Gravitational Stresses on Deep Tunnels

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Abstract
Gravitational stresses around a horizontal tunnel opening are determined by means of Muschelišvili’s complex variable method for solving two-dimensional elasticity problems. The tunnel is located at a large but finite depth underneath the horizontal ground surface. It has the shape of a general ovaloid, including the rounded-cornered square, the ellipse, and the circle as its special cases. The surrounding material is assumed to be elastic, isotropic, and homogeneous. Two problems are solved. In one problem an unlined tunnel is considered, which has a boundary free from external stresses. In the other the tunnel has a rigid lining, and a perfect bond is assumed to exist between the lining and the surrounding material so that the displacements at the boundary are zero.

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