Uncertainty effect on seismic capacity assessment in the out-of-plane failure mechanisms of masonry structures by probabilistic and non-probabilistic approaches

The present paper aims to provide a contribution in the study of the seismic analysis of existing masonry structures in presence of uncertain parameters described by following both probabilistic and non-probabilistic models. By posing the attention on the local out-of-plane failure mechanisms, the non-deterministic analysis is conducted on the kinematic chains of masonry portions by first applying the upper bound theorem of the limit analysis providing the expressions of the load multiplier parameter and in turn the acceleration capacity of the local mechanism with an explicit dependence on the uncertainties. Specifically, two particular local failure mechanisms commonly observed in post-earthquake scenarios, namely the vertical bending mechanism and the corner overturning mechanism, are analyzed considering the masonry-specific weight, the position of the cylindrical hinge and the cracks lines inclination as uncertain variables. In the framework of a stochastic approach, the uncertain parameters are described by random variables with assigned probability density functions (PDFs) and the Probability Transformation Method is applied to return the PDFs of the seismic response functions. In a non-probabilistic setting, the same parameters are defined as uncertain-but-bounded variables in terms of lower and upper bounds and a global optimization technique straightforwardly allows to estimate the intervals for the seismic response functions. Taking full advantage of the close link between the two proposed approaches, the numerical investigations allow to better understand whether the interval analysis is adequate for a reliable assessment of the seismic acceleration capacity or a stochastic analysis is preferable and therefore a more indepth experimental campaign is required to fully describe the uncertain input parameters as random variables. Moreover, results on the separate and combined effect of the uncertain parameters on the seismic response functions provide other useful information to predict the masonry capacity and preserve integrity.