Model updating procedures based on experimental data are commonly used in case of historic buildings to identify numerical models that are subsequently employed to assess their structural behaviour. The reliability of these models is closely related to their ability to account for all the uncertainties that are involved in the knowledge process. In this regard, to handle these uncertainties and quantify their propagation, Bayesian inference is frequently employed being able to deal with the effects of parameter uncertainty, observation errors and model inadequacy. The computation of the posterior distribution through Bayesian inference needs–however–the evaluation of the likelihood function, which requires solving complex multi-dimensional integration problems. To bridge this shortcoming, the paper compares two Bayesian inference approaches to show how different approximations affect the results of simulated inference: a discrete approach for the likelihood computation in the Bayesian Model Updating (BMU) and a Monte Carlo likelihood-free method known as Approximate Bayesian Computation (ABC) are reported. As reference, the typology of historic masonry towers was considered by using their natural frequencies as experimental data for model updating. The two procedures provide very similar results supporting the validity of both methods despite ABC turns out to be a more flexible approach.

This paper focuses on the seismic risk assessment of historic masonry towers according to the Italian “Guidelines for the Assessment and Mitigation of the Seismic Risk of the Cultural Heritage.” The latter identifies a methodology of analysis based on three different levels of evaluation, according to increasing requirements on the structural knowledge: LV1 (analysis at territorial level), LV2 (local analysis), and LV3 (global analysis). Regardless of the methodology of analysis, the more advanced the achieved level of knowledge, the higher the reliability of these approaches becomes. In this field, a fundamental task is the estimation of the uncertain parameters (both material properties and boundary conditions) affecting the structural behavior. The effect of these uncertainties on the global structural response is herein approached through the discussion of an illustrative case study of some of the historic masonry towers in the city center of San Gimignano (Siena, Italy). The seismic risk of these towers was analyzed in the framework of Seismic Risk of Monumental Buildings (RiSEM is the Italian acronym), a research project granted by the Tuscany Regional Administration, and this paper summarizes the results obtained for two of the preceding three levels, which highlights a few issues concerning the seismic risk of historic masonry towers. Useful conclusions are drawn in order to quantify, when performing an LV3 approach through nonlinear models, the effects of the uncertainties on the seismic risk evaluation of such structural typology. The paper, in particular, confirms once more how strongly the effect of confinement reflected on tower seismic performances and stresses that specific attention should be paid to the definition of the effective portion of the structure to be considered as confined (with respect to adjacent buildings).

The paper focuses on the analysis of the outcomes of some experimental tests carried out in San Gimignano (Siena, Italy), aimed at measuring the natural frequencies of the medieval masonry towers still present in the historic city center. Information on the investigated towers was inserted into a wider database that collected dynamic, mechanical, and geometrical features of masonry towers. A large amount of data was collected from a literature review, then summing up as many as 43 different case studies. Collected data were then used to identify the main physical parameters influencing the dynamic behavior of slender masonry towers and to critically evaluate the existing empirical formulations proposed for the estimation of the first natural frequency of such structural typology. Correlations between fundamental frequencies and the geometric characteristics and mechanical parameters are discussed, and a novel semiempirical formulation is eventually proposed for a reliable prediction of the main frequency of slender masonry towers.

Seismic assessment of existing masonry structures requires a numerical model able to both reproduce their nonlinear behaviour and account for the different sources of uncertainties; the latter have to be dealt with since the unavoidable lack of knowledge on the input parameters (material properties, geometry, boundary conditions, etc.) has a relevant effect on the reliability of the seismic response provided by the numerical approaches. The steadily increasing necessity of combining different sources of information/knowledge makes the Bayesian approach an appealing technique, not yet fully investigated for historic masonry constructions. In fact, while the Bayesian paradigm is currently employed to solve inverse problems in several sectors of the structural engineering domain, only a few studies pay attention to its effectiveness for parameter identification on historic masonry structures. This study combines a Bayesian framework with probabilistic structural analyses: starting from the Bayesian finite element model updating by using experimental data it provides the definition of robust seismic fragility curves for non-isolated masonry towers. A comparison between this method and the standard deterministic approach illustrates its benefits. This article is part of the theme issue ‘Environmental loading of heritage structures’.