closer to being uniform.
For non-uniform beds, time of approach to uniformity varies
with bed thickness etc. Thin beds (- 1-10 cm thick) become
fairly uniform in 10 days.

Thin beds can supply significant amounts of suspended
sediment. Thus in many estuaries, the thickness of "active"
bed layer is often thin.




EYAm PL E:
SuTici'oJ bed tlcuer 4 ckvesns& = 0. 6- cm
Bet (dL.L4) devnsi+ = 0.o.3 /cmr3
aJ4-%er C couLmn d.eP--t h 4 ry\
> 5^spernsiao cc+n&enbodb'n 7 35 mr L.


3-7


_










T
n




n-I

n..


TbA Tb Tbc TbD


Given such a distribution of
TS(z), under a bed shear
TS stress rbA the bed will erode
to a depth zA at which point
TbA = TsA. The rate of
erosion therefore depends on
the "excess" shear stress
Tb Ts. Similarly, if the
shear stress is
TbB or TbC, the corresponding
depths of erosion will be
zB or zC.
Fig. 9. Depth-variation of
cohesive bed shear
strength (with respect
to erosion).


3-8


From the point of view of
----- -- Discretized erosion, the cohesive
shear strength of the bed
and its variation with
S--depth and time are
important. While the shear
---- strength and the density
both increase with
consolidation, Krone
(1963) observed that the
Former increases in steps,
a-
W I i.e. in a discretized
manner.




Fig. 8. Schematic description of
the relationship between
bed structure and the
cohesive shear strength.
Source: Mehta (1983)

* Since each aggregate order has a certain cohesive strength, a
deposit of a particular order will be able to withstand a
certain overburden before it is crushed to the next lower
order. On the left hand side, layers of deposit of orders n,
n-l, n-2, n-3 and n-4 are piled up, one upon the other. The
order n>4. If n=4, the bottom layer will be of zero order,
and will not be crushed further. The corresponding shear
strength profile is shown on the right hand side. While the
bed description given would result in a step-wise,
discretized variation of the shear strength, such steps are
not always identified from laboratory data, and a continuous
profile is usually obtained as shown.















Nl
'4

'4


Iia


f7-'C- CA 0


Fig. 10. Time-concentration
response of kaolinite
beds during erosion a)
non-uniform, b) unifor
bed.
Source: Mehta and Partheniades
(1979) N

Q.
Note step at 1.5 cm depth at 1
day. Step not visible after 8
days.


05-


1 z
C = J p(z)dz
0
provided h is assumed to be
constant. Since p also
increases with z, the
difference between CC and
Cg will be much greater than
the difference between Cg
and CA. This aspect is
further noted later.
Finally, for a shear
stress TbD, the bed will
continue to erode indefi-
nitely, at least in
principle, since the
condition rbD = TsD
cannot be attained. In a
test conducted by Krone
(1962) using a silty-clay
from San Francisco Bay,
erosion continued even after
500 hours.

SResponse of a non-uniform
kaolinite bed.

Response of a uniform
kaolinite bed of same mean
density.

BED SHEAR STRENGTH, T(N/m2)
0.2 03 04 O.S


KAoUMITE


8 Days -


I Do y-


1.01-


Fig. 11. Kaolinite bed shear strength profiles after one day and
eight days.
Source: Parchure and Mehta (1985)


3-9


--- -- -- --- ---


-- i


""











GRAMS OF DRY SEDIMENT PER LITER
S00 0 8.6 V 25
A 14 0 40
Z 0 o20
S500- SALINITY, 23 g/I
g CYLINDER DIAMETER, 5.95 cm .

S400 / k
z
oF









0 I I I I
0 0.01 0.02 0.03 0.04 0.05
lit, min"1 I .




Fig. 12. Consolidation of mud in 1-liter cylinder.
Source: Krone (1962)

According to Bosworth (1956):


S+ 1
H t

where H. is height H of the final consolidated sediment at
infinite time and k is an empirical constant.


Change in line slope marks a change in consolidation
behavior, possibly connected with aggregate breakdown.


Self-weight consolidation is more efficient than
consolidation under continued depositional flux which hinders
dewatering.


If the depositional flux exceeds a certain critical value,
dewatering is minimized and fluid mud is formed.


3-10




















W.
C-








z
0
U.









O


0- 0.1 02 0.304 0.5

Crb- -C)(N /m)

Fig. 13. Erosion rate expression
for non-uniform bed.
Source: Parchure and Mehta
(1985)

TABLE 2.- Erosion rate parameters a and ef

Sediment Investigator(s) a


(mN-


Sf x 105
1/2) (gcm-2min-1)


Bay mud

Lake mud

Kaolinite (tap wi

Kaolinite (salt

Estuarial mud


Partheniades (1962)

Lee (1979)

iter) Parchure and Mehta (1985)

Jater) Parchure and Mehta (1985)

Villaret and Paulic (1986)


Source: Mehta (1986)

3-11


A problem with this erosion
rate expression is that it
is not dimensionless and
therefore not universal. On
the other hand, data from a
number of tests of different
investigators seem to
conform to this
relationship.


8.3

8.3

18.4

17.2

7.9


0.04

0.42

0.50

1.40

5.30


..---.-..-..-.. "-













SAR sodium adsorption ratio L/ SAR
.02042
SAR = Na + 23'C

E1/
\2 (CA + Mg )] .015 181C .

where the cation 9.5SC
concentrations are in 010
milliequivalents per liter a
(Arulanandan, 1975). z
S .005 -

C = EMB 1)
s 0
0 10 20 30 40 50 60 7
-- SHEAR STRESS dyms/cm2

Fig. 14. Erosion rate for 30%
illite (Yolo loam) at
various temperatures.
Source: Ariathurai and
Arulanandan (1978)

* The effect of temperature on erosion has been modeled as a
rate process equation (for chemical reaction rates) (Kelly
and Gularte, 1981).

TABLE 3.- Erosion rate constant, CM, shear strength, Ts



Sediment Investigators M s
(gcm-2min-1) (Nm-2)


Yolo Loam (9.5C) Ariathurai and Arulanandan (1978) 8.3 x 10-3 2.70

Yolo Loam (180C) Ariathurai and Arulanandan (1978) 9.9 x 10-3 2.40

Yolo Loam (23C) Ariathurai and Arulanandan (1978) 1.5 x 10-2 2.20
-2
Yolo Loam (420C) Ariathurai and Arulanandan (1978) 2.5 x 10-2 1.20

Estuarial mud Villaret and Paulic (1986) 9.7 x 10-5 0.20

Bay mud Villaret and Paulic (1986) 2.8 x 10-4 0.12


Source: Mehta (1986)


3-12
































"o 20 40 60 80
SODIUM ADSORPTION RATIO. SAR

Fig. 15. Critical shear stress
versis SAR for
montmorillonite soil.
Source: Alizadeh (1974)


< 10
()I


Critical shear stress is the
same as bed shear strength. In
a uniform bed (as in this
case), the value does not
change with depth.


