Limit analysis of masonry arches with unconventional stereotomy considering uncertain mechanical parameters

The classical limit analysis of masonry arches provides a value of the collapse load without adequately considering the uncertainties related to the compressive strength of the material. With the aim of reflecting on this issue, this contribution, starting from deterministic investigations conducted by means of a multi-constrained funicular method based on the lower bound theorem of limit analysis, presents a simple but effective procedure for estimating the probability of failure for any given magnitude of the live load, which depends on the value of the friction coefficient, assuming uncertain compressive strength. The masonry arch is modelled as an assembly of voussoirs with any stereotomy; the compressive strength is described as a random variable with predetermined log-normal distributions. Iteratively utilizing the funicular approach while considering samples of the random variable mentioned above, a Monte Carlo study is carried out by considering a representative range of friction coefficient. The results are validated by means of a new version of the Durand-Claye method. In addition, the failure modes of masonry arches are explored.