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Figure 7.2: Illustration of Bracketed Intensity
A simple spreadsheet program was used to calculate both the Bracketed Intensity and
displacement using the Newmark sliding block method. This program was applied to a suite of
acceleration time histories scaled to different peak accelerations, and applied for various values
of the yield acceleration for sliding blocks. The acceleration time histories were recorded at rock
and soil sites during earthquakes ranging in magnitude from 5.6 to 8.5. Several of the time
histories were scaled to provide a comprehensive range of peak ground acceleration (PGA)
values. The application of this simplified deformation-based procedure requires four steps as
discussed below.
1. Determine the static FS of the slope using appropriate dynamic soil strengths. The static
stability analysis accounts for dynamic soil strengths; however, the pseudostatic lateral
force coefficient (k h ) is not incorporated into the analysis when determining the FS. The
critical, or yield, acceleration is then computed using standard slope stability programs.
For the sake of approximate solutions, the yield acceleration can be estimated from the
formula a crit = (FS – 1.0)/b, where the parameter b is commonly between 3 and 4. A value
for b of 3.33 has been recommended as an appropriate value for earthdams (Sarma and
Bhave 1974). This simplification can be used to bracket the likely range of a crit values.
2. Obtain the PGA on rock from a seismic hazard study (Geomatrix 1995; USGS 2000) and
modify the PGA to account for site effects. The difference (PGA - a crit ) can be computed
giving a preliminary indication of the seismic stability of the slope.
3. The Bracketed Intensity of the ground motions contributing to the slope movement can
be estimated from Figure 7.3.
4. Given I b , the displacement of the slope is then estimated from Figure 7.4.
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