Stability Analysis of Masonry Domes and Crack Interpretation Through a 3D-Rigid-Block Model with Concentrated Deformability

The preservation of buildings belonging to architectural heritage is a topic that is very close to society’s heart. They are mainly constructed of load-bearing masonry and feature typical architectural and structural components such as arches, colonnades, vaults and domes. These components often have cracks and, in some cases, an extensive crack pattern can even be observed. Cracking is a common occurrence in masonry structures, given the very low tensile strength of the mortar joints used to bind the masonry units. What really matters is determining the causes to prevent local or global collapse and to design appropriate reinforcement measures. To this purpose, structural analyses must be performed. Therefore, targeted mechanical models and analysis methods must be developed. This paper focuses especially on domes, for the analysis of which methods based on graphic statics were developed in the past. According to them, a dome was analyzed as a series of meridian slices acting as individual arches and the stability was assessed using the thrust line method. The advent of elasticity theory in the 19th century introduced new methods of analysis, such as the membrane theory; however, this theory is not particularly suitable for the study of masonry domes because, to satisfy the equilibrium conditions, it also considers tensile stresses along the lower parallels. In this paper, a 3D-Rigid-block model with concentrated deformability is presented. The deformability is concentrated in the joints, to which a no-tension behavior or a low threshold strength can be assigned. This model can predict the occurrence of cracks in joints and, consequently, interpret their cause. Its reliability is demonstrated by the analysis of a well-known and much-debated case study.