On unilateral contact between rigid masonry blocks

In this contribution we discuss a new framework for the analysis of the bearing capacity of masonry structures, modeled as assemblies of rigid blocks, which allows to correctly take into account the influence of foundation settlements. The crack pattern at failure and the associated mechanism are described by means of a proper treatment of unilateral contact constraints arising between contiguous rigid blocks, in which the structure is partitioned. We extend two classic variational formulations for the Signorini problem, namely the minimum of the total potential energy and a boundary complementary formulation where the unknowns are contact pressures only, to the case of the contact between multiple rigid no-tension masonry bodies, for which Heyman hypotheses are satisfied. The discretization of these two variational formulations leads to two dual linear programming problems. While the first one is classical and maximizes the work of external loads, the second one minimizes the work of constraint reactions for the assigned displacements and it appears new in the literature.