Revisiting the face stability of rock tunnels in the Hoek–Brown strength criterion with tension cutoff

In this work, the three-dimensional stability of deep tunnel faces is evaluated in rock masses characterized by the generalized Hoek–Brown (H–B) criterion from the perspective of the limit analysis theorem. Considering that underground engineering is gradually developing towards larger burial depths and larger sizes, and the tensile strength of rocks is usually overestimated, the concept of tension cutoff (T-C) is introduced to substitute the parabolic form of the H–B envelope in the tensile region with a circular arc. The multitangent technique is used to piecewise approximate the H–B envelope, instead of the conventional linear substitution, accounting for the nonlinear dependence of the shear strength on the pressure. Meanwhile, the earthquake loading is considered by the classic pseudostatic method. The tunnel face stability is measured by a stability number, which is calculated based on a newly developed multicone failure mechanism. Parameter studies indicate that the T-C has almost no impact on the critical support pressure, while has a significant effect on the critical stability number, especially in the presence of earthquakes. Nearly all stress points back-calculated from the rupture angles fall within the T-C region, except for the first stress point associated with the first segment. Interestingly, the influence of the geological strength index (GSI) on the face stability is inverse to that of m_i due to the brittleness of rocks. Moreover, the critical stability number is not sensitive to m_i, but sensitive with the introduction of earthquake loadings.