Simplified out-of-plane modelling of three-leaf masonry walls accounting for the material texture

In this paper, three approaches with different levels of accuracy and approximation are proposed and critically discussed with the aim to model the non-linear out-of-plane response of three-leaf masonry walls. Two examples of masonry textures are considered, the first consisting in a quasi-periodic arrangement of large blocks with different length and a weak transversal interconnection, the second in a more interconnected three leaf masonry, with the external leaves constituted by two running bond wythes. These textures were analyzed by means of (i) a FE homogenization procedure performed on sufficiently large test windows subjected to increasing bending and torsion; (ii) an analytical approach based on the assumption of a simplified RVE kinematic; (iii) a non-linear heuristic model where the non-linearity and damage are concentrated into springs with suitable mechanical properties. These approaches provided good estimates of macroscopic moment–curvature diagrams for both textures, by reproducing the orthotropy of flexural peak strength in relation with the texture geometry, the different shape of the post-peak response and the residual strength due to the orthotropic influence of the average vertical compression stress. The final application consists of a seismic analysis by means of a Rigid Body and Spring Model (RBSM) specifically designed to describe the flexural–torsional response at the macro-scale level. This choice allowed a straightforward implementation of the non-linear heuristic model at a realistic scale after a simple preliminary analysis made for estimating the level of average vertical axial compression in the wall. The results highlighted how the texture plays a crucial role on the determination of the out-of-plane flexural–torsional façade response under seismic excitation. The paper contributes to offer a rational basis when modelling, albeit with many simplifications, the micro-structure masonry characteristics in the non-linear field with damage.