Masonry structures in the presence of foundation settlements and unilateral contact problems

This paper aims at presenting a new perspective on the modeling of the influence of foundation settlements in masonry structures. We show that it is possible to model in a consistent way the crack pattern and the associated mechanism induced by applied settlements starting from a proper treatment of unilateral contact constraints between contiguous blocks, in which the structure is partitioned after the onset of settlements. We extend two classic variational formulations for the Signorini problem, namely the minimum of the total potential energy and a complementary boundary formulation, to the case of contact between multiple no-tension rigid bodies satisfying Heyman's hypotheses for the limit analysis of masonry structures. The discretization of the proposed variational formulations directly entails two dual linear programming problems. The proposed formulations allow to correctly evaluate the effects of foundation settlements and their influence on the ultimate load bearing capacity of masonry structures.