Three-dimensional stability assessments of a non-circular tunnel face reinforced by bolts under seepage flow conditions.

• Stability of non-circular tunnel face reinforced by bolts under seepage is assessed. • Upper-bound estimations to the safety factor of tunnel faces are provided. • Pore pressures considerably influence the required bolt layouts. This paper aims to develop a three-dimensional (3D) analytical framework to assess the safety factors of realistic non-circular tunnel faces reinforced by longitudinal bolts under seepage conditions from a discretization-based perspective. The axial failure mode of bolts (including the tensile failure of the bolt and the pull-out failure at the bolt-soil interface) paired with the introduction of the interaction zone is employed to describe the reinforcement effect of bolts. A numerical fluid calculation is performed to simulate the 3D seepage towards the non-circular tunnel face, and the resulting pore pressure distribution is extracted and further interpolated to determine the pore pressure of each discrete point on the 3D discretization-based failure mechanism. Within the kinematical approach of limit analysis, the work rate balance equation incorporating the role of the axial force along the interaction zone and the pore pressure due to the 3D seepage is established based on the discretization-based failure mechanism. Afterward, combining the strength reduction method with the dichotomy, the upper-bound estimations of safety factors can be obtained by an optimization process. The developed framework is compared with numerical fluid-mechanical calculations and other analytical methods with respect to an actual horseshoe tunnel, which proves that the developed framework is effective in providing fast and reasonable estimates of reinforced tunnel face under seepage conditions. Parametric analyses are performed to investigate the effect of bolt layouts (including the length and density of bolts) and seepage conditions (including the groundwater level and permeability anisotropy). Finally, a series of design nomograms for various water levels and soil strength parameters are provided for reference. [ABSTRACT FROM AUTHOR]