Shear Strength Applications in Plastic and Limit Equilibrium - Unsaturated Soil Mechanics in Engineering Practice - page 597

AEV = 10 kPa

AEV = 100 kPa

1.0

0.8

0.6

0.4

0.2

Bao et al. (1998)

0.0

− 0.2

1 10 100 1000 10,000

Soil suction, kPa

Figure 12.11 The ζ parameter associated with Bao et al. (1998) estimation equation corre-
sponding to air-entry values of 10 and 100 kPa and residual suction values of 100 and 1000 kPa,
respectively.

by dividing by the saturated volumetric water content (i.e.,
d =

The fitting parameter κ used in the Fredlund et al. (1996)
shear strength equation was designated as a constant value.
Values for the κ parameter were obtained by Garven and
Vanapalli (2006) through use of a curve-fitting correlation
with the plasticity index of the soil. Later, Goh et al. (2010)
suggested that the fitting parameter κ used in the Fredlund
et al. (1996) equation [and the Lee et al. (2005) equation],
varied nonlinearly with matric suction. This conclusion was
arrived at after performing back-calculations on a series of
published shear strength and SWCC data. Shear strength
data were separated into two categories: namely, soils tested
after drying towards an equilibrium state and soils tested
after wetting towards an equilibrium state. The observed κ
values for several soils dried to an equilibrium state are
shown in shown in Fig. 12.12. The new fitting parameter
was designated as κ and had a value of zero when matric
suction was equal to or lower than the air-entry value of
the soil. The κ value was found to increase in accordance
with the logarithm difference between a designated matric
suction value and the air-entry value.
A parametric study was undertaken by Goh et al. (2010) to
incorporate the κ parameter into the proposed shear strength
equation. Some parameters were used together with the log-
arithm term to represent the κ parameter. The parameters
cover a relatively wide range of soil properties as well as
a wide range of soil suction values. The regression anal-
ysis showed that two parameters: namely, y and b were
needed to determine the parameters for estimating the shear
strength of an unsaturated soil. The y and b variables were
found to be related to other soil properties through use of
a correlation with experimental data. The estimation of the
unsaturated soil shear strength was divided into two parts:
namely, one equation was applied up to the air-entry value of
the soil [i.e., (u a −

θ/θ s ). The SWCC was used to control the secant slope
between soil suction and unsaturated shear strength. The
assumption was made that the φ b angle is equal to the effec-
tive angle of internal friction for matric suctions lower than
the air-entry value of the soil. Matric suction values below
the air-entry value contribute to the effective stresses of a
saturated soil.
The empirical equation proposed by Goh et al. (2010)
was developed based on three data sets where shear
strengths corresponding to the drying curve (i.e., drying
shear strength) were measured and three data sets where
shear strengths corresponding to the drying and wetting
were measured along with the SWCCs. The data sets used
by Goh et al. (2010) are shown in Table 12.1.

Table 12.1 Summary of Published Soil Data Sets Used
in Development of Goh et al. (2010) Equation

USCS

Authors Materials Classification

Escario and Juca
(1989)

Madrid clay sand CL

Han (1996) Bukit Timah granitic

residual soil

CL

Lee et al. (2005) Korea weathered
granitic residual soil

SM

Miao et al.
(2002)

Nanyang expansive
soil

CH

Rahardjo et al.
(2004)

Jurong sedimentary
formation residual
soil

CL

u w ) b ], and another equation was applied
for suctions beyond the air-entry value. The equations are

Thu et al. (2006) Compacted kaolin MH