On the stability of tunnels under gravity loading, with post-peak softening of the ground

The stability of a circular tunnel in an elasto-plastic (brittle) material subjected to gravitational loading is studied by considering the occurrence of a minimum in the ground reaction curve (i.e. the characteristic load-deformation curve for the opening). The relations between the gravitational load and the post-peak load strength of the material are expressed in the form of limit-depth charts, i.e. dimensionless graphical representations that allow a direct assessment of the stability conditions. The analysis is extended to the face of the tunnel where the 3-D problem is treated analytically under certain restrictive assumptions. Practical examples illustrating the use of the charts for shallow tunnels in weak material and for deep tunnels in hard rock are presented.