The present invention relates to a process for producing a granular material 26 for mixing with at least a hydraulic binding agent and with water to produce mortar or concrete. This process comprises at least an aggregation step and a carbonation step. In the aggregation step, steel slag particles from at least a fine fraction 24 of steel slag, in particular a fine fraction of steel slag containing a significant amount of γ-dicalcium silicate, are aggregated into larger grains so as to form a coarser granular material 25. In the carbonation step, said aggregated particles in said coarser granular material 25 are carbonated by means of carbon dioxide so as to produce a carbonated granular material 26. The present invention also relates to a carbonated granular material of aggregated steel slag particles containing a significant amount of γ-dicalcium silicate, in particular at least 3 wt. %, preferably at least 5 wt. % and more preferably at least 7 wt. %, and bound within each grain by a solid matrix containing at least calcium and/or magnesium carbonates.