1 School of Environmental Sciences, University of East Anglia,

1
Self Weight Consolidation of Soft Sediments
Some Implications for Climate Studies N. Keith
Tovey1 , Mike Paul2, Yap Chui-Wah3, and Simon
Tovey 4
University of West Indies, Trinidad 9th January
2003
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

• British Council

2
The Problem

• 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?

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Holocene Marine Deposits modelling self-weight
consolidation
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
4
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.
5
Holocene Marine Deposits modelling self-weight
consolidation
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
6
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Bothkennar Site, Scotland
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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.
10m
M1
In the Holocene, the sea probably covered the
area around 6000 - 8000 years ago deposition
of unit M1
T1
M2
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From core record, several different sequences
have been identified
Classification after Yim
Present work models Holocene sequence
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Holocene Marine Deposits modelling self-weight
consolidation
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
11
Consolidation in Marine Sediments Two pore
pressures to consider

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

Assumes sand body is continuous and daylights
to sea bed -i.e. two-way drainage.
Single drainage - implies sand body is
discontinuous and does not daylight
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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.

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Decompaction of Deposits

• If the Void Ratio is known, then the saturated
  bulk unit weight (?i) in the ith layer is given
  by-

where Gs is Specific gravity The stress ?i at
the mid point of the ith layer is given by-
However, ei depends on ?v(i)
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Decompaction of Deposits

• First assume a value of ei (say 1.0) and
  evaluate ?i in the ith layer from-

• Now determine ?i at the mid point of
• the ith layer-

• If the e -??v relationship is known
• determine a revised value of ei and
• repeat above two steps iteratively.

Must work down through layers not upwards!
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e1 3.1269 - 0.841 log(?) R2 0.9954
The parameter e1 3.1269 void ratio at 1 kPa
and gradient of line Cc are used in the
algorithms.
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Holocene Marine Deposits modelling self-weight
consolidation
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
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This is an interesting result The relationship
holds over all three units! It means that we only
need to determine Cc
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However, an even more interesting correlation
emerges
e1 0.8154 2.8473 Cc
It appears that data from Hong Kong and Scotland
follow same trend
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Do you believe in Omega?
Omega Point
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Omega Point
If this relationship were to hold more generally,
then we can predict e1 from Cc
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Inclusion of many more data points still confirms
a relationship
e1 0.8662 2.7111 Cc R2 0.9775
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Holocene Marine Deposits modelling self-weight
consolidation
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
23
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For typical Holocene deposits, the true
sedimentation rate may be up to 2 times the raw
sedimentation rate.
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What is a typical value for sedimentation rate?

• Assume 10 m Holocene sequence and Cc
  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 gt 3 mm per year.
• Any modelling must use layers no thicker than
  this.

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A Problem

• Measurement of Cc requires special testing

But estimates are available using Liquid Limit
measurements
27
An alternative if neither consolidation or
liquid limit data are available
-valid for Holocene - i.e. degree of saturation
is 100 .
Assume a detailed moisture/water content can be
measured at moderate/high resolution.

• Now determine ?i at the mid point of the ith
  layer-

• e -??v can be plotted directly and hence Cc can
  be deduced.

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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
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The values of moisture content are almost always
above the mean prediction suggesting a more open
structure than expected
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Holocene Marine Deposits modelling self-weight
consolidation
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
30
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• 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?

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The governing equation for dissipation of pore
pressure (u) by-
where cv is the coefficient of consolidation and
may be found from
where k is permeability and mv is determined from
Cc
To proceed we need a relationship to determine k
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There appears to be a relationship between void
ratio and permeability
However, this relationship is likely to vary
from one location to another.
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The dynamic model

• Properties of each layer vary as a result of
  self-weight consolidation.
• For a given value of Cc determine
• equilibrium void ratio and hence unit weight and
  stress for each layer
• permeability from e - k relationship
• and hence estimate
• mv (from e - ? relationship)
• cv. ( k / ?mv)

If data exists, Cc can also be allowed to vary
between layers
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Choice of initial layer thickness
The void ratio varying rapidly in top 1 - 2m, and
layer thickness must reflect this and also be
able to model and annual accumulation. gt Layer
thicknesses 3mm should be used. gt 3000 layers

• A Problem
• simple analysis using FTCS method will require
  time steps lt 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.

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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.

• 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

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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.
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Results from 10 - 500 years - assume Holocene
depth - 10m
Partial dissipation is taking place at base of
Holocene - dissipation lines are getting closer
together
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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?
Unlikely to be the sole cause as deviation
increases with depth just as residual pore
pressures do.
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Recent results from Japan

• 18 consolidation tests were done on a single
  borehole
• different values of Cc 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 gt
  double drainage.

41
Holocene Marine Deposits modelling self-weight
consolidation
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
41
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Conclusions

• 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
• gt higher than predicted equilibrium moisture
  contents
• the excess moisture content distribution gives an
  indication of drainage conditions prevailing.

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The future

• correlation of excess pore water pressures with
  excess water content - does this explain the full
  difference between steady state model and actual
  data points?
• gt need to model over the whole Holocene period
• develop model to include pre-Holocene layers
• gt 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).
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Holocene Marine Deposits modelling self-weight
consolidation
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
44
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Implications for estimating the consolidation
behaviour of soils
From the relationship between e1 and Cc e1
0.8662 2.7111 Cc Estimate Cc from Plasticity
Index i.e. Cc 0.5 PI Gs or ?
1.325 PI for PL 32 and LL 68 Plasticity
index 36 Cc 1.325 0.36
0.477 Hence e1 2.159
Equation of Virgin Consolidation Line gt e
2.159 - 0.477log ? or e 2.159 1.325PIlog ?
Provides a more robust method to estimate
consolidation behaviour from Atterberg Limits
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Implications for estimating the consolidation
behaviour of soils
Use data of mvc to estimate settlement from ?
mvc ?z ? ?