Equilibrium of masonry sail vaults: The case study of a subterranean vault by antonio da sangallo the elder in the “fortezza vecchia” in livorno

The present paper addresses the problem of determining the safety level under vertical dead loads of the sail vault covering a trapezoidal room in the “Cavaniglia” bastion of Livorno’s “Fortezza Vecchia”. The work illustrates some first results obtained by the Pisa University Research Group on Historic Masonry Construction within the framework of a research project whose ultimate goal is to understand the structural behavior of the vault. The analysis is performed within the framework of the safe theorem of limit analysis by searching for statically admissible stress fields within the vault. The weights of the vault and the overlying soil layers have both been considered. According to Heyman’s hypotheses, it is assumed that the vault’s constituent material has no tensile strength and that no sliding is allowed between its component masonry units. The equilibrium problem is tackled by considering the vault as a thin shell. Working within the framework of the theory of shells, we build two suitable sets of explicit expressions for statically admissible stresses defined over the middle surface of the vault, characterized by a spherical profile and trapezoidal plan. The intrados surface has been carefully reconstructed by laser scanner survey and approximated by means of a regular surface that allows for a relatively simple analytical description. The results obtained provide a preliminary estimate of the safety level of the vault under vertical loads, in terms of both a geometrical safety factor and a mechanical safety factor.