Stabilization of rock slopes by anchor based on upper bound analysis incorporating Hoek-Brown failure criterion

In this paper, Hoek-Brown (HB) failure criterion in combination with kinematic approach of limit analysis is employed to develop an upper bound solution to the factor of safety (FoS) of an anchor-reinforced rock slope. The shear strength reduction method is adopted to define FoS using an approach based on the parametric form of the HB shear envelope. Two ways to incorporate the non-linear HB criterion into limit analysis are considered: the tangential technique and the equivalent Mohr-Coulomb parameters method. Two objective functions are accordingly derived by equating the rates of external works done by rock weight and anchor force to the internal energy dissipation rate. Then, an optimization scheme is programmed in Matlab to capture an upper bound to the slope FoS by trying all kinematically admissible failure mechanisms. The numerical results show that the proposed solutions agree very well with other approaches including the limit equilibrium method and numerical simulations. However, despite its convenience, the equivalent method generally overestimates FoS when compared to the tangential technique, meaning that it should be used with some degree of prudence. The effects of the anchor position and its horizontal inclination on the slope FoS are also discussed.

Automated summary

In this paper, an upper bound solution to the factor of safety (FoS) of an anchor-reinforced rock slope is developed using the Hoek-Brown failure criterion in combination with kinematic approach of limit analysis. Two ways to incorporate the non-linear HB criterion into limit analysis are considered: the tangential technique and the equivalent Mohr-Coulomb parameters method. An optimization scheme is programmed in Matlab to capture an upper bound to the slope FoS by trying all kinematically admissible failure mechanisms. The numerical results show good agreement with other approaches. However, the equivalent method generally overestimates FoS when compared to the tangential technique, meaning that caution should be exercised when using it.