ABSTRACT
These models are based on a “thick wall sphere” (3D model) and on a “thick wall cylinder” (2D model) in which part of the sphere or the cylinder is in elastic state and the remainder in plastic state. The area of the tunnel where support is considered either to be not effective, or where a supporting pressure p can be applied, is simulated as a sphere (Fig. 1) with an inner radius Ri. The outer radius Ro (Fig. 2) simulates the ground surface, where a surcharge pressure load s can be considered. This concept has already been used by Muhlhaus (1985) for a limit analysis where the whole sphere is assumed to be in plastic state, but no information is obtained on displacements prior to collapse.
