Factor of Safety by the Strength-Reduction Technique Applied to the Hoek–Brown Model

Abstract

This paper describes the implementation of the Hoek–Brown model as a perfect elastoplasticity model in a finite element code. The yield function is a standard Mohr–Coulomb surface incorporating a stress-dependent friction angle which accomplishes an exact reproduction of the HoekBrown strength envelope for all stress states. The formulation of the model is performed in such a way as to allow for a direct implementation of the shear strength-reduction technique in order to calculate the factor of safety of boundary-value problems. The efficiency of the numerical algorithm is discussed, with emphasis in the effect of the numerical implementation of three dilatancy models: deviatoric associativity, full non-associativity employing a Mohr–Coulomb shaped plastic potential and radial return. A comparison is presented between the results obtained for slope stability analyses using limit equilibrium methods and the built-in Hoek–Brown model available in Plaxis. Finally, the application of the model to an excavation for an underground mine in Uruguay is presented and discussed.