Environmental Engineering Reference
In-Depth Information
Poisson's ratio
μ
is defined as
relatively narrow band that is defined by Eq. 14.3 (Skemp-
ton, 1944):
dε
r
dε
a
μ
=
(14.2)
C
c
=
0
.
007
(
LL
−
10
)
(14.3)
where:
where:
=
ε
r
=
radial strain.
LL
liquid limit of the soil.
Terzaghi and Peck (1948) noted that the field compression
curve was about 30% steeper than the measured laboratory
compression curve, giving rise to the following equation for
the in situ compression index:
Even the simplest material behavioral model requires that
two material properties be defined. The elastic properties
E
and
μ
for a saturated soil generally vary with the stress
state and must be written as a function of stress state. Unsat-
urated soil behavior has a third elastic parameter,
H
, which
must be defined for a change in matric suction
u
a
−
C
c
=
0
.
009
(
LL
−
10
)
(14.4)
u
w
[i.e.,
H
u
w
)/dε
a
]
.
Changes in matric suction are
isotropic in the sense that suction acts equally in three coor-
dinate directions. However, it is possible for the elastic soil
property
H
to be anisotropic in character.
Hysteresis generally exists between the loading and
unloading sequences. Hysteresis gives rise to elastic material
properties that are further stress path and stress reversal
dependent. More elaborate elastoplastic behavioral models
for unsaturated soils address many of the issues associated
with nonlinearity and hysteresis under loading and unloading
conditions; however, these models are considered to be
outside the scope of this topic.
=
d(u
a
−
Aitkinson (1993) used typical relationships for normally
consolidated soils to arrive at the following empirical corre-
lation for the compression index of a normally consolidated
soil:
G
s
200
×
PI
C
c
=
C
c
=
0
.
0138
×
or
PI
(14.5)
where:
PI
=
plasticity index of the soil in percent and
G
s
=
2.76.
Several other empirical correlations have been published
for the compression index of a soil (Azzouz et al., 1976)
but the above-mentioned equations are sufficient for an
estimation of soil compressibility. The above-mentioned
correlations have been made for normally consolidated soils
that are generally saturated. Unsaturated soils are often
overconsolidated and the stress history must be taken into
consideration when interpreting laboratory-measured com-
pressibilities. The interpretation of consolidation test results
on overconsolidated soils is discussed later in this chapter.
Compacted soil test results also require special consideration
when assessing the compressibility of the soil.
14.2.1 Estimation of Elastic Soil Properties from
Compressibility Soil Properties
There are a number of laboratory tests that can be performed
on saturated and unsaturated soils in a conventional soil
mechanics laboratory. Modifications must be made on some
laboratory equipment in order to independently control or
measure the pore-air and pore-water pressures when testing
unsaturated soils. Laboratory tests measure the compressibil-
ity of the soil under a particular set of boundary and loading
conditions. The compressibility of a soil can change signif-
icantly along a particular stress path. The soil behavior can
generally be linearized by plotting the stress state on a log-
arithmic scale [i.e., logarithm of net normal stress loading
(σ
14.2.1.1 Estimation of Swelling Index
The swelling index
C
s
is measured during the unloading of a
soil. The swelling index is of particular interest when dealing
with unsaturated expansive soils with negative pore-water
pressures (i.e., matric suctions). Soil suction may change
with time and as a result the soil may undergo changes in
volume.
The rebound or swelling index of normally consolidated
clay soils is often about 5-10% of the compression index.
Leonards and Altschaeffl (1964) suggested that the rebound
or swelling index is usually in the range of 0.015-0.035.
Overconsolidated, expansive soils, however, can have
swelling indices
C
s
that exceed 0.10. High swelling indices
along with high initial matric suctions in the soil can result
in in situ vertical heave of 0.3-0.6m and greater.
u
a
)
].
The compression curve for a normally consolidated sat-
urated soil forms an important reference condition when
considering the behavior of unsaturated soils with a com-
plex stress history. There should be a smooth transition in
volume change behavior when moving from saturated soil
conditions to unsaturated soil conditions and vice versa. The
compression index
C
c
for a normally consolidated saturated
soil serves as a reference compressibility condition.
Numerous correlations have been made between the com-
pression index
C
c
of a normally consolidated saturated soil
and classification properties such as liquid limit. The com-
pression index measured on clay samples in an oedometer
from various countries of the world consistently fall in a
−
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