PSI - Issue 80

Riccardo Giacometti et al. / Procedia Structural Integrity 80 (2026) 219–231 R. Giacometti, N. Grillanda, V. Mallardo / Structural Integrity Procedia 00 (2023) 000–000

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1. Introduction

Masonry structures represent the most di ff use type of construction in the historical centres all over Europe. They are the inheritance left by our ancestors and need to be preserved for di ff erent reasons. First of all, they are often them selves valuable architectural examples, furthermore, may contain artistic and elements of great value, both features attracting tourists from all over the world and, hence, providing an added income to the local communities. Secondly, due to their privileged position, historical masonry strucures usually host important public establishments such as mu seums, galleries, government o ffi ces, or representative shops, apartments, ateliers, private o ffi ces. Last but not least, the growing need to reduce pollution and waste production pushes towards rehabilitation rather than demolition and reconstruction. It is worthy to underline that even simple masonry structures, i.e. lacking in artistic characteristics wor thy to be preserved, may entice private and public authorities to protect them because of their intrinsic good urbanistic standards (low height, wide bu ff er zones often rich of vegetation) and thermo-acoustic insulation properties. It is therefore clear that maintenance and rehabilitation are of primary importance with masonry structures. Such tasks are to go through a correct and realistic estimation of the safety level: the closest it is to truth, the better will be the design of the refurbishment actions. For instance the earthquakes occurred in Italy between 1980 and 2000 have shown that reinforced concrete (r.c.) intervention techniques have often exhibited their inability in protecting the masonry structures. The ”therapy” may become worse than the ”disease” when it is not supported by reliable prediction procedures. The vulnerability of masonry structures are mainly of two types: against seismic events, even moderate, and against soil interaction. Such topics have involved many researchers along the past decades, with special attention to the theoretical and numerical methods to be adopted for the best structural comprehension of their e ff ects. A recent review and classification of the modeling strategies for the computational analysis of unreinforced masonry structures is given in D’Altri et al. (2020). Limit analysis along with the assumption of negligible elastic strains and null tensile strength, is the most trodden approach that has been adoped to deal with the seismic analysis on masonry structures. Numerous studies have been carried out especially in the context of the thrust line theory Block et al. (2006), Nodargi and Bisegna (2022) and on the basis of the kinematic theorem Milani et al. (2007). In the latter an upper bound of the seismic-bearing capacity is found if a compatible mechanism is defined. This means more mechanisms need to be investigated in order to minimize such a capacity and compute a realistic estimation of the safety coe ffi cient. Besides, the necessary discretization requires huge computational demand and poses some limits in the application to real cases. Homogenization techniques Milani et al. (2006); Grillanda and Mallardo (2025) have then been developed to overcome such an issue but the research is still open as not fully applicable to real cases. In the present contribution the authors present some recent results on the optimization of the discretization and on the application of homogenization techniques in the context of the seismic analysis by upper-bound limit analysis. The goal is to reduce the computational e ff ort to be made to predict the actual mechanism of large buildings. Another source of damage in masonry structures is due to soil di ff erential settlements. Soil movements represent a variation of the boundary conditions with consequent development of cracks. Seismic events, even moderate, tra ffi c vibrations, nearby refurbishment works may produce perturbation in the soil foundation that entice base settlements; changes in the water content of the soil, tunneling, excavations, are often source of stress redistribution in the soil with resulting di ff erential movements at the foundation level of the masonry building. In the last years, much e ff ort has been devoted to the analysis of the influence of the base di ff erential settlements on existing masonry structures Tralli et al. (2020), Zampieri et al. (2017), Portioli and Cascini (2016), Iannuzzo et al. (2018), Cardinali et al. (2023). In this context the case of masonry arch bridges is of particular interest. For masonry arch bridges, floods can cause local pier scour phenomena, inducing the rotation of the pier and leading to unexpected collapse. Given their strategic function, together with the historical values, the assessment of masonry arch bridges under the most critical causes of collapse is currently an active research field Zampieri et al. (2018), Zampieri et al. (2024). The numerical strategies conceived for analysis of masonry structures interacting with soil adopt a very simplified soil modelling. Indeed, while the advanced optimization-based procedures are used to simulate the masonry response, soil settlements are usually represented as simple boundary conditions for the masonry domain, for instance as fixed displacement at the base. In general, there are a few models capable to investigate the soil-structure interaction both under loads applied directly to the masonry and under stress modifications in the underneath soil. However, in a recent work by some of the authors Mallardo and Iannuzzo (2025) a novel numerical approach for the soil-structure