Report - Oregon State Library: State Employee Information Center ...

Figure 4.10: Model of Hypothetical Slope: Basal Shear Surface is heavy line;
FS is Factor of Safety; Thrust Angle is 30 Degrees (Jibson 1993).
The second step involves the introduction of an acceleration time history. When the ground
motion acceleration exceeds the critical acceleration (a crit , a y , k y ) the block begins to move down
slope. By double integrating the area of the acceleration time history that exceeds a crit , the
relative displacement of the block is determined. A simple spreadsheet routine can be used to
perform this calculation (Jibson 1993). The method is capable of accounting for the
characteristics of the input ground motions; therefore, the duration of the ground motions is
explicitly accounted for, a significant improvement over the pseudostatic method of analysis.
Although the result of the pseudostatic analysis (i.e., yield acceleration) is a requisite input
parameter, the method provides expected displacements rather than factors of safety.
Numerical studies based on this method of analysis have lead to the development of useful
relationships between ground motion intensity and the seismically-induced deformations (Sarma
1975; Makdisi and Seed 1978; Ambraseys and Menu 1988; Yegian et al. 1991; Jibson 1993).
The relationship proposed by Makdisi and Seed for large earth dams is shown in Figure 4.11.
While this relationship was not originally developed for short embankments or foundation
conditions involving liquefied materials, this chart is one of the most widely adopted references
for evaluating seismic deformations. Therefore, it is useful to see how the chart solution
compares with more rigorous analysis methods. Applications of the Newmark-type approach
involving soil improvement and highway embankments have been described by several
investigators (Manyando et al. 1993; Jackura and Abghari 1994; Riemer et al. 1996).
Due to its simplicity, Newmark’s sliding block approach has been widely adopted in practice for
predicting permanent deformations in embankments for both drained and undrained conditions. The
procedure generally estimates the displacement of a rigid block resting on an inclined failure plane
that is subjected to earthquake shaking. That model can be analyzed as a single-degree-of-freedom
rigid plastic system. Given that the sliding block analyses are based on limit equilibrium
techniques, they suffer from many of the same deficiencies noted for pseudostatic analyses.
Their primary limitations with respect to liquefiable soils include: (1) the soil, particularly in the
liquefiable zones, does not behave as a rigid-plastic material although this model is commonly
employed in practice; and (2) the single-degree-of-freedom model does not allow for a pattern of
displacements to be computed. The latter deficiency is critical to lateral spreads near free faces,
92