Status and prospects of researches on rheology of paste backfill using unclassified-tailings (Part 1): concepts, characteristics and models
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摘要: 膏體充填為礦產資源的深部開采及可持續發展提供了安全、綠色、高效的技術保障，已成為礦業領域的研究熱點和發展趨勢之一。全尾砂膏體流變學是膏體充填全套工藝流程的重要理論基礎，深刻影響著膏體充填技術的發展。本文從膏體的內涵出發，系統性地論述了膏體流變學研究的必要性、特殊性及復雜性。并以膏體流變實驗結果為基礎，分析了全尾砂膏體的典型流變特性及最新研究成果。總結了常用的屈服型非牛頓流體流變模型，并探討了常用流變本構方程對膏體料漿的適用性，對其實際應用提出合理建議。同時對膏體流變特性的關鍵影響因素進行了概述。根據膏體流變學的研究現狀，歸納總結并提出了膏體流變學研究的重點與難點，指出現階段膏體流變學須從測試標準、本構方程、微觀機理及工程應用等方面深入研究。Abstract: The cemented paste backfill (CPB) technology provides a safe, green and efficient access to deep underground mining and sustainable exploitation of mineral resources, and it has become one of the research focuses and development trends in the mining field. The CPB technology mainly includes four key processes, namely, the thickening of unclassified tailings, homogeneous mixing of multi-scale materials, pipeline transportation of fresh CPB, and its consolidation in the mined-out underground stopes. As a relatively new material that is comprised of various constituents, typically the tailings, cement, and water, as well as a high solid concentration, CPB tends to show complicated behaviors under the effects of surroundings. Therefore, understanding CPB behaviors is of practical significance for the development of the technology, since knowledge of CPB behavior is essential in the preliminary backfill system design and operation. It has been pointed out that the use of solid-liquid two-phase flows shows some limitations for the paste. In comparison, the rheology which targets on the flow and deformation of the paste under the influence of external shearing can provide a theoretical basis for the whole processes of paste backfill technology and deeply affect its development. Based on the characteristics of the paste materials, the necessity, particularity and complexity of the research on paste rheology were systematically discussed. Typical rheological properties of paste and the latest achievements were analyzed with the summarized results from rheological experiments. The commonly used rheological models of yielding non-Newtonian fluids were reviewed, and the applicability of corresponding constitutive equations to paste slurry was discussed with reasonable suggestions provided for its practical application. Meanwhile, the key influence factors of paste rheological properties were summarized. According to the research status, the priorities and difficulties of research on paste rheology were summarized and proposed, with emphases on test standards, constitutive equations, microscopic mechanisms and engineering applications.
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Key words:
- paste /
- rheology /
- unclassified tailings /
- rheological models /
- backfill mining /
- development trend
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圖 2 不同剪切作用下膏體細觀演變示意圖[37]
Figure 2. Changes in the microstructure of paste under different shear intensities
圖 4 觸變性表征方法[24]。（a）應力松弛特征曲線；（b）屈服應力回歸
Figure 4. A method for thixotropy characterization: (a) stress relaxation curves; (b) yield stress regression
圖 5 常見的非牛頓體流變關系曲線。（a）剪切應力曲線；（b）表觀黏度曲線
Figure 5. Rheological curves of common non-Newtonian fluids: (a) shear stress curves; (b) apparent viscosity curves
圖 7 膏體固態?流態轉變過程。（a）剪切應力曲線；（b）表觀黏度曲線[25]
Figure 7. Solid to liquid transitions of paste: (a) shear stress curves; (b) apparent viscosity curves
圖 8 料漿體積分數與質量分數關系圖
Figure 8. Relationship between volume fraction and mass fraction of the slurry
圖 9 全尾砂與常用硅酸鹽水泥粒徑分布
Figure 9. Particle distribution of unclassified tailings and common Portland cements
表 1 非牛頓流體常用流變模型
Table 1. A list of non-Newtonian rheological models
Name of models Equations Power-law[42] $\begin{array}{l} \tau {\rm{ = }}K{\left( {\dot \gamma } \right)^n} \\ n = 1,{\rm{ Newtonian}} \\ n > 1,{\rm{ Shear \;thickening}} \\ n < 1,{\rm{ Shear \;thinning}} \\ \end{array} $ (1) Bingham[43] $\begin{array}{*{20}{l}}{\dot \gamma = 0}&{\tau < {\tau _{\rm{y}}}}\\{\tau {\rm{ = }}{\tau _{\rm{y}}} + {\eta _{\rm{p}}}\dot \gamma}&{\tau \geqslant {\tau _{\rm{y}}}}\end{array}$ (2) Herschel and Bulkley $\begin{array}{*{20}{l}} {\tau {\rm{ = }}{\tau _{\rm{y}}} + K{\left( {\dot \gamma } \right)^n} }&{\tau > {\tau _{\rm{y}}}}\\ {\dot \gamma = 0 }&{\tau \leqslant {\tau _{\rm{y}}}} \end{array}$ (3) Casson[44] $\begin{array}{*{20}{l}} {\sqrt \tau {\rm{ = }}\sqrt {{\tau _{\rm{y}}}} + \sqrt {{\eta _{\rm{c}}}\dot \gamma }}&{\left( {\tau > {\tau _{\rm{y}}}} \right) \left( {{\rm{or }}\;\tau = {\tau _{\rm{y}}} + {\eta _{\rm{p}}}\dot \gamma + 2\sqrt {{\tau _{\rm{y}}}{\eta _{\rm{p}}}\dot \gamma } } \right)}\\ {\dot \gamma = 0}&{\left( {\tau \leqslant {\tau _{\rm{y}}}} \right) } \end{array} $ (4) Buckingham-Reiner[45] $\tau _{\rm{w}} \approx \dfrac{{\Delta PD}}{{4L}} $ (5a) $\tau_{\rm{w}} = {\eta _{\rm{p}}}\dfrac{{8v}}{D}{\left[ {1 - \dfrac{4}{3}\left( {{\tau _{\rm{y}}}\dfrac{{4L}}{{\Delta PD}}} \right) + \dfrac{1}{3}{{\left( {{\tau _{\rm{y}}}\dfrac{{4L}}{{\Delta PD}}} \right)}^4}} \right]^{ - 1}} $ (5b) $ {\tau _{\rm{w}}} \approx \dfrac{4}{3}{\tau _{\rm{y}}} + {\eta _{\rm{p}}}\left( {\dfrac{{8v}}{D}} \right), \;{\rm{for}} \;\tau \gg {\tau _{\rm{y}}} $ (5c) 
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