OL
0


SALINITY_(meq/I) _.
Fig. 16. Variation of SAR with
salinity (sea salt con-
centration).
Source: Ariathurai (1974)


20 40
TOTAL CATION CONC.(meq/l)


Fig. 17. Coagulation-dis-
persion boundary
curves for montmor-
illonite at three
pH ranges.
Source: Kandiah (1974)


3-13









3. SHEAR STRENGTH AND DENSITY


* Bed density profiles are similar to shear strength profiles
for non-uniform and uniform beds.


.LOF


Consolidation Period
(hrs)


0.1-


S2
S5

* 24


SConsolidation Period
(hrs)
48
0 72
o 96
S* 144
a 240


0.1-


0.3


P /


Fig. 18. z/H vs p/p for the
consolidation periods
less than 48 hours.
Source: Dixit (1982)


Fig. 19. z/H vs p/p for the
consolidation periods
less than 48 hours.
Source: Dixit (1982)


* p = depth-mean density; H = bed depth. Note the affine nature
of the data after 48 hours. Although there may be no unique
connection, it is worth noting that it takes about 1-2 days
(~ 48 hrs) for the process of gelling to complete.

* Even though density and shear strength cannot be correlated
uniquely (because for instance aggregate shear strength can
be the same for different aggregate packing density) a useful
approximate relationship between the two is found.


3-14










The relationship


B 5.0 7.288 4.6 9.74
T = ap o 8.392 8.8 976 O
S Co (10.272 16.8 1002
a 6.866 33.3 9.72
a 6.810 0.8 9.74
is very useful for "tracking 6. 9.74
erodibility with bed density T -
change under cycles of erosion, E "
deposition and consolidation. Z



S- p s 0 oo0
5 W
s w
0
ps = sediment density
pw = water density 1.0 -
PB = bed bulk density

x

0.5

60 80 100 150 250 350
DENSITY p(kg/m3 )

Fig. 20. Correlation of bed
shear strength with
bed density.
Source: Owen (1970)

4. A PRACTICAL EROSION RELATIONSHIP

E" EM ( T-1) (g/m2 -min)
Tc
Tc= .04(p,-1) (N/m2)
M = 0.0106exp(-2.33 Tc) (g/cm2-min)
SixiO = (N/b2) Problem of dealing with dredged
b material slurry density which
Swill be adequate to allow
E erosion of spoil at the dump
site near Alcatraz in San
Francisco Bay.
> n 0.020
z h= IO

S5p- 1.2/cm
o
LA_

, Fig. 21. Dependence of erosion
S -rate on current speed
Sand bulk density.
/?g= pSource: Villaret and Paulic
(1986)


CURRENT SPEED, u (m/sec)














Samples tested
simultaneously
in rocking
flume and
annular flume
to "calibrate"
for bed shear
stress.


Fig. 22. Rocking flume.
Source: Villaret and Paulic
(1986)


Fig. 23. Rocking flume modified to create a rocking "tunnel".
Source: Villaret and Paulic (1986)
Mixing1 Deposition and Erosion
Consolidation


For analysis of
resultant time-
| concentration
relationship
see Parchure
and Mehta
(1985).


I I
75 9

Fig. 24. Experimental test
procedure (shear stress
variation).


3-16


I 2 3 4 5 15 3 4.5 i
Doys .Hours


Oo






--2 cm dia. plastic tube


S15 cm dia. plexiglass cylinder
2.5 cm dia metal tube


----- Annulor space for mixture of alcohol
and dry ice


A similar
freezing
procedure has
been used
successfully in
the field.


Piston with Screw Rod


Fig. 25. Apparatus for measurement
of density as a function
of depth.
Source: Parchure (1984)


Fig. 26. Alcatraz disposal s:



TABLE 4.- Erosion histogram
-- CURRENT (cm sec-1)
*L-"O to 30 40 50 6 _0 70


ite. Fig. 27.

Source:



80 90 100 110


Depths (ft. mllw) at
site.
Trawle and
Johnson (1986)


120 130 140 1s0 1t0


---------- ------ ------ ------------ ----------I----------- -------
I I I 4 4.3I I 2 .1 l

1.151 0o 0o 1,6741 t,831 4,1641 5,4911 5,1431 5,7831 4,2631 3,3451 3,4181 e,5091 1,9241 3T71 s31 41,o201
111 1 1 1 1II I I I1 I 1I
I.21o 01 o0 7941 1,3061 1,9761 t ,6061 |,4411 8,7441 2,0831 1,5881 1,6191 1,1911 9131 1791 51 19,4681
1t.si ol 0o oI 7541 1,081 1,4361 1,3461 ,5131 1,14| 8175S 89el 65ss s03|1 9 141 10,t931
I I I I I II I 4 1 11
S1.3 ol o0 o0 45ssi 65sl 681 8131 9141 741 5e9l 5391 391 3041 601 81 6.171
I I I I I I I I I IIIIII I
1.351 Ol Ol 0 2931 4231 5571 Se21 5871 4331 3401 3461 55I 1951 381 SI 3.9s51
II I II I I IIlII I
1.401 01 ol o o01 2641 3741 3s11 3941 2911 221 2331 1. 71 1311 261 41 2.1871
1.451 0! oi Ol *I 1971 2601 2441 2741 2021 1591 1ie2 1191 911 18I 31 ,7281
I I I I I I I I I I I I I I I I I
1.501 o0l O of01 1411 1861 1741 195l 1441 1131 151 851 051 131 2I 1.3M3
----------------------------------------------------------------------------- -
SLURRY DENSITY (gcm-3) EROSION (1000 cu.yds./month)
Source: Teeter (personal communication)


3-17


T
15cm

I_


Porcelain
Dish -








5. ENTRAINMENT
* To date, entrainment rates of fluid mud have not been
measured and correlated.
* The question of interfacial instability has been examined
only briefly.
* Kelvin-Helmhotz problem

-1
At ir

-R
p, #
---- ~ .... ^o^/ a= ^ <-^ ;^ ^ ^^


E!Uot


kr c x
0.41e Co.$


Fig. 26. K-H boundary value problem. Note pressure and
displacement are continuous across the interface.


CPI. -
(p"#e 2


c2
Cu, -Uo J
__ J


C'.


C -'S )f'Of v
400


A/-w


d-Ce4 Y


.%^~/VVV\ Cff'&v7M
# A-Ae 4

~ c~vvz/ ~&V :rv


3-18


C -I -f- /I9 -
P^ t 1
____


f PO
P-O spa


+ IfI~c


fRorw .


























Fig. 27. Interface in run 2.


