Three-dimensional analysis of masonry vaults using limit state analysis with finite friction

Within the past 20 years, a growing number of methods for the analysis of masonry vaults have been developed. However, most methods idealize the vaults as a system of many arches. This oversimplification could be admissible for barrel vaults and spherical domes under simple gravitational loads, but it cannot do justice to the three-dimensional effects developing in other types of vaults, especially in complex vaults without smooth and continuous surface. Moreover, although the results could be conservative for uniform load distributions, this model limits substantially the set of loading conditions that can be analyzed and hence provide an accurate assessment of vaults performance. To clear this limitation, this article proposes a tool for three-dimensional analysis of masonry vaults. Using the lower bound approach and taking into account the friction among block interfaces, the proposed analytical method may give a good indication of the actual surface of thrust within the framework of limit state analysis. Therefore, limit state analysis with finite friction is able to provide the crack pattern, the stress resultants and the horizontal thrust at the supports, important elements with regard to strengthening interventions. To show its simplicity and rigor, the procedure has been applied to pavilion vaults. The results obtained are validated by comparison with nonlinear finite element analysis and an application to a real case study is presented.