Compared to simple masonry walls, numerical modelling of masonry vaulted structures is particularly complex due to their three-dimensional curved geometry and articulated masonry pattern. Moreover, the scarce availability of experimental data makes it difficult to validate numerical models for these types of structures. Recently, the simplified micro-modelling approach has been applied by different authors, despite some intrinsic limits, such as huge numerical effort and adoption of ad-hoc written numerical codes. The aim of this study is to overcome these difficulties by using a commercial software with built-in friction interface models and to validate the proposed simplified-micro model through experimental tests on in-scale specimens of arch and cross vault. The proposed approach has shown promising features: experimental results have been numerically reproduced with a high degree of accuracy, both in case of planar and space structures, with both dry and mortar joints. The final result of the study is a validated modelling strategy that could be confidently applied to real masonry vaulted structures.

Cross masonry vaults are common structural elements in historical buildings. They are largely diffused in all European countries, including those characterized by higher levels of seismicity. Although they have been constructed for centuries, they represent some of the most vulnerable elements of traditional architecture, especially with reference to horizontal loads. The understanding of their structural behaviour under seismic loading is a crucial aspect for the accurate assessment of the safety of historical buildings. In the present work, the seismic response of cross masonry vaults is analysed through the Finite Element Method (FEM) and static non-linear analyses considering the effect of different brick patterns and boundary conditions. A simplified micro-modelling approach is adopted for the generation of the FEM models and two different brick arrangements are considered, i.e., radial bricks and diagonal bricks, which are the most widespread in European cross vaults. Two different boundary conditions are assumed in order to simulate a vault with and without lateral confinement. Static non-linear analyses are performed by monotonically incrementing a lateral acceleration until collapse. Results are analysed in terms of maximum load factor, stiffness, ductility, crack pattern and damage mechanisms. The analysis of the results shows that not only boundary conditions, but also the brick pattern strongly influences the vault seismic response both in terms of stiffness and ductility as well as in terms of global capacity.

In this paper, the structural performance of masonry cross vaults is investigated with regard to the most common differential settlements occurring in historical constructions. Numerical parametric models are developed for vaults with different brick patterns and lateral constraints, in the presence/absence of infill. In particular, radial, diagonal and pitched brick patterns are taken into account and opening, shear and vertical settlements are analyzed. Moreover, the behaviour of laterally unconfined vaults is compared with the response of vaults restrained with rigid perimeter walls or with lateral masonry arches. The analyses highlight the strengths and weaknesses of each configuration, providing a scientific validation to some speculations found in historical technical literature on the most widespread use of some brick patterns. The outcomes of this research provide a deep knowledge of masonry vaults behaviour in view of more effective interventions on historical buildings, supplying the practitioners with a crack-pattern chart useful for better interpreting the damage pattern in historical vaults with different brick courses.