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A complex variable solution for a deforming circular tunnel in an elastic half-plane. (English) Zbl 0894.73127
Summary: An analytical solution is presented of problems for an elastic half-plane with a circular tunnel, which undergoes a certain given deformation. The solution uses complex variables, with a conformal mapping onto a circular ring. The coefficients in the Laurent series expansion of the stress functions are determined by a combination of analytical and numerical computations. As an example, the case of a uniform radial displacement of the tunnel boundary is considered in some detail. It appears that a uniform radial displacement is accompanied by a downward displacement of the tunnel as a whole. This phenomenon also means that the distribution of the apparent spring constant is strongly non-uniform.

MSC:
74L10 Soil and rock mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
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