On the mixed collapse mechanism of semi-circular masonry arches

Starting from classical Heyman’s studies on the purely-rotational collapse mode of circular masonry arches, the hypothesis that friction is high enough to prevent sliding among the blocks, implying no sliding failure, is released. The onset of sliding is ruled by a classical Coulomb’s static friction law. The influence of the friction coefficient on the collapse mechanism is analysed, both analytically and numerically, by locating instances of purely-rotational, mixed sliding-rotational and purely-sliding mechanisms. A doubly built-in, symmetric, complete semi-circular masonry arch subjected only to its own weight is considered. The characteristic values of the friction coefficient that limit the ranges associated to each collapse mode are identified. Analytical formulas are provided to estimate the geometrical parameters that define the limit equilibrium states of the arch, in primis the minimum thickness to radius ratio. These formulas, starting from the analysis of the classical instance of purely-rotational collapse, make new explicit reference to the mixed sliding-rotational collapse mechanism. The obtained results are compared consistently to those available in the literature.