The SEPUC for the estimation of failure surface of quasi-periodic masonries

A quasi-periodic masonry is particular type of masonry which is made of blocks of different dimensions, arranged in order to realize row of stones of almost same height. The obtained texture is neither periodic nor completely random, and therefore it is necessary to adopt specific methods of analysis. The approach proposed in the present paper is to statistically analyze the quasi-periodic masonry, in order to obtain the main parameters which characterize the texture: dimension of the stones and mortar joints, height of the rows, alignment between the joints, etc. These parameters are subsequently used to obtain a Statistical Equivalent Periodic Unit Cell (SEPUC), defined as the periodic unit cell which is equivalent, according to a purely geometrical criterion, to the original masonry texture. Subsequently, the SEPUC is used in order to estimate the failure surface of masonry through two methods already proposed in literature for periodic masonry: a method which employs a micromechanical approach, and a method which adopts a limit analysis approach and solves the problem by means of linear programming. The obtained results suggest that the analysis of quasi-periodic masonries can be performed through the use of a SEPUC, and therefore using one of the several methods proposed in literature for periodic composites.