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Several masonry structures of cultural and historical interest are made with a non-periodic masonry material. In the case of periodic textures, several methods are available to estimate the strength of the masonry; however, in the case of non-periodic masonry, few methods are available, and they are frequently difficult to use. In the present paper we propose using discontinuity layout optimization (DLO) to estimate the failure load and mechanism of a masonry wall made with non-periodic texture. We developed a parametric analysis to account for the main features involved in the estimation of failure: in particular we considered three different textures (periodic, quasi-periodic, and chaotic), variable height-to-width ratio of the wall (from 0 to 3) and of the blocks (from 0.25 to 1), different mechanical properties of mortar joints and blocks, and possible presence of a load on the top. The results highlight the importance of the parameters considered in the analysis, both on the values of the failure load and on the failure mechanism. Therefore, it is found that DLO can be an useful and affordable method in order to assess the mechanical strength of masonry wall made with non-periodic textures.

Discontinuity layout optimization (DLO) is a powerful numerical limit analysis technique that can be used to identify the collapse load and associated failure mechanism of a solid or structure. The method successfully automates the traditional ‘upper bound’ method of plasticity, with applications including metal extrusion problems, where die forces are sought, and geotechnical engineering problems, where the stability of foundations or retaining walls are to be established. Notably the basic DLO method uses the same underlying mathematical formulation as ‘ground structure’-based truss layout (or ‘topology’) optimization and is demonstrated in this contribution via a Python script capable of solving plane strain limit analysis problems. Extensions to the basic method are presented to allow treatment of larger-scale problems incorporating cohesive-frictional materials, and with self-weight treated in a new and conceptually elegant way. Finally, various examples are presented to illustrate the capabilities of DLO, with displacement vectors shown to aid interpretation.