Theoretical analysis of stresses and displacements of twin tunnels excavated in saturated ground

Abstract

The main objective of this study is to establish a general analytical model for investigating the hydro-mechanical problems of twin tunnels excavated in elastic saturated ground, taking into account the influence of seepage flow on the mechanical responses. All hydro-mechanical (HM) boundary conditions are satisfied to derive the analytical solutions. An innovative analytical complex function in the HM coupled framework, integrating complex variable theory and the Schwarz alternating method, has been developed with the consideration of arbitrary sizes and arrangements of twin tunnels. The convergence speed of the alternating method is quite fast, generally achieving enough accuracy within three iteration steps in the solving procedure, guaranteeing the application of the developed solutions in geotechnical engineering. The results obtained from these solutions match well with those of the numerical predictions, verifying the proposed analytical theory and the developed analytical solutions.

Additionally, sensitivity analyses are performed to investigate mechanical responses of stresses and displacements of host rocks subjected to different engineering cases, including geometry and boundary conditions of twin tunnels. Results indicate a significant increase in the major principal stresses and deformations with rising seepage forces, suggesting that seepage flow can pose underground structures to dangerous conditions. Consequently, the influence of seepage flow plays a significant role in the stability analysis of tunnelling in water-rich geological areas. The proposed analytical approach offers an innovative and efficient alternative for the preliminary design of twin tunnels excavated in saturated ground, providing valuable insights for engineering applications.