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摘要: 高濃度尾砂料漿具有復雜的觸變性，顆粒粒徑是影響料漿觸變性的重要因素，顆粒粒徑對觸變性影響的定量研究尚不豐富。為探究高濃度尾砂膏體的顆粒粒徑對觸變性的影響，使用同種尾砂制備了不同平均粒徑的樣品并制成膏體，開展恒剪切速率實驗。結果表明，尾砂膏體具有顯著的觸變性，恒剪切速率條件下呈剪切稀化。穩態條件下，料漿靜態屈服應力、動態屈服應力、賓漢姆黏度均與顆粒平均粒徑平方的倒數呈線性正相關。瞬態條件下，顆粒平均粒徑和相應瞬態擬合參數呈線性關聯。推薦的穩態和觸變性模型均表現出較高的適用性。通過數據擬合構建了穩態剪切應力和瞬態剪切應力的預測模型，定量表征顆粒平均粒徑對觸變性料漿穩態和瞬態流變行為的影響。Abstract: High-concentration tailings pastes are commonly encountered in the surface deposition and underground cemented paste backfill. It is necessary to forecast the pressure loss along the pipe and the flow behavior in the mined-out area when tailings pastes are transported in a pipeline or stored up in goaf. Traditionally, thixotropy has often been overlooked while designing tailings paste transport and disposal systems due to the complexity of thixotropy characterization. However, thixotropy plays an essential role in the rheology of tailings pastes. To achieve the accurate representation of thixotropy, a suitable constitutive model has to be selected in advance. Unfortunately, there is no current available thixotropic model for tailings pastes up to date. Moreover, tailings pastes exhibit complex thixotropy that is significantly affected by the particle size of tailings, though the relevant studies are not abundant. It is important to analyze quantitively the relationship between particle size and thixotropic parameters based on an appropriate constitutive model. In this work, the constitutive thixotropic model for tailings pastes proposed by Zhang et al. was adopted. To reveal the influence of particle size on the thixotropy of tailings pastes, samples of various mean particle sizes prepared from the same tailings were applied to constant shear rate experiments. Results show that the target tailings pastes display significant thixotropy, leading to shear thinning under steady shear rates. In the steady state, the static yield stress, dynamic yield stress, and Bingham viscosity appear to correlate linearly to the reciprocal of the square of the mean particle size. As for the transient state, the corresponding fit parameters show a strong linear dependence on the mean particle size. The proposed equilibrium and thixotropic models are valid. The forecasting models for equilibrium and transient shear stress are established based on data fit, which is attributed to the quantitative characterization of steady-state and transient rheology for thixotropic tailings pastes under the effect of particle size.
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Key words:
- particle size /
- tailings paste /
- thixotropy /
- rheological parameters /
- forecasting model
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圖 3 不同顆粒粒徑尾砂料漿的穩態流變曲線
Figure 3. Equilibrium rheological curves of tailings suspensions at various particle sizes
圖 4 穩態流變模型各參數與
${\bar \phi ^{ - 2}}$ 之間的關系Figure 4. Relationships between parameters of the proposed equilibrium model and
${\bar \phi ^{ - 2}}$ 
圖 5 不同顆粒平均粒徑和剪切速率下料漿穩態剪切應力曲面圖
Figure 5. Surface plot of equilibrium shear stress of suspensions at various mean particle sizes and shear rates
圖 6 不同剪切速率下料漿剪切應力衰減曲線.（a）1#；（b）2#；（c）3#；（d）4#
Figure 6. Shear stress decay curves at various shear rates: (a) 1#; (b) 2#; (c) 3#; (d) 4#
圖 7 參數
$a$ 與$\ln \dot \gamma $ 的關系曲線Figure 7. Relationships of parameter
$ \mathit{a} $ and$\ln \dot \gamma $ 
圖 8 四種尾砂不同剪切速率下實驗值和預測值的比較.（a）1#；（b）2#；（c）3#；（d）4#
Figure 8. Comparison between experimental and predicted shear stress at various shear rates s for the four kinds of tailings: (a) 1#; (b) 2#; (c) 3#; (d) 4#
圖 9 擬合參數與平均粒徑的關系曲線.（a）
$A$ ；（b）$w$ ；（c）$\ln {\dot \gamma _0}$ Figure 9. Relationships of fit parameter and mean particle size: (a)
$A$ ; (b)$w$ ; (c)$\ln {\dot \gamma _0}$ 
圖 10 恒剪切速率條件下時間、顆粒平均粒徑與瞬態剪切應力的關系曲面圖
Figure 10. Three-dimensional graph of transient shear stress under the effects of time and mean particle size at constant shear rates
表 1 不同粒徑尾砂的粒徑分布結果
Table 1. Particle size distribution details for different tailings
Type of tailings ${D_{10}}$ ${D_{50}}$ ${D_{80}}$ ${D_{90}}$ $D\left[ {4,3} \right]$ 1# 1.448 20.198 68.568 98.549 37.003 2# 1.260 16.358 57.572 82.303 30.676 3# 1.130 13.895 48.810 70.219 26.167 4# 1.022 10.020 34.471 49.461 18.617 
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表 2 穩態流變曲線擬合參數
Table 2. Fit parameters of equilibrium rheological curves
Type of tailings ${\tau _{\text{B}}}$ ${\tau _{\text{D}}}$ ${\mu _{\text{B}}}$ $k$ Adjusted R-Square 1# 37.82 11.28 0.219 0.125 0.994 2# 43.54 12.65 0.224 0.144 0.989 3# 53.8 12.61 0.244 0.152 0.997 4# 72.92 15.24 0.277 0.197 0.977
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