The present invention provides a process for dry grinding one or more mineral materials which include at least calcium carbonate. The process includes a) crushing the mineral material or materials in at least one crushing unit until a crushed material is obtained with a d95 of less than 10 cm, and dry grinding the material in at least one grinding unit (i) in the presence of at least one comb-type hydrophilic polymer containing at least polyalkylene oxide function grafted on to at least one unsaturated ethylene monomer, and (ii) in such a manner that the quantity of liquid in the grinding unit is less than 15% by dry weight of the material crushed in the crushing unit, wherein recovered material has a d50 of 0.5 to 500 microns.