3D limit analysis of Roman groin vaults

In Roman Baths (e.g. the Baths of Diocletian in Rome) the Romans employed groin vaults of great dimension. The maximum span is more than 20 m. The central body of the structure is made of a series of seven aisles with semicircular barrel vaults intersecting three aisles; outer groin vaults of minor dimensions provide counteraction of thrust of central vaults. In the aim of structural conservation of ancient wide span vaulted halls, simple tools of analysis are still lacking, despite the many sophisticated computational methods now available; due to geometrical and material complexity the theme is not commonly faced in technical literature. In this paper, we study the collapse behavior of cross vaults, damaged or undamaged, under horizontal static action. In the present modelling, masonry is discretized as a system of interacting rigid blocks in no-tension and frictional contact. The computational code used consists of an optimization algorithm which, based on the theorems of non-standard Limit Analysis (in the presence of non-associative rules), searches for the minimum statically admissible load factor ensuring a kinematically admissible collapse mechanism. Although the presence of friction makes the problem non-convex, non-linear and deprived of the uniqueness of solution, the possibility to detect a ‘safe’ optimal solution is guaranteed by a quasifeasible initial estimate of the unknowns, corresponding to the solution of a system with dilatancy instead of friction (Linear Programming—LP). To simplify the study, only LP approach is here used. The main difficult consists in a suitable description of the 3D geometry and of the proper geometry of the joints, varying from a joint to the other. The effectiveness of the proposed approach is shown through several examples.