Environmental Engineering Reference
In-Depth Information
100
ψ
aev
80
60
40
20
ψ
r
- Residual suction
(
ψ
r
,
S
r
)
S
r
- Residual degree of saturation
0
10
6
1
10
100
1000
10,000
100,000
Soil suction, kPa
(a)
600
400
c
ult
200
φ
'
c'
0
0
200
400
600
800 1000 1200 1400 1600 1800 2000
Soil suction, kPa
(b)
Figure 12.18
Assumed relationship between SWCC and shear strength envelope for unsaturated
soil: (a) SWCC and key features; (b) hyperbolic function and assumed conditions to derive
a
and
b
(after Vilar, 2006).
where:
equation was proposed for the soil suctions from the air-
entry value up to the high-soil-suction range. The Lee et al.
(2005) equation uses the SWCC and two fitting parameters,
namely,
κ
and
λ
to provide a best fit for shear strength
beyond the air-entry value of the soil:
c
measured
=
shear strength at the measured high soil suc-
tion and
ψ
measured
=
high measured suction representing equilib-
rium conditions.
c
+
u
w
)
b
]tan
φ
τ
=
[
(σ
−
u
a
)
+
(u
a
−
u
w
)
b
]
κ
d
[1
λ
(σ
u
a
)
]tan
φ
(12.30)
+
[
(u
a
−
u
w
)
−
(u
a
−
+
−
It should be noted that no soil parameters from the SWCC
are directly used in the development of the Vilar (2006)
model. However, the general character of the SWCC was
used as justification for the form of the unsaturated soil
shear strength equation.
One shear strength test on a soil specimen that is at or
above the residual suction state is all that is required to use
the Vilar (2006) model as long as the saturated effective
shear strength parameters are known. Figure 12.18 illus-
trates the definition of the
c
ult
term that is used in estimating
the unsaturated soil shear strength envelope. Comparisons
between the Vilar (2006) model estimations and laboratory
test results have been shown to be reasonable (Fig. 12.19).
where:
κ
and
λ
=
fitting parameters,
(u
a
−
u
w
)
b
=
air-entry value of the soil, and
d
=
dimensionless volumetric water content.
12.2.5 Comparison of Estimated and Measured
Unsaturated Soil Shear Strengths
Each of the proposed equations for estimating unsaturated
soil shear strength has been verified using a limited number
of data sets. It is always desirable to verify any proposed
shear strength equations with many sets of laboratory results
tested over a wide range of soil suctions. Independent labo-
ratory data sets are presently somewhat limited. Therefore,
it is difficult to undertake detailed verification studies on
all equations that have been proposed for the estimation of
unsaturated shear strength.
Table 12.2 summarizes equations that utilize the SWCC
for
12.2.4.9 Lee et al. (2005) Unsaturated Soil Shear
Strength Equation
Lee et al., (2005) suggested using one linear shear strength
equation for soil suctions up to the air-entry value. The shear
strength equation prior to the air-entry value has the shear
strength parameters of a saturated soil. Another nonlinear
the estimation of
the shear
strength relationship.
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