Civil Engineering Reference
In-Depth Information
Wa
max
Wa
___
_____
F
h
ma
g
g
k
h
W
(9.1)
where
F
h
horizontal pseudostatic force acting through the centroid of sliding
mass, in an out-of-slope direction, lb or kN. For slope stability analy-
sis, slope is usually assumed to have a unit length (i.e., two-dimen-
sional analysis).
m
total mass of slide material, lb or kg, which is equal to
W
g
.
W
total weight of slide material, lb or kN.
a
acceleration, which in this case is the maximum horizontal accelera-
tion at ground surface caused by earthquake (
a
a
max
), ft /s
2
or m/s
2
.
a
max
maximum horizontal acceleration at ground surface that is induced by
the earthquake, ft /s
2
or m/s
2
. The maximum horizontal acceleration is
also commonly referred to as the peak ground acceleration (see Sec. 5.6).
a
max
g
k
h
seismic coefficient, also known as pseudostatic coefficient (dimen-
sionless).
Note that an earthquake could subject the sliding mass to both vertical and horizontal
pseudostatic forces. However, the vertical force is usually ignored in the standard pseudo-
static analysis. This is because the vertical pseudostatic force acting on the sliding mass
usually has much less effect on the stability of a slope. In addition, most earthquakes pro-
duce a peak vertical acceleration that is less than the peak horizontal acceleration, and
hence
k
v
is smaller than
k
h
.
As indicated in Eq. (9.1), the only unknowns in the pseudostatic method are the weight
of the sliding mass
W
and the seismic coefficient
k
h
.
Based on the results of subsurface
exploration and laboratory testing, the unit weight of the soil or rock can be determined,
and then the weight of the sliding mass
W
can be readily calculated. The other unknown is
the seismic coefficient
k
h
,
which is much more difficult to determine. The next section dis-
cusses guidelines for the selection of the seismic coefficient
k
h
for the pseudostatic method.
9.2.2
Selection of the Seismic Coefficient
The selection of the seismic coefficient
k
h
takes considerable experience and judgment.
Guidelines for the selection of
k
h
are as follows:
1.
Peak ground acceleration:
Section 5.6 presents an in-depth discussion of the deter-
mination of the peak ground acceleration
a
max
for a given site. The higher the value of
the peak ground acceleration
a
max
, the higher the value of
k
h
that should be used in the
pseudostatic analysis.
2.
Earthquake magnitude:
The higher the magnitude of the earthquake, the longer the
ground will shake (see Table 2.2) and consequently the higher the value of
k
h
that should
be used in the pseudostatic analysis.
3.
Maximum value of k
h
:
When items 1 and 2 as outlined above are considered, keep in
mind that the value of
k
h
should never be greater than the value of
a
max
g.
4.
Minimum value of k
h
:
Check to determine if there are any agency rules that require a
specific seismic coefficient. For example, a common requirement by many local agen-
cies in California is the use of a minimum seismic coefficient
k
h
0.15 (Division of
Mines and Geology 1997).
5.
Size of the sliding mass:
Use a lower seismic coefficient as the size of the slope fail-
ure mass increases. The larger the slope failure mass, the less likely that during the
earthquake the entire slope mass will be subjected to a destabilizing seismic force act-
ing in the out-of-slope direction. Suggested guidelines are as follows:
