Transcript Document 7813052
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 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
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Acknowledgements: Geotechnical Engineering Office, Hong Kong Civil Engineering Office, Hong Kong Prof. Muneki Mitamura, Osaka Carolyn Sharp, University of East Anglia
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British Council
The Problem
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What effect does self-weight consolidation (auto-compaction) have on our understanding of Marine Sequences?
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What processes are involved?
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What are the magnitudes of such effects?
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How easy is it to correct for these effects?
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
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.
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. Conclu si ons 8. Postscript for ENV-2E1Y
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.
M1
In the Holocene, the sea probably covered the area around 6000 - 8000 years ago deposition of unit M1
T1 M2 ~ 10m
From core record, several different sequences have been identified Classification after Yim Present work models Holocene sequence
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
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.
Clay Single drainage implies sand body is discontinuous and does not “daylight” Sand 11
Decompaction of Deposits
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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.
True deposition rate
time i n
1
d i period
Decompaction of Deposits
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If the Void Ratio is known, then the saturated bulk unit weight (
i ) in the i th layer is given by:-
s i
i
G
1
e
.
w i where G s is Specific gravity
The stress
i the i th at the mid point of layer is given by: v
(
i
)
v
(
i
1 )
i
1 .
d i
1
i
.
d i
2
However, e i depends on
v(i)
Decompaction of Deposits
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First assume a value of e i and evaluate
i in the i th (say 1.0) layer from:-
s i
i
G
1
e
.
w i Now determine
i at the mid point of the i th layer:-
v ( i )
v ( i
1 )
i
1 .
d i
1
i .
d i 2
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If the e -
v relationship is known determine a revised value of e i and repeat above two steps iteratively.
Must work down through layers not upwards!
1.5
2
Typical Consolidation Curve
1 0.5
10 100 Vertical Stress (kPa) 1000
3.5
Typical Virgin Consolidation Curve for M1 Unit 3 2.5
2 1.5
1 e 1 = 3.1269 - 0.841 log(
) R 2 = 0.9954
0.5
1 10 100 Vertical Stress (kPa) 1000
The parameter e 1 = 3.1269 [void ratio at 1 kPa] and gradient of line C c are used in the algorithms.
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 C c
However, an even more interesting correlation emerges 7 Hong Kong 6 Bothkennar 5 Tovey & Paul (2002) 4 3 2 1 e1 = 0.8154 + 2.8473 Cc 0 0.0
0.2
0.4
0.6
0.8
Cc 1.0
1.2
1.4
It appears that data from Hong Kong and Scotland follow same trend 1.6
2.5
2 1.5
3 Do you believe in Omega?
Virgin Consolidation Trend Lines for Hong Kong M arine Sediments
CLKB12 CLKB9 - T1 Unit) KC6 - M1 Unit CLKB8/2 CLKB9a KC5/2
1 0.5
0 10 100 1000 Vertical Stress (kPa) 10000 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 7 6 5 4 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 3 2 1 0 0.0
T1 0.2
0.4
M2 0.6
M1 Gassy sediments 0.8
1.0
Cc 1.2
1.4
1.6
1.8
2.0
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
10 15 0 1 5 Sedimentation Ratio (Z r ) 1.5
2 0.2
0.4
0.6
0.8
1.0
1.2
1.4
2.5
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For typical Holocene deposits, the true sedimentation rate may be up to 2+ times the raw sedimentation rate.
What is a typical value for sedimentation rate?
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Assume 10 m Holocene sequence and C c approximately 1.0.
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If sea level rose about 6500 years ago, then raw sedimentation rate is about 1.5 mm per year
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But after correction, the true rate for the Hong Kong M1 unit is > 3 mm per year.
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Any modelling must use layers no thicker than this.
A Problem
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Measurement of Cc requires special testing 1.4
Variation of Cc with Liquid Limit [ Hong Kong Marine Sediments] 1.2
1.0
M2 Unit T1 Unit Kwai Chung M1 Unit Chek Lap Kok M1 Unit 0.8
0.6
0.4
0.2
0.0
0 20 40 60 Liquid Limit (%)
y = 0.0189x - 0.5898
R 2 = 0.7693
80 100 But estimates are available using Liquid Limit measurements
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.
i
G
s
1
e i e i
.
w
:
but e i
m i
.
G s hence
i
G s
1 1
m
m i
.
G s i
.
w
• Now determine i at the mid point of the i th layer:
v ( i )
v ( i
1 )
i
1 .
d i
1
i .
d i 2
•
e -
v C c can be plotted directly and hence can be deduced. 3.5
Typical Virgin Consolidation Curve for M1 Unit 3 2.5
2 1.5
1 0.5
1 10 100 Vertical Stress (kPa) 1000
0 0 2 Porosity varies significantly in uppermost 2m.
2 Void Ratio (e) 4 6 Void Ratio in uppermost layers ~ 9.5
8 10 Void ratio of 2 is equivalent to a porosity of 0.667
4 6 Void ratio of 4 is equivalent to a porosity of 0.8
8 10
0 1 2 7 8 3 4 5 6 9 10 0 Comparison of predicted moisture content with depth for actual data from Chek Lap Kok - M1 unit 50 points in blue refer to actual values where LL was more than 3 standard deviations from mean 100 150 200 Moisture Content (% dry weight) Minimum Cc Average Cc Maximum Cc actual 250 300 The values of moisture content are almost always above the mean prediction suggesting a more open structure than expected
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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Equilibrium self-weight consolidation analysis assumes that after each increment all excess pore pressure is dissipated.
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Conventional wisdom suggests that with all normal sedimentation rates, dissipation will be complete within an annual deposition cycle.
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This is true provided drainage paths are NOT long.
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However, will this be true for deep sequences where drainage paths are long?
The governing equation for dissipation of pore pressure (u) by:
u
t
c v
2 u
z 2
where c v is the coefficient of consolidation and may be found from:
c v
w k m v
where k is permeability and m v is determined from C c To proceed we need a relationship to determine k
There appears to be a relationship between void ratio and permeability 3.5
3 y = 0.4967Ln(x) + 9.9839
R 2 = 0.8767
2.5
2 1.5
1 0.5
M2 Unit M1 Unit 0 1.0E-09 1.0E-08 1.0E-07 Permeability (k - cm / sec) However, this relationship is likely to vary from one location to another.
1.0E-06
The dynamic model
Properties of each layer vary as a result of self-weight consolidation.
For a given value of C c determine
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equilibrium void ratio and hence unit weight and stress for each layer
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permeability from e - k relationship and hence estimate
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m v (from e -
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c v . (= k /
m v ) relationship) If data exists, C c can also be allowed to vary between layers
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.
> Layer thicknesses ~ 3mm should be used.
> ~ 3000 layers A Problem:
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simple analysis using FTCS method will require time steps < 100 secs for stability very computer intensive.
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Crank Nicholson method is stable irrespective of time step, although 100 iterations per year are still needed for spatial precision.
Crank-Nicholson requires inversion of matrices which have the number of rows and columns equal to number of layers.
Void Ratio (e) 4 6 0 0 2 8 2 Void Ratio in uppermost layers ~ 9.5
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Solution - use layer thickness which progressively double at greater depths.
4 6 8 10
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Current model starts with 150 layers 10
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But, number of layers increases each year, and time to model 500 years becomes very long ~ 10 - 20 hours with modern computers.
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However trends can be seen
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
The presence of excess pore pressures would lead to higher water contents than predicted by steady state analysis 6 7 8 9 10 0 1 2 3 4 5 0 A B Actual Data Predicted C 50 100 150 Water Content (% dry weight) 200 0 1 2 3 4 9 10 5 6 7 8 0 5 Difference in Water Content (%) 10 15 20 25 30 35 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.
Recent results from Japan
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18 consolidation tests were done on a single borehole
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different values of C c were measured.
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modify steady state analysis to allow for this variation 0 0 20
Predicted Actual Data
Water Content (%) 40 60 80 100 5 120 10 15 base of Holocene 20 25 10 15 20 25 0 0 Difference in Water Content (%) 5 10 15 20 25 5
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predicted and actual water are similar at base of Holocene
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implies full dissipation of pore pressure > double drainage.
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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Conclusions
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raw sedimentation rates significantly underestimate true sedimentation rates by a factor of 2 or more
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from consolidation theory, estimates of true porosity and hence sedimentation rates are possible
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excess pore pressures arising from annual deposition remain at the end of the year in sequences thicker than about 2m
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pore pressures continue to build up each year > higher than predicted equilibrium moisture contents
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the excess moisture content distribution gives an indication of drainage conditions prevailing.
The future
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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
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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).
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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Implications for estimating the consolidation behaviour of soils 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
1.325 * PI for PL = 32 and LL = 68 Plasticity index = 36 C c = 1.325 * 0.36 = 0.477
Hence e 1 = 2.159
Equation of Virgin Consolidation Line > e = 2.159 - 0.477*log
or e = 2.159 – 1.325*PI*log
Provides a more robust method to estimate consolidation behaviour from Atterberg Limits
2.4
2.2
2 1.8
1.6
1.4
1.2
1 1 10 stress(kPa) 100 1000
Implications for estimating the consolidation behaviour of soils Plot e vs
Evaluate m vc at relevant stresses 2.4
2.2
2 1.8
1.6
1.4
1.2
1
0 20 40 60
stress (kPa)
80 100 120
0.020
0.018
0.016
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0.000
0 20 40 60 80 100 120 stress (kPa) 140 160 Use data of m vc settlement from: to estimate
m vc
z