A stochastic approach for the limit analysis of masonry arches with uncertain material properties

As is well known, masonry arches’ bearing capacity can be determined by the traditional limit analysis; however, classical approaches fail to sufficiently account for the material’s properties uncertainty. This research starts with classical limit analyses using a method grounded on the multi-constrained equilibrium of a network; subsequently, a straightforward yet efficient technique is proposed for assessing the collapse probability under the assumption of uncertain masonry compression strength when assigned a value for the static imposed live load and for the finite friction. The masonry limited strength is described as a stochastic variable, while the arch is described as a system of voussoirs characterised by an assigned stereotomy. Monte Carlo simulations are conducted by taking into consideration a realistic friction coefficients range, by repeating the funicular procedure while drawing random variable’s samples. Finally, a modified stability area approach is used to investigate the failure mechanisms which can be activated.