Safety factor calculations of a tunnel face reinforced with umbrella pipes: A comparison analysis

•A method to compute FS of tunnel faces reinforced with umbrella pipes.•Two failure models of umbrella pipes are proposed.•The model of SPA gives strict but overlarge estimates.•The model of PPA provides good FS estimates. Effective analytical models that can assess safety factors of a tunnel face with crown-type reinforcements are very important for the preliminary design phase of tunnel excavations. However, such a model is rarely reported in the literature. By combining the strength reduction method and the kinematic approach of limit analysis, an advanced three-dimensional (3D) failure mechanism is extended to calculate the safety factor of a realistic non-circular tunnel face reinforced with umbrella pipes. A strict plastic failure model of umbrella pipes fully considering the plastic yielding of both axial tensile resistance and the bending moments is first coupled with the 3D failure mechanism. A comparison with numerical simulations conducted in this study shows that the strict plastic analysis (SPA) model leads to rigorous but excessively large upper-bound solutions of safety factors. To overcome this drawback, a pseudo-plastic analysis (PPA) model that employs an axial deformation model and a Winkler-spring model to simulate the interactions between soils and steel pipes is proposed. The computed safety factors of the proposed PPA model agree well with those of the numerical simulations. At the end of this work, a parametric analysis is conducted to discuss the effects of the pipe length, the pipe number, the elevation angle of pipes and the excavation method on the tunnel face stability.