Earthquake risk management of civil infrastructure: integrating soft and hard risks - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 233

cedure developed by FEMA (2011) is a simplifi ed structural mechanics
approach, based on fragility curves for archetypical structures. They
acknowledged its use to evaluate the probability of reaching or exceeding
specifi c damage limit states from a given ground motion for a variety of
building types, such as wooden light frame, steel moment frame, concrete
shear wall, and unreinforced masonry. But then they knew that fragility
curves well fi tted to the seismic behaviour of idealistic types of modern
construction types cannot easily be extended to a more general context -
especially in Italy (or more generally in Europe and other continents). They
agreed that a correlation between structural and macroseismic approaches
may be possible and could be used for reciprocal calibration of the models
and the calculation of vulnerability curves. However, this can only be done
if all of the known uncertainties are considered together with recognition
that there may be uncertainties which, as history tells us, as yet are not
known to us. This simple recognition inevitably leads us to a new approach
as we shall describe later.
Bernardini and Lagomarsino (2008) defi ned a mean damage grade using
two parameters, the vulnerability index V and the ductility index Q . Clearly,
a vulnerability index assigned to a monument by a typological classifi cation
represents an average value, which does not take into account the distinc-
tiveness of a single building and does not allow the most vulnerable struc-
tures among buildings of the same type to be singled out. To refi ne the
vulnerability assessment, a survey is required to collect details of other
parameters, such as state of maintenance, quality of materials, structural
regularity (in plan and in elevation), size and slenderness of relevant
structural elements, interaction with adjacent structures, presence of retro-
fi tting interventions and site morphology. These are all attributes that often
cannot be defi ned with the level of precision required for a reliability
calculation.
This kind of approach to the vulnerability of the form of a structure has
to be compared with methodologies which attempt to model any suscepti-
bility to cascading failures (Agarwal and England, 2008; England et al. , 2007;
Starossek, 2007; Tesfamariam and Saatcioglu, 2010). Here vulnerability
analysis is aimed at identifying situations where a relatively small amount
of damage to one part of a structure can lead to the structure 'unzipping'
to total, or near total, collapse. This type of analysis is important, because
standard reliability theory cannot capture the uncertainties and complexi-
ties in the structural model of the form and behaviour of structures, such
as the effects of adjacent buildings, mezzanines, weak and soft storeys, geo-
metrical irregularities, vertical discontinuities as well as many other factors.
Structures have also to respond to unknown unexpected seismic effects
(Blockley and Godfrey 2000; Nafday, 2010) which by defi nition cannot be
included in a probabilistic sample space - even with Bayesian updating.