NPTEL- Advanced Geotechnical Engineering
Module 5
Lecture 29
Consolidation-3
Topics
1.1.6 Standard One-Dimensional Consolidation Test and Interpretation
1.1.7 Preconsolidation pressure.

Compression index

Effect of sample disturbance on the e vs. log
cirve
1.1.8 Calculation of one-dimensional consolidation settlement
1.1.6 Standard One-Dimensional Consolidation Test and Interpretation
The standard one-dimensional consolidation test is usually carried out on saturated specimens about 1 in
(25.4 mm) thick and 2.5 in (63.5 mm) in diameter (Figure 5.25). The soil sample is kept inside a metal ring,
with a porous stone at the top and another at the bottom. The load P on the sample is applied through a lever
arm, and the compression of the specimen is measured by a micrometer dial gauge. The load is usually
doubled every 24 hours. The specimen is kept under water throughout the test. (F0r detailed test procedures,
see ASTM test designation D-2435.)
Figure 5.25 Standard one dimensional consolidation apparatus
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For each load increment, the sample deformation and the corresponding time t is plotted on semilogarithmic
graph paper. Figure 5.26 shows a typical deformation vs. log t graph. The graph consists of three distinct
parts:
1. Upper curved portion (stage I). This is mainly the result of precompression of the specimen.
2. A straight-line portion (stage II). This is referred to as primary consolidation. At the end of the
primary consolidation, the excess pore water pressure generated by the incremental loading is
dissipated to a large extent.
3. A lower straight-line portion (stage III). This is called secondary consolidation. During this stage, the
specimen undergoes small deformation with time. in fact, there must be immeasurably small excess
pore water pressure in the specimen during secondary consolidation.
Figure 5.26 Typical sample deformation vs. log-of-time plot for a given load increment
Note that at the end of the test for each incremental loading the stress on the specimen is the effective stress,
. Once the specific gravity of the soil solids, the initial specimen dimensions, and the specimen
deformation at the end of each load has been determined, the corresponding void ratio can be calculated. A
typical void ratio vs. effective pressure relationship plotted on semilogarithmic graph paper is shown in
Figure 5.27.
Figure 5.27 Typical e vs. log
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plot
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1.1.7 Preconsolidation pressure.
Typical e vs. log
plot shown in Figure 5.28, it can be seen that the upper part is curved; however, at
higher pressure, e and log
bear a linear relationship. The upper part is curved because when the soil
specimen was obtained from the field, it was subjected to a certain maximum effective pressure. During the
process of soil exploration, the pressure is released. In the laboratory, when the soil sample is loaded, it will
show relatively small decrease of void ratio with load up to the maximum effective stress to which the soil
was subjected in the past. This is represented by the upper curved portion in Figure 5.28. If the effective
stress on the soil sample is increased further, the decrease of void ratio with stress level will be larger. This
is represented by the straight-lime portion in the e vs. log plot. The effect can also be demonstrated in the
laboratory by unloading and reloading a soil sample, as shown in Figure 5.28. In this Figure 5.28,
is the
void ratio-effective stress relation as the sample is unloaded, and
is the reloading branch. At , the
sample is being subjected to a lower effective stress than the maximum stress
to which the soil was ever
subjected. So
will show a flatter curved portion. Beyond point f, the void ratio will decrease at a larger
rate with effective stress, and
will have the same slope as .
Figure 5.28 Plot of void ratio vs. effective pressure showing unloading and reloading branches
Based on the above explanation, the two conditions of a soil can be defined
1. Normally consolidated. A soil is called normally consolidated if the present effective overburden
pressure is the maximum to which the soil has ever been subjected,
.
2. Overconsolidated. A soil is called overcosolidated if the present effective overburden pressure is less
than the maximum to which the soil was ever subjected in the past
In Figure 5.28 the branches
are the overconsolidated state of a soil, and the branches
are the normally consolidated state of a soil.
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In the natural condition in the field, a soil may be either normally consolidated or overconsolidated.
A soil in the field may become overconsolidated through several mechanisms, some of which are
listed in table 2.
The preconsolidation pressure from a e vs. log
plot is generally determined by a graphical
procedure suggested by Casagrande (1936), as shown in Figure 5.29. The steps are as follows:
1. Visually determine the point P (on the upper curved portion of the e vs. log plot) that has the
maximum curvature.
2. Draw a horizontal line PQ.
3. Draw a tangent PR at P.
4. Draw the line PS bisecting the angle QPR.
5. Produce the straight-line portion of the e vs. log plot backward to intersect PS at T.
6. The effective pressure corresponding to point T is the preconsolidation pressure
.
Another method for the determination of
is given in Burmister (1951)
Table 2 Mechanisms causing overconsolidation (Brumund et al 1976)
Mechanisms
Remarks and references
Changes in total stress due to:
Removal of overburden pressure
Past structures
Glaciation
Changes in pore water pressure due to change in
water table elevation:
Artesian pressures
Deep pumping
Desiccation due to drying
Desiccation due to plant life
Kanny (1964) gives sea level changes
Common in glaciated areas
Common in many cities
Many have occurred during deposition
Many have occurred during deposition
Changes in soil structure due to secondary Raju (1965); Leonards and Ramiah (1960);
compression (aging)*
Leonards and Altschacffl (1964); Bijerrum
(1967, 1972)
Environmental changes such as pH, temperature, Lambe (1958)
and salt concentration
Chemical alteration due to “weathering,” Bjerrum (1967)
precipitation of cementing agents , ion exchange
Change of strain rate on loading
Lowe (1974)
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Figure 5.29 Graphical procedure for determination of preconsolidation pressure
 Compression index
The slope of the e vs. log
From Figure 5.30,
plot for normally consolidated soil is referred to as the compression index
Figure 5.30 Compression index
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.
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(66)
For normally consolidated clays. Terzaghi and Peck (1967) gave a correlation for the compression index as
(67)
Where LL is the liquid limit. The preceding relation has reliability in the range of
be used for clays with sensitivity ratios greater than 4.
and should not to
Terzaghi and Peck also gave a similar correlation for remolded clays:
Several other correlations for the compression index with the basic index properties of soils have been made,
and some of these are given below (see Azzouz et al., 1976):
(68)
(69)
(70)
(71)
(72)
Where
is the natural moisture content (%) and
is the in situ void ratio.
Nacci et al. (1975) tested some natural deep-ocean soil samples from the North Atlantic. The calcite content
varied from 10 to 80%. Based on their results, the following equation has also been proposed:
(73)
Where PI is the plasticity index.

