The macro behavior of granular materials is strongly influenced by their micro-structure. In developing multi-scale models for granular materials, group-averaged quantities (i.e. averages over groups of contacts with the same contact orientation) serve as a bridge between the micro and macro behaviors. In micromechanical models, the particle equilibrium equations are only used in deriving the micromechanical expression for the stress tensor. Here an additional, exact equation is derived for group-averaged forces of contacts with similar orientations, based on the particle equilibrium equations. The formulated equation is obtained by adding subsets of particle equilibrium equations and is independent of particle shapes and loading conditions. The equation involves a geometrical structure function that characterizes three-particle correlations for the particle positions. The obtained relationship is validated through two-dimensional DEM simulations on specimens with disk- and peanut-shaped particles. The research results contribute to developing multi-scale constitutive models that account for neighbouring contacts.