Theory to Practice of Unsaturated Soil Mechanics - Unsaturated Soil Mechanics in Engineering Practice - page 23

Z Y

X

4,000

550

Z (m)

530
0

3,000

1,000

2,000

Y (m)

X (m)

2,000

1,000

2,500 500

Figure 1.21 Finite element mesh for three-dimensional seepage analysis of a tailings pond.

1.6.8 Example of Stress and Shear Strength
Applications
Slope stability analyses have conventionally been performed
using one of several possible methods of slices where the
normal stresses at the base of a slice are computed from
static equilibrium of the complete slice. Each method of
slices uses different assumptions and elements of statics to
render the solution determinate. Consequently, each method
computes a slightly different normal force at the base of each
slice. More recently it has been shown that the normal force
at the base of a slice can be computed from a stress analysis
that involves “switching-on” the gravity body force (Yam-
agami and Ueta, 1988; Pham and Fredlund, 2003). The total
unit weight of the soil is used in the analysis as the gravity
body force. Positive and negative pore-water pressures are
computed using an independent analysis.
The normal forces computed by “switching on” gravity
are quite similar to those computed using the methods of
slices, but the stress analysis approach provides some addi-
tional advantages (Pham and Fredlund, 2003). For example,
the stress analysis needs to be performed one time and the
nonlinearity associated with computing the normal forces
at the base of a slice is removed. It is possible to use an
optimization technique to determine the shape and loca-
tion of the critical slip surface once the stress states have

been computed. Pore-water pressure can be computed in
an uncoupled manner using a saturated-unsaturated seepage
analysis. Figure 1.22 shows the results of using a stress anal-
ysis on a slope to determine the location of the critical slip
surface. The location of the critical slip surface is part of
the “dynamic programming” technique.
Figure 1.23 shows the results of a comparative study
between the “dynamic programming” approach and a
conventional method-of-slices approach. Method-of-slices
results and dynamic programming results have been shown
to be quite similar (Pham et al., 2001). The computed fac-
tors of safety are slightly affected by the assumed Poisson's
ratio for the soil. The dynamic programming technique has
advantages from a theoretical, computational, and practical
standpoint. The stress-deformation model utilized does not
appear to significantly affect the computation of in situ

stresses.

1.6.9 Example of Combined Stress, Seepage,
and Deformation Analysis
A common and relevant problem in unsaturated soil
mechanics involves the prediction of the rate and amount of
swelling that an expansive soil might experience under vari-
ous moisture flux boundary conditions. The rate and amount
of collapse that a collapsible soil might experience are also