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studies of the as-built and retrofitted models of multi-column bents, and (5) an exploratory study of
the application of innovative materials for retrofit. Due to space limitation only a summary of the
research in Tasks 2 and 5 is presented in this article.
INCOHERENT GROUND MOTION EFFECTS
Although commonly assumed to be uniform, ground motion at different supports of a structure may
vary from one support to the next. Variation in support excitation may be due to three causes: (1)
geometric incoherency, (2) wave-passage, and (3) local site geotechnical characteristics. The first
effect is due to randomness of the earthquake motion even at a given site with practically the same
distance from the earthquake source. The second effect is caused by delay in the motion from one
support to the next as the earthquake wave passes through the site. Finally the third source of
variation is that, for the same bedrock motion, soils of different properties and depth transfer the
motion to the surface differently. The first two factors can be particularly important for relatively long
structures, whereas the third factor can be important even for short structures with supports located on
soils layers that are different from one another.
The total length of the bridge is 552.7 m. Furthermore soil investigation of the site prior to
construction have shown that the soil type over the western third of the bridge may be categorized as
soft, while the soil for the rest of the bridge is in the category of medium firm. Considering the length
and the variation in the soil type it was decided to include all three sources of deficiencies in the study.
No site-specific seismic studies and detailed soil investigations have been conducted for the viaduct.
As a result it was felt that the study of the incoherency effects would have to be approximate. A
reduced linear model of the viaduct was used to determine the trends in the response relative to the
response for uniform ground motions. The structure was treated as a planar system subjected to inplane
ground motion loading in the longitudinal direction of the bridge. Details of the study are
presented by Yang et al. 2002.
Figure 4 shows the elevation of the reduced model of the viaduct. To develop the reduced model,
each segment of the structure between adjacent hinges was modeled by a single mass supported on a
column that had the same lateral stiffness as that of the bridge segment. Bridge hinges were modeled
as pin connections. The coherency function was adopted from a previous study that was based on
random processes principles developed by Yang and Chen (2000). Eight acceleration records were
generated at bedrock with slightly different peaks in a range of 0,38 to 0.41g. These motions were
used to determine the displacement and acceleration histories at the ground level of the soil column
under each support of the reduced model. To study the effect of wave passage, a wave velocity of 600
m/sec. was used for the entire viaduct even though the soil varied from the west to the east. This was
done because blow counts of the western and eastern parts, although placed the soils in different
categories, were not drastically different.
The effect of different combinations of incoherency parameters were studied by focusing on the
"column" base shears in the reduced model. An artificial acceleration record generated for a
magnitude 7.4 at 40 km distance from the epicenter was used. To establish a benchmark, the model
was analyzed for two uniform ground motions obtained by combining the bedrock motion near the
middle of the viaduct one with amplification due to soft soil and the other with amplification with
medium firm soil. The average of the two responses was used as the representative response for
uniform ground motion.