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Figures 7.3 and 7.4 were developed using a suite of recorded earthquake motions and computing
Bracketed Intensities and Newmark displacements for various values of a y . Figure 7.3 relates the
Bracketed Intensity to the difference between the peak ground acceleration and the critical
acceleration (PGA - a crit ) as a function of PGA. An effort was made to normalize the data into a
single curve; however, contours of PGA were clearly evident in most relationships. Figure 7.4
shows displacement computed using the standard Newmark sliding block technique versus the
Bracketed Intensity for over 100 trials. The method has been employed on several projects and
found to provide displacement estimates that are more reliable and potentially much less
conservative than the estimates provided by the simplified Makdisi and Seed method developed
for large earth dams. The displacements computed using the Bracketed Intensity technique are
similar to displacements estimated from charts developed by Ambraseys and Menu (1988).
The Bracketed Intensity method proposed here is intended to supplement the established
methods referenced in this report. It is recommended that the Bracketed Intensity method be used
as an initial screening tool to obtain preliminary estimates of the susceptibility of slopes to
earthquake-induced displacement. If this method predicts significant displacement, a more
rigorous evaluation is highly recommended. It should also be noted that the Bracketed Intensity
procedure suffers from the same limitations inherent in the other limit equilibrium methods as
previously discussed.
7.2.5 Advanced Numerical Modeling
In situations where permanent ground deformations may impact the bridge foundation and/or
abutments, it is becoming common to rely on numerical modeling methods to estimate the range
of ground displacements that may be induced by design level ground motions. Advanced
numerical models are capable of generating ground deformation patterns as opposed to single
displacement values, and of incorporating coupled effective stress analyses thereby accounting
for excess pore pressure generation and complex soil-structure interaction.
Numerical models are recommended for estimating permanent displacements of slopes and
embankments for critical projects. The primary advantages of these models include: (1) complex
embankment geometries can be evaluated, (2) sensitivity studies can be made to determine the
influence of various parameters on the seismic stability of the structure, (3) dynamic soil
behavior is much more realistically reproduced, and (4) coupled analyses can be used which
allow for such factors as excess pore pressure generation in contractive soils during ground
shaking and the associated reduction of soil stiffness and strength.
Disadvantages of numerical methods include: (1) the engineering time required to construct the
numerical model can be extensive, (2) numerous soil parameters are often required, thereby
increasing laboratory testing costs (the number of soil properties required is a function of the
constitutive soil model employed), and (3) very few of the available models have been validated
with well documented case studies of the seismic performance of actual embankments; therefore,
the level of uncertainty in the analysis is often unknown.
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