Waves were generally high and
wave periods quite small. Wave
heights were between 0.5-1.5 cm
and periods between 1.6-3.5
seconds. Periods were initially
on the order of 3+ seconds and
gradually reduced to 1.6 seconds
followed by wave breaking
activity. Waves appeared non-
linear with long, extended
shallow troughs and short, high
crests.




Started out with 1.3 cm wave
height which increased. Heights
were generally high-ranging from
1.3 to 2.5 cm. Periods ranged
from 3 to 5 seconds. Breaking
was visible towards the end.


Fig. 28. Interface in run 4.


Q3__ L_ J
.1 1 1 1 I-e I I I ~rI -r^ r^ i
t--|
___.. { (g) 0


ELEVATION


ML x -


lQTx I


I Flume
2 Pivot
3 Power Jocks
4 Woter Supply
5 Drain
6 Diffuser
7 Sledges
8 Toil Gole


9 Pump
10 Valve
II Return Pipe
12 Orifice Meler
13 Ramp
14 Pipe with Vents
15 Tronsition Tonk


Fig. 29. Flume used in interfacial (fluid mud/water) behavior
study.


3-19


PLAN


1 111 1


-' I


,p


0 9 1 qJ


" T









TABLE 5.- Summary of interfacial behavior test data



Po P1 Ap U h
Run # 1
g/cm3 g/ca3 g/cm3 (x103) cm/s cm

1 1.0080 1.0012 0.0068 6.79 3.4 34.0 19.1
2 1.0102 1.0016 0.0086 8.59 8.9 32.4 3.5
3 1.0098 1.0024 0.0074 7.38 6.8 33.0 5.1
4 1.0100 1.0027 0.0073 7.28 6.8 33.0 5.0
5 1.0069 1.0017 0.0052 5.19 10.1 34.0 1.7



* In the above table po is the mean density_of the upper fluid,
Pl that of the lower fluid, Ap = P1-Por U = mean (over total
flow depth) flow velocity and h = total flow depth. Ri =
gh(Ap/pl)U2 is the Richardson number.


6. ORDER OF AGGREGATION AND TRANSPORT

* This is an approximate, "conceptual" approach.

* Aggregates possess shear strengths which, if exceeded, will
cause them to breakup and be entrained.

TABLE 6.- Properties of Brunswick harbor sediment


Order of Density Shear Strength
Aggregation Pf(gm/cm3) Ts (N/m2)



0 1.164 3.40
1 1.090 0.41
2 1.067 0.12
3 1.056 0.062


Source: Krone (1963)


Pf = floc or
aggregate
density


3-20










* The average internal shearing in a fluid, G, is obtained from


/ du
II
where P = energy dissipated per unit volume of the fluid, p =
dynamic viscosity and T = shear at any elevation z above the
bed. This relationship is obtained by considering the balance
of forces and conservation of energy for a differential fluid
element (Streeter and Wylie, 1975). In the laminar case, G =
du/dz, whereas in the turbulent case the above equation is an
approximation (Friedlander, 1977).

Shearing rate which can be withstood by 0-order aggregates of
Brunswick sediment is 3,370 sec-1, whereas 3-order aggregates
will be severed when the shearing rate exceeds 61 sec -1.


T = pu*2( -)
T =h

du _
dz Kz

.* 3/2 1/2
/2 1/2 -1)



667 I I I I These shearing
Station 4 rates suggest a
relatively low
Energy micro-
0.00 tidal
0 environment.
,
6.67-
-/h .1 0


w

20r I I I I I I I I I I
.00 8JO 1000 I2oO 1400 16.00 18.00
TIME (Hours)

Fig. 30. Shearing rates at
different relative
elevations in Cumbarjua
Canal, India.
Source: Mehta and Hayter (1981)


3-21









40





w
I-

a-


8 10 12


Fig. 31. Typical variation of the depth-mean velocity over a
tidal cycle in an estuary.
Source: Mehta and Hayter (1981)


4 0C I I I I I I 1 I I r


30- zo/h=0.5



-- or-order
0z/h 3 0.





20-
-I1-order
iTMI order
-i 1I I I I I 1 I
30 2 4 6 8 10 12
TIME (Hours)


Fig. 32. Shearing rate as a function of elevation above
over a tidal cycle an illustrative example.
Source: Mehta and Hayter (1981)


the bed


* The increase in G with depth means that, once formed,
aggregates of a given "base" order will survive near the
surface in preference to the bottom layers where they will be
broken up more easily. There will therefore be a tendency for
the comparatively large aggregates to settle downward (due to
their high settling velocities), and for smaller aggregates
to move upward by diffusion, thus setting up a vertical
sediment circulation cell. The strength of this circulation
will, in general, vary temporally as well.
* During flood only 0- and 1-order aggregates will be able to
withstand the level of shearing at the strength of flow
(assuming the shearing rate at z/h = 0.1 to be representative
of the near-bed shearing regime), whereas during ebb 0-, 1-
and 2-order aggregates can occur, as the shearing rates are
observed to be insufficient to break up 2-order aggregates.
The implication is that the aggregates deposited at slack
after flood will tend to be an order lower than those
deposited at slack after ebb.


3-22


6
TIME (Hours)


2 4


0.6 i i i -- I- I-I



0

-Q3-

n_- I I I I I I I I I I I I


--"o









LECTURE 4


RESUSPENSION BY WAVES

SIGNIFICANCE
Generation of coastal turbidity with a high degree of
seasonal variation governed by the wave climate.
Damping of nearshore waves as they approach muddy shoreline.
Erosion of estuarine flats, banks and tide-driven transport
of eroded material to areas prone to sedimentation.


Fig. 1. Mudshoals and Amazon mud stream off Surinam.
Source: Wells (1983)


TABLE 1. Muddy Coast Physical Parameters for Louisiana, Surinam
and Korea


Mudshoal dimension Fluid mud

Tidal Wave Bulk Particle
Location range energy Alongshore Offshore Thickness density size
(m) (km) (km) (m) (g/cm3) (pm)




Louisiana 0.5 Low- 1-5 0.5-3 0.2-1.5 1.15-1.30 3-5
moderate

Surinam 2 Moderate 10-20 10-20 0.5-2.0 1.03-1.30 0.5-1

Korea 5-9 High 1-30 5-50 0.1-3.0 1.20-1.30 6-11


Source: Wells (1983)









* Muddy coasts exist even under high wave energy environment
because of the presence of (usually fluvial) source of fine-
grained sediment.
* 150 x 106m3yr-1 transport rate in the Amazon mud stream.


A



* R.M.S. WAVE HEIGHT
MEASURED AT
PLATFORM S


* *0 R.M.S. WAVE HEIGHT
A MEASURED AT PLATFORM V
T = 7.75 sec





* --COMPUTED FROM PUTNAM &
JOHNSON USING f = .01


A -COMPUTED USING RELATIONSHIP
FOR THE FORCING OF A MUD
WAVE


1I I I I 1 1
0 10 20 30 40 50 60
DEPTH OF CONTOUR (FT)


2
rpgMH sin)
-Dm 2..


