Experimental Study on Compressive Strength of Coal Gangue Cemented Backfill Based on Response Surface Method
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摘要:
煤矸石胶结充填可有效控制煤矿开采造成的地表沉陷，减少环境破坏。为研究细矸率、水泥掺量和料浆质量浓度对充填体抗压强度的影响规律，优化充填材料配比，在单因素试验基础上采用响应面法设计3因素17组配比试验，构建响应面回归模型并计算优化配比，为工程上获得合理充填材料配比提供科学方法。研究表明：单因素对充填体抗压强度的影响大小依次为料浆质量浓度、水泥掺量、细矸率；细矸率和料浆质量浓度交互作用对充填体早期抗压强度影响较小，水泥掺量和料浆质量浓度交互作用对充填体中后期抗压强度影响最大；为满足充填强度要求（一般≥5.0 MPa），经模型优化确定充填料浆最佳配比为m（煤矸石）︰m（粉煤灰）︰m（水泥）︰m（水）=50%︰22%︰8%︰20%，细矸率为52%时，充填体28 d抗压强度为5.07 MPa，验证试验误差范围在2%左右，模型精准可靠；水泥水化生成Ca(OH)2激发粉煤灰和煤矸石活性物质生成钙矾石（AFt）和水化硅酸钙（C-S-H）凝胶，随着龄期不断增长对胶凝体系起到了良好的连接作用，网状结构更加稳定，能有效提高充填体抗压强度。
Abstract:Ground subsidence caused by coal mining could be sufficiently controlled using cemented coal gangue backfilling materials. In order to study the influence of fine gangue rate, cement content and mass concentration of slurry on the compressive strength of backfilling materials and optimize mixture ratio of backfilling materials. Response surface method was used to design an experiment with 3 factors and 17 proportions based on the single factor experiment, furthermore, the response surface regression model was constructed, and the optimal ratio was calculated, which could provide a scientific method for obtaining a reasonable proportion of filling materials in industry. The results showed that the influence of single factor on the compressive strength of backfilling materials was in order of mass concentration of slurry, cement content and fine gangue rate. The influence of interactions between fine gangue rate and mass concentration of slurry on compressive strength of backfilling materials in the early stage was slight, while the influence of interactions between cement content and mass concentration of slurry on compressive strength of backfilling materials in the middle and later stages was the greatest. The optimal ratio of backfilling slurry was determined by the results of model optimization as m (coal gangue)∶m (fly ash)∶m (cement)∶m (water) = 50%∶22%∶8%∶20%, and the fine gangue rate was 52%, The compressive strength of backfilling materials curing for 28 days was 5.07 MPa, and the error range of the verification test was about 2%, the model was accurate and reliable. The Ca(OH)2 generated by cement hydration motivates the active substances of fly ash and coal gangue and generates ettringite (AFt) and calcium silicate hydrate (C-S-H) gels. The continuous growth of curing age plays a good role in connecting the cementing system, making the network structure more stable and effectively improving the compressive strength of backfill.
