Rigid Block Limit Analysis of Masonry Arches with Associated and Non-associated Slides

Heterogeneous limit analysis with infinitely resistant blocks and rigid-plastic joints reduced to interfaces is a powerful tool for the prediction of the collapse behavior of historical arch and vault masonry structures. Such analysis not only can provide the collapse mechanism and ultimate load of the structures in a quick and direct manner in a single step, but can precisely take into account the heterogeneous nature of the masonry in the most precise way. This chapter deliberates the theoretical background of such a powerful tool. First, the governing theoretical formulation of the collapse is elaborated, including the equilibrium conditions, the compatibility conditions, the constitutive and flow laws, the non-negative external work condition, and the complementary condition. After that, the solution of the collapse problem employing associated or non-associated flow rules for the joints is discussed respectively. Finally, a simple approach to consider the strengthening effect in the frame of limit analysis is proposed. Several examples and parametric studies are given to show the implementation of the theory and put at disposal to the reader an operative tool for design and assessment.