4Tcosh kh


H = wave height
T = wave period
S=ir *
9 = phase angle
between bottom
pressure wave
and mud wave
h = depth
k = wave number


M = pressure ampli-
tude divided by
mud amplitude
p = fluid density


g = gravitational
acceleration
Fig. 2. Measured and computed
wave height decay with
distance. Distance
between platform S and
platform V = 3.35 km. f
is bottom friction
coefficient.
Source: Tubman and Suhayda (1976)


* Average energy transmitted through the sea/sediment interface
per unit area per unit time over one wave cycle (Gade, 1968):


T
Dm = T p dh dt
0 dt


p = wave-induced bottom pressure
dh = infinitesimal increase in interface height

o Mud viscosity results in a phase shift (lag) between forcing
wave and mud wave. This results in the transfer of energy to
bottom sediment.
* Energy loss found to be at least an order of magnitude
greater than that resulting from friction and percolation
over a sandy bottom.


4-2


60r


20 -









TABLE 2. Dissipation of Wave Energy_
J.A.Putnam & J.W. Johnson I R.O. Reid & K. Kajiura IResults of East Bay Study
Impermeable rigid bottom Permeable rigid bottom

D 4 w2pfH3 Dp = w pKH2 Dm rPMH2sin
3 T3sinh3kh 4Lvcosh kh 4Tcosh2kh

IN 19.2m OF WATER

T=7.75sec M=.0388
#x 220
f=.01 K=10'6cm2 D 2.99x10 2
Dm D 2.99x 10- H
Df= 3.67x10-12H3 Dp =1.86xl0-1H2 .10
Dm= 1.2Sx 10-8H2

IN 4.5m OF WATER

Df =1.23x i10-H3 Dp =1.14 x 10-9H2 Dm=1.07x10-7H2
(v = kinematic Dm 4.99x10-8H2
viscosity)
Source: Tubman and Suhayda (1976)


a. IDEALIZED TIME SERIES
t2 13
ti I


Expression for
Dm is obtained
using linear
wave theory.
Units of Dm
are Joules
cm-2S-1. 4
measured by an
accelerometer
embedded in
mud. Measured
# was 220.
Correct energy
dissipation
rate is
obtained by
# = 10.


WAVE FORM
C yv


6 7 8 9 10 11 12 13 14 15 16 17


MAXIMUM DENSITY Time (sec) DIFFERENTIAL DENSITY
--MINIMUM DENSITY -

ZONE OF ZONE OF
INSTANT SUSPENSION GRADUAL SETTLING


b. SEQUENCE OF SUSPENSION-DEPOSITION



L2 ,
A Fl

slC i


11


,, ,


Fig. 3. Wave-induced resuspension
over mudshoal. A and B are
elevations of pressure
gages. t refers to time.
Source: Wells and Kemp (1986)


Observations in Surinam
indicated change of wave
form from sinusoidal to
solitary, traveling
onshore.
Concentration (density)
change measured by
pressure change:

P = Pw + (Ps Pw) C


AP =


P g[Az +(-s- 1)
w


depth at A
depth at B
PB-PA
ZB-ZA


ZB
SCdZ]
ZA


* Energy dissipation substantially is higher than in the case
of a rigid bed. Soft mud bed oscillates and fluidizes in
response to wave loading.


0 1 2 3 4 5










2. BACKGROUND

* Resuspension/erosion, wave damping and bed motion are inter-
linked. ......--
-- ^T -


Fig. 3. Inter-relationship between erosion, wave damping and mud
motion.
Source: Maa and Mehta (1988)

Explanation

1,2 Waves determine turbulent flow structure in water.
3 Flow structure in water influences mud-water interface and
vice versa.
4 Mud bed properties and dynamic behavior influence mud-
water interface and vice versa.
5,6 Wave loading and consolidation of the mud bed cause long-
term (>> wave period), time-dependent changes in mud
properties and dynamic behavior.
7,8 Turbulent flow structure and interfacial fluid properties
determine interfacial shear stress.
9,10 Interfacial shear stress and interfacial mud properties
determine the rate of erosion.
11,12 Interfacial shear and pressure forces together with mud
properties determine the dynamics of mud motion.
13 Dissipation of energy in mud damps (attenuates) surface
waves.


4-4


L









* Energy dissipation in the mud bed is related to theological
properties of the bed.
Rate of energy dissipation per unit volume of fluid = TE
T = stress

E = rate of strain
* One type of description found to be adequate for correctly
estimating the energy dissipative characteristics of soft mud
beds considers mud constitutive behavior to be viscoelastic.
For small strains, the response can be considered to be
linear:

T = 2GE + 2 pE


T = shear stress E- eonst.

G = shear modulus of 7
elasticity

, = dynamic viscosity

E = strain

E = rate of strain

Data are obtained by 2,E
deforming the sample i
at a constant rate
of strain.


Fig. 4a. Linearized viscoelastic stress-
8 Istrain relationship
0


Data suggest a fairly
4* linear response up to
6(roda/ec) shear strain 8 = 0.03
o .206 (rad). The rate of
2 .0265 strain (rate of angular
2 .0122 displacement) is 8.
.00135 Torque relates to
applied stress.

0 .02 .06 .08

S"EAR STRAIN (ra)
Fig. 4b. Viscoelastic behavior of a
clay.
Source: Stevenson (1973)









* The simplest description for viscoelastic type of a solid is
represented by the Voigt element.


A. CV


Spring and damper are in
parallel arrangement. A series
arrangement will give a
Maxwell fluid element. Stress
relaxation tests can be
conducted to determine if a
given material is Voigt f
(initially applied stress does
not dissipate) or Maxwell
(stress dissipates)


ELLt&TIC RESPOhNSE



VI VSCO&LASTIC.
URSPoNSe


TIME


Fig. 5a. Voigt element and its
response.

* G and u can be determined very approximately in a rotating
spindle, constant rate of strain (Brookfield-type)
viscometer. Accurate determination of G can be made using a
pulse shearometer and p through a constant stress viscometer
(James et al., 1986).
* By selecting mud slurries of different densities, empirical
relationships between G and density and p and density can be
established.


k ---Video Comero


Angular Displacement Viscometer
Pointer
Vane

Angular Displacement Mud Container
Scale
Fig. 5b. Apparatus for relaxation
tests and viscoelastic constants
measurement.
Source: Maa (1986)


Brookfield (model LVT)
viscometer with miniature
vanes. Eight rotating
speeds from 0.3 to 60 rpm.
Maximum driving torque
673.7 dyne-cm.


