Limit analysis of masonry walls using discontinuity layout optimization and homogenization

A numerical limit analysis model for masonry walls subject to in-plane loading is posed as a discontinuity layout optimization (DLO) problem, with the masonry conveniently modeled using a smeared continuum (“macromodeling”) approach and a homogenized yield surface. Unlike finite element limit analysis, DLO is formulated entirely in terms of discontinuities and can produce accurate solutions for problems involving singularities naturally, without the need for mesh refinement. In the homogenized model presented, masonry joints are reduced to interfaces, with sliding governed by an associative friction flow rule and blocks are assumed to be infinitely resistant. The model takes account of the interlock ratio of the masonry blocks, their aspect ratio and the cohesion and coefficient of friction of interfaces in both the vertical and horizontal directions. Results from the proposed model are compared with those from the literature, showing that complex failure mechanisms can be identified and that safe estimates of load carrying capacity can be obtained. Finally, to demonstrate the utility of the proposed modeling approach, it is applied to more complex problems involving interactions with other elements, such as voussoir arches and weak underlying soil layers.