The safety of masonry arches with uncertain geometry

This paper aims to evaluate the effect of the geometrical uncertainties on the collapse condition of the circular masonry arch in presence of horizontal actions. Adopting Heyman's hypotheses about the material, a limit analysis based procedure has been developed in order to evaluate the horizontal loads multiplier, taking into account the uncertainties related to the imprecisions of construction, the shape defects of the voussoirs or the deterioration level. The collapse state has been determined in terms of horizontal loads multiplier, whose statistical moments up to second order and probability density functions have been evaluated versus a stereometry parameter. The comparison between the obtained results and those related to the nominal geometry highlighted that the uncertainties effects could reduce significantly the nominal bearing capacity of the structure. Within this context, a safety factor, which takes into account such effects, is introduced.