An energy-based strategy to find admissible thrust networks compatible with foundation settlements in masonry structures

This paper presents an energy-based methodology to compute internal stress states compatible with foundation settlements in masonry structures. The method is based on the application of Thrust Network Analysis (TNA). TNA is a lower-bound method that searches for admissible force networks in masonry structures by solving a constrained nonlinear optimisation problem (NLP) in which constraints enforce the limit analysis’ admissibility criteria. In this paper, the objective function minimises the complementary energy, which directly considers prescribed foundation displacements. This minimum energy criterion allows selecting among the infinite admissible stress states, the ones compatible with the settlements, suggesting potential crack regions at the onset of the motion. Application to general two- and three-dimensional masonry structures under vertical and horizontal loads are presented. The method has the potential to link internal stress states to boundary displacements and, thus, give mechanical meaning to typical crack patterns observed in masonry structures.