Shear Strength Applications in Plastic and Limit Equilibrium - Unsaturated Soil Mechanics in Engineering Practice - page 642

Figure 12.79 Use of piezometric line to designate pore-water pressures.

Table 12.7 Elements of Static Equilibrium Satisfied by Various Limit Equilibrium Methods

Force Equilibrium

First Direction a Second Direction a Method (e.g., Vertical) (e.g., Horizontal) Moment Equilibrium

Ordinary or Fellenius Yes No Yes

Bishop's simplified Yes No Yes

Janbu's simplified Yes Yes No

b —

Janbu's generalized Yes Yes

Spencer Yes Yes Yes

Morgenstern-Price Yes Yes Yes

Corps of Engineers Yes Yes No

Lowe-Karafiath Yes Yes No

a Any of two orthogonal directions can be selected for the summation of forces.
b Moment equilibrium is used to calculate interslice shear forces.

methods of slices. The statics used in each of the methods of
slices for computing the factor of safety are summarized in
Table 12.8. The ordinary and Bishop's simplified methods
use moment equilibrium, while Janbu's simplified, Janbu's
generalized, the Lowe and Kariafiath, and the Corps of Engi-
neers methods use force equilibrium in computing the factor
of safety. The Spencer and Morgenstern-Price methods sat-
isfy both moment and force equilibrium when computing
the factor of safety. The Spencer and Morgenstern-Price
methods are similar in principle to the GLE method which
satisfies force and moment equilibrium when calculating the
factor of safety. The interslice force assumptions used in
simulating the various methods are given in Table 12.8.

12.6 OPTIMIZATION PROCEDURES TO SOLVE
FOR FACTOR OF SAFETY

The assumptions related to the interslice force function in
limit equilibrium methods are not required when a finite
element stress-strain analysis is used to obtain the normal
and shear stresses acting at the base of slices (Fredlund
and Scoular, 1999). A stress analysis provides normal and
shear stresses through the use of the finite element numerical
method where gravity forces are switched on. The equation
for calculating the factor of safety becomes linear. Assump-
tions regarding the shape of the critical slip surface are
not necessary when an appropriate optimization technique
is introduced into the analysis.