Civil Engineering Reference
In-Depth Information
Effective stress pseudostatic analysis:
c
L
(
W
cos
F
h
sin
uL
) tan
c
L
N
tan
________________
_________________________________
FS
W
sin
F
h
cos
W
sin
F
h
cos
(9.2
b
)
where FS
factor of safety for the pseudostatic slope stability (dimensionless parameter)
average pore water pressure along the slip surface, kPa or lb/ft
2
Because the wedge method is a two-dimensional analysis based on a unit length of slope
(i.e., length
1 m or 1 ft), the numerator and denominator of Eq. (9.2) are in pounds (or
kilonewtons). The resisting force in Eq. (9.2) is equal to the shear strength (in terms of total
stress or effective stress) of the soil along the slip surface. The driving forces [Eq. (9.2)] are
caused by the pull of gravity and the pseudostatic force and are equal to their components
that are parallel to the slip surface.
The total stress pseudostatic analysis is performed in those cases where the total stress
parameters of the soil are known. A total stress analysis could be performed by using the
consolidated undrained shear strength
c
and
or the undrained shear strength
s
u
of the slip
surface material. When the undrained shear strength is used,
s
u
c
and
0 are substi-
tuted into Eq. (9.2
a
). A total stress pseudostatic analysis is often performed for cohesive
soil, such as silts and clays.
The effective stress pseudostatic analysis is performed in those cases where the effective
stress parameters (
c
and
) of the soil are known. Note that in order to use an effective stress
analysis [Eq. (9.2
b
)], the pore water pressure
u
along the slip surface must also be known. The
effective stress analysis is often performed for cohesionless soil, such as sands and gravels.
u
9.2.4
Method of Slices
The most commonly used method of slope stability analysis is the
method of slices,
where
the failure mass is subdivided into vertical slices and the factor of safety is calculated based
on force equilibrium equations. A circular arc slip surface and rotational type of failure
mode are often used for the method of slices, and for homogeneous soil, a circular arc slip
surface provides a lower factor of safety than assuming a planar slip surface.
The calculations for the method of slices are similar to those for the wedge-type analy-
sis, except that the resisting and driving forces are calculated for each slice and then
summed in order to obtain the factor of safety of the slope. For the
ordinary method of slices
[also known as the
Swedish circle method
or
Fellenius method,
(Fellenius 1936)], the equa-
tion used to calculate the factor of safety is identical to Eq. (9.2), with the resisting and dri-
ving forces calculated for each slice and then summed to obtain the factor of safety.
Commonly used methods of slices to obtain the factor of safety are listed in Table 9.3.
The method of slices is not an exact method because there are more unknowns than equi-
librium equations. This requires that an assumption be made concerning the interslice
forces. Table 9.3 presents a summary of the assumptions for the various methods. For
example, for the ordinary method of slices (Fellenius 1936), it is assumed that the resultant
of the interslice forces is parallel to the average inclination of the slice
. It has been deter-
mined that because of this interslice assumption for the ordinary method of slices, this
method provides a factor of safety that is too low for some situations (Whitman and Bailey
1967). As a result, the other methods listed in Table 9.3 are used more often than the ordi-
nary method of slices.
Because of the tedious nature of the calculations, computer programs are routinely used
to perform the analysis. Most slope stability computer programs have the ability to perform
pseudostatic slope stability analyses, and the only additional item that needs to be input is
the seismic coefficient
k
h
.
In southern California, an acceptable minimum factor of safety
of the slope is 1.1 to 1.15 for a pseudostatic slope stability analysis.
