Assessing the seismic vulnerability of masonry buildings - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 330

(Grünthal, 1998). This approach has been further developed in the Euro-
pean RISK-UE project for a larger number of building typologies and
vulnerability classes (Lagomarsino and Giovinazzi, 2006). The EMS-98
scale (Grünthal, 1998) is in itself a DPM approach, where vulnerability
classes are defi ned across different construction typologies. The uncertainty
inherent of attribution of a typology to a class and of its response to a
seismic event in terms of damage level is dealt with by assuming a central
value and a fuzzy set membership, so that both vulnerability and damage
can be expressed in verbal (few, many, most) rather than numerical terms.
A fi rst attempt at deriving generic fragility curves was made by Spence
et al. (1992) with the parameterless scale intensity (PSI), aimed at providing
fragility curves for different building typologies and at quantifying benefi ts
from upgrading and strengthening interventions of the building stock. The
advantage of this approach is that damage grades and fragility curves are
independent of macro-seismic intensity scales, as they are defi ned relative
to each other, on the assumption that for each building type it is possible
to defi ne the level of the scale corresponding to the median of the fragility
curve for level of damage D3 (structural damage). Limitations of applicabil-
ity are, however, related to the extensive need for observations to calibrate
each fragility curve and to the diffi culty in translating observed or expected
damage into structural characteristics. Recent applications based on this
methodology were developed in the works of Sabetta et al. (1998) and Rota
et al. (2006).
13.2.2 Analytical methods
With respect to the empirical methods, analytical ones have the advantage
of framing the problem of seismic vulnerability of masonry structures in
structural engineering terms, defi ning a direct relationship among construc-
tion characteristics, structural response to seismic action and damage effects.
The development of attenuation equations for specifi c seismic regions and
corresponding derivation of seismic hazard maps in terms of spectral ordi-
nates, as opposed to macro-seismic intensity or PGA, has given impetuous
to the development of analytical methods. These methods tend to feature
more detailed and transparent vulnerability assessment algorithms with
direct physical meaning. In the development of analytical fragility functions
for masonry structures, two methods can be identifi ed: (i) correlation
between damage index and damage thresholds and (ii) correlation between
acceleration/displacement capacity curves and spectral demand curves, fol-
lowing the HAZUS-MH (FEMA, 1999) or N2 method (Fajfar and Gaˇ perˇiˇ,
1996). These two procedures, in line with the performance-based design for
new builds, defi ne the seismic assessment of existing building stock and
prediction of losses. The required analysis steps are: (i) classifi cation of