PSI - Issue 78

Ciro Canditone et al. / Procedia Structural Integrity 78 (2026) 379–386

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1. Introduction Unreinforced masonry (URM) buildings have remarkable vulnerability to both natural and anthropic hazards, potentially leading to significant losses both in socio-economic, cultural and human life terms. URM structural response to earthquake-induced loads has been substantially explored in the literature, both via simple tools such as Equivalent Frame Modelling (Parisi & Augenti, 2013; Lagomarsino et al., 2014; Quagliarini et al., 2017; Sivori et al., 2023) and more advanced continuum and discontinuum-based techniques (Lemos, 2007; Canditone et al., 2023; Calò et al., 2021; Ravichandran et al., 2021; Schiavoni et al., 2024; Canditone et al., 2025). By contrast, structural response and vulnerability to other hazards, such as landslides and soil settlements, is relatively less explored. Recurring failure mechanisms of URM churches subjected to landslide phenomena were addressed, for instance, in works such as (Ferrero et al., 2021). The response of URM wall systems to soil settlement scenarios was explored in works such as (Giardina et al., 2013; Ferlisi et al., 2020; Ehresman et al., 2021; Atmaca et al., 2023; Canditone & Parisi, 2025). Despite significant differences in the modelling of URM mechanical/structural response and soil-structure interaction (SSI), such studies highlight the important effects played by soil-settlement-induced load redistribution amongst structural members on load paths and potential element-scale and building-scale failure mechanisms. However, it should be noted that such studies typically focus on quasi-static phenomena, such as slow-moving landslides or subsidence-induced settlements. A research gap is found with regards to other abnormal loading conditions, such as those induced by sudden rock/bedrock failure scenarios. These brittle phenomena, which can be induced, e.g., by local stress concentrations, progressive erosion due to water seepage or active and capable seismic faults, may cause abrupt stress redistribution in the superstructure and possibly trigger progressive collapse scenarios (Waltham et al., 2005; Gutierrez et al., 2009; Cennamo et al., 2017) which may be dealt with via dynamic analyses. Within this study, the structural robustness of an URM heritage structure - the Consoli Palace Loggia in Gubbio, Italy - is explored via dynamic analyses of a high-fidelity discontinuous model. URM bond pattern is simulated via rigid blocks, connected via nonlinear contact springs where material deformability and failure modes are lumped. The presence of pre-existing damage conditions, associated with vertical loading and past earthquakes, is accounted for via zero-tension and zero-cohesion interfaces distributed in the structural model based on in-situ surveys. A highly detailed modelling of the barrel and cross vaults of th e palace’s Loggia is pursued, to simulate actual load distribution and the potential for load redistribution in a realistic way. The interaction of the Loggia with the main palace body is captured in a simplified way, that is, modelling return walls according to Eurocode 6 (2005) provisions with regards to effective flange wall length. Foundation-level bedrock failure is implicitly simulated by removing base restraints, hence activating the potential for inertial load redistribution and progressive collapse. Multiple bedrock failure scenarios are considered, progressively increasing the extent of failed bedrock below the Loggia’s footprint. Load redistribution phenomena, structural element and global level failures are then discussed, providing valuable insights into the structural robustness of the case study and showcasing the potential for AEM-based progressive collapse The AEM is an explicitly discontinuous numerical technique, based on the premise of structural discretization via rigid cuboids connected via nonlinear springs. System deformability and potential failure modes are hence lumped into the contact interfaces, making the AEM a discrete crack-based technique, suitable for large displacement, near collapse and progressive collapse analysis of URM structural elements and buildings (Malomo & Pulatsu, 2024). Within the AEM, a simplified micro-modelling ―also called meso-modelling approach (Lourenço, 1996) ― is typically pursued, representing masonry bond pattern as an assembly of expanded blocks interacting via an m × n grid of axial and tangential springs (see Figure 1a). Each spring accounts for the deformability and strength of a finite volume,  v , defined as a function of ( i ) contact plane ― and, hence, for regularly coursed masonries, block ― height and thickness, h and t , ( ii ) the adopted m × n discretization of the contact plane, and ( iii ) centroid distance between adjacent blocks d . Axial and tangential spring stiffness, k n and k s , are automatically evaluated and updated based on the nonlinear stress – strain relationships adopted in tension, compression and shear. In this study, fracture energy based softening functions based on the work by (Feenstra & De Borst, 1996) were adopted for uniaxial behavior (see Figure 1b). Fracture energies were regularized based on average block size, and hence proportional to average value analysis of URM buildings subjected to sudden foundation-level failure. 2. Applied Element-based micro-modelling of URM structures