Civil Engineering Reference
In-Depth Information
Because Eq. (9.3) utilizes the peak ground acceleration
a
max
from the earthquake, the
analysis tends to be more accurate for small or medium-sized failure masses where the seis-
mic coefficient
k
h
is approximately equal to
a
max
g
(see Sec. 9.2.2).
9.3.2 Example Problem
Consider the example problem in Sec. 9.2.7. For this example problem, it was determined
that the pseudostatic factor of safety
0.734 for a peak ground acceleration
a
max
0.40
g
(i.e., the seismic coefficient
k
h
is equal to 0.40). Since the pseudostatic factor of safety is
less than 1.0, the Newmark (1965) method can be used to estimate the slope deformation.
Although the stability analysis is not shown, the SLOPE/W (Geo-Slope 1991) computer
program was utilized to determine the value of
k
h
that corresponds to a pseudostatic factor
of safety of 1.0. This value of
k
h
is equal to 0.22, and thus the yield acceleration
a
y
is equal
to 0.22
g.
Substituting the ratio of
a
y
a
max
0.22
g
0.40
g
0.55 into Eq. (9.3) yields
log
d
0.90
log [(1
0.55)
2.53
(0.55)
1.09
]
or
log
d
0.90
log 0.254
0.306
And solving the above equation reveals the slope deformation
d
is equal to about 2 cm.
Thus, although the pseudostatic factor of safety is well below 1.0 (i.e., pseudostatic factor
of safety
0.734), Eq. (9.3) predicts that only about 2 cm of downslope movement will
occur during the earthquake.
9.3.3
Limitation of the Newmark Method
Introduction.
The major assumption of the Newmark (1965) method is that the slope will
deform only when the peak ground acceleration
a
max
exceeds the yield acceleration
a
y
.
This
type of analysis is most appropriate for a slope that deforms as a single massive block, such
as a wedge-type failure. In fact, Newmark (1965) used the analogy of a sliding block on an
inclined plane to develop the displacement equations.
A limitation of the Newmark (1965) method is that it may prove unreliable for those
slopes that do not tend to deform as a single massive block. An example is a slope com-
posed of dry and loose granular soil (i.e., sands and gravels). The individual soil grains that
compose a dry and loose granular soil will tend to individually deform, rather than the
entire slope deforming as one massive block.
The earthquake-induced settlement of dry and loose granular soil is discussed in Sec. 7.4
(i.e., volumetric compression). As discussed in that section, the settlement of a dry and loose
granular soil is primarily dependent on three factors: (1) the relative density
D
r
of the soil,
which can be correlated with the SPT blow count (
N
1
)
60
value; (2) the maximum shear strain
induced by the design earthquake; and (3) the number of shear strain cycles.
The amount of lateral movement of slopes composed of dry and loose granular soils is
difficult to determine. The method outlined in Sec. 7.4 will tend to underestimate the
amount of settlement of a slope composed of dry and loose granular soil. This is because in
a sloping environment, the individual soil particles not only will settle, but also will deform
laterally in response to the unconfined slope face. In terms of initial calculations, the
method outlined in Sec. 7.4 could be used to determine the minimum settlement at the top
of slope. However, the actual settlement will be greater because of the unconfined slope
condition. In addition, it is anticipated that the lateral movement will be the same order of
