Before attempting a modelling approach to the crushing mechanisms of "cement clinker" it was necessary to characterize the mechanical behaviour of this material up to breakage. The diametrical compressive test was chosen, as it is the closest to the typical loading within a packing of grains and a very convenient experimental approach for the analysis of mechanical behaviour law up to fragmentation of brittle granular material. The modellization of the grain as a hard brittle core surrounded by a thin crumbly skin leads us to associate the contact setting with the crumbly skin behaviour and the breakage with the brittle core behaviour. This analysis allowed us to define scaling laws for the skin thickness and breakage load. The breakage force increases as a power raw of the grain diameter with an exponent of 1.5 and it is shown that the mean prefactor K-0 is an intrinsic characteristic parameter proportional to the tenacity of the material.