Adaptive models of no-tension masonry vaults

Historical buildings of the international architectural heritage are traditionally made of masonry. The study of mechanical behavior of these structures under static and seismic loads is necessary to evaluate their vulnerability and to preserve them over the time by means optimised strengthening interventions. Several mechanical models were proposed in literature to analyses masonry frameworks, including those based on the Heyman limit analysis. These modelling approaches cannot be easily implemented within FEM codes. In this context, an adaptive finite element model based on a Genetic Algorithm is formulated. It starts by an approximation of vault by means of shell elements with dominant membrane behavior and allows us to obtain a ‘safe’ thrust surface of a masonry vault within a design domain. This domain coincides with the vault volume, in the case of an unreinforced masonry, while it may be extended to external regions of vault in correspondence with reinforced areas, in the case of a vault strengthened with composite materials. The research of a safe thrust surface is performed by minimizing a fitness function, corresponding to the mean value of the principal tensile stresses carried by the unreinforced portion of vault. The proposed r-adaptive finite element model is capable to evaluate the structural safety of masonry vault and it may represent a useful tool to design optimal reinforcement patterns.