A novel complex variable solution for the stress and displacement fields around a shallow non-circular tunnel

Abstract

A novel complex variable solution is derived in this paper for the stress and displacement fields around a shallow non-circular tunnel. The proposed method allows explicit computations in matrix form and has advantages of considerable efficiency and high accuracy. Firstly, the stress and displacement boundary conditions for the shallow non-circular tunnel are obtained using the generalized complex variable theory and conformal mapping technique. Then, the fast Fourier transform algorithm is employed to effectively perform the Fourier series fitting for these boundary conditions, and matrix equations for the potential functions in the frequency domain are established. Later, a matrix solution for the potential functions is formulated to determine the stress and displacement fields around the shallow non-circular tunnel. Finally, select numerical analyses are conducted to verify the proposed method, discuss the key parameters in the algorithm, and reveal the effect of the acceleration strategy using FFT as well as the effect of non-circular geometries on the stress and displacement fields.