Evaluation of the Load-Bearing Capacity of Cylindrical Stone Vaults Taking their Damage into Account

Introduction. The calculation of cylindrical stone arches of historical buildings is often performed in a core setting. At the same time, the ratio of bending moments M and longitudinal forces N, as well as cracks has a major effect on the loadbearing capacity of arches. The latter does not allow the analysis of the load-bearing capacity of arches by means of the standard methods. The aim of the study is to develop a methodology for assessing the load-bearing capacity of cylindrical stone arches with cracks. Materials and Methods. The experimental studies confirm that one or even a few cracks are not invariably a sign of exhaustion of the load-bearing capacity of arches. The upper limit of the load-bearing capacity is due to such a number of conditional hinges (cracks), which converts the arch into a kinematic mechanism. It is possible to analyze the operation of vaults with cracks up to their physical destruction by means of the so–called interaction dependencies reflecting the limiting ratios M Rd –N Rd . Research Results. The interactive dependencies of M Rd –N Rd were identified experimentally. The experiments also revealed the mechanisms of destruction of the cylindrical vault depending on the ratio M Rd –N Rd . Thus, under the action of only the bending moment, the destruction of the sample occurred along an unconnected section of the masonry; under the action of only the compressive force, as a result of the formation of longitudinal cracks; under the combined action of the compressive force and the bending moment, nature of the destruction depended on the ratio of these forces. The numerical model have been verified that can be used in order to design interactive dependencies. Discussion and Conclusion. A methodology has been developed for assessing the load-bearing capacity of cylindrical stone arches with cracks using interactive dependencies reflecting the limiting ratios M Rd –N Rd . It is shown that it is possible to directly design interactive dependencies with numerical solid-state models, having previously "fine-tuned" them to the results of a number of simple masonry tests. The actual values of M and N in the cross sections are identified using the rod models of the arches. The load-bearing capacity of the arches is evaluated by comparing a certain combination of M-N with the interaction dependence curve.