Elastic analytical solution of shallow tunnel owing to twin tunnelling based on a unified displacement function

Abstract

• Unified displacement function of cross-section of each tunnel owing to twin tunnelling. • Complex variable method and Schwartz alternating method. • Elastic analytical solution for ground displacement of twin tunnels • The laws of ground displacement field for twin tunnels. A unified displacement function is used as the displacement boundary condition of the cross-section of each tunnel, which can be used to capture the asymmetrical deformation behaviors about the horizontal and vertical center line . Complex variable method is adopted to obtain the analytical solution of a single tunnel. Based on the Schwartz alternating method, the analytical solution of twin tunnels is obtained and the correctness of the analytical solution of twin tunnels is verified. A series of analyses are carried out to investigate the effects of the displacement boundary condition of the tunnel cross-section and the distance of twin tunnels on the ground surface settlement trough curve and the ground displacement field. Based on the proposed method, the parameters of displacement mode of the cross-section of twin tunnels are calibrated through field monitoring data of the Bangkok Subway Tunnel project, and the displacement field of the whole ground are analyzed. The proposed method can provides guidance in the conceptual stage of the design process of twin tunnels.