Buckling of Cylindrical Tunnel Liners

Buckling of thin cylindrical shell liners used for the stabilization of soft ground tunnels is treated as the buckling of an elastic ring restrained radially and tangentially by an infinite surrounding elastic medium. Stiffness components for the elastic medium are derived and used to provide various levels of approximation for the elastic critical loads and associated modes of the liner when subject to overburden pressure loading. For most practical tunnel liners, elastic buckling is found to occur in modes having relatively short circumferential wavelengths. In these circumstances an approximation introduced into the critical pressure analysis allows both the lowest critical pressure and its associated mode shape to be represented explicitly in terms of a single "soft ground tunnel buckling parameter"; this single composite parameter encapsulates all the relevant ground and liner geometric and material properties. It is this closed-form analytical representation of elastic critical buckling that provides a particularly convenient basis for predicting elastic-plastic failure. When imperfections are introduced, liner collapse and the various forms of ground failure can be modeled by methods analogous to the Ayrton-Perry expression for columns. Two generalized imperfection parameters emerge: one for liner collapse and the other for each of three possible, soft ground, failure modes. It is suggested that the analytical simplicity of the approach should make it an attractive alternative basis for at least the initial, rational, design of soft ground tunnel liners.