Closed-form solution on the thermoplastic behaviour of a deep tunnel in a thermal-softening material

A closed-form solution of deep tunnel subject to an internal pressure and to an axisymmetrical time-dependent temperature field is presented. The material is supposed to have a thermal-softening behaviour, the cohesion decreasing with the temperature. The thermal expansion generates plastic zones with face flow and corner flow, which can coexist and interact. The explicit character of the solution allows rigorous demonstrations of the evolution of such plastic zones, as well as other interesting and fundamental properties of the thermoplastic behaviour of deep tunnels. On the other hand, the causal relationship between the thermomechanical loading and the structural response (convergence, extension of rupture zones) is rendered transparent, thanks to the simplicity of the analytical solution. The consequence of thermal-softening is clearly shown by comparison with the analytical solution for a constant cohesion previously established. Quantitatively, its importance is illustrated by a restricted parametric study, to which the analytical solution is ideally suited. © 1997 John Wiley & Sons, Ltd.