The yield stress model based on the concept of degrees of freedom of a particulate system in an aqueous medium has been experimentally validated with quartz suspensions with concentrations of phi=0.25 to 0.51. The particle size of each suspension involved in the model has been successfully corroborated with a Rosin-Rammler size modulus of k = 11 to 46 mu m. It has also been successfully applied to a suspension of copper tailings from the Great Chilean Copper Mine. The model involves the maximum fraction of packing, phi(M) a very important parameter related to the interaction between the particles that form the suspension. The suspensions of fine particles report packing values of low density in relation to the coarse sizes. Concentrations close to the maximum packing lead to very high yield stress values. The model is capable of predicting the critical concentration of solids in the discharge of an industrial thickener of copper tailing. The maximum fraction of packing in the thickening discharge is phi(M) = 0.35. (C) 2009 Elsevier B.V. All rights reserved.