Environmental Engineering Reference
In-Depth Information
where:
35
Best-fit, Fredlund and Xing (1994)
Experimental data
c =
effective cohesion intercept,
30
u a
=
pore-air pressure,
25
u w =
pore-water pressure ,
20
u a
u w =
matric suction, also shown as ψ for soil
suction,
15
σ
u a
=
net normal stress on the failure plane,
10
φ =
effective angle of internal friction for the sat-
urated soil,
5
φ b
=
contribution to the shear strength due to soil
suction (i.e., matric suction or total suction).
0
10 6
1
10
100
1000
10,000
100,000
Soil suction, kPa
Equation 12.1 shows that there are independent contribu-
tions to shear strength from soil suction and net normal stress.
Early data sets indicated that the φ b angle might be relatively
constant over a limited range of matric suctions that might be
encountered in situ. Later data sets revealed that there was sig-
nificant nonlinearity in the φ b angle when larger soil suction
ranges were taken into consideration. This gave rise to nonlin-
ear equations for the unsaturated soil shear strength criterion.
(a)
100
Best-fit, Fredlund and Xing (1994)
Experimental data
80
60
40
12.2.3.2 D.G. Fredlund et al. (1996) Nonlinear Shear
Strength Equation
The D.G. Fredlund et al., (1996) equation incorporated the
SWCC written in terms of dimensionless water content d
into the unsaturated soil shear strength equation. The SWCC
was raised to a power κ which was used as a fitting param-
eter. The resulting shear strength equation was nonlinear in
form due to the nonlinearity of the SWCC:
20
0
10 6
1
10
100
1000
10,000
100,000
Soil suction, kPa
(b)
Figure 12.5 SWCCs for (a) silt soil and (b) kaolin (after
Nishimura and Fredlund, 2002).
c +
u a ) tan φ +
u w ) [ d ]tan φ
τ
=
(u a
(12.2)
where:
d
took the form of an extension of the Mohr-Coulomb failure
criterion:
=
dimensionless water content defined as θ/θ s , where
θ is any volumetric water content and θ s is the
saturated volumetric water content, and
c +
u a ) tan φ +
u w ) tan φ b
τ
=
(u a
(12.1)
κ
=
fitting parameter for the SWCC.
100
80
60
40
20
0
0
25,000
50,000
75,000
100,000
125,000
150,000
Total suction, kPa
Figure 12.6 Relationship between compressive strength and total suction for silt soil (Nishimura
and Fredlund, 2002).
 
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