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

TL;DR

This paper introduces a novel complex variable analytical solution for noncircular shallow tunnelling that accounts for initial stress and eliminates displacement singularity, providing accurate predictions of ground and tunnel displacements.

Contribution

It develops a new mechanical model transforming the problem into a Riemann-Hilbert problem and applies an iterative solution with advanced filtering for improved accuracy.

Findings

The solution accurately predicts displacement and stress distributions.

Numerical results agree well with existing solutions and experimental data.

Engineering recommendations are provided based on the analysis.

Abstract

A new mechanical model on noncircular shallow tunnelling considering initial stress field is proposed in this paper by constraining far-field ground surface to eliminate displacement singularity at infinity, and the originally unbalanced tunnel excavation problem in existing solutions is turned to an equilibrium one of mixed boundaries. By applying analytic continuation, the mixed boundaries are transformed to a homogenerous 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 for more accurte results. Several numerical cases are conducted to intensively verify the proposed solution by examining boundary conditions and comparing with existing solutions, and all the results are in good agreements. Then more numerical cases are conducted to investigate the stress and deformation distribution along ground surface and tunnel periphery, and several engineering advices are given. Further discussions on the defects of the proposed solution are also conducted for objectivity.