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a standard uniform number and checking between which curves it falls, at
the intensity sampled for the current run. For line-like components, such as
component 4 in Fig. 18.9, the fragility model usually consists of a Poisson
distribution giving the number of damages per unit length, with rate (
λ
4
in
Fig. 18.10) function of the local intensity. Sampling the damage number and
severity (breakage probability is also a function of
λ
4
) is performed from
the Poisson distribution.
When the damage states of the four components are known, the func-
tional models of the two systems are used to evaluate the functional con-
sequences. At this stage, performance metrics (
PI
c
,
PI
s
,
PI
inf
) for components,
systems and the whole Infrastructure can be evaluated.
18.8 Example of an application of seismic
vulnerability analysis
18.8.1 Description of the study area
This section presents some results of a simple application of the described
model to the hypothetical small region already shown in Fig. 18.3 and
Plate
I
(between pages 452 and 453). Figure 18.11 shows the region, which has
three urban areas, denominated cities A to C, of which the easternmost is
closest to the three seismogenic zones. Each city is subdivided in a different
number of building census areas, sub-city districts and land use plan areas,
numbered according to the fi gure. These sets of polygons are associated
with data, reported in Table 18.1, ranging from land use, to population, to
building typology and number. For this simple example only two broad
buildings categories are considered, roughly representative of Italian pre-
WWII and post-WWII construction, denominated unreinforced masonry
(URM) and reinforced concrete (RC) buildings.
The seismic fragility model for the two typologies is provided in the form
of a set of two fragility curves (one for the
yield
and the other for the
col-
lapse
limit state). These curves have been derived as part of the SYNER-G
project by statistical post-processing of multiple fragility studies: different
curves have been attributed to classes in the mentioned taxonomy, and
harmonisation of limit-state defi nition and intensity measure has been per-
formed (all curves are expressed in terms of PGA), coming up with lognor-
mal shapes specifi ed in terms of their two parameters, complemented with
a characterisation of the epistemic uncertainty on the latter (for each typol-
ogy a joint distribution of the log-mean and log-standard deviation of each
limit-state is available). Details can be found in Crowley (2011). Table 18.2
reports the employed parameters. The fi nal model of the buildings consists
of a set of 181 rectangular cells, as already shown in Fig. 18.3 and
Plate I
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