Numerical DEM (DDA) analysis on the collapse mode of circular masonry arches

In this paper, the collapse mode of circular masonry arches is investigated, through the guideline of analytical solutions, by the Discrete Element Method (DEM), in the form of an available Discontinuous Deformation Analysis (DDA) numerical tool. Specifically, the so-called Couplet-Heyman problem of finding the minimum thickness necessary for equilibrium of a circular masonry arch, with general angle of embrace, subjected only to its own weight is addressed, in both analytical and numerical terms. The scope of the study is that of assessing the validity of different analytical solutions that can be derived for the problem, with reference to the purely-rotational collapse mode. Starting from the classical analytical solution pioneered by J. Heyman, different recently-found analytical solutions that are based on the true line of thrust (locus of pressure points) are first re-derived independently here and re-framed in the present context. Then, multiple numerical experiments on discretised arches are performed, which show that the numerical results are in very good agreement with the theoretical predictions and better adhere, in academic terms, to the latter newly-introduced solutions, rather than to classical Heyman’s solution.