Analytical and numerical DDA analysis on the collapse mode of circular masonry arches

• Static analysis of symmetric circular masonry arches with different opening angles.
• Explicit critical condition of least arch thickness (Couplet–Heyman problem).
• Collapse characteristics: hinge position, critical thickness, horizontal thrust.
• Analytical solutions accounting for correct line of thrust intrados tangency.
• Numerical (DDA) solutions with consistent estimates of collapse characteristics.

The purely-rotational collapse mode of circular masonry arches is investigated, through the guideline of new analytical solutions, by a Discontinuous Deformation Analysis (DDA) numerical tool. The so-called Couplet–Heyman problem, of finding the minimum thickness of a circular masonry arch with general angle of embrace standing under self-weight, is addressed, both analytically and numerically. The main scope of the study is assessing the validity of different analytical solutions that can be derived for the problem. Starting from classical Heyman’s solution, different recently-found solutions based on the true line of thrust (locus of pressure points) are first independently re-derived. Then, multiple experiments on discretised arches are performed, which show that the numerical results are in very good agreement with theory.