Analytic Solutions of Elastic Tunneling Problems

Analytic Solutions of Elastic Tunneling Problems

Strack, O.E.

Verruijt, A. (promotor)

Civil Engineering and Geosciences

2002-09-09

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. A general solution is derived for a single, circular tunnel in an elastic halfplane that includes a buoyancy force. The boundary conditions in this solution are that the surface of the half-plane is stress-free and that the displacements are specified along the tunnel boundary. This general solution is used in the rest of the thesis as the framework for considering three fundamental tunneling problems: the problem of a rigid, buoyant tunnel, the ground loss problem, and the ovalization problem. The three fundamental solutions are combined to illustrate their possible use as tools for the prediction of settlement troughs. The inclusion of buoyancy effects in the solution is shown to have a possibly considerable narrowing effect on settlement troughs. Neglect of the buoyancy effect might well be a reason why settlement troughs calculated in theory are often wider than those measured in practice.

elasticity
tunnel
complex variables

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doctoral thesis

(c) 2002 O.E. Strack