1
School of Environmental Sciences, University of East Anglia,
Norwich, NR4 7TJ, UK
2
School of Life Sciences, Heriot Watt University, Edinburgh,
EH14 4AS, UK
3
Singapore Meteorological Service, Changi Airport, Singapore 918141
4
101 Media Ltd, Keswick Hall, NR4 6TJ, Norwich, UK
Acknowledgements:
•
Geotechnical Engineering Office, Hong Kong
•
Civil Engineering Office, Hong Kong
•
Prof. Muneki Mitamura, Osaka
•
Carolyn Sharp, University of East Anglia
Self Weight Consolidation of Soft Sediments:
Some Implications for Climate Studies
N.
Keith Tovey
1
,
Mike Paul
2
,
Yap Chui

Wah
3
,
and Simon Tovey
4
University of West Indies, Trinidad 9th January 2003
•
British Council
•
What effect does self

weight consolidation
(auto

compaction) have on our understanding
of Marine Sequences?
•
What processes are involved?
•
What are the magnitudes of such effects?
•
How easy is it to correct for these effects?
The Problem
1. Background to self

weight consolidation issues
2. Site Locations
3. Equilibrium Self

Weight Compaction
4. Existence of Omega Point?
5. True Sedimentation Rates
6. Modelling pore

pressure dissipation
7. Conclusions
8. Postscript for ENV

2E1Y
Holocene Marine Deposits: modelling self

weight consolidation
Why are such studies of relevance?
Interpretation of sequences is often done on a linear
length
basis.
i.e. two points in a sequence may be dated and a
sedimentation rate estimated from dates and
distances
between the two points
.
This does not allow for self

weight consolidation

strictly it
should be done using a linear
mass
interpolation

rarely is
this the case.
This is of particular importance in unravelling Holocene
sequences where the
apparent
deposition rate is of the
order of 0.5

5 mm per year.
It is of significance in dating studies, estimation of palaeo

water
depths in tidal modelling, salt marsh studies, archeology etc.
1. Background to self

weight consolidation issues
2. Site Locations
3. Equilibrium Self

Weight Compaction
4. Existence of Omega Point?
5. True Sedimentation Rates
6. Modelling pore

pressure dissipation
7. Conclu
si
ons
8. Postscript for ENV

2E1Y
Holocene Marine Deposits: modelling self

weight consolidation
Isopach of M1 Unit at Chek
Lap Kok
Good quality continuous cores are
available from Hong Kong to
depths of 20+m
Bothkennar Site, Scotland
Simplified Sequence of Deposition
During last inter

glacial
deposition of unit M2
When sea level fell, surface layer
was exposed to desiccation,
oxidation, pedogenesis, etc.
In the Holocene, the sea probably
covered the area around 6000

8000
years ago
deposition of unit M1
M1
T1
M2
~
10m
From core record, several different sequences have been identified
Present work models Holocene sequence
Classification after Yim
1. Background to self

weight consolidation issues
2. Site Locations
3. Equilibrium Self

Weight Compaction
4. Existence of Omega Point?
5. True Sedimentation Rates
6. Modelling pore

pressure dissipation
7. Conclusions
8. Postscript for ENV

2E1Y
Holocene Marine Deposits: modelling self

weight consolidation
Consolidation in Marine Sediments
Two pore pressures to consider
Sand
Clay
Assumes sand body is
continuous and “daylights”
to sea bed

i.e. two

way
drainage.
•
Hydrostatic pressure changes from sea level changes are
insignificant with regard to sediment compression.
•
Excess pore pressures are of critical importance.
Single drainage

implies sand body is
discontinuous and
does not “daylight”
11
Decompaction of Deposits
•
During deposition, successive
layers will cause under

lying
layers to compress
•
Dividing the total thickness by
the time interval will lead to an
under

estimation of true
deposition rates.
period
time
d
rate
deposition
True
n
i
i
1
Decompaction of Deposits
•
If the Void Ratio is known, then
the saturated bulk unit weight
(
i
) in the i
th
layer is given by:

w
i
i
s
i
e
e
G
.
1
2
.
.
1
1
)
1
(
)
(
i
i
i
i
i
v
i
v
d
d
However, e
i
depends on
v(i)
where G
s
is Specific gravity
The stress
i
at the mid point of
the i
th
layer is given by:

Decompaction of Deposits
•
First assume a value of
e
i
(say 1.0)
and evaluate
i
in the i
th
layer from:

w
i
i
s
i
e
e
G
.
1
2
d
.
d
.
i
i
1
i
1
i
)
1
i
(
v
)
i
(
v
Must work down through layers not upwards!
•
Now determine
i
at the mid point of
the i
th
layer:

•
If the e

v
relationship is known
determine a revised value of e
i
and
repeat above two steps iteratively.
Typical Consolidation Curve
0.5
1
1.5
2
10
100
1000
Vertical Stress (kPa)
Void ratio (e)
Typical Virgin Consolidation Curve for M1
Unit
0.5
1
1.5
2
2.5
3
3.5
1
10
100
1000
Vertical Stress (kPa)
Void ratio (e)
e
1
= 3.1269

0.841 log(
)
R
2
= 0.9954
The parameter e
1
= 3.1269 [void ratio at 1 kPa] and gradient of line
C
c
are used in the algorithms.
1. Background to self

weight consolidation issues
2. Site Locations
3. Equilibrium Self

Weight Compaction
4. Existence of Omega Point?
5. True Sedimentation Rates
6. Modelling pore

pressure dissipation
7. Conclusions
8. Postscript for ENV

2E1Y
Holocene Marine Deposits: modelling self

weight consolidation
17
This is an interesting result:
The relationship holds over all three units!
It means that we only need to determine C
c
0
1
2
3
4
5
6
7
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Cc
e1
Hong Kong
Bothkennar
Tovey & Paul (2002)
e1 = 0.8154 + 2.8473 Cc
However, an even more interesting correlation emerges
It appears that data from Hong Kong and Scotland follow same trend
Virgin Consolidation Trend Lines for Hong Kong
Marine Sediments
0
0.5
1
1.5
2
2.5
3
10
100
1000
10000
Vertical Stress (kPa)
Void Ratio
CLKB12
CLKB9  T1 Unit)
KC6  M1 Unit
CLKB8/2
CLKB9a
KC5/2
Do you believe in Omega?
Omega
Point
Omega Point
If this relationship were to hold more generally, then we can predict e
1
from C
c
Inclusion of many more data points still confirms a relationship
0
1
2
3
4
5
6
7
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Cc
e1
Japan
Hong Kong
Bothkennar
Humber
Li (1990)
New HK
Essex Saltmarsh
Tovey & Paul (2002)
All Data
e1 = 0.8662 + 2.7111 Cc
R
2
= 0.9775
Gassy sediments
M1
M2
T1
1. Background to self

weight consolidation issues
2. Site Locations
3. Equilibrium Self

Weight Compaction
4. Existence of Omega Point?
5. True Sedimentation Rates
6. Modelling pore

pressure dissipation
7. Conclusions
8. Postscript for ENV

2E1Y
Holocene Marine Deposits: modelling self

weight consolidation
23
0
5
10
15
20
1
1.5
2
2.5
Sedimentation Ratio (Z
r
)
Depth (m)
0.2
0.4
0.6
0.8
1.0
1.4
1.2
For typical Holocene deposits, the true sedimentation rate may be
up to 2+ times the raw sedimentation rate.
•
Assume 10 m Holocene sequence and C
c
approximately 1.0.
•
If sea level rose about 6500 years ago, then raw
sedimentation rate is about 1.5 mm per year
•
But after correction, the true rate for the Hong Kong M1
unit is > 3 mm per year.
•
Any modelling must use layers no thicker than this.
What is a typical value for sedimentation rate?
•
Measurement of Cc requires special testing
A Problem
Variation of Cc with Liquid Limit [ Hong Kong Marine Sediments]
y = 0.0189x  0.5898
R
2
= 0.7693
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0
20
40
60
80
100
Liquid Limit (%)
Cc
M2 Unit
T1 Unit
Kwai Chung M1 Unit
Chek Lap Kok M1 Unit
But estimates are available using Liquid Limit measurements
w
s
i
i
s
i
s
i
i
w
i
i
s
i
G
m
m
G
hence
G
m
e
but
e
e
G
.
.
.
:
.
1
1
1
2
d
.
d
.
i
i
1
i
1
i
)
1
i
(
v
)
i
(
v
•
Now determine
i
at the mid point of the i
th
layer:

•
e

v
can be plotted directly and hence
C
c
can be deduced.
An alternative if neither consolidation or liquid limit data are available
Assume a detailed moisture/water content can
be measured at moderate/high resolution.
Typical Virgin Consolidation Curve for M1
Unit
0.5
1
1.5
2
2.5
3
3.5
1
10
100
1000
Vertical Stress (kPa)
Void ratio (e)

valid for Holocene

i.e. degree of saturation is 100%
.
0
2
4
6
8
10
0
2
4
6
8
10
Void Ratio (e)
Depth (m)
Void Ratio in
uppermost layers
~ 9.5
Porosity varies significantly in uppermost 2m.
Void ratio of 2
is equivalent
to a porosity
of 0.667
Void ratio of 4
is equivalent
to a porosity
of 0.8
Comparison of predicted moisture content with depth for
actual data from Chek Lap Kok  M1 unit
0
1
2
3
4
5
6
7
8
9
10
0
50
100
150
200
250
300
Moisture Content (% dry weight)
Depth (m)
Minimum Cc
Average Cc
Maximum Cc
actual
points in blue refer
to actual values
where LL was
more than 3
standard deviations
from mean
The values of moisture content are almost always above the mean
prediction suggesting a more open structure than expected
1. Background to self

weight consolidation issues
2. Site Locations
3. Equilibrium Self

Weight Compaction
4. Existence of Omega Point?
5. True Sedimentation Rates
6. Modelling pore

pressure dissipation
7. Conclusions
8. Postscript for ENV

2E1Y
Holocene Marine Deposits: modelling self

weight consolidation
30
•
Equilibrium self

weight consolidation analysis assumes that
after each increment all excess pore pressure is dissipated.
•
Conventional wisdom suggests that with all normal
sedimentation rates, dissipation will be complete within an
annual deposition cycle.
•
This is true provided drainage paths are
NOT
long.
•
However, will this be true for deep sequences where drainage
paths are long?
2
2
v
z
u
c
t
u
v
w
v
m
k
c
The governing equation for dissipation of pore pressure (u)
by:

where c
v
is the coefficient of consolidation and may be
found from:
where k is permeability and m
v
is determined from C
c
To proceed we need a relationship to determine k
y = 0.4967Ln(x) + 9.9839
R
2
= 0.8767
0
0.5
1
1.5
2
2.5
3
3.5
1.0E09
1.0E08
1.0E07
1.0E06
Permeability (k  cm / sec)
Void Ratio (e)
M2 Unit
M1 Unit
There appears to be a relationship
between void ratio and permeability
However, this relationship is likely to
vary from one location to another.
The dynamic model
Properties of each layer vary as a result of
self

weight consolidation.
For a given value of C
c
determine
•
equilibrium void ratio and hence unit
weight and stress for each layer
•
permeability from e

k relationship
and hence estimate
•
m
v
(from e

relationship)
•
c
v
.
(= k /
m
v
)
If data exists, C
c
can also be allowed to vary between layers
The void ratio varying rapidly in top 1

2m, and layer
thickness must reflect this and also be able to model and annual
accumulation.
> Layer thicknesses ~ 3mm should be used.
> ~ 3000 layers
Choice of initial layer thickness
A Problem:
•
simple analysis using FTCS method will
require time steps < 100 secs for stability

very computer intensive.
•
Crank Nicholson method is stable
irrespective of time step, although 100
iterations per year are still needed for
spatial precision.
•
Current model starts with 150 layers
•
But, number of layers increases each year, and time to
model 500 years becomes very long ~ 10

20 hours with
modern computers.
•
However trends can be seen
0
2
4
6
8
10
0
2
4
6
8
10
Void Ratio (e)
Depth (m)
Void Ratio in
uppermost layers
~ 9.5
Crank

Nicholson requires inversion of matrices which have
the number of rows and columns equal to number of layers.
•
Solution

use layer thickness
which progressively double at
greater depths.
Results of pore pressure dissipation over first 10 years

annual increment as determined by equilibrium analysis
Below 3m there is no dissipation in year 1. There is evidence of
a small amount of dissipation after 10 years.
Results from 10

500 years

assume Holocene depth

10m
Partial dissipation is taking place at base of Holocene

dissipation lines are getting closer together
0
1
2
3
4
5
6
7
8
9
10
0
50
100
150
200
Water Content (% dry weight)
Depth (m)
A
B
C
Actual Data
Predicted
The presence of excess pore pressures would lead to higher
water contents than predicted by steady state analysis
Could this be difference be a result of bio

turbation?
0
1
2
3
4
5
6
7
8
9
10
0
5
10
15
20
25
30
35
Difference in Water Content (%)
Depth (m)
Unlikely to be the sole cause as deviation increases with depth
just as residual pore pressures do.
0
5
10
15
20
25
0
20
40
60
80
100
120
Water Content (%)
Depth (m)
Predicted
Actual Data
base of Holocene
0
5
10
15
20
25
0
5
10
15
20
25
Difference in Water Content (%)
Depth (m)
Recent results from Japan
•
18 consolidation tests were done on a single borehole
•
different values of C
c
were measured.
•
modify steady state analysis to allow for this variation
•
predicted and actual water are similar at base of Holocene
•
implies full dissipation of pore pressure > double drainage.
1. Background to self

weight consolidation issues
2. Site Locations
3. Equilibrium Self

Weight Compaction
4. Existence of Omega Point?
5. True Sedimentation Rates
6. Modelling pore

pressure dissipation
7. Conclusions
8. Postscript for ENV

2E1Y
Holocene Marine Deposits: modelling self

weight consolidation
41
•
raw sedimentation rates significantly underestimate true
sedimentation rates by a factor of 2 or more
•
from consolidation theory, estimates of true porosity and
hence sedimentation rates are possible
•
excess pore pressures arising from annual deposition remain at
the end of the year in sequences thicker than about 2m
•
pore pressures continue to build up each year
> higher than predicted equilibrium moisture contents
•
the excess moisture content distribution gives an indication of
drainage conditions prevailing.
Conclusions
•
correlation of excess pore water pressures with excess water
content

does this explain the full difference between steady state
model and actual data points?
> need to model over the whole Holocene period
•
develop model to include pre

Holocene layers
> estimates of palaeo

hydrology
And finally:
The research in this paper is a direct consequence of
discussions held at the 2nd Annual Meeting of IGCP

396 in
Durham UK (1997).
The future
1. Background to self

weight consolidation issues
2. Site Locations
3. Equilibrium Self

Weight Compaction
4. Existence of Omega Point?
5. True Sedimentation Rates
6. Modelling pore

pressure dissipation
7. Conclusions
8. Postscript for ENV

2E1Y
Holocene Marine Deposits: modelling self

weight consolidation
44
From the relationship between e
1
and C
c
e
1
= 0.8662 + 2.7111 C
c
Estimate C
c
from Plasticity Index
i.e. C
c
= 0.5 * PI * G
s
or
†
ㄮ㌲㔠⨠偉
景r偌‽㌲慮搠䱌‽‶㠠†偬獴楣st礠楮摥砠㴠㌶
†††††††
C
c
= 1.325 * 0.36 = 0.477
Hence e
1
= 2.159
Implications for estimating the consolidation behaviour of soils
1
1.2
1.4
1.6
1.8
2
2.2
2.4
1
10
100
1000
stress(kPa)
Void Ratio
Equation of Virgin Consolidation
Line >
e = 2.159

0.477*log
潲
攠㴠㈮ㄵ㤠
–
1.325*PI*log
Provides a more robust method
to estimate consolidation
behaviour from Atterberg Limits
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
0.020
0
20
40
60
80
100
120
140
160
stress (kPa)
m
vc
(kPa
1
)
1
1.2
1.4
1.6
1.8
2
2.2
2.4
0
20
40
60
80
100
120
stress (kPa)
Void Ratio
Implications for estimating the consolidation behaviour of soils
Use data of m
vc
to estimate
settlement from:
m
vc
稠
Plot e vs
Evaluate m
vc
at
relevant stresses
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