Upper bound limit analysis of collapse shape for circular tunnel subjected to pore pressure based on the Hoek–Brown failure criterion

Based on Hoek–Brown failure criterion and using the upper bound theorem of limit analysis, a numerical solution for the shape of collapsing block in circular tunnel subjected to pore pressure is derived. The effect of water pressure which is assumed to be a work rate of external force is included in the upper bound analysis. By employing variational calculation to minimize the objective function, the upper solution of collapsing block is obtained. In order to evaluate the validity of the method used in this paper, the result for pore pressure coefficient ru = 0, with no effect of pore pressure taken into account, is compared with previous work. The good agreement shows that the method of calculating the upper solution for the shape of collapsing block subjected to pore pressure is valid.

► The shape of collapsing block in tunnel subjected to pore pressure is derived.
► The effect of water pressure is assumed to be a work rate of external force.
► The collapsing block decrease with the increase of pore pressure coefficient.
► The collapsing block increase with the increase of tunnel radius.