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be equal to (
S
tan
φ
) and the shear strength equation was
written as
12.2.4.5 Bao et al. (1998) Estimation Shear Strength
Equation
Bao et al., (1998) assumed that the soil behaved as a sat-
urated soil as long as the matric suction was less than the
air-entry value of the soil:
c
+
u
a
)
tan
φ
+
u
w
)
[
S
]tan
φ
τ
=
(σ
−
(u
a
−
(12.9)
12.2.4.4 Khalili and Khabbaz (1998) Estimation Shear
Strength Equation
Khalili and Khabbaz (1998) assumed that the soil behaved
as a saturated soil as long as the matric suction was less
than the air-entry value of the soil:
c
+
u
a
)
tan
φ
+
u
w
)
tan
φ
τ
=
(σ
−
(u
a
−
(12.13)
Once the air-entry value was exceeded, the suction com-
ponent of shear strength was reduced by multiplying soil
suction by the variable
ζ
, as shown in the equation
c
+
u
a
)
tan
φ
+
u
w
)
tan
φ
τ
=
(σ
−
(u
a
−
(12.10)
c
+
u
a
)
tan
φ
+
u
w
)
[
ζ
]tan
φ
τ
=
(σ
−
(u
a
−
(12.14)
The parameter
ζ
was defined as
Once the air-entry value was exceeded, the suction com-
ponent of shear strength was reduced by multiplying soil
suction by the variable
λ
, and the shear strength equation
was written as
log
(u
a
−
u
w
)
r
−
log
(u
a
−
u
w
)
ζ
=
(12.15)
log
(u
a
−
u
w
)
r
−
log
(u
a
−
u
w
)
b
Figure 12.11 shows a plot of
ζ
versus soil suction for two
air-entry values. The
ζ
value is 1.0 at any air-entry value and
decreases to a value of zero at residual suction conditions.
In other words, the influence of soil suction on the shear
strength of an unsaturated soil was normalized between the
air-entry value and residual suction. It was assumed that the
shear strength of the soil remained constant beyond residual
suction. This behavior is quite consistent with shear strength
behavior observed for fine-grained soils.
c
+
u
a
)
tan
φ
+
u
w
)
[
λ
]tan
φ
τ
=
(σ
−
(u
a
−
(12.11)
The parameter
λ
was defined as
−
0
.
55
u
a
−
u
w
λ
=
(12.12)
(u
a
−
u
w
)
b
Figure 12.10 shows a plot of
λ
versus soil suction for
two air-entry values. The
λ
value is 1.0 for shear strengths
up to the air-entry value and then decreases without any
influence from residual suction. The rate of decrease of
λ
is simply influenced by the air-entry value of the soil. It is
assumed that soil suction always provides a positive increase
in strength up to 10
6
kPa. In each case, the
λ
parameter
decreases in response to an exponent power of -0.55 for all
soil types.
12.2.4.6 Goh et al. (2010) Estimation Shear Strength
Equation
Goh et al. (2010) proposed an equation to estimate the shear
strength under drying and wetting conditions. The Goh et al.
(2010) equation is a modification of the D.G. Fredlund et al.
(1996) equation and the Lee et al. (2005) equation. Volu-
metric water content was written in a dimensionless form
AEV
=
10 kPa
AEV
=
100 kPa
1.0
0.8
0.6
0.4
0.2
Khalili & Khabbaz (1998)
0.0
−
0.2
1
10
100
1000
10,000
Soil suction, kPa
Figure 12.10
The
λ
parameter associated with Khalili and Khabbaz (1998) estimation equation
corresponding to air-entry values of 10 and 100 kPa.
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