When Heyman’s Safe Theorem of rigid block systems fails: Non-Heymanian collapse modes of masonry structures

Heyman’s Safe Theorem is the theoretical basis for several calculation methods in masonry analysis. According to the theorem, the existence of an internal force system which equilibrates the external loads guarantees that the masonry structure is in a stable equilibrium state, assuming that a few conditions on the material behaviour are satisfied: the stone blocks have infinite compressional resistance, and the contacts between them resist only compression and friction. This paper presents simple examples in which the Safe Theorem fails: collapse occurs in spite of the existence of an equilibrated force system. A theoretical analysis of the stability of assemblies of rigid blocks with frictional contacts is then introduced: the virtual work theorem is derived, and a refined formulation of the Safe Theorem is given.