It has been established that the second-order work criterion is a general necessary condition for all instabilities by divergence in rate-independent granular materials. The relation between the values of discrete second-order work at the intergranular contact point level and its global macroscopic value is recalled at the beginning of this paper. Then, the basic purpose of the paper is tackled by an analysis of the main features of second-order work criterion in relation with the granular microstructure. For that, it is considered a novel micromechanical model (the so-called ‘H-microdirectional model’), which has the property to involve three scales: grain scale, mesoscale with a specific granular configuration and continuum mechanics macroscale. Eventually, these exhibited features (a bifurcation stress domain and some instability cones) are qualitatively compared with the ones provided by direct numerical simulations issued from a discrete element model. The ultimate goal is to analyse what happens at the granular scale, when the macrosecond-order work is vanishing at the macrolevel. Copyright © 2013 John Wiley & Sons, Ltd.