A New Discrete Form of Hoek–Brown Criterion and Its Application to Limit Equilibrium Analysis of Rock Slope Stability

The generalized Hoek–Brown criterion (GHB) is recognized as one of the standard failure criteria in rock engineering and its validity extends to a wide range mass quality. A drawback this difficulty transforming it into an explicit form defining Mohr envelope when strength parameter not equal 0.5. information on functional for full conditions enables implementation classical approaches, such limit equilibrium method analysis, framework GHB criterion. Knowing that a≠0.5 exact closed-form representation feasible, alternative express approximate analytical form. main purpose study propose new improved define much more accurate compared with recently published approximations. idea behind formulation expand Balmer’s equation, which defines relationship between normal stress minor principal at failure, by invoking finite Taylor series centered known solution a=0.5. then completed substituting another shear stress. polynomial approximations up third degree are considered formulation. accuracy prediction shown be better than formula Lee Pietruszczak proposed 2021. An illustrative example analysis slope stability, incorporating expression envelope, provided. incorporates modified version Bishop approach, simpler rigorous original nonlinear expression. confirms can facilitate application practical calculations.