The spacing of drains to achieve this, if placed in a square pattern is given by
S= R = =
0 564 1 8 0 564 3 2 .
.
. . m
Consolidation
water pressure can be monitored by installing piezometers (Chapter 6), thus providing a means of controlling the rate of loading. It should be appreciated that differential settlement will occur if non-uniform soil conditions exist and the ground surface may need re-levelling at the end of the pre-loading period. One of the principal disadvantages of pre-loading is the need to wait for consolidation to be complete under the pre-load before construction can begin on the foundation.
One solution to this is to combine pre-loading with vertical drains (Section 4.11) to speed up the pre-load stage.
The principle of pre-loading can also be applied to accelerate the settlement of embankments by surcharging with an additional depth of fill. At the end of an appropriate period, surcharge is removed down to the final (formation) level.
Summary
1 Due to the finite permeability of soils, changes in applied (total) stress or fluctua- tions in groundwater level do not immediately lead to corresponding increments in effective stress. Under such conditions, the volume of the soil will change with time. Dissipation of positive excess pore pressures (due to loading or lowering of the water table) leads to compression which is largely irrecoverable. Dissipation of negative excess pore pressures (unloading or raising of the water table) leads to swelling which is recoverable and of much lower magnitude than initial Figure 4.29 Application of pre-loading: (a) foundation construction on highly com-
pressible soil, (b) foundation constructed following pre-loading.
compression. The compression behaviour is quantified mathematically by the virgin compression and unload/re-load lines in e—logσ′ space and the compres- sion and swelling indices (Cc and Ce, respectively). The compressibility (mv), coeffi- cient of consolidation (cv) and (indirectly) the permeability (k) may be determined within the oedometer.
2 Simple index tests (described in Chapter 1) may be used with empirical correla- tions to estimate values of compressibility properties (namely Cc and Ce). Such data can be useful when high-quality laboratory test data are unavailable and for providing additional complementary data to support the results of such tests.
While useful, empirical correlations should never be used to replace a compre- hensive programme of laboratory (or in-situ) testing.
3 The final amount of settlement due to one-dimensional consolidation can be straightforwardly determined using the compressibility (mv) and the known changes in total stress or pore pressure conditions induced by construction pro- cesses. A more detailed description of settlement (or heave) with time may be found either analytically or using the Finite Difference Method. A spreadsheet implementation of this method is available on the Companion Website.
4 For soils of low permeability (e.g. fine-grained soils) it may be necessary in con- struction to speed up the process of consolidation. This may be achieved by adding vertical drains. An appropriate drain specification and layout can be determined using standard solutions for radial pore water drainage to meet a specified level of performance (e.g. Ur % consolidation by time t).
Problems
4.1 In an oedometer test on a specimen of saturated clay (Gs = 2.72), the applied pressure was increased from 107 to 214 kPa and the following compression readings recorded:
TABLE I
Time (min) 0 0.25 0.5 1 2.25 4 6.25 9 16
Gauge (mm) 7.82 7.42 7.32 7.21 6.99 6.78 6.61 6.49 6.37
Time (min) 25 36 49 64 81 100 300 1440
Gauge (mm) 6.29 6.24 6.21 6.18 6.16 6.15 6.10 6.02
After 1440 min, the thickness of the specimen was 15.30 mm and the water content was 23.2%. Determine the values of the coefficient of consolidation and the compression ratios from (a) the root time plot and (b) the log time plot. Determine also the values of the coef- ficient of volume compressibility and the coefficient of permeability.
4.2 In an oedometer test, a specimen of saturated clay 19 mm thick reaches 50% consolidation in 20 min. How long would it take a layer of this clay 5 m thick to reach the same degree of consolidation under the same stress and drainage conditions? How long would it take the layer to reach 30% consolidation?
4.3 The following results were obtained from an oedometer test on a specimen of saturated clay:
Consolidation TABLE J
Pressure (kPa) 27 54 107 214 429 214 107 54
Void ratio 1.243 1.217 1.144 1.068 0.994 1.001 1.012 1.024
A layer of this clay 8 m thick lies below a 4 m depth of sand, the water table being at the sur- face. The saturated unit weight for both soils is 19kN/m3. A 4 m depth of fill of unit weight 21kN/m3 is placed on the sand over an extensive area. Determine the final settlement due to consolidation of the clay. If the fill were to be removed some time after the completion of consolidation, what heave would eventually take place due to swelling of the clay?
4.4 Assuming the fill in Problem 4.3 is dumped very rapidly, what would be the value of excess pore water pressure at the centre of the clay layer after a period of three years? The layer is open and the value of cv is 2.4 m2/year.
4.5 A 10 m depth of sand overlies an 8 m layer of clay, below which is a further depth of sand.
For the clay, mv = 0.83 m2/MN and cv = 4.4 m2/year. The water table is at surface level but is to be lowered permanently by 4 m, the initial lowering taking place over a period of 40 weeks.
Calculate the final settlement due to consolidation of the clay, assuming no change in the weight of the sand, and the settlement two years after the start of lowering.
4.6 An open clay layer is 6 m thick, the value of cv being 1.0 m2/year. The initial distribution of excess pore water pressure varies linearly from 60 kPa at the top of the layer to zero at the bottom. Using the finite difference approximation of the one-dimensional consolida- tion equation, plot the isochrone after consolidation has been in progress for a period of three years, and from the isochrone determine the average degree of consolidation in the layer.
4.7 A half-closed clay layer is 8 m thick and it can be assumed that cv = ch. Vertical sand drains 300 mm in diameter, spaced at 3 m centres in a square pattern, are to be used to increase the rate of consolidation of the clay under the increased vertical stress due to the construction of an embankment. Without sand drains, the degree of consolidation at the time the embank- ment is due to come into use has been calculated as 25%. What degree of consolidation would be reached with the sand drains at the same time?
4.8 A layer of saturated clay is 10 m thick, the lower boundary being impermeable; an embank- ment is to be constructed above the clay. Determine the time required for 90% consolidation of the clay layer. If 300 mm diameter sand drains at 4 m centres in a square pattern were installed in the clay, in what time would the same overall degree of consolidation be reached?
The coefficients of consolidation in the vertical and horizontal directions, respectively, are 9.6 and 14.0 m2/year.
References
Al-Tabbaa, A. and Wood, D.M. (1987) Some measurements of the permeability of kaolin, Géotechnique, 37(4), 499–503.
ASTM D2435 (2011) Standard Test Methods for One-Dimensional Consolidation Properties of Soils Using Incremental Loading, American Society for Testing and Materials, West Conshohocken, PA.
Barron, R.A. (1948) Consolidation of fine grained soils by drain wells, Transactions of the ASCE, 113, 718–742.
Bjerrum, L. (1967) Engineering geology of Norwegian normally-consolidated marine clays as related to settlement of buildings, Géotechnique, 17(2), 83–118.
British Standard BS EN ISO 17892-5 (2017) Geotechnical Investigation and Testing – Laboratory Testing of Soil: Incremental Loading Oedometer Test (ISO 17892-5: 2017), British Standards Institution, London.
Casagrande, A. (1936) Determination of the preconsolidation load and its practical significance, in Proceedings of the International Conference on SMFE, Harvard University, Cambridge, MA, Vol. III, pp. 60–64.
CEN ISO/TS 17892–5 (2017) Geotechnical Investigation and Testing—Laboratory Testing of Soil: Incremental Loading Oedometer Test, International Organisation for Standardisation, Geneva.
Cour, F.R. (1971) Inflection point method for computing cv, Technical Note, Journal of the ASCE, 97(SM5), 827–831.
Das, B.M. (1985) Principles of Geotechnical Engineering, PWS Publishers, Boston, MA.
EC7-2 (2007) Eurocode 7: Geotechnical Design—Part 2: Ground Investigation and Testing, BS EN 1997-2:2007, British Standards Institution, London.
Gibson, R.E. (1966) A note on the constant head test to measure soil permeability in-situ, Géotechnique, 16(3), 256–259.
Gibson, R.E. (1970) An extension to the theory of the constant head in-situ permeability test, Géotechnique, 20(2), 193–197.
Hansbo, S. (1979) Consolidation of clay by band-shaped prefabricated drains, Ground Engineering, 12(5), 16–25.
Hansbo, S. (1981) Consolidation of fine-grained soils by prefabricated drains, in Proceedings of the 10th International Conference on SMFE, Stockholm, Vol. III, pp. 677–682.
Mitchell, J.K. and Soga, K. (2005) Fundamentals of Soil Behaviour (3rd edn), John Wiley &
Sons, New York, NY.
Naylor, A.H. and Doran, I.G. (1948) Precise determination of primary consolidation, in Proceedings of the 2nd International Conference on SMFE, Rotterdam, Vol. 1, pp. 34–40.
Robinson, R.G. and Allam, M.M. (1996) Determination of coefficient of consolidation from early stage of log t plot, Geotechnical Testing Journal, ASTM, 19(3), 316–320.
Rowe, P.W. (1968) The influence of geological features of clay deposits on the design and perfor- mance of sand drains, in Proceedings ICE (Suppl. Vol.), Paper 70585.
Rowe, P.W. and Barden, L. (1966) A new consolidation cell, Géotechnique, 16(4), 162–170.
Schmertmann, J.H. (1953) Estimating the true consolidation behaviour of clay from laboratory test results, Proceedings ASCE, 79, 1–26.
Scott, R.F. (1961) New method of consolidation coefficient evaluation, Journal of the ASCE, 87(SM1).
Sridharan, A. and Nagaraj, H.B. (2000) Compressibility behaviour of remoulded, fine-grained soils and correlation with index properties, Canadian Geotechnical Journal, 37(3), 712–722.
Terzaghi, K. (1943) Theoretical Soil Mechanics, John Wiley & Sons, New York.
Terzaghi, K. and Peck, R.B. (1967) Soil Mechanics in Engineering Practice (2nd edn), John Wiley
& Sons, New York.
Wilkinson, W.B. (1968) Constant head in-situ permeability tests in clay strata, Géotechnique, 18(2), 172–194.
Wood, D.M. (1991) Soil Behaviour and Critical State Soil Mechanics, Cambridge University Press.
Wroth, C.P. (1979) Correlations of some engineering properties of soils, in Proceedings of the 2nd International Conference on Behaviour of Offshore Structures, London, Vol. 1, pp.
121–132.
Consolidation
Further reading
Burland, J.B. (1990) On the compressibility and shear strength of natural clays, Géotechnique, 40(3), 329–378.
This paper describes in detail the role of depositional structure on the initial compressibility of natural clays (rather than those reconstituted in the laboratory). It contains a large amount of experimental data, and is therefore useful for reference.
McGown, A. and Hughes, F.H. (1981) Practical aspects of the design and installation of deep vertical drains, Géotechnique, 31(1), 3–17.
This paper discusses practical aspects related to the use of vertical drains, which were introduced in Section 4.11.
For further student and instructor resources for this chapter, please visit the Companion Website at www.routledge.com/cw/craig
Soil behaviour in shear
Chapter 5
Soil behaviour in shear
Learning outcomes
After working through the material in this chapter, you should be able to:
1 Understand how soil may be modelled as a continuum, and how its mechanical behaviour (strength and stiffness) may be adequately described using elastic and plastic material (constitutive) models (Section 5.1–5.3);
2 Understand the method of operation of standard laboratory testing apparatus and derive strength and stiffness properties of soil from these tests for use in subsequent geotechnical analyses (Section 5.4);
3 Appreciate the different strength characteristics of coarse and fine-grained soils and derive material parameters to model these (Sections 5.5–5.6 and Section 5.8);
4 Understand the critical state concept and its important role in coupling strength and volumetric behaviour in soil (Section 5.7);
5 Use simple empirical correlations to estimate strength and stiffness properties of soil based on the results of index tests (see Chapter 1) and appreciate how these may be used to support the results from laboratory tests (Section 5.9).