An innovative voxel-based approach for the out-of-plane homogenized limit analysis of non-periodic multi-leaf masonry walls

A recurring construction technique in many European countries (Italy included) is based on the erection of multi-leaf walls. Their seismic vulnerability is usually high, due to the fact that the wythes are poorly or by no means connected one each other. Hence, masonry buildings with multi-leaf walls regularly display an insufficient strength against out-of-plane actions (such as those caused by earthquakes and those causing the highest vulnerability), which leads to partial or total collapse. This paper proposes a novel approach devoted to the out-of-plane analysis of masonry multi-leaf walls at collapse, with special attention given to the case of non-periodic masonry - in which the units display different geometries and are randomly arranged in the walls. This approach is based on the so-called “voxel strategy”, in which the 3D finite element mesh of a multi-leaf wall is created directly from the rasterized images of its external wythes. Every pixel of the rasterized images is transformed into its 3D counterpart (the “voxel”, indeed), which is then converted into a solid finite element. The “voxel strategy” for generating the finite element mesh is translated into a MATLAB function, which is itself part of a broader limit analysis approach based on the upper bound theorem, that aims at deriving homogenized out-of-plane failure surfaces. These represent macroscopic out-of-plane strength criteria for the selected non-periodic multi-leaf masonry walls; they are expressed in terms of flexural and torsional moments around the horizontal and vertical axes of the considered wall. The approach also enables the extraction of the deformed shapes at collapse for single out-of-plane load conditions. The homogenized out-of-plane failure surfaces are the results of an upper bound limit analysis problem coupled with homogenization, aptly formulated as a standard-form linear programming problem. The solid finite elements of the created mesh are rigid, and the velocity jumps at the interfaces between adjacent finite elements obey a Mohr-Coulomb failure criterion with separate tension and compression cut-offs and associated flow rule. A case study is investigated to benchmark the procedure, namely a rubble masonry three-leaf wall with absente interconnection between leaves.