Assessing the seismic vulnerability of masonry buildings - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 329

13.2 Vulnerability approaches: empirical and analytical

13.2.1 Empirical methods

The damage probability matrix (DPM) method has been the most common
vulnerability assessment method in Europe. Based on fi eld observations, it
expresses in a discrete form the conditional probability of obtaining a
damage level j , due to a ground motion of macro-intensity i , P ( D )

D j / I i ]. The method relies on the wealth of observed damage data available
from past earthquakes, and the correlation of these with construction mate-
rials and methods in different geographical and seismic regions. First pro-
posed by Whitman et al. (1973) after the San Fernando earthquake of 1971,
specifi c applications of this method to masonry structures are numerous
(Braga et al. , 1982; Corsanego and Petrini, 1990; Di Pasquale et al. , 2005)
and still widely used in developing countries and regions with extensive
historic seismicity records (Askan and Yucemen, 2010; Zobin et al. , 2010).
Notwithstanding its popularity, the DPM has major limitations: discrete
defi nition of damage levels/states and dependence on a specifi c seismic and
architectural context. Hence, it may not be applicable to different geo-
graphic locations, in the absence of direct damage data.
Some of these limitations are overcome by the vulnerability index method
(VIM) (Benedetti et al. , 1988), based on the vulnerability index I v . The
vulnerability index is a summation of weighted parameters, each associated
with a constructional or structural feature of the typology, which affects its
vulnerability. In this way the defi nition of vulnerability relates only to the
mechanical characteristics of the building, while damage data from past
earthquakes are used to calibrate the vulnerability functions, by relating I v
to observed global damage levels for buildings of the same typology, and
hence extending applicability in regions having experienced the same level
of macro-seismic intensity or peak ground acceleration (PGA).
The most substantial improvement of the VIM over the DPM is that the
former provides a continuous vulnerability function, while the latter uses
discrete vulnerability classes expressed in terms of expected damage. This
means that possible interventions to shift the vulnerability level of a struc-
tural typology are readily quantifi able with I v , while they are only recorded
in the DPM if the intervention results in a shift of damage class. Moreover,
the correlation of VIM with an instrumental measure of seismic action
allows for application to and comparison between different seismic zones,
even though in the last decade the reliability of correlating PGA and
damage has been questioned by various authors (Elenas, 2000; Wu et al. ,
2003). Giovinazzi and Lagomarsino (2004) have proposed a direct corre-
lation of the two methods by introducing a defi nition of damage states
and DPM as a function of I V according to the EMS-98 macroseismic scale

= P [ D =