PSI - Issue 78

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

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of  v , to guarantee mesh insensitivity. Shear behavior was assumed linear up to the attainment of peak shear stress, expressed according to a Mohr-Coulomb formulation, and hence as a function of masonry pure shear strength,  0 , friction coefficient,  , and stresses acting on the slippage plane,  v . This is then followed by a brittle cohesion softening and the spring entering a residual frictional-based regime. The adopted failure criterion is Mohr-Coulomb with tensile and compressive cut-offs, as shown in Figure 1c. As such, springs may experience tensile, compressive and/or shear failure, and exhibit residual frictional strength as a function of compressive stress acting normal to the slip surface. Springs subsequently deform at residual strength, until a user-defined separation strain is met, hence leading to their removal from the model and the previously connected elements behaving as free rigid bodies. Further details on the adopted failure criteria and modelling choices can be found in (Canditone et al., 2025).

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Figure 1. AEM-based simplified micro-modelling of URM assemblies: (a) bond pattern discretization, (b) uniaxial stress – strain relationships, (c) Mohr-Coulomb failure criterion with caps in tension and compression.

3. Description of the numerical model of Consoli Palace in Gubbio, Italy Consoli Palace is a 14 th Century landmark URM building complex in Gubbio, Italy, approximately 60 m tall and overlooking the main square of the town. The palace, built between 1332 and 1349 in calcareous, regularly coursed stone masonry, was erected on the slope of a mountain, so its foundations are placed at two different depths with approximately 10-m difference. The palace, with an approximately 20 m × 40 m rectangular-shaped plan, is accessed through a staircase and is composed of a central body, a bell tower, and a panoramic Loggia. A continuous structural health monitoring (SHM) system was first installed in 2017 and subsequently updated in 2020 by increasing the number of sensors, identifying several structural response parameters associated with the building’s health in operating conditions. Furthermore , the seismic response of the palace to low-intensity earthquakes that occurred in May 2021 was also monitored and used to calibrate both EFM and FEM-based distributed plasticity models of the Palace, based on observed frequency decays; see the work described in (Sivori et al., 2023). SHM data availability also enabled temperature effects on the static and dynamic behavior of the Palace to be addressed in (Kita et al., 2019). Details on the SHM setup and results from continuous SHM, as well as those obtained via machine learning-based and statistical treatment of SHM data, can be found in works such as (Garcia-Macias & Ubertini, 2022; Ierimonti et al., 2023). The loggia, sitting on a rocky ridge, is the subject of the present study and was, hence, modelled with great accuracy in an AEM environment (see Figure 2a). Information on masonry bond patterns, thickness, wall to-wall connections and presence of pre-existing cracks was gathered from in-situ surveys, which are discussed in, for instance, (Catapano et al., 2018). Masonry wall thickness was observed to approximately vary between 0.50 m at top story ( that is, the Loggia’s panoramic terrace ) and 2.80 m at lower story. A regular 0.95 × 0.25 m 2 block size was adopted, based on average block and mortar joint dimensions, and monolithic cross-sectional behavior was assumed, hence limiting the number of degrees-of-freedom (DOFs). A detailed modelling of the vaulted ceiling system (Figure 2b) was performed, thereby incorporating vault thrusts and overburden, as well as the effects of potential vault geometry changes due to support displacements, in the analysis. Good-quality wall-to-wall interlocking was assumed and modelled via staggered blocks distributed along wall-to wall intersections. The presence of pre-existing damage was considered by incorporating zero-tension, zero-cohesion contact interfaces within the model, based on the observed crack pattern (see Figure 2c). The interaction with the main