Influence of the Hoek–Brown failure criterion with tensile strength cut-off on the roof stability in deep rock tunnels

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The Hoek–Brown (HB) failure criterion provides reasonable estimates of the peak strength of isotropic rocks for shear failure; however, this is less so for tensile fractures. Hoek and Brown advised against the direct application of the HB criterion during excavation at deep depths and introduced a tension cut-off (TC) based on reliable extension test data. However, its influence on rock structures remains unclear, with no previous studies on safety assessment considering TC. In this study, a stability analysis of deep tunnel roofs was performed using the HB yield function with reduced or eliminated tensile strength. The parabolic form of the HB envelope was terminated using a circular arc in the tensile stress regime. Such a modification allows some part of the failure mechanism to be separated from the stationary rock with a large volumetric strain governed by the TC. The kinematic approach of limit analysis was utilized as the study approach. The computation results revealed that, among the two common tunnel cross-sections, rectangular tunnels were susceptible to the TC, i.e., the stability number with 10% of the theoretical tensile strength was more than twice that of the original envelope. Circular tunnel roofs can be self-supported even with a zero tensile strength (19% increase in the stability number) owing to the addition of a confining stress. For different HB constants, the relative increase in the stability number subjected to the TC was surprisingly consistent. The factor of safety, defined as the shear strength and required supporting pressure, was derived from the envelope with a TC.

Original languageEnglish
Article number105016
JournalTunnelling and Underground Space Technology
StatePublished - Jun 2023


  • Hoek–Brown failure criterion
  • Limit analysis
  • Rock tensile strength
  • Roof stability
  • Tension cut-off


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