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

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