PSI - Issue 64

Corrado Chisari et al. / Procedia Structural Integrity 64 (2024) 199–205 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

200

2

1. Introduction Recent studies highlighted how curved elements, and in particular vaults, may suffer severe damage in masonry constructions when subjected to seismic excitations (D'Altri, et al., 2017; De Matteis and Zizi, 2019). This holds particularly true in the cases of masonry churches and historical palaces, where these distinctive elements usually were adopted to realize roofing and flooring systems, respectively. Due to their typical geometrical features, vaults are generally characterized by a low stiffness. This, combined with the usual poor mechanical characteristics of masonry material, makes them significantly vulnerable in case of horizontal actions. Based on this, the problem of the seismic protection of masonry vaults has received a notable scientific interest in the last decades. Many experimental, numerical and analytical studies were performed by several authors aimed at investigating the seismic response of these elements and the proposal of compatible retrofitting solutions (Roselli, et al., 2023; Bianchini, et al., 2021; Baraccani, et al., 2020; Bianchini, et al., 2023; Gioffré, et al., 2023). Among the wide variety of vault typologies that can be found in historical masonry constructions, cross vaults certainly represent one of the most interesting and complex systems from a structural point of view (Alforno, et al., 2022; Chàcara, et al., 2023). In ancient churches, they were mainly adopted to mark the rhythm of the bays, as well as roofing systems for the transept zone. In this latter case, the presence of asymmetrical boundary conditions makes the problem of the seismic assessment even more complex (Bianchini, et al., 2023). Typically, cross vaults in transept zone are supported by stiff walls on three sides, while the fourth side (e.g. the one on the intersection between transept and central nave) is open and supported by columns. This configuration may represent a source of fragility and cracking propagation during an earthquake due to the differential stiffness of the four sides of the vault. In this study, the horizontal shear deformability and capacity of this typical system are investigated. A total number of 16 numerical prototypes are analyzed by varying the main geometrical parameters to assess the overall response of the system subjected to in-plane shear displacements at the springings. The present study must be intended as preparatory for an experimental study aimed at testing a real scale prototype of a masonry cross vaults within the activities of the research project GENESIS (seismic risk manaGEmeNt for tourist valorization thE hiStorIcal centers of Southern Italy). 2. Numerical modelling of a cross vault 2.1 Description of the material model The macro-scale modelling approach used in this paper represents masonry within a Finite Element (FE) framework as a homogeneous material. This is characterized by nonlinear constitutive relationship based on isotropic damage mechanics. Using the equivalent strain concept developed in (Mazars, et al., 2015), two equivalent strains are defined for damage in tension (cracking) and in compression (crushing), respectively: = 〈 ̃〉 (1) = 1 −1 [ 1 1 − 2 + √3 2 1+ −(1+ )〈 ̃〉 − 〈− ̃〉] (2) where: ̃ = 1 (1+ )(1−2 ) + 1+ (3) and: