Derivation of fragility curves from non linear dynamic analyses for URM school buildings

Fragility curves constitute an essential tool in risk studies. Together with the hazard representation and exposed assets databases, they are used to provide an estimate of physical or economic losses. This is typically achieved by introducing consequence functions, which correlate the probability of reaching specific damage levels (DL) – estimated via the fragility curves – with the losses under consideration. Although the physical meaning of DL is well established in engineering practice and various references are available in the literature and shared by the scientific community (like the damage grades and definition introduced by the European Macroseismic Scale), the ways adopted in mechanical-analytical, mechanical-numerical and empirical approaches for converting these principles and thus deriving fragility curves are multiple. That constitutes uncertainty in risk studies which still lacks a consensus on the scientific literature. In this context, the paper explores converting and interpreting the huge amount of data provided by three-dimensional models analysed through nonlinear dynamic analyses (NLDA) into synthetic DLs. One of the main novelties of the procedure is that, differently from the most common approach in numerical methods, it does not require the introduction of inter-storey or roof drift thresholds – conventionally defined a priori – to associate the attainment of DLs. The paper focuses on existing unreinforced masonry (URM) buildings. Specifically, seven different URM structures, inspired by real schools, are analysed adopting the equivalent frame modelling approach. The software package adopted – i.e. Tremuri – has been extensively validated in strong nonlinear range in previous research. The analysed buildings were selected based on their comprehensive documentation of geometric and mechanical characteristics, but the methodology applied has general validity. A Cloud-based approach, refined through the combined use of Incremental Dynamic Analyses is adopted to derive the fragility curves, which are compared with other references available in the literature. The proposed approach revealed quite effective and replicable. Moreover, the results gathered through accurate NLDAs are also processed to establish reference values of inter-storey or roof drift thresholds to be used in more simplified approaches (e.g. based on the use of SDOFs system or mechanical-analytical models).