Civil Engineering Reference
In-Depth Information
FIGURE 9.19
Diagram illustrating the Newmark method. (
a
)
Acceleration versus time; (
b
) velocity versus time for the darkened por-
tions of the acceleration pulses; (
c
) the corresponding downslope dis-
placement versus time in response to the velocity pulses. (
After Wilson
and Keefer 1985.
)
of the four main parameters discussed above is as follows (Ambraseys and
Menu 1988):
log
d
0.90
log
[
(
1
a
y
a
max
)
2.53
(
a
max
)
1.09
]
a
y
____
____
(9.3)
where
d
estimated downslope movement caused by the earthquake, cm
a
y
yield acceleration, defined as the horizontal earthquake acceleration that
results in a pseudostatic factor of safety that is exactly equal to 1.0
a
max
peak ground acceleration of the design earthquake
Based on the Newmark (1965) method, Eq. (9.3) is valid only for those cases where the
pseudostatic factor of safety is less than 1.0. In essence, the peak ground acceleration
a
max
must be greater then the horizontal yield acceleration
a
y
.
To use Eq. (9.3), the first step is
to determine the pseudostatic factor of safety, using the method outlined in Sec. 9.2.
Provided the pseudostatic factor of safety is less than 1.0, the next step is to reduce the value
of the seismic coefficient
k
h
until a factor of safety exactly equal to 1.0 is obtained. This can
usually be quickly accomplished when using a slope stability computer program. The value
of
k
h
that corresponds to a pseudostatic factor of safety equal to 1.0 can easily be converted
to the yield acceleration [i.e., see Eq. (9.1)]. Substituting the values of the peak ground
acceleration
a
max
and the yield acceleration
a
y
into Eq. (9.3), we can determine the slope
deformation in centimeters.
