Seismic events in Italy and worldwide have highlighted the high vulnerability of unreinforced masonry (URM) structures in small historical centres. A key feature of these settlements is to be mostly composed of buildings in aggregate, i.e., interconnected by a more or less structurally effective connection. The seismic assessment of such buildings is quite debated in the literature and no shared tools procedures are currently available. The difficulty of standardization derives from the fact that structural units can be characterized by multiple features and configurations that determine a vast number of vulnerability factors, whose interdependency is not straightforward to be identified. The paper addresses this issue by combining evidence-based damage data with the potential offered by Machine Learning (ML) technique. Real data are used in combination with state-of-the-art ML algorithms carefully tuned via an advanced statistical procedure for two main purposes. The first one will be able to predict possible URM damages based on the vulnerability factor in both interpolation and extrapolation scenarios. The second purpose of the ML-based techniques will be to predict the most important vulnerability factors in making these predictions, namely to make the ML-based model explainable and informative about the underlying phenomena and not just predictive. The small historic centre of Casentino, hit by the 2009 L'Aquila earthquake, is adopted in the paper as the first test case study. A large amount of data was collected after the earthquake through in-situ surveys made by the Universities of Genova, Catania and Rome. Data include both geometric and structural factors, i.e., the input data supplied to the ML algorithm, as well as the actual seismic damage mechanisms, i.e., the output data expected to be predicted by the ML algorithm. As first application, ML techniques are applied only to data acquired on out-of-plane mechanisms.

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This paper presents a benchmark exercise for the seismic assessment of unreinforced masonry (URM) buildings as a follow-up of a blind prediction test organized in the context of the European Conference of Earthquake Engineering Series. The blind prediction exercise was aimed at better defining the open issues in current procedures for modeling and performing seismic analysis of URM buildings, by highlighting the uncertainty that can influence the results. This work presents an overview of the approaches used by different research teams and the scope of predictions. The benchmark structure was a three-story building with traditional European architecture from which two Cases were considered: A) stone masonry walls and flexible horizontal diaphragms and B) brick masonry walls and rigid horizontal diaphragms. A wide range of approaches was used by the participating teams concerning modeling strategies, methods of analysis and criteria for the attainment of limit states, which are here addressed as potential sources for the dispersion of predictions. The results were compared in terms of capacity curves, predicted failure mechanisms compatible with the fulfillment of limit states of near collapse and damage limitation, and related minimum values of peak ground acceleration (PGA). The results show an overall good agreement for damage patterns and collapse mechanisms in both benchmark structures, presenting some differences in the type of failure mode and its extent. However, the scatter of predicted capacity curves and critical PGAs is very high, especially for the Case with brick masonry and rigid diaphragms, indicating that clearer procedures in the building codes are required for professionals.

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Several tools for the prediction and the assessment of the structural behavior of masonry buildings have been developed in recent decades. Numerical tools have been favorably developed and preferred over analytical approaches, given the complex mechanical response of masonry and the irregular geometries of historic masonry buildings. In this chapter, a thorough review of numerical strategies for the analysis of masonry structures is presented. Additionally, classification of these strategies is also suggested to logically organize the extensive literature on this topic. Even though a wholly congruent categorization of all the numerical tools is essentially unrealistic given the specific aspects of each solution developed, the existing numerical strategies are subdivided into four classes: block-based models, continuum models, geometry-based models, and macroelement models. Each class is thoroughly reviewed and the open challenges in numerical modeling of masonry structures are critically examined.@en

Masonry structures, although classically suitable to withstand gravitational loads, are sensibly vulnerable if subjected to extraordinary actions such as earthquakes, exhibiting cracks even for events of moderate intensity compared to other structural typologies like as reinforced concrete or steel buildings. In the last half-century, the scientific community devoted a consistent effort to the computational analysis of masonry structures in order to develop tools for the prediction (and the assessment) of their structural behavior. Given the complexity of the mechanics of masonry, different approaches and scales of representation of the mechanical behavior of masonry, as well as different strategies of analysis, have been proposed. In this paper, a comprehensive review of the existing modeling strategies for masonry structures, as well as a novel classification of these strategies are presented. Although a fully coherent collocation of all the modeling approaches is substantially impossible due to the peculiar features of each solution proposed, this classification attempts to make some order on the wide scientific production on this field. The modeling strategies are herein classified into four main categories: block-based models, continuum models, geometry-based models, and macroelement models. Each category is comprehensively reviewed. The future challenges of computational analysis of masonry structures are also discussed.@en