A solution for the frictional resistance in macro-block limit analysis of non-periodic masonry

This paper proposes a general equation to assess the crack inclination upper threshold when non-periodic textures characterise masonry walls. The proposed formulation introduces the computation of the frictional resistance at the macro-block interface by evaluating two masonry quality indexes, i.e., vertical and horizontal lines of trace. The proposed equation is adopted in conjunction with a macro-block limit analysis formulation in which the failure mechanism is parametrised and formulated according to the upper bound limit analysis theorem, coupled with a heuristic solver that is able to minimise the load multiplier and identify the geometry of the associated macro-block. The proposed analytical model is verified in a number of case studies by comparing advanced DEM simulations and numerical results arising from the literature.