Upper-Bound Finite-Element Analysis of Characteristics of Critical Settlement Induced by Tunneling in Undrained Clay

An interesting operation has been developed to estimate the critical normalized surface settlement for shallow tunnels in undrained clay (idealized as a homogeneously Tresca material). The upper-bound finite-element method in combination with a plastic-dissipation-based mesh adaptive strategy is used to obtain upper-bound solutions and velocity fields. Based on the vertical velocity field, the corresponding critical surface settlement field is obtained by introducing an assumed constraint related to soil deformation. The results show that the critical normalized surface settlement pattern is similar to a plug with concentrated strain at the bottom, and the calculated settlement data are fitted well by superimposing two Gaussian curves. The widths of the main settlement trough and the plug increase with increasing dimensionless unit weight D/c, and the plug-type settlement pattern is easily recognized with an increase of dimensionless depth H/D. For different combinations of H/D and D/c, a new normalized equation is developed to evaluate the critical normalized surface settlement. The results agree reasonably well with the solutions reported in the literature.