3D EXPLORATION OF INTERNAL STRESSES DUE TO LATERAL LOADS AND FOUNDATION MOVEMENTS IN A SEMICIRCULAR ARCH

The paper explores the internal stress states of masonry structures as composed of no-tension material using an energy-based variational criterion. The numerical formulation directly considers general boundary conditions in terms of loads and displacements and treats the structure as an assembly of rigid bodies, resulting in a three-dimensional partition of the structural domain. The analysis is performed on the interfaces defined by this partition to determine internal forces in equilibrium with given external loads and compatible with potential non-zero boundary displacements. The mechanical problem is formulated as the Total Complementary Energy (TCE) minimum, which is then discretized and framed into a Linear Program (LP) or a Second-Order Cone Program (SOCP). The TCE objective function considers the non-homogeneous boundary conditions, while the problem's constraints enforce equilibrium and material compatibility conditions represented by a Mohr-Coulomb criterion. The solution to this minimum problem provides internal, admissible, equilibrated stress states that are also compatible with non-zero boundary displacements. It is shown how different boundary conditions can drastically influence and redirect the internal stress states, and, thus, the internal force pattern. Importantly, the use of foundation settlements allows to explore set of statically admissible stress and thus to define the resilience of the structure to the variation of external actions.