Homogenization mathematical model of the cemented filling slurry with crushing waste rock and whole tailings
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摘要: 針對廢石全尾砂高濃度充填料漿管輸易堵管及充填體分層的問題，開展減水劑、攪拌參數等對料漿均質性影響的試驗及料漿均質化定量表征的研究。首先基于泌水?坍落度試驗確定了聚羧酸系(PC)減水劑及其摻量區間，獲得了PC作用下的料漿流變參數及充填體強度的變化規律。其次，通過圖像處理技術分析攪拌料漿表面特征，明確了PC作用下攪拌時長及廢尾比(廢石與尾礦質量比)對料漿均質化的影響規律。最后，構建了廢石全尾砂高濃度充填料漿的均質化模型。結果表明，PC作用能夠降低料漿的屈服應力與塑性黏度系數，改善料漿流動性。合理摻量可以提升充填體的早期強度，但對28 d強度有削弱。料漿表面圖像信息熵越高、黑色像素點占比越小，料漿均質化程度越高，且均質化程度隨攪拌時長、廢尾比的增大呈先增大后減小趨勢。當PC的質量分數為0.26%~0.5%時，料漿均質化程度高，PC質量分數為0.5%時料漿屈服應力和塑性黏度達到最小值，分別為202.25 Pa和0.79 Pa·s。Abstract: Aiming at the problems of pipeline transportation blockage and filling body stratification caused by waste rock–unclassified tailings high-concentration slurry, the effects of superplasticizer and stirring parameters on the slurry homogenization were experimented with, and the quantitative characterization of slurry homogenization was explored. Initially, the polycarboxylate (PC) superplasticizer with the best suitability was screened out based on the bleeding-slump test, and the mathematical correlations of the slump and bleeding rate with the optimal superplasticizer dosage range were obtained by regression. The rheological properties of the slurry and the filling body strength were then determined at different PC superplasticizer dosages, and separate mathematical models for correlations of slurry rheological parameters and mechanical properties with superplasticizer dosage were built. Next, the slurry surface images under different stirring conditions were acquired with the Nikon D350 camera, and their information entropies were calculated. Meanwhile, the OTSU algorithm was used to perform image segmentation thresholding, and the images were binarized via Matlab, followed by a calculation of the proportion of black pixels in the binarized images. Further, the variation trends of image information entropy and black pixels proportion with PC superplasticizer, rock/tailing ratio (mass ratio of waste rock to unclassified tailings), and stirring time were derived. Finally, the homogenization mechanism in the waste rock–unclassified tailings filling slurry was revealed based on the PC superplasticizer’s regulatory role in fine particle absorption and dispersion, which was further validated by the relationship between the zeta potential of cement paste and the dosage of PC superplasticizer. On this basis, a quantitative model of slurry homogenization was developed based on the slump, bleeding rate, rheological properties, strength characteristics, and image information, and the optimal parameters of waste rock–unclassified tailings high-concentration filling slurry were obtained by multi-objective programming. The results show that the PC superplasticizer is highly suitable for the slurry, which can reduce its yield stress and plastic viscosity coefficient and improve its fluidity. When the dosage of PC superplasticizer is 0.50%, the yield stress and plastic viscosity of the slurry is reduced by 34.4% and 21.2%, respectively, in comparison to the case without superplasticizer. The slurry rheological properties conform to the Bingham plastic model. Increasing the PC superplasticizer dosage improves the early strength of the filling body and weakens the 28-d strength. Nonetheless, within the optimal dosage range, all the filling body strengths can meet the mine filling requirements. Slurry surface images with higher information entropy and a smaller proportion of black pixels indicate a higher degree of slurry homogenization. Moreover, the entropy value of slurry surface images tends to increase initially and then decrease with the prolonging of stirring time and the heightening of the rock/tailing ratio. When the rock/tailing ratio is constant, the proportion of black pixels is the largest at a stirring time of 3 min, followed by 5 min, and the smallest at 4 min. According to the quantitative model results of slurry homogenization, the reasonable dosage range of PC superplasticizer is 0.26%–0.5%, and the optimal stirring time is 4.3 min. The degree of homogenization is the best at a 0.5% dosage, at which point the slurry has a plastic viscosity μ of 0.79 Pa·s and a yield stress τ of 202.25 Pa.
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圖 1 粒徑特征分布曲線. (a)廢石; (b)尾砂
Figure 1. Characteristic distribution curve of particle size: (a)waste rock; (b)tailings
圖 2 減水劑作用下料漿泌水?坍落變化情況
Figure 2. Changes of slurry bleeding and slump under the action of water?reducing agent
圖 3 PC作用下料漿的剪切應力?剪切速率曲線
Figure 3. Shear stress?shear rate curve of slurry under the action of PC
圖 4 PC摻量與屈服應力、塑性黏度的回歸結果
Figure 4. Regression results of PC content, yield stress and plastic viscosity
圖 5 充填體抗壓強度曲線
Figure 5. Characterization curve of compressive strength of filling body
圖 6 充填體抗壓強度與影響因素關系曲面
Figure 6. Relationship between compressive strength of filling body and factors
圖 7 不同PC質量分數條件下的攪拌試驗結果. （a）ω=0；（b）ω=0.50%
Figure 7. Stirring test result with different ω: （a）ω=0；（b）ω=0.50%
圖 8 攪拌時間與廢尾比交互作用下表面圖像信息熵變化. (a) ω=0(R2=0.9951)；(b) ω=0.5%(R2=0.9333)
Figure 8. Change of surface image information entropy under the interaction of mixing time and rock/tailingratio:(a) ω=0(R2=0.9951) ； (b) ω=0.5%(R2=0.9333)
圖 9 黑色像素點占比及二值化結果. (a)ω=0.5%；(b)ω=0
Figure 9. Proportion of black pixels and the result of binarization:(a) ω = 0.5% ； (b) ω = 0
圖 10 全尾砂廢石充填料漿中PC的均質化作用機理
Figure 10. Homogenization mechanism of polycarboxylate in filler slurry of whole tailings and waste rock
圖 11 水泥凈漿的Zeta電位與PC摻量的關系圖
Figure 11. Relationship between the Zeta potential of the cement paste and the PC content
表 1 減水劑的性能指標
Table 1. Performance index of water-reducing agent
Type pH Cl? content/% Na2SO4 content/% PC 6.20 0.06 2.60 FDN 7.00–9.00 ≤1.00 ≤5.00 AK 9.72 0.28 0.74 
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表 2 摻PC減水劑膠結體強度測試結果
Table 2. Strength test results of cement mixed with PC water-reducing agent
No. ω/% Compressive strength, σ/MPa 3 d 7 d 28 d 1 0.00 2.35 3.77 6.54 2 0.10 3.11 5.14 7.72 3 0.20 3.46 4.97 6.31 4 0.30 3.26 5.09 5.77 5 0.40 2.78 4.42 5.59 6 0.50 2.43 3.95 5.26
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表 3 不同條件下料漿表面單元及整體圖像的熵值
Table 3. Entropy of the surface unit and the overall image of the slurry under different conditions
No. Time/min Rock/tailing ratio ω = 0 ω = 0.50% Maximum entropy
unitMinimum
entropy unitAverage unit entropy Overall
imageMaximum entropy
unitMinimum entropy
unitAverage unit entropy Overall
image1 3 6:4 3.96 3.73 3.85 57.74 4.20 3.96 4.08 61.18 2 3 7:3 3.98 3.75 3.87 58.00 4.21 3.92 4.06 60.95 3 3 5:5 3.97 3.70 3.84 57.59 4.17 3.93 4.05 60.80 4 4 6:4 4.07 3.85 3.96 59.41 4.27 4.04 4.16 62.36 5 4 7:3 4.06 3.83 3.95 59.18 4.27 4.02 4.15 62.21 6 4 5:5 4.02 3.78 3.90 58.51 4.23 4.00 4.11 61.72 7 5 6:4 4.01 3.77 3.89 58.37 4.26 4.00 4.13 61.98 8 5 7:3 4.00 3.76 3.88 58.18 4.19 3.95 4.07 61.01 9 5 5:5 4.04 3.81 3.92 58.86 4.21 3.96 4.09 61.29
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久色视频表 4 料漿表面圖像二值化后的黑色像素點占比
Table 4. Percentage of black pixels after binarization of the slurry surface image
No. Time/min Waste to tail ratio Percentage of black pixels (h)/% ω=0 ω = 0.50% 1 3 5∶5 62.23 40.33 2 3 6∶4 63.65 35.15 3 3 7∶3 58.55 42.43 4 4 5∶5 16.46 14.40 5 4 6∶4 13.98 13.85 6 4 7∶3 15.22 14.64 7 5 5∶5 23.25 19.44 8 5 6∶4 21.54 20.05 9 5 7∶3 21.94 21.85
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