The characteristics of a soil during one-dimensional consolidation or swelling can be deter- mined in the laboratory by means of the oedometer test. Figure 4.1 shows diagrammatically a cross-section through an oedometer. The test specimen is in the form of a disc of soil, held inside a metal ring and lying between two porous stones. The upper porous stone, which can move inside the ring with a small clearance, is fixed below a metal loading cap through which pressure can be applied to the specimen. The whole assembly sits in an open cell of water to which the pore water in the specimen has free access. The ring confining the specimen may be either fixed (clamped to
Figure 4.1 The oedometer: (a) test apparatus, (b) test arrangement (image courtesy of Impact Test Equipment Ltd.).
Consolidation the body of the cell) or floating (being free to move vertically); the inside of the ring should have a smooth polished surface to reduce side friction. The confining ring imposes a condition of zero lateral strain on the specimen. The compression of the specimen under pressure is measured by means of a dial gauge or electronic displacement transducer operating on the loading cap.
The test procedure has been standardised in BS EN ISO 17892-5 (2017) in the UK; this is the same as CEN ISO/TS17892–5 (2017) used in Europe. In the US, ASTM D2435 (2011) is used. The initial pressure (total stress) applied will depend on the type of soil; following this, a sequence of pressures is applied to the specimen, each being double the previous value. Each pressure is normally maintained for a period of 24 h (in exceptional cases a period of 48 h may be required), compression readings being recorded at suitable intervals during this period. At the end of the increment period, when the excess pore water pressure has completely dissipated, the applied total stress equals the effective vertical stress in the specimen. The results are presented by plotting the thickness (or percentage change in thickness) of the specimen or the void ratio at the end of each increment period against the corresponding effective stress. The effective stress may be plotted to either a natural or a logarithmic scale, though the latter is normally adopted due to the reduction in volume change in a given increment as total stress increases. If desired, the expansion of the specimen can additionally be measured under successive decreases in applied pressure to observe the swelling behaviour. However, even if the swelling character- istics of the soil are not required, the expansion of the specimen due to the removal of the final pressure should be measured.
Eurocode 7, Part 2 (EC7-2, 2007) recommends that a minimum of two tests are conducted in a given soil stratum; this value should be doubled if there is considerable discrepancy in the measured compressibility, especially if there is little or no previous experience relating to the soil in question.
The void ratio at the end of each increment period can be calculated from the displacement readings and either the water content or the dry weight of the specimen at the end of the test.
Referring to the phase diagram in Figure 4.2, the two methods of calculation are as follows:
1 Water content measured at end of test = w1
Void ratio at end of test = e1= w1Gs (assuming Sr = 100%) Thickness of specimen at start of test = H0
Figure 4.2 Phase diagram.
Change in thickness during test = ΔH Void ratio at start of test = e0 = e1+Δe where
D D
e H
e
= 1H+ 0 0
(4.1) In the same way Δe can be calculated up to the end of any increment period.
2 Dry weight measured at end of test = Ms (i.e. mass of solids) Thickness at end of any increment period = H1
Area of specimen = A
Equivalent thickness of solids = Hs=Ms/AGsρw
Void ratio,
e H H
H
H
1= 1- s = H1-1
s s
(4.2)
Stress history
The relationship between void ratio and effective stress depends on the stress history of the soil.
If the present effective stress is the maximum to which the soil has ever been subjected, the soil is said to be normally consolidated. If, on the other hand, the effective stress at some time in the past has been greater than the present value, the soil is said to be overconsolidated. The maximum value of effective stress in the past divided by the present value is defined as the overconsolidation ratio (OCR). A normally consolidated soil thus has an overconsolidation ratio of unity; an over- consolidated soil has an overconsolidation ratio greater than unity. The overconsolidation ratio can never be less than one.
Most soils will initially be formed by sedimentation or deposition of particles, which leads to gradual consolidation under increasing self-weight. Under these conditions, the effective stresses within the soil will be constantly increasing as deposition continues, and the soil will therefore be normally consolidated. Seabed or riverbed soils are common examples of soils which are natu- rally in a normally consolidated state (or close to it). Overconsolidation is usually the result of geological factors – for example, the erosion of overburden (due to glacier motion, wind, wave or ocean currents), the melting of ice sheets (and therefore reduction in stress) after glaciation, or permanent rise of the water table. Overconsolidation may also occur due to man-made processes:
for example, the demolition of an old structure to redevelop the land will remove the total stresses that were applied by the building’s foundations causing heave, such that, for the redevelopment, the soil will initially be overconsolidated.
