Evaluation of a Statistically Equivalent Periodic Unit Cell for a quasi-periodic masonry

The paper presents a method to estimate the Statistically Equivalent Periodic Unit Cell (SEPUC) corresponding to a masonry with quasi-periodic texture. The identification of the texture and the constituent phases (unit blocks and mortar joints) is achieved by means of digital image processing techniques applied to color image of the masonry wall. A statistical analysis of geometrical parameters (width and height of blocks, thickness and length of mortar joints) allows to estimate their probability distribution and to identify the typology of the texture. Subsequently a Monte Carlo analysis is performed using several tentative SEPUCs generated with different dimensions of blocks and joints according to the estimated distributions. A criterion was eventually proposed to identify, among the numerically generated ones, the SEPUC which is more suitable to model the behavior of masonry wall. The SEPUC is analyzed with techniques available for periodic texture, applying periodic boundary conditions, in order to estimate the equivalent elastic stiffness. The proposed method is validated comparing the results in the elastic range obtained with SEPUC and those obtained imposing essential and natural boundary conditions on the original texture.