Soil Mechanics
Settlement and Consolidation
page 1
Contents of this chapter :
CHAPITRE 4.
4.1
4.2
4.3
4.4
4.5
4.6
4.7
SETTLEMENT AND CONSOLIDATION................................................................1
INTRODUCTION .........................................................................................................................1
SPRING ANALOGY ....................................................................................................................3
ONE DIMENSIONAL LOADING CONDITIONS .................................................................................4
THE OEDOMETER .....................................................................................................................4
BEHAVIOUR OF SOIL UNDER ONE DIMENSIONAL LOADING ...........................................................6
IDEALISED SOIL BEHAVIOUR ......................................................................................................7
EXERCISE ................................................................................................................................8
Settlement and Consolidation1
Chapitre 4.
4.1
Introduction
An important task in the design of foundations is to determine the settlement; this is shown
schematically in Figure 1.
Maximum
Settlement
Soil Layer
Fig. 1 Settlement of a loaded footing
The skeletal soil material and the pore water are relatively incompressible and any change in
volume can only occur due to change in the volume of the voids. For the volume of the voids to
change, pore water must flow into or out of a soil element. Because this cannot happen
instantaneously when a load is first applied to a soil there cannot be any immediate change in its
volume.
2
For one-dimensional conditions with no lateral strain this implies that there is no immediate
vertical strain and hence that the excess pore pressure is equal to the change in vertical stress.
However, under more general conditions both lateral (or horizontal) and vertical strains can occur.
Immediately after load is applied there will be no change in volume, but the soil deformations will
result in an initial settlement. This is said to occur under undrained conditions because no pore
water has been able to drain from the soil. With time the excess pore pressures generated during
1
2
Consolidation
Déformation (relative)
Soil Mechanics
Settlement and Consolidation
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the undrained loading will dissipate and further lateral and vertical strains will occur. Ultimately the
settlement will reach its long term or drained value.
The process by which soils decrease in volume is called consolidation and is shown
schematically in Figure 2.
It should be stated that the process described above represents a simplification because some
soils tend to creep. For such soils there will be additional creep settlements even though the
effective stress does not change.
Total
Stress
Time
Excess
Pore
Pressure
Time
Effective
Stress
Time
Fig. 2a Variation of stress and pore pressure at a typical point under a footing3
3
Semelle (de fondation)
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Settlement and Consolidation
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Settlement
Consolidation
settlement
Final
settlement
Initial
settlement
Time
In summary :
Consolidation is a process by which soils decrease in volume. It occurs when stress is
applied to a soil that causes the soil particles to pack together more tightly, therefore
reducing volume. When this occurs in a soil that is saturated with water, water will be
squeezed out of the soil.
4.2
Spring Analogy
Source: http://en.wikipedia.org/wiki/Consolidation_(soil)
The consolidation process is often explained with an idealized system composed of a spring, a
container with a hole in its cover, and water. In this system, the spring represents the
compressibility or the structure itself of the soil, and the water which fills the container represents
the pore water in the soil.
On figure 3, the tube on the left of the container shows the water pressure in the container.
Figure 3 Process of Consolidation
1. The container is completely filled with water, and the hole is closed. (Fully saturated soil)
2. A load is applied onto the cover, while the hole is still unopened. At this stage, only the
water resists the applied load. (Development of excessive pore water pressure)
3. As soon as the hole is opened, water starts to drain out through the hole and the spring
shortens. (Drainage of excessive pore water)
4. After some time, the drainage of water no longer occurs. Now, the spring alone resists the
applied load. (Full dissipation of excessive pore water pressure. End of consolidation)
Soil Mechanics
4.3
Settlement and Consolidation
page 4
One Dimensional Loading Conditions
Soils are often subjected to uniform loading over large areas, such as shown in Figure 4, from an
embankment. Under such conditions soil which is remote from the edges of the loaded area
undergoes vertical strain, but no horizontal strain. That is strains, and hence surface settlement,
only occur in one-dimension.
Embankment
x
Soil layer 1
Soil layer 2
z
Rock
Figure 4 Embankment loading on a layered soil
The accuracy of this assumption depends on the relative dimensions of the loaded area and
thickness of the soil layer. If the area is relatively large and the thickness of the soil layer relatively
small then the assumption of 1-D conditions will be reasonable.
It is possible to make approximate estimates of surface settlement using the 1-D approach even
when the loaded area is not relatively large. The procedures for doing this will be discussed in the
next chapter.
4.4
The Oedometer
The behaviour of soil during one-dimensional loading can be tested using a device called an
oedometer4, which is shown schematically in Fig. 5. The one-dimensional condition in which the
vertical strain, εzz ≠ 0, and the lateral strains, εxx = εyy = 0 is also referred to as confined
compression.
4
oedomètre
Soil Mechanics
Settlement and Consolidation
Load
page 5
Displacement gauge
Loading cap
Cell
water
h
Soil sample
Porous
disks
Figure 5 Schematic diagram of an oedometer
The following points may be noted:
The soil is loaded under conditions of no lateral strain (expansion), as the soil fits tightly
into a relatively rigid ring.
Uncontrolled drainage is provided at the top and bottom of the specimen by porous discs
(two way drainage). In more sophisticated oedometer apparatus control of drainage is
possible.
A vertical load is applied to the specimen and a record
of the settlement versus time is made. The load is left
on until primary consolidation ceases (usually 24 hours
although this depends on the soil type, impermeable
clays may take longer). See Figure 6.
