The analysis of masonry structures is of particular interest in the civil engineering and architecture community due to the large amount of historical masonry constructions in Europe and in Italy in particular. Masonry is a heterogeneous material obtained by composition of blocks connected by dry or mortar joints. The use of refined models for investigating the in and out of plane nonlinear behaviour of masonry is an active field of research. Considering historical masonry, the mechanical

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... ties of joints are usually lower than those of blocks, allowing to assume that damage occurs more frequently along joints. For this reason, discrete element models (DEMs) may be frequently adopted for representing masonry behaviour, assuming blocks as rigid bodies and joints as interfaces, with a small number of degrees of freedom and parameters involved in the analysis. As well known, masonry walls may be considered as the most important category of load-bearing elements in masonry structures and they are subject to vertical and horizontal actions generated by gravitational loads and seismic actions, respectively. Horizontal loads may act in plane or out of plane, causing two different collapse mechanisms for a masonry wall. In this work a simple and effective discrete element model, already developed in linear field for in and out of plane analysis and already extended in nonlinear field but only for in plane analysis, is here extended to the three dimensional nonlinear analysis of masonry walls. A Mohr-Coulomb yield criterion is adopted for modelling interface behaviour. A numerical experimentation is carried on in order to determine the limit load multiplier, together with the collapse behaviour, of several masonry walls. Moreover, existing results are taken in consideration in order to calibrate the proposed model and to evaluate its effectiveness.