Discrete model for out-of-plane loaded random masonry

In this contribution, a simple and effective discrete element model based on rigid blocks and elastic interfaces with fixed contact topology, originally introduced for modeling regular masonry panels, is extended to the case of random masonry by introducing a perturbation parameter able to vary the width of each block. The proposed model is then able to better reproduce the microstructural behavior of historical masonry, that is characterized by dry or weak mortar joints between strong blocks, and, in particular, that is characterized by blocks often arranged irregularly. The hypothesis of rigid blocks, together with fixed contact topology between blocks due to the small displacements assumption, allows adopting an efficient solution method based on the determination of the stiffness matrix of the masonry assemblage. In this case, the stiffness matrix is able to account for the irregular block arrangement and, similarly to the case of regular masonry, the stiffness matrix is based on local joint stiffness, given that the contact actions along the joints are function of the relative displacements between adjacent blocks and the corresponding interface stiffness. Several numerical tests varying the random perturbation parameter are performed in order to evaluate the influence of randomness on masonry specimen behavior with respect to the regular case. Particular attention is given to the dynamic field by performing out-of-plane modal analysis of masonry panels. Furthermore, a homogenization procedure is applied to the random masonry and a numerical evaluation of the scatter between the discrete models and a 2D Reissner-Mindlin plate model is performed for varying perturbation parameter and for increasing heterogeneity parameter. As expected, when the number of heterogeneities in the structure is large enough, the average response of the random discrete model converges to an asymptotic response.