Assessing the seismic vulnerability of masonry buildings - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 353

To quantify the effect of the epistemic uncertainty on the fragility curves
obtained with the FaMIVE procedure, cases from the three different loca-
tions in Italy and for the different failure behaviours introduced in the
previous section, are analysed together. For each case a separate reliability
parameter is calculated, as indicated above, and then two new sets of values
representing the lower bound and upper bound for each case are computed.
For the two sets, logarithmic mean and standard deviation are computed
(Equations 13.6 and 13.7) to develop the lognormal models. These are pre-
sented in Fig. 13.9 for the three displacement limit states, respectively. The
reliability indicator for the entire data is 11%, showing that the data reli-

ability is medium-low, i.e. no availability of drawings in most cases and on
site measurement for a modest number of cases. This is a typical situation
in the aftermath of an earthquake, such as the conditions in which damage
data in Nocera Umbra and L'Aquila were collected.
The FaMIVE procedure does not relate a different uncertainty rating to
the ability of the methodology to identify the correct class of behaviour
given a set of data and, within that class, to identify the correct value of
limit state values. To quantify such uncertainty in a robust way, it is neces-
sary to correlate the capability of the FaMIVE method to predict the
correct mechanism, with an actual mechanism occurrence in buildings hit
by an earthquake. Such analyses carried out for the case of L'Aquila
(D'Ayalia and Paganoni, 2011) show that the prevalent observed mecha-
nism is correctly predicted in 50% of cases and the alternative most likely
in 27% of cases, while possible and local mechanisms represent a minority,
and no correct prediction represent 9% of cases. This level of error is com-
parable to the uncertainty associated with the data input quality as dis-
cussed above.

±

13.5 Conclusions

Traditionally seismic vulnerability of historic buildings has been evaluated
using empirical methods based either on damage observation or construc-
tion data. In the last decade, analytical methods for assessment of masonry
structures have increased in number and quality. However, most of them
assume only in-plane failure behaviour, reducing the walls to frame-like
behaviour. This approach has serious limitations and it is non-conservative,
as it overlooks out-of-plane behaviour which might occur for structures
with insuffi cient out-of-plane wall capacity. Nevertheless, recommendations
of the Eurocode 8 consider only basic in-plane behaviour, either controlled
by fl exure or by shear, and set limit drifts for the performance criteria.
Comparison with experimental evidence shows that these limits are usually
underestimated.