CLOSED-FORM SOLUTION ON THE THERMOPLASTIC BEHAVIOR 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 genera tes plastic zones with face flow and corner flow, which can coexist an d interact. The explicit character of the solution allows rigorous dem onstrations of the evolution of such plastic zones, as well as other i nteresting and fundamental properties of the thermoplastic behaviour o f deep tunnels. On the other hand, the causal relationship between the thermomechanical loading and the structural response (convergence, ex tension of rupture zones) is rendered transparent, thanks to the simpl icity of the analytical solution. The consequence of thermal-softening is clearly shown by comparison with the analytical solution for a con stant cohesion previously established. Quantitatively, its importance is illustrated by a restricted parametric study, to which the analytic al solution is ideally suited. (C) 1997 John Wiley & Sons, Ltd.