Effect of sample disturbance on the e vs. log
cirve
Soil samples obtained from the field are somewhat disturbed. When consolidation tests are conducted on
these samples, we obtain e vs. log
plots that are slightly different from those in the field. This is
demonstrated in Figure 5.31.
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Figure 5.31 Effect of sample disturbance on e vs. log
curve
Curve I in Figure 5.31a shows the nature of the e vs. log
variation that an undisturbed normally
consolidated clay (present effective overburden pressure
; void ratio ) in the field would exhibit. This is
called the virgin compression curve. A laboratory consolidation test on a carefully recovered sample would
result in e vs. log
plot such as curve II. If the same soil is completely remolded and then tested in a
consolidometer, the resulting void ratio-pressure plot will be like curve III. The virgin compression curve
(curve I) and the laboratory e vs. log curve obtained from a carefully recovered sample (curve II) intersect
at a void ratio of about
(Terzaghi and Peck, 1967).
Curve I in Figure 5.31b shows the nature of the field consolidation curve of an over consolidated clay. Note
that the present effective overburden pressure is
and the corresponding void ratio is
is the
preconsolidation pressure, and
is a part of the virgin compression curve. Curve II is the corresponding
laboratory consolidation curve. After careful testing, Schmertmann (1953) concluded that the field
recompression branch ( in Figure 5.34b) has approximately the same slope as the laboratory unloading
branch,
. The slope of the laboratory unloading branch is referred to as
. The range of
is
approximately from one-fifth to one-tenth of .
1.1.8 Calculation of one-dimensional consolidation settlement
The basic principle of one-dimensional consolidation settlement calculation is demonstrated in Figure 5.32.
If a clay layer of total thickness
is subjected to an increase of average effective overburden pressure from
, it will undergo a consolidation settlement of
. Hence the strain can be given by
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Figure 5.32 Calculation of one-dimensional consolidation settlement
(74)
Where e is strain. Again, if an undisturbed laboratory specimen is subjected to the same effective stress
increase, the void ratio will decrease by . Thus, the strain is equal to
(75)
Where
is the void ratio at an effective stress of
.
Thus, from equations (74) and (75),
(76)
For a normally consolidated clay in the field (Figure 5.33a),
(77)
For an overconsoidated clay, (1) if
(i.e., overconsolidated pressure )(Figure 5.33b)
(78)
And (2) if
(Figure 5.33c)
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(79)
Figure 5.33 Calculation of
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[equations (77) to (79)]
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