DERIVATION OF YIELD CRITERION FOR GENERALIZED HOEK-BROWN EMPIRICAL MODEL IN STRESS INVARIANTS SPACE: DERIVATION OF SOME PLASTIC THEORY RELATIONSHIPS

In the present paper, derivation of the yield function of the Hoek-Brown model in stress invariant space is investigated. This model is an empirical model that is dened for estimating the bearing capacity of rocks. The main equations of this model, according to principal stresses and in 3D stress space, are dened here . By dening of the model in the stress invariant space, the yield criterion will be independent from the coordinate directions and the rotation of stress axes in general static loadings. By denition of the Lode angle presented in certain papers and books, basically one cannot derive the relationship between the yield function of the model in the principal stress space and stress invariants space. This problem is because of ignoring the 30 degrees difference between the Lodes angle and the used angle in the denition of the models. After denition of the yield function, the plastic potential function of the model is also investigated. In this study, Hessian matrices are obtained by means of the chain rule in dierentiating stress invariants. Basically, any arbitrary constitutive model that is expressed by principal stresses can transform to the stress invariant space via the basic relationships presented here. After this step, by computation of the elasto-plastic constitutive matrix, we can estimate the stress-strain behavior of material using that arbitrary constitutive model. This paper focuses on the elasto-plastic behavior and corresponding elasto-plastic relationships of the Hoek-Brown generalized criterion in three dimensional principal stress space and introduces a simple way to convert these relationships to three dimensional stress invariant space.