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摘要: 充填料浆的管道输送是充填采矿法的一个重要环节，而充填料浆的流变参数是评价充填料浆管输特性的重要指标，目前主要采用流变仪进行测定，但矿山现场通常不具备流变实验条件，主要通过塌落度实验来评价充填料浆的流动性能。本文采用微型塌落筒进行不同质量分数、灰砂比的充填料浆塌落度实验，建立微型塌落筒扩展度与屈服应力之间的解析模型，根据料浆停止流动后的形态得到简化计算模型，基于简化模型理论计算料浆的屈服应力，并将理论值与流变仪测试同等配比条件下得到的屈服应力实验值进行对比分析，同时通过双因素方差分析研究了不同质量分数、灰砂比对充填料浆扩展度的影响规律。结果表明，扩展度主要受质量分数的影响，灰砂比对其影响不显著，充填料浆的屈服应力随质量分数的增大而增大。在质量分数较低时，理论值与实验值的相对误差范围较大，二者的相对误差在25%以内，平均误差为16.79%；随着质量分数增大，误差逐渐减小至15%以内，平均误差为8.81%。综合考虑质量分数的影响，提出基于质量分数的修正系数，修正后的屈服应力理论值与实验值的相对误差降至10%以内，平均误差为3.54%。本研究微型塌落筒实验较传统塌落度实验不仅节省实验用料和劳动强度，还可有效表征料浆屈服应力，对于矿山充填料的流动性能评价具有实际指导意义。Abstract: The backfill mining method is widely used in mines because of its advantages of environmental protection, safety, and efficiency and includes filling slurry pipeline transportation as an important part. The rheological parameters of filling slurry are important indicators for evaluating the characteristics of filling slurry pipeline transport; these parameters are mainly determined by rheometers at present, while the rheological experimental conditions are usually unavailable at the mine site. Because of its simplicity and speed, mines mainly use a slump test to evaluate the flow properties of a filling slurry. In this paper, we used a mini-slump cone to conduct a slump experiment of filling slurry with different mass fractions and cement–tailings ratios (the two most common variable parameters in filling slurry ratios), established an analytical model between the spread of a mini-slump cone and yield stress, obtained a simplified calculation model according to the shape of the filling slurry after flowing, calculated the yield stress of the slurry based on the simplified model, and compared the theoretical value with the experimental value of the yield stress of the filling slurry under the condition of the same ratio tested by a rheometer. At the same time, the influence law of different mass fractions and cement–sand ratios on the expansion degree of the filling slurry was studied using a two-factor analysis of variance. The results show that the spread is mainly influenced by the mass fraction and unsubstantially affected by the cement–sand ratio. The yield stress of the filling slurry increases with the mass fraction. When the mass fraction is low, the error in the theoretical value relative to the experimental value has a large range, and the error in the theoretical value is within 25%, averaging 16.79%; as the mass fraction increases, this error gradually decreases below 15%, averaging 8.81%. Considering its effect, a correction factor based on the mass fraction was proposed, and the error in the theoretical yield stress value after the correction was reduced below 10%, averaging 3.54%. In this study, the mini-slump cone test not only reduces the experimental material and labor intensity compared with the traditional slump test but also effectively characterizes the yield stress of the slurry, which provides practical guidance for evaluating the flowability of mine filling slurry.
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Key words:
- filling slurry /
- spread /
- yield stress /
- analytical model /
- correction factor
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图 3 不同配比尾砂料浆扩展度演化规律. （a）扩展度随不同质量分数的变化；（b）扩展度随不同灰砂比的变化
Figure 3. Evolution law of the spread of tailings slurry with different filling ratios: (a) spread change with different mass fractions; (b) spread change with different cement–tailings ratios
图 4 微型塌落度实验充填料受力分析图(图中R0为上口半径，RH为下口半径，H为高度，R1为未变形部分下口半径，h0为未变形部分高度，h1为已屈服部分高度，s为塌落度，τy为料浆的屈服应力). （a）初始应力分析；（b）最终应力分析；（c）料浆最终扩展度形态
Figure 4. Mechanical analysis diagram of the filling slurry in a mini-slump cone test (in the figure, R0 is the upper radius, RH is the lower radius, H is the height, R1 is the radius of the lower plane of the undeformed part, h0 is the height of the undeformed part, h1 is the height of the yielded part, s is the slump, and τy is the yield stress of filling slurry): (a) initial stress analysis; (b) final stress analysis; (c) final spread shape of the slurry
表 1 扩展度与流变参数测试结果
Table 1. Results of the spread and rheological parameters test
Mass fraction/% Cement–tailings ratio Spread/cm Yield stress/Pa Viscosity/
(Pa·s)68 1∶4 35.8 8.82 0.2782 68 1∶8 36.15 8.32 0.2769 68 1∶12 35.8 9.01 0.2583 68 1∶15 35.6 9.50 0.2535 68 1∶18 35.6 8.46 0.2804 70 1∶4 33.3 15.19 0.2435 70 1∶8 33.4 14.29 0.2687 70 1∶12 33.6 14.83 0.2940 70 1∶15 33.5 13.56 0.3008 70 1∶18 33.4 12.89 0.2882 72 1∶4 28.5 26.59 0.3337 72 1∶8 29.3 24.54 0.4039 72 1∶12 29.8 23.66 0.5445 72 1∶15 30 21.34 0.4652 72 1∶18 30.1 22.46 0.4523 
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表 2 方差分析结果
Table 2. Results of variance analysis
Source Type III sum of squares Df Mean square F Sig. Mass fraction 98.983 2 49.492 278.433 0.000 Cement–tailings ratio 0.624 4 0.156 0.878 0.518 Error 1.422 8 0.178 Total 101.029 14
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表 3 解析模型计算屈服应力与测试屈服应力对比
Table 3. Comparison of yield stress calculated by an analytical model and measured yield stress
Mass fraction/% Cement–tailings ratio Spread/cm Test yield stress/Pa Calculation yield stress/Pa Absolute error Relative error/% 68 1∶4 35.8 8.82 10.216 1.3958 15.83 68 1∶8 36.15 8.32 9.892 1.5756 18.95 68 1∶12 35.8 9.01 10.216 1.20735 13.4 68 1∶15 35.6 9.50 10.546 1.04685 11.02 68 1∶18 35.6 8.46 10.546 2.0906 24.73 70 1∶4 33.3 15.19 14.152 −1.0415 6.85 70 1∶8 33.4 14.29 14.029 −0.2625 1.84 70 1∶12 33.6 14.83 13.897 −0.9335 6.3 70 1∶15 33.5 13.56 13.717 0.16 1.18 70 1∶18 33.4 12.89 14.029 1.138 8.83 72 1∶4 28.5 26.59 22.532 −4.056 15.26 72 1∶8 29.3 24.54 20.919 −3.62 14.75 72 1∶12 29.8 23.66 20.506 −3.1555 13.34 72 1∶15 30 21.34 19.892 −1.4435 6.76 72 1∶18 30.1 22.46 19.529 −2.93 13.04
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表 4 修正后屈服应力对比
Table 4. Comparison of yield stress after correction
Mass fraction/% Cement–tailings ratio Test yield stress/Pa Corrected yield stress/Pa Correcting errors Corrected error rate/% 68 1∶4 8.82 8.814 0.0062 0.07 68 1∶8 8.32 8.535 −0.2186 2.63 68 1∶12 9.01 8.814 0.1946 2.16 68 1∶15 9.50 9.099 0.4002 4.21 68 1∶18 8.46 9.099 −0.6436 7.61 70 1∶4 15.19 14.251 0.9425 6.2 70 1∶8 14.29 14.127 0.1645 1.15 70 1∶12 14.83 13.994 0.8365 5.64 70 1∶15 13.56 13.813 −0.2560 1.89 70 1∶18 12.89 14.127 −1.2360 9.59 72 1∶4 26.59 25.939 0.6490 2.44 72 1∶8 24.54 24.082 0.4570 1.86 72 1∶12 23.66 23.607 0.0545 0.23 72 1∶15 21.34 22.9 −1.5645 7.33 72 1∶18 22.46 22.482 −0.0230 0.1
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