Eulerian finite element model for stability analysis of circular tunnels in undrained clay

Traditional Lagrangian finite element (FE) method may encounter numerical problems due to severe element distortion in the analysis of tunnel stability, which requires the simulation of large deformation and post-failure behaviour of soil. To overcome these limitations, this paper presents an Eulerian FE model, developed to evaluate the stability of circular tunnels in undrained clay. An application example was first presented in detail to illustrate both the approaches and principles for the simulation. Then parametric analyses of tunnel stability using the Eulerian FE method were performed to verify the validity of the developed model. The computed limit support pressures showed good agreements with the solutions from the finite element limit analysis, demonstrating that it is applicable in the stability analysis of a circular tunnel. Meanwhile, Lagrangian FE analysis was also performed for a comparison of performance with the developed Eulerian FE model. The computed results by Lagrangian FE models were shown significantly overestimating the stability of the circular tunnels, which was found to be caused by the decrease of tunnel diameter during the analysis. The Eulerian FE method developed in this paper can inherently avoid this problem, highlighting its advantage in the stability analysis of circular tunnels.