Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek–Brown failure criterion

The reliable prediction of the state of collapse in tunnels and natural cavities is still one of the most difficult tasks in rock engineering. By making reference to the Hoek–Brown failure criterion, an exact solution is presented in the realm of plasticity theory with the help of classical tools of the calculus of variations. The resulting formulae are extremely simple and can be very useful to make comparisons with empirical methods and numerical analyses. Examples by means of some widely used software packages are also provided and discussed.