F-17. The displacements shown on Figures F-16 and
Sarma, 1975; Franklin and Chang, 1977; Makdisi and
F-17 are normalized with respect to the amplitude of
Seed, 1978; Hynes-Griffin and Franklin, 1984; Wilson
and Keefer, 1985; Lin and Whitman, 1986, Yegian et
al., 1991). The procedure assumes that movement
decimal fraction of gravity), and the predominant
occurs on a well-defined slip surface and that the
period of the induced acceleration time-history, To.
material behaves elastically at acceleration levels
below the yield acceleration but develops a perfectly
(b) A convenient relationship (Egan, 1994)
plastic behavior above yield. The procedure involves
derived from the results of Makdisi and Seed (1978) is
the following steps:
shown on Figure F-18. The displacement per cycle of
significant shaking normalized with respect to the
! A yield acceleration, ky, i.e., the acceleration at
induced peak acceleration (expressed as a decimal
which a potential sliding surface would develop a
fraction of gravity) is plotted against the ratio of the
factor of safety of unity, is determined using limit
yield acceleration to the induced peak acceleration.
equilibrium pseudo static slope stability methods.
The curves are most representative for ground motions
Values of the yield acceleration are dependent on
having a predominant period of about one second.
the slope geometry, groundwater conditions, the
Shown on the same figure is a relationship between
undrained shear strength of the slope material (or
earthquake magnitude and number of cycles of
the reduced strength due to earthquake shaking),
significant shaking (Seed and Idriss, 1982).
and the location of the potential sliding surface.
(c) The Newmark sliding block analysis concept
! The peak or maximum acceleration, kmax, induced
was also employed by Franklin and Chang (1977) who
computed permanent displacements based on a large
within a potential sliding mass (average of the peak
number of recorded acceleration time-histories from
accelerations over the mass) must be estimated.
previous earthquakes and a number of synthetic
Often this value is assumed equal to the free field
records. Their results are shown on Figure F-19 in
ground surface acceleration, amax. This neglects
terms of upper bound envelop curves for standardized
possible amplification of accelerations on a slope
maximum displacements versus the ratio of the yield
due to topographic effects, but also neglects
acceleration to the maximum earthquake acceleration.
reduction of acceleration due to reduction of ground
The time-histories used by Franklin and Chang (1977)
motion with depth and averaging over the sliding
were all scaled to a peak ground acceleration of 0.5g
mass. A specific evaluation of kmax considering
and peak ground velocity of 30 inches per second. The
amplifying and reducing effects can always be made
displacement (inches) for particular values of peak
using dynamic response analysis or simplified
ground acceleration, A, and velocity, V, may be
methods.
obtained by multiplying the standardized maximum
displacement by the quantity V2/1800A, where V is in
units of inches per second and A is a decimal fraction
the yield acceleration, ky, downslope movement of
of gravity.
the sliding mass occurs. Conceptually, if there is a
time history of induced accelerations, some of
(d) Yegian et al. (1991) performed similar
which exceed the yield acceleration, downslope
analyses using 86 ground motion records. Their
movement occurs when the induced accelerations
computed normalized displacements are shown on
exceed the yield acceleration. Movement stops after
Figure F-20. Their computed displacements were
the time when the induced acceleration level drops
normalized with respect to the peak-induced
below the yield acceleration. The magnitude of the
potential displacements can be calculated by a
simple double integration procedure of an
accelerogram (see Figure F-15 for an illustration).
(a) The above procedure was used by Makdisi
and Seed (1978) to develop a simplified procedure for
estimating displacements in dams and embankments.
Charts relating the displacements as a function of the
ratio of the yield acceleration to the maximum induced
F-30
Previous Page
