Using a performance-based earthquake engineering (PBEE) approach to estimate structural performance targets for bridges - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 542

for different ground motion components, the scatter in EDP is reduced
signifi cantly (Fig. 20.5). Still, some of the records with large-scale factors
produce responses close to average, and some of the records with scale
factors close to unity generate response values greater than or less than the
average. That leads to the conclusion that it is possible to obtain unbiased
results even for large-scale factors if the records are selected appropriately
and that factors other than the scale factor, such as proper selection of IMs,
are critical. Figures 20.4 and 20.5 validate the scaling robustness property
of the selected IMs and ground motion recordings in the UC Davis study.

20.5.1 PSDMs for scalar IMs

Different PSDMs for the horizontal ground motion effects on the seismic
response of ordinary highway bridges are available in the literature (Mackie
and Stojadinovic, 2003; Nielson and DesRoches, 2007; Padgett et al. , 2008).
The UC Davis study extends the previous studies in two important aspects:
the analysis focused on the combined effects of vertical and horizontal
ground motion components, and the functional form of the seismic demand
models was not pre-determined as given in Equation 20.8 (Gülerce et al. ,
2012). Nonlinear dynamic analyses results were used in regression analysis
to develop scalar-valued PSDMs given only horizontal IMs for the fi rst
stage and to develop vector-valued PSDMs given both horizontal and verti-
cal IMs for the second stage (Step 4 in Fig. 20.2). From preliminary analyses,
it was found that a quadratic dependence on the IMs was applicable to (e.g.
Fig. 20.6) Type 1-EDPs, whereas a linear dependence was adequate for Type
2-EDPs, as given in Equations 20.14 and 20.15.

[ ] =× ( [ ]

2

( ) ) −

ln EDP Type 1 c ln IM c ± σ Stage [20.14]

1 2 1

[

( )

] =+

( ) ± σ Stage

ln EDP Type 2 c c ln IM [20.15]

3 4 1

where c 1 , c 2 , c 3 and c 4 are the model coeffi cients estimated using nonlinear
regression, and

Stage1 is the standard deviation of the scalar PSDMs at the
fi rst stage. Note that the functional form of the PSDMs for Type 2-EDPs is
identical to the form recommended by Cornell and Krawinkler (2000).
Figure 20.6 presents the actual data points (in terms of the natural loga-
rithms of Type 1-EDPs) and two PSDMs that model the same structural
response data using different IMs; S a at the longitudinal period of the bridge
and S a at the transverse period of the bridge. The actual data points in Fig.
20.6 clearly show the quadratic dependence of Type 1-EDPs to the selected
IMs. The scatter in the actual structural response data increases when the
horizontal S a at the transverse period of the bridge model was used. Gülerce
et al. (2012) analyzed all bridge confi gurations and concluded that the

σ