Civil Engineering Association

Analytic Solutions of Elastic Tuneling problems

ABSTRACT

The complex variable method for solving two dimensional linearly elastic problems is used to obtain several fundamental analytical solutions of tunneling problems.
The method is used to derive the general mathematical representation of problems involving resultant forces on holes in a half-plane. Such problems are encountered in geomechanics during the excavation of tunnels. When tunnels are excavated the removal of the weighted material inside the tunnel causes the ground under the tunnel to rebound. This in turn causes a resultant force, referred to here as the buoyancy force, to act on the tunnel until the stresses return to a state of equilibrium. The mathematical representation derived in this thesis shows that the displacements will usually be unbounded at infinity in solutions of two-dimensional problems involving resultant forces acting on holes in a half-plane.

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