Analysis and design of an underground hard rock voussoir beam roof

The behaviour of a voussoir hard rock beam roof is investigated by considering it to act as a symmetric flat arch with cracks at the abutments and at midspan. Analytical formulae are derived initially that evaluate, for any given geometry, loading and mechanical parameters of the beam, its deflection and strain within it in terms of the extreme and mean arch thicknesses. The latter are determined statistically by best fitting a targe amount of available computer beam model responses. Three relations ape then established one for each of the three examined modes of failure, i.e. snap through, crushing of the rock and transverse slip at the abutment, that relate the loading of the beam, its mechanical parameters and its dimensions. Finally all three relations are incorporated in a single non-dimensional graph where the loading and the mechanical parameters of the beam are related to the geometry of the beam for various factors of safely of the three modes of failure.