Non-linear programming numerical formulation to acquire limit self-standing conditions of circular masonry arches accounting for limited friction

Abstract

The modern rational limit analysis (LA) of masonry arches typically takes off from classical three Heyman hypotheses, a main one of them assuming that sliding failure shall not occur, like linked to unbounded friction. This allows for the computation of the least thickness of circular masonry arches under self-weight (Couplet-Heyman problem) and of the associated purely rotational collapse mode, by different analytical and numerical approaches. The aim of this work is to further investigate the collapse of circular masonry arches in the presence of limited friction. Here, the normality of the flow rule may no longer apply and the whole LA analysis shall be revisited. A new computational methodology based on nonlinear programming is set forward, toward investigating all possible collapse states, by jointly looking at admissible equilibrium configurations and associated kinematic compatibility, in the spirit of the 'uniqueness' theorem of LA. Critical values of friction coefficient are highlighted, marking the transitions of the arising collapse modes, possibly involving sliding. Uniqueness of critical arch thickness is still revealed, for symmetric arches of variable opening, at any given supercritical friction coefficient allowing the arch to withstand, despite the visible role of friction in shifting the final appearance of the collapse mode.