Computational methods for masonry vaults: a review of recent results

The present paper makes a critical review of some methods and models, now available in the technical litera-ture and commonly used in the analysis of masonry vaults up to their collapse, by highlighting advantages and drawbacks of each approach. All methods adopted to describe the mechanical behavior of masonry structures, in order to be reliable, must take into account the distinctive aspects of masonry, namely the scarce (or zero) tensile strength, the good resistance in compression and the occurrence of failure mechanisms through rotation-translation of rigid macro-blocks. Classic no-tension material models disregard the small existing tensile strength and make the assumption of (1) infinitely elastic be-havior in compression and (2) isotropy, giving thus the possibility to deal with either semi-analytical approaches (espe-cially for arches) or robust numerical procedures. More advanced but rather complex models are nowadays able to deal al-so with anisotropy induced by texture, small tensile strength and softening in tension, as well as by finite strength in com-pression. Traditionally – and nowadays it is still an opinion commonly accepted, in contrast with step by step complex procedures, Limit Analysis has proved to be the most effective Method for a fast and reliable evaluation of the load bear-ing capacity of vaulted masonry structures: classic lower and upper bound theorems recall respectively the concepts of equilibrium and occurrence of failure mechanisms with rigid elements. The so-called Thrust Network Method moves its steps from lower bound theorems, whereas FE limit analysis approaches with infinitely resistant elements and dissipation on interfaces take inspiration from the upper bound point of view. An alternative to Limit Analysis is represented by tradi-tional FEM combined with either elastic-plastic or damaging models with softening, commonly used for other materials but recently adapted also to masonry. They are able to provide a large set of output numerical information but further studies are still needed to ensure their proper application.