Beta functions adaptation on empirical damage for a fragility model of Italian buildings

In this study, heuristic vulnerability model is presented providing damage distribution as a function of ground motion severity, through the use of given distribution function. Firstly, observational damage distribution are obtained from data collected after the recent earthquakes occurred in Italy and made available by DPC through Da.D.O. platform. The latter collect information on the main characteristics about building position, metrical data (e.g., number of storeys, interstorey height, storey area and construction age), structural types, severity and extension of observed damage on different building components. Moreover, the ground motion characterization was described via the ShakeMap published by the National Institute of Geophysics and Volcanology. Then, the two statistical models mostly used in the literature, i.e. binomial and beta, are used to determine the one most suitable to reproduce the observational damage distributions by means of godness-of-fit test. An introductive section properly examine the pro and cons in their use (number of parameters, flexibility). The observation of mean value and variance couple for more than 2000 damage samples obtained based on the considered database is used to obtain a general relationship which allows to reduce the number of parameters required by beta distribution, preserving its renomate flexibility. This enables the formulation of a novel heuristic vulnerability model for derivation of fragility curves. The model relies on the knoledge of mean damage trend with intensity measure and employs a probability distribution function. In this study, specifically, binomial and beta distributions are utilized. The generality of the method is then customized to suit the characteristics of Italian residential building stock, leveraging the information gathered after the 2009 L'Aquila Earthquake. This database presented an unprecedented opportunity due to the extensive data available on building geometrical and typological characteristics, seismic vulnerability, to the high level of representativeness of samples at municipality level, and to the thorough representation of damage patterns observed on building components. The fragility curves obtained through the presented vulnerability model are compared with those empirically derived from the observational data and are used to fully derive seismic risk scenario after 2009 L'Aquila Earthquake, in terms of economic losses, number of long term unusable buildings, the number of collapse, the number of deaths and severely injuries. The ensuing consequences deriving from the adoption of different fragility curves, i.e. empirical or with beta and binomial vulnerability models are deeply investigated.