ABSTRACT
The most typical and popular shape of tunnels is considered to be circular. The circular shape of cavity can perform in a stabilized manner under a wide range of initial stresses since the vertical contraction of the circular tunnel yields a similar amount of horizontal expansion to make the surrounding stress state around the tunnel almost isotropic. This mechanism is the fundamental principle of the NATM (New Austrian Tunneling Method) and based upon the tacit assumption that the tunnel is located with a enough overburden larger than its diameter at least. It is, however, a still controversial issue to determine the optimal shape of the tunnel or the cavity under a given initial stress field from the mechanical point of a view. In this paper, the optimal shape of the underground structure is studied by using a simple mathematical formulation.
