Research on the mathematical relationship between mud height and underflow concentration of deep cone thickener based on effective stress
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摘要: 首先，從Terzaghi有效應力原理定義出發，證明了有效應力原理在深錐濃密機泥層壓力分析中的適用性。其次，以壓縮系數
$ \alpha $ 與泥層壓力之間的關系為紐帶，建立了不同情況（$ \alpha $ 為常數和$ \alpha $ 為變量）下泥層高度和底流濃度數學模型。然后，結合礦山實例對數學模型進行工業應用和差異性分析，研究結果表明：兩種情況下泥層高度與底流濃度均呈冪函數關系；在$ \alpha $ 為常數時，隨泥層高度增加，泥層高度變化率（dh/dc）逐漸減少，并且泥層高度為29.4 m時底流濃度就達到100%，與現實不符；在$ \alpha $ 為變量時，隨泥層高度增加，dh/dc逐漸增加，泥層越來越不容易被壓縮，該模型與現實相符合。最后，根據數學模型表達式及實際應用，將深錐濃密機中尾礦劃分為混合沉降區、減速壓縮區和極限壓縮區。泥層高度與底流濃度關系的揭示對實際生產中底流濃度的精準控制具有較好的指導意義。Abstract: 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. -
圖 1 深錐濃密機中尾礦顆粒沉降過程及受力分析示意圖
Figure 1. Diagram of the sedimentation process and stress analysis of tailings particles in a deep cone thickener
圖 2 基于臨界壓縮點建立的泥層高度與濃密機半徑直角坐標系
Figure 2. Rectangular coordinate system of mud height and thickener radius based on the critical compression point
圖 3 泥層高度與底流濃度關系曲線
Figure 3. Curves of the relationship between mud height and underflow concentration
圖 4 壓縮系數、dh/dc與底流濃度關系曲線
Figure 4. Curves of the relationship between compressibility, dh/dc, and underflow concentration
圖 5 泥層高度與底流濃度數學模型曲線示意及沉降區域劃分
Figure 5. Curve of the mathematical model of mud height, underflow concentration, and division of sedimentation area
表 1 尾礦物理性質參數表
Table 1. Physical property parameters of tailings
Dry density/
(g·cm?3)Density/
(g·cm?3)Loose density/
(g·cm?3)Dense porosity/% Loose porosity/% 2.970 1.568 1.001 47.20 66.28 
下載: 導出CSV
久色视频表 2 數學模型關鍵參數表
Table 2. Key parameters of the mathematical model
Critical compression concentration/% Underflow concentration/% Maximum mud height/m Compressibility/MPa?1 Correction factor 60.18 70.0 13.7 6.87 0.18
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