A new complex variable solution on noncircular shallow tunnelling with reasonable far-field displacement

Abstract

A new static equilibrium mechanical model on noncircular shallow tunnelling considering initial stress field is proposed in this paper by constraining far-field ground surface, and a mixed boundary value problem thus forms with elimination of displacement singularity at infinity. By applying analytic continuation, the mixed boundaries are transformed to a homogeneous Riemann–Hilbert problem, which is subsequently solved via an efficient and accurate iterative method with boundary conditions of static equilibrium, displacement single-valuedness, and traction along tunnel periphery. The Lanczos filtering technique is used in the final stress and displacement solution to reduce the Gibbs phenomena caused by the constrained far-field ground surface to obtain more reasonable results. Several numerical cases are conducted to intensively verify the proposed solution by examining the utilization of Lanczos filtering, the elimination of displacement singularity, and solution convergence of constraining arc and truncation number, and comparisons with existing solutions, and all the results are in good agreements. Finally, more numerical cases are conducted to investigate the stress and deformation distribution along ground surface and tunnel periphery considering different tunnel geometries, lateral coefficients, and tunnel depths. Further discussions on the defects of the proposed solution are also conducted for objectivity.