A limit equilibrium model for the reinforced face stability analysis of a shallow tunnel in cohesive-frictional soils

Abstract

Although a variety of theoretical models have been developed to assess the stability of reinforced tunnel faces, the failure mechanisms in these models are inconsistent with the experimental results. This study establishes a 3D model for the stability analysis of a reinforced tunnel face based on the limit equilibrium method and strength reduction technique. This model considers the horizontal soil arching effect and has a reasonable failure mechanism that is composed of two parts: a truncated elliptical cylinder (upper part) and a wedge bound by a log-spiral-shaped slip surface (lower part). The tension failure of the bolts and shear failure of the grout-soil interface are considered in the calculation of the supporting force of the face bolts. For the sake of verification, the results are compared with those from numerical method and typical limit equilibrium methods. The comparisons show that the results obtained by the proposed model agree well with the numerical simulation results, and the average relative difference and absolute difference are 4.89% and 0.10, respectively.Moreover, when the bolt length is shorter than the optimum length, the safety factor and failure mechanism increase with increasing length; when the bolt length exceeds the optimum length, the safety factor remains constant, while the failure mechanism decreases and then remains unchanged. In addition, the applicability of the proposed model for a circular tunnel face is demonstrated by comparing the results of the proposed model with those of previous studies. At the end of this work, design nomograms are presented to allow the proposed model to be used by engineers.