PSI - Issue 78

Mattia Zizi et al. / Procedia Structural Integrity 78 (2026) 1721–1728

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3. Preliminary numerical modelling 3.1. Prototype geometry and test set-up

The present section describes preliminary numerical simulation of the experimental test that will be performed at the Structural Laboratory of the LEDA Research Centre (Fossetti et al., 2017) in Italy. The test will involve the application of monotonic horizontal displacements at two supports of the vault, specifically the ones adjacent to the dome in the reference structure, up to the failure. This loading configuration is considered representative of the effects produced by a seismic event acting along the longitudinal direction of the church, given the significant stiffness provided by the infill walls on the other three sides of the vault. Due to laboratory constraints, the vault dimensions were scaled down by a factor of 1.3, while still reflecting the proportions of similar real Italian examples. In addition, some of the more complex geometrical details were simplified to facilitate the construction of the vault prototype. A parametric numerical study was performed in order to investigate the influence of unknown geometrical parameters, i.e. thickness of the vault, as well as to estimate the maximum capacity of the prototype to be tested. Thus, four different cases were analysed by assuming thickness ( t ) of 6, 9, 12 and 15 cm. 3.2. Numerical modelling Finite Element models were developed using ABAQUS software (Dassault Systèmes Simulia Corp., 2023), employing a macro-modeling approach for the discretization of masonry material. The masonry behavior was simulated through the Concrete Damage Plasticity constitutive model included in the software’s library (Lee & Fenves, 1998; Lubliner et al., 1989). Material properties were determined based on typical values of tuff masonry. The assigned material characteristics comprised a density of 1600 kg/m³, an elastic modulus of 1410 MPa, a compressive strength of 2.60 MPa, and a tensile strength of 0.1 MPa. The compressive response was modeled with a parabolic stress-strain relationship, whereas the post-peak tensile behavior was simulated by means of a linear softening law with a fracture energy of 20 N/m. Damage progression in both compression and tension was assumed to follow a linear trend starting from the peak strength. Further parameters were defined according to the standard values suggested in the software documentation. The Finite Element models were assembled with 10-node quadratic tetrahedral elements (2 nd order), using an average mesh size of 25 cm, which was determined based on a preliminary sensitivity analysis. Fig. 3 shows the implemented geometries and mesh for the analysed cases with a vault thickness of 12 cm.

(b)

(a)

Fig. 3. The adopted numerical model: (a) geometry and (b) mesh of the case with vault thickness of 12 cm

The analysis process was divided into two main phases. In the initial Static/General phase, the self-weight load was applied under the assumption that the base of the vault supports was perfectly fixed. The second phase involved