PSI - Issue 78

Maria Eleonora Pipistrelli et al. / Procedia Structural Integrity 78 (2026) 1911–1918

1912

architectural style and construction typology (Pellegrini et al., 2019). This process led to the formation of building clusters, that can be frequently observed in abbeys, churches, and residential structures throughout the country (Pinasco et al., 2025; Celetti et al., 2023). When retrofitting historical masonry aggregates, a preliminary seismic vulnerability assessment is required to consider both the inherent weaknesses of masonry and the complexities arising from aggregate formation. A key aspect of this process is analyzing the interaction between structural units (S.U.s), which are the fundamental components of the aggregate. According to the 2018 Italian Technical Standards for Construction, a S.U. is a vertically continuous portion of a building, from roof to foundation, typically bounded by open spaces, joints, or adjoining typologically distinct structures. These units often vary in construction period, materials, geometry, number of stories, and inter-story heights (Chieffo et al., 2023). The overall response is commonly interpreted through the so-called “aggregate effect” (Angiolilli, 2023). Given this complexity, identifying and analyzing S.U.s demands a multilayered approach. Preliminary investigations are essential and should include a historical-critical study, detailed geometric and material surveys, and an assessment of visible damage such as cracks or deformations (Acito et al., 2023). Based on this information, an analytical model can be developed to evaluate the building’s seismic capacity relative to the expected seismic demand. Depending on the assessment goals, either static or dynamic analyses may be used, in linear or nonlinear behaviour. Among these, nonlinear static (pushover) analysis is widely adopted in practice, offering a good balance between accuracy and computational efficiency. When dealing with regular geometries, the pushover analysis is commonly paired with Equivalent Frame Model (EFM). According to this approach, masonry structures are discretized into interconnected piers, spandrels, and rigid nodes, allowing the simulation of global nonlinear behavior. However, this method cannot capture local collapse mechanisms or detailed crack propagation (Acito et al., 2023). These are generally studied through discrete macro-element models using kinematic limit analysis. In this approach, walls are represented as rigid or deformable blocks to evaluate potential collapse mechanisms under seismic loads (Acito et al., 2023). Yet, the absence of material cracking or crushing in the model may result in underestimated strength. To improve reliability, these results are often compared with elastic modal analyses to ensure all critical failure modes are captured. A crucial modeling decision in the seismic assessment of masonry aggregates concerns the extent of the structure to be represented. This means deciding whether it's more appropriate to model S.U. in isolation, or if it's necessary to include adjacent parts of the aggregate as well. This choice depends on both the analysis type and available computational resources. Several recent studies examined the implications of this modeling choice. Di Trapani et al. (2024) conducted a detailed numerical analysis comparing S.U.s modeled both in isolation and within a simplified linear aggregate of three connected units. Their findings suggested that while isolated modeling produced conservative results in terms of global response, it failed to capture the actual vulnerabilities of specific elements. Similarly, Acito et al. (2023) analyzed a real case study by modeling three partial sections of a building aggregate. They showed that the use of elastic springs or fixed boundary conditions must be carefully selected depending on the structural continuity with adjacent units. Modeling in isolation, they concluded, may only be conservative when load-bearing capacity is the primary concern. Formisano et al. (2018) proposed a simplified method using EFM and pushover analysis to assess the seismic performance of a structural unit within an aggregate. By comparing the behavior of a unit modeled in isolation, as part of a full aggregate, and with calibrated boundary conditions, they demonstrated that while isolated modeling can be acceptable in the longitudinal direction, it failed to reproduce the transverse response unless proper boundary constraints are introduced. Battaglia et al. (2020) further highlighted that interaction effects within aggregates significantly influenced seismic fragility and stiffness. Their comparative study of isolated and aggregated S.U.s showed that modeling a unit in isolation may either overestimate or underestimate vulnerability depending on directionality and structural context. Despite a growing body of work, many studies in this field use idealized scenarios and do not validate their methodologies against real-world masonry aggregates. Furthermore, when analyzing S.U.s within aggregates, current approaches either propose isolated partial models or model the entire aggregate, without evaluating the validity of simplified methods that partially include adjacent S.U.s. To address this gap, the present study investigates multiple modeling configurations of a S.U. from a real masonry aggregate in Todi, Italy. Using nonlinear analyses based on EFM, three scenarios are compared: the unit modeled in isolation, the unit with elastic