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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.

The manuscript provides a wide database for historic masonry towers collecting their modal, mechanical and geometrical features. This large amount of data was collected according to a literature review, then summing up as many as 56 different case studies. The collected data was then used to identify the main physical parameters influencing the modal behaviour of slender masonry towers, including the openings on the facades. After a critical discussion of the data reported in the database, the existing empirical or semi-empirical formulations available for the estimation of the first natural frequency of such structural typology are first evaluated. Subsequently the effects of the openings, as revealed through the analysis of the experimental results reported in the database, are discussed by comparison with a simple but effective numerical model. Despite the difficulties to quantify the effect of the openings along the height of the tower on the main frequency due to a cross-contribution of mass and stiffness, a simple but effective formulation is proposed which is able to account for this parameter.

This paper reports the results of a ground penetrating radar (GPR) survey of the ground-floor of Academia Gallery (Florence, Italy) where the Michelangelo’s David is exhibited to the public. The equipment used was a step-frequency GPR operating in the 100 MHz-1 GHz band, named ORFEUS. The survey covered an area of 13 m × 7.3 m, and the scans were performed along two orthogonal directions. Acquisitions in the same direction were separated by 0.25 m from each other. The GPR was able to confirm the underground structure, as it can be deducted by planimetry and historical documentation. In particular, the radar clearly detected the air-conditioning ducts under the floor and an approximately circular foundation below the basement of the statue.

In order to estimate their behaviour as realistic as possible, masonry structures and historical complex buildings are frequently assessed with demanding non-linear procedures, whether for static or dynamic purposes. However, uncertainties related to the epistemic and aleatory field, especially for historical masonry, can widely influence the output reliability and diminish the value of the deterministic approach (one input – one output) in a decision making workflow: for instance, the necessity for urgent structural interventions or even the possibility to close the building or civil object for safety reasons. This paper aims to show how these uncertainties could be quantified, based on a multi-parameter input approach, and consequently handled. In sequence, (i) the knowledge, based on the state-of-the-art survey of the object (geometry, quality and characteristics of the materials, etc.) and scientific or engineering contents (constitutive laws, possible sources of excitation, solution methods, etc.) can be put inside a numerical model in order to find a solution for the desired output, (ii) input parameters could be treated as variables, so that the model space could be explored for different sets of values and (iii) a probabilistic model or distribution could be adopted for each parameter, based on previous known observations. The outputs of such a model will be of statistic nature and will have a probabilistic distribution as well: based on this data, produced by the numerical model (f.i. a finite element model), a relationship between inputs and outputs could be established in an approximated mathematical formulation, the so-called metamodel. In this context, the newly generated (meta)model has the following characteristics: (i) it has been validated as the correct representation of the original model, (ii) it is much less computationally demanding than the original model, (iii) it establishes a direct relationship between the input parameters and the output, (iv) it can be used both for input parameters calibration, based on new observations, and, possibly, for the risk assessment. Based on these considerations, the metamodel could be assumed as a fast and validated decision-making tool. An elucidating example is herein discussed with reference to a historic masonry tower.

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.

The mistake to be corrected is the one named “1” in the attached pdf (i.e. to add the subscript ”,e” to the symbol “f1” at the beginning of the second row of Table 8).

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 Herit...

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 ...

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’.