A complex variable solution for a deforming buoyant tunnel in a heavy elastic half-plane

An analytical solution is presented for a buoyant tunnel in an elastic half-plane. The tunnel undergoes a prescribed displacement along its boundary, and the surface of the half-plane is stress-free. The solution uses the complex variable method and consists of conformally mapping the hole and half-plane to an annular region. The complex potentials each contain two logarithmic terms due to the resultant buoyancy force acting on the tunnel, and as a result the displacements at infinity are unbounded. An example is presented for the case of a rigid buoyant tunnel in a half-plane with gravity loading. Even though the tunnel does not deform, the buoyancy effect can be clearly seen in the contours of the displacements and stresses. Copyright © 2002 John Wiley & Sons, Ltd.