3D homogenized limit analysis of non-periodic multi-leaf masonry walls

This paper presents a 3D model aiming at investigating the out-of-plane collapse behavior of multi-leaf non-periodic masonry walls. These structural elements are widely employed in several constructions that are part of the European architectural heritage, but have been seldom addressed in the available literature due to their natural complexity and uniqueness. Specifically, the model here proposed allows a quick assessment of the out-of-plane collapse behavior of multi-leaf walls through the extraction of out-of-plane homogenized failure surfaces, acting as macroscopic failure criteria in bending and torsion. These failure surfaces are obtained after solving a standard-form linear programming problem written into a MATLAB script, which expresses a limit analysis problem pairing the well-established upper bound theorem and a homogenization approach. A twofold numerical application is performed by investigating a rubble masonry three-leaf wall and a quasi-regular three-leaf wall; in the latter case study, the influence of the rate of transversal interconnection between the outer wythes of the wall is also investigated. The results show that the presence of two different masonry bonds in the outer wythes entails some changes in the out-of-plane collapse behavior of the two case studies: namely, the out-of-plane response of the wall both under flexural and torsional actions is increased for the rubble masonry three-leaf wall, whereas it is decreased for the quasi-regular three-leaf wall. Moreover, in the latter case it is once more confirmed that a good transversal interconnection between the outer wythes - usually brought by the presence of transversal bricks – has beneficial effects on its out-of-plane collapse behavior, which are displayed both by the out-of-plane homogenized failure surfaces and deformed shapes at collapse.