Limit analysis of 2D non-periodic masonry walls via discontinuity layout optimization

Many historic masonry constructions comprise elements formed using brick or stone masonry units arranged in an irregular, or non-periodic bonding pattern. However, when the arrangement of units is not completely random the texture is frequently referred to as quasi-periodic; such masonry is a key focus in this work. However, the influence of any non-periodicity on structural performance can be difficult to establish. In this contribution, the discontinuity layout optimization (DLO) numerical limit analysis procedure is used to investigate the influence of non-periodicity on structural performance. Both discrete and smeared continuum representations of the masonry are considered and applied to a range of representative example problems, including in-plane analysis of square panels and more complex buildings under horizontal seismic action and rigid settlement. Although the discrete, rigid block method can be used to compare the performance of different textures, it requires the whole wall to be modelled in detail; this is not required with the proposed DLO smeared continuum representation. Various example problems are considered, indicating that the smeared continuum representation allows conservative solutions to be obtained for problems involving quasi-periodic masonry.