Compressibility characteristics
Typical plots of void ratio (e) after consolidation against effective stress (σ′) for a saturated soil are shown in Figure 4.3, the plots showing an initial compression followed by unloading and recompression. The shapes of the curves are related to the stress history of the soil. The e–log σ′ relationship for a normally consolidated soil is linear (or nearly so), and is called the virgin (one‑dimensional) compression line (1DCL). During compression along this line, perma- nent (irreversible) changes in soil structure continuously take place and the soil does not revert to the original structure during expansion. If a soil is overconsolidated, its initial state will be
Consolidation
represented by a point on the expansion part of the e–log σ′ plot, i.e. below/to the left of the 1DCL. The changes in soil structure along this line are almost wholly recoverable as shown in Figure 4.3. The recompression curve ultimately rejoins the virgin compression line: further com- pression then occurs along the virgin line. The plots show that a soil in the overconsolidated state (on an unload–reload line) will be much less compressible than that in a normally consolidated state (on the 1DCL).
The compressibility of the soil can be quantified by one of the following coefficients:
1 The coefficient of volume compressibility (mv), defined as the volume change per unit vol- ume per unit increase in effective stress (i.e. ratio of volumetric strain to applied stress). The units of mv are the inverse of stiffness (m2/MN). The volume change may be expressed in terms of either void ratio or specimen thickness. If, for an increase in effective stress from s0¢ to s1¢, the void ratio decreases from e0 to e1, then
m e
e e
v= +
−
′ − ′
1 1 0
0 1
1 0
s s (4.3)
m H
H H
v= −
′ − ′
1
0
0 1
1 0
s s (4.4)
The value of mv for a particular soil is not constant but depends on the stress range over which it is calculated, as this parameter appears in the denominator of Equations 4.3 and 4.4. Most test standards specify a single value of the coefficient mv calculated for a stress increment of 100 kPa in excess of the in-situ vertical effective stress of the soil sample at the depth it was sampled from (also termed the effective overburden pres‑
sure), although the coefficient may also be calculated, if required, for any other stress range, selected to represent the expected stress changes due to a particular geotechnical construction.
Figure 4.3 Void ratio–effective stress relationship.
2 The constrained modulus (also called one-dimensional elastic modulus) E'oed is the reciprocal of mv (i.e. having units of stiffness, MN/m2 = MPa) where:
¢ = Eoed mv
1 (4.5)
3 The compression index (Cc) is the slope of the 1DCL, which is a straight line on the e–log σ′
plot, and is dimensionless. For any two points on the linear portion of the plot
C e e
c = -
¢ ¢
(
0 1 1 0)
log s s/ (4.6)
The expansion part of the e–log σ′ plot can also be approximated to a straight line as indicated in Figure 4.3, the slope of which is referred to as the expansion index Ce (also called swell-back index). The expansion index is approximately five times smaller than the compression index (i.e. Ce≈ 0.2Cc).
It should be noted that although Cc and Ce represent negative gradients on the e–log σ′ plot, their value is always given as positive (i.e. they represent the magnitude of the gradients).
Preconsolidation pressure
Casagrande (1936) proposed an empirical construction to obtain, from the e–log σ′ curve for an overconsolidated soil, the maximum effective vertical stress that has acted on the soil in the past, referred to as the preconsolidation pressure (smax¢ ). This parameter may be used to determine the in-situ OCR for the soil tested:
OCR= ¢
¢ s
s
max v0
(4.7) where s¢v0 is the in-situ vertical effective stress of the soil sample at the depth it was sampled from (effective overburden pressure), which may be calculated using the methods outlined in Chapter 3.
Figure 4.4 shows a typical e–log σ′ curve for a specimen of soil which is initially overconsoli- dated. The initial curve (AB) and subsequent transition to a linear compression (BC) indicate that the soil is initially undergoing recompression in the oedometer, having at some stage in its history undergone swelling. Swelling of the soil in-situ may, for example, have been due to melting of ice sheets, erosion of overburden, or a rise in water table level. The construction for estimating the preconsolidation pressure consists of the following steps:
1 Extrapolate back the straight-line part (BC) of the curve;
2 Determine the point (D) of maximum curvature on the recompression part (AB) of the curve;
3 Draw a horizontal line through D;
4 Draw the tangent to the curve at D and bisect the angle between the tangent and the horizon- tal through D;
5 The vertical through the point of intersection of the bisector and extrapolation of CB pro- duced gives the approximate value of the preconsolidation pressure.
