Lower bound approach to the limit analysis of 3D vaulted block masonry structures

A review of existing lower bound approaches for dry block masonry structures reveals a lack of reliable analytical methods applicable to most general conditions. Usually the analysis is restricted to cases in which sliding is prevented by high friction among block interfaces. This leads, for arches, to the well-known hinging mechanisms first discussed in terms of plastic analysis by Heyman (1966). However, especially for historic buildings the quality of the contact surfaces or of the binding materials might be deteriorated so as to substantially reduce the original friction coefficient. In addition, some particular shapes of curvilinear structures, e.g. flat arches, would never collapse unless sliding occurred. Hence the necessity of studying this group of problems under the more realistic assumptions of presence of sliding and absence of dilatancy. Herewith first is presented a proof of uniqueness of the solution for the limit state analysis of 3D masonry arches, in the condition of axial symmetry of geometry and loading. This proof is crucial to the robustness of the results and allows a straightforward treatment of this class of problems as one of standard limit-state analysis. The analysis can easily be extended to barrel vaults, common in historic buildings and forming the structure of masonry bridges. On these assumptions a simple but very adaptable computer procedure, using a lower bound approach, has been developed for the calculation of the minimum thickness required to ensure stability for such structures. Parametric analysis shows how the geometry of the barrel vault varies depending on the eccentricity and inclination of the applied loads.