Ground motion selection for seismic risk analysis of civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 97

tion of the ground motions selected in Fig. 4.4 and Fig. 4.5. It can be seen
that there is a noticeable difference in the distribution of amplitude scale
factors required for these ground motion sets, with median, 10th and 90th
percentile scale factors of 1.9, 0.5 and 9.0, respectively, for the ground
motions selected considering only SA ordinates, and median, 10th and 90th
percentile scale factors of 1.1, 0.8 and 2.0, respectively, for the ground
motions selected considering SA , CAV , Ds 575 and Ds 595. That is, in the
latter case the amplitude scale factors are much closer to 1.0, than the
former case. Further insight into the reason for the larger scale factors
required for the ground motion selected based on SA ordinates only can
be obtained from the M w R rup distribution in Fig. 4.6b. Figure 4.6b illus-

trates that, for this particular example, when selecting ground motions
based on SA ordinates only, the selected ground motions tend to have larger
source-to-site distances for a given M w . For example, 10 of the 30 ' SA only'
ground motions have a M w

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R rup combination 'below' the line indicated in
Fig. 4.6b, while there is only a single ground motion selected based on con-
sidering SA , CAV , Ds 575 and Ds 595. As a result, such ground motions tend
to have a lower SA (3.0) amplitude, thus requiring a larger amplitude scale
factor. Given that signifi cant duration increases, on average, with source-to-
site distance (Bommer et al. , 2009) this is the likely reason for the bias
observed in the CAV , Ds 575 and Ds 595 distributions of the ground motions
selected considering SA ordinates only (i.e. Fig. 4.4c and d).

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4.6.3 Ground motion selection for different
exceedance probabilities

Following the results obtained in Fig. 4.5, the ground motion selection algo-
rithm was used to select ground motions for two other exceedance proba-
bilities of 50% and 1% in 50 years. All other details used to obtain the
selected set of ground motions in Fig. 4.5 were retained (in particular, the
weight vector is given by Equation (4.17)). Similar to Fig. 4.4 and Fig. 4.5,
sets of ground motions for these two additional exceedance probabilities
were obtained with unbiased distributions of the considered intensity mea-
sures. Hence, for clarify in the fi gures to follow, comparisons between the
ground motions selected at the three exceedance probabilities omit the
underlying GCIM distributions and realizations.
Fig. 4.7 compares the ground motions selected for the three different
exceedance probabilities considered. In Fig. 4.7a, the statistics of the SA
ordinates of the selected ground motions are depicted via the median, 16th
and 84th percentiles, while in Fig. 4.7b-d, the EDF is used. Table 4.3 pro-
vides a comparison between the median IM i values of ground motions
selected for those IM i s presented in Fig. 4.7. It is worth noting that the 50%,
10% and 1% probability of exceedance values of IM j = SA (3.0) were 0.038,