Energy-based fracture identification in masonry structures: the case study of the church of Pietá dei Turchini

The present work deals with the identification of fractures in "old" masonry structures modelled by extending the Heyman model to continua, particularly to 2D structures composed of normal rigid no-tension material, and subjected to given loads and settlements. The equilibrium problem is formulated as an energy minimum search and two numerical methods for approximating the solution are adopted, namely the PRD method and the C0 method. By using the PRD method, the energy is minimized within the set of piecewise rigid displacements (PRD), whilst with the second one, the search of the minimum is restricted to continuous (C0) displacement fields. A case study, regarding the church of "Pieta dei Turchini" (an XVII century church located in Naples), is here presented to illustrate how an admissible class of kinematical data (i.e., foundation displacements) associated to a given crack pattern can be identified by using an iterative procedure. Firstly, the analysis is conducted through the PRD method and secondly, the C0 method is used to assess the quality of the first solution, and to make comparisons between these two approaches showing pro and contra of both methods.