A discontinuum finite element modelling approach for reproducing the structural behaviour of masonry walls

This paper defines an innovative approach for modelling masonry walls when the structural behaviour of new or existing buildings, subjected to vertical and lateral load, has to be evaluated. Such an approach aims to provide a calculation tool that allows to model the non-linear behaviour of masonry structures with a reduced numerical effort, but, nonetheless, without jeopardizing the accuracy of obtained results. The proposed model is a typical D-FEM (Discontinuum-Finite Element Model) that, differently by the most common methodologies, is composed by deformable blocks separated by interface elements arranged along pre-established surfaces of potential cracks. To this aim, the "Combined Cracking-Shearing-Crushing" model, proposed by Lourenco for the FEM analysis with the so called simplified micro-models, is used. Some experimental tests taken by litterature are described. Such tests are used as reference for setting up a non-linear model with the "simplified micro-modelling" approach, which considers the presence of blocks, of the same geometry of the stone units, separated by interface elements. Once that this modelling approach is validated, it is used to obtain the nonlinear response of 65 masonry panels which differ in terms of geometry, vertical loads, as well as in terms of the most significant mechanical parameters. The obtained responses for the 65 panels are taken into account for the calibration of the here proposed model. In detail, a proper variation of the coefficients contributing to the "Combined Cracking-Shearing-Crushing" formulation is implemented through a trial and error procedure, which ends when a satisfying comparison between the results provided by the two different methods of modelling is achieved; this for taking into consideration the constraints imposed on the development of cracking surfaces. The outcomes obtained with the here proposed modelling approach are then elaborated in order to develop suitable closed form equations, which provide the necessary coefficients that have to be used for implementing the modified "Combined Cracking-Shearing-Crushing" when a generic masonry panel has to be modelled.