Seismic vulnerability analysis of a complex interconnected civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 475

functional consequences and capture the full range on intermediate
working conditions that can characterise these systems after a seismic
event.
For instance, after a seismic event health-care facilities can have a vari-
able number of beds available for hospitalisation, and of functional/staffed
operating theatres for delivering surgical treatments. These quantities (beds
and operating theatres) are a function of human, organisational and physi-
cal macro-components, and are determined based on the physical and func-
tional damage to the structures and non-structural components. A method-
ology to model a health care facility in this detail is available in Lupoi
et al. (2008), and is implemented in the model.

18.5.4 The ' Seismic ' class

This class implements a distributed seismic hazard model, which, starting
from an event on one of the sources/faults in the regional seismic environ-
ment ( Event and Source classes in Fig. 18.2) predicts at each site the vector-
valued IM ( LocalIntensity class in Fig. 18.2) needed as an input to
components' fragility models to evaluate their state of physical damage. The
reason why the hazard model must be capable of predicting vector-valued
IMs is fi rstly that fragility models can be function of vector IMs and, more
generally, that several components may be located at the same site, each
sensitive to different IMs. Moreover, vectors needed at site i and at site j
may be different. Hence the output of the model implemented in the
Seismic class is a vector s

= ∑

= { s 1 . . . s n } of length m , where s i is the

i

vector of length m i of seismic IMs at the i th site.
This vector exhibits a variable degree of statistical dependence between
its components, decaying with the distance between the sites, and usually
larger between the components within each s i (zero distance). There is suf-
fi cient statistical support for adopting a joint lognormal distribution for s ,
under which assumption the statistical dependence is fully described in
terms of the correlation among the components of s .
Available data from past earthquakes have been exploited to estimate
models for both the within-site correlation between different IMs (notably,
spectral ordinates, e.g. Inoue and Cornell 1990; Baker and Cornell 2006),
and to estimate models of across-sites or spatial correlation for the same
IM (Jayaram and Baker, 2009). Ongoing work is also aimed at developing
a cross-IM spatial correlation model (Weatherill et al. , 2012), which would
allow sampling directly spatially distributed seismic intensities ('shake
fi elds') from the probability density of s , an approach already found, e.g. in
Goda and Hong (2008).
The approach adopted in the implemented class does not rely on cross-
IM spatial correlation. The hazard model is a sequential one where local