A A





70


r, R n I Vorit ilemenr "-
"0o IN*".To0 ue Trv ( 73 dye em61
% -4- 6.2 m 2


14o0 -

30-



0 1 --

I 2O o II 12 1 44 45 46 47 48

ELAPSED TI-M6E (m)n)
Fig. 6. Stress relaxation test using kaolinite.
Source: Maa (1986)
* Above test shows kaolinite slurry does not have a Maxwell
response since, after an initial decay associated with
instrument inertia, the applied torque did not dissipate.
Tests were carried out at two depths, -1.5 cm and -6.2 cm
below bed surface.






S:oo
0r10-







A2 4 S /G
7. V ome (a lcm i



Fig. 7. Viscometer-determined G- relationship.
Source: Maa (1986)


4-7


i 1 I I I I 2 A I


I









F1

I?



S
z


!L


r I I


n


too

50


'CL


'0 ( .2 O.3 0.4 '.9 o



Fig. 8. Viscometer-determined P-PD relationship.
Source: Maa (1986)
0 Runs 1-6 correspond to beds used in flume tests on
resuspension described later. Refer to the following t
TABLE 3. Test Parameters in Wave-mud Interaction Study


able.


Run Sediment Consolidation Water Mud
No. type period depth depth TbL Tel Tb2_ Te2
(days) (cm) (cm) (Nm-) (hr) (Nm- ) (hr)

1 Kaolinite 7 23 13 0.17 7.0 0.24 7.3
2 Kaolinite 14 19 11 0.13 5.5 0.21 5.5
3 Kaolinite 2 17 13 0.11 5.0 0.13 6.3
4 Cedar Key Mud 7 28 8 0.16 4.8 0.26 5.0
5 Cedar Key Mud 2 20 16 0.14 3.8 0.26 5.1
6a Cedar Key Mud 14 25 11 0.20 3.0 0.25 4.0

aTb3 0.29 Nm-2, Te3 4.0 hr Source: Maa (1986)
In Table 3, Tb refers to applied (wave-induced, maximum) bed
shear stress; Te is the duration of application.


4-8


- *I
*R2
A,
Alt
4





II I I I











* G typically increases with increasing p while p decreases
except in run 5. The latter result is Reemingly paradoxical,
since one would expect p to increase with p This paradox
is however resolved when it is recognized tnat these G and P
values are to be considered principally as coefficients
satisfying the linearized constitutive equation for visco-
elastic response. The rate of.energy dissipation per unit
volume for such materials is TE, which actually decreases
with increasing p in the range of p examined, because rigid
beds oscillate less than soft beds and thereby dissipate less
energy. The trend of decreasing u with increasing p ,
coupled with the trend of increasing G with p is consistent
with a decrease in the rate of energy dissipaPion with
increasing pD'
3. DYNAMICS OF MUD-WATER SYSTEM











+) EROSION





* el Ig Is Iei I / I I Isum* *a e

----^ ? .....- -, --\,--- ---g



"A aottoM


Fig. 9. Schematic description of mud-water system, v denotes
kinematic viscosity, Em to vertical diffusion
coefficient, and r are mud wave amplitudes. Layer 1 is
water and the remaining (2,3...) are sub-layers of mud,
each with constant properties (p,v,G).
Source: Maa (1986)







Governing Equations (linearized-small strain):
mnOTow ( I nearizad)


bULi


ax+
(^1


Pi ~A


Pi
Pi


bz


i)j+ ~h
- jG;


i. 1

i 2...,N


Pi Pit + P PI + P


weRE


oht4 pressure


a.\d


i2 .t
i. l

i. 2..., N1I


0,


1to Us2r is
C.O~tJTf ~Ug'ry.


+w
+ a


(kx ..Ae-t)
* u ,w ar r al and vertical amplitudes of oscillatory
wave velocities.
* Expression for viscosity Vei (a complex number since j
= T--) is based on Voigt solid representation.
* For boundary conditions and solution technique see Maa
(1986).


4-10


bwi


W _.


-I


bui
bx


pit,








Flume experiments designed to examine
mud bed response
wave damping
erosion

Roughened Wove
Beoch x Maker

Roughened beach 15 Water
to minimize 5
wave reflection ___2
S8m
h ----------------20m- --- ^ ---
Fig. 10. Experimental wave flume.
Source: Maa (1986)

Velocity overshoot just
above the interface is
35- characteristics of the
SSWL influence of viscous
w 0 boundary layer within
SRun 5 the mud.
S30 Ho=3.2cm
2T = 1.8 sec
S25- *- Measured
ao Simulated
o A representative shear
Strain (inverse tangent
20 of one-half ampl. of mud
S- oscillation at interface
S Tb=O.1 4Nm* interface divided by mud thickness)
2 50 which is small.
S' Tubman and Suhayda
3cm (1976) found small
OZ strains in field
K0 measurements.
5cm
SHBo is wave amplitude
-J upstream of mud bed. T
L is wave period.


0 5 10 15 20 25
VELOCITY AMPLITUDE (cm sec-1)


Fig. 11. Measured and simulated velocity amplitudes.
Source: Maa (1986)


4-11









* Compare with similar data obtained by Migniot (1968) which
also show effect of consolidation (reduced orbital velocities
with increasing bed rigidity).
SPon d 9o0
(fomlxn -) I -. l,

I T1
Fig. 12. Horizontal velocity
viscosity.
Source: Migniot (1968)
1 35" Run5
S Meosured
S--Simulooted
200M
0
m 25-
9


20 "
S20- f2an


5man
I -


Inertial effects and
pressure effects are
dominant in the
upper layer except
very close to inter-
face where wave
boundary layer
occurs. Kinematics
approach ideal flow
description even
though flow may be
turbulent.


0.50 0.70 0.90 1.10
NORMALIZED PRESSURE AMPULI,E.p/go
Fig. 13. Measured and simulated dynamic pressure variation.
a = Ho/L is surface wave amplitude.
Source: Maa (1986)


4-12








Wave damping coefficient,
D, is defined by

ax = aoe-D
Wave damping is a measure
of energy dissipation
within the bed.
Uncertainty in measure-
ment of viscoelastic
constants v and G is
partly responsible for
data scatter.


r.










'A


WAhvIe & W-,.Sc-r
WAV 5 PURB.AOo -= \.2.S


WATelR


PREDICTED COEFFICIENT, D (m"')
Fig. 14. Comparison between
measured and predicted
values of D.
Source: Maa (1986)
Sex_


RnotAmCgE


BeTD


I I.I |.l I.
luLa DE-IT% (gC c-w)
Fig. 15. Effect of bed "rigidity" on wave damping.
* Resonance condition corresponds to greatest transmission of
wave energy into the mud bed. Simulation is based on
"typical values" of v, G and other parameters related to
flume tests.


4-13








1.10


BULK DENSITY, p(g/cm3)
1.15 1.20 1.25


1.30


( I IV I I I I I I I
o0 180 260 340 420
BED SEDIMENT CONCENTRATION (g/L)


Fig. 16.

