Three-dimensional failure mechanism of a rectangular cavity in a Hoek–Brown rock medium

•For deep cavities, three-dimensional rotational failure mechanism is proposed for calculating the work rate of external force and the internal energy dissipation.•Collapsing magnitude increases with the increase of the strength parameter A, while decreases with the increase of the strength parameter B and rock unit weight.•The surface equation of the three-dimensional collapsing block is derived and presented for practical use in engineering.