Shear failure of rock joints: Appropriate constraints for empirical relations

The notion of a rock joint as consisting of an array of contacts is used as a basis in determining its mechanical properties, the shear strength of the joint being inferred as consisting of “fracture” and “friction” components. At a high level of normal stress, the strength of the rock joint eventually reaches the strength of the material comprising the asperities in the joint surfaces. This “transition stress” is used as a reference in the development of formulations for strength and dilatancy. The effect of normal stress on the shear strength and dilatant characteristics of the joint is examined in terms of related physical constraints that are assumed to apply for extreme values of the normal stress, i.e. approaching either zero or the “transition stress”. Three forms of empirical relations are examined with regard to their ability to incorporate the required physical constraints. Only two enable the convenient incorporation of these, and are developed to provide smooth variations for intermediate levels of normal stress. The resultant expressions for the shear strength and dilatancy of rock joints, as functions of the normal stress, are compared with previous theories. They are shown to have advantages in terms of their compliance with the required physical constraints as well as improved consistency and versatility. This study clearly indicates that any comprehensive expression for the strength and dilatancy of rock joints must include relevant data on the following aspects, (a) coefficient of friction for both “damage free” and residual conditions, (b) pattern of inclinations at asperity contacts, (c) shear strength envelope of asperity material, and (d)“transition stress”.