PSI - Issue 78

Ciro Canditone et al. / Procedia Structural Integrity 78 (2026) 1855–1862

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1. Introduction Unreinforced masonry (URM) buildings, particularly historic ones, are characterized by remarkable vulnerability to both natural and anthropic hazards, such as earthquake ground motion, landslides, or soil settlements. The seismic performance of both ordinary and heritage URM buildings is, for instance, quite poor and characterized by: (i) the development of extensive cracking phenomena, due to the quasi-brittle nature of URM and its constituents; (ii) the activation and development of element-scale, sub-assemblage-scale, and building-scale collapse mechanisms, due to both in-plane (IP) and out-of-plane (OOP) loads. The failure of these constructions lead to economic severe losses due to repair or retrofit costs, as well as cultural value and human life losses, as evidenced in seismic events such as the 2009 L’Aquila earthquake (Augenti & Parisi, 2010; D’Ayala & Paganoni, 2011; Parisi & Augenti, 2013). A similarly poor performance is also observed regarding other abnormal loading conditions, such as subsidence or excavation-induced soil settlements. Indeed, scientific research has investigated the response of URM buildings to such loads, including the analysis of foundational settlements (Skempton & MacDonald, 1956; Burland & Wroth, 1974) and the relationship between load magnitude and position and the experienced structural damage and associated economic losses. Further studies have also explored the relationship between initial stress state, structural detailing, element aspect ratios and damage, as well as the deformation and capacity response of URM pier and spandrel elements subjected to vertical settlement (Beyer, 2012; Beyer & Dazio, 2012; Karanikoloudis, 2024; Meoni, et al., 2024). Both empirical and experimental evidence have highlighted the possibility of early detection, and, potentially, localization of damage by monitoring key structural static and dynamic responses via so-called Structural Health Monitoring (SHM) systems (see, for instance, (Kouris, et al., 2019; Ierimonti, et al., 2023; Meoni, et al., 2024)). Continuous SHM offers an effective perspective to assess structural response under both ordinary and abnormal loading conditions, potentially enabling: (i) structural maintenance, safety assessment, and targeted repair and/or retrofitting of both ordinary and heritage buildings; (ii) the calibration of simplified or advanced numerical models of the structure to obtain valuable insights into the expected structural response. Despite the clear motivation for SHM, it should be noted that the proper design of monitoring systems is not an easy task, especially when multiple hazards are to be considered and the relationship between such hazards and the expected structural performance is unclear. To this end, advanced numerical modelling, possibly based on SHM data obtained via a preliminary SHM system setup, may support the identification of potential damage-sensitive regions, hence leading to the development of an improved system, and providing decision-makers with valuable insights into the structural performance to be expected by the building in its actual, repaired, or retrofitted states; see, e.g., (Sivori, et al., 2023). Structural analysis of URM buildings may be performed via a variety of numerical strategies, with the so-called Equivalent Frame Modelling (EFM) as one of the most widely adopted. Within the EFM, URM buildings are discretized a priori into an assembly of deformable macro-elements, interacting via rigid end offsets, hence making this approach computationally inefficient, but unsuitable for capturing the behaviour of buildings with an irregular openings layout (Parisi & Augenti, 2013; Quagliarini, et al., 2017). Hence, it is recommended to couple EFM with other computational strategies, such as limit equilibrium analysis or macro-modelling approaches; see (Sivori, et al., 2023). Within macro-modelling approaches, URM is treated as a homogenized, distributed plasticity continuum, facilitating the modelling of complex, irregular geometries. Examples of macro-modelling analysis of URM buildings subjected to earthquake ground motion and settlement loads can be found in (Giardina, et al., 2013; Canditone, et al., 2023; Atmaca, et al., 2023; Meoni, et al., 2024). Continuum-based macro-modelling strategies may, on the other hand, fail in capturing bond pattern effects onto structural response, as well as actual collapse behaviour. To this end, discontinuum-based techniques, such as the Discrete Element Method (DEM), Non-Smooth Contact Dynamics (NSCDs), and the Applied Element Method (AEM) have seen rising interest in the literature; see (Lemos, 2007; Calò, et al., 2021; Schiavoni, et al., 2024; Canditone & Parisi, 2025; Canditone, et al., 2025). Within such approaches, URM is generally discretized via sets of discrete bodies interacting via nonlinear interface springs, hence capturing bond pattern effects (Malomo & Pulatsu, 2024; Canditone & Parisi, 2024). Both macro and micro-modelling approaches entail, however, significant computational burden, which makes the execution of many analyses computationally demanding. To address this challenge, it is possible to use the output of advanced numerical models to train robust surrogate models. These models represent a mathematical model mapping certain input and output variables of the forward model, bypassing the latter with a considerably lower computational cost and enabling the potential to address large numbers of loading conditions. The latter aspect is of particular interest