Shear Strength Applications in Plastic and Limit Equilibrium - Unsaturated Soil Mechanics in Engineering Practice - page 633

Figure 12.70 Typical steep natural slope with deep groundwater table.

surface through use of a trial-and-error search technique.
A large number of potential slip surfaces were analyzed
through the soil mass, and the slip surface which yielded
the minimum computed factor of safety was selected as the
critical slip surface. There were a variety of methods of
slices that made use of a similar procedure to calculate the
minimum factor of safety of a slope.
The analytical formulations proved to be indeterminate
and as a result there were numerous methods of slices pro-
posed over time. The formulation showed that there were
more unknowns than there were equations to solve the prob-
lem. Consequently, a variety of assumptions were made to
render the slope stability analysis determinate. The name of
researcher(s) who made each of the assumptions was usually
attached to the method for calculating the factor of safety.
The summation of forces in orthogonal directions, as well as
the moment equilibrium, were given consideration in each
analysis; however, it is possible to consider all the methods
of slices within a general limit equilibrium framework (Fred-
lund and Krahn, 1977). The primary difference between the
various methods of slices proposed can be traced to differ-
ences in the manner in which the normal force at the base
of a slice was calculated. There was also a difference in the
manner in which overall static equilibrium was satisfied.
Computational advancements have led to the realization
that other approaches can also be used to perform a slope
stability analysis. For example, it was realized that it was

possible to use numerical modeling and the “switch-on” of
gravity forces to determine the state of stress in a soil mass.
It was also possible to utilize optimization techniques devel-
oped in other areas of engineering for the determination of
the minimum factor of safety of a slope. It also became pos-
sible for the shape of the slip surface and the critical location
of the slip surface to become part of the overall solution for
the minimum factor of safety.
The optimization procedure that has been most commonly
used to locate the critical slip surface is referred to as the
“dynamic programming” technique. There are distinct advan-
tages associated with the use of optimization techniques for
the calculation of the factor of safety of a slope; however,
engineers have gained extensive experience in the method-of-
slices procedures. It is important that studies be undertaken to
verify the similarities and differences that may exist between
the two approaches to the analysis of a slope.
Figure 12.71 subdivides methods of slope stability analysis
into two broad categories: methods of slices and optimiza-
tion methods. Methods of slices have been extensively used
in engineering practice, but the optimization technique lends
itself well to computational procedures. At the core of the
optimization technique is the solution of two or more partial
differential equations for the computation of the stress states
inasoilmass.
The trend in solving all saturated-unsaturated soil prob-
lems is toward the solution of one or more partial differential