Shear Strength Applications in Plastic and Limit Equilibrium - Unsaturated Soil Mechanics in Engineering Practice - page 634

Categorization of slope stability methods
(based on calculation of normal stress on slip surface)

"Switching on" gravity force

Statics of individual slices

Methods of slices

Optimization techniques

Dynamic programming

General limit equilibrium, GLE
Moment equibrium factor of
safety and / or
force equilibrium factor of
safety

Calculation of the minimum
factor of safety and the shape
and location of the critical slip
surface

Calculation of the minimum
factor of safety through a trial-
and-error process to find the
location of the critical slip
surface (shape assumed)

Figure 12.71 Categorization of slope stability methods based on methodology for calculating
normal stress at various points along slip surface.

equations through numerical modeling. It is anticipated that
with time optimization techniques will increase in popularity
for the computation of the factor of safety of a slope. Pore-
water pressures are also commonly assessed using numerical
modeling and the results can readily be combined with the
slope stability analysis.

12.5.3 General Procedure for Methods of Slices
A study of the stability of a slope with negative pore-water
pressures involves the following steps: (1) a survey of the
elevation of the ground surface on a selected section perpen-
dicular to the slope, (2) advancement of several boreholes to
identify the stratigraphy and obtain undisturbed soil samples,
(3) laboratory testing of undisturbed soil specimens to obtain
suitable shear strength parameters for each stratigraphic unit
(i.e., c , φ , and φ b ), and (4) measurement or estimation of
negative pore-water pressures above the groundwater table.
These steps provide the input data for performing a stability
analysis. However, the location and shape of the most critical
slip surface is unknown (Fig. 12.70). A particular combina-
tion of actuating and resisting forces along a slip surface of
unknown shape and location will produce the lowest factor of
safety for the slope. The location of the slip surface is known
in the case of a slope that has already failed.
The methods of slices are presented within the context
of the general limit equilibrium (GLE) method which con-
siders force and moment equilibrium. The GLE equations
can then be specialized to each of the common methods of
slices. Common to all the methods of slices is an assumption
regarding the shape of the slip surface.

12.5.2 Determination of Normal Stress on Slip Surface
for Methods of Slices
There are a number of differences between each of the meth-
ods of slope stability analysis; however, probably of most
significant difference is the manner in which the normal
force is computed at the base of a slice. The various meth-
ods of slices give rise to differences in the calculated normal
force at the base of a slice because of the assumptions that
are made with regard to interslice forces. Each method of
slices considers vertical force equilibrium on a slice and the
primary variable influencing the calculation of the normal
force is gravity force (i.e., unit weight of the soil), immedi-
ately above the base of the slip surface.
The optimization technique switches on the gravity force
over the entire soil mass and uses a typical stress-strain con-
stitutive model for the computation of the stress state at all
points in the soil mass. This process can be performed one
time and the analysis for the factor of safety becomes deter-
minate from the standpoint of calculating the normal force at
the base of a slice.
The commonly used methods of slices can be extended to
embrace the analysis involving unsaturated soils. Optimiza-
tion techniques can also be extended to consider unsaturated
soils. The use of the optimization procedure is explained
after the methods-of-slices procedure.

12.5.4 Trial-and-Error Search for Critical Slip
Surface When Using Methods of Slices
The shape of the unknown slip surface is generally assumed.
The location of the critical slip surface is determined using a
trial-and-error procedure. Let us first assume that the shape of
the slip surface is circular. Agrid of centers can be selected and
the radius is varied at each center of rotation. The end result