A complex variable solution for a deforming buoyant tunnel in a heavy elastic half-plane. (English) Zbl 1032.74038

Summary: 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 displacements and stresses.


74L10 Soil and rock mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
30C20 Conformal mappings of special domains
74G05 Explicit solutions of equilibrium problems in solid mechanics
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