Geoscience Reference
In-Depth Information
1000
M = 8 1/4
100
M = 7 1/2
10
M = 6 1/2
1
0.1
0.01
0
0.2
0.4
0.6
0.8
1.0
k
y
/
k
max
Fig. 14.7. Seismicdisplacement vs.
ky/kmax
and magnitude (Makdisi and Seed, 1978)
The Makdisi and Seed (1978) simplified seismic displacement method is one of the
most significant contributions to geotechnical earthquake engineering over the past few
decades. But as they recommended, their design curves should be updated as the profes-
sion advances. Since 1989, the number of recorded ground motions has increased dra-
matically. Thousands of well recorded ground motions are now available. The Makdisi
and Seed (1978) work is based on a limited number of recorded and modified ground
motions. Moreover, the important earthquake ground motion at a site is characterized by
the
PGA
at the crest of the slope and earthquake magnitude. The
PGA
at the crest of the
slopeishighlyvariableandimportantfrequencycontentaspectsofthegroundmotionare
not captured. The analytical method employed was relatively simple (e.g., primarily the
shear slice method and a few equivalent-linear 2D finite element analyses). The decou-
pled approximation was employed, there is no estimate of uncertainty, and the bounds
shown inthe design curves are not trueupper and lower bounds.
4.4. BRAY ET AL. (1998) SIMPLIFIED SEISMICDISPLACEMENT APPROACH
The Bray et al. (1998) method is largely based on the work of Bray and Rathje (1998)
whichinturnfollowsontheworksofSeedandMartin(1966),MakdisiandSeed(1978),
and Bray et al. (1995). The methodology is based on the results of fully nonlinear
decoupled one-dimensional D-MOD (Matasovic and Vucetic, 1995) dynamic analyses
combined with the Newmark rigid sliding block procedure. To address the importance
of the dynamic response characteristics of the sliding mass, six fill heights with three
shear wave velocity profiles each with multiple unit weight profiles and two sets of
strain-dependentshearmodulusreductionandmaterialdampingrelationshipswereused.
