Numerical Investigation of the Limit Equilibrium Method in Tunnel Stability Using Finite Element (FEM)

Document Type : Original Manuscript


Department: Civil Engineering, Science and Research Branch٫Islamic Azad University, Tehran, Iran



The upper bound solution of the factor of safety is obtained by optimization calculation. To evaluate the feasibility of the method proposed in this paper, it was compared with the safety factor calculated by the marginal equilibrium method. Were the method to evaluate the stability of the tunnel face in the framework of the upper limit theorem. Consists of two newly defined parameters: one normal stability ratio and the critical stability ratio. Therefore when the initial tunnel is stable or unstable, the relationship between the electric field stability ratio and the critical stability ratio is determined. The stability of the tunnel surface is estimated by the upper limit theorem of the limit analysis together with the strength reduction technique by the safety factor widely used in the slope stability analysis. There are two methods to reach the critical steady state by increasing the tunnel according to the field stabilization factor. One is to calculate external work (increase the external load) and the other internal energy dissipation in a kinematically acceptable velocity field (decrease the internal load). The tunnel bearing capacity relationship is arranged to reach the critical stability ratio of the two external force enhancement methods. In this way, the upper limit solutions of single tunnels, twin tunnels of the same diameter, and twin tunnels of different diameters are analyzed. TAs a result of the comparison, the solutions derived from these two methods agree well with each other, so the method proposed in this paper can be considered effective.