GNGTS 2013 - Atti del 32° Convegno Nazionale

and building typology (Masonry or RC buildings) for the spatial unit, that is the “census cell”. Nevertheless due to confidentiality requirements these statistics were presented in an aggregate manner, in which the information is not immediately identifiable as a function of the identified classes; for example, it is not possible to get the number of RC buildings in a cell dating back to a specific age of construction and characterized by a specific number of storeys, but only to know how many RC buildings, how many buildings dating back to that of construction and how many buildings with that number of storeys are present in that cell as a whole. Seismic vulnerability assessment. In (Lagomarsino and Giovinazzi, 2006) two methods were proposed for the vulnerability assessment of current buildings and for the evaluation of earthquake risk scenarios: a macroseismic model, to be used with macroseismic intensity hazard maps, and a mechanical based model, to be applied when the hazard is provided in terms of peak ground accelerations and spectral values. The vulnerability of the buildings is defined by vulnerability curves, within the macroseismic method, and in terms of capacity curves, within the mechanical method. The method can be essentially summarized by the following steps: (i) assumption of a typological classification system, (ii) definition of implicit Damage Probability Matrices (DPMs) and (iii) translation into vulnerability curves through the combined use of the fuzzy set theory and of the probability theory. The method originates from the assumption of a typological classification system essentially corresponding to that adopted by EMS-98 (Grunthal, 1998), apart from the inclusion of sub- typologies. In particular, the type of horizontal structure has been considered for masonry buildings: wood slabs, masonry vaults, composite steel and masonry slabs, reinforced concrete slabs. For all building typologies three classes of height have been considered differently defined in terms of number of storeys for masonry and reinforced concrete buildings. For buildings designed according to a seismic code the following have been considered: the level of seismic action depending on seismicity; the ductility class, depending on the prescriptions for ductility and hysteretic capacity. The EMS-98 macroseimic scale provides a model for the measure of the earthquake from the observation of the damage suffered by buildings. In particular, EMS-98 scale groups together buildings into six vulnerability classes, from A to F, with decreasing vulnerability. For each vulnerability class the frequency of the expected damaged is defined through linguistic terms considering five damage grades, that can regarded as an implicit DPM. Hence trough the combined use of the fuzzy set theory and of the probability theory a vulnerability curve described by a closed analytical function can be evaluated: (1) where I is the seismic input provided in terms of a macroseimic intensity, and V and Q are the vulnerability and the ductility index, respectively, and μ D (0 < μ D < 5) represent the mean damage value of the expected discrete damage distribution. (2) The probabilistic assessment, in terms of both damage distributions and fragility curves, for the mean damage value μ D , is obtained assuming a binomial distribution. Then for each Building Typology, identified by vertical structure, and sub-Typologies, identified by the horizontal structure, a vulnerability curve in terms of mean damage and macroseimic intensity in addition to a capacity curve are defined, representing the correlation between the seismic input and the expected damage. 53 GNGTS 2013 S essione 2.1