In- and out-of-plane analysis of multi-leaf masonry walls via an elementary homogenized numerical procedure

An elementary homogenized numerical procedure for the analysis of multi-leaf walls is discussed, capable of describing both in- and out-of-plane behaviors. Multi-leaf walls are frequent features in old European masonry structures, and they usually collapse during earthquakes due to their scarce resistance to out-of-plane loads. The procedure first consists in the generation of a 2D FE mesh to represent a masonry test-window, and second in the derivation of the in- and out-of-plane homogenized failure surfaces. The in-plane surface of the multi-leaf is obtained through a weighted average among the homogenized stresses of each layer. Afterwards, the out-of-plane bending moment is calculated from the resulting in-plane surfaces of each layer, under the assumption of a constant distribution over the thickness of the homogenized stress. The global out-of-plane failure surfaces of the multi-leaf are then evaluated as the sum of the various homogenized moments. The procedure is applied to two test-windows displaying distinct block layouts: one is running bond masonry consisting of tuff blocks; the other is rubble masonry consisting of stones. The results indicate a greater resistance of rubble masonry than for running bond, both for the in- and out-of-plane behaviors.