Stress Distribution around a Tunnel

The problem of the disturbance of stress around a tunnel is treated in this paper from the point of view of the theory of elasticity. The tunnel is considered to be a horizontal cylindrical hole of circular cross-section situated in a semi-infinite elastic solid under the action of gravity. Through the introduction of the bipolar co-ordinate system an exact solution of the classical elasticity equations is obtained which satisfies the boundary conditions at both the upper free surface of the solid and the free surface of the hole.