Bayesian model updating of historic masonry towers through dynamic experimental data

The numerical model of existing masonry buildings, especially in case of monumental constructions, must consider the unavoidable lack of knowledge and the consequent effects of the uncertain parameters (material properties, geometry, boundary conditions, etc.). In this work, a Bayesian approach is proposed to update the finite element model of masonry towers by using experimental data. The towers of San Gimignano (Italy) were considered as an effective case study to test this approach thanks to the availability both of geometric data and dynamic measurements. The possibility to obtain a reliable numerical model is relevant also from the point of view of the seismic risk assessment, which is a crucial issue to ensure the conservation of heritage over the centuries. In fact, both seismic capacity and demand are strictly dependent on the dynamic characteristics of the structure, and a reliable updating of the modal properties of numerical models plays a primary role in the assessment of the seismic risk. In this respect, Bayes’ theorem is herein employed to convert the prior distribution of the elastic modulus E, into the posterior distribution by using the experimental data (first and second natural period). The measurement errors were accounted for by means of a Gaussian distribution centred on the measured values of the natural periods. In addition, modelling uncertainties were defined to incorporate the lack of knowledge on the restraint effect caused by the neighbouring buildings. The oscillating height of the tower was modelled according to a lognormal distribution whose interval starts from the height of the confined buildings to the tower top. Particular attention was devoted to the parameters involved in the Bayesian procedure to define their effect on the obtained posterior distributions. The achieved results encourage the spread this approach, already employed in many engineering fields, to the safeguard of cultural heritage. In view of further challenges, the methodology will be extended to seismic analyses, aiming to obtain the assessment of the seismic risk of the particular structural typology herein considered: the historic masonry towers.