Primary consolidation is caused by drainage of
excessive pore water. Secondary consolidation is
caused by creep5, viscous behaviour of the clay-water
system, compression of organic matter, and other
processes. In sand, settlement caused by secondary
consolidation is negligible, but in peat, it is very
significant.
The load is then increased (usually by a factor of 2, so
the vertical stresses might be e.g. 20, 40, 80, 160 kPa).
When the maximum load is reached, the soil is
unloaded in several increments. If desired reloading can
be carried out. At each step, time-settlement records
are made.
Log(time)
Primary
consolidation
Secondary
consolidation
Settlement ∆h
Fig.6: time-settlement record
Voids
S
5
fluage
Fig.7 Voids ratio–
settlement relationship
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Settlement and Consolidation
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It is conventional to plot the void ratio versus the logarithm of the effective stress in
examining the behaviour of soil, rather than plotting the relationship between effective
stress and strain as is often done in materials testing. The reason for this is that the
relationship between effective stress and voids ratio is fundamental to an understanding of
soil behaviour.
∆h e f − ei
=
.
h
1 + ei
From Fig. 7, we have :
Thus the final voids ratio can be determined by measuring ∆h, and the initial voids ratio ei :
ef =
4.5
∆h(1 + ei )
+ ei
h
Behaviour of soil under one dimensional loading
During deposition of a soil (which usually takes place through sedimentation), the weight of the soil
(which increases with depth below the surface) causes a decrease in void ratio.
Suppose that, at a particular depth below the surface, the soil is represented by point P in Figure
6. If the soil is now subjected to an effective stress increase under 1-D conditions the path that will
be followed in the e-log10 σ′ plot will be along the extension of the deposition line as shown in Fig.
8. A soil which lies at any point on this line is called normally consolidated, and the line is called
the normal consolidation line.
Normally consolidated soils are usually found as recent alluvial deposits, and are mainly
composed of silt and clay sized particles. It is extremely rare to find normally consolidated soils
inland, away from the rivers or lakes in which they were deposited.
e
Impossible states
Normal
Consolidation
Line
P
Over-consolidated
states
log10 (σ’)
Figure 8 The normal consolidation line
When stress is removed from a consolidated soil, the soil will rebound, regaining some of the
volume it had lost in the consolidation process. If the stress is reapplied, the soil will consolidate
again along a recompression curve, defined by the recompression index. The soil which had its
load removed is considered to be overconsolidated6. This is the case for soils which have
6
surconsolidé
Soil Mechanics
Settlement and Consolidation
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previously had glaciers on them. The highest stress that it has been subjected to is termed the
preconsolidation stress7 (for soil at state Q this would correspond to the effective stress at point
P in Fig. 9.)
The behaviour of an initially unloaded soil under one-dimensional conditions is illustrated in Fig. 9.
O
e=e
0
e=e
f
Q
F
P
R
log10(σ'
(σ PC)
Figure 9 Typical effective stress, voids ratio response
OP corresponds to initial loading of the soil.
PQ corresponds to an unloading of the soil.
QR corresponds to a reloading of the soil.
Upon reloading the soil beyond P the soil continues along the path that it would have followed if
loaded from O to R.
If a soil, after deposition, is normally consolidated to point P and then unloaded (perhaps because
of erosion of the surface layers of soil) it may exist in the state indicated by point Q in Figure 9.
The path QFR will be followed upon reloading of the soil.
It may be seen that for the same increase in effective stress, the change in void ratio will be much
less for an overconsolidated soil (from e0 to ef ) than it would have been for a normally
consolidated soil. Hence settlements will generally be much smaller for structures built on
overconsolidated soils.
4.6
Idealised soil behaviour
The behaviour shown in Figure 9 may be idealised by simple linear relationships in a void ratio, e,
logarithm of effective stress, σ´, plot as shown in Figure 10. This idealisation is based on
observations that:
7
pression de préconsolidation
Soil Mechanics
Settlement and Consolidation
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the behaviour of most normally consolidated soils can be approximated by straight lines for
the range of stresses that are of interest. The absolute value of the slope of such a line is
called the compression index8 Cc.
the response of most over-consolidated soils can be approximated by straight lines, and
further:
o
the behaviour is assumed to be reversible, unloading and reloading follow the same
path
o
the absolute value of the slope of the unload-reload response is constant and called
the recompression index9 Cr.
e
Slope : -Cc
Slope : -Cr
log10(σ'
(σ I)
log10(σ'
(σ F)
Figure 10 Idealised voids ratio, effective stress relationship
Thus, for normally consolidated soils, we have : e F = e I − C c log 10 (σ ′F / σ ′I ) ,
And for over-consolidated soils : e F = e I − C r log 10 (σ ′F / σ ′I )
4.7
Exercise
1.
The following results were obtained from an oedometer test carried out on a sample of clay.
The data of void ratio (e) and effective stress (σ′) were determined after equilibrium had been
reached for each applied load. Draw a graph and hence calculate the compression index of the
soil (Cc), the re-compression index (Cr) and the pre-consolidation stress (σ′pc).
8
9
indice de compression
indice de décompression ou indice de gonflement
Soil Mechanics
Settlement and Consolidation
e
σ′ (kN/m²)
0.705
18
0.698
36
0.688
72
0.673
144
0.645
288
0.600
576
0.550
1152
0.500
2304
0.508
576
0.518
144
0.532
36
0.540
18
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