Matrici di probabilità di danno implicite nella scala EMS-98
Numerical and complete Damage probability Matrices (DPM) have been derived in this paper from the ones implicitly contained in the EMS-98 Macroseismic Scale. The DPM have been derived for the 6 vulnerability classes considered by the scale, the 6 damage grades and the macroseismic intensity from V to XII considered meaningful from the point of view of the seismic behaviour of buildings. To this aim the linguistic definitions provided by the scale, and the associated fuzzy sub-sets of the percentage of building, have been completed according to reliable hypotheses. The probability of each single damage grade is measured in terms of a hierarchy of intervals depending on a parameter α (α-cuts of the fuzzy set associated with the linguistic definitions provided by the scale), together with a specific value (white expected) measuring the central average behaviour of the vulnerability class. A parametric representation of the corresponding cumulative probability distributions is moreover provided, deriving discrete integer values from the beta distribution on the range from 0 to 5. A unique parameter variable in the range from 0 to 1 and independent from the macroseismic intensity has been adopted to this aim. Coherently with others vulnerability approach, the adopted parameter can be recognised as a vulnerability index. The uncertainties connected with the definition of the model are moreover discussed. Finally, correlation between the macroseismic intensity and the peak ground acceleration (PGA) are presented, to be used for the inclusion of the proposed model within damage scenarios and seismic risk analyses, where hazard is measured by means of mechanical parameters.