3D Semi-Analytical and Numerical Upper-Bound Homogenisation Approaches to the Out-of-Plane Strength Domain of a Running-Bond Masonry Wall

The present contribution proposes a new semi-analytical homogenisation approach to determine a running-bond masonry wall's in- and out-of-plane strength domain based on the yield design framework. The main novelty of such an approach is that it does not rely on simplifying assumptions such as infinitely thin joints or plane stress state within the blocks, by making use of 3D virtual failure mechanisms in the kinematic approach. The new semi-analytical approach is then compared to a state-of-the-art numerical implementation of the kinematic approach of yield design, relying on semi-definite programming. Several comparisons show a good agreement between the semi-analytical and the numerical approaches and outline the computational efficiency of the semi-analytical approach as well as the fact that it is very well suited for engineering design purposes. Both proposed approaches are then compared to existing approaches based on the limit analysis or yield design framework.