Thrust Surface Method: An innovative approach for the three-dimensional lower bound Limit Analysis of masonry vaults

We propose a new computational equilibrium approach for the structural safety assessment of historical masonry vaults of any geometry under general loading conditions. This approach, called Thrust Surface Method (TSM), represents an innovative application of the lower bound theorem of Limit Analysis to masonry vaults modeled as continuous No-Tension bodies. In particular, on allowing for singular stresses, the search of statically admissible stress field is reduced to the search of purely compressed membranes in equilibrium with the applied loads and entirely contained into the thickness of the vault. Based on a convenient numerical procedure and the formulation of a suitable constrained optimization problem, TSM is a method of practical application that, looking for "extremal" or "optimal" solutions, is capable of fully exploring the entire load-bearing capacity spectrum of a vault having an arbitrary geometry. Since the particular formulation, TSM can take into account not only any kind of vertical loads, but also horizontal loads like those simulating the maxima inertia effects related to seismic actions. In addition, the proposed approach could be a useful tool for visualizing and understanding the complex three-dimensional behavior and the close relationship between form and structure characterizing masonry vaults. The effectiveness and the capabilities of the method are discussed in light of some representative case studies, allowing for suitable comparisons with the results of other analytical and experimental approaches in the literature.