Ground motion selection for seismic risk analysis of civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 90

where D IM i is the KS test statistic for IM i based on N gm ground motions;
F IMi | IM j ( im i | im j ) is the theoretical CDF (obtained from the GCIM approach);
and S N gm ( im i ) is the EDF (of IM i ) of the suite of ground motions selected.
The null hypothesis that the distribution of IM i of the suite of ground
motions is representative of the theoretical distribution is rejected, if D is
greater than the critical KS test statistic for a given confi dence level, . The

result of the KS test can be easily interpreted graphically based on whether
or not the EDF of the selected ground motions intersects the KS test sta-
tistic 'bounds'. Further explanation is given in Bradley (2010a).

α

4.5.5 Explicit measures of ground motion vs implicit
causal parameters
Conventional ground motion selection is typically based on the consider-
ation of explicit measures of the ground motion and implicit criteria based
on ground motion causal parameters. The most common example of this is
the explicit consideration of the pseudo-response spectral ordinates of a
ground motion, and the implicit consideration of causal parameters, such
as rupture magnitude, source-to-site distance, focal mechanism, site shear
wave velocity, among others, which is prevalent in both research and prac-
tice (ASCE, 2006; Bommer and Acevedo, 2004; Katsanos et al. , 2010; Kottke
and Rathje, 2008; NZS 1170.5, 2004; Wang, 2011). Such causal parameters
are often considered because of the acknowledged limitation of the explicit
parameters used. For example, a range of applicable earthquake magni-
tudes, source-to-site distances, etc. is typically specifi ed to obtain a set of
prospective ground motions before selecting from this prospective set
based on spectral shape, because it is acknowledged that response spectra
provide little insight into the cumulative and duration phenomena of a
ground motion (Bommer and Acevedo, 2004; Bommer et al. , 2004; Bradley,
2011a; Wang, 2011).
The use of implicit causal parameters in aiding ground motion selection
has two primary limitations. Firstly, the applicability criteria for each causal
parameter are often ad-hoc. For example, although moment magnitude is
generally recognized as an important causal parameter when selecting
ground motions, there is generally no consensus as to what is the range of
moment magnitude which will lead to unbiased results without being overly
restrictive in reducing the size of the prospective ground motion dataset.
This is further exacerbated in the case of a probabilistic analysis in which
multiple causative ruptures typically contribute to the seismic hazard for a
given exceedance probability. Secondly, and more importantly, causal
parameters such as moment magnitude, source-to-site distance, etc., are
parameters that are only implicit factors affecting a ground motion, but are
not explicit measures of the severity of the ground motion itself.