Environmental Engineering Reference
In-Depth Information
(Fredlund and Rahardjo, 1993a, Lytton, 1994). Test proce-
dures for the estimation of swelling indices are presented
in Fredlund and Rahardjo (1993a) and ASTM standard. The
ASTM standards related to the measuring of swelling indices
include ASTM D4546, ASTM D2435, and ASTM D427. It
is suggested that the swelling indices commonly used for a
conventional heave analysis in one dimension can be used
for general two- and three-dimensional numerical modeling.
for the estimation of the coefficient of earth pressure at rest.
Fredlund and Rahardjo (1993a) considered elastic equilib-
rium within a homogenous, isotropic soil mass and presented
the following equation for the coefficient of earth pressure
at rest:
μ
E
u
a
−
u
w
K
0
=
μ
−
(14.69)
1
−
(
1
−
μ)H
σ
ν
−
u
a
Equation 14.69 can be rewritten as follows:
14.7.3 Determination of Poisson's Ratio
Poisson's ratio may not be a constant value for an
unsaturated, expansive soil but may be a function of stress
state (i.e., net normal stress and matric suction). Poisson's
ratio appears to increase with increasing net mean stress
and decreasing matric suction (Pereira and Fredlund 2000).
Numerous researchers (Miranda, 1988; Alonso et al., 1988;
Lloret and Ledesma, 1993) have used a constant Poisson's
ratio of 0.3 when performing numerical simulations of
unsaturated, collapsing soils. It was suggested that a Pois-
son's ratio of 0.3 might reflect the as-compacted condition
of a loosely compacted embankment. The choice of a value
for Poisson's ratio can also be related to an experimentally
observed relationship between
K
0
and OCR. Poisson's ratio
is assumed to be related to the coefficient of earth pressure
at rest,
K
0
:
μ
−
2
μ
C
m
C
s
u
a
−
u
w
1
K
0
=
μ
−
(14.70)
1
−
1
−
μ
σ
ν
−
u
a
Considering the effect of previous stress paths (i.e., previ-
ous wetting and drying, loading and unloading), the coeffi-
cient of earth pressure should have the following tangential
value:
μ
1
−
2
μ
C
m
C
s
(u
a
−
u
w
)
K
0
=
μ
−
(14.71)
1
−
1
−
μ
(σ
ν
−
u
a
)
Jaky (1944) estimated the coefficient of earth pressure for
normally consolidated soils,
K
nc
, from the effective stress
parameter
φ
:
K
nc
=
1
−
sin
φ
(14.72)
K
0
Wroth (1979) proposed two empirical
relationships
μ
=
(14.66)
+
K
0
1
between
K
0
,K
nc
, and OCR:
μ
14.7.4 Initial Matric Suction and Stress Conditions
Initial matric suction conditions can be measured in the field
or laboratory (Fredlund and Rahardjo, 1993a), but this can
be a challenging and costly process. It is also possible to
estimate in situ suctions based on theoretical considerations.
Net normal stress state within the soil mass can either
be computed by switching on gravity or simply estimated
from the total unit weight of the soil. Horizontal net normal
stresses are empirically linked to the vertical stresses through
the coefficient of earth pressure at rest,
K
0
:
K
0
=
K
nc
OCR
−
μ
(
OCR
−
1
)
(14.73)
1
−
m
3
(
1
ln
(
1
−
K
nc
)
3
(
1
−
K
0
)
+
2
K
nc
)
OCR
2
K
nc
−
=
1
+
1
+
2
K
0
1
+
2
K
0
(14.74)
where:
m
=
0.0022875PI
+
1.22 and
PI
=
plasticity index.
H
Equation 14.73 provides a reasonable fit to existing data
for soils up to an OCR of about 5. The value of Poisson's
ratio necessary to fit observed data lies in the range of
0.25-0.37 for a number of different soils. Equation 14.74
has also been proposed for soils with even higher values of
OCR (Wroth, 1979).
Mayne and Kulhawy (1982) suggested that a modified
Jaky's equation be used to estimate the coefficient of earth
pressure at rest:
σ
y
=
ρg
dy
(14.67)
0
σ
x
=
K
0
σ
y
(14.68)
where:
σ
x
,σ
y
=
horizontal and vertical net normal stress, respec-
tively,
y
=
vertical distance from ground surface, and
H
=
depth of soil under consideration.
K
nc
OCR
sin
φ
K
0
=
(14.75)
14.7.5 Coefficient of Earth Pressure At Rest
The coefficient of earth pressure can be as low as zero and
as high as the coefficient of passive earth pressure. Some
procedures have been suggested in the research literature
where:
φ
=
angle of internal friction and
OCR
=
overconsolidation ratio.
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