G-5.
Example 5 - Landslide hazard evaluation
(4) Deformation. Several simplified methods
based on the concept of yield acceleration originally
The general method for evaluating the seismic stability
proposed by Newmark (1965) are utilized to estimate
of slopes involves both pseudo-static and deformation
deformation.
analysis procedures, as illustrated below.
a.
Pseudo-static slope stability analysis
(a)
Makdisi and Seed (1978). The Makdisi and
Seed (1978) method normalizes displacement
by kmax, To, and gravity (Figure F-17). Based
Pseudo-static slope stability analyses conservatively
on the ratio of k y to kmax of 0.75 and a moment
evaluate the occurrence of a slope failure due to
magnitude of 6.5, the normalized displacement
earthquake loading. If the results of the pseudo-static
is equal to approximately 0.003 seconds (note
analysis indicate potential deformation of the slope
that the units of seconds will be replaced by
(factor of safety < 1), a deformation analysis is
inches when the normalizing values are
performed to estimate the displacement. A static limit-
factored out). An estimated deformation of
equilibrium slope stability analysis performed for the
0.14 inches (0.4 cm) was calculated by
site determined that the critical failure surface would
multiplying the normalized displacement by
intersect the foundation of the building (Figure G-14).
the values of k max, T o, and gravity.
This failure surface was then used for the pseudo-static
slope stability analysis. The seismic coefficient was
(b)
Egan (1994). The Egan (1994) relationship
assumed to be equal to the peak horizontal acceleration
between deformation and the ratio of critical
of 0.40 g. The results of the pseudo-static analysis
acceleration is normalized by k max and the
indicate a marginal susceptibility to earthquake-induced
number of earthquake cycles. A magnitude 6.5
landsliding with a factor of safety of 0.92. A
earthquake contains approximately eight cycles
deformation analysis was then performed to estimate the
(Figure F-18a). Based on the ratio of ky to kmax
displacement.
of 0.75, the displacement factor was estimated
b.
Deformation analysis
to be 0.3 (Figure F-18b). An estimated
deformation of 0.4 inches (1 cm) was
determined by multiplying the displacement
The deformation analysis procedure is based on
factor by the values of k max and the number of
Newmark' (1965) concept of yield acceleration. For a
s
cycles.
specified potential sliding mass, the acceleration
induced by the earthquake is compared with the yield
(c)
Franklin and Chang (1977). The range of the
acceleration. When the induced acceleration exceeds
Franklin and Chang (1977) simplified method
the yield acceleration, downslope movements will occur
has a lower bound of one inch of deformation
along the direction of the assumed failure plane. The
(Figure F-19). The critical acceleration ratio of
movement will stop when the induced acceleration
0.75 is outside this range. However, judging
drops below the yield acceleration.
from the trend of the curves, a deformation of
less than one inch (2.5 cm) can be assessed.
(1) Yield acceleration, ky. The yield acceleration
is the acceleration at which the potential sliding surface
(d)
Yegian et al. (1991). The Yegian et al. (1991)
would develop a factor of safety of unity. For this site,
simplified method for estimating permanent
ky was determined to be 0.30 g by iteratively adjusting
deformation normalizes displacement by k max,
the seismic coefficient in the pseudo-static analysis until
the factor of safety reached a value of unity.
To2 , number of cycles, and gravity (Figure F-
20). A magnitude 6.5 earthquake contains
approximately eight cycles (Figure F-18a).
parameter represents the peak or maximum acceleration
Based on the ratio of ky to kmax of 0.75, the
induced within the sliding mass. kmax was assumed to
normalized permanent deformation was
be equal to the peak horizontal acceleration of 0.40 g.
estimated to be 0.001. An estimated
deformation of 0.1 inches (0.03 cm) was
(3) Acceleration ratio. The acceleration ratio is
determined by multiplying the normalized
calculated by dividing the yield acceleration, ky, by the
displacement value of 0.001 by the values of
2
kmax, To , number of cycles, and gravity.
acceleration ratio is equal to 0.75.
G-21
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