Shear Strength Applications in Plastic and Limit Equilibrium - Unsaturated Soil Mechanics in Engineering Practice - page 595

Shear strength equations for
unsaturated Soils

Fitting equations
- Equations that can be best fit to a
dataset for the determination of one or
more fitting parameters

Estimation equations
- Based on saturated shear strength
parameters and other information

SWCC and strength at
residual suction

SWCC and classification
properties

Fredlund et al. (1978)

Fredlund et al. (1996)

Rassam and Cook (2005)

Vanapalli et al. (1996b)

Fredlund et al. (1996)

Vilar (2006)

Oberg and Sallfors (1997)

Khalili and Khabbaz (1998)

Bao et al. (1998)

Goh et al. (2010)

Figure 12.8 Categorization of shear strength equations for unsaturated soils.

The shear strength associated with soil suction, τ s , can be
written as

Equation 12.8 was originally developed through compar-
isons of measured and predicted values of shear strength for
determining the fitting parameter κ This process has been
continued as further experimental shear strength data have
become available.

u w ) θ
θ s

κ

tan φ τ s = (u a − (12.7)

Garven and Vanapalli (2006) provided an empirical rela-
tionship between the fitting parameter κ and the plasticity
index of the soil, PI. The proposed empirical equation link-
ing the κ factor to the plasticity index has been revised a
couple times but Figure 12.9 shows the latest experimental
results and the form for the κ factor equation.

12.2.4.3 Oberg and Sallfors (1997) Estimation Shear
Strength Equation
Oberg and Sallfors (1997) proposed an unsaturated soil shear
strength equation that used the instantaneous degree of sat-
uration S of the soil to describe shear strength. The con-
tribution of soil suction to shear strength was assumed to

0 . 0016 ( PI ) 2 κ =− + 0 . 0975 ( PI ) + 1 (12.8)

8

F. Botkin silt
G. Ste. Rosalie clay
H. LD Dhanauri clay
I. HD Dhanauri clay
K. Nanyang clay

A. Red silty clay
B. Madrid gray clay
C. Adam clay
D. Indian Head till (dry of optimum)
E. Indian Head till (dry of optimum)

7

6

5

4

= -0.0016 x (IP) 2 + 0.0975 x IP +1 κ

3

C B

I

K

F D , E

A

2

H

G

Best-fit parameter
68% Confident interval

1

0

0 10 20 30 40 50

Plasticity index, I p

Figure 12.9 Relationship between parameter κ and plasticity index for natural and statically
compacted soils (after Garven and Vanapalli, 2006).