Upper-Bound Solution for Stability Number of Elliptical Tunnel in Cohesionless Soils: Fid-Bau Portal

Upper-Bound Solution for Stability Number of Elliptical Tunnel in Cohesionless Soils

Zhang, Jian / Yang, Junsheng / Yang, Feng / Zhang, Xuemin / Zheng, Xiangcou

In this study, the stability of an elliptical tunnel in cohesionless soils was determined by an upper-bound theorem in combination with triangular rigid translatory moving elements. The elliptical tunnel had a height D under a depth of cover C and a span B. The lining, used to support the tunnel, was equivalent to applying uniform internal compressive normal pressure on its periphery. In the proposed method, the nodal coordinates and velocities of rigid elements are treated as unknowns, without considering the rotating freedom. Upper bounds on the internal tunnel pressure were proposed using nonlinear programming, and the optimal geometry of the collapse mechanism was determined by removing nonactive velocity discontinuities where the two adjacent elements had no relative movement or zero velocities. The variation of the stability numbers (N_r) with dimensionless spans (B/D) is presented for various combinations of dimensionless depths (C/D) and internal friction angles (ϕ). The stability number increased obviously with C/D in cases where ϕ ≤ 25°, and it decreased with ϕ. Compared to the case where B/D = 0.5, N_r was found to increase approximately in a range of (1) 6.8–27.6% for ϕ = 10°, and (2) 94.1–134.9% for ϕ = 25° with B/D = 2. The collapse mechanisms of elliptical tunnels comprising two groups of slip lines are also presented. The results show that ϕ has a significant effect on the collapse mode, and the collapse zone was sensitive to ϕ and C/D. To verify the solutions, the computed stability numbers are compared with those reported in literature.