DEM Analysis of Masonry Open Vaults with Square Bays

Masonry vaults are usually considered as shell structures, whose geometry strongly determines the mechanical behaviour. In this article, the discrete element method is applied as a tool to perform virtual experiments to study three different types of open vaults (sail vault, fan vault, and cross vault). The three vaults have the same ground plan, but the sail vault is an elliptical shell, the fan vault is hyperbolic, and the cross vault is parabolic. All vaults are first gradually equilibrated under their self-weight, and then submitted to gradually increasing downwards forces at different positions, or to quasi-statically increasing outwards support displacements. The ultimate loads and the failure mechanisms of the vaults are compared. The orientation of the reactions is measured. The main results of the investigations are that (1) under concentrated loads, while the elliptic shell (the sail vault) fails locally, the hyperbolic vault (i.e. the fan vault) show either global failure or local failure but global cracking, depending on the position of the load; (2) under gradually increasing outwards support displacements, the orientation of the reactions is most favourable for the fan vault and worst is for the cross vault.