(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)

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

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.

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

Integrated Publishing, Inc. |