Source:
34 r


Initial decrease and
subsequent increase
in density are due
to combined effects
of wave-induced bed,
fluidization and
self-weight
consolidation under
wave action.


500


Bed density profiles during
resuspension.


103 10 105
SEDIMENT CONCENTRATION (mgl 1)
Fig. 17. Evolution of suspension con-
centration profile during wave-
resuspension.
Source: Maa (1986)


Due to the inability
of waves to upward-
entrain the eroded
sediment and
buoyancy
stabilization, a
fluid mud layer is
easily formed.

Richardson Number,
Ri, represents the
ratio of upward
entrainment to
buoyancy stabiliza-
tion (by gravity).



., g (0.2z


RiA 0.22


Pip = 900oo


4-14









Concentration profiles indicate 24
that in the fluid mud layer, as ()t=0.5s (b) t=5s
well as in the upper water
column, the variation of the
logarithm of concentration with -
elevation was approximately
linear. Such an exponential
trend is compatible with the
existence of a constant mass 8-
diffusion coefficient in each
layer. -

S0 6 4 0 -4 16 12 8 4 .0
LONGITUDINAL DISTANCE (cm)


Fig. 18. Diffusion of line source of
dye by waves of 1.25 sec
period and 7 cm height.
Source: Maa (1986)
-6
0 The mass diffusion coefficient, Dm, ranged from 2 x 106 to 4
x 10-5 m2sec-1, with a mean of about 1.2 x 10-5 m2sec-l in
the upper water column. In the (near-bed) fluid mud portion
of te water column, it was on the order of 1 x 10-6 m2
sec Thus in the upper column, Dm was an order of magnitude
higher than in the fluid mud; the latter value being of the
same order as the cinematic viscosityof water.




opCeDL L--102




NFi. 1.E A description o wave-znuc. difsion proc No


1 Hrv> 10000 (tvl4buiyL)
W410000 (ViScoL&LS Sub- \cLr)
WAVE eYNO LDS NmrEJGPE. w k2

N4tGA Ric*OAkD6oiJ Nur 6 L)s
Fg 1 STA 8 il i NTMLA,-6
Fig. 19. A description ot wave-induced diffusion process. Note
that ex is influenced by mud wave oscillation and by
residual mass transport associated with wave non-
linearities.


4-15








0 Q20NAn--*a0.25N/n-^m 2
-e- -Q29N ./m 4

10 Run 6



Q5-
2_ f/ Meon Trend *



0o 200 400 600

Fig. 20. Fluid i;JAfdiB )tion under wave action.
Source: Maa (1986)

Deviations from the mean occur at times when the bed shear
stress is increased by increasing wave action, 180 min and
420 min after test initiation. In both instances, spikes
first occur followed by decay to mean value; the excess
material being removed from the layer by upward entrainment,
rather than by deposition.

101 -. '""I lilt'""I l'"I '"1


The erosion rate expression is a i /
very approximate representation
of a complex physical process. *
In particular it is noteworthy
that on account of fluid mud -1 .
generation, the near-bed boundary .
layer flow and, z
therefore, Tb, are modified. A *
consequence of this effect, and .*
the influence of waves, on bed 10 *
resistance TR, is that the*
ratio, (Tb-TR)/TR, tends to N_ E T -
exhibit a degree of variability /
which cannot be easily a- -
quantified. z.

1f I e. 1 1 1 1 I l 1 1 1 I I l l m l l -I 1 1 1 1 1 J
0 1102 10C' 5 K)'1
NORMALIZED STRESS, b -TR
r,
Fig. 21. Erosion rate
expression.
Source: Maa and Mehta (1987)


4-16














E
z
w
0



w
Cn
cc
,,)


o No Waves
* Waves


-/'
/
I


I
I-r


I- -


U
0 5 10 1
PERIOD OF CONSOLIDATION (days)


Fig. 22. Effect of waves on bed shear resistance (strength).
Source: Mehta (1986)

* The effect of waves on bed resistance to erosion is
highlighted above. Data for kaolinite beds of different
consolidation periods are shown. Bed shear strengths in the
upper curve were obtained by Parchure and Mehta (1985) under
steady current. Representative mean values of bed shear
resistance under waves in the lower curve were obtained by
Maa (1986). As an example, for a bed of 2.5 day
consolidation, bed resistance is observed to have been
reduced from about 0.25 Nm-2 to 0.03 Nm-2 due to wave action.

* Waves essentially provide a mechanism for erosion and
entrainment without a significant net horizontal transport.
Their principal role is therefore to assist current (e.g.
tidal) in transporting eroded material to areas prone to
sedimentation.


4-17


-


Wave
Effect


i


I








LECTURE 5
VERTICAL STRUCTURE OF CONCENTRATION PROFILE
1. SIGNIFICANCE
* Role of fluid mud in horizontal transport of mud to
sedimentation-prone areas.

_


4,


4'^^QJ v,4/Ceo*^' ;A 7e' ^ v/ 4"J4 I PA)
Fig. la. Estuary defined by depth/length << 1.



S* ^ fA, ^^"4.0' Vop0,l.rVsWW 1CS
s'r.Gc v-t ow j-.v J^^ S'e/


"' '/p 6 /rA/fdA9 F


-- ',,* ? ., ,, ,*., *q,


Fig. lb. "Fluff" accumu-
7- 'I/ //7 / nation process
in navigation
W& A,7 channel.


5-1


#DkJbC ra g 7/Q1d#4r.


Zl~rA ;r/~cP /~V~R~PLE








* Ignoring fluid mud contribution to total transport load can
lead to gross underestimation of sedimentation rates.


I


'4I-c


coA IuR
Cawtv


tfgui> ft *VU-.&


fMp


4 z ArVD P


o- /


Uto


Fig. Ic. Suspended load is sum of upper column load and fluid mud.


au


4 ,Udc.q


Of -OEfudf8


4__ It
~I


df .2 mO
U ( /.D %c/

O( 4033


v 'O


S70, 000


/S = / 47- eg^ s
'00;1C ^C/ C^ ^^
711 v OP^^ ^


a g 00


5-2


,


E~G4MP~~








Il/ac

'I


CA rCHEE COYV MveIA vA



= oo0.2 COcE









2 "HIGH" VERSUS "LOW" CONCENTRATE


Basin
B s ... .. .

Fig. 2a. Camachee
Cove Marina,
Florida.


Ftot4 ENTRANce VASUtMENT


Fort BASIN SURVey


Conventional Definition of Fluid Mud by Density/
Concentration Range


Investigators)


Inglis and Allen l1957)

rone (1962)

Wells (1983)

richols (1985)

Kendrick and Derbyshire (1985)

Sills and Elder (1986)

Odd and Rodger (1986)

Kirby (1986)


Density/Cone. Range

Bulk Density Concentration
(gcm3) -3 1 (msl
(gem ) x LO (ingl ).


10

10

50

5

200

80

60
?


- -r0

- 170

- 480a

- 480a

- 400

- 220

- 120

- 480a


I


1.03

i.01

1.03

1.003

1.20

1.05

1.04

?


- 1.30

- 1.10a

- 1.30

- 1.30

- 1.25a

- 1.14a

- 1.07a

- 1.30


5-3


TABLE 1.


trY,,4R*- /*o 3-/tO io zto
aConversion between density and concentration based on assumed sediment density
of 2.65 gcm.


-~--













"Soft silt" is a o T s =s- A.
relatively loosely -
defined term as used F- R'ES



I -





44 8.40 y 8 09.s
31- 7. l962
Is




6 +S 44 +) 3 1 *1 0 -1 -2 -3 -4
LOCATION IN KM

Fig. 2b. Longitudinal section of the Chao Phya
estuary during ebb in the wet season.
Source: Allersma (1980)


* What do we mean by "high" concentration?



Concentration (mg/)


rIswironmenI I I


Rivers
Estuories surface
bottom
Shetwes -surfoce
-middle
bottom
Oceans -surfoce
-middle
bottom


1 10 102 103 104 105 to


Seoi


a, 14IG


Fig. 3. Ranges of suspended sediment concentrations common in
different aquatic environment.
Source: Modified from Kranck (1980)


5-4


r I


i


0"-4 IOr-3 It-2 i- I


s_" 4---












A^ 0V 6OVC. 4Vrw/'onv *

* PGGA6'cGRQ7PO Cc/76S 2Y'7R0* 4' r7

* $drr^,A/ 4i'z'uA v/Z'defP serrL/h'v"

T* 2.asfi.'^caif Flo wAr)hS9C/lo/ S/ePOAAnc7o
* f#rj o' Z-os/Trcv is. *17E or s>^r^RNi'v

TABLE 2. Classification of Flow with High Sediment Concentration


SOURCE CONCENTRATIO PERCENT NT VOLUME (S.G. 2.65)
10 20 30 40 50 60 70 80 90 100
Beverage and
Culbertson (1964) High Extreme Hyperconcentrated Mud Flow

Costa (1984) Water Flood Hyperconcentrated Debris Flow

O'Brien and Julien Mud
(1985) using National Water Flood Mud Flood Flow Landslide
Research Council (1982)
Fall, Landslide,
Takahashi (1981) Fluid Flow Debris or train Flow Creep, Sturzstron,
____ Pyroclastic Flow

Chinese Investigators j<---- Debris or Mud Flow ----->
(Fan and Oou, 1980)
. |- ---------- Hyperconcentrated Flow---------
Sediment Laden I
STREAMFLOW SLURRYi FLOW GRANULAR FLOW
Pierson Costa (1984) Normal:T Hyrconcentrated (Debris Torrent). Sturzstrom; Debris
Debris a Mud Flow, Avalanche, Earthflow,
Soliflection Soil Creep


Source: Bradley and McCutcheon (1987)



Onset of fluid-particle interaction is an important (and
accurate) way to define the boundary between "low" and "high"
concentration (rheologically based definition). However, in
a practical sense a unique definition may not be all that
useful.


5-5









TABLE 3. Regime Classification for Cohesive Sediment Transport


Characteristic Regime
factors 1 2 3

"Energy" Low Moderate High
Tidal range (m) < 1 1 3 > 3
Forcing factors current/waves/wind current/waves current
Concentration (mgl-1) < 103 103 104 > 104


Source: Mehta (1986)

3. VERTICAL STRUCTURE OF CONCENTRATION

CONCENTRATION, C(mgl "1)
1 2 3 4 5 6
10 101 0 10 10
0 r-- --- -- I


0 0.25 0.50 0.75 1.00

VELOCITY, u (ms -1)
5-6


4.


It is inappropriate
to characterize
fluid mud independ-
ent of the velocity
field.









q- -1
/Q5 ff


-1
MIL^


J Fig. 4. Typical
instantaneous
velocity and
1.25 concentration
profiles.
Source: Ross et al (1987)


E
N


0



(O


.J
m

I-
0
u-

Q


, K /o










4. COHESIVE BED BOUNDARY


* Corresponding to elevation B in Fig. 4.

* Soil mechanical definition bed has a structure character-
ized by an effective stress a' = total pressure pore
pressure.


0.081 I I
1.75 2.00 2.25 2.50
GAGE PRESSURE x1O (Nm2)


Excess pore water
S pressure has
developed due to
"pumping" action by
- waves over the mud
bed.











2.75


Fig. 5. Development of effective stress below
cohesive bed boundary.
Source: Ross et al (1987)


* "Visual" interface is not the cohesive bed.


* Mud layer between "visual" interface and level B below which
effective stress occurs is a stationary "fluid" mud.


* Cohesive bed boundary is not defined by a unique bed density
(conc. in present case 105mgL-1).


5-7







5. HORIZONTAL TRANSPORT OF FLUID MUD


CONCENTRATION,
Cx 10"3(mgl"1)
100 200 300 400


CONCENTRATION,
Cx 10-3(mgl"1)
100 200 300 400


0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4
VELOCITY, u (ms 1') VELOCITY, u (ms 1)


500


A o"

0.04

0.08

0.12

0.16

0.18

0.24


Fig. 6. Concentration and velocity profiles below the surface of
turbid layer (lutocline) from the Avon river, UK:
(a) measured at IW-0.33 hr, (b) measured at IW+3.5 hr.
Source: Kendrick and Derbyshire (1985)
Z/U/P^t tv A--ene 0 e ry CV 0 9r xe^xCleA


vCo tR o2"


--a


0?/4


&> Rr hA


Fig. 7. Problem definition.
oR


5-8


0.5


Ir
" ~$


cc C~


e_______i_








&* Fzo /.S .1'rFAA -P WRCF uf,,..)

i. e ,, tF 'T",e,/9i S 'f .,q .s:/,,# /) ,,r .>

PA L~Ad IRA C' 4-7


o0q


io'iJ


o'S


Cm/. 7",


1.2


x r


I. d


u, uevk ~


A


4 -YO 74jv0


Aw/ rt J>r'40 U0


Fig. 8. Stokes flow (Rayleigh flow) solution.


100 200 300 400
SUSPENDED SEDIMENT CONCENTRATION (g/I)


P m = p = suspension
viscosity. a,P
depend on the rate
of shearing pm =
,w(l + aCB)









500


Fig. 9. Relationship between apparent viscosity and sediment
concentration (Data from Krone, 1963; Delft Hydraulic
Lab, 1985; Englund and Zhaohui, 1984).
Source: Ross (1988)


5-9


0* 0V^yV"T V 4


CO--/rVe4R A


.UrgeCo' &V eX


100
80
S60
E
L 40

S20
Cf)
0
0
C 10
> 8
w 6
4
-J
CC 2

0


lai- ulu


~dZdu


A. a 4V#


7/2 Vr.- = 1







Y
* y
A4t/l :2o 00
'' A
W 7110V


SPW C
. P1 -c(so-/ C )

~'v x4~CIoc'c


dv.&.rcff


' 0 2 Oo02


u. 0-
00
m 0.02 -




i-
. E 0.04
M C0.06 -10i



So 0.10 l

A R.
&O M

Q 0.18

0.0 0.1 C

VELOCITY, u (rr

Fig. lO0a. Growth of mobile
fluid mud layer due
to an applied stress
at the lutocline.
Source: Ross (1988)


0.30 1


2 3 4 5 6 7


MASS FLUX, F (kgm2s"1)


Fig. 10b. Depth-varying horizontal
mass flux at steady
state in fluid mud.
Source: Ross (1988)


qu.rY ,,Pt ,9 > C04 Wr rF r


. o.7, ,^'s o.7/ kf^ ,; '; '
rfw,,-v,,S / ,' c -


Lr*lO4 C*r/ f 4 dot-r a fi O *2d" f sA
4ri~C OFuo$'(gco) 125 0,vjV L


5-10









6. LUTOCLINE EVOLUTION DEPOSITION


la-









0*I,








0'0I
o*~I


lo






Io


1









80


C7cC6A/ ;r.e9' Oi C


1)


Fig. 11. Relationship between settling velocity and concentra-
tion, and between settling flux and concentration.
Source: Ross (1988)


60






-IA
*o
E'
x 20
rrj


CONCENTRATION,C(mgl )


2x10 4x104 5x104 6x104
CONCENTRATION,C(mgl- )
CONCENTRATION,C(mg )


Fig. 12. Settling flux against concentration (left), and con-
centration profile (right), from Parrett River, UK.
Source: Odd and Rodger (1986)


5-11











,or


. 0
-< .-


7. LUTOCLINE EVOLUTION


- EROSION/DEPOSITION


'te d--*0
^I* a


SLutocline Layer


.0 5 9
concentration I I I I I I II
vcloci:y rn s"1 ---
0 .8


i-0 I I L t 0 --.4
0 .4 .8 1. 10- .4 .,


-.u U (


Fig. 13. Lutocline oscillation in
Source: Kirby (1986)


the Severn estuary, UK.


5-12


4*W
0C















T,
7-1


i I
f-T .F -1 -7

1, 41,


f~f----1-~-Ti-'r-~-- f
?-
T


* .. --- ......---


.ZA1..; iL..







4 .




:._-J---- J.
,. I,


5-1
gI i i j g l ^' -- -i-Lj--~ -_ _:_ ..
t--, I- I ...-
^- ,- -i -- ... .. -- .... ""..... -1 -- +-- l------* -
!__l T i- i :--- +. .L. .
:- :--: --- ---'-.---:---- --/ -- -- -- ,, -- -


.__:. _^^ f '_. ..._-____ ...... .'. .


















Fig. 14. Log velocity layer in the upper column
from data.. in Fig. 13.



t .".5-13.





5-13


Existence of a log
velocity profile
in the upper water
column (at least
up to 2-4 m above
the lutocline)
provides some
justification in
using turbulent
diffusivity coef-
ficients based on
open channel
flows.


!


!
II




















Zo'.ie S


Zone 1


6 Concentration -. 0 ConcentratioN on 0 Cocntraon 0 Concentration -p 0 Concentralion O Concentration --
Jelocity --- --- -11

O = Origins for profile L = Lutocline Sequence 1-5
decelerating phase Sequence 5-1 accelerating phase


Fig. 15.


Source:


Conceptual model of evolution of layered suspensions and
their relationship to "total energy". Model fits both
Severn and Rhine estuaries evolutionary sequences.
Kirby (1986)


CONCENTRATION, c or VELOCITY, u
V


Moue
Suspension


Lutocine
----------------------

-----------^---Rx------
Sta Sfaonary Mud
FORMATION BCohesiv
BeCONSOLIDATION
CONSOLIDATION |


CONCENTRATION, C or VELOCITY, u


Mobile
Suspension


Cohesve
Bed


CONSOLIDATION


Fig. 16. Vertical structure of concentration determined by
vertical mass fluxes: In the presence of fluidized bed
(left), and in the absence of fluidized bed (right).
5-14


Zone 1







Zone 2











OE r a)


r c t C


-;a 2


4Aff4rjA'L S/. P


rdoc .
." rPd.


.rf TA .
fT ^ *


R Az r. oY
y 7?^ / Ory i



/r C /yo
v xl


A-E~ S As-~ /oA~ c'~ l-eA z' C'
15~nJcP 7~


* y? r 7 f ,t F, -/ ~- =, <


~~~-* I; 7- ~
C.f /r ^^ i


A---I


*ov= foex 2F r


/ a
f> a2 L ^Z


Cu^t/^f


5-15


.


d* JW -4PoV#jo/9O^s 9 ^^9. / &JftrV ,Osra/.


Sc
, PA











, -f o n- '. 5
^~~3 ^S^


C,,/O,,A, f; ., A, W bd
/9 )


Aw-#^r ^,j/9 -

#vA v6*,z*

'9 CepAj "


s18
X18
14



8


41


o Measured data
(0900 Hours) j


0 2 3 4
Concentration (g/1)

Fig. 17. Measured and model simulated concentration
the Severn at 0900 hrs.
9A.------------------------. --- -


E 18


14
12
S10

a8
i.


A A Measured dc
4 (1100 Houre)


-A
-4


- A\


A

.. ."-.A...... .
Aa


ita


profile in


U
0 1 2 3 4 5
Concentraton (g/1)
Fig. 18. Measured and model simulated concentration profile in
the Severn at 1100 hrs.


5-16


o/ K




























*. .. : ..



0 00 120 180 240 300 00 420 480 540
Time After Low Water Slack Cmlin)


Fig. 19. Measured lutocline layer in the Severn
Source: Kirby (1986)


estuary, UK.


0 80 120 180 240 300 380 420 480 640
Time After Low Water Slack (mine)

Fig. 20. Model predicted lutocline layer in the Severn estuary, UK.
Source: Ross (1988)


5-17










8. FLUID MUD RHEOLOGY

* Does fluid mud have a yield strength?

* Depends on concentration, sediment cohesion and time-scale
over which response is sought.


20
2 "More" Bingham
0 1 6sotd behavior at
6 higher solids
.13 content.
,2- Basically
pseudoplastic
however.


0 0709 sold


0 50


Shearing rate (S-1)


Fig. 21.

Source:


Stress-rate of strain curves for Rotterdam mud samples
at two solids concentrations.
Williams and James (1978)



Max.
slopes
....:(I~ ._. -3-5-.


Fig. 22. 30 KHz echo sounder record showing multiple layered
stationary suspension on slope in the Severn.
Source: Kirby (1986)


5-18


r
:
~f""




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs