E P Curve Overconsolidated Clay
GsPw
GspwA
By way of illustration let us use the test results of Example 9.4 together with the following information:
Original dimensions of test sample: 75 mm diameter, 20 mm thickness Mass of sample after removing complete from consolidation apparatus at end of test and drying in oven = 135.6 g.
2.65 x 1 x4418
Now, as shown above:
Hence the void ratio to pressure relationship can be found.
50 19.65 0.697
100 19.52 0.685
200 19.35 0.671
400 19.15 0.653
800 18.95 0.636
Note Such close agreement between the two methods for determining the ep relationship could only happen in a theoretical example. In practice one often finds large discrepancies between the two methods.
9.3.6 The virgin consolidation curve
Clay is generally formed by the process of sedimentation from a liquid in which the soil particles were gradually deposited and compressed as more material was placed above them. The ep curve corresponding to this natural process of consolidation is known as the virgin consolidation curve (Fig. 9.9a).
This curve is approximately logarithmic. If the values are plotted to a semilog scale (e to a natural scale, p to a logarithmic scale), the result is a straight line of equation:
(a) Natural consolidation
(b) Normally consolidated clay
Fig. 9.9 ep and elogp curves for natural consolidation and for a normally consolidated clay.
Hence e2 can be expressed in terms of e^
Cc is known as the compression index of the clay. Compression curve for a normally consolidated clay
A normally consolidated clay is one that has never experienced a consolidation pressure greater than that corresponding to its present overburden. The compression curve of such a soil is shown in Fig. 9.9b.
The clay was originally compressed, by the weight of material above, along the virgin consolidation curve to some point A. Owing to the removal of pressure during sampling the soil has expanded to point B. Hence from B to A the soil is being recompressed whereas from A to C the virgin consolidation curve is followed.
The semilog plot is shown in Fig. 9.9b. As before on the straight line part: p2
Compression curve for an overconsolidated clay
An overconsolidated clay is one which has been subjected to a preconsolidation pressure in excess of its existing overburden (Fig. 9.10a), the resulting compression being much less than for a normally consolidated clay. The semilog plot is no longer a straight line and a compression index value for an overconsolidated clay is no longer a constant.
From the ep curve it is possible to determine an approximate value for the preconsolidated pressure with the use of a graphical method proposed by Casagrande (1936). First estimate the point of greatest curvature, A, then draw a horizontal line through A (AB) and the tangent to the curve at A (AC). Bisect the angle BAC to give the line AD, and locate the straight part of the compression curve (in Fig. 9.10a the straight part commences at point E). Finally project the straight part of the curve upwards to cut AD in F. The point F then gives the value of the preconsolidation pressure.
(a) Graphical determination of preconsolidation pressure (Casagrande)
(b) Determination of corrected compression curve (Schmertmann)
Overburden
Preconsolidation
Log pressure
Log pressure
(a) Graphical determination of preconsolidation pressure (Casagrande)
(b) Determination of corrected compression curve (Schmertmann)
Fig. 9.10 Compression curves for an overconsolidated clay.
Evaluation of consolidation settlement from the compression index dH ei — e2 Hl"= 1 +ei
1 +ei eL  e2 = Cc logio — Pi p = dH = Cc logio — Hi 1+ei pi
This equation is only relevant when a clay is being compressed for the first time and therefore cannot be used for an overconsolidated clay.
Determination of compression index Cc
Terzaghi and Peck (1948) have shown that there is an approximate relationship between the liquid limit of a normally consolidated clay and its compression index. This relationship has been established experimentally and is:
A soft, normally consolidated clay layer is 15 m thick with a natural moisture content of 45 per cent. The clay has a saturated unit weight of 17.2 kN/m3, a particle specific gravity of 2.68 and a liquid limit of 65 per cent. A foundation load will subject the centre of the layer to a vertical stress increase of 10.0 kN/m2.
Determine an approximate value for the settlement of the foundation if ground water level is at the surface of the clay.
Solution
Initial vertical effective stress at centre of layer = (17.29.81) y = 55.4 kN/m2
Final effective vertical stress = 55.4+ 10 = 65.4 kN/m2 Initial void ratio, ej = wGs = 0.45 x 2.68 = 1.21
This method can be used for a rough settlement analysis of a relatively unimportant small structure on a soft clay layer. For large structures, consolidation tests would be carried out.
9.3.7 Application of consolidation test results
The range of pressure generally considered in a settlement analysis is the increase from pi (the existing vertical effective overburden pressure) to P2 (the vertical effective pressure that will operate once the foundation load has been applied and consolidation has taken place), so that in the previous discussion ei represents the void ratio corresponding to the effective overburden pressure and C2 represents the final void ratio after consolidation. In some text books and papers the initial void ratio, ei, is given the symbol e0.
Obtaining a test sample entails removing all of the stresses which are applied to it, this reduction in effective stress causing the sample to either swell or develop negative pore water pressures within itself. Owing to the restraining effect of the sampling tube most soil samples tend to have a negative pore pressure.
In the consolidation test the sample is submerged in water to prevent evaporation losses, with the result that the negative pore pressures will tend to draw in water and the sample consequently swells. To obviate this effect the normal procedure is to start the test by applying the first load increment and then to add the water, but if the sample still tends to swell an increased load increment must be added and the test readings started again. The point ei is taken to be the position on the test ep curve that corresponds to the effective overburden pressure at the depth from which the sample was taken; in the case of a uniform deposit various values of ei can be obtained for selected points throughout the layer by reading off the test values of void ratio corresponding to the relevant effective overburden pressures. Generally the test ep curve lies a little below the actual in situ ep curve, the amount of departure depending upon the degree of disturbance in the test sample. Bearing in mind the inaccuracies involved in any analysis, this departure from the consolidation curve will generally be of small significance unless the sample is severely disturbed and most settlement analyses are based on the actual test results.
An alternative method, mainly applicable to overconsolidated clays, has been proposed by Schmertmann (1953), who points out that ei (he uses the symbol e0) must be equal to wGs, where w is the in situ moisture content at the point considered, and that in a consolidation test on an ideal soil with no disturbance the void ratio of the sample should remain constant at e, throughout the pressure range from zero to the effective overburden pressure value. Schmertmann found that the test ep curve tends to cut the in situ virgin consolidation curve at a void ratio value somewhere between 37 and 42 per cent of Cj and concluded that a reasonable figure for this intersection is e = 0.42e,.
In order to obtain the corrected curve, with disturbance effects removed, the test sample is either loaded through a pressure range that eventually reduces the void ratio of the sample to 0.42e] or else the test is extended far enough for extrapolated values to be obtained, at least one cycle of expansion and recompression being carried out during the test. The approximate value of the preconsolidation pressure is obtained and the test results are put in the form of a semilog plot of void ratio to log p (Fig. 9.10b). The value of ei is obtained from wGs, w being found from a separate test sample (usually cuttings obtained during the preparation of the consolidation test sample). It is now possible to plot on the test curve (point A) and a horizontal line (AB) is drawn to cut the ordinate of the existing overburden pressure at point B; a line BC is next drawn parallel to the mean slope of the laboratory rebound curve to cut the preconsolidation pressure ordinate at point C, and the value of void ratio equal to 0.42ei is obtained and established on the test curve (point D). Finally points C and D are joined. The corrected curve therefore consists of the three straight lines: AB (parallel to the pressure axis with a constant void ratio value e^, BC (representing the recompression of the soil up to the preconsolidation pressure), and CD (representing initial compression along the virgin consolidation line).
Apart from the elimination of disturbance effects the method is useful because it permits the use of a formula similar to the compression index of a normally consolidated clay:
Pc = — logio — H 1+ei pi where C is the slope of the corrected curve (generally recompression). If the pressure range extends into initial compression the calculation must be carried out in two parts using the two different C values.
9.3.8 General consolidation
In the case of a foundation of finite dimensions, such as a footing sitting on a thick bed of clay, lateral strains will occur and the consolidation is no longer onedimensional. If two saturated clays of equal compressibility and thickness are subjected to the same size of foundation and loading, the resulting settlements may be quite different even though the consolidation tests on the clays would give identical results. This is because lateral strain effects in the field may induce unequal pore pressures whereas in the consolidation test the induced pore pressure is always equal to the increment of applied stress. For a saturated soil:
Pi = initial effective major principal stress Aci = increment of total major principal stress due to the foundation loading
Au = excess pore water pressure induced by the load. The effective major principal stress on load application will be: Pi + Acti  Au
The effective major principal stress after consolidation will be: Pi + Acri
Let p'3 = initial effective minor principal stress A.CT3 = increment of total minor principal stress due to the foundation
The horizontal effective stress on load application will be: p'3 + Act,  Au
If the expression for Au is examined it will be seen that Au is greater than Adj. The horizontal effective stress therefore reduces when the load is applied and there will be a lateral expansion of the soil. Hence in the early stages of consolidation the clay will undergo a recompression in the horizontal direction for an effective stress increase of Au — Act3; the strain from this recompression will be small but as consolidation continues the effective stress increases beyond the original value of p'3 and the strain effects will become larger until consolidation ceases.
Settlement analysis
The method of settlement analysis most commonly in use is that proposed by Skempton and Bjerrum (1957). In this procedure the lateral expansion and compression effects are ignored, since the authors maintain that such a simplification cannot introduce a maximum error of more than 20 per cent and when they compared the actual settlements of several structures with predicted values using their method the greatest difference was in fact only 15 per cent.
Ignoring secondary consolidation, the total settlement of a foundation is given by the expression:
P = Pi + Pc where pi = immediate settlement pc = consolidation settlement.
In the consolidation test:
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