Assessing the seismic vulnerability of masonry buildings - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 331

buildings by typology and seismic design; (ii) defi nition of damage states;
(iii) assignment of capacity curves; (iv) defi nition of demand spectra (associ-
ated with return periods and performance targets); and (v) evaluation of
building response in terms of performance points. The two procedures,
applied to large sets of buildings, allow the derivation of fragility curves and
damage scenarios for given sites and as a function of ground motion param-
eters which are linked with hazard levels. The damage levels are directly
related to the demand parameter, which is expressed in terms of displace-
ment or drift. As the fragility curves are developed on the basis of lognor-
mal distribution, once the typologies have been defi ned, it is not necessary
to have a detailed knowledge of the building stock. All that is required are
the parameters defi ning the capacity curve for each typology, various
damage thresholds, and the number of buildings belonging to each typology.
Once capacity curves have been developed then the range of behaviour and
variability of fragility within a building class or stock can be analysed by
parametric analysis, providing important insight for retrofi tting (see
D'Ayala, 2005).
Analytical approaches to defi ne seismic vulnerability of masonry build-
ings are becoming more and more popular, as improved engineering knowl-
edge of the behaviour of masonry structures increases confi dence in the
reliability of such models. In the past decade, a relatively signifi cant number
of procedures aimed at defi ning reliable analytical vulnerability functions
for masonry structures in urban context have been proposed (Erdik et al. ,
2003; Lang and Bachmann, 2004; Borzi et al. , 2008; Erberik, 2008). Although
they share similar conceptual hypotheses, they differ substantially in model-
ling/numerical complexity and treatment of uncertainties. Two main limita-
tions are common to all: limited geographic applicability and limited number
of failure mechanisms. Specifi cally, for the latter, most of the analytical
models consider only in-plane or frame-like behaviour, disregarding over-
turning and out-of-plane mechanisms, often occurring at lower levels of
shaking and hence substantially affecting the seismic vulnerability in an
urban context. Analytical vulnerability assessment of existing masonry
buildings features in many risk assessment integrated systems, from
HAZUS-MH (FEMA, 1999), to SELENA (Molina et al. , 2009), to ELER
(Demircioglu et al. , 2009); however, their choices of capacity curves are
predetermined.
Among nonlinear analysis methods, the collapse-mechanism method
presents the advantage of requiring few input parameters and allowing
consideration of different failure modes. Procedures using this approach are
based on collapse multipliers which identify the occurrence of different
possible mechanisms for the given typology and structural characteristics.
Among the fi rst to use this approach was Bernardini et al. (1990) who
developed a numerical routine (VULNUS), combined with a fuzzy set