Civil Engineering Reference
In-Depth Information
magnitude as the calculated settlement. The following example problem illustrates these
calculations.
Example Problem.
To illustrate the analysis for dry and loose sand, assume that a
slope has a height of 50 ft (15.2 m) and consists of dry and loose sand that has an (
N
1
)
60
value equal to 5. Further assume that the slope has a 22
slope inclination and that the
slope is underlain by rock. A cross section illustrating these conditions is presented in
Fig. 9.20.
To use the pseudostatic method, the earthquake must not weaken the soil. Assume the
pseudostatic slope stability method can be used for the dry and loose sand and it will not
lose shear strength during the earthquake. The friction angle
of well-graded dry and
loose sand typically varies from about 30
to 34
(Table 6.12, Day 2001b). Based on an
average value, a friction angle
of the dry and loose sand that is equal to 32
will be used
in the slope stability analysis. In addition, for the design earthquake, a peak ground accel-
eration
a
max
equal to 0.20
g
will be used. Furthermore, the unit weight of the sand is assumed
to be equal to 95 lb/ft
3
(15 kN/m
3
).
Figure 9.21 shows the results of the pseudostatic slope stability analysis. For a peak
ground acceleration
a
max
of 0.20
g,
the pseudostatic factor of safety is equal to 1.116. Since
the pseudostatic factor of safety is greater than 1.0, there will be no slope deformation per
the Newmark (1965) method. However, by using the method by Tokimatsu and Seed pre-
sented in Sec. 7.4.3, a 50-ft- (15.2-m-) thick layer of dry and loose sand having an (
N
1
)
60
value of 5 will experience about 2 in (5 cm) of settlement (see Prob. 7.25). Thus the mini-
mum amount of downward movement of the top of slope will be 2 in (5 cm). Because of
FIGURE 9.20
Cross section of the slope used for the example problem.
