A numerical upper-bound approach to the strength of a masonry wall under combined in-plane and out-of-plane loadings

The present contribution proposes a novel yield design, finite element based approach to determine the strength of a masonry wall. The proposed approach relies on a semi-analytical upper bound estimate of the in-plane and out-of-plane strength domain of a running bond masonry wall, recently proposed by Donval et al. (2024). Such an estimate is versatile, as it accounts for a finite strength for the blocks and the mortar, and a non-zero thickness for the joints, without any specific assumption on the state of stress or strain of the structure. This estimate may be expressed as a second-order cone optimization problem. We build on this property to derive a kinematic, finite element based formulation of the yield design problem. After describing the finite element implementation, some examples highlight the specificities of the approach. In particular, it accounts for the coupling between membrane stresses and bending moments, depends little on the mesh orientation, and provides a rigorous upper bound on the failure load of the structure. Then, the proposed approach is favorably compared to existing methods based on the limit analysis framework and to experiments. • The approach relies on a strength criterion that couples in-and out-of-plane efforts. • We formulate the FE yield design problem as a second-order cone optimization program. • The FE formulation provides a rigorous upper bound to the failure load of the wall. • Numerical predictions agree well with experimental results and existing models. • Computation times are suitable for engineering-oriented applications.