Discrete and continuous models for static and modal analysis of out of plane loaded masonry

This paper presents a critical review of several analytical and numerical models that may be adopted for studying the out of plane behaviour of one leaf masonry panels with regular texture, with particular attention to the case of historical masonry, that may be modelled by means of rigid blocks connected by dry or mortar joints. Discrete element model, Love-Kirchhoff and Reissner-Mindlin plate models and full 3D heterogeneous Finite Element model are considered. Static analysis and modal analysis are performed. Analyses are developed in the linear elastic field but the formulation adopted will allow to extend the present work to the nonlinear field. An existing simple and effective discrete model is adopted and improved by applying traditional matrix structural analysis techniques for performing out of plane static and modal analysis of masonry walls. The elastic parameters of both plate models are based on an existing compatible identification between 3D discrete model and 2D plate models. A wide experimental campaign is carried on by performing static and modal analysis of masonry walls with several boundary conditions. Numerical tests are carried on paying attention to an in plane scale factor, representing the size of heterogeneity of the masonry pattern, and to an out of plane scale factor, representing the thickness of the structure. Numerical tests show that the existing discrete model is simple and effective for representing masonry behaviour, especially when size of heterogeneity is small with respect to the overall size of the panel. Decreasing in plane scale factor, both plate models converge to the discrete one, but Reissner-Mindlin plate model shows a better convergence and also allows to adopt a simple plate Finite Element for performing numerical analysis.