This paper presents a stability study on the collapse mechanisms of a plane-strain tunnel face in c-ϕ soils using the upper bound finite element method with rigid translatory moving elements (UBFELA-RTME) and nonlinear programming technique. Practical considerations are given to the unlined length influence behind the tunnel face. An advanced mesh adaptive updating strategy is adopted, aiming to improve the computational efficiency, the accuracy of upper-bound solutions, as well as the produced collapse mechanisms. The unlined length influence on the face stability and collapse mechanism of the tunnel face are determined with various combinations of tunnel depth ratios, soil friction angles, and dilatancy angles. Using the UBFELA-RTME with the Davis's approach and a mesh adapting strategy, the non-associated plasticity flow rule can be well approximated. The developed technique was validated against different numerical methods, and it is concluded that the tunnel face stability can be improved by increasing soil friction and dilatancy angles, and yet weakens as the unlined length increases where a mesh-liked collapse zone gradually appears on the tunnel vault top. It gradually evolves to a global collapse failure till the ground surface. The findings contribute to a better understanding of the ground surface failure under the unlined support length influence in tunnel construction.

The stability and collapse mechanism of tunnel faces are simplified conservatively to two-dimensional plane strain models along the longitudinal middle line of tunnel. Using the upper bound finite element method with rigid translatory moving element (UBFEM-RTME), a series of stability factors N_cr and collapse mechanisms displayed with active discontinuities are deduced. The influences of dimensionless buried depth ratio H/D, internal friction angle φ and dilatancy angle ψ on the variations of N_cr and mesh-like collapse mechanisms that are identical to the form of slip lines are discussed. A fitting formula of N_cr for the influence factors H/D and φ is deduced, and the effects of numbers and locations of active discontinuities are also investigated. This study illustrates that the UBFEM-RTME with combination of mesh adaptive updating strategies and reasonable and sufficient mesh density can improve the accuracy of the obtained N_cr values and the refinement of mesh-like collapse mechanism. The results reveal the main characteristics of the ultimate collapse mechanisms of tunnel faces, and they can provide theoretical supports for the stability evaluations of tunnel faces and pre-reinforcement scheme of soil strata.