Collapse analysis of masonry arches and domes considering finite friction and uncertainties in compressive strength

Within the context of the lower bound theorem of classical limit analysis, the collapse of stone masonry arches and domes characterized by finite friction and uncertain finite compressive strength is addressed. Self-weight is considered, along with a live point load applied at the crown. A multi-constrained funicular approach based on the concept of force densities is implemented to provide the maximum static load multiplier for any assigned value of the friction coefficient and of the compressive strength. The numerical method, which takes into full account the stereotomy of blocky stone structures, is validated by using a novel version of the semi-analytical Durand-Claye’s stability area method. Two different types of brickwork are considered in the investigation, addressing the compressive strength as a random variable with prescribed log-normal distributions. Due to the limited availability of data to elaborate probabilistic models for the angle of friction, the effect of this mechanical parameter on the probability of failure of the blocky structures is assessed by developing a set of fragility curves. For each discrete value in a representative range of friction coefficients, a Monte Carlo investigation is performed by iteratively applying the funicular method considering samples of the random variable that describes the compressive strength. The retrieved load multipliers are processed to estimate the probability of failure for any given magnitude of live load, which depends on the value of the friction coefficient. An insight into the collapse modes occurring in the masonry arches and domes under examination is provided, as well.