Wear is well known for causing material loss in a sliding interface. Available macroscopic approaches are bound to empirical fitting parameters, which range several orders of magnitude. Major advances in tribology have recently been achieved via Molecular Dynamics, although its use is strongly limited by computational cost. Here, we propose a study of the physical processes that lead to wear at the scale of the surface roughness, where adhesive junctions are formed between the asperities on the surface of the materials. Using a brittle formulation of the variational phase-field approach to fracture, we demonstrate that the failure mechanisms of an adhesive junction can be linked to its geometry. By imposing specific couplings between the damage and the elastic energy, we further investigate the triggering processes underlying each failure mechanism. We show that a large debris formation is mostly triggered by tensile stresses while shear stresses lead to small or no particle formation. We also study groups of junctions and discuss how microcontact interactions can be favored in some geometries to form macro-particles. This leads us to propose a classification in terms of macroscopic wear rate. Although based on a continuum approach, our phase-field calculations are able to effectively capture the failure of adhesive junctions, as observed through discrete Molecular Dynamics simulations.