Ground motion selection for seismic risk analysis of civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 102

4.7 Checking for bias in seismic response analysis

due to ground motion selection

In the selection of ground motion records, it was necessary to defi ne a
weight vector, w i , specifying the hierarchy of importance of various ground
motion intensity measures in IM . As a result, the set of selected ground
motions may have an empirical distribution, for one or more intensity mea-
sures which were given a relatively low (or even zero) weighting, which
differs from the theoretical distribution provided by the GCIM approach.
Such a weighting would have been assigned on the assumption that the
particular intensity measure represented aspects of the ground motion
which are not important in the considered seismic response model. Such an
assumption can be easily checked, and if incorrect an estimate of bias can
be obtained. Bradley (2010a) provides the theoretical details behind such
bias estimation, and emphasis here is placed on the illustration of this pro-
cedure. The ground motion sets discussed below were obtained by Bradley
(2012a).
Figure 4.10 illustrates two of the possible three outcomes from examining
bias of the distribution of seismic demand due to the selected set of ground
motions used in seismic response analysis (for a different case study struc-
ture). In the fi rst case, Fig. 4.10a illustrates the dependence of the peak deck
acceleration, a D , as a function of the PGA of ground motions which were
scaled to PGV

27.7 cm/s (10% exceedance in 50 years). For this particular
exceedance probability, the ground motion set used to obtain the results in
Fig. 4.10 had a minor bias in the distribution of PGA values of the ground
motions scaled to this value of PGV (see Bradley, 2012a, fi gure 4a). Figure
4.10a however illustrates that a D is not dependent on the PGA values of
the selected ground motions, and therefore there is no bias in the distribu-
tion of EDP | IM j due to PGA (Figure 4.10b). Figure 4.10c illustrates the
second possible outcome where, unlike Fig. 4.10a, it can be seen that for
ground motions scaled to IM j

=

0.36 g , the distribution of peak free-
fi eld displacement, U FF , has a signifi cant dependence on the SI values of the
selected ground motions. However, despite this dependence of U FF | PGA on
SI , because the distribution of ground motion selected were consistent with
the theoretical distribution (see Bradley (2012a, fi gure 9d)), the distribution
of the demand is also unbiased (Fig. 4.10d). Bradley (2010a) presents an
example of the third possible outcome, in which both the seismic demand
considered is dependent on a particular intensity measure, and the selected
ground motions have a distribution of this intensity measure which is
signifi cantly different from the theoretical distribution, consequently result-
ing in a biased distribution of seismic demand that can be approximately
estimated.

= PGA =