Research on the mathematical relationship between mud height and underflow concentration of deep cone thickener based on effective stress

Low grade is one of the three characteristics of mineral resources in China. With the exploitation of a large number of mineral resources, more tailings will inevitably be produced in the concentrator, and transporting them to the goaf is the best way to deal with tailings. The tailings are compacted by a deep cone thickener (DCT) to prepare a paste. The mud height and underflow concentration are the key parameters to ensure the filling efficiency and quality. To explore the relationship between mud height and underflow concentration of the DCT, mathematical models of mud height and underflow concentration under different conditions were established based on the Terzaghi effective stress principle and the relationship between compressibility $ \alpha $ and mud pressure. Taking a mine as an example, the industrial application and difference analysis of the mathematical model are conducted. Results show that the relationship between mud height and underflow concentration is a power function. When $ \alpha $ is constant, dh/dc decreases gradually with the increase of mud height, and the underflow concentration reaches 100% when the mud height is 29.4 m, which is inconsistent with reality. When $ \alpha $ varies, dh/dc increases gradually with the increase of mud height, and the mud layer becomes difficult to compress. This model is consistent with reality. Moreover, for this mine, the mud height is 5.79 m when the underflow concentration of the DCT increases from 60% to 65% and 11.22 m when the underflow concentration increases from 70% to 75%; the mud height required by the latter is approximately 1.94 times that of the former. The physical significance of the mathematical model is that the effective stress and intergranular porosity vary at different mud heights. As the height of the upper mud layer increases, the tailings particles at the bottom are rearranged and combined under pressure, the water between the pores is discharged, and the particles are compressed more densely. That is, the higher the mud height is, the smaller the intergranular porosity and the higher the underflow concentration. Notably, the mathematical model is applicable to both dynamic and static operations of the DCT from two perspectives, that is, compaction mechanism and effective stress; however, it cannot be generalized. Finally, according to the mathematical model expression and practical application, the mud layer in the DCT is divided into mixed sedimentation, deceleration compression, and limit compression areas.