Image-based structural kinematic limit analysis for historical masonry structures

Evaluating the state of historical masonry structures, particularly those built with irregular masonry, presents challenges in determining their load-bearing capacity. Most current approaches use macroscopic numerical models that treat the material as a homogeneous continuum, where defining an appropriate constitutive law is essential. To this end, homogenization has proven useful in bridging the gap between meso and macro-scales, yet using homogenized macromodels may prevent to capture specific failure modes. Alternatively, mesoscopic methodologies represent stacking modes explicitly. However, full structural analysis at this scale has mainly been applied to regular masonry due to the complexities of explicitly representing the geometry of the irregular stones. The present contribution aims to propose a method that leverages image acquisition techniques, such as orthophotos, to address these challenges. Mortar joints are lumped onto zero-thickness interfaces, determined through a distance field-based morphing procedure and medial axis principles. The load-bearing capacity is assessed using a Kinematic Limit Analysis problem, formulated and solved as a linear programming problem. A Mohr-Coulomb frictional behavior, modified with a tensile cut-off and a linearized compression cap, is assigned to the mortar joints. The blocks are considered infinitely rigid and strong. It is shown that the proposed methodology can efficiently model structures of large sizes, by illustrating its use on two 2D problems.