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the rigid body methods. The point at which the deformations were the greatest consistently
occurred beneath the toe and lower third portion of the slope. This is considered a critical area
due to the possible location of abutments, pier foundations, and structural components located
upslope.
The differences associated with the various cases are described below.
7.3.1 Embankment Geometry
The generalized geometric configuration of the model was shown in Figure 7.5, but several
different configurations were investigated in an attempt to include a range of conditions that exist
in the field. Embankment heights of 3 and 9 m were modeled and the thickness of the liquefiable
layer was varied from 4.5 to 21 m. The location and width of soil improvement was also
investigated. Based on the sensitivity analyses and on constructability issues, the improved soil
block was centered about the toe of the slope. Numerical analyses were also performed for sites
with no soil improvement. In subsequent analyses the width of the improved block was increased
from roughly 4.5 m to a maximum of width of 44 m. In addition to investigating the influence of
embankment geometry, the influence of groundwater level was evaluated. For the majority of the
study, the groundwater level was modeled to be at the ground surface (top of the liquefiable
material) but was lowered to 2 m below the ground surface for some of the cases.
7.3.2 Material Properties
The material properties used in the analyses are shown in Figure 7.5 and summarized in Table
7.1. The liquefiable and improved soils are both cohesionless materials, each layer modeled with
uniform density. The embankment was modeled as consisting of compacted clayey sand/sandy
clay, common in many field applications. The soil improvement was generally modeled with
densification provided by a vibro-compaction method, wherein the loose sandy soil is densified
and modeled as a uniform deposit throughout the treated zone. This is a simplification of the
actual pattern of densification and the variation in soil density that would be expected from most
ground improvement techniques; however, this approach has been used in many case studies.
7.3.3 Ground Motions
Six earthquake motions covering the magnitude range of engineering interest (approximately M w
6.0 to M w 8.0) were selected for the parametric study (Table 7.2). The selected acceleration time
histories are slightly conservative in the sense that each one is characterized as having greater
than average duration for that magnitude, thereby yielding slightly conservative displacement
results. All earthquake motions were utilized at their recorded PGA value, with the exception of
the 1985 Michoacán record. The latter record was scaled slightly to a PGA of 0.39 g. Plots of the
unscaled records are shown in Figure 7.6.
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