Probability of collapse of monumental buildings under horizontal loads

In recent years, the assessment of the seismic reliability of monumental buildings has been the object of several studies: in order to take into account the large uncertainties in the loads and in the material and structural properties, in most studies the seismic action has been mimicked by quasi-static horizontal forces of magnitude depending on the intensity of the considered earthquake. In particular, it has been shown that the probabilities of damage and collapse and their distributions can be obtained by looking at a monumental building as an assemblage of macroelements of known static and collapse behaviour, and considering the relevant mechanisms: in this way, the so called kinematic approach to limit analysis is followed, and in rigour only lower bounds to the probability of collapse are obtained. In order to obtain also upper (i.e. “safe”) bounds to the probability of collapse under a given load, the static theorem of probabilistic limit analysis must be used. In this lecture, the two theorems are presented, and the procedure of seismic reliability assessment exemplified on two churches damaged in the 1976 earthquake of Friuli (North-East Italy): upper and lower bounds to the probability of collapse of each macroelement and of the whole church are obtained as a function of the applied horizontal load, i.e. of the earthquake intensity.