Elastic analysis of ground movements around a tunnel considering a buoyant lining moving upwards

A complex variable solution is derived for the ground movements around a tunnel considering the lining at different positions in the drilled hole in a linear elastic half-plane. The soil displacements for three different convergence patterns are presented and compared. It is shown that the surface settlement trough will become flatter and wider when the lining moves upwards; the horizontal displacements are more concentrated in the region below the lining; and the region influenced by displacements is wider. Most calculated settlement troughs can be well represented by Gaussian curves with simple parameters, but the obtained width parameters are larger than the traditional empirical values. The rigorous solution can be used as a simple tool to understand the fundamental mechanism of the lining buoyancy problem and as a benchmark for numerical procedures based on more sophisticated models. The importance of buoyancy effect on the displacement field should be taken into account.