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Key words:
- cemented filling /
- response surface method /
- compressive strength /
- gangue /
- fly ash /
- cement /
- hydration mechanism
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表 1 煤矸石粒度分级
Table 1. Granularity classification of coal gangue
粒径/mm <3 3-5 5-8 8-15 >15 占比/% 22.50 22.50 25.00 20.00 10.00 
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表 2 充填材料的化学成分
Table 2. Chemical composition of filling materials
/% 材料 SiO2 Al2O3 Fe2O3 CaO MgO SO3 其他 煤矸石 48.14 19.42 14.64 6.74 2.35 0.73 8.00 粉煤灰 48.58 19.59 16.45 4.37 1.50 2.82 6.70 水泥 17.67 4.25 3.84 65.22 2.22 4.27 2.54
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表 3 试验设计因素与水平编码值
Table 3. Experimental design factors and horizontal coding values
影响因素 水平编码值 −1 0 1 水泥掺量A/% 4 8 12 细矸率B/% 35 45 55 料浆质量浓度C/% 76 78 80
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表 4 抗压强度试验值与预测值
Table 4. Compressive strength test value and predicted value
编号 编码值 试验强度/MPa 预测强度/MPa A B C Y3d Y7d Y28d Y3d* Y7d* Y28d* 1 −1 0 1 0.8 1.2 2.2 0.80 1.28 2.25 2 −1 0 −1 0.5 0.9 1.7 0.46 0.78 1.37 3 −1 1 0 0.7 0.9 1.5 0.71 0.90 1.81 4 −1 −1 0 0.6 0.8 1.5 0.65 0.85 1.46 5 0 −1 −1 0.6 0.9 2.8 0.65 0.90 2.81 6 0 1 −1 0.7 1 2.5 0.71 1.13 2.86 7 0 0 0 1 1.5 4.2 0.98 1.52 4.26 8 0 0 0 1 1.5 4.2 0.98 1.52 4.26 9 0 0 0 1 1.6 4.4 0.98 1.52 4.26 10 0 0 0 1 1.5 4.3 0.98 1.52 4.30 11 0 0 0 0.9 1.5 4.2 0.98 1.52 4.26 12 0 −1 1 1 1.7 4.4 0.98 1.58 4.26 13 0 1 1 1.2 1.8 5.1 1.16 1.73 5.09 14 1 −1 0 1.3 1.4 4.2 1.29 1.33 4.26 15 1 0 1 1.5 1.9 6.1 1.54 2.02 6.43 16 1 1 0 1.4 1.7 5.7 1.41 1.65 5.39 17 1 0 −1 1.2 1.4 3.6 1.15 1.40 3.55
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表 5 回归模型方差分析结果
Table 5. Regression model variance analysis results
养护龄期/d 变异来源 平方和 自由度 均方 F值 P值 备注 3 模型 1.34 9 0.15 50.78 <0.0001 Significant A 0.98 1 0.98 334.63 <0.0001 B 0.031 1 0.031 10.67 0.0137 C 0.28 1 0.28 96.04 <0.0001 AB 0.00 1 0.00 0.00 1.00 AC 0.00 1 0.00 0.00 1.00 BC 2.5×10−3 1 2.5×10−3 0.85 0.3863 A2 0.022 1 0.022 7.56 0.0285 B2 0.012 1 0.012 3.96 0.0868 C2 0.012 1 0.012 3.96 0.0868 残差 8.0×10−3 4 2.0×10−3 − − 失拟项 0.013 3 4.6×10−3 2.08 0.2451 Not significant 变异来源 平方和 自由度 均方 F值 P值 备注
7模型 1.86 9 0.21 14.77 0.0009 Significant A 0.85 1 0.85 60.36 0.0001 B 0.045 1 0.045 3.21 0.1161 C 0.72 1 0.72 51.43 0.0002 AB 0.01 1 0.01 0.20 0.4260 AC 0.01 1 0.01 3.20 0.4260 BC 2.2×10−16 1 2.2×10−16 0.20 1.0000 A2 0.11 1 0.11 35.58 0.0275 B2 0.11 1 0.11 7.58 0.0275 C2 4.21×10−4 1 4.21×10−4 10.32 0.8672 残差 8.0×10−3 4 2.0×10−3 − − 失拟项 0.090 3 0.03 4.50 0.0121 Not significant 变异来源 平方和 自由度 均方 F值 P值 备注 28 模型 32.05 9 3.56 35.13 <0.0001 Significant A 20.16 1 20.16 198.91 <0.0001 B 0.32 1 0.32 3.16 0.1188 C 7.03 1 7.03 69.37 <0.0001 AB 0.56 1 0.56 5.55 0.0507 AC 1.00 1 1.00 9.87 0.0164 BC 0.12 1 0.12 1.21 0.3080 A2 2.09 1 2.09 20.65 0.0027 B2 0.46 1 0.46 4.52 0.0710 C2 0.10 1 0.10 1.00 0.3511 残差 0.032 4 8.0×10−3 − − 失拟项 0.68 3 0.23 28.23 0.0038 Not significant 注：1）P为回归方程拒绝原假设的值；2）F为检验回归模