Effects of the thickness and angle of embrace uncertainties on the limit equilibrium of masonry arches under horizontal loads

The load bearing capacity of masonry arches is strictly dependent on their geometric features, such as thickness, rise and span. The safety assessment of these structures is carried out by considering deterministic values of the geometric features, while it should be noticed that the inevitable defects of shape of the voussoirs, as well as imprecisions of execution, make these uncertain variables. The paper is focused on the geometrical uncertainties of the voussoirs and their influence on the horizontal loads bearing capacity of the circular arch. The thickness and the angle of embrace of the voussoirs are taken into account as random variables along the centreline. The collapse analysis is based on the limit analysis and carried out by adopting the well known Heyman's hypotheses about the masonry: i) absence of tensile strength, ii) infinite compressive strength, iii) absence of sliding between the voussoirs. At the collapse the four-hinges arch is considered and the position of hinges evaluated, with the corresponding horizontal load multiplier, by an iterative procedure. The probability density function of the collapse multiplier is estimated by means of Monte Carlo analysis.