Consolidation
Whenever possible, the preconsolidation pressure for an overconsolidated clay should not be exceeded in construction. Compression will not usually be great if the effective vertical stress remains below s¢max, as the soil will be always on the unload–reload part of the compression curve.
Only if s¢max is exceeded will compression be large. This is the key principle behind preloading, which is a technique used to reduce the compressibility of soils to make them more suitable for use in foundations; this is discussed in Section 4.12.
In-situ e–log σ′ curve
Due to the effects of sampling (see Chapter 6) and test preparation, the specimen in an oedom- eter test will be slightly disturbed. It has been shown that an increase in the degree of specimen disturbance results in a slight decrease in the slope of the virgin compression line. It can therefore be expected that the slope of the line representing virgin compression of the in-situ soil will be slightly greater than the slope of the virgin line obtained in a laboratory test.
No appreciable error will be involved in taking the in-situ void ratio as being equal to the void ratio (e0) at the start of the laboratory test. Schmertmann (1953) pointed out that the laboratory virgin line may be expected to intersect the in-situ virgin line at a void ratio of approximately 0.42 times the initial void ratio. Thus the in-situ virgin line can be taken as the line EF in Figure 4.5 where the coordinates of E are log smax¢ and e0, and F is the point on the laboratory virgin line at a void ratio of 0.42e0.
In the case of overconsolidated clays, the in-situ condition is represented by the point (G) in Figure 4.5 having coordinates sv0¢ and e0, where s′v0 is the present effective overburden pressure.
The in-situ recompression curve can be approximated to the straight line GH parallel to the mean slope of the laboratory recompression curve.
Figure 4.4 Determination of preconsolidation pressure.
Example 4.1
The following compression readings were obtained in an oedometer test on a specimen of saturated clay (Gs = 2.73):
TABLE F
Pressure (kPa) 0 54 107 214 429 858 1716 3432 0
Dial gauge after 24 h (mm)
5.000 4.747 4.493 4.108 3.449 2.608 1.676 0.737 1.480
The initial thickness of the specimen was 19.0 mm, and at the end of the test the water content was 19.8%. Plot the e–log σ′ curve and determine the preconsolidation pressure.
Determine the values of mv for the stress increments 100–200 and 1000–1500 kPa. What is the value of Cc for the latter increment?
Solution
Void ratio at end of test = e1 = w1GS = 0.198 × 2.73 = 0.541 Void ratio at end of test = e0 = e1 + Δe
Now D D
e D H
e H
e e
= + H
= + +
1 0 1
0
1 0
Figure 4.5 In-situ e–log σ′ curve.
Consolidation
i.e.
D 3.520
D D
e e
e e
= +
=
= + =
1 541 19 0 0 350
0 541 0 350 0 891
0
. . .
. . .
In general, the relationship between Δe and ΔH is given by D
D e
H =1 891 19 0
. .
i.e. Δe = 0.0996 ΔH, and can be used to obtain the void ratio at the end of each increment period (see Table 4.1). The e–log σ′ curve using these values is shown in Figure 4.6. Using Casagrande’s construction, the value of the preconsolidation pressure is 325 kPa.
Figure 4.6 Example 4.1.
Table 4.1 Example 4.1
Pressure (kPa) ∆H (mm) ∆e e
0 0 0 0.891
54 0.253 0.025 0.866
107 0.507 0.050 0.841
214 0.892 0.089 0.802
429 1.551 0.154 0.737
858 2.392 0.238 0.653
1716 3.324 0.331 0.560
3432 4.263 0.424 0.467
0 3.520 0.350 0.541
m e
e e
v=
+ × -
¢ - ¢ 1
1 0
0 1
1 0
s s
For s0′ =100 kPa and s1′ =200 kPa e0 = 0.845 and e1 = 0.808
and therefore
mv= 1 ´ = ´ - m /kN = m /MN
1 845
0 037
100 2 0 104 2 0 20 2 .
. . .
For s0′ =1000 kPa and s1′ =1500 kPa e0 = 0.632 and e1 = 0.577
and therefore
mv= 1 ´ = ´ - m /kN= m /MN
1 845
0 055
500 6 7 105 2 0 07 2 .
. . .
and
CC= -
( )
= =0 632 0 557 1500 1000
0 055 0 176 0 31
. .
log /
.
. .
Note that Cc will be the same for any stress range on the linear part of the e–log σ′ curve;
mv will vary according to the stress range, even for ranges on the linear part of the curve.