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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 Slide 2 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 Slide 3 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 Slide 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. Slide 5 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 Slide 6 Isopach of M1 Unit at Chek Lap Kok Good quality continuous cores are available from Hong Kong to depths of 20+m Slide 7 Bothkennar Site, Scotland Slide 8 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 Slide 9 From core record, several different sequences have been identified Present work models Holocene sequence Classification after Yim Slide 10 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 Slide 11 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 Slide 12 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. Slide 13 Decompaction of Deposits If the Void Ratio is known, then the saturated bulk unit weight ( i ) in the i th layer is given by:- 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:- Slide 14 Decompaction of Deposits First assume a value of e i (say 1.0) and evaluate i in the i th layer from:- 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. Slide 15 Slide 16 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. Slide 17 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 Slide 18 This is an interesting result: The relationship holds over all three units! It means that we only need to determine C c Slide 19 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 Slide 20 Do you believe in Omega? Omega Point Slide 21 If this relationship were to hold more generally, then we can predict e 1 from C c Slide 22 Inclusion of many more data points still confirms a relationship e1 = 0.8662 + 2.7111 Cc R 2 = 0.9775 Gassy sedimentsM1M2 T1 Slide 23 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 Slide 24 For typical Holocene deposits, the true sedimentation rate may be up to 2+ times the raw sedimentation rate. Slide 25 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? Slide 26 Measurement of Cc requires special testing A Problem But estimates are available using Liquid Limit measurements Slide 27 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. -valid for Holocene - i.e. degree of saturation is 100%. Slide 28 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 Slide 29 The values of moisture content are almost always above the mean prediction suggesting a more open structure than expected Slide 30 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 Slide 31 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? Slide 32 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 Slide 33 There appears to be a relationship between void ratio and permeability However, this relationship is likely to vary from one location to another. Slide 34 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 Slide 35 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. Slide 36 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 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. Slide 37 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. Slide 38 Results from 10 - 500 years - assume Holocene depth - 10m Partial dissipation is taking place at base of Holocene - dissipation lines are getting closer together Slide 39 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. Slide 40 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. Slide 41 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 Slide 42 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 Slide 43 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 Slide 44 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 Slide 45 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 Implications for estimating the consolidation behaviour of soils 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 Slide 46 Implications for estimating the consolidation behaviour of soils Use data of m vc to estimate settlement from: m vc z Plot e vs Evaluate m vc at relevant stresses