38. Erosion of natural sediments fromThe Netherlands
Analysis of laboratory experiments
1
Report 38. Erosion of natural sediments from The Netherlands
Analysis of laboratory experiments
J.C. Winterwerp
J.M. Cornelisse
C. Kuijper
March 1992
Cohesive Sediments
RIJKSWATERSTAAT
Dienst Binne^vaWer) &IZA
Rijkswaterstaat
Delft Hydraulics
Summary and C o n c l u s i o n s
This
report
presents
a
first
a n a l y s i s o f the experiments c a r r i e d out
w i t h mud samples from the H o l l a n d s c h
brug),
the Western S c h e l d t
Meuse ( B e l f e l d ) ,
(North
Sea)
the
and
analyses
in
step,
some
dynamic
(Spijkerboor).
physico-chemical
correlation
describes
bulk
Noord
mutual
parameters,
experiments i n the a n n u l a r
their
between
the
specific
and
flume.
analyses
s u r f a c e o f the
the sediments d e c r e a s e s w i t h
3
a t c o n c e n t r a t i o n beyond about 300 kg/m .
3. The y i e l d s t r e n g t h
rate
It
Loswal
fraction.
viscosity
sand content
The
Harbour),
has l e d t o the f o l l o w i n g c o n c l u s i o n s :
sediments and the lutum
2. The
Moerdijk-
used a r e adapted from well-known p r o c e d u r e s encountered
l i t e r a t u r e . The study
is
and
the methodology of the experiments and
the f o r m u l a
1. There
(Delfzijl
Biesbosch
various
(Sassenplaat
Lake Ketelmeer (Lake K e t e l ) , the
of s u r f a c e e r o s i o n and t i d a l
As a f i r s t
and
(Breskens),
Eems-Dollard
the
r e l a t i o n s between the
Diep
of
with increasing
increases
this
concentration;
of
the
a
sediment
function
increase
is
results
agre e w i t h
of
increasing
concentration.
the
sediment
r e s u l t s published
by Krone,
Owen and M i g n i o t .
4. The
with
5. The
yield
strength
increases with
i n c r e a s i n g C a t i o n Exchange
height
i n c r e a s i n g s p e c i f i c s u r f a c e and
Capacity.
of the i n t e r f a c e H d u r i n g
be d e s c r i b e d w i t h a formula
c o n s o l i d a t i o n experiments can
due t o Krone:
n H t
H/H
where H
and
1,2.
e
- 1 = (k/t)
e
e q u i l i b r i u m height,
i s the f i n a l
t = time i n minutes, and k
nHt a r e parameters i n the range of 30 < k < 170 and 0,5 < nHt <
The
consolidation
transition
between
curves
hindered
sometimes
settling
show
a
kink
at
the
and c o n s o l i d a t i o n ( p o i n t of
contraction).
6. The
not
measurements
accurate
distribution
of
enough
the sediment c o n c e n t r a t i o n w i t h i n the bed a r e
to
assess
the
sediment
concentration
i n the upper (1 cm) p a r t of the bed i n d e t a i l . T h i s i s
a b i g c o n s t r a i n t i n the a n a l y s i s of the e r o s i o n
experiments.
- 2 -
7. Large sand c o n t e n t s
and
i n the mud samples (> 50 X?) hamper the a n a l y s e s
i n t e r p r e t a t i o n of the r e s u l t s c o n s i d e r a b l y .
deposited
bed
For
instance,
the
from Loswal Noord mud shows a l a y e r e d s t r u c t u r e , and
s o r t i n g e f f e c t s take p l a c e d u r i n g
the
experiments
in
the
annular
flume.
8. The sediment c o n c e n t r a t i o n
p r o f i l e s w i t h i n the bed show a s i m i l a r i t y
b e h a v i o u r , i . e . the shape o f the p r o f i l e s a r e s i m i l a r throughout the
c o n s o l i d a t i o n process.
T h i s s i m i l a r i t y behaviour
can
be
described
by:
c/c
with
and
c
is
- kcz
(z/H)"
mean c o n c e n t r a t i o n
n C Z
of the bed w i t h
t h i c k n e s s H, and kcz
ncz are parameters i n the range 0,1 < kcz < 0,8 and 0,3 < ncz
1,7; ncz i n c r e a s i n g w i t h
i n c r e a s i n g sand
9. The depth mean c o n c e n t r a t i o n
time T
<
content.
c can be r e l a t e d t o
the
consolidation
through:
n C t
c = c
T
ref
c
120 < c „ < 360, depending on the sand c o n t e n t ,
ref
f
with
and net - 0,1
a 0,2.
10.
During
the
consolidation
oxidized material
properties
anaerobic
of
i s formed
this
bed: t h i s
The c r i t i c a l
with
the
differ
oxidized
a light
bed
layer
The c r i t i c a l
is
The
mechanical
first
before
the
appears
to
increase
c - T h i s however c o u l d not be
b
because o f the i n a c c u r a c i e s i n c, .
shear s t r e n g t h a g a i n s t
time
eroded
erosion z
the upper 10 - 20 % of the bed from
consolidation
surface.
t h i n l a y e r of
l a y e r i s been eroded.
shear s t r e n g t h a g a i n s t
in detail,
coloured,
from the p r o p e r t i e s o f the lower
i n c r e a s i n g sediment c o n c e n t r a t i o n
quantified
12.
on
layer
remaining n o n - o x i d i z e d
11.
process,
of
1
day
erosion t
about
and
0,1
varies largely within
to
0,7
Pa
for a
from about 0,2 t o 0,8 Pa f o r a
c o n s o l i d a t i o n time of 7 days.
13.
The
the
data
on
the e r o s i o n r a t e s show a l a r g e s c a t t e r , comparable t o
s c a t t e r encountered
surface
erosion
be d e s c r i b e d
i n l i t e r a t u r e . For a f i r s t
r a t e E observed d u r i n g
the present
as by:
E = E
f
exp {a(*
h
~
a p p r o x i m a t i o n the
^ )}
&
experiments can
- 3 -
w i t h the f l o e e r o s i o n r a t e E„ " 10~ kg/ra s and a « 30 Pa , though
6
~6
2
the s c a t t e r i s l a r g e : 0,5.10~ < E < 52.10~ kg/m s and 27 < a < 60
f
Pa
14.
- 1
).
The
These parameters a r e i n the range encountered
floe
erosion
rate
show an a s y m p t o t i c
15. The
variation
in
than t h e v a r i a t i o n
the t i d a l
f
and the maximum e r o s i o n r a t e E
seem t o
m
i n c r e a s e w i t h i n c r e a s i n g bed shear s t r e s s z^.
z
e
However, t h e v a r i a t i o n
16. During
E
in literature.
f o r the
v a r i o u s samples i s not v e r y
(accuracy) i n E
f
large.
i s huge, and i n f a c t
larger
i n p h y s i c o - c h e m i c a l p r o p e r t i e s of the samples.
experiments
Pa o n l y v e r y l i t t l e
w i t h a maximum bed shear s t r e s s of
0,2
sediment c o u l d be r e - e n t r a i n e d from t h e bed i n t o
suspension.
17. During
Pa
a
the t i d a l
dynamic
experiments
equilibrium
consolidation
and
about 10 t i d a l
cycles.
18. The e f f e c t i v e
tide
the
processes occurred
of
flocculation
by
phase
processes.
entrainment
during
after
hindered
During
Initially
the
soft
tide
fluid
p r o c e s s e s a t the i n t e r f a c e .
surface
is
mud
After
erosion
observed.
observed
observed
in
p r o c e s s e s mentioned above a r e v e r y s i m i l a r t o
stratified
two
r a t e of entrainment
observed
surface
layer
fresh-saline
erosion
It
t h a t t h i s two mode response
by a secondary
compaction
water f l o w s . The
can be d e s c r i b e d w i t h t h e c l a s s i c a l
mentioned under c o n c l u s i o n 13.
i s hypothesized
those
however i s much lower.
formula by Parchure
the
and
accelerating
t h e i n t e r f a c e becomes s t a b l e and smooth
20. The entrainment
22.
deposition,
f l u i d mud l a y e r i s formed.
i s eroded
some time,
21. The
flocculation,
comparable t o o b s e r v a t i o n s r e p o r t e d i n l i t e r a t u r e .
governed by two d i f f e r e n t
is
processes
erosion/re-entrainment
layer
the
re-entrainment/erosion
by
t h i s phase a s o f t
19. The
in
s e t t l i n g v e l o c i t y d u r i n g the d e p o s i t i o n a l phase o f t h e
i s affected
settling,
w i t h a maximum bed shear s t r e s s o f 0,4
of the bed due t o t h e
of the bed i s caused
internal
i n t e r f a c e and/or the c h a r a c t e r of the i n s t a b i l i t i e s
waves
at
themselves.
- 4 -
Table of c o n t e n t s .
Page
Summary and c o n c l u s i o n s .
1
T a b l e of c o n t e n t s .
4
List
6
of symbols.
1.
Introduction.
8
2.
Summary of p h y s i c o - c h e m i c a l p r o p e r t i e s .
9
3.
Bed development.
16
3.1
Water-bed
3.2
Bed c o n c e n t r a t i o n p r o f i l e s .
4.
interface.
16
18
Steady s t a t e e r o s i o n experiments
i n the a n n u l a r flume.
23
4.1
G e n e r a l o b s e r v a t i o n s and remarks.
23
4.2
Method of a n a l y s i s .
25
4.3
S t r e n g t h d i s t r i b u t i o n w i t h i n the bed.
27
4.4
Erosion rate.
29
5.
T i d a l experiments
i n the a n n u l a r flume.
33
5.1
General.
5.2
Phenomenological d e s c r i p t i o n of the p r o c e s s e s d u r i n g
tidal
33
cycle.
34
5.3
Resuspension by entrainment - a l i t e r a t u r e
5.4
Series
5.5
5.6
1 T i d a l experiments
review.
35
(xb,max=0,2 P a ) .
39
S e r i e s 2 T i d a l experiments
(r.b,max=0,4 P a ) : D e p o s i t i o n .
40
S e r i e s 2 T i d a l experiments
(T,b,max-0,4 P a ) : E r o s i o n .
42
Acknowledgements.
49
Literature.
50
Table 2.1: P h y s i c a l - c h e m i c a l p r o p e r t i e s of the water and
sed iment.
Figures.
- 5 -
Appendix
A: T e s t programme t o determine
sedimentation
behaviour
the
flow
induced
erosion
of n a t u r a l muds encountered
and
i n The
Netherlands.
Appendix
B: Method o f a n a l y s i s of e r o s i o n
Appendix
C: C o r r e l a t i o n s between e r o s i o n r a t e and some f u n c t i o n s of t h e
bed shear
Appendix
experiments.
stress.
D: Summary of entrainment experiments d e s c r i b e d
in literature.
- 6 -
List
of symbols,
Units
kg/m
c
sediment
c
depth mean sediment
Cq
initial
c,
b
c
e
sediment c o n c e n t r a t i o n w i t h i n the bed
kg/m"
final
kg/m"
pa
C
rel
c
s
c
concentration
sediment
kg/m"
concentration
kg/m"
concentration
sediment c o n c e n t r a t i o n a f t e r c o n s o l i d a t i o n
sediment c o n c e n t r a t i o n of p r i m a r y aggregates
relative
sediment c o n c e n t r a t i o n ;
c ^
re
c
• /
c
e
sediment c o n c e n t r a t i o n o f the s u s p e n s i o n
C a t i o n Exchange
meq/lOOgr
Capacity
m
p a r t i c l e diameter
D
deposition
D
kg/ra
sediment c o n c e n t r a t i o n by volume
V
CEC
kg/m"
kg/m^s
rate
erosion rate
E
floe erosion rate
f
E
observed maximum e r o s i o n r a t e
max
p o t e n t i a l e r o s i o n r a t e ( P a r c h u r e ' s formula)
kg/m^s
kg/m^s
E
kg/m s
kg/m^s
entrainment r a t e ; E ^ = u / U
e
F
v*
entrainment r a t e : E
l
lutum
A
= u^/U
fraction
g
a c c e l e r a t i o n of g r a v i t y
m/s
H
t h i c k n e s s of sediment bed
m
H
final
t h i c k n e s s of sediment bed a f t e r c o n s o l i d a t i o n
e
h
k
k
l
m
water depth
coefficient
m
i n equ. (3.1)
wave number: k • 2n/X.
k
coefficient
i n equ. (5.9)
k
2
kcz
coefficient
i n equ. (5.9)
coefficient
i n equ. (3.3)
M
erosion
Ms
mass p e r u n i t area of sediment w i t h i n bed
n
coefficient
i n equ. (5.9)
net
coefficient
i n equ. (3.5)
ncz
coefficient
i n equ. (3.3)
net
coefficient
i n equ. (2.4)
nHt
coefficient
i n equ. (3.1)
0
specific
s u r f a c e of sediment
s
Ri
gradient
R i c h a r d s o n number
Rig
o v e r a l l R i c h a r d s o n number
Ri
o v e r a l l R i c h a r d s o n number; see equ.(5.21)
parameter
1/m
kg/m^s
kg/m
2
m 2/
/gr
- 7 -
R i
*
overall
R i c h a r d s o n number; see equ.(5.18)
SAR
sodium a d s o r p t i o n
T
temperature
T
consolidation
t
c
sec
u
velocity
u
W
shear
i n suspension
m/s
m/s
entrainment
*
c
min
time
time
mean v e l o c i t y
e
meq/1
0
U
u
ratio
velocity
m/s
velocity
effective
m/s
settling
velocity
m/s
reference s e t t l i n g
velocity
m/s
s
sO
z
vertical
coordinate
m
z
relative
v e r t i c a l c o o r d i n a t e w i t h i n bed: z ,=z /H
rel
-
W
rel
a
erosion coefficient
i n equ.(4.5)
Pa"
6
erosion c o e f f i c i e n t
i n equ.(4.5)
-
6
coefficient
6
u
6
p
E
t h i c k n e s s of l a y e r
with v e l o c i t y
thickness of layer
with concentration
c
amplitude i n t e r n a l
length internal
M
^0
P
p
b
Ap
a
C
b
t.
•c
e
r.
y
gradient
gradient
r a t i o 5^ and 6^ o f m i x i n g l a y e r
waves
dynamic v i s c o s i t y
m
-
m
sediment
viscosity
m
m
waves
dynamic v i s c o s i t y
effective
-
i n equ.(5.9)
parameter d e s c r i b i n g
1
suspension
sediment
mPas
suspension
raPas
of pore water
mPas
density
kg/m
3
d e n s i t y w i t h i n bed
kg/m
3
density
kg/m
3
difference
c e l e r i t y of i n t e r n a l
waves
m/s
upper Bingham s t r e n g t h of sediment
Pa
bed
Pa
shear
stress
maximum bed shear s t r e s s
critical
yield
shear s t r e s s
during a t i d a l
f o r erosion
s t r e n g t h of sediment
experiment
Pa
Pa
Pa
- 8 -
1.
Introduction.
In commission of and
Transport
(Tidal
and
cohesive
the
Public
Waters
Hydraulics
and
Netherlands),
RIZA
(Inland
Appendix A)
and
deposition
Netherlands
the
(see Table
execution
1990
and
the
2.1
for
K u i j p e r et a l [1990],
The
present
and
tidal
first
analysis
parameters
data
of
possible
are
beds are
of the
relations
discussed.
measurements
c a r r i e d out
results
are m a i n l y compared
in l i t e r a t u r e ,
between
and
present
from
with
f o r the
study
i n the Chapters 4 and
of
annular
i n c r e a s i n g the bed
results
experiments
the
bed
were
are
discussed
in
were
conducted
under
sinusoidally varying
major p a r t of the
the
-
the
yet
of
other,
analyses
therefore
the
explicitly
r e s u l t , Chapter 4 and
measured
the
4.
bed.
during
shear s t r e s s
tidal
of
of these t i d a l
the
5 are not
steady
report,
as
5 are h i g h l y a f f e c t e d by
within
Chapter
bulk-
( d e n s i t y ) s t r u c t u r e of
in
two
the
steps.
preliminary
conditions
(i.e.
a
i n Chapter 5.
experiments were
state
all
erosion
successive
Finally,
flow
The
the
experiments i n the
flow v e l o c i t y ) . These are d i s c u s s e d
analyses
analyses
physico-chemical
i s a b a s i c p a r t of the
sediment c o n c e n t r a t i o n s
flume by
the
In Chapter 3 the
studied. This
r e s u l t s presented
before
the
e x i s t i n g data were not
characteristics
The
flume and
analyses.
In Chapter 2
accuracy
was
comparisons between the p r o p e r t i e s
encountered
Moreover, many of the
used i n the
the
This
regarded o n l y as a step towards a b e t t e r u n d e r s t a n d i n g of
processes.
deposited
various
[1991].
experiments and
data
studying
i n a s e r i e s of r e p o r t s
e x i s t i n g , o f t e n used formula are a p p l i e d . The
be
Delft
programme" (see
bulk parameters. T h i s work was
sediment samples. The
well-established
to
summary).
of a "Standard e x p e r i m e n t a l
report gives a
the v a r i o u s
should
a
r e s u l t s were p r e s e n t e d
see
erosion
Division)
c h a r a c t e r i s t i c s of sediments from
physico-chemical
and
of
Getijdewateren
dedicated
i n v o l v i n g experiments i n the a n n u l a r
various
Dienst
Water
sediments. A p a r t of t h i s programme was
through
i n 1989
The
(Ministry
p e r f o r m i n g a long term b a s i c study i n t o the b e h a v i o u r of
l o c a t i o n s i n The
of
Works,
Division)
is
erosion
done
in c o l l a b o r a t i o n with Rijkswaterstaat
carried
out
e r o s i o n experiments. As
entirely consistent
everywhere.
A
a
J
- 9 -
2. Summary of p h y s i c o - c h e m i c a l p r o p e r t i e s .
Programme on mud
During the Standard
chemical
Table
The
properties
various
physico-
measured. These p r o p e r t i e s are summarized i n
2.1.
table
salinity
to
were
characteristics,
shows t h a t the samples can be c l a s s i f i e d w i t h r e s p e c t t o the
of t h e i r environment. The
3
about
17
to
20
kg/m
( B r e s k e n s ) , Eems-Dollard
were taken
Sea
amounts
Thus the samples from the Western S c h e l d t
(Delfzijl
Harbor) and Loswal Noord
(North
Sea)
i n s a l i n e water, whereas the samples from the H o l l a n d s c h
(Sassenplaat
Biesbosch
.
c h l o r i n i t y of the North
and
Moerdijkbrug),
Lake
( S p i j k e r b o o r ) were taken
Ketel,
Meuse
(Belfeld)
and
i n f r e s h water.
From a m i n e r a l o g i c a l p o i n t of view, the v a r i o u s sediments do not
much. A l l sediments c o n t a i n a c o n s i d e r a b l e amount of i l l i t e
c l a y s , and
is
Diep
a major f r a c t i o n of q u a r t z and
and
feldspar minerals.
have
a
large
chlorite
Remarkable
the absence of the h i g h l y c o h e s i v e m o n t m o r i l l o n i t e i n the
Even a s m a l l f r a c t i o n of t h i s c l a y w i l l
differ
sediments.
effect
on
the
sediment p r o p e r t i e s .
The m i n e r a l o g i c a l c o m p o s i t i o n was
method. The
sediment
is first
a s s e s s e d w i t h the
d i s p e r s e d and
rSntgen-diffraction
then s i e v e d through
s i e v e . However, i t should be remarked t h a t at t h i s moment
of
determining
a 150
the
um
accuracy
the m i n e r a l o g i c a l components i s not w e l l u n d e r s t o o d .
This
i s s u b j e c t of f u r t h e r s t u d i e s .
The
organic
except
of those
content
of
conditions
water
content
of
taken
the
(this
a l l samples i s f a i r l y
in D e l f z i j l
sediments
is
This
a
for
Breskens.
No
The
(Zobell
relatively
observed
sand
high
the
fraction
experimental
causes
(D
characteristic
for
concentrations
for
sediments
oxygen
negative
content
and
from
Hollandsch
found
for this
> 63 um)
in
Diep
the
that s p e c i f i c
E
h
high
combination
redox
potential
(Moerdijkbrug)
and
behaviour.
f o r the samples from D e l f z i j l
considerable
with
of the sediment samples v a r i e s
interpretation
problems: i t i s d i f f i c u l t
characteristic
reduced
anomaly i s the
e x p l a n a t i o n was
This
to n i l , indicating
[1946]). A remarkable
samples
w i t h a v e r y h i g h content
Noord.
low
oxygen
agrees w i t h the v a l u e s of the Redox P o t e n t i a l
which are s t r o n g l y n e g a t i v e ,
of
fairly
5 t o 12 % ) ,
a t Loswal Noord. The
i n c o n t r a s t t o the h i g h oxygen
samples).
organic content
Harbor and
h i g h (about
to o b t a i n a
sediment, sand
Harbor and
widely,
Loswal
problems, as w e l l as
homogeneous
sample,
g r a i n s can d i s t u r b
the
-
proper f u n c t i o n i n g
10
-
of the
rheometer, the
d u r i n g experiments i n the
a n n u l a r flume,
A l s o the
f r a c t i o n of
14
30
and
fraction
%.
the
for
spheres and
For
a f r a c t i o n F^
* F^;
s p e c i f i c surface
clay plates
0
by
to
sort
about a f a c t o r 2 between
[m
g
/gr]
of the
of one
of s p h e r i c a l
lutum
sediment. To
expected, t h i s r e l a t i o n can
be
get
established
diameter.
p a r t i c l e s of d i a m e t e r D,
hence f o r example f o r D « 2 um,
0
likely
[1988] suggests a c o r r e l a t i o n between the
2
v a l u e s to be
a f e e l i n g of the
is
etc.
lutum (D < 2 urn) v a r i e s
Verreet
and
sediment
0
» 1,13
g
F^,
0
and
» 2,26.10
g
^/D
f o r D - 0,5
urn,
4,5
F .
Typical
values
for 0
f o r v a r i o u s c l a y minerals are:
s
2
2
chlorite: 5 < 0
< 50 m /gr, k a o l i n i t e : 25 < 0
< 50 m /gr, i l l i t e : 75 <
2
2
0
< 125 m /gr and m o n t m o r i l l o n i t e : ca 750 m /gr.
1
s
s
S
g
The
diameter d of
illite
clay varies
t h i c k n e s s amounts to about 0,1
F
between
0,1
and
2
um,
d. Hence, f o r example d - 0,5
and
its
0
=18
um,
r
The
2.1
values
of the
showing the
0
w i t h F^
s
Dutch sediments and
those of V e r r e e t g i v e n i n F i g u r e
correlation:
" 2,5
* F.
i
i n [%]. For
the
(2.1)
sub-sample
of
Dutch
estuarine
Dutch i n l a n d water sediments o t h e r c o r r e l a t i o n s
0
0
The
large
clay,
f o r marine mud
(2.1a)
s
« 5 * F.
1
f o r i n l a n d water mud
(2.1b)
scatter
i n the
data points
measure
given
in
character
3
kg/m
with
. This
strength
f o r c o h e s i o n are
starts.
related
the
showing
thixotropic
be
the
the
presence
of
both
quartz p a r t i c l e s in
rheological
cylinder
the
"applied
argued
strength
a
properties.
strain"
These
are
rheo-meter.
general-plastic
behaviour
as
(Otsubo
of the
the
is
(shear
thinning)
James
against
cannot be measured unambiguously w i t h an
the measured v a l u e i s a f u n c t i o n
characterised
by
a
100
yield
shear s t r e s s at which d e f o r m a t i o n
[1985],
bed
A
H o l l a n d s c h Diep ( S a s s e n p l a a t ) i s
behaviour f o r c o n c e n t r a t i o n s beyond c »
which i s d e f i n e d
I t can
to
2.2,
general-plastic
t ,
the more s p h e r i c a l
f o r sediments from the
Figure
to
um.
being measured i n a r o t a t i n g
result
i s due
and
established:
• 8 * F.
i
samples w i t h D < 2
typical
be
s
p l a t e - l i k e p a r t i c l e and
Another
can
sediments
of the
[1987])
erosion.
applied
strain
acceleration
that
z
is
Unfortunately, i t
rheo-meter,
of the
cylinders.
as
A
- 11 -
more unambiguous parameter i s the Bingham shear s t r e n g t h
r.^, which
is
d e f i n e d as the i n t e r c e p t of the s t r a i g h t p a r t of the f l o w curve w i t h the
vertical
a x i s . The r h e o l o g i c a l
Bingham
p l a s t i c model. The a c c e l e r a t i n g curve d e p i c t s an o v e r s h o o t ; the
d e c e l e r a t i n g curve
the
structure
called
this
is
i s smoother. The overshoot
of
the sediment, r e s u l t i n g
thixotropic effects
overshoot
behaviour
(see Blom e t a l
i s probably
a
function
then
approximated
i s caused
by
in different
[1986]).
of
changes
a
in
curves: the so-
The
the
by
magnitude
of
a c c e l e r a t i o n o f the
rheometer; t h i s was however not e l a b o r a t e d .
Rheological
measurements
r e s u l t s are a f f e c t e d
cylinders,
the
are
fairly
by the c h o i c e of the rheo-meter and
acceleration
of
samples, e t c . These a s p e c t s w i l l
The
present
s u b j e c t i v e i n the sense
results
were
the
cylinders,
with
measuring
preparation
be s u b j e c t of another
obtained
the
t h a t the
of the
study.
a Haake RV100 rheometer. An
a c c e l e r a t i o n p e r i o d of 1 minute was a p p l i e d , a c h i e v i n g a maximum
shear
-1
rate
of 150 s . A l l measurements were c a r r i e d out a t 20 C. Data were
0
sampled a t a frequency
sediment
low cone,
from
H-Diep ( S a s s p l )
H-Diep (Moerdb)
w'Scheldt
Lake K e t e l
Meuse
Eems-Dollard
Loswal Noord
Biesbosch
Table
-
200:
250:
300:
300:
400:
300:
230:
- 250:
-
i
h i g h cone,
sensor
CV100,
CV100,
CV100,
CV100,
CV100,
CV100,
CV100,
CV100,
DA45
DA45
DA45
DA45
DA45
DA45
DA45
DA45
200200
300
400
400
220
> 250
-
used:
sensor
CV100, ME15
RV100,
RV100,
CV100,
CV100,
CV100,
CV100,
MEI I
MEI I
Q30/2
Q30/2
Q30/2
Q30/2
2.2: Sensors used w i t h
Haake RV100 rheo-meter
f o r rheological
measurements
(N.B. CV100 i s a s p e c i a l c o n f i g u r a t i o n o f the
measuring
sensor.
DA45, ME15 and MEII
are
cylindrical
elements and Q30/2 i s a p l a t e - l i k e element)
A final
remark concerns
probably
due
additional
The
of 4 Hz. The f o l l o w i n g s e n s o r s were
to
sand
the s m a l l
particles
vibration
the
curves.
This
is
i n the sample, which cause o c c a s i o n a l
f r i c t i o n w i t h i n the rheo-meter.
Figures
2.3a
and 2.3b show the measured dynamic v i s c o s i t y u . as a
f u n c t i o n of sediment c o n c e n t r a t i o n ; u
straight
of
d
i s d e f i n e d as the
slope
of the
p a r t of the d e c e l e r a t i n g f l o w curve. At sediment c o n c e n t r a t i o n s
below c = 200 kg/m
the v a r i o u s curves c o i n c i d e w e l l ,
and no s i g n i f i c a n t
- 12 -
trend
with
any
of
the p h y s i c o - c h e m i c a l
higher concentrations
u^j a p p a r e n t l y
l a r g e r d i f f e r e n c e s are observed.
i s d i r e c t l y related
Though t h i s seems p l a u s i b l e ,
observed
at smaller
p r o p e r t i e s can be deduced. At
3
t o the sand content
At c • 400
kg/m
- see F i g u r e 2.4a.
i t i s not c l e a r why t h i s behaviour
i s not
concentrations.
0
For c l e a r water a t T = 20
reference
value
dilute
suspensions.
internal
w
-
1
mPas,
which
d
U
d w
is
taken
as
the e f f e c t
of e l a s t i c ,
the
particles,
which
due t o n o n - l i n e a r e f f e c t s .
between
spherical particles in
fluid
and
be
will
accelerated
result
in
effective
Together w i t h the a d d i t i o n a l
p a r t i c l e s , an e f f e c t i v e
viscosity
f o r the
d
-
M
0
(1
+ 2,5 c )
(2.2)
v
where c i s the c o n c e n t r a t i o n o f the p a r t i c l e s
v
by volume [-] and u
dynamic
= P
v
and
as a f u n c t i o n of p a r t i c l e c o n c e n t r a t i o n can be deduced:
u
(c
the
-
He reasoned t h a t the f l o w w i l l
around
strains
friction
fluid
P /
[1906] c o n s i d e r e d
decelerated
d
i n the f o l l o w i n g a n a l y s i s by c o n s i d e r i n g the behaviour
of the r e l a t i v e v i s c o s i t y
Einstein
C, u
•
viscosity
0,04)
numerous
u
d
-
[Pas]
1,09
experiments
shape up t o h i g h
M
d
- p
for c
Lee
UQ.
with
= 0 (i.e. u
gives
[1969]
rigid,
Q
d w
)•
another
F o r c » 1 0 0 kg/m
formula
based
incompressible p a r t i c l e s
on
of v a r i o u s
concentrations:
2
Q
v
the
_
n
U
(1- c r< '
5
9
\ '
+
v
c
v
+
7
'
7
c
v>
(2.3)
3
yielding
u
d
"
u
• 1,10 u
Q
f o r c - 1 0 0 kg/m
3
3 U Q f o r c • 1 0 0 kg/m
. In the examples above, c
volume c o n c e n t r a t i o n of the primary
to
use
. F i g u r e 2.3a shows t h a t f o r mud,
particles.
i s taken
as the
I t would make more
sense
v
the volume c o n c e n t r a t i o n s o f the p a r t i c l e aggregates.
These a r e
not known however. On the o t h e r hand, from equ. (2.3) i t f o l l o w s t h a t c
should
be 0,27 t o get u
d
= 3 U Q . T h i s seems a r e a s o n a b l e
value
v
(see a l s o
T a b l e 2.3).
From
this
analysis
between the p a r t i c l e s ,
which a f f e c t
i t i s clear
but a l s o the presence of
the v i s c o s i t y
of the
F i g u r e 2.4b shows a comparison of
sources
(Ross
[1988]).
The
meq/100 g r ) c o n t a i n k a o l i n i t e ,
and
feldspar,
gr)
kaolinite,
t h a t i t i s not o n l y the c o h e s i v e
the
grains
with
data
bonds
themselves
suspensions.
the
results
from
other
sediments from Brunswick Harbor (CEC = 38
montmorillonite,
chlorite,
the sediments from Wilmington D i s t r i c t
montmorillonite,
vermiculite
and
illite,
quartz
(CEC - 32 meq/100
quartz,
and
the
- 13 -
sediments
from
San
Francisco
k a o l i n i t e , montmorillonite
difference
with
the
and
Bay
illite
(major?)
original
However,
viscosities.
The
reason
lies
Ross
Other data
results
of
only
the y i e l d
to compare the
Owen [1975] and
Migniot
i n F i g u r e 2.5a.
The
the
gr)
the
cohesive
data
scatter
presented
strength z
2.5a
contain
chlorite.
montmorillonite.
used by Ross. A l s o
for
the
the
various
i n the
r e s u l t s w i t h the
2.5b;
r.
y
is
authors
r e s u l t s w i t h those
[1968],
[1989],
given
[1989]. T h i s
results.
sediment
as
i
experiments were performed, t h e i r r e s u l t s do
merely do not
t
overlap.
- c
the
It i s
Krone
[1986],
i s done g r a p h i c a l l y
d i f f e r e n c e i n f u n c t i o n a l b e h a v i o u r observed by
becomes c l e a r at once: w i t h i n the
is
highest
defined
by
A
tests
are p l o t t e d a g a i n s t the
and
The
explained
of the d e c e l e r a t i n g f l o w curve w i t h the v e r t i c a l - a x i s .
interesting
three
meq/100
by Krone agree b e t t e r w i t h the p r e s e n t
c o n c e n t r a t i o n c i n the F i g u r e s
intercept
34
some q u a r t z and
strong
in
r e s u l t s by Krone a l a r g e
observed.
and
-
r e s u l t s by Krone i s s t r i k i n g . T h i s can be
o n l y p a r t l y by the presence of the
second
(CEC
range of
not
these
concentrations
disagree
-
they
Hence:
n C Z
(2.4)
y
with
2,5
<
net < 6,
depending on the sediment c o n c e n t r a t i o n .
the p h y s i c a l mechanisms behind
Verreet
[1988] t r i e d
However,
t h i s behaviour are p r e s e n t l y not
to c o r r e l a t e
with
clear.
several physico-chemical
bulk
15
parameters. He
favoured
i s shown i n F i g u r e
C_
(c - 300
the s p e c i f i c
2.7
0 .
This
g
2.6:
3
kg/m ) - O
B
Figure
s u r f a c e of the p a r t i c l e s
2 , 8
(2.5)
S
shows
that z
and
the C a t i o n Exchange C a p a c i t y
CEC
are
not
well correlated.
Another r e l a t i o n o f t e n encountered
z„(c
) - 0,39
B
pa
1.
in literature
+ 0,084 (CEC-clay)
i s due
t o Krone
[1986]:
(2.6)
In
the
following
analyses,
z
i s compared w i t h
values
of r.
encountered
i n l i t e r a t u r e . Though the v a r i a t i o n s of z and z^ w i t h
various
o t h e r parameters are expected to be s i m i l a r , the magnitudes
may
differ
considerably,
as
z
i s always
s m a l l e r than z , and
sometimes
z
«
z^. I t i s t h e r e f o r e recommended to d e f i n e a l s o c
from the e x i s t i n g flow c u r v e s .
g
- 14 -
CEC-clay
clay
i s defined
as
f o r the s m a l l e s t
particles:
CEC
c
The
the C a t i o n Exchange C a p a c i t y
i
a
y
"
of sediment sample ( i n c l . sand)
lutum f r a c t i o n (< 2 um)
CEC-values were measured on
organic
material
material
through:
CEC
at
no o r g .
pH
-
the
complete
,
9
u
sample,
,
.
'
7
/
i.e.
including
7. T h i s v a l u e can be c o r r e c t e d f o r o r g a n i c
= CEC ...
- a.[X o r g . m a t t e r ]
w i t h org.
•
where 1,5 < a < 6,5 depending on the o r g a n i c c o n t e n t , w i t h a mean
of
value
about a = 3,5.
Typical
v a l u e s f o r the CEC a r e : c h l o r i t e : 20 meq/100 g r , k a o l i n i t e : 5
10 meq/100 g r , i l l i t e :
20 - 40 meq/100 g r and m o n t m o r i l l o n i t e :
80 t o 125
meq/100 g r .
t_
(c ) i s the Bingham shear
pa
D
s t r e n g t h of the primary
aggregates o f the
sediment, which can be o b t a i n e d w i t h a procedure e x p l a i n e d
Krone [1986].
A summary i s g i v e n
infinite
For
particle,
dilute
in detail
here.
suspensions,
i.e. a
suspension
containing
equ. (2.2) can be a p p l i e d . I f a second p a r t i c l e
viscosity
in
one
i s added, the
becomes:
p
= u
d
d
(1 + 2,5 c )
(2.8)
v
T h i s can be e l a b o r a t e d f o r a
third,
fourth
particle,
etc.
yielding
eventually:
U
Also
= p
d
the
Q
exp {2,5 c J
experimental
w i t h an e x p o n e n t i a l
p
d
= p
0
(2.9)
v
viscosity
curves
i n F i g u r e 2.3b can be d e s c r i b e d
curve:
exp {k.c}
(2.10)
From equs. (2.9) and (2.10) and the e x p e r i m e n t a l
slopes
k,
c
y
can
be
established
as a f u n c t i o n of the c o n c e n t r a t i o n c. The s l o p e s k from the
experimental
curves
between
about
shown i n F i g u r e 2.3b are g i v e n
0,004
the r e s u l t s
2.3, v a r y i n g
and 0,01. T h i s would y i e l d a volume c o n c e n t r a t i o n
3
f o r f o r example c = 100 kg/m
of
i n Table
of c
d i s c u s s e d above.
v
= 0,16 t o 0,4. T h i s i s i n the
range
- 15 -
Yield, s t r .
t
(c )
y
pa'
slope k
ra /kg
cone, c
prim. a|gr.
H-Diep ( S a s s p l )
H-Diep (Moerdb)
w'Scheldt
Lake K e t e l
Meuse
Eems-Dollard
Loswal Noord
Biesbosch
0,0106
0,0075
0,0075
0,0078
0,0071
0,0057
0,0037
0,0096
235
kg/m
334
334
319
353
441
668
259
Table 2.3: Y i e l d
s t r e n g t h f o r primary p a r t i c l e s
sediment
from
Next,
the
primary
f o r which c = 1 .
v
sediment
p a r t i c l e aggregates
Using the
concentrations,
the primary
obtained
aggregates
from
1,4
1,9
0,7
2,1
0,7
1,1
6,0
1,8
3
Pa
( c = 1).
v
are d e f i n e d as those
experimental
slope
k,
aggregates
obtained
f o r low
Krone c o u l d o b t a i n the h i g h c o n c e n t r a t i o n s of
through
experimental
extrapolation.
Thus,
his
results
are
results
with
a c a p i l l a r y visco-meter f o r
3
sediment c o n c e n t r a t i o n s below c - 80 kg/m , and e x t r a p o l a t i n g these t o
3
c o n c e n t r a t i o n s up t o s e v e r a l hundred kg/m .
F o r the p r e s e n t study, c
can be read d i r e c t l y from F i g u r e
2.3a
(from
pa
r
H /u
d
Q
listed
that
=
exp
i n Table
{2,5}),
and
t
(
c
p a
)
f r o r a
F
i
8
r
e
2.5b. The r e s u l t s a r e
2.3 and shown i n the F i g u r e s 2.8 and 2.9. I t can be seen
the r e s u l t s
of the p r e s e n t study show no c o r r e l a t i o n
v a l u e s however a r e i n the range o f the v a l u e s
lower.
u
given
by
w i t h CEC. The
Krone,
T h i s l a t t e r i s p r o b a b l y due t o the f a c t t h a t i n g e n e r a l z
However, t h i s c o u l d not be q u a n t i f i e d .
though
< z^.
- 16 -
3. Bed
3.1
development.
Water-bed
interface.
During the f o r m a t i o n of the bed
grained,
cohesive
sediments
in
the
of
the
flume
column,
monitored.
r e s u l t s are shown i n the F i g u r e s 3.1a
last
lowering
annular
consolidation
The
the
from d e p o s i t i o n of a s u s p e n s i o n of
an H vs 1/t p l o t ,
curves
are
fairly
straight
for
about
- see F i g u r e 3.8.
through
This
t o a second
by
. 2
consolidation).
Krone
through
1/t
i n a 36 cm
comparable
to
the
3.7a.
< 0,01,
high
The
3.7b
[1962].
was
in
These
which i s
consolidation
c o n s o l i d a t i o n and
processes
of
hindered
At s m a l l e r v a l u e s of 1/t, a s i g n i f i c a n t d e v i a t i o n i s observed.
i s due
squeezed
<
T h i s phase i s c a l l e d primary
the r e l e v a n t p r o c e s s e s are
settling.
0,1
the
interface
s i m i l a r t o the r e p r e s e n t a t i o n by Krone
comparable t o the r e s u l t s Krone o b t a i n e d
column
and/or
water-bed
p a r t of the c u r v e s are redrawn i n the F i g u r e s 3.1b
fine-
out
[1962]
the
found
phase of c o n s o l i d a t i o n when the
weight
of
pore
the sediment p a r t i c l e s
water
(self
is
weight-
t h a t t h i s c o n s o l i d a t i o n p r o c e s s c o u l d be d e s c r i b e d
as:
g- - 1 = ( £ )
H
t
e
where H ( t ) - h e i g h t
complete
The
A
interface, H
linear
through
Figure
t
3.7
e
- i s ultimate interface
- time
[min], and
are r e p l o t t e d
f i t i s drawn through
c u r v e s are g i v e n . The
T a b l e 3.1
(3.1)
consolidation,
F i g u r e s 3.1
3.15.
n H t
resulting
in
k and
the
nHt
height
are
Figures
after
parameters.
3.9
through
the d a t a ; f o r t h r e e sediments
c o e f f i c i e n t s k and
nHt
are
compared
w i t h the r e s u l t s by Krone f o r San F r a n c i s c o Bay mud
- see
two
in
also
3.8.
Relation
( 3 . 1 ) , w i t h nHt
t o 200 min.
( 1 / t = 0,01
= 1 r e p r e s e n t s Krone's r e s u l t s up t o about
to 0,005) f a i r l y
well
-
see
Figure
3.8.
100
At
2. N.B.
U n f o r t u n a t e l y t h e r e i s some unambiguity i n the t e r m i n o l o g y : the
first
c o n s o l i d a t i o n phase
is often referred
t o as the phase of
hindered
settling,
whereas
the
second
phase
i s c a l l e d "primary
consolidation";
secondary
c o n s o l i d a t i o n i s then
the f i n a l phase
d u r i n g which (a p a r t o f ) the aggregates are broken up, the t h i c k n e s s
of
the
bed
continues
t o decrease s l i g h t l y and c h e m i c a l p r o c e s s e s
become
important.
In g e n e r a l
however,
the
s t r e n g t h of the bed
i n c r e a s e s l a r g e l y d u r i n g t h i s "secondary c o n s o l i d a t i o n " p r o c e s s .
- 17 -
l a r g e r times, a s i g n i f i c a n t d e v i a t i o n i s observed.
I t should be remarked
t h a t f o r l a r g e t the r e s u l t s become i n a c c u r a t e , as H approaches H .
Mud
source
HDiep
(Sassenplaat)
HDiep
(Moerdijkbrug)
(Breskens)
Lake K e t e l
Meuse
1
1
1
1
-
57
72
0,5
first
second
49
49
31
73
0,5
0,9
first
second
56
56
155
171
0,5
0,8
first
second
56
56
47
62
0,7
1,2
-
53
22
0,6
-
60
79
0,5
-
60
76
0,6
(Delfzijl)
T a b l e 3.1: Bed-water i n t e r f a c e d u r i n g
3.9
through
nHt
28
31
45
54
36
Loswal Noord (North Sea)
Figure
k
8,6
14
20
25
40
(Belfeld)
E-Dollard
3
[kg/m ]
Q
-
_
San F r a n c i s c o Bay
(Krone [1962])
W'Scheldt
c
Curve
1
consolidation.
3.15 show t h a t some of the c o n s o l i d a t i o n c u r v e s o f
Dutch mud show a k i n k between 100 and 300 min. T h i s k i n k c o r r e s p o n d s
the
transition
suspension
between
the
shown
in
Figure
contraction point after S i l l s
branch
of
the
3.16.
consolidation
i s recommended t o i n c l u d e t h i s
The
first
part
observations,
of
the
show
0,5
p r o b a b l y due t o the
processes
fact
curves,
<
The
[1986]. During
between the bed and the suspension
It
of
hindered s e t t l i n g
and c o n s o l i d a t i o n of a mud bed, as e x p l a i n e d above.
schematically
lower
processes
nHt
that
of hindered s e t t l i n g
curve
of a mud
This
the p r e s e n t experiments the
( t h e " d e n s i t y s t e p change"
- see F i g u r e 3.16) were not r e c o r d e d .
i n future
which
experiments.
should
correspond
to
Krone's
< 0,7, hence lower than Krone. T h i s i s
nHt
should
not
be
a
constant:
are a f u n c t i o n o f the ( i n i t i a l )
the
sediment
don't
too much.
From the schematic
show
is
t r a n s i t i o n point i s called
c o n c e n t r a t i o n and bed t h i c k n e s s , c.q. column h e i g h t , though these
differ
to
diagram i t should be expected
a k i n k . However, 4 out of the 7 curves
that a l l
curves
(H'Diep/Sassenplaat,
would
Meuse,
- 18 -
E - D o l l a r d / D e l f z i j 1 and Loswal Noord) do not show t h i s t r e n d . A
explanation
sediments
content
might
be
found
i n the sand c o n t e n t , which
from the Meuse, Eems-Dollard and Loswal
may
promote
channels along
the
the
wall
outflow
of
of
the
pore
consolidation
i s h i g h f o r the
Noord.
water
possible
A
high
sand
( f . i . through small
column),
which
will
a c c e l e r a t e the c o n s o l i d a t i o n p r o c e s s . Hence, o n l y the r i g h t hand p a r t of
the
c o n s o l i d a t i o n c u r v e s (beyond
This w i l l
3.2
be s u b j e c t of f u t u r e
the p o i n t of
contraction)
are
found.
studies.
Bed c o n c e n t r a t i o n p r o f i l e s .
The
concentration
profiles
shown i n the F i g u r e s 3.17
i n a non-dimensional
measured
i n the v a r i o u s c o h e s i v e beds are
through 3.24.
form by
These
p r o f i l e s can be
presented
defining:
Relative concentration - c
r
g
l
= c / c
(3.2)
R e l a t i v e depth
= z
= z / H
re l
3
where
c(t)
thickness
3.25a
-
depth-averaged
concentration
[m]. These non-dimensional
through
3.32a
[kg/m
],
and
p r o f i l e s are shown i n
H ( t ) - bed
the
Figures
t o c o l l a p s e r e a s o n a b l y i n t o one c u r v e , except f o r
the
mud
from Loswal Noord. T h i s i s p r o b a b l y due
of
the Loswal Noord samples. T h i s causes a l a y e r e d s t r u c t u r e of the bed
- see the z i g - z a g curve i n F i g u r e
Next,
the
the non-dimensional
t o the h i g h sand c o n t e n t
3.23.
p r o f i l e s are r e p l o t t e d on l o g a r i t h m i c s c a l e i n
F i g u r e s 3.25b through 3.32b. A p p a r e n t l y , most of the p r o f i l e s can be
described
by:
£ = kcz ( i r
—
ri
c
This
relation
Parson
Table
was
n
c
z
used
(3.3)
b e f o r e by f o r i n s t a n c e Owen [1975], Thorn
[1980] and by Mehta et a l [1982]. The
r e s u l t s are
and
summarized
in
measured
bed
3.2.
The F i g u r e s 3.33
through 3.40
profiles.
empirical f i t s
and the e x p e r i m e n t a l d a t a i s f a i r ,
surface
the
sediments
is
shown
predicted
concentration
for
It
compare the
from
that
Hollandsch
and
the agreement between the
except
Diep,
near
Lake
the
bed
Ketel
and
B i e s b o s c h . The d a t a suggest a f a i r l y smooth c o n c e n t r a t i o n g r a d i e n t
near
- 19 -
the
bed s u r f a c e f o r these
However, the accuracy
diameter
of
the
sediments, which i s not r e p r e s e n t e d
of the measurements here i s q u e s t i o n a b l e ,
acoustic
probe
4,
t h a t the r e s u l t s of the a n a l y s e s
are v e r y s e n s i t i v e t o the c o n c e n t r a t i o n
layer.
be argued
distribution
within
this
source
248
287
0,069
0,060
0,3
0,3
300
288
0,051
0,3
56
305
365
0,046
0,8
Lake K e t e l
56
302
262
0,064
0,3
Meuse ( B e l f e l d )
53
415
418
0,038
0,5
E-Dollard
60
495
450
0,040
0,6
134
867
1517
0,040
1,7
55
248
0,065
0,4
HDiep
HDiep
c
(Sassenplaat
(Sassenplaat
HDiep
Q
1)
2)
(Moerdijkbrug)
w'Scheldt
(Breskens)
(Delfzijl)
Loswal Noord (North Sea)
Biesbosch
(Spijkerboor)
Avonmouth (Owen [1975])
Brisbane
c
[kg/m ]
ac.m
intf
57
57
253
271
49
g
7,7
15,4
17,3
H
254
253
198
*)
*)
e
0,3
0,3
0,3
0,293
0,775
150-200 *)
0,25-,41
0,3
Grangemouth (Thorn [80])
150-200 *)
0,25-,41
0,3
Belawan
150-200 *)
0,25-,41
0,3
Table
(Thorn
[kg/m ]
[1980])
(Thorn
[1980])
3.2: D e n s i t y p r o f i l e s
The
second v a l u e
(equ 3.3)
the
*) = cons, p e r i o d of 48 h r s .
f o r kcz a p p l i e s f o r T
3.2 g i v e s two columns f o r the
indicating
final
i n t e g r a t i o n by t r a p e z i u m
depth
mean
concentration
from
c
- 7 days.
concentration
the
indicating
initial
g
ac.m ,
computation
conditions
t h i c k n e s s of the bed. The d i f f e r e n c e s f o r mud from the
Lake K e t e l are p r o b a b l y
c :
r u l e of the bed c o n c e n t r a t i o n s
measured w i t h the a c o u s t i c probe, and " i n t f " ,
and
top
on measuring the bed c o n c e n t r a t i o n w i t h i n t h i s t o p l a y e r .
ncz
the
in
of the e r o s i o n experiments
[m]
Table
the
I t i s t h e r e f o r e recommended t o c a r r y out a d d i t i o n a l experiments,
focussed
Mud
as
i s 0,5 cm, hence beyond the r e q u i r e d
r e s o l u t i o n t o measure w i t h i n the top of the l a y e r . I t w i l l
Chapter
by ( 3 . 3 ) .
Western
of
and the
Scheldt
due t o i n a c c u r a c i e s i n h e r e n t t o the a c o u s t i c
- 20 -
probe;
sand
the l a r g e d i f f e r e n c e f o r Loswal Noord mud
content
of
the
v i s u a l comparison
showing
sample
finally
i s due
to
the
extreme
and the s e g r e g a t i o n d u r i n g d e p o s i t i o n . A
i s given
in
the
Figures
3.41a
and
3.41b,
a s i m i l a r behaviour f o r a l l sediments. From these graphs
be concluded t h a t the mean bed c o n c e n t r a t i o n i n c r e a s e s
sand c o n t e n t , as
with
i t can
increasing
expected.
Owen [1975] and Thorn and Parson
p r o f i l e s measured
[1980]
found
that
the
concentration
i n a c o n s o l i d a t i o n column c o u l d be d e s r i b e d r e a s o n a b l y
with:
c = 0,8
(N.B.
The
sum
c (Q)
n
_ 0 , 3
, f o r z > 0,1
H
(3.3)
of kcz and ncz s h o u l d be u n i t y t o match the mass
balance.
T h i s can be shown as f o l l o w s . L e t :
.
c = kcz c
Then,
,z.-ncz
(^)
by d e f i n i t i o n :
—
1 H
c - - J c dz, from which
n
= i. However, the c o e f f i c i e n t s
empirical
Parchure
[1984]
tap
salt
and
c
that
the
s t u d i e d the c o n s o l i d a t i o n of China C l a y ( k a o l i n i t e ) i n
water
b
- 0,38
this
E
b
and
Lake
(source
unknown)
expfl^.pp}
e
ncz
is
concentration p r o f i l e s .
more
sand c o n t e n t . T h i s
found
i n the d e n s i t y
(3.2) and ( 3 . 3 ) ,
profiles.
a " p r o f i l e parameter"
g i v i n g the s l o p e of the
I t can be argued t h a t s t e e p e r s l o p e s are
thus f o r i n s t a n c e w i t h
i s shown i n F i g u r e 3.42.
the sand c o n t e n t i n the c o n s o l i d a t i n g
sample;
to get a homogeneous m i x t u r e .
due
an
(3.4)
graded sediments,
measured i n the o r i g i n a l
and
Mud:
r e l a t i o n d i f f e r s from the power r e l a t i o n s
coefficient
for
Mud
r e a d i n g f o r the Lake
Parchure a l s o found s i m i l a r i t y
expected
such
bed.)
exponential r e l a t i o n ,
The
were chosen
f i t (3.3) agrees r e a s o n a b l y w i t h the e x p e r i m e n t a l d a t a i n the
upper p a r t of the
Though
i n T a b l e 3.2
i t f o l l o w s t h a t ncz + kcz
I t s h o u l d be
sample may
differ
to s o r t i n g e f f e c t s
to
be
increasing
remarked
that
from the c o n t e n t
i t is
difficult
- 21 -
Plotting
T
the depth mean c o n c e n t r a t i o n
[ h r s ] (see
c
Figure
3.43)
curves can be d e s c r i b e d
t - c ,.T
ref
c
c versus
shows again
(3.5)
Hence from equ (3.5) i t f o l l o w s
T"
and
e
Both f o r m u l a t i o n s
This
The
n C t
but not i d e n t i c a l . T h i s can
be constant
because of c o n t i n u i t y .
that:
,
t
_
n
H
t
that:
+ H
e
are s i m i l a r ,
except the c o n s t a n t
i s due t o the e m p i r i c a l c h a r a c t e r
H
g
i n the second one.
o f the s t u d i e s .
c o e f f i c i e n t s of equ (3.5) are summarized i n T a b l e 3.3. I t should
remarked
be
t h a t though t h i s seems an a t t r a c t i v e d e s c r i p t i o n , the upper 10
% ( o r l e s s ) of the bed i s not i n c l u d e d
in
this
formulation.
give c o n s t r a i n t s f o r p r a c t i c a l a p p l i c a t i o n s .
Mud
be
C
from equ (3.1) i t f o l l o w s
H - k H
time
a remarkable s i m i l a r i t y : the
n C t
shown as f o l l o w s : c.H - a should
C
consolidation
with:
T h i s f o r m u l a i s comparable t o equ (3.1),
H = -Sref
the
c
source
H D i e p (Sassenplaat
H'Diep ( S a s s e n p l a a t
[kg/m ]
net
120
120
0,2
0,2
130
0,2
140
0,2
Lake K e t e l
140
0,1
Meuse ( B e l f e l d )
140
0,1
E-Dollard
220
0,2
360
0,1
140
0,2
H'Diep
1)
2)
3
r e f
(Moerdijkbrug)
W'Scheldt
(Breskens)
(Delfzijl)
Loswal Noord
Biesbosch
(North
Sea)
(Spijkerboor)
T a b l e 3.3: C o n s o l i d a t i o n
curves (see equ ( 3 . 5 ) ) .
This
may
- 22 -
As
a first
a p p r o x i m a t i o n the curves
0
c - T '
The
can be d e s c r i b e d
2
with:
(3.6)
depth mean c o n c e n t r a t i o n c and bed t h i c k n e s s H (and o f course
H ) are d i r e c t l y
e
Hollandsch
c
r e l a t e d t o each o t h e r . A c l o s e r look a t the curves
Diep,
Western
Scheldt
Lake
for
K e t e l mud i n F i g u r e 3.43
shows k i n k s
3.17.
These k i n k s a r e however f a r l e s s pronounced, which i s due t o l e s s
c
observed
and
indeed
data
s i m i l a r t o those
and
g
i n the F i g u r e s 3.11 through
points.
can be determined from the lowering
of the i n t e r f a c e , and ncz w i l l be
a f u n c t i o n of the sediment p r o p e r t i e s , among which sand content
to
be
significant.
These
deposition/conso1idation
It
can
be concluded
parameters
will
describe
the
have t o be measured
during
experiments.
t h a t equ. (3.3) seems t o g i v e a u s e f u l r e l a t i o n t o
d e s c r i b e the d e n s i t y s t r u c t u r e o f a c o h e s i v e
to
appears
development
in
bed. Equ. 3.5 can
time, f o r i n s t a n c e d u r i n g
be
used
non-steady
conditions.
The
physical
reasoning
why these
i n f l u e n c e of the p h y s i c o - c h e m i c a l
study.
r e l a t i o n s seem t o work, and the exact
properties w i l l
be s u b j e c t of
another
- 23 -
4. Steady s t a t e e r o s i o n experiments
i n the a n n u l a r flume.
4.1 General o b s e r v a t i o n s and remarks.
During the e r o s i o n
(and c o n s o l i d a t i o n ) experiments a number
of
general
f e a t u r e s were observed. These a r e summarized i n t h i s c h a p t e r .
As e x p l a i n e d e a r l i e r ,
beds were formed
W i t h i n about 2 hours a f t e r the s t a r t
coloured
by d e p o s i t i o n from a
suspension.
of t h i s bed f o r m a t i o n a t h i n ,
l a y e r was formed on t o p of the bed. T h i s
was
observed
light
during
most experiments. These o b s e r v a t i o n s are summarized i n T a b l e 4.1:
Table 4.1: O b s e r v a t i o n s of top l a y e r on sediment.
O b s e r v a t i o n s of top l a y e r
Sediment
source
Cons.
t ime
H o l l . Diep
Sassenplaat
1 day
7 day
T h i n white top l a y e r o f about 3 mm
idem
H o l l . Diep
Moerdij kbrug
1 day
7 day
T h i n white top l a y e r of about
idem
West. S c h e l d t
1 day
No top l a y e r observed
Lake K e t e l
1 day
7 day
No top l a y e r
Yellow-brown l a y | r o f 2 mm on top o f
black-brown bed
Meuse
1 day
Light-brown top l a y e r of 2-3 mm; a f t e r
t h i s l a y e r was eroded, a new top l a y e r
was formed d i f f e r e n t from the f i r s t one
I n i t i a l top l a y e r of 2 mm, a f t e r e r o s i o n
white top l a y e r of about 1 cm; shows
dark s p o t s a f t e r some time
7 day
Eems-Dollard
1 day
White t h i n top l a y e r
Loswal Noord
1 day
7 day
Light-brown top l a y e r o f 1 mm,
No top l a y e r
Biesbosch
1 day
Top l a y e r of about 5 mm; a f t e r e r o s i o n o f
of t h i s l a y e r , the bed s t a r t s t o change
colour again
idem
7 day
Probably these top l a y e r s are not formed
but
2 mm
as a r e s u l t
as a r e s u l t
very soft
of s o r t i n g
effects,
of o x i d i z i n g p r o c e s s e s of the sediments. The time
3. During
field
surveys by Toet
greyish i n general.
scale
[1991], t h i s top l a y e r was found t o be
- 24 -
of these p r o c e s s e s i s of the o r d e r of minutes. Hence, the o x i d i z i n g
of the e n t i r e
layer
availability
of
(i.e.
oxygen
the change
and
the
in
colour)
diffusion
is
by
the
p r o c e s s e s w i t h i n the
bed.
However, no c o n f i r m i n g d a t a on the oxygen c o n t e n t
governed
rate
within
the
bed
are
available.
The e r o s i o n a l behaviour of t h i s
top
layer
differed
for
the
various
sediments.
F o r H o l l a n d s c h Diep ( S a s s e n p l a a t ) mud,
gradually.
eroded
resuspended.
deep)
was
= 0,65
Pa.
For
At x
fa
At
z^
- 0,55
»
Pa,
the
top
up t o about
s t a r t e d t o erode suddenly i n l a r g e f r a c t i o n s ,
an
(r.^ - 0,4
was
mud,
r a i s e d t o r.^ - 0,35
Pa, the top l a y e r was
and the top l a y e r was
gone
local
The
at
z^
=
0,45
s c o u r h o l e s of about
bed
of
completely
7 days, the top
hour
after
layer
the
bed
During
the
T
to erode
next
resuspended c o m p l e t e l y .
• 1 day,
erosion
l o c a l l y a t z^ =
Pa. At z^ = 0,75
1 cm
2 cm
s t e p w i t h z.
was
eroded c o m p l e t e l y at z. • 0,45
= 7 days, the top l a y e r s t a r t e d
was
was
Pa. During the f o l l o w i n g s u b - t e s t
For H o l l a n d s c h Diep ( M o e r d i j k b r u g ) mud,
smooth,
layer
l a y e r was
Pa), h a r d l y any f u r t h e r e r o s i o n took p l a c e .
s t e p , at r.^ - 0,55
top
i n the f i n a l
-
stress
(Sassenplaat)
10 cm
T
shear
Diep
» 1 days, the
c
Pa a deep s c o u r h o l e (about 6 cm long and
observed, growing
Hollandsch
0,35
T
fairly
Pa. F o r T
0,25
Pa,
and
Pa, mass e r o s i o n r e s u l t e d i n
depth.
Western S c h e l d t mud
was
not e n t i r e l y
flat;
however, smooth
surface erosion occurred.
Lake
Ketel
mud,
T
the top l a y e r was
Meuse
mud
was
= 1 day was
f a
a l s o eroded smoothly.
eroded c o m p l e t e l y at z^ = 0,35
eroded smoothly.
c o m p l e t e l y at t
(bed
£
= 0,55
For T
c
» 1 day,
For T
= 7 days,
c
Pa.
the top l a y e r was
Pa. During the next s t e p , mass e r o s i o n
eroded
occurred
failure).
At z. ' 0,55
b
Pa, Eems-Dollard mud
some
scour
large
holes,
s t a r t e d t o show mass
erosion
through
m a i n l y near the i n n e r w a l l of the flume.
e r o s i o n r a t e of such a scour h o l e seems t o be c o n s i d e r a b l y
larger
The
than
the e r o s i o n r a t e of the u n d i s t u r b e d bed.
A main problem w i t h the i n t e r p r e t a t i o n of the
Noord mud
was
the h i g h sand c o n t e n t . As a r e s u l t ,
take i d e n t i c a l
erosion
samples f o r the c o n s o l i d a t i o n
experiments.
For
The
=
= 7
days
Pa
and
0,38
Pa. At z
T
£
= 1 day erodes
= 0,48
Loswal
not p o s s i b l e t o
experiments
aggregates were observed t o wander over the
top l a y e r of B i e s b o s c h mud,
0,31
i t was
with
and
example, the bed t h i c k n e s s v a r i e d
and 60 ram f o r the v a r i o u s samples. For
dilute
experiments
large
the
two
between 40
(ca
4
ram),
bed.
irregularly
between z^
Pa, the remaining bed s t a r t s to
- 25
change c o l o u r again.
0. 3
Pa.
Again,
For T
at
t.
-
= 7 days, the top l a y e r c o l l a p s e s
=
0,48
Pa,
the
remaining
bed
at
z^
-
s t a r t s t o change
colour.
During
and
at
the end
of some t e s t s (some) mass e r o s i o n was
observed.
This
i m p l i e s t h a t c l u s t e r s of a g g r e g a t e s are t o r n out of the bed.
not
likely
t h a t these
sampled p r o p e r l y w i t h
in
the
annular
clusters,
e s p e c i a l l y when they
the sampling tubes and
flume.
Hence,
one
of
pumps
the
c o n c e n t r a t i o n measurements cannot be a c c u r a t e
4.2
Method of a n a l y s i s .
The
experiments were c a r r i e d out
1 to 1,5
The
of the e x p e r i m e n t a l
First,
the
data
presently
f e
in successive
sub-tests
in this
are c a r r i e d out
in
is
be
installed
when mass e r o s i o n
v e r t i c a l d i s t r i b u t i o n of the bed
shear s t r e s s f o r e r o s i o n ) z
l a r g e , can
consequences i s t h a t
increasing r
hours each. These s t e p s are c a l l e d
analyses
steps.
by
are
It
the
occurs.
steps
of
report.
two
separate
strength
(critical
i s deduced from the d a t a . Next the
erosion
e
r a t e E i s determined.
The
strength z
bed
1. The
i s determined
measured bed
concentration p r o f i l e
e m p i r i c a l f i t (3.3)
discussed
2. By
and
i n t e g r a t i n g (3.3)
fc
i n Table
shown i n the F i g u r e s 3.33
3.2.
This
through
was
per
i s found:
H
c
c ( z ) dz =
b
the
3.40.
over the depth, the mass d i s t r i b u t i o n Ms(z)
u n i t area w i t h i n the bed
= J
c ( z ) i s approximated w i t h
the parameters l i s t e d
i n Chapter 3 and
Ms(z)
i n 6 steps:
kc z H
\ _
n
c
z
1
[1 - ( z ^ H ) "
1 1
"]
(4.1)
b
where
z ( t ) = a c t u a l t h i c k n e s s of the bed
b
( e r o s i o n depth) [m],
and
H = initial
during
the e r o s i o n
t h i c k n e s s of the bed
process
[m]
prior
to e r o s i o n .
3. The
measured suspended sediment c o n c e n t r a t i o n c ( t ) measured
annular
g
flume
area Ms(t)
at
of the
mid
in
the
depth i s used to determine the mass per u n i t
sediment i n
suspension:
- 26 -
M s ( t ) = c .(H - z.)
s
b
(4.2)
z t
H
4. From Ms(z) • M s ( t ) , the e r o s i o n depth
z, i s found, as i s shown i n the s k e t c h .
b
Mass
Ms(z)
z.b
2
5. The e r o s i o n r a t e E ( t ) [kg/m
s] i s o b t a i n e d from d i f f e r e n t i a t i n g
c :
g
dc
E - (h - H)
(4.3)
where h = depth of a n n u l a r flume. Hence, E ( t ) i s r e l a t e d t o c ( t ) and
s
thus t o M s ( t ) . During a s u b - t e s t , the bed f i r s t
erodes r a p i d l y .
After
some time t = t ^ , E becomes c o n s t a n t . I t i s assumed t h a t t h i s happens
when
the
bed
strength
t ( z ) becomes equal t o the a c t u a l bed
g
stress r ^ ( t ) .
The
s m a l l remaining e r o s i o n a t r a t e E^ i s
erosion
is
due
and
and/or
the
shear
called
floe
t o a slow, but c o n t i n u o u s weakening of the bed
fluctuations
of
the
turbulent
shear
stresses
(e.g.
Winterwerp [1989]).
By s u b s t i t u t i n g
6. At
t
t = t ^ i n M s ( t ) , Ms(z)
=
t„
i t i s assumed
that
f
d i s t r i b u t i o n of z ( z ) i s o b t a i n e d ,
e
T h i s procedure
It
is
z
[1984]. The
obvious
z^(t^).
z, , and thus the v e r t i c a l
b
e
i s s i m i l a r t o the procedure a p p l i e d
and by Parchure
4.3.
i s found and thus
by Mehta et a l [1982]
r e s u l t s are shown and d i s c u s s e d
that
the
results
i n f l u e n c e d by the form of the bed
of
the
concentration
in
analyses
Chapter
are h i g h l y
distribution
that
is
chosen.
For
the
analysis
correlations
were
of
the
tried
erosion
by
plotting
maximum observed e r o s i o n r a t e E
This
procedure
disadvantages.
are
is
differentiated
fraction
of a?) mm
the
simple
the
results
4.4.
[1984] generate a d d i t i o n a l data f o r
in
Appendix
B.
interpolation
It
has
the
procedure.
two
major
a c c u r a c y i s v e r y low: the e x p e r i m e n t a l d a t a
numerically
and
interpolated
within
some
of the bed. A second, more important problem
t h i s procedure does not r e a l l y g i v e a d d i t i o n a l d a t a , but
correlations.
empirical
the f l o e e r o s i o n r a t e E^ and
s u b - t e s t by a s p e c i a l
described
First,
some
6
are shown and d i s c u s s e d i n Chapter
Mehta et a l [1982] and Parchure
E
a g a i n s t z , z. - z , e t c . The
e
b
e'
max
e r o s i o n r a t e E w i t h i n one
rate
only
T h i s i s a l s o f u r t h e r e l a b o r a t e d i n Appendix B.
(a
i s that
spurious
- 27
4.3
S t r e n g t h d i s t r i b u t i o n w i t h i n the
The
-
bed.
d i s t r i b u t i o n of the s t r e n g t h a g a i n s t e r o s i o n
(critical
for
e r o s i o n z ) w i t h i n the bed
e
i s shown i n the F i g u r e s 4.1
for
the v a r i o u s sediments. The
vertical
made d i m e n s i o n l e s s
results
w i t h the
bed
the
present
experimental
by
thickness
H
experiments).
This
is
factors.
c o n s o l i d a t i o n time T
The
graphs
results
to
more
or
less
f u r t h e r down i n the
erosion.
The
o n l y be e s t a b l i s h e d f o r
1
cm
a consequence of the a p p l i e d
also
1 cm,
show
i n an o v e r a l l
t:
increases
that
an
rapidly
increase
i n c r e a s e of z
C
Pa,
4.8
hand a x i s ) i s
(which i s of the o r d e r of at most
procedure. However, w i t h i n t h i s
several
through
(left
prior
show t h a t the s t r e n g t h d i s t r i b u t i o n can
the upper 10 to 20 % of the bed
for
z-coordinate
shear s t r e s s
in
by about
0,1
6
evenly
over the depth. A more pronounced d i f f e r e n c e
bed would
be
i n s t a n c e Mehta e t a l [1982] and
expected,
Parchure
as
was
observed
by
for
[1984].
The r i g h t hand v e r t i c a l a x i s of the F i g u r e s 4.1
4.8
yield
the
bed
concentration
c,.
Hence these graphs a l s o show the z vs c, r e l a t i o n ,
b
e
D
y i e l d i n g the f o l l o w i n g r e l a t i o n :
z
w i t h neb
Owen
c b
«
e
c
"
b
of the o r d e r of 10.
[1970],
who
r e s u l t s t h a t the
will
yield
surface
(4.4)
T h i s i s much l a r g e r than the v a l u e
reported
neb
•
2,3.
However, i t i s c l e a r from
r e s u l t s are not v e r y a c c u r a t e :
a large v a r i a t i o n
i s questionable.
in z
and
Hence, i t
is
given
a small v a r i a t i o n
the a c c u r a c y
not
by
the
in
c^
of c^ near the
bed
recommended
to
use
these
results.
The
r e s u l t s are summarized i n the F i g u r e s 4.9
4.9
and
4.10
show
sediments, though the
stronger,
and
those
no
significant
sediments.
The
r e s u l t s presented
3.3)
used
Equ.
(3.3)
the
Western
However, no
to
differences
from the B i e s b o s c h
be
are a d i r e c t
interpolate
and
The
between
sediments from Eeras-Dollard seem
sediments. T h i s c o u l d however not
the
t h r o u g h 4.12.
the
to
be
Figures
various
slightly
s l i g h t l y weaker than the
r e l a t e d t o the
bulk
properties
f u n c t i o n of the e m p i r i c a l
e x t r a p o l a t e the
seems to agree b e t t e r w i t h the data
bed
for
other
of
fit
(equ.
concentration
data.
the
sediments
S c h e l d t , Lake K e t e l , Meuse, E e m s - D o l l a r d and
s i g n i f i c a n t d i f f e r e n c e between t h i s group of
from
Loswal Noord.
sediments
and
the o t h e r group i s found.
Apparently
upper
part
i t can
of
be concluded,
the
bed
t h a t the
strength
distribution
does not v a r y much f o r the
in
the
8 sediment samples
- 28 -
p r e s e n t l y s t u d i e d . An i n c r e a s e
yields
an
increase
distributed
beds
in
z
i n c o n s o l i d a t i o n time from 1
by
about
0,1
Pa,
more
or
over the bed. However, i t s h o u l d be kept i n
presently
studied
were
a l l made
in
the
to
days
less evenly
mind
same
7
that
the
and
all
way,
e x p e r i e n c e d the same h i s t o r y .
The
Figures
4.11
and 4.12
show the z
vs c. r e l a t i o n s . The
e
bed
concen-
D
t r a t i o n c^ does not v a r y much, which of c o u r s e i s a g a i n a consequence
the
empirical
between
the
sediments:
f i t (3.3) used. The graphs show a s i g n i f i c a n t
curves
marine
for
the
fresh
sediments
show
concentrations. This observation
double
water
the
is
same
in
l a y e r t h e o r y (e.g. Winterwerp
sediment
strength
agreement
by
the
resulting
content
the
The
to
and
the
marine
during
bed
sediment
will
have
a
larger
then f r e s h water sediments ( t h e pore water cannot escape
bed
s a l i n i t y does
Hence,
i n l a r g e r aggregates, c o n t a i n i n g more water. Hence
from the a g g r e g a t e s ) . Moreover,
within
diffusive
t o the (pore)
thinner.
form more f l o e s p r i o r
the (upper p a r t of t h e ) bed of a marine
water
much lower
the
[1989]). Adding s a l t
marine
Van Der Waals f o r c e s becomes s t r o n g e r . Thus,
sediments i n s u s p e n s i o n w i l l
formation,
difference
the
at
with
water causes the d i f f u s i v e double l a y e r t o become
attraction
and
are
also
the mutual bonds between the
aggregates
s t r o n g e r f o r marine sediments. As a r e s u l t ,
i n c r e a s e the s t r e n g t h of the bed.
mutual d i f f e r e n c e
i n the behaviour of the f r e s h water sediments and
of the marine sediments can be d e f i n e d through the bed c o n c e n t r a t i o n
at T. = 0,3 Pa. These v a l u e s are l i s t e d i n T a b l e 4.2.
e
A close
i n s p e c t i o n of
instance
for
the
by
F i g u r e 2.5
another
the
Table
fresh
s t r o n g e r than the mud
clouded
of
4.2
water
and
Figure
sediments
from Lake K e t e l
4.11
the
(though
reveals
mud
this
that
c^
for
from the Meuse i s
picture
might
be
a c c u r a c y of the c o n c e n t r a t i o n p r o f i l e s ) . However, from
i t i s expected t h a t the l a t t e r mud
would
i n d i c a t i o n t h a t the r e l a t i o n between y i e l d
be s t r o n g e r . T h i s i s
s t r e n g t h and
erosion
s t r e n g t h i s not y e t c l e a r .
As
mentioned
b e f o r e , the a c c u r a c y of the bed c o n c e n t r a t i o n p r o f i l e s i s
q u e s t i o n a b l e , and t h e r e f o r e the a c c u r a c y of the s t r e n g t h p r o f i l e s .
therefore
It i s
recommended t o repeat the a n a l y s e s by u s i n g more d e t a i l e d
a c c u r a t e data on the sediment c o n c e n t r a t i o n i n the
upper
part
of
and
the
bed. For the time b e i n g , the s t r e n g t h d i s t r i b u t i o n s shown i n the F i g u r e s
4.9
and 4.10
necessary
studied.
can be used f o r p r a c t i c a l
to
distinguish
between
purpose. At the moment i t i s
the
various
sediments
not
presently
- 29 -
Table
4.2: Bed c o n c e n t r a t i o n
Cons.
time
H o l l . Diep
Sassenplaat
1 day
7 day
167
211
H o l l . Diep
M o e r d i j kbrug
1 day
7 day
157
211
West.
1 day
124
Lake K e t e l
1 day
7 day
179
190
Meuse
1 day
7 day
146
Eems-Dollard
1 day
121
Loswal Noord
1 day
7 day
104
94
Biesbosch
1 day
7 day
156
167
Scheldt
- 0,3 Pa.
Bed c o n c e n t r .
cb [kg/ra3]
Sediment
source
4.4 E r o s i o n
—
rate.
In t h i s c h a p t e r
only surface erosion
s u i t a b l e to analyse
The
at t
i s t r e a t e d ; the experiments a r e not
the mass e r o s i o n p r o c e s s e s
o c c a s i o n a l l y observed.
f o l l o w i n g d e f i n i t i o n s are used:
1) E r o s i o n
2
r a t e E [kg/m S J :
dc
E = h — ^
dt
2) F l o e
when z
erosion
e
(4.3)
E
f
is
the e r o s i o n r a t e E observed d u r i n g
= z, , i . e . when E ( t ) becomes constant
b
a sub-test
(occasionally zero),
3) Maximum
erosion
E
i s the maximum e r o s i o n r a t e observed d u r i n g a
'
m
s u b - t e s t , i . e . when z^ - z
has about i t s maximum v a l u e .
b
e
- 30 -
During
the
studied,
course
of
the
analyses,
s e v e r a l e m p i r i c a l r e l a t i o n s were
based on well-known r e l a t i o n s found
E - E
in literature:
P
exp {cr(T. - t - ( z ) ) }
f
B
z
(4.5)
e
- z
E - M -2-z—-
(4.6)
e
The
Figures
4.13 and 4.14 show t h a t the f l o e e r o s i o n
w i t h bed shear s t r e s s z^. A s i m i l a r c o r r e l a t i o n was
[1984],
rate E
found
increases
f
by
Parchure
but t h i s was not e x p l i c i t l y mentioned i n h i s r e p o r t . The graphs
suggest t h a t E^ does not i n c r e a s e
approaches
some
asymptotic
unlimited
value.
This
with
increasing
behaviour
will
z^,
be
but
discussed
below.
Also
the
observed maximum e r o s i o n
r a t e E can be c o r r e l a t e d t o the bed
m
shear s t r e s s z^, as shown i n the F i g u r e s
graphs suggest an a s y m p t o t i c
It
4.15 and 4.16,
and
again
the
behaviour.
i s i n t e r e s t i n g t o note t h a t L a v e l l e e t a l [1984] found t h a t E can
related
to
z^,
which they c o n c l u d e d
from a r e a n a l y s i s of d a t a from 10
experiments by L a v e l l e e t a l , Fukuda and L i c k , Sheng and
al,
Gularte
E
e t a l and P a r t h e n i a d e s . T h i s
E
= 0
be
relation
Lick,
Lee
et
reads:
(
*b
4
-
7
)
in
which
E_
i s an e r o s i o n r a t e parameter, i t s value v a r y i n g between
—8
-5
2
1,9.10
and 3,7.10
kg/m s, and n v a r i e s
between
1,2 and 5.
This
result
The
i s shown i n F i g u r e
Figures
rate
E
m
4.17a.
4.18 and 4.19 show the r e l a t i o n
and
the
maximum v a l u e
T
c
c
= 24 h r s :
E - 8,5.10~
m
'
= 7 days:
E
m
}
regression
and
lines
solid
lines
in
the
graphs,
be deduced:
T
The
erosion
of (z, - z )
. Though the s c a t t e r i s
b
e max
°
huge, some c o r r e l a t i o n , i n d i c a t e d by the
could
between the maximum
r
=
coefficient
0,75.
The
i n the F i g u r e s
6
- 14.1.10
'
exp { 3 6 ( t
b
-6
- z )
}
e max'
u
r
exp { 2 7 ( r
b
v
1
v
w
- z )
e'max
J
v
(4.8)
'
} (4.9)
'
f o r (4.8) and (4.) a r e r e s p e c t i v e l y r -
0,81
s c a t t e r i n the r e s u l t s i s i n d i c a t e d by the broken
4.18 and 4.19, y i e l d i n g :
- 31 -
E
m
E
= (0,5
- 52).10"
6
= (2,9
- 20).10"
6
exp
{(60
- 27)(t
exp
{(34
- 20)(r
- * )
b
e
)
m a x
- t )
(4.8a)
J
(4.9a)
~6
By
comparing
the
r e s u l t s presented
(4.9)
value
of
f
8,5
and
to 14,1.10"
it
comparable
is
to
Mehta [1985] - see
(see
equ. (4.5))
Winterwerp
inherent
(4.8)
and
s c a t t e r of the d a t a .
This
also
the
to the e x p e r i m e n t a l
4.17b. The
in
the
kg/m
fits
procedure a p p l i e d ,
obtained
obtained
values
range
reported
by P a r c h u r e
for E
f
,
a
(4.8)
and
(4.9)
erosion process,
the
practical
describing
use,
sediments from one
E = 10"
accuracy
5
should
following
of the
exp
of the
be
bulk
Finally,
it
empirical
the
formula
erosion
of
soft
locations presently
{30(c
is
f o r the
deposited
- Z )}
b
is
was
too
low
i s shown i n Appendix C,
beds
to
distinguish
conceptual
r e s u l t s t o one
of the
frame
[1984], and
work
however
shear
stress
and
into
the
main
flow
physico-
v e l o c i t y of the s w e l l i n g
cohesive
of the
consistent
bed,
properties
s t r u c t u r e of the
with
found
formula
beds.
theory,
r e c e n t l y by Mehta
be
found by
of
eroding
this
and
fluid.
theory.
This
[1991].
considering
idea
is
that
these
aggregates
are
movement.
The
defines
the
turbulent
the
bed
then
i s expected t o be a f u n c t i o n of
sediment
The
that
into
i t s water content
the
The
(sediment c o n c e n t r a t i o n ) ,
and
of
course
dependency of E
It
framework i n a f o l l o w i n g phase of the
is
in
( f l u c t u a t i o n s ) weaken and/or
through
possible erosion rate. This
permeability
rate process
can
pressure
the a g g r e g a t e s w i t h i n the bed,
maximum
the
t h a t no c o r r e l a t i o n c o u l d be
i n v e r s e c o n s o l i d a t i o n or s w e l l p r o c e s s .
turbulent
propagation
of
between
shear s t r e s s determines the a c t i v a t i o n energy.
advocated by Parchure
transported
for
parameters.
e r o s i o n as an
loosen
entire
(4.10)
Q
results
which the excess bed
the
(see
studied:
observed b e h a v i o u r i s i n agreement w i t h the
Another
8
recommended
between E, or E/E,. and (z. - z )/z , i n d i c a t i n g t h a t the simple
f
b e e
(4.6) i s not a p p l i c a b l e f o r d e s c r i b i n g the e r o s i o n of d e p o s i t e d
theory
and
and
in l i t e r a t u r e
representative
sediments and/or to c o r r e l a t e the
chemical
The
as
[1989]).
equ.'s
various
the
the s c a t t e r i n the data
Figure
are
s with
4.14b,
agree w e l l . Another remark concerns the
i s apparently
The
E
i n the F i g u r e s 4.13b
scatter
As
for
2
proposed
study.
f
to
and
the
E^
the
the
turbulent
on
z
is
elaborate
on
this
b
- 32 -
From
the
present
analysis,
i t should
be c o n c l u d e d t h a t more d e t a i l e d
measurements of the sediment c o n c e n t r a t i o n
are
required.
Only
then
i n the upper p a r t o f the
i t may be p o s s i b l e t o q u a n t i f y
e r o s i o n p r o c e s s e s i n more d e t a i l .
bed
the observed
- 33 -
5. T i d a l experiments
5.1
i n the a n n u l a r flume.
General.
Tidal
experiments were conducted
i n the a n n u l a r flume w i t h mud
Western S c h e l d t and from the Eems-Dollard
velocity
and +0,2
+0,4
was
varied
for
the
s e r i e s of experiments, and
second
consolidate
increasing
decreasing
of about
for
6
the
60 kg/ra
hours
bed
shear
i t a g a i n . The
suspension
with
(see T a b l e 2.1). The
before
the
stress
tidal
and
formed
from
an
bed was
experiments
5.7
were
continued
a c h i e v e d a f t e r about
show the observed v a r i a t i o n
show
the v a r i a t i o n
initial
allowed to
started
until
by
a
dynamic
4
cycles.
10 t i d a l
5.3,
5.5
i n time of the c o n c e n t r a t i o n i n the
water column measured at mid depth, and the F i g u r e s 5.2,
5.8
-0,2
-0,4
r e s u l t s of the f o u r experiments g i v e n i n the F i g u r e s 5.1,
and
flow
from z e r o t o i t s maximum v a l u e , and
experiments
e q u i l i b r i u m o c c u r r e d , which was
The
The
between
s e r i e s of experiments. A bed was
d e p o s i t i o n of a homogeneous water-sediment
3
concentration
Harbor).
s i n u s o i d a l l y w i t h bed shear s t r e s s e s between
Pa f o r the f i r s t
Pa
(Delfzijl
from the
5.4,
5.6
i n c o n c e n t r a t i o n as a f u n c t i o n of the bed
and
shear
stress.
In
the
slightly
first
series
of
experiments,
exceed
the c r i t i c a l
threshold
the
for
bed shear s t r e s s d i d o n l y
erosion
(see
Chapter
4).
c o n c e n t r a t i o n s i n the water column
3
were v e r y low, v a r y i n g between 0,1 and 0,35 kg/m
f o r Western S c h e l d t
3
mud
and
between
0,25
and
0,4 kg/m
f o r Eems-Dollard mud. Assuming a
3
Consequently
the
observed
sediment
sediment
c o n c e n t r a t i o n of 50 kg/m
Chapter
5.6),
d u r i n g the t i d a l
this
would
yield
i n the upper p a r t
of
the
the e r o s i o n of about
1 mm
bed
of the
(see
bed
cycle.
Though the c o n c e n t r a t i o n s i n the water
column are much h i g h e r than those
observed
t h a t the
flume
the
is
i n n a t u r e , one
only
0,3
m,
should r e a l i z e
of
the
annular
i . e . at l e a s t an o r d e r of magnitude s m a l l e r t h a t
depth of n a t u r a l water
observed
depth
systems. T h i s b r i n g s
i n the a n n u l a r flume
the
erosion
i n the range of those observed
processes
i n nature.
4~! During p r e l i m i n a r y experiments w i t h China C l a y , dynamic
equilibrium
was not a c h i e v e d , even
after
1000
(!)
tidal
cycles.
This
was
a t t r i b u t e d t o the c o n s o l i d a t i o n time of 7 days t h a t
was
applied
see C o r n e l i s s e et a l [1990].
- 34 -
The
maximum
concentrations
experiments
10 kg/m
large
(t,
= 0,4
observed
the
Pa) are much h i g h e r ,
second
difference
following
series
centimetre.
section.
layer. This i s elaborated further i n
I t i s emphasized
t h a t the p r e s e n t t e s t s have a
hypotheses. T h i s i m p l i e s t h a t the r e s u l t s are merely
on
a
number
Phenomenological d e s c r i p t i o n of the p r o c e s s e s d u r i n g a t i d a l
In
this
paragraph
a
phenomenological
b e h a v i o u r i n the a n n u l a r flume
this
during
description
is
description
a
tidal
of
cycle
restricted
of
qualitative.
5.2
sediment
The
i n behaviour between the two s e r i e s of experiments i s
p r e l i m i n a r y c h a r a c t e r and t h a t the a n a l y s e s are based
convenience,
of
r a n g i n g from about 0 t o
, c o r r e s p o n d i n g t o an e r o s i o n depth of s e v e r a l
due t o the f o r m a t i o n of a f l u i d mud
the
during
cycle.
the
is
sediment
given.
For
t o the experiments w i t h
from the Western S c h e l d t ; a s i m i l a r p i c t u r e can
be
drawn
for
during
the
the experiments w i t h jsediment from the E e m s - D o l l a r d .
The
sediment exchange between the bed and the water
first
s e r i e s of experiments (z,
= 0,2
column
Pa) i s governed by the common
D } IT13X
e r o s i o n and d e p o s i t i o n p r o c e s s e s . T h i s i m p l i e s t h a t d u r i n g
t i d e , when the flow v e l o c i t y becomes s u f f i c i e n t l y
the water column can s e t t l e on the bed. Around
velocity
is
slack tide,
smoothly.
small,
and
smooth
s m a l l , the sediment i n
the
flow
the d e p o s i t e d sediment can c o n s o l i d a t e .
After
the f l o w v e l o c i t y
This
slack
i n c r e a s e s a g a i n , and
erosion
i s known as s u r f a c e
water,
the
bed
is
eroded
p r o c e s s i s a l s o observed d u r i n g s t e a d y
s t a t e experiments when the excess bed shear s t r e s s
it
decelerating
i s not too l a r g e
and
erosion.
During the second s e r i e s of experiments (z.
= 0,4
Pa)
a
different
b, max
picture
min,
i s observed - see F i g u r e 5.3.
the c o n c e n t r a t i o n
i n the water column i s almost
sediment p a r t i c l e s are s m a l l . When z^
about 0,15
process
about
be
and
the
d e c r e a s e s and becomes s m a l l e r than
this
period
i s the f o r m a t i o n of f a i r l y
l a r g e f l o e s of
diameter i n s i z e . These were observed v i s u a l l y ,
r e c o r d e d p h o t o g r a p h i c a l l y . The s e t t l i n g v e l o c i t y
becomes l a r g e , and a h i g h c o n c e n t r a t i o n
consolidates
during
about
s m a l l channels are compressed
flow i t s e l f .
The
layer
is
but c o u l d not
of the sediment
formed.
This
1 hour i n the s l a c k water p e r i o d . Pore
flows out of the l a y e r through s m a l l
increasing
constant
300
Pa, the d e p o s i t i o n p r o c e s s s t a r t s up s l o w l y . A more important
during
1 mm
From about t * 180 min. t o t "
irrigation
channels
until
now
layer
water
these
by s e l f - w e i g h t c o n s o l i d a t i o n and/or by the
sediment
concentration
within
this
layer
- 35 -
amounts
0,1
t o about 50 kg/m
Pa,
(see F i g u r e 5.26). At about t - 400 min,
i n t e r n a l waves are observed
F i g u r e 5.9a.
filled
3
The
The
lower
part
of
i n t e r n a l waves was
disappeared
can
layer
bed
and
dense
fluid-mud
smooth
smoothly at a moderate r a t e ,
fluid-mud
the
then t o
two
fluid
Pa,
of
the
erosion
waves
occurs.
of:
t h a t i s not
erosion
like
of
t h a t i s not
this
i n steady
layer
flow,
affected
strongly
i s very
mixing
l a y e r s of d i f f e r e n t d e n s i t y , and
i n the water column.
thus r e s u s p e n s i o n r a t e i s a l s o
feature
of t h i s dual-mode response
of the bed
only
i s not
resemble those o c c u r r i n g d u r i n g the
curves
i n F i g u r e 5.4.
this
decrease
the i n t e r n a l waves; the e r o s i o n r a t e of t h i s l a y e r
i n the c o n c e n t r a t i o n - t i m e
observed
- 0,3
layer, that i s
observed
Pa,
into
amplitude
l a y e r up t o about z - 648 mm,
change i n r e s u s p e n s i o n p r o c e s s , and
0,2
and
consisting
proceeds
-a s u s p e n s i o n
=
b
the
surface
by the i n t e r n a l waves;
h i g h , the p r o c e s s e s
curve
see
tide,
-a l o o s e v e r y s o f t
This
*
affected
of
down
( n o n - e r o d i b l e l a y e r ) up t o z - 632 mm,
a f f e c t e d by the
by
-
i s more homogeneous and
At about t - 430 min,
completely
-a f i x e d
penetrate
to increase f i r s t ,
A p p a r e n t l y a f o u r l a y e r system d e v e l o p s ,
-a
interface
i s increased further,
f a
observed
a g a i n - see F i g u r e 5.9b.
have
waves
the
deformed by the waves. When t
the
fluid-bed
b
upper p a r t of the l a y e r i s shown t o c o n t a i n l a r g e pores
w i t h water; the i n t e r n a l
layer.
at the
T: >
in
Figure
5.3.
surface
i n the c - z. curve
erosion
( F i g u r e 5.2).
did
A
typical
i s the k i n k i n the c - r-
During the o t h e r s e r i e s of experiments
smooth
A
with
*
b
occur, and no k i n k
close
inspection
of
m
a
b
x
was
the
D
r e s u l t s of the t i d a l
s m a l l tendency
entrainment
experiments
presented
by Umita et a l [1984] shows a
of the a c c e l e r a t i n g curve t o k i n k , i n d i c a t i n g
could
have o c c u r r e d , though n o t h i n g was
that
some
mentioned i n t h e i r
paper.
In
the
following
paragraphs
this
a n a l y s e d . T h i s i s done by s t u d y i n g
This
analysis
entrainment
5.3
preceded
processes
Resuspension
Entrainment
is
the
by entrainment
relevant
t h a t the lower
picture
processes
is
further
separately.
review c o n c e r n i n g
the
f l o w systems.
- a literature
i s d e f i n e d as the mixing
turbulence
various
by a s h o r t l i t e r a t u r e
i n two-layer
different
qualitative
review.
p r o c e s s e s between f l u i d
layers
with
i n t e n s i t y . F o r the p r e s e n t study the s i t u a t i o n i s
layer
is
stagnant
and
the
upper
layer
is
- 36 -
flowing.
The
t u r b u l e n t motions
and mixes the lower
layer
becomes
layer f l u i d
thinner.
When
i n the upper
l a y e r erode the lower
i n t o the upper
the
two
layer.
layers
d e n s i t y , buoyancy e f f e c t s become important
as
Thus,
are
layer
the
lower
a l s o of d i f f e r e n t
these
will
oppose
the
mixing p r o c e s s e s .
The
hydrodynamics of t w o - l a y e r flow systems
density
is
stability
well
studied
in
literature
of
fluids
(e.g.
with
Turner
of these systems can be d e s c r i b e d by the
different
[1973]).
gradient
The
Richardson
number R i :
R
. _ g W ^ ?
i
(
5
#
1
)
p (9u/9z)
For
large
Ri
(Ri
>
0,25
stable s t r a t i f i c a t i o n w i l l
decay.
For
small
Ri
occur, i . e .
interfacial
stability
theory) a
instabilities
will
unstable s t r a t i f i c a t i o n occurs, i . e . i n t e r f a c i a l
instabilities will
grow.
Mixing
in
processes
according to c l a s s i c a l
stratified
flows are o f t e n r e l a t e d t o an
overall
R i c h a r d s o n number R i . I t i s d e f i n e d as:
0
R i
0
. * - ^
P X
where 1 i s a t y p i c a l
(5.2)
l e n g t h s c a l e and x
a p p r o p r i a t e c h o i c e s of S> and \» Rio
the p o t e n t i a l energy
required
e f f e c t opposing mixing) and
to
of
n
b e
velocity
layer)
definitions
are
concluded t h a t E
of
and
used
establish
mixing
in
to
available
grid
flow
From
an
are
be drawn from these
1. From the experiments
stirring
literature.
experiments
(or
buoyancy
f o r mixing.
rate
overall
summarised
(here, the
in
Various
experiments
Richardson
« Ri
n
.
A
Appendix D. S e v e r a l
studies:
where one of the l a y e r s i s f l o w i n g ( i . e . not the
experiments)
0
i t was
number.
the entrainment
of f r e s h / c l e a r water
s a l i n e / t u r b i d water i s g i v e n by:
E
E^,
thinning
velocity.
many
For
between
the
are d e f i n e d by the entrainment
characteristic
is correlated
v
these
c o n c l u s i o n s may
some
scale.
regarded as the r a t i o
i s the r a t i o between the entrainment v e l o c i t y
lower
number
a
typical
the k i n e t i c energy
The mixing p r o c e s s e s themselves
which
c
a
where 0,5
< n <
1,2
(5.3)
into
- 37 -
2. The
scatter
of
the
e x p e r i m e n t a l d a t a i s v e r y l a r g e , a f f e c t i n g the
accuracy o f the e x p e r i m e n t a l d a t a , and thus r e l a t i o n
3. The
r e s u l t s by Turner
significant
rate
at
[1968] and Wolanski
and Brush
i n f l u e n c e of the m o l e c u l a r d i f f u s i v i t y
low
(5.3).
[1975] suggest a
on the entrainment
Reynolds number. At h i g h e r Reynolds numbers, mixing i s
dominated by t u r b u l e n t p r o c e s s e s . T h i s would imply
that
entrainment
t o be s i g n i f i c a n t
rate
occurring
l a r g e r than those observed
The
i s expected
during small scale l a b o r a t o r y
t h e o r y o u t l i n e d above i s v a l i d
Richardson
The
i n nature
the
f o r weakly s t r a t i f i e d
actual
experiments.
flow,
numbers (see Lawrence e t a l [1990] and Smyth e t
i . e . low
al
[1990]).
dynamic i n s t a b i l i t i e s then l e a d t o the f o r m a t i o n o f a p e r i o d i c
of v o r t e x - l i k e s t r u c t u r e s , known as K e l v i n - H e l m h o l z
train
waves. T h i s i s shown
i n a photograph c o p i e d from Lawrence e t a l [1990] - see F i g u r e 5.10.
For h i g h l y s t r a t i f i e d
thickness
of
c o n d i t i o n s (high Richardson
the shear
number), the
relative
l a y e r 6 (6 - t h i c k n e s s o f l a y e r w i t h
u
u
velocity
J
g r a d i e n t ) w i t h r e s p e c t t o the t h i c k n e s s of the m i x i n g
layer
6
t h i c k n e s s of l a y e r w i t h d e n s i t y g r a d i e n t ) becomes important.
instabilities
flow
i n the f l o w a r e damped due t o
becomes
more
stable
occurs i n s t r a t i f i e d
buoyancy
(6
p
=
I f 6^ • 6^,
effects
and
with increasing R i . This s i t u a t i o n
flows were the lower, denser
p
l a y e r flows
the
probably
underneath
a stagnant f r e s h water l a y e r , as i s the case f o r t u r b i d i t y c u r r e n t s .
I f 6 » 5 , i n s t a b i l i t i e s i n the h i g h speed
upper
layer
can develop
u
p
more
easily.
These
instabilities
will
i n t e r f e r e w i t h the i n t e r n a l waves on the
internal
layer.
waves
I f the
injecting
tend
to
cusps
even
cusp,
become
more
denser
these cusping
saline
water
lower
spanwise v o r t i c e s , t h a t
interface.
injecting
As
a
result
the
denser water i n t o the upper
pronounced,
the
waves
may
break,
sediment i n t o the upper l a y e r . T h i s a l s o e x p l a i n s
why o n l y one-way entrainment
the
very
form
i s observed:
no v o r t i c e s are
generated
in
l a y e r . F i g u r e 5.11 (from Lawrence e t a l [1990]) shows
i n t e r n a l waves observed
two-layer
during
experiments
on
a
fresh-
flow. The resemblance w i t h the photograph shown
i n F i g u r e 5.9a i s s t r i k i n g .
This
picture
i s quantified
by Lawrence et a l [1990] i n the form of the
s t a b i l i t y diagrams shown i n F i g u r e 5.12. The i n t e r n a l wave h e i g t h C
d e s c r i b e d by:
^/
. ».
» t \
ik(x - ot)
C(x,z,t) = C ( z ) e
0
where
k = wave number, k = 2ir/X. and
/c ,\
(5.4)
can
- 38 -
o = complex group c e l e r i t y ,
From
equ
(5.4)
i t can
o » o
f
+ io^
be seen t h a t f o r o\ < 0, C w i l l decrease
time: the f l o w i s s t a b l e . F o r
> 0, C w i l l
with
i n c r e a s e w i t h time and the
flow i s unstable.
The
Richardson
number R i . (»J) on the v e r t i c a l
a x i s and a on
o
h o r i z o n t a l a x i s o f F i g u r e 5.12 and the parameter E are d e f i n e d a s :
8
R i
6
"
A
S
J
the
u
—
U
a = k 6
u
(5.5)
6 - 6
E
=
—
^
6
u
On the b a s i s o f these parameters,
For E « 0, 6
' u
distinct
Ri
" 6 , i . e . the c l a s s i c a l
p
modes of i n s t a b i l i t y .
mode i s a d i s p e r s i v e ,
case
(see F i g u r e 5.12)
The f i r s t mode w i t h c
< 0,07 and i s commonly r e f e r r e d
second
Lawrence g i v e s the f o l l o w i n g a n a l y s i s .
the
of
Kelvin-Helmholz
two
- 0 only occurs at
f
t o as the K e l v i n - H e l m h o l z
mode.
The
o v e r s t a b l e mode and i s known as the Holmboe
mode. I t o c c u r s at a l l R i . F o r 0 < R i < 0,07 both
but
with
instabilities
mode has the h i g h e r a m p l i f i c a t i o n r a t e .
occur,
Curves
c o n s t a n t a m p l i f i c a t i o n r a t e f o r the Holmboe mode form c l o s e d l o o p s .
The
case
studied
by Lawrence i s c h a r a c t e r i s e d by E -» 1, 6 » 6 (see
u p
F i g u r e 5.8c, d and e ) . The c h a r a c t e r of the diagram changes as t h e
of
instability
b i f u r c a t e s i n t o two branches.
The lower, u n s t a b l e
r e t a i n s the c h a r a c t e r i s t i c s of the Holmboe mode, the second
extension
of
the
Kelvin-Helmholz
consequence of t h i s behaviour
constant,
those
f o r example
f o r the p r e s e n t
infinity
yielding
rapid
increase
tidal
again
i t clearly
more
when
experiments)
Let
roots.
a
may
Ri
demonstrates
help
The
E
and
be
and
l e t Ri
decrease
flow.
as i t i s based
the
effect
a n n u l a r flume d u r i n g the t i d a l
understand
experiments.
0,3
shows
and f i n a l l y a
effects).
on l i n e a r
perturbation
of
modes on the
other
5.6 i t w i l l
the
about
A f u r t h e r decrease
approaches zero (no buoyancy
flows. In Paragraph
to
from
diagrams show t h a t f o r h i g h R i , the
unstable
i s idealized,
of s t r a t i f i e d
picture
interesting.
two
i n c^, then an i n c r e a s e , a g a i n a decrease
Though t h i s p i c t u r e
this
with
i s an
= 0,6 and E = 0,8 (these v a l u e s a r e c l o s e t o
a
progressively
a decrease
stability
but
branch
branch
( c ^ = 0 ) . F o r 1 < R i < 0,5 c. i n c r e a s e s up t o
first
theory,
i s very
down t o z e r o . The s t a b i l i t y
flow i s s t a b l e
mode,
zone
be
shown
phenomena observed
that
i n the
- 39 -
5.4
Series
1 Tidal
A detailed
view
experiments
of
with
F i g u r e s 5.13a
Figures
experiments
the
(r.b.max - 0.2
depositional
sediments
from
and 5.14b. The
and
erosional
phase
for
the
the Western S c h e l d t are shown i n the
and 5.13b, and f o r the
5.14a
Pa).
Eems-Dollard
experiments
in
the
f i g u r e s show the bed shear s t r e s s r , the
b
sediment
c o n c e n t r a t i o n measured i n the s u s p e n s i o n c , and the d e p o s i t i o n
s
and e r o s i o n r a t e s D and E. These l a t t e r are d e f i n e d as:
dc
D
h
= dT
(5.6)
E
dc
dT
h
=
From D the e f f e c t i v e s e t t l i n g v e l o c i t y W
can be
derived:
s
W
W
is
= - D/c
s
plotted
(5-7)
s
a g a i n s t c i n the F i g u r e s 5.15a
and
5.16a. No
correlation
s
i s observed. However, i t i s
noted
Western S c h e l d t , W
t w i c e the v a l u e s f o r the sediments
g
i s about
that
for
the
sediments
from
the
from the
Eems-Dollard. Measurements w i t h the s e d i m e n t a t i o n
balance
show
be due t o s e g r e g a t i o n
the
effects
opposite
5.15b
settling
velocity
g
W
s
should
« c7
b
includes
the
tube,
etc.):
effects
The
profile
maximum
experiments
erosion
is
of
in
still
to 0,35
settling velocity
water
turbulence
differs
( i . e . sedimentation
the e f f e c t i v e s e t t l i n g v e l o c i t y
(vertical
can o n l y be c o r r e c t e d
implicitly
diffusion)
on
the
f o r when the
vertical
i s measured.
shear
s t r e s s a p p l i e d amounted t o 0,2
showed t h a t at these s m a l l v a l u e s of
to
be
expected.
This
was
3
kg/m , and
t
Pa. The
f a
only
steady s t a t e
very
a l s o observed d u r i n g the
experiments. F o r the Western S c h e l d t sediments,
0,1
For
found:
i n mind t h a t the e f f e c t i v e
deposition rate. This effect
sediment
r^.
(5-8)
from s e t t l i n g v e l o c i t i e s measured
Owen
i n the F i g u r e s
1 , 7
be kept
balance,
f e
decreases with i n c r e a s i n g
the same c o r r e l a t i o n was
2.1)
experiments.
i s plotted against r
and 5.16b. I t i s shown t h a t W
both sediments
It
T h i s d i f f e r e n c e might
i n the a n n u l a r flume d u r i n g the t i d a l
effective
The
trend.
(Table
f o r the Eems-Dollard
c
g
increased
sediments
from
little
tidal
about
from about 0,12
to
- 40
0,2
kg/m
. Assuming a bed
c o n c e n t r a t i o n of 50 kg/m
the e r o s i o n of about 1 mm
the bed,
the F i g u r e s 5.13b
then
decreases,
distribution
It
of the bed
a pronounced g r a d i e n t
from
and
though
,
this
in strength i s present.
increases
continuously.
of
f u r t h e r through n u m e r i c a l
this
the
further
Chapter
5.5
analyses
mm,
seen
and
strength
this
present.
will
be
"DELWAQ-S1ib" and
the
latter
based
s t a t e experiments d e s c r i b e d
in
4.
S e r i e s 2 T i d a l experiments (tb.max = 0.4
A p a r t of the measured c o n c e n t r a t i o n - t i m e
5.3
The
research,
simulations with
of the steady
1
increases
w i t h i n such a t h i n l a y e r cannot be e s t a b l i s h e d at
some r e a l i s t i c guesses of t h i s s t r e n g t h d i s t r i b u t i o n ;
on
yield
T h i s can be
5.14b, which show t h a t E f i r s t
z^
would
or l e s s . However, w i t h i n t h i s
i s proposed t h a t i n a next phase
elaborated
-
and
5.7,
are g i v e n
obtained
curves,
i n the F i g u r e s 5.17
on the d e p o s i t i o n p e r i o d
and
include
from the mass balance
Pa):
and
the
(see s e c t i o n
Deposition.
shown i n
5.18.
the
Figures
These f i g u r e s f o c u s
deposition
rate
D.
D
is
5.4):
dc
D
The
=
h
( 5 > 6 )
dT
deposition
F i g u r e 5.17.
curve
This
Eems-Dollard mud
The
i n F i g u r e 5.18
i s due
i s much smoother than the curve
to a n u m e r i c a l
p r i o r to d e t e r m i n i n g
settling velocity W
g
Krone's law
of the sediments can be
D =
- W
c
(Krone
[1962]):
(-^r
~)
different
u,K
defined
a
threshold
eventually settle,
and
of
from
the
definitions:
(5.9)
'
= Krone's c r i t i c a l
as
established
f o r t. < z
d K
where z
curve
the time d e r i v a t i v e .
d e p o s i t i o n r a t e . T h i s i s done u s i n g two
1. Using
smoothing of the c - t
in
shear s t r e s s f o r d e p o s i t i o n ,
shear
stress
beyond which no
below
which
which
is
a l l sediments
sediment s e t t l e s at
all.
For
graded sediments, a l s o a minimum c r i t i c a l shear s t r e s s f o r d e p o s i t i o n
z . e x i s t s , d e f i n e d as the t h r e s h o l d
shear
s t r e s s below which a l l
d
sediments
was
0,03
eventually
settle.
found to be z^ - 0,06
±
0,01
Pa
for
From the steady
± 0,01
s t a t e experiments
Pa f o r Western S c h e l d t mud,
Eems-Dollard
mud.
Applying
these
and
this
z^ =
figures in
- 41
-
Krone's law would y i e l d no d e p o s i t i o n b e f o r e t - 330 min
min
for
Western S c h e l d t mud
the F i g u r e s 5.17
and
to
earlier,
start
much
and Eems-Dollard
5.18). From the graphs,
i.e.
at
t
<
f e
r e s p e c t i v e l y . T h e r e f o r e , these v a l u e s are
Western
Scheldt
mud,
and
t -
340
respectively
(see
deposition
0,15
is
Pa and
used
in
c
equ
fe
observed
< 0,09
Pa
(5.9):
for
mud
„ • 0,15 Pa and f o r Eems-Dollard mud z.
=
d, K
u , K.
i s shown i n the
Figures
0,09 Pa. The r e s u l t i n g s e t t l i n g v e l o c i t y W
5.19a
and
5.20a. The
large values
of W
around t * 380 min. are
s
v
g
attributed
t o the i n a c c u r a c y of the d a t a when D becomes z e r o .
2. Using the " e f f e c t i v e s e t t l i n g v e l o c i t y
D - - W
c
s
s
The
The
concept":
(5.7)
r e s u l t s are shown i n the F i g u r e s 5.19b
two
s e t s of f i g u r e s show t h a t the
generally
smaller
than
W
effective
determined
g
and
5.20b.
settling
velocity
w i t h Krone's law.
Considerable
d i f f e r e n c e s o c c u r d u r i n g the b e g i n n i n g of d e p o s i t i o n , when
i.e.
In
when (z^
R
- ^ )/
b
r
i s
d
K
is
z^
•
z^
,
R
small.
the f o l l o w i n g a n a l y s i s , the concept
of e f f e c t i v e s e t t l i n g v e l o c i t y i s
used.
The
F i g u r e s 5.21a
and
5.22a show the v a r i a t i o n of W
with
the
sediment
concentration
c . The
same p i c t u r e s are shown on l o g a r i t h m i c s c a l e i n
s
the F i g u r e s 5.21b and 5.22b. The
large scatter
in W
at
the
lower
g
concentrations
is
due
to the i n a c c u r a c y of the r e s u l t s at low c . The
3
v e r y r a p i d drop a t
c
=10
kg/m
has
another
cause.
The
maximum
s
2
c o n c e n t r a t i o n measured d u r i n g the experiments i s about 10 kg/m . So t h i s
s
value
i s an asymptote y i e l d i n g
deposition
when
W
is
the W -c
relation
g
at
the
beginning
s m a l l . T h i s means t h a t (some) d a t a
i n the
of
left
s
p a r t and
When
this
estuary
were
and
i n the r i g h t p a r t of the f i g u r e s s h o u l d be
is
(Thorn
done,
10
cm
definition
the data can be compared w i t h data f o r the
[1982]) and Tampa Bay
obtained
with a s e t t l i n g
diameter.
from
the
Hence,
(Ross
[1988]). Both
column; Ross used
these
effective
settling
occur
w i t h c due
i n both cases. The
velocities
s e t t l i n g v e l o c i t i e s used
f i g u r e s show an
t o f l o c c u l a t i o n e f f e c t s , next
then a decrease
due
to hindered s e t t l i n g .
Mehta [1986] w i t h the f o l l o w i n g f o r m u l a :
sets
Severn
of
data
a column of 2 m l e n g t h
a n a l y s i s . However, the phenomena of f l o c c u l a t i o n and
should
omitted.
differ
i n the
hindered
initial
in
present
settling
i n c r e a s e of
a subsequent s t a b i l i z a t i o n
These e f f e c t s were c a p t u r e d
W
g
and
by
- 42 -
W
11
- k, c
I s
s
flocculation
effect
(5.10)
o
W
= W . (1 - k„c )
sO
2 s
s
F o r Severn mud:
4,65.
and
The
hindered s e t t l i n g
- 0,513, n - 1,29,
^
F o r Tampa Bay mud:
^
- 0,11,
W
- 2,6
gQ
n - 1,6,
W
effect
mm/s,
- 0,37
sQ
- 0,008 and
2
mm/s,
k
2
n -
- 0,008
n » 5.
agreement
S c h e l d t mud,
in
difference
Plotting
w i t h these data and the p r e s e n t d a t a
but much l e s s f o r Eems-Dollard
difference
character
W
s
versus
correlation
at
vs t p l o t s
a l l . This
flocculation effect
Finally,
on W
obscurating
presented
the
two
No
explanation for this
sediments was
z. , as i n the F i g u r e s 5.15b
b
g
phase,
between
mud.
i s good f o r Western
found
but
the
i n the d e f i n i t i o n of W .
s
comparable t o the W
g
all
is
ad 5.16b
i n the F i g u r e s 5.19a
because
of
and
showed graphs
5.20a, thus
no
the l a r g e i n f l u e n c e of the
d u r i n g the f i r s t
h a l f hour of
other
These p l o t s are t h e r e f o r e not
effects.
the
deposition
here.
the v a r i a t i o n of the s e t t l i n g v e l o c i t y a c c o r d i n g t o Krone's
w i t h sediment c o n c e n t r a t i o n i s g i v e n i n F i g u r e 5.23,
t r e n d as the e f f e c t i v e
5.6
k
setting
showing
the
law
same
velocity.
S e r i e s 2 T i d a l experiments
(tb.max - 0.4
Pa):
Erosion/re-entrainment.
A p a r t of the measured c o n c e n t r a t i o n - t i m e c u r v e s , shown i n
5.3
and
5.7,
are g i v e n i n the F i g u r e s 5.24
on the e r o s i o n / r e - e n t r a i n m e n t
p e r i o d and
and
5.25.
the
Figures
These f i g u r e s
focus
i n c l u d e the e r o s i o n r a t e
E.
E
i s o b t a i n e d from the mass b a l a n c e :
dc
E - h — ^
dt
(5.6)
For the a n a l y s i s of the experiments,
entrainment
phase are used.
w i t h Eems-Dollard
mud
do not
The
the photographs made d u r i n g the r e -
photographs taken d u r i n g the
include a v e r t i c a l
not be q u a n t i f i e d . Hence, the f o l l o w i n g a n a l y s i s
experiments
s c a l e , and
is
experiments
can t h e r e f o r e
restricted
to
the
w i t h sediment from the Western S c h e l d t .
D i r e c t l y a f t e r the s t a r t
of re-entrainment,
maximum
and
around 420 min,
F i g u r e 5.24). The
then drops
E becomes v e r y l a r g e , w i t h a
t o an almost
a n a l y s i s of t h i s behaviour
constant
i s presented
level
i n two
(see
steps:
- 43
first
the
erosion
rate
is
-
estimated using
the model by Parchure
second the
concept of entrainment of s t r a t i f i e d
For
methods
both
the
known. T h i s p r o f i l e
in
the
Chapters
r e l a t i o n s may
within
the
and
a l s o be
mud
3.
It
is
t w o - l a y e r f l o w s i s used.
p r o f i l e w i t h i n the
i s e s t i m a t e d w i t h the
2
fluid
concentration
bed
should
c o n s o l i d a t i o n curves
assumed
a p p l i e d t o e s t i m a t e the
and
t h a t these
be
described
consolidation
concentration d i s t r i b u t i o n
layer. Possible errors w i l l
be due
to f o r
instance
s o r t i n g e f f e c t s (the c o n s o l i d a t i o n curve i s a f f e c t e d by the p r e s e n c e
sand
mud
i n the
original
l a y e r ) . The
b
a
bed
= 0,6
b
thickness
of
consolidation
+
concentration
was
The
= 240
b
=
to e r o s i o n
(5.11)
the c o n s o l i d a t i o n
i s expected a f t e r 6,5
mm
before
3
erosion
tests,
hours (6 hours
starts).
, so t h a t the mean bed
kg/m
reads :
The
initial
concentration
c
b
.
during
the
H
tidal
= 31 mm,
x
experiments show t h a t the
and
the
f l u i d mud
layer
nonjust
a thickness
g
54 kg/m
. The
therefore
measured
Figure
70
a thickness
has
mud
fluid
H„
= 50 mm. The maximum c o n c e n t r a t i o n
rm
2
_
s u s p e n s i o n j u s t p r i o r to d e p o s i t i o n i s c
= 10 kg/m
, so t h a t c
shown i n F i g u r e
is
=56
taken
e r o d i b l e l a y e r has
of the
hour
c
kg/m
=
i n the
0 , 4
curves measured d u r i n g
H
0,5
photographs
prior
(z/H)"
interface-time
becomes c
( l i t t l e ) sand i s expected
c o n s o l i d a t i o n r e l a t i o n f o r Western S c h e l d t
c (z)/E
From the
sample - no
of
bed
concentration
5.26a. I t i s the
recommended
that
f m
curve ( C b - p r e d i c t e d ) thus o b t a i n e d
b a s i s f o r the
in
future
f u r t h e r analyses,
experiments
and
is
it
t h i s curve i s
directly.
5.26a
also
shows
suspension concentration
and
the
erosion
the p r e d i c t e d
depth,
based
f l u i d mud
on the
measured
concentration.
3
The
f l u i d mud
means t h a t z
e
in
described
is
v a r i e s between about 30
cannot be e s t a b l i s h e d
Chapter 4. T h e r e f o r e
from the
steady
and
180
state
kg/m
. This
experiments
an e m p i r i c a l r e l a t i o n by Owen [1970]
adapted:
t
5.
concentration
3
e
« c}'
b
(5-12)
For the p r e s e n t a n a l y s i s i t i s n e c e s s a r y t h a t
the
total
amount
of
sediment i n the f l u i d mud l a y e r i s c o r r e c t . Hence a +
6
should
be
u n i t y , as e x p l a i n e d on page 21 (equ ( 3 . 3 ) ) . Consequently, equ (5.11)
does not n e c e s s a r i l y y i e l d the best o v e r a l l e m p i r i c a l f i t .
- 44 -
The maximum bed shear s t r e s s d u r i n g the t i d a l c y c l e
is
t h e r e f o r e reasonable
is
- 0,4
t o assume t h a t t h e e r o s i o n s t r e n g t h z
Pa. I t
- 0,4 Pa
at the i n t e r f a c e between the f l u i d mud l a y e r and the n o n - e r o d i b l e bed ( z
• 0,031 ra). Then equ (5.12) becomes f o r Western S c h e l d t mud:
z
This
- 2,6.10~
relation
6
c
2
,
3
i s given
(5.13)
i n Figure
5.26b,
c o n c e n t r a t i o n d i s t r i b u t i o n . Note t h a t the l e f t
l i n e a r s c a l e and the r i g h t hand v e r t i c a l
E
p
of
the
al
o b t a i n e d through d a t a - f i t t i n g ,
In
= 2.10"
p
6
hand v e r t i c a l
a x i s has
[1984],
[1985],
[1990],
and
the
floe
erosion
the
exp {10 / ( t . - c ( z ) ) }
b
larger
(5.14)
e
rate
indicating
than
E^.
Apparently
Before t • 440
other
and
entrainment
the o v e r f l o w i n g f l u i d ,
instability
processes play a r o l e
as d i s c u s s e d i n paragraph 5.3.
processes
gradient
in
gradient
Richardson
approximating
the mixing
are
related
i n g e n e r a l t o the R i c h a r d s o n
l a y e r and the
density
l a y e r were not measured, a f a i r e s t i m a t e of t h e
number
can
be
obtained.
This
is
done
by
R i as f o l l o w s :
Ri = -
g
(
9
P
/
3
Z
)
2
- - *-*f (6 /6)
p (3u/3zr
P u
2
z
u
(5.15)
p
be o b t a i n e d from the p r e d i c t e d c o n c e n t r a t i o n p r o f i l e c ^
f l u i d mud l a y e r ,
Karelse
however,
p r o c e s s e s between t h e f l u i d mud l a y e r
number. Though the v e l o c i t y g r a d i e n t i n the shear
can
rain.
The e r o s i o n i n t h i s phase of the t i d e s h o u l d be a t t r i b u t e d t o
instability
These
An
is
yielding:
from steady s t a t e experiments.
i s much
initially.
Ap
f
the e r o s i o n d u r i n g t h i s p e r i o d can be d e s c r i b e d w i t h common t h e o r y
established
and
E
F i g u r e 5.27 E^ i s compared w i t h the a c t u a l measured entrainment
that
a
the e r o s i o n
E. I t i s shown t h a t beyond t = 440 rain the agreement i s f a i r ,
E
the bed
bed can be e s t a b l i s h e d . The c o e f f i c i e n t s a and 8
were deduced by K u i j p e r et
E
with
axis a logarithmic scale.
U s i n g the common e r o s i o n formula by Parchure
potential
together
[1990]),
m
i n the
6^ from v e l o c i t y measurements i n t h e a n n u l a r flume (see
and 6^ from the photographs of the t i d a l
experiments.
average v a l u e f o r 6 " 7 mm, w i t h a minimum of 5 mm and a maximum of
•
u
10
mm,
and f o r 6 " 1 , 5 mm, w i t h a minimum of 1 mm and a maximum of 2
P
mm. F i g u r e 5.28 g i v e s the r e s u l t i n g R i as a f u n c t i o n o f time showing an
- 45 -
initial
decrease
i n c r e a s e , due
a
critical
due
t o the i n c r e a s e i n f l o w v e l o c i t y U,
t o the i n c r e a s e i n bed d e n s i t y . From t h e o r e t i c a l
v a l u e of R i » 0,25
d i s t u r b a n c e s cannot
t h a t the e s t i m a t e d Richardson
the range where i n t e r f a c i a l
should be noted
augment
the
account
next
known
o c c u r f o r R i up t o u n i t y . F i g u r e 5.28
shows
numbers f o r the p r e s e n t experiments
i n s t a b i l i t i e s may
be expected
t h a t the e f f e c t s of c o h e s i o n ,
stability
of
number.
it
0,25,
is
the
mixing
which
l i e in
t o grow.
certainly
will
l a y e r , have not been taken
i n t h i s a n a l y s i s . T h i s p r o b a b l y can
Richardson
however
an
analyses
i s known, i n d i c a t i n g t h a t f o r R i >
grow. From e x p e r i m e n t a l work
t h a t u n s t a b l e i n t e r f a c e s may
It
f o l l o w e d by
be
done
with
a
into
modified
I t i s recommended t o e l a b o r a t e on t h i s f u r t h e r
in a
study.
One
of
the
first
i n s t a b i l i t i e s was
interfacial
extensive
behaviour
(cusped,
sharp
crests
crested
present
on
into
the
waves
interfacial
results,
flow)
shows
those by
a
Srinivas
determined
by
the
by
implying
behaviour
i n t e r f a c e . Hence, Keulegan c o u l d e s t i m a t e the maximum
the
is
hardly affected
the f l o w v e l o c i t y ,
of
X.
break and
observation, again c o n s i s t e n t with
i s t h a t the wave l e n g t h X. was
that
that
moving
resemblance w i t h the p r e s e n t o b s e r v a t i o n s and
and Mehta [1990]. Another i n t e r e s t i n g
the
studies
c a r r i e d out by Keulegan [1949]. H i s d e s c r i p t i o n of the
i n j e c t i o n of e d d i e s from the
striking
experimental
stability
p o s s i b l e wave l e n g t h from the wave e q u a t i o n :
.
k
raln
= -22- = 1_|_A£
Nnax
U
2
(5.16)
p
c
i n which U
i s the c r i t i c a l v e l o c i t y at which the i n s t a b i l i t i e s s t a r t t o
c
( i . e . when entrainment
s t a r t s ) . From F i g u r e 5.27 i t can be seen
grow
that z
- 0,07 Pa, hence U
- 0,08
m/s
(see
Karelse
[1990] f o r the
c
c
2
relation
between t
and
U).
S u b s t i t u t i n g f o r Ap = 20 kg/m
( c * 30
kc/m ) and p = 1025 kg/m , X
- 0,1 m, which i s o n l y a
little
larger
°
max
than the observed wave l e n g t h s of 5 t o 8 cm.
f e
3
f a
3
To a n a l y s e e x p e r i m e n t a l data, an o v e r a l l R i c h a r d s o n
i n g e n e r a l , d e f i n e d as (see Chapter
1
5,
is
a
typical
5
< -
length
V a r i o u s d e f i n i t i o n s are used
and
Phillips
is
Q
used
5.3):
Ri o = S - ^ V 2
P X
where
number R i
scale
and x
in literature.
[1969] and Kantha, P h i l l i p s
a
2 )
typical velocity
First
and Azad
the approach
by
scale.
Kato
[1977] i s f o l l o w e d , as
- 46 -
t h e i r experiments w i t h f r e s h - s a l i n e s t r a t i f i e d water
(N.B.
with
only
upper
lid
rotation)
highly
i n an a n n u l a r flume
resemble
the
present
experiments. They d e f i n e d the f o l l o w i n g o v e r a l l R i c h a r d s o n number:
Ri* -
(5.17)
P J *,u
.
u
Here h - water depth
upper
lid.
[m] and u.
- the
shear v e l o c i t y
[m/s]
*»«
entrainment r a t e E . i s a l s o r e l a t e d to u.
and
The
at
the
reads:
" j u
V*
u
v*
where
u
defined
those
u.
*,u
is
e
the
i n equ
by
(5.18)
c, u,
b
*,u
vertical
entrainment v e l o c i t y and E the e r o s i o n
( 5 . 6 ) . The p r e s e n t t i d a l experiments can be compared w i t h
Kato and P h i l l i p s and by Kantha
a n n u l a r flume
i s known. For t h i s purpose,
c o n s i d e r e d t o be ( q u a s i - ) s t e a d y . Let z
lid,
et a l when u*
the
flow
flume
on
the
(h = 0,3
water-sediment
m)
f o r the D e l f t
u
in
the
flume
be the shear s t r e s s on the
T. the shear s t r e s s on the s i d e w a l l of the
w
stress
rate
interface
flume,
z,
b
the
is
upper
shear
(the bed), h the h e i g h t of the
and B the width of the flume
(B = 0,2 ra). Then
because
of e q u i l i b r i u m of f o r c e s :
B.z
If
= B.C. + 2.h.x.
b
w
u
(5.19)
i t i s assumed t h a t z. * z , then z " 4.T.. . Hence, u.
* 2.u., i . e .
b
w
u
b
*,u
*
the shear v e l o c i t y at the upper
the
bed. U s i n g t h i s v a l u e , the v a r i a t i o n of R i * w i t h time i s p l o t t e d i n
F i g u r e 5.29.
Richardson
Next,
A behaviour s i m i l a r to
number
is
found
that
observed
(see F i g u r e 5.28),
with
the
though more
v
390
<
t
< 440 min.
r e s u l t s by Kato and P h i l l i p s
the r e s u l t s by Kantha,
a comparison
[1990],
obtained
i s shown i n F i g u r e 5.30,
in
the
t o g e t h e r w i t h the
( E * - 2,5/Ri* f o r 20 < R i * < 400)
v
P h i l l i p s and
gradient
pronounced.
the v a r i a t i o n of E * w i t h R i * f o r the p r e s e n t experiments
period
Next,
l i d i s about t w i c e the shear v e l o c i t y a t
and w i t h
Azad.
i s made w i t h the r e c e n t r e s u l t s by S r i n i v a s and Mehta
in
a " r a c e - t r a c k " flume w i t h k a o l i n i t e and b e n t o n i t e
c l a y . The r e s u l t s are shown i n F i g u r e
'
slightly different:
5.31.
Ri
o
and
E„
v
are
defined
(5.20)
- 47 -
(5.21)
The
F i g u r e s 5.30
1. An
and
inverse
trend
extend around R i
2. The
slope
5.31
of
l e a d to s e v e r a l
is
observed
"
5,5).
the
data
u
observations:
around
R i * " 170
agrees o n l y f o r a v e r y
r e s u l t s by Kantha et a l and
w e l l w i t h the
(and
to a l e s s e r
small part with
results
by
the
Srinivas
and
Mehta.
3. For d e c r e a s i n g
<
The
inverse trend
around R i * - 170
in E *
v
which i s shown as a k i n k
( F i g u r e 5.29). T h i s
min.
profile
this
show a r a p i d drop when R i * < 170,
t h a t i s used
i s elaborated
(equ
S r i n i v a s and
and
yield
z
Mehta i s s i g n i f i c a n t .
not
a
to
a
r e s u l t s and
in
around t -
deviation
those
Though c o h e s i o n
play a role,
and
2.5),
and
of
the
420
c
fe
profile;
i t s effect
by Kantha et a l
(augmented
i s probably
of i n t e r e s t
and
viscosity
s m a l l , as y
3
kg/m
;
see
(c. * 30
the experiments by S r i n i v a s and
arguments
by
experiments
respond
time
material. This conclusion
Turner
d i f f e r e n c e between the p r e s e n t
present
inverse trend
b
2.3
the
show
u
f u r t h e r below.
a l s o c a r r i e d out w i t h c o h e s i v e
may
due
are s m a l l at the c o n c e n t r a t i o n s
y
Figures
with
t o an
(5.11)) from the a c t u a l c o n c e n t r a t i o n
a little
s t r e n g t h ) may
i s due
i n the R i * - t curve
i s probably
d i f f e r e n c e between the p r e s e n t
and
or R i
5,5.
Ri* itself,
The
R i , the data
are t i d a l
The
the
role
experiments and
instantaneously
lag.
on
experiments;
of
the o t h e r s
are
c o n d i t i o n s . A t h i r d problem i s t h a t n e i t h e r z
h
around R i * - 170.
first
i n c r e a s e s and
explanations
exist
However, the
then
that
the
concentration
shear s t r e s s , hence
based
on e q u i l i b r i u m
nor u* are known p r o p e r l y
be e l a b o r a t e d upon f u r t h e r .
There are some u n c e r t a i n t i e s on the a c t u a l v a l u e s
curve
consistent
is
i n t e r f a c e and
experiments
f o r the v a r i o u s s t u d i e s . T h i s should
is
v i s c o s i t y . A second
to v a r i a t i o n s i n bed
other
Mehta were
of
the
E *
vs
v
Ri*
r e s u l t s show q u a l i t a t i v e l y t h a t
decreases
f o r t h i s behaviour,
again
with
increasing
which are both f a i r l y
Ri*.
E *
v
Two
speculative
however.
From the v i s u a l
observations
high concentrated
p a r t s . The
and
the k i n k
i n the
sediment l a y e r on the bed
of
two
and
i s eroded through i n t e r f a c i a l
can
c vs t curve,
be
regarded
upper, s o f t e r l a y e r behaves as a f l u i d
instabilities.
The
the
to
consist
(viscous
lower
soft,
part)
(plastic?)
- 48 -
layer
i s o n l y exposed t o s u r f a c e e r o s i o n ; no waves can be formed on i t s
i n t e r f a c e . As a r e s u l t of the e r o s i o n , the upper l a y e r becomes
and
the
initial
from
in
waves
cannot p e n e t r a t e
thinner,
as f a r down i n t o the bed as d u r i n g the
phase, and t h e r e f o r e decrease i n wave h e i g h t .
one e r o s i o n mode t o the o t h e r
As
the
transfer
i s f a i r l y abrupt, some d i s c o n t i n u i t y
the c ^ ( z ) and/or t ( z ) i s t o be expected. T h i s d i s c o n t i n u i t y
may
g
formed d u r i n g
i s not v e r y
the c o n s o l i d a t i o n process
likely,
simultaneous
as
no
such
around s l a c k t i d e . T h i s , however
behaviour
was
observed
during
c o n s o l i d a t i o n experiments. P o s s i b l y , the c y c l i c
the
interfacial
instabilities
of
the lower l a y e r , c a u s i n g
be
the
l o a d i n g by
themselves may cause a d d i t i o n a l compaction
a d i s c o n t i n u i t y i n the d e n s i t y p r o f i l e , and
thus i n the e r o s i o n mode. T h i s compaction i s not taken i n t o account
equ
(5.11).
Figure
It
a l s o e x p l a i n s the doubts on the i n v e r s e t r e n d
5.29. I t i s t h e r e f o r e
density d i s t r i b u t i o n
The
recommended t o measure the
i n t h i s layer i n d e t a i l during
i n c r e a s e and subsequent decrease i n
character
of
the
interfacial
(variation
Lawrence
[1987]
instabilities.
At
low
a
the
R i , i . e . large
s t r o n g m i x i n g between
p i c t u r e . However, Holmboe [1962]
observed
in)
f u r t h e r experiments.
l a y e r s o f f l u i d may take p l a c e . When R i i n c r e a s e s , the m i x i n g
i s the c l a s s i c a l
shown i n
i s p o s s i b l y a l s o due t o
k i n e t i c energy and/or s m a l l buoyancy e f f e c t s ,
This
in
and
two
decreases.
later f . i .
second mode of i n s t a b i l i t y when 6 »
u
6 .
p
J
Then v o r t i c e s can develop i n the shear l a y e r , not h i n d e r e d
e f f e c t s . These v o r t i c e s i n t e r f e r e w i t h
by
buoyancy
the waves on the i n t e r f a c e , which
become cusped, s h a r p l y c r e s t e d . These waves are known as Holmboe
and
these a r e the waves observed
i n the p r e s e n t
experiments, but a l s o by
Keulegan [1949], Narimousa et a l [1987], S r i n i v a s and Mehta
many
others.
When
[1990]
It i s
clear
that
R i i s not the s o l e parameter anymore t h a t d e s c r i b e s
in
with
Ri.
p i c t u r e was q u a n t i f i e d by Lawrence [1987] i n a s t a b i l i t y a n a l y s i s ,
showing t h a t the a m p l i f i c a t i o n f a c t o r i s governed by R i , a wave
and
the
estimation
so
that
the s t a b i l i t y
of the i n t e r f a c e . Hence, the entrainment may seem t o i n c r e a s e
This
and
these waves steepen up, they may o v e r t o p and i n j e c t
l a r g e q u a n t i t i e s of sediment i n t o the flow.
case,
waves,
ratio
6/6
u
p
-
see
Paragraph
5.3
and F i g u r e
number,
5.12. A crude
6
f o r the p r e s e n t
experiments y i e l d s X. • 5 cm, and 6
"
5
mm,
t h a t a and E can be e s t a b l i s h e d a t E * 0,8 and a • 0,6. F i g u r e 5.12d
shows a remarkable agreement w i t h F i g u r e
5.30b: f o r
first
Ri
increases
and
decreases
(N.B.
0
and
J
decreasing
=
Ri
0
E^
Rig are defined
differently).
Figure
5.32 f i n a l l y
shows the c o r r e l a t i o n between the e r o s i o n r a t e E and
the bed shear s t r e s s z
. This figure
includes
the
relation
found
by
- 49
Uraita
mud.
et a l [1984],
They d i d not
much
lower
who
a l s o performed t i d a l
r e p o r t the o c c u r r e n c e
sediment
r e s u l t , there
-
concentrations
experiments w i t h a n a t u r a l
of f l u i d mud;
(much
probably
due
to
lower e r o s i o n r a t e s ) . As
i s no agreement between the p r e s e n t
r e s u l t s and
those
a
by
Umita.
Acknowledgements.
T h i s r e s e a r c h i s performed i n commission of R i j k s w a t e r s t a a t
Transport
and
Netherlands
We
for
like
P u b l i c Works, The
Integrated Soil
Netherlands).
It i s also
skilful
i n s t r u m e n t a t i o n and
part
of
"The
Research Programme".
to acknowledge Kees Koree, E r i k van V e l z e n
their
( M i n i s t r y of
contribution
executing
the
in
running
experiments.
and
the
Frans
de
Vreede
facilities
and
- 50 -
References.
K.
Ashida,
S.
Egashira,
[1975],
" B a s i c study on t u r b i d i t y
H y d r a u l i c and S a n i t a r y E n g i n e e r i n g D i v i s i o n , T r a n s a c t i o n s of
currents",
JSCE,
Vol
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S p e c i f i c surface
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Specific surface [m2/gl
160
z
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s
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20
30
40
50
Lutum fraction (D<2mu) [%l
-
Berlam.-marine mud
*• Berlam.-inland mud
s
Nethorl.-eat.mud
*
Fig 2.1
DELFT HYDRAULICS
kaolinite
60
Nethorl.-inland mud
70
2 8
SHEAR
RATE
in
RHEOLOGICAL FLOW
sensor:
DA45
1 /s
CURVES
50
SHEAR
RATE
in
RHEOLOGICAL FLOW
sensor:
ME15
Rheological flow-curves.
DELFT HYDRAULICS
1/s
CURVES
H'Diep. S.plaat
Fig. 2.2
Dynamic v i s c o s i t y
versus concentration
Dynamic viscosity [mPasI
-
100
P
10
fr
10
100
Concentration tkg/m3l
1000
HD-Splaat
HD-Moardbr.
WSchaldt
Lake Ketel
Meuse
E-Dollard
Loswal Noord
Biaabosch
Fig 2.3a
Dynamic viscosity [mPasJ
1000
-
: ^
0
100
200
300
400
500
600
700
800
Concentration [kg/m3|
HD-Splaat
-*- Mauaa
—1~ HD-Moardbr. -*- WSchaldt
-e— E-Dollard
Fig 2.3b
DELFT
HYDRAULICS
-a- Lake Katal
Loawal Noord -»- Biesbosch
900
Dynamic viscosity versus sand
content at c - 400 kg/m3
100
Dynamic viscosity [mPas]
L
a
i: c
i
1
10
Sand content [%)
D
100
Netherlands mud
Fig 2.4a
0
100
200
300
400
Fig. 2.4 b SUSPENDED SEDIMENT CONCENTRATION (g/l)
DELFT HYDRAULICS
500
Yield strength
versus concentration
Yield strength [Pal
100
100
concentration [kg/m3l
Fig
1000
HD-Splaat
HD-Moardbr.
WSchaldt
Lake Ketel
Mouse
E-Dollard
Loswal Noord
Biaabosch
2.5a
Yield strength [Pal
100
E
1
1
1
100
1
200
1
0.01
0
-~- HD-Splaat
-*- Mauaa
Fig
1
1
1
1
300
400
500
600
concentration [kg/m3l
4
~ — HD-Moardbr. -*~ WSchaldt
E-Dollard
2.5b
DELFT
HYDRAULICS
Loswal Noord
1
700
1
800
- B - Lake Ketel
Biaabosch
1
900
Yield strength versus specific surface
Sediment concentration - 300 kg/m3
_ Yield strength [Pal
100 P
1
r-
J
0.1'
0
Fig 2.6
1
40
20
1
1
1
60
80
100
Specific surface [m2/g]
I
120
z
Barlam.-marine mud
x
Berlam.-ost.mud
*
Natharl.-lniand mud
a
Netharl.-eat.mud
I
140
I
160
Berlammont: Bingham strength
Yield strength versus C E C
Sediment concentration - 300 kg/m3
Yield strength [Pal
5
10
15
20
Cation Exchange Capacity CEC [meq/100g]
Netherl.-inland mud
Fig 2.7
DELFT
HYDRAULICS
D
Netherl.-est. mud
25
Yield strength versus C E C - c l a y
for primary floe densities
Yield strength [Pal
0
20
40
60
80
Cation Exchange Capacity CEC [meq/100gl
*
Nathan.-inland mud
*
Krona (1963)
Fig 2.8
°
Netherl.-e«t. mud
Equation (2.8)
Krone: Bingham strength
Yield strength versus C E C - c l a y
Sediment concentration - 300 kg/m3
Yield strength [Pa]
6
20
40
60
80
Cation Exchange Capacity CEC [meq/100gl
*
Nathorl.-inland mud
Natherl.-eat. mud
*
Krone (1963)
Equation (2.6)
Fig 2.9
Krone: primary floes, Bingh.str
DELFT
HYDRAULICS
100
Hollandsch Diep (Sassenplaat)
Consolidation
Interface [mml
300
\•
250
\
200
X%
Vs
150
100
•
60
0
1
I11
10
1
1
100
1000
Consolidation time [min]
I
— — Erosion exp. 1
Fig 3.1a
Fig. 3.1b
DELFT
HYDRAULICS
° Erosion exp. 2
1 11
10000
Hollandsch Diep (Moerdijkbrug)
Consolidation
250
Interface [mml
\
1
•
•
E E]
•IJ
-
10
100
Consolidation time [mini
—*— Erosion exp. 1
Fig
3.2a
Fig.
3.2b
DELFT
HYDRAULICS
Q
1000
Erosion exp. 2
i ii
10000
Western Scheldt (Breskens)
Consolidation
Interface [mml
350
300
250
200
VIj
150
100
50
I11I
10
0
1
Cons, column
ii
i • ii
i i i11
100
1000
10000
Consolidation time [min]
— E r o s i o n exp. 1
D
i
100000
Erosion exp. 2
Fig 3.3a
Interface [mm]
300
-I1
250
200
160
100
IP
/
50 r
0
0
0.01 0.02 0.03 0.04 0.06 0.06 0.07 0.08 0.09 0.1 0.11
Inverse time [1/mln]
Cons, column
—*- Erosion exp. 1
Fig 3.3b
DELFT
HYDRAULICS
Erosion exp. 2
Lake Ketel
Consolidation
350
Interface [mm]
300
250
200
150
100
100
1000
Consolidation time [min]
Q
— — Erosion exp. 1
Fig
10000
100000
Erosion exp. 2
3.4a
Interface [mm]
2601
0i
0
1
r
1
1
1
0.01
0.02
0.03
1
Erosion exp. 1
Fig.
1
1
1
1
0.04 0.06 0.06 0.07 0.08
Inverse time [1/min]
3.4b
DELFT HYDRAULICS
- a - Erosion exp. 2
1
1
0.09
0.1
River Meuse (Belfeld)
Consolidation
Interface [mml
160
140
120
[]
100
J
ti
80
60
I*
40
nit g. -••a
L ••
CI
20
0
10
—
100
Consolidation time [mini
Erosion exp. 1
D
1000
10000
Erosion exp. 2
Fig 3.5a
Interface [mm]
0
0.01 0.02 0.03 0.04 0.06 0.06 0.07 0.08 0.09
Inverse time [1/minl
Erosion exp. 1
Fig.
3.5b
DELFT HYDRAULICS
Erosion exp. 2
0.1 0.11
Eems-Dollard (Delfzijl Harbour)
Consolidation
Interface [mm]
360
300
250
200
10
100
1000
Consolidation time [min]
Erosion exp.
Fig
Fig.
3.6a
3.6b
DELFT
HYDRAULICS
a
Tidal exp.
10000
Loswal Noord (North Sea)
Consolidation
Interface [mml
250
a
200
150
\
D
C
\
100
Fl
I
60
I
10
0
—
Fig
I I I
I
100
1000
Consolidation time [mini
Erosion exp. 1
3.7a
2501
Fig.
Interface [mm]
1
r
3.7b
DELFT
HYDRAULICS
Q
Erosion exp. 2
Ii i i
10000
r-
«o
m
si-
fO
cvi
—
iuo no \LN3Wia3S 9NllVQnOSNO0 JO 3WfnOA
Krone [1962]
Consolidation of San Francisco Bay Mud
DELFT HYDRAULICS
Fig. 3.8
Hollandsch Diep (Sassenplaat)
Sediment-water interface H(t)
H/He - 1 [-]
s.
I I
i
I
1
10
100
Consolidation time [mini
—-- Erosion exp. 1
Fig
D
i I I
I I
Erosion exp. 2
1000
10000
Fit equ (3.1)
3.9
Hollandsch Diep (Moerdijkbrug)
Sediment-water interface H(t)
H/He - 1 [-1
—: P
a.
Q
*
^
0.1
rj
I II I
I I
0.01
1
10
100
Consolidation time [mini
Erosion exp. 1
Fig 3.10
DELFT
HYDRAULICS
° Erosion exp. 2
I iI
i
i
i
1000
Fit equ (3.1)
10000
Western Scheldt (Breskens)
Sediment-water interface H(t)
H/He - 1 [-1
0.1
1
i i i i 111
1
10
.. 1
1 11111
100
1000
Consolidation time [mini
1
1
-*— Cons, column
0
—
Erosion exp. 2
1 1
III!
10000
1 11 1
100000
Erosion exp. 1
Fit equ (3.1)
Fig 3.11
Lake Ketel
Sediment-water interface H(t)
H/He -1 [-1
0.01
0.001'
1
1
'— '' 11 ill
10
i — i i i i ml
1—i i i i i ul
100
1000
Consolidation time [mini
— — Erosion exp. 1
Fig 3.12
DELFT
HYDRAULICS
a
Erosion exp. 2
j i i i 11 ul
10000
i i i i 11 ul
100000
Fit equ (3.1)
River M e u s e (Belfeld)
Sediment-water interface H(t)
H/He - 1 [-1
0.1
n
I
0.01
I
1
11 1 1
10
1
I 1
100
Consolidation time [mini
i
I
Q
Erosion exp. 1
Erosion exp. 2
i
1
i
1000
i i
i
10000
Fit equ (3.1)
Fig 3.13
Eems-Dollard (Delfzijl Harbour)
Sediment-water interface H(t)
H/He - 1 [-]
1*1
0.1
ji
1i
0.01
1
11
10
1ii
1
i ii1
100
1000
Consolidation time [mini
— - Erosion exp.
Fig 3.14
DELFT
i i
i
HYDRAULICS
Q
Tidal exp.
i
Fit equ (3.1)
1
ii 1
10000
Loswal Noord (North Sea)
Sediment-water interface H(t)
H/He - 1 [-I
\
-TtHr
lilt
1
I Ii ii i
10
—
100
Consolidation time [min]
Erosion exp 1
Fig 3.15
DELFT
i iMil
HYDRAULICS
a
Erosion exp. 2
11111
1000
Fit equ (3.1)
10000
A
Lines of constant density
Time
Sills [1986]
Contraction during consolidation
DELFT HYDRAULICS
Fig. 3.16
100n
E
E
80-
c
70-
-5
O
i—
o
CO
=
-» T
-o T
T
-o T
T
-0 T
T
T
T
90-
60-
—
-
=
=
=
=
—
=
28
60
120
240
360
22
99
147
190
MIN
MIN
MIN
MIN
MIN
HRS
HRS
HRS
HRS
50-
>
O
CD
<
r—
X
o
UJ
X
403020100-0
Fig.
3.17
100
200
DRY DENSITY
H o l l a n d s c h Diep
in
300
kg/m
400
500
3
(Sassenplaat)
100
*
^
-
908070-
o
I—
I—
60-
o
CD
>
o
T
T
T
T
T
T
T
T
T
0.5
—
-
=
=
=
-
1
2
3
4
6
8
24
168
HR
HR
HRS
HRS
HRS
HRS
HRS
HRS
HRS
50-
<
x
3C
o
LU
x
20100
0
F i g . 3.18
100
200
DRY DENSITY
H o l l a n d s c h Diep
Bed c o n c e n t r a t i o n p r o f i l e s
consolidation.
DELFT
HYDRAULICS
in
300
kg/m
400
3
(Moerdijkbrug)
during
500
100
Fig.
3.20
Lake
Ketel
Bed c o n c e n t r a t i o n
consolidation.
DELFT
profiles
HYDRAULICS
during
100
90
•••••T
80
0 0 0 0 0 T
70
i i i
4
24
48
I 20
145
iiT
HRS
HRS
HRS
HRS
HRS
o
hr-
O
CD
60
50
>
o
CD
<
X
4030-
o
2010ft
0200
400
600
DRY
F i g . 3.21
Meuse
'
800
DENSITY
in
1000
kg/m
1200
1 400
3
(Belfeld)
100
• • • • • T
Aiti^iiiA T
0 0000 T
ft** o ft T
1 i i i i T
90^
E
c
80
2
o
70-
g
60-
CD
LxJ
50-
m
40H
x
30-
LxJ
x
20H
>
o
o
T
4
28
100
124
148
172
195
HRS
HRS
HRS
HRS
HRS
HRS
HRS
10-
0
100
200
300
DRY
F i g . 3.22
400
m
Eems-Dollard ( D e l f z i j l )
Bed c o n c e n t r a t i o n
consolidation.
DELFT
DENSITY
profiles
HYDRAULICS
during
kg/m
500
3
600
700
200
' 400
' 600
' 800 ' 1000 ' 1200 ' 1400
DRY DENSITY in k g / m
3
F i g . 3.23
Loswal Noord (North Sea)
Bed c o n c e n t r a t i o n
consolidation.
DELFT
profiles
HYDRAULICS
during
' 1600
' 1800
Hollandsch Diep (Sassenplaat)
Bed density profiles
Relative concentration [-1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.1
Relative depth [-]
Cons.time, av. cone.
3,3 hr, UO Kfl/m3
6,6 hr, 1B1 kg/m3
4,3 hr, 154 kg/m3
- 24 hr, 234 kg/m3
5,4 hr, 169 Kg/rn3
29 hr, 293 kfl/m3
Fig 3.25a
I I I !! I
Relative concentration
0.01
0.1
1
Relative depth
Cons.time, av.conc.
3,3 hr, 140 kg/m3
6,6 hr, 181 kg/m3
4,3 hr, 154 kg/m3
—•— 24 hr, 234 kg/m3
Fig 3.25b
DELFT
HYDRAULICS
- - 5,4 hr, 169 kg/m3
— 2 9
hr, 253 Kg/m3
Hollandsch Diep (Moerdijkbrug)
Bed density profiles
Relative concentration [-]
2
s
1.6
1
£•
0.5
s
N
*
0
0.1
0.2
0.3
0.4
0.6
0.6
0.7
0.8
0.9
1.1
Relative depth [-1
Cons.time, av.conc.
B hr, 184 kg/m3
4 hr, 161 kg/m3
48 hr, 266 kg/m3
- 96 hr, 264 kg/m3
24 hr, 216 kg/m3
168 hr, 300 kg/m3
Fig 3.26a
Relative concentration [-]
0.1
Relative depth [-1
0.01
Cons.time, Av.conc.
8 hr, 184 kg/m3
4 hr, 161 kg/m3
48 hr, 266 kg/m3
- 96 hr, 264 kg/m3
Fig 3.26b
DELFT
HYDRAULICS
24 hr, 216 kg/m3
168 hr, 300 kg/m3
1.2
Western Scheldt (Breskens)
Bed density profiles
Relative concentration [-1
Relative depth [-]
Cons.time, av.conc.
*
hr, 158 kfl/ras
22,8 hr, 262 kg/m3
- - 48,8 hr, 286 kg/m3
72
hr, 308 kg/m3
Fig 3.27a
_ Relative concentration [-]
10 u
i
i ii
0.1
0.01
0.1
Relative depth [-]
Cona.time, av.conc.
4 hr,
189 kg/m3
46,6 hr, 2B6 kg/m3
Fig 3.27b
DELFT
HYDRAULICS
22,8 hr, 262 kg/m3
72 hr,
306 ko/m3
Lake Ketel
Bed density profiles
Relative concentration [-]
\
1.6
1
0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Relative depth H
Cons.time, av.conc.
4 hr, 218 kg/m3
24 hr, 272 kg/m3
50 hr, 289 kg/m3
72 hr, 313 kg/m3
151 hr, 332 kg/ra3
158 hr, 302 kg/m3
Fig 3.28a
Relative concentration [-1
0.1
Relative depth [-1
0.01
Cona.tima, av.conc.
24 hr, 272 kg/m3
4 hr, 21B kg/m3
72 hr, 313 kg/m3
- 151 hr, 332 kg/m3
Fig 3.28b
DELFT
HYDRAULICS
50 hr, 299 kg/m3
168 hr, 302 kg/m3
Meuse (Belfeld)
Bed density profiles
Relative concentration [-]
2
1
1.6
1
s
0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Relative depth [-]
Cona.time, av.conc.
4 hr,
228 kg/m3
124 hr, 33S kg/m3
28 hr,
297 kg/m
- 148 hr, 351 kg/m3 — *
100 hr, 310 kg/m3
195 hr, 415 kg/m3
Fig 3.29a
Relative concentration [-1
10 u
i
Relative depth [-]
Cona.time, av.conc.
28 hr, 297 kg/m3
100 hr, 310 kg/m3
- 148 hr, 361 kg/m3
196 hr, 416 kg/m3
4 hr, 228 kg/m3
124 hr, 336 kg/m3
Fig 3.29b
DELFT
HYDRAULICS
1.2
Eems-Dollard (Delfzijl Harbour)
Bed density profiles
Relative concentration [-]
3.6
3
2.6
2
1.6
1
0.5
0
0
0.1
0.2 0.3 0.4
0.5 0.6 0.7 0.8
Relative depth [-]
0.9
1
1.1 1.2
Cons.time, av.conc.
120 hr, 506 kg/m3
48 hr, 442 kg/mS
24 hr, 399 kg/m3
4 hr, 273 kg/m3
- 143 hr, 496 kg/m3
Fig 3.30a
Relative concentration [-1
10 p
Relative depth [-1
Cona.time, av.conc.
24 hr, 399 kg/m3
4 hr, 273 kg/m3
—
120 hr, 506 kg/m3
- 145 hr, 495 kg/m3
Fig 3.30b
DELFT
HYDRAULICS
-
48 hr, 442 kg/m3
Loswal Noord (North Sea)
Bed density profiles
Relative concentration [-1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Relative depth H
Cons.time, av.conc.
Fig
4.8 hr, 618 kg/mS
24.8 hr, 679 kg/m3
72
146
hr, 676 kg/m3
48
hr, 746 kg/m3
hr, 867 kg/n>3
3.31a
10
Relative concentration [-1
1
0.1
0.01
0.001
0.1
Relative depth [-]
Cona.time, av.conc.
4,8 hr, 616 kg/m3
72 hr,
Fig
676 kg/m3
3.31b
DELFT
HYDRAULICS
24,5 hr, 679 kg/m3
*- 146 hr, 867 kg/m3
48 hr, 748 kg/m3
B i e s b o s c h (Spijkerboor)
Bed density profiles
Relative concentration [-1
1.5
1
0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Relative depth [-]
Cona.time, av.conc.
4 hr, 206 kg/rnS
28 hr, 264 kg/m3
76 hr, 266 kg/m3
-*- 148 hr, 278 kg/m3
-
82 hr, 262 kg/m3
«- 172 hr, 275 kg/m3
Fig 3.32a
Relative concentration [-]
10
1
cr—:
1
T
—
T
-
0.01
0.1
Relative depth H
Cona.time, av.conc.
28 hr, 234 kg/m3
4 hr, 206 kg/m3
76 hr, 266 kg/m3
- 14B hr, 276 kg/m3
Fig 3.32b
DELFT
HYDRAULICS
82 hr, 262 kg/m3
172 hr, 276 kg/m3
1.1
Hollandsch Diep (Sassenplaat)
Bed concentration
Bed concentration cb [kg/m3l
600
400
\
\
(
^\
300
L-* ° _,
rL —
- -*v
200
100
•
0
10
-
20
30
40
60
Depth z [mm]
Tc • 22 hr, mess.
70
80
Tc • 24 hr, prod.
- ° - Tc • 1*7 hr, mess.
Fig
60
• * • Tc • 168 hr, pred.
3.33
Hollandsch Diep (Moerdijkbrug)
Bed concentration
Bed concentration cb [kg/m3]
10
20
Tc • 24 hr, mess.
Tc • 168 hr, maas.
Fig
3.34
DELFT
HYDRAULICS
30
Depth z [mm]
40
—
*~~ Tc • 24 hr, pred.
-*
Tc • 168 hr, pred.
50
60
Western Scheldt (Breskens)
Bed concentration
Bed concentration cb [kg/m3l
20
30
40
Depth z [mm]
Tc - 22.5 hr, meas.
60
60
Tc • 24 hr, pred.
Fig 3.35
Lake Ketel
Bed concentration
700
Bed concentration cb [kg/m3l
600
\\
V
500
IX. v
400
300
200
100
0
10
20
30
40
Depth z [mm]
Tc • 24 hr, maas.
Tc • 168 hr, maaa.
Fig
3.36
DELFT
HYDRAULICS
50
Tc • 24 hr, prad.
*•
Tc • 168 hr, prad.
60
70
Meuse (Belfeld)
Bed concentration cb [kg/m3]
600
Bed concentration cb [kg/m3l
I
] \
500
\ \
V\
400
\ \
\\
\\
300
200
100
0
'
10
20
30
Depth z [mm]
~°~ Tc • 28 hr, meaa.
a
Fig
40
50
Tc • 24 hr, prad.
Tc • 172 hr, maas.
*
Tc • 188 hr, prad.
3.37
Eems-Dollard (Delfzijl Harbour)
Bed concentration
1000
Bed concentration cb [kg/m3]
800
600
400
200
t
10
20
30
Depth z [mm]
Tc • 24 hr, meas.
Fig
3.38
DELFT
HYDRAULICS
40
Tc - 24 hr, pred.
50
Loswal Noord (North Sea)
Bed concentration
Bed concentration cb [kg/m3l
4000
3600
*\
\\
3000
V\\\
2500
\\
2000
v\
A
1600
n
"
1
s
1000
\
s
600
1
W -r*-~^_J"V..
»
0
i
20
30
Depth z [mm]
10
Fig
60
40
Tc • 24 hr, prad.
TC • 24 hr, maas.
• T e
<r| •
•*• Te • 168 hr, prad.
• 147 hr, meaa.
3.39
Biesbosch (Spijkerboor)
Bed concentration
Bed concentration cb [kg/m3l
600
400
,\\
\ \
v
1
300
1
" - <U
200
p ~ y —
100
0
10
20
30
40
Depth z [mm]
Tc • 28 hr, pred.
-°- Tc • 28 hr, maas.
° - Tc • 172 hr, maas.
Fig
3.40
DELFT
HYDRAULICS
50
*
Tc • 188 hr, pred.
60
70
Variation of mean concentration
with consolidation time
1000
Depth mean concentration [kg/m3l
100
10
100
1000
Consolidation time [min]
10000
100000
HD-Splaat 1
HD-Moardbr.
W-Scheldt
Lake Ketel
Meuse
E-Dollard
Loswal Noord
Biaaboach
Fig 3.41a; from acoustic measurements
Depth mean concentration [kg/m3]
0 1
1
10
100
1000
Consolidation time [mini
HD-Splaat
-*+- HD-Moardbr. -*- W Scheldt
Mauaa
-o- E-Dollard
Fig 3.41b; from interface
DELFT
HYDRAULICS
-*- Biaaboach
10000
100000
- a - Lake Ketel
Slope of bed density vs
original sand content
Coefficient ncz [-1
2.5 i
1
1
0^
0
1
10
HD-Splaat
'
Fig
Meuse
1
1
1
20
30
40
60
Sand content [% by weight!
a
HD-Moardbr.
*
E-Dollard
*• W Schaldt
"
Loewai Noord
60
*
Lake Katol
*
3.42
Variation of mean concentration
with consolidation time
Depth mean concentration [kg/m3l
10001
1—i i ii U M — — i — r
Fig
3.43
DELFT
HYDRAULICS
1
'
Biaaboach
70
Hollandsch Diep (Sassenplaat)
Strength distribution
1
Bed concentration cb [kg/m3l
Relative depth z/H [-1
>
|_
-
•>
_a
o- -
—
^
•
220
210
200
0.96
190
\
0.9
180
V\
170
160
0.7
0.85
0.1
0.2
0.3
0.4
0.6
Bed strength Taue [Pal
0.6
Tc • 24 hr, Tau - z
* ' Tc • 24 hr, Tau - cb
Tc • 7 day, T«u - I
B
Tc • 7 day, Tau - cb
Fig 4.1
Hollandsch Diep (Moerdijkbrug)
Strength distribution
Bed concentration cb [kg/m3]
260
Relative depth z/H [-1
1
1
0.96
]
0.9
\
230
X
.
_ a
210
190
0.86
170
0.8
._-»-- - ~ - - ~
1i
I—*
-
-
0.76
0.1
0.2
0.3
0.4
0.5
0.6
Bed strength Taue [Pal
0.7
Tc • 24 hr, Tau - z
*" Tc • 24 hr, Tau - cb
Tc • 7 day, Tau - i
° - Tc • 7 day, Tau - cb
Fig 4.2
DELFT
HYDRAULICS
160
0.8
Western Scheldt (Breskens)
Strength distribution
Bed concentration cb [kg/m3]
160
Relative depth z/H [-]
1
*
X !
(
145
0.96
/
/
/
0.9
140
/
\V /!(
/ \
0.86
135
/
/
/
0.8
\(
-
0.75
126
_ J<
4
JK J
0.7
0.1
130
0.2
0.3
0.4
0.5
Bed strength Taue [Pa]
Tc • 24 hr. Tau - z
0.6
120
0.7
* Tc - 24 hr, Tau - cb
Fig 4.3
Lake Ketel
Strength distribution
Bed concentration cb [kg/m3]
200
Relative depth z/H [-]
1
0.95
/
^
195
/
a'
190
0.9
•-
i
or '
0.85
V
185
s
*•
180
0.8
:
W "
0.75
0.1
0.2
0.3
0.4
Bed strength Taue [Pa]
0.5
Tc • 24 hr, Tau - r
- * - Tc • 24 hr, Tau - cb
Tc • 7 day, Tau - z
- ° - Tc • 7 day, Tau - cb
Fig 4.4
DELFT
HYDRAULICS
175
0.6
Meuse (Belfeld)
Strength distribution
Relative depth z/H [-]
N
1
0.96
Bed concentration cb [kg/m3l
165
P
I
K-
/
/
/
0.9
/
\
\
/
0.86
- -*
160
I
\ i
r
*
/
165
'
\ i
160
o
0.8
145
0.75
0.1
0.2
0.3
0.4
0.5
Bed strength Taue [Pal
0.6
Tc • 24 hr, T«u - z.
* • Tc • 24 hr, Tau - cb
Tc • 7 day, Tau - z
°
140
0.7
Tc • 7 day, Tau - cb
Fig 4.5
Eems-Dollard (Delfzijl)
Strength distribution
Relative depth z/H [-]
1 r—
i
Bed concentration cb [kg/m3l
135
0.95
130
0.9
125
Jk- -
it'
0.85
0.1
0.2
0.3
0.4
0.6
Bed strength Taue [Pal
Tc • 24 hr, Tau - z
Fig 4.6
DELFT
HYDRAULICS
0.6
* Tc • 24 hr, Tau - cb
120
0.7
Loswal Noord (North Sea)
Strength distribution
Bed concentration cb [kg/m3l
170
Relative depth z/H [-1
1
fc
160
R
;I
150
0.96
/
/
140
\'
0.9
\
130
\
120
1
110
0.86
JET
*
100
0.8
0.1
0.2
0.3
0.4
0.5
Bed strength Taue [Pal
0.6
Tc • 24 hr, T»u - r
* • Tc • 24 hr, Tau - cb
Tc • 7 day, Tau - z
°
90
0.7
Tc • 7 day, Tau - cb
Fig 4.7
B i e s b o s c h (Spijkerboor)
Strength distribution
Relative depth z/H [-1
0.1
0.2
Bed concentration cb [kg/m3l
0.3
0.4
0.5
Bed strength Taue [Pal
0.6
Tc • 24 hr, Tau - z
• *- Tc • 24 hr, Tau - cb
Tc • 7 day, Tau - z
-°
Fig 4.8
DELFT
HYDRAULICS
Tc • 7 day, Tau - cb
Strength distribution
Consolidation time Tc - 24 hrs
Relative depth z/H [-1
1.05
l
1
OK 1 (
X
1
Jt
• iI
1
4:
;
6
x
a
t
z
40
4-
1
•
1
1
t
0
0.1
0.2
0.3
0.4
0.6
4-
0.6
0.7
0.8
Strength Taue [Pa]
x
H.Diap (Spl)
*•
H-Diep (Mdbr) *
Meuse
*
Eema-Dollard
a
w.Scheldt
'
- Loawal Noord
Lake Ketel
* Biaaboach
Fig 4.9
Strength distribution
Consolidation time Tc - 7 d a y s
Relative depth z/H [-]
a
«v*
]
•
4•
4z
1.
1
4-
X
:
0
0.1
0.2
0.3
0.4
0.5
|
0.6
0.7
Strength Taue [Pal
*
H.Diap (Spl)
*• H.Diap (Mdbr)
Mouse
&
Fig 4.10
DELFT
HYDRAULICS
Loawal Noord
0
Lake Ketel
* Biaaboach
0.8
Strength distribution
Consolidation time Tc - 24 hrs
Bed concentration cb [kg/m3]
200
0.1
0.3
0.4
0.5
Strength Taue [Pal
0.2
H.Diap (Spl)
—*~ H.Diep (Mdbr) - *
A
Mauaa
Eema-Doiiard -
0.6
W.Schaldt
0.7
- ° - Laka Ketol
Loawal Noord -*- Biaaboach
Fig 4.11
Strength distribution
Consolidation time Tc • 7 days
Bed concentration cb [kg/m3]
260
200
11—•—B-
y
160
100
50
0.1
0.2
0.3
0.4
0.5
Strength Taue [Pal
H.Diap (Spl)
—*— Mauaa
Fig 4.12
DELFT
HYDRAULICS
0.6
0.7
H.Diep (Mdbr)
Laka Katel
Loswal Noord
Biaaboach
0.8
Variation of floe erosion rate
with b e d shear s t r e s s (Tc - 24 hrs).
Floe erosion rate Ef [E-3 kg/m2sl
0.12
0.1
/
0.08
/
0.06
/
0.04
0.02
Ii
0
Om>H
0.1
0.2
0.3
Bed
Fig
0.4
0.6
0.6
0.7
0.8
shear stress Taub [Pa]
H'Diep (Spl)
-+- H'Diep (Mdbr) - *
WSchaldt
Mauaa
-*
Loawal Noord —*- Biaaboach
Eama-Dollard - *>
Laka Katel
4.13a
Floe erosion rate Ef [E-3 kg/m2s]
0.01
0.001
0.2
0.3
Bed
0.4
Fig
-»
DELFT
A
Eama-Dollard -
4.13b
HYDRAULICS
0.6
0.7
shear stress Taub [Pa]
H'Diep (Spl) T + - H'Diep (Mdbr)- *
Mauaa
0.5
WSchaldt
-»
Lake Ketel
Loawal Noord -*•
Bleaboach
0.8
Variation of floe erosion rate
with bed shear stress (Tc - 7 days).
Floe erosion rate Ef [E-3 kg/m2s]
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0
0.1
H'Diep (Spl)
—*— Meuse
0.2
0.3
0.4
0.5
0.6
Bed shear stress Taub [Pa]
-
&
H'Diep (Mdbr)
Loewal Noord
Fig 4.14a
Floe erosion rate Ef [E-3 kg/m2s]
0.1 XT
I
I
I
Fig 4.14b
DELFT
HYDRAULICS
0.7
- ° ~ Lake Ketel
~*~ Biesbosch
0.8
Variation of maximum erosion rate
with bed shear stress (Tc • 24 hrs).
Max. erosion rate Em [E-3 kg/m2s]
1.4
/
1.2
7^
/
1
/
A
0.8
/
A
0.6
I
0.4
/
-«*
0.2
— —
****
y\ V
0
0.1
H'Diep (Spl)
Meuse
0.2
0.3
0.4
0.6
0.6
Bed shear stress Taub [Pal
-
H'Diep (Mrdb) - *
Eems-Dollard
Fig 4.15a
Fig 4.15b
DELFT
HYDRAULICS
WScheldt
0.7
- » Lake Ketel
Loswal Noord -*•
Biaaboach
0.8
Variation of maximum erosion rate
with bed shear stress (Tc - 7 days).
Fig 4.16a
Fig 4.16b
DELFT
HYDRAULICS
<
0
i
logmt (dynes/cm)
2
3
Fig. 4.17a Rates of erosion versus bottom stress from laboratory
flume experiments and from measurements in Puget Sound Limitations of space do not permit the presentation of all laboratory
results. Numbers refer to the references in Table 3. The lines are least
squares fits of the erosion lav. £ = | | \ the resulting values of a and
17 are given in Table 3.
a
<
t
T
=Q5xlO qvtm^-min
0.1 J
1
1
1
0 01 0.2 0.3 04 0.5
1/
(r -r )^(N^/m)
b
s
FIG. 4.17b—Variation of In (</«,) wfth (r„ - ,) , Series LM
M
T
DELFT
HYDRAULICS
Maximum erosion rate
Consolidation time Tc - 24 hrs
Maximum erosion rate Em [E-4 kg/m2el
z
1
t
I
dt
0.2
I
0
[
X
3 x
* 1l *
*
0.06
0.1
0.16
Maximum (Tau - Taue) [Pal
H.Diap (Spl)
•
*• H.Diap (Mdbr)
A
Mouses s
(
Eema-Doiiard
*
A
0.2
w.Scheldt
Loawal Noord
°
1
0.25
Laka Ketel
Biaaboach
Fig 4.18a
Maximum erosion rate Em [E-3 kg/m2s]
0.01
0.001
0.05
H.Diep (Spl)
Meuaaa 5
Fig
+
H.Diep (Mdbr) *
*
Earna-Doilard
4.18b
DELFT
0.2
0.1
0.15
Maximum (Tau - Taue) [Pal
HYDRAULICS
A
W.Scheldt
n
Lake Ketel
Loawal Noord
x
Biaaboach
0.25
Maximum erosion rate
Consolidation time Tc - 7 days
Maximum erosion rate Em [E-3 kg/m2sl
0.8
0.6
0.4
02
0
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
Maximum (Tau - Taue) [Pal
0.2 0.22 0.24
H.Diep (Spl)
*•
H.Diap (Mdbr)
0
Laka Ketal
Meuses 5
'•
Loawal Noord
z
Biaaboach
Fig 4.19a
iMin
Maximum erosion rate Em [E-3 kg/m2s]
:
i \y
-/ i
y
y
:
y
y
:
!
0.1
/
^ —
i iii
;
/
/
s
+
A
y
0
L
y
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24
Maximum (Tau - Taue) [Pa]
'
x
H.Diap (Spl)
t
Mauaea S
•
'
• Loawal Noord
Fig 4.19b
DELFT
HYDRAULICS
H.Diap (Mdbr)
"
Laka Ketal
x
Biaaboach
DELFT HYDRAULICS
Western
20 00
Scheldt
(Breskens)
/
\
SEDIMENT ^CONCENTRATION
18.00
720
TIME
Fig.
5.3:
D E P O S I T I O N A N D E R O S I O N U N D E R TIDAL
m a x i m u m b e d s h e a r s t r e s s : 0.4
Western
— i
0.04
Fig.
5.4:
(min)
1
r
0.08
0.12
0.16
Scheldt
0.20
CONDITIONS
Pa
(Breskens)
0.24
0 28
—I
0.32
1
BED SHEAR STRESS (Pa)
SEDIMENT CONCENTRATION AS A FUNCTION OF THE
m a x i m u m bed shear stress: 0,4 P a
DELFT HYDRAULICS
T
0.36
1
-
0.40
BED SHEAR
STRESS
Eems-Dollard
(Delfzijl
Harbour)
0.50
-
SEDIMENT CONCENTRATION
BED SHEAR STRESS
-0.40
O
a.
1
00
-0.30
0.30 -
—'
i/i
UJ
cc
a
z
o
o
—
1
in
-
oc
<
HE
—
I
z 0.20 UJ
-0.20
Ul
/
\
O
_
Q
UJ
00
CD
\
/
\
0.10 -
/
\
/
\
/
/
0.00
—I—I—I—I—I—I—I—I—I—I—f—'—I— —I—'—I— —I
1
60
120
180
240
300
360
420
1
480
540
1
600
I
<
~
660
720
TIME ( m i n )
Fig.
5 . 5 : D E P O S I T I O N A N D E R O S I O N U N D E R TIDAL C O N D I T I O N S
maximum
bed shear stress: 0,2 P a
Eems-Dollard
(Delfzijl
Harbour)
decelerating
0.40 -
CP
0.35
Z
o
p
0.30
<
OC
Z 0.25 LU
u
Z
O 0.20
o
accelerating
—
I
Z 0.15
UJ
2
Q
UJ 0.10
IS)
0.05
_
0.00
0.02
0.06
0.08
BED
Fig.
1
,
0 10
SHEAR
0.12 0.1
0.18
STRESS (Pa)
5 . 6 : SEDIMENT CONCENTRATION AS A FUNCTION OF THE B E D bHEAR
maximum
b e d s h e a r s t r e s s : 0,2 P a
DELFT HYDRAULICS
STRESS
Eems-Dollord
20.00
(Delfzijl
Harbour)
•0.40
/
18.00 -
-
\
SEDIMENT CONCENTRATION
BSD S H E A R \ S T R E S S
/
\
-0.32
16.00 -
TIME
Fig.
(min)
5 . 7 : D E P O S I T I O N A N D E R O S I O N U N D E R TIDAL C O N D I T I O N S
m a x i m u m b e d s h e a r s t r e s s : 0,4- P a
Eems-Dollard
(Delfzijl
Harbour)
12.00
—i
0.16
Fig.
5.8:
0.20
1
1—
0.24
— i
0.28
0.36
'
0.40
BED SHEAR STRESS ( P a )
SEDIMENT CONCENTRATION AS A FUNCTION OF THE B E D SHEAR
m a x i m u m b e d s h e a r s t r e s s : 0,4 P a
DELFT HYDRAULICS
STRESS
Fig. 5.9 a Interfacial instability at t « 420 min.
Fig. 5.9 b Interface at t » 430 min.
DELFT
HYDRAULICS
Fig. 5.10 Kelvin-Helmholtz like billowing but with very thin wisps of fluid
in the billows
Fig. 5.11 Photograph taken 30 cm downstream of the splitter plate showing
the concentration of vorticity above the interface
DELFT HYDRAULICS
Tidal experiments (Taub.max - 0,2 Pa)
Western Scheldt (Breskens)
D [E-4 kg/m2s]
-0.6
270
290
310
Taub [Pal, C [kg/m3l
330
Bad ahaar atraaa
360
370
Time [mini
390
Concentration C
410
436
Deposition rata D
Fig 5.13a
Western Scheldt (Breskens)
0.26
C [kg/m3l
Taub [Pal, E [E-4 kg/m2sl
0.06
420
440 460 480 600 620 640 660 680 600 620
Time [mini
Concentration C
- Bad ahaar atraaa
Fig 5.13b
DELFT HYDRAULICS
Erosion rata E
Tidal experiments (Taub,max - 0,2 Pa)
Eems-Dollard (Delfzijl Harbour)
D [E-4 kg/rn2s)
270
290
Taub [Pal. C [kg/m3l
310
330
Bad ahaar atraaa
360
370
Time [min]
Concentration C
390
410
430
Depoaition rata •
Fig 5.14a
Eems-Dollard (Delfzijl Harbour)
C tkg/m3l
420
440
Taub [Pal. E [E-4 kg/m2sl
460
480
— Bad ahaar atraaa
600
620
Time [mini
• Concentration C
Fig 5.14b
DELFT
640
HYDRAULICS
660
680
Eroaion rata E
-0.06
600
Tidal experiments (Taub.max - 0,2 Pa)
Western Scheldt (Breskens)
0.3
Effective settling velocity Ws [mm/si
0.25
0.2
•
0.16
•
0.1
•.
.
•
0.05
•
•
r ••
0.1
0.15
0.2
0.25
Concentration C [kg/m3]
0.3
0.35
Fig 6.15a
Western Scheldt (Breskens)
Effective settling velocity Ws tmm/sl
0.1
-n
•
'••
W
a on o °
0.01
r
R
.9 .
0.001
0.02
0.04
0.06
0.08
0.1
Bed shear stress Taub [Pal
Fig 5.15b
DELFT
HYDRAULICS
0.12
0.14
Tidal experiments (Taub.max - 0,2 Pa)
Eems-Dollard (Delfzijl Harbour)
0.14
Effective settling velocity Ws [mm/s]
0.12
0.1
0.08
0.06
•
•
0.04
0.02
:.;>••?
0
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Concentration C [kg/m3l
Fg 5.16a
Eems-Dollard (Delfzijl Harbour)
1.0000
Effective settling velocity Ws [mm/sl
0.1000
0.0100
a
0.0010
0.0001
0.02
0.04
0.06
0.08
0.1
Bed shear stress Taub [Pa]
Fig 5.16b
DELFT
HYDRAULICS
0.12
0.14
Western S c h e l d t (Breskens)
Tidal experiments
C [kg/m3|, D [E-4 kg/m2sl
Taub [Pal
0.6
270 280 290 300 310 320 330 340 360 360 370 380 390
Time [mini
Bad ahaar atraaa
Concentration C
•apoaition rata •
Fig 5.17
Eems-Dollard (Delfzijl Harbour)
Tidal experiments
C [kg/m3l, D [E-4 kg/m2sl
20
Taub [Pal
0.4
10
0.2
10
•0.2
•20
-30
300
-0.4
310
320
330
Bad ahaar atraaa
340 350 360
Time [mini
Concentration C
Fig 5.18
DELFT HYDRAULICS
370
380
390
0.6
400
Deposition rata D
Western Scheldt (Breskens)
Tidal experiments
Ws [mm/s]
•
T8 ud - D,16 I »a
•
•
•
•
..
•
•
•
*
a
'•
•
270 280 290 300 310 320 330 340 350 360 370 380 390
Time [min]
Fig 5.19a: W s from Krone's law
Ws [mm/s]
1.1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
270 280 290 300 310 320 330 340 350 360 370 380 390
Time [mini
Fig 5.19b: E f f . settl. velocity
DELFT
HYDRAULICS
Eems-Dollard (Delfzijl Harbour)
Tidal experiments
Ws [mm/si
Tau d - 0,( )9 P a
•
•
•
••
•
• • •* •1
300
310
320
330
340
360
360
Time [min]
*••
370
•
380
390
400
Fig 5.20a: Ws from Krone's law
Ws [mm/s]
1|
1
1
1
1
i —
1
1
1
1
380
'.J
390
0.9
0.8
0.7
0.6
sn;
0.6
7—:
0.4
-•
0.3
0.2
f
~
0.1
L.
300
Q
;
»;
\
^r--.
1. .n.-4°°°°
1
310
320
330
Fig 5.20b: Eff. settl. velocity
DELFT HYDRAULICS
1
1
1
340
360
360
Time [mini
a
> t
-
1
370
400
Western Scheldt (Breskens)
Tidal experiments
Ws [mm/sl
B
•
o
r.
c
•
a
•
D
•
r-,
r
•
•
•
D
•
D
n
f
4
6
8
Concentration [kg/m3l
2
mj a
tO
12
Fig 6.21a E f f e c t i v e settling velocity
Ws [mm/sj
10
a
a
.00anarl °rli 4,
n
Oc n
ft
0.1
0.01 =
0.001
0.1
°
_
•
1
10
Concentration [kg/m3l
Tidal experiments
Tampa Bay (Rosa •88)''
Fig 5.21b E f f e c t i v e settling velocity
DELFT
HYDRAULICS
Severn (Thorn 82)
100
Eems-Dollard (Delfzijl Harbour)
Tidal experiments
Ws [mm/sl
0.7
0.6
•
•
u
°
•
0.6
•
•
•
0.4
cI
•
o
•
•
•
0.3
0.2
•
•
c9—
LJ
•
•
Q
•
%§
0.1
—
f
0
°
Q -
_ ^
2
4
6
8
Concentration [kg/m3]
1
10
12
Fig 5.22a Effective settling velocity
Ws [mm/sl
0.001
1
10
Concentration [kg/m3l
D
Tidal experiments
-
Tampa Bay (Ross 'SB)
Fig 5.22b Effective settling velocity
DELFT
HYDRAULICS
Severn (Thorn '82)
100
Western Scheldt (Breskens)
Tidal experiments
Ws [mm/s]
10F
|
0.1
0.01
0.1
1
10
Concentration C [kg/m.3]
100
Fig 6.23a: Ws from Krone's law
E e m s - D o l l a r d (Delfzijl Harbour)
Tidal experiments
Ws [mm/si
1
0.1 -
0.01
0.001
0.1
1
10
Concentration C [kg/m3l
Fig 5.23b: Ws from Krone's law
DELFT
HYDRAULICS
100
Western Scheldt (Breskens)
Tidal experiments
C [kg/m3l; E [E-4 kg/m2sl
16
14
Bed shear stress Tau-b [Pa]
0.8
/
12
0.6
\
1
10
1
-» ^ '
1
8
—Vj
0.4
—1
—~
/
6
I
1 •.
t
I
4
_
0.2
I
.
\
2
. -J
s
/ _.
I
i
1
\
\
\
It
V \ \
t
,
-\\'l,->
0
' 1
-2
380
400
Tau-b
420
440
460
480
Time [min]
• Concentration C
600
520
J
640
Erosion rate E
Fig 6.24
Eems-Dollard (Delfzijl Harbor)
Tidal experiments
C [kg/m3] E [E-4 kg/m2s]
;
390
410
Tau-b
430
460
470
Time [min]
Concentration C
Fig 5.25
DELFT
Bed shear stress Tau-b [Pa]
HYDRAULICS
490
510
530
Erosion rate E
Western Scheldt (Breskens)
Tidal experiments
Bed concentration Cb [kg/m3]
600
Time [min]
600
550
500
•
500
400
450
300
•
200
400
100
350
0
0
E Ixed lavitL
0.01
0.02
0.03
0.04
0.06
Depth z [ml
Cb-pre dieted
0.06
0.07
300
0.08
Erosion depth
Fig 6.26a
Predicted shear strength distribution
Tau-e [Pa]
i 100
Cb [kg/m3]
500
400
300
0
0.01
0.02
0.03 0.04 0.05
Depth z [ml
Bed concentration Cb
Fig 5.26b
DELFT
HYDRAULICS
0.06
0.07
Crit. shear stress
0.001
0.08
Western Scheldt (Breskens)
Tidal experiments
C [kg/m3L Erosion rate E [E-4 kg/m2l
380
400
420
440
460
480
Time [mini
Tau-b [Pal
600
Bod ahaar atraaa
Concentration C
E measured
Potantial Er. rate
520
540
Fig 5.27
Variation of gradient
Richardson number with time
Gradient Richardson number Ri
380
Fig
400
420
440
460 480 500
Time [mini
5.28
DELFT
HYDRAULICS
520
540
560
580
Western Scheldt (Breskens)
Tidal experiments
Overall Richardson number Ri* [300
250
200
150
100
380
400
420
440
460
480
Time [min]
500
520
540
F i g 5 . 2 9 (N.B. i r u p p e r lid)
Entrainment rate Ev* [E-4]
1000
100
10 =
1 =
0.1
100
120
140
160 180 2 0 0 2 2 0 2 4 0 2 6 0
Overall Richardson number Ri* [-]
" Tidal experiments
F i g 5 . 3 0 (N.B. u* u p p e r lid)
DELFT
HYDRAULICS
Kantha et al
280 300
Kato s Phillips
Western Scheldt (Breskens)
Tidal experiments
Entrainment rate Ev [E-41
100
E
10
0.1 r
1
0.01
1
4
1
5
1
6
1
I
I
7
8
9
10
Richardson number Ri-u [-]
• Tidal experiments
Srinivas & Mehta
Fig 5.31
Variation of erosion rate with
bed shear stress
10
Erosion rate [E-4 kg/m2sl
I I I 11 III
100
=
V.
I I I
N
*
III I
~
Illl I
0.1
•
0.01
Fig
0.1
Tau-b [Pa]
5.32
DELFT
y U m i ta et i\ it
>84
HYDRAULICS
I
11
12
- 56 -
Appendix A:
Test
programme
to
determine
s e d i m e n t a t i o n behaviour of
Netherlands.
the
flow
induced
e r o s i o n and
natural
muds
encountered
in
the
- 57 -
Test programme t o determine
the flow induced e r o s i o n
behaviour of n a t u r a l muds encountered
1.
and
sedimentation
i n the Netherlands.
Sampling.
a. S e l e c t i o n and d e s c r i p t i o n of the l o c a t i o n .
b. Sample about 30 kg dry bed m a t e r i a l (e.g. about 100 kg wet
from
a
sedimentation
area
with
a
material)
small "Van Veen" grab
sampler;
probably the sediments i n a sedimentation area are r e p r e s e n t a t i v e f o r
the
sediments
i n the s e l e c t e d l o c a t i o n , whereas i n an e r o d i n g area,
the f i n e r p a r t i c l e s may have been washed out.
The
sampler
should
surface layer,
brought
be
small
to
o b t a i n mainly
i . e . not from one deep p i t .
ashore
as
The
sediments from the
sediment
should
be
f a s t as p o s s i b l e and t r a n s p o r t e d and s t o r e d i n a
c o o l i n g box.
Sample
simultaneously
conditions; this
water
also
can
500
be
l t r water
transported
under
and
quiet
stored
weather
in
25
1
j errycans.
c. Describe the area and the l o c a l c o n d i t i o n s , take photographs
site
and of the mud. Measure the temperature,
salinity
a t the
( i f relevant)
and oxygen content of the water, and the redox p o t e n t i a l of the water
and the mud.
2. Determine the p h y s i c a l - c h e m i c a l p r o p e r t i e s .
a. The composition of the mud:
- D e f l o c c u l a t e the mud and determine
the g r a i n s i z e
w i t h the MALVERN and w i t h the sedimentation
distribution
balance.
-Determine the s p e c i f i c s u r f a c e of the mud (by GD,
Delft
Soil
Mechanics).
-Determine the m i n e r a l o g i c a l composition of the mud (GD).
-Determine
the
o r g a n i c content, the 0
2
content, and the redox
potent i a l .
-Determine the pH, temperature
and s a l i n i t y .
-Measure the SAR and CEC (GD).
-Make some photographs of the sediments w i t h the microscope.
- 58 -
b. The p r o p e r t i e s of the mud:
-Determine the d i s t r i b u t i o n of the s e t t l i n g v e l o c i t y of the mud
i n the sedimentation
-Determine
and
the
yield
up-going
of
0
(without d e - f l o c c u l a n t ) .
and down-going flow curve
strength)
concentrations
•
150 s
balance
with
(50) c
the
Haake-viscometer
at
.
. g/1 up t o a shear r a t e of
natural
and a temperature of 20 C. Use the n a t u r a l water.
-Determine the c o n s o l i d a t i o n behaviour
the height of the
Measure
the
interface
vertical
c o n s o l i d a t i o n column
probe
(and
and
dry
with
a
i n a column by measuring
the
water
density
over
profile
conductivity
pressure.
within
and/or
the
accoustic
measure the vane shear s t r e n g t h at the end of the
t e s t at v a r i o u s
depths).
3. Determine the e r o s i o n and sedimentation
a. General
(viscosity
behaviour
i n the c a r o u s s e l .
t e s t s f o r a l l samples:
-Perform
a sedimentation
t e s t at an i n i t i a l
c o n c e n t r a t i o n of 1
g/1 by lowering the bed shear s t r e s s from about 0,40 t o
about
0,05 Pa i n small steps of about 0,02 t o 0,10 Pa. Each s u b - t e s t
will
be continued
until
equilibrium i s
attained.
During
the
t e s t s , the v a r i a t i o n s i n suspended sediment c o n c e n t r a t i o n w i l l
will
be
measured
concentration
continuously
measuring
with
probe);
samples
r e g u l a r i n t e r v a l s to c a l i b r a t e the
determine the organic content
the
OSLIM
OSLIM
will
(optical
be
taken at
recordings
and g r a i n s i z e
and
distribution.
-Carry out an e r o s i o n t e s t . A s o - c a l l e d d e p o s i t e d bed
formed
in
suspension
(after
still
of c
water
stopping
the
will
be
from the d e p o s i t i o n of a homogeneous
= 60 g/1. A c o n s o l i d a t i o n time
Q
to
annular
p r o f i l e w i t h i n t h i s bed w i l l
of
24
hours
flume) i s used. The dry d e n s i t y
be deduced from the c o n s o l i d a t i o n
t e s t d e s c r i b e d above. The e r o s i o n a l behaviour
i n c r e a s i n g the bed shear s t r e s s from 0
to
i s determined by
about
0,7
Pa
in
steps of o,02 to 0,1 Pa.; each sub-test i s continued
f o r about
one
suspended
hour.
During
the
tests,
sediment c o n c e n t r a t i o n w i l l w i l l
the OSLIM; samples w i l l
calibrate
content
the
OSLIM
and g r a i n s i z e
be
the
variations
in
be measured c o n t i n u o u s l y
taken
at
regular
intervals
with
to
r e c o r d i n g s and t o determine the organic
distribution.
- 59 -
b. Sediments from n o n - t i d a l
locations;
Next to the t e s t s mentioned
be
under 3.a. the f o l l o w i n g t e s t s
will
performed:
-A sedimentation
test
as
described
above
with
an
initial
c o n c e n t r a t i o n of C Q » 0,2 g/1.
-An e r o s i o n t e s t as d e s c r i b e d above w i t h a
of
time
7 days.
c. Sediments from t i d a l
locations:
Next t o the t e s t s mentioned
be
consolidation
under 3. a. the f o l l o w i n g t e s t s
will
performed:
-A
test
with
a
sinusoidal
varying
bed
shear
s t r e s s on a
d e p o s i t e d bed (see 3.a), w i t h a c o n s o l i d a t i o n time of 6 hours.
The
t i d a l period w i l l
amount t o 12 hours, and the amplitude of
the bed shear s t r e s s t o 0,4 Pa. The
until
equilibrium
is
v a r i a t i o n s i n suspended
achieved.
sediment
test
will
During
be
the
concentration
tests,
will
measured c o n t i n u o u s l y w i t h the OSLIM; samples w i l l
r e g u l a r i n t e r v a l s t o c a l i b r a t e the
determine
OSLIM
continued
will
be
be taken at
recordings
the organic content and g r a i n s i z e
the
and
to
distribution.
-A s i m i l a r t i d a l t e s t w i t h a shear s t r e s s amplitude of 0,2 Pa.
4. Reporting.
The
r e s u l t s and experimental data of
tests
will
determine
be
summarized
the c r i t i c a l
in
the
composition,
properties
a r e p o r t . These r e s u l t s w i l l
shear s t r e n g t h f o r e r o s i o n and
and
be used t o
sedimentation
of
the mud and i t s e r o s i o n r a t e .
5. Determination of the f l o c c u l a t i o n p r o p e r t i e s i n the
settling
column
(p.m.)
Determine
properties
initial
from
13
the d i s t r i b u t i o n of the s e t t l i n g
at
a
grid
frequency
c o n c e n t r a t i o n s of c
Q
velocity
and
floccualation
of 0,05 Hz (amplitude - 0,075 m) and
= 0,1 and 0,5 g/1. Samples
will
be
taken
l o c a t i o n s over the e n t i r e height of the column at r e g u l a r time
i n t e r v a l s . The s e t t l i n g mud f l o e s w i l l
the bottom of the column.
be monitored w i t h a CCD-camera at
- 60 -
APPENDIX B:
Method of a n a l y s i s of e r o s i o n
experiments.
- 61
-
In t h i s Appendix the method of a n a l y s i s
elaborated
little
a
further.
t r a t i o n i n suspension
c ,
g
It
described
was
in
Chapter
s
in
which
fe
as measured i n the annular
- Ms(z)
g
h - height of annular
- /
is
shown that the sediment concenflume, i s
r e l a t e d to the c o n c e n t r a t i o n d i s t r i b u t i o n w i t h i n the bed
c . ( h - z ) - h.c
4.2
H
z
c
dz
fe
through:
(B.l)
flume, H - i n i t i a l
z . ((tt)) i s e r o s i o n depth. By diff<
differentiating
b
one obtains the e r o s i o n rate E:
c.
directly
t h i c k n e s s of bed
and
( B . l ) w i t h respect to time t ,
dz
E
= 4r
h c
dt
s
= Jr
J
c.
dt z,
b
dz
- - c. ( Z . ) . - T - ^
b
b
(B.2)
at
D
I f c. (z) i s known, dz./dt can be assessed from (B.2), as c
i s measured,
b
b
s
For instance, by s u b s t i t u t i n g equ (3.4), one o b t a i n s :
P
z
dz
{-^~}--^b
E - - a c
b
exp
b
(B.3)
from which i t f o l l o w s that E i s an e x p o n e n t i a l
further
assumed that the c r i t i c a l
l i n e a r l y w i t h depth z, (B.3)
f u n c t i o n of z
b >
If i t
shear s t r e s s f o r e r o s i o n z (z)
varies
&
shows that E i s an e x p o n e n t i a l
is
function
of
T; . The F i g u r e s 4.9 and 4.10 show that t h i s assumption i s not too bad.
e
For each sub t e s t , z i s only known at the beginning of
this
sub
test
and
at
the end.
A d d i t i o n a l data can be obtained
through i n t e r p o l a t i o n ,
using the z (z) r e l a t i o n mentioned above. However, i t f o l l o w s , that
e
will
only
result
i n a d d i t i o n a l p o i n t s on the e x p o n e n t i a l
Hence, no r e a l a d d i t i o n a l i n f o r m a t i o n
This
can
be
illustrated
clearly
curve
this
(B.3).
i s added.
with the e r o s i o n curves
Mehta et a l [1982], showing almost s t r a i g h t curves
obtained
i n the E vs X
fi
plane
see F i g u r e B . l - f o r each sub t e s t . Only the p o i n t s at the o r i g i n
the e n c i r c l e d p o i n t s were
obtained
measured
the
other
points
and
were
through some i n t e r p o l a t i o n procedure, the d e t a i l s of which are
not given. However, probably
used,
directly,
by
some g r a p h i c a l i n t e r p o l a t i o n procedure
which e x p l a i n s the small d e v i a t i o n s of the
straight
(exponential)
Hence,
it
can
be
was
"data p o i n t s " from the
curve.
concluded,
that
procedure, i t i s not p o s s i b l e to o b t a i n
through i n t e r p o l a t i o n w i t h i n a sub
test.
with
the
present
additional,
experimental
non-spurious
data
3.20
2.80-
V
2 4
hrs
Symbd 9ep T
a,
(
o
X
0.20
€
0 (
xlO
2
'
(N/m )
1
2
3
4
5
0037
0.060
0.086
0.129
0.188
0.40
(fjnvtjr?^Pin)
498 0 38
14.44 0.80
O.90 1.30
I2J7 1.20
1138 1.53
060
0.80
[T, - T (z)] /r (z)
c
Figure B.1 Normalized
hi
c
rate oj erosion. ti/t„. versus normalized
- tJz)]/T.(z). using kaolinite in tap water with
excess shear
- 24 hrs.
stress,
(From Metha et al,
1982)
DELFT
HYDRAULICS
- 62 -
APPENDIX C:
C o r r e l a t i o n s between e r o s i o n
shear s t r e s s .
r a t e and some f u n c t i o n s
of the bed
Maximum erosion rate
Consolidation time T c - 24 hrs
Maximum erosion rate Em [E-3 kg/m2sl
1.4
1.2
0.8
0.6
0.4
0.2
0.1
HDiep (Spl)
Mouses 5
0.6
0.2
0.3
0.4
0.6
Maximum (Tau - Taue)/Taue [-1
*
H-Diep (Mdbr)
*
D
W.Scheldt
:
' Eems-Dollard - Loawal Noord
1
0.7
Lake Ketal
Biaaboach
Fig C.1
Maximum erosion rate
Consolidation time Tc - 7 days
Maximum erosion rate Em [E-3 kg/m2s]
1
0.8
0.6
0.4
0.2
0
0.06
0.1
0.16 0.2 0.26 0.3 0.36 0.4 0.46
Maximum (Tau - Taue)/Taue [-]
H.Diap (Mdbr)
HDiep (Spl)
Meuaea 9
•
Fig C.2
DELFT HYDRAULICS
Loawal Noord
a
*
0.5 0.65 0.6
Laka Ketel
Biaaboach
Relative erosion rate
Consolidation time Tc - 24 hrs
Relative erosion rate Em/Ef [-]
z
z
z z
X
A
A
1
•
J•
4-
*
4-
8 !
J-
0
0.1
*
0.2
0.3
0.4
Maximum (Tau - Taue)/Taue [-]
0
H.Diap (Spl)
*• HDiep (Mdbr) *
W.Scheldt
Mauaa
*
Loawal Noord
Eama-Doiiard
0.5
0.6
Lake Katal
*
Biaaboach
Fig C.3
Relative erosion rate
Consolidation time Tc - 7 days
60
Relative erosion rate Em/Ef [-]
60
40
30
20
10
0
0.06 0.1 0.16 0.2 0.25 0.3 0.36 0.4 0.46 0.6 0.55 0.6
Maximum (Tau - Taue)/Taue [-1
H.Diap (Spl)
*•
Mauaa
'• Loawal Noord
Fig C.4
DELFT
HYDRAULICS
H.Diap (Mdbr)
Laka Katal
Biaaboach
- 63 -
APPENDIX D:
Summary of entrainment experiments d e s c r i b e d
in literature.
- 64 -
Summary of entrainment experiments d e s c r i b e d
in literature,
D.l Experiments on fresh-water - s a l i n e - w a t e r experiments.
E l l i s o n and Turner
E l l i s o n and
referred
\19591.
Turner
to
as
performed
two
sets
of
entrainment
"Surface
j e t experiments"
and
experiments,
"inclined
plume
experiments".
surface
The
j e t experiments were c a r r i e d out i n a flume of 15 cm width,
20 cm depth and 2 m length.
a
depth
of about
The lower s a l i n e l a y e r was stagnant and
15 cm. The flowing
upper
cm. The experiments d e s c r i b e the entrainment
stagnant
lower
layer
water
o v e r a l l R i c h a r d s o n number R i
0
o
A
of
saline
f r e s h water upper
from
a
l a y e r . An
(D.l)
2
ir
- r e l a t i v e density
TJ
water
i s d e f i n e d as:
h i - t h i c k n e s s flowing
During
l a y e r had a depth of about 5
. BuJJii
R i
where
i n t o a flowing
had
= v e l o c i t y flowing
the
difference
upper
upper
(A = (p -
P )/PQ),
Q
l a y e r , and
layer.
experiments, R i was v a r i e d
0
between about 0,05 and 0,75. No
other data on the experiments are g i v e n .
The
inclined
closed
was
plume
experiments were c a r r i e d out i n a 200 * 60 * 10 cm
tank, which could
be t i l t e d
t o any d e s i r e d
angle.
water
i n j e c t e d through a s l o t near the bottom of the tank and f r e s h
was i n j e c t e d through a c l o t h c y l i n d e r mounted at the top
Thus
the
driven
water
Saline
saline
layer
by g r a v i t y .
could
flow
of
the
underneath the f r e s h upper
These experiments d e s c r i b e the entrainment
from a stagnant upper
layer
i n t o a flowing
s a l i n e lower
was
90°,
0
kept
and R i was v a r i e d
number R i
0
at 3 %, and the slope a was v a r i e d
between 0,05 and
0,4.
The
IT
layer,
fresh
layer.
density
between 9
overall
and
Richardson
i s now d e f i n e d as:
. e A h2 cos a
tank.
of
A maximum v e l o c i t y of about 0,15 ra/s was recorded, the r e l a t i v e
difference
water
( D - 2
)
- 65 -
The r e s u l t s are presented i n a E
E
" V
v
with
This
E
v
V
fi
versus R i
v
0
graph, E
v
d e f i n e d as:
(B.3)
u
- entrainment r a t e
[-]
- entrainment v e l o c i t y
(V
- dh/dt)
graph, g i v e n i n F i g u r e D.l shows that E
[m/s].
- f(l/Ri ).
This
0
i s not s p e c i f i e d f u r t h e r i n the paper. However, i t shows no
difference
between
the
remarkable, as i t would
velocity
profile,
results
be
of
the
expected
two
because
experiments.
of
layer
are
different
entrainment of s a l i n e water i n t o the f r e s h upper
Kato and P h i l l i p s
and
significant
the
This
is
differences
in
that the processes of the entrainment of f r e s h water
i n t o a f l o w i n g s a l i n e lower
Kato
relation
from
those
of
layer.
f19691.
P h i l l i p s c a r r i e d out experiments w i t h f r e s h and s a l t water i n
an annular flume. The outer diameter of t h i s flume amounted t o 1,524
the
i n n e r diameter to 1,067
A maximum depth of 0,28
A
the
linear
density
m,
thus the width of the flume was
m,
0,228 m.
m could be a t t a i n e d .
gradient
was
obtained by i n j e c t i n g water of v a r y i n g
s a l i n i t y through 20 o r i f i c e s e q u a l l y spaced over the depth of the flume.
The upper l a y e r always contained f r e s h water. During the experiments the
e n t i r e water column was
water
surface,
the
f l o w i n g . But, as the
flow
was
driven
at
the
upper part of the flow was more t u r b u l e n t than the
lower p a r t , and the experiments d e s c r i b e the entrainment of more
water from the lower l a y e r s i n t o the l e s s s a l i n e water
saline
i n the upper
part
of the flow.
Three
series
of
experiments
density differences:
1092
1000
were
carried
3
to 1042 kg/m , 1000
out
w i t h three d i f f e r e n t
3
to 1084 kg/ra , and
1000 to
3
kg/m .
The flow v e l o c i t y was
t y p i c a l l y v a r i e d between 0,25
and 0,35
m/s.
During
the experiments the Richardson number R i ^ was v a r i e d between 15 and
Ri
A
i s d e f i n e d as:
R i
*
S
" ~S
i
D
4
<-)
350.
- 66 -
with
6 = depth of mixed
depth
layer (intermediate turbulent
increases
layer);
this
during the experiments from 0 t o about
15
cm.
u,=
shear v e l o c i t y at the r o t a t i n g upper
lid.
From the experiments the f o l l o w i n g e m p i r i c a l r e l a t i o n was
derived:
B
< D
"* • k • K
-
5 >
Thomson [1979] re-analysed the data by Kato and P h i l l i p s and o b t a i n e d
somewhat
different
a
r e l a t i o n by c o r r e c t i n g the experimental c o r r e l a t i o n s
f o r the Froude number. T h i s r e s u l t e d i n :
Ev, - ^
Also Price
Phillips
(D.6)
[1979] apparently was
and
i n s p i r e d by the experiments of Kato and
a l s o d i d some r e - a n a l y s i s . He c o r r e c t e d the o r i g i n a l data
f o r the e f f e c t s of the drag of the s i d e - w a l l of the flume. Through
this
e x e r c i s e he o b t a i n e d a r e l a t i o n s i m i l a r t o equ (D.6).
Kantha, P h i l l i p s and Azad [1977],
Kantha,
Phillips
and Azad c a r r i e d out another s e r i e s of experiments i n
the annular flume d e s c r i b e d by Kato and P h i l l i p s . T h i s time however, the
flume
initially
contained two homogeneous l a y e r s of d i f f e r e n t
The r e l a t i v e d e n s i t y d i f f e r e n c e
0,4
density.
(Ap/p ) was v a r i e d between about 0,1
and
0
and the shear s t r e s s (at the water s u r f a c e ) between 0,2
and 0,37
Pa.
The o v e r a l l Richardson number R i , (see (D.4)) was v a r i e d between 30
and
1100.
The r e s u l t s of these experiments are shown i n F i g u r e D.2
the
results
stratified
the t u r b u l e n t
with
by Kato and P h i l l i p s . The l a t t e r found an entrainment r a t e
of about h a l f of t h a t found by Kantha et a l . Kato and
linear
together
density
Phillips
used
g r a d i e n t , so t h a t energy could be l o s t
l a y e r by r a d i a t i o n as w e l l as i n t e r n a l waves
a
from
(explanation
from Kantha et a l ) .
A f u r t h e r o b s e r v a t i o n i s that the entrainment r a t e has no simple
law
dependence
on
power-
R i , over the whole range s t u d i e d . For R i , < 400 the
slope i s about R i ~ , but beyond
that the decrease i n E v , i s much l a r g e r .
- 67 -
Lofquist
[19601.
Lofquist
c a r r i e d out experiments i n a s t r a i g h t flume w i t h a length
m and a width 23,3
a still
depth
cm. The lower, s a l i n e water was
c i r c u l a t e d underneath
l a y e r of f r e s h water at a v e l o c i t y between 2 and
of
the
lower
10
cm/s.
l a y e r h2 was v a r i e d between 18 and 20 cm,
t o t a l depth of the two l a y e r s amounted to about 46 cm.
describe
of 24
The
and the
experiments
the entrainment of f r e s h water from a stagnant upper l a y e r
a flowing,
Observed
The
into
s a l i n e lower l a y e r .
entrainment
rates
were
Froude number, which i s the inverse
correlated
against
the d e n s i m e t r i c
of the o v e r a l l Richardson number:
2
F
1
U
= Ri- = m i T
i
During the experiments R i
D
7
<->
0
was v a r i e d between about 8
r e l a t i o n s i m i l a r t o E l l i s o n and Turner was
and
100,
and
a
found:
(D.8)
Narimousa
and Fernando
Narimousa
and Fernando c a r r i e d out experiments
water
in
a
[1987 1.
with
fresh
"disk flume, or race-track-flume". T h i s
2 m,
by r o t a t i n g
disks
above each other. The t e s t s e c t i on of the flume has a length of
i t s width i s 15 cm and i t s depth 60 cm. The v e l o c i t y of
layer
saline
is a recirculating
flume i n which the flow ( i n the upper l a y e r ) i s d r i v e n
mounted
and
was
difference
varied
between
5 and 15 cm/s;
the
the v a r i a t i o n of the
i s not given.
The o v e r a l l Richardson R i
5
between about 1 and 20, where R i i s defined as:
c
number
was
upper
density
varied
c
0
R i
where
At
of
6
= ^
U
6 » thickness
(D.9)
of mixed
layer.
low Richardson number ( R i < 5) the i n t e r f a c e was
g
regularly
containing
Richardson
spaced
irregular
observed to c o n s i s t
b i l l o w s . These b i l l o w s break down to form regions
small
features.
Over
a
wide
range
of
higher
numbers (5 < Rig < 20) breaking i n t e r n a l waves were observed
i n which wisps of f l u i d are e j e c t e d
to the mixed
l a y e r . The frequency of
- 68 -
breaking waves decreases w i t h i n c r e a s i n g Richardson number. At
these
< Ri
< 20 l a r g e amplitude s o l i t a r y waves were
without
b r e a k i n g . At R i
g
observed,
which
10
travel
> 20 m o l e c u l a r processes seem to take over the
entrainment mechanism.
D.2
Experiments
on entrainment of t u r b i d i t y
currents.
Ashida and E g a s h i r a [19751.
Ashida
and
Egashira
studied
the entrainment of stagnant, c l e a r water
i n t o a t u r b i d i t y c u r r e n t . They c a r r i e d out experiments
length,
0,55
m depth and 0,5
i n a tank of 20 m
m width. The t u r b i d water was
obtained by
mixing f r e s h water with f i n e sand w i t h a median diameter of about 30
um.
The t h i c k n e s s of the f l o w i n g lower l a y e r v a r i e d between 7 and
the
d e n s i t y d i f f e r e n c e between upper and
3
kg/m ,
and
0,8
and
lower l a y e r v a r i e d between 5 and
lower l a y e r v e l o c i t i e s of 8 to 19 cm/s
the experiments
13 cm,
the o v e r a l l Richardson number was
22
were measured. During
varied
between
about
8.
Parker. P a n t i n and Fukushima [19851.
Parker et a l d e s c r i b e the a n a l y s i s by E g a s h i r a [1980] of the
experiments
and
Kato
d e s c r i b e d above and those by E l l i s o n
and
following
Phillips
and
entrainment
Turner,
Lofquist
( a g a i n a f t e r a r e - a n a l y s i s ) . They o b t a i n e d the
relation:
» —
U
E
v
= P^°°15
Ri
(D.10)
0
Using the same data, G a r c i a [1989] found a somewhat d i f f e r e n t
E
=
V
Data and equ.
II
U
P_iOZ5
=
(1 • 718
(D.10) and
relation:
(D.ll)
2
Ri 'V'
5
( D . l l ) are shown i n F i g u r e
D.3.
- 69 -
S r i n i v a s and Mehta [19901.
S r i n i v a s and Mehta r e p o r t on experiments
c a r r i e d out
in
a
"race-track
flume" s i m i l a r to that used by Narimousa et a l . The t e s t s e c t i o n of t h i s
flume
i s about
initial
velocity
and the flume height 50 cm.
The
were c a r r i e d out w i t h k a o l i n i t e and b e n t o n i t e i n tap water.
experiments
The
2 long, i t s width 10 cm,
bulk d e n s i t y was
v a r i e d between 1030
i s estimated at about
o v e r a l l Richardson number R i
u
10 cm/s,
was
and
1080
kg/m
;
the
though no d e t a i l s are g i v e n . An
v a r i e d between 4 and 30 and
i s defined
as:
^
where
m
B
u
^u T
<».13)
h - e n t i r e flow depth.
From the experiments
the f o l l o w i n g r e l a t i o n was
0,27
E
v
=
-
Ri
0
,
deduced:
9
L
(400 +
Or, as a f i r s t
( D
2 T~66
RiV'
u
approximation: E
9
v
• 1 / R i ^ ' , which
is
-
again
1 3 )
consistent
with the r e s u l t s of other experiments.
D.3
E f f e c t of d i f f u s i v i t v .
Turner
\ 19681.
Turner c a r r i e d out entrainment experiments
square
and
i n a perspex
at
5
cm
constant at about
water,
with
25,4
cm
40 cm height w i t h an o s c i l l a t i n g g r i d mounted i n e i t h e r the
lower l a y e r or i n both l a y e r s . The g r i d c o n s i s t e d of 1
aligned
tank,
*
1
cm
strips
i n t e r v a l . The amplitude of the o s c i l l a t i o n s was
1 cm.
fresh
and
Experiments were c a r r i e d out w i t h c o l d
saline
water,
and
kept
hot
and a combination of these. The
f o l l o w i n g o v e r a l l Richardson number was d e f i n e d :
Rio
8
= -^2
ft f
i n which ft i s some a r b i t r a r y
grid.
1 4
(°- )
l e n g t h s c a l e and f i s the frequency of
the
- 70 -
For d e n s i t y d i f f e r e n c e s produced by heat
appeared
closely
dependent
on R i
alone,
the
entrainment
, except at small v a l u e s of R i . For
experiments w i t h a s a l i n i t y d i f f e r e n c e across the i n t e r f a c e , the
rate
appeared
mixing
the same as i n the heat experiments at low v a l u e s of R i ,
-3/2
but becomes p r o p o r t i o n a l t o R i
the
rate
entrainment
rate
when R i i s i n c r e a s e d .
differed
As
a
result,
by almost an o r d e r of magnitude at the
h i g h e r Richardson number experiments.
Turner
attributes
this
difference
molecular d i f f u s i v i t y . At low
diffusivity
that
mixes
i n behaviour to the d i f f e r e n c e s i n
Reynolds
number,
packages of f l u i d ,
it
is
the
e j e c t e d from one l a y e r
the other, w i t h i t s environment. At h i g h e r Reynolds number,
w i l l be dominated
The v i s c o s i t y
significant
mixing
varied
only
slightly
and
can
therefore
not
play
a
r o l e , a c c o r d i n g to Turner.
[19751.
and Brush c a r r i e d out entrainment experiments i n a d e v i c e w i t h
Wolanski
the same dimensions as the one used by Turner [1968]. The
oscillations
was
kept
v a r i e d between 120 and
at
the
into
by small s c a l e t u r b u l e n t motions.
Wolanski and Brush
the
molecular
about
360 rpm.
3
0,005
constant
kg/m .
at about
1 cm,
amplitude
i t s frequency was
The d e n s i t y d i f f e r e n c e was
T h i s was
of
kept
small
a t t a i n e d by u s i n g c o l d and hot water,
f r e s h and s a l i n e water, f r e s h water and a sugar s o l u t i o n and f r e s h water
and
suspensions
of
Silica
spheres
and
k a o l i n i t e c l a y . The
Reynolds
number Re, d e f i n e d as:
u. D
Re - —
v
(D.15)
where D - depth lower l a y e r = depth upper l a y e r . Re was
10
3
10
and
- 1 4
2
m /s
12
3
10 .
The m o l e c u l a r d i f f u s i v i t y of these f l u i d s v a r i e d
f o r the k a o l i n i t e suspension to 1.4
From the experiments the f o l l o w i n g r e l a t i o n was
Ev. = —
*
*
u
« RiT
*
the
kaolinite
10
m/s
f o r hot
from
water.
deduced:
n
with n v a r y i n g from about
for
v a r i e d between 4
0>.16)
1 f o r hot water,
suspension.
Richardson number R i , i s now
This
d e f i n e d as:
is
1,3
f o r s a l i n e water, up to 4
shown
in
Figure
D.4.
The
- 71 -
,
4
2
IT
g A h
(D.17)
with
u , - 2 it a f , where a and f are the amplitude and frequency of the
oscillating
on
the
number.
g r i d . These experiments
significant
role
agree w i t h the hypothesis by
Turner
of the molecular d i f f u s i v i t y at low Reynolds
009
—r
— r
1-
-1
1
1
1
1
-
008
Neutral jet
0-07
006
005
E
Surface jet
Plume: layer time
Plume: outer part
o Georgeson
• Leach
- \\
\\
\ \
\ \
\ \
004
O03
002
001
o
I
I
0
01
1
I
1I
02
03
I
I
04
I
l1
06
I
05
" T 1-" ~^ L— tt07
08
Ri
Fig. D 1
T
1
Ellison and Turner
1—I I I I I I
Fig. D 2
1
1
1—I I I I I I
Kantha , Phillips and Azad
Entrainment rates
DELFT HYDRAULICS
Fig. D 1,2
O
O
'O
O
'O
'O
Entrainment rates
DELFT HYDRAULICS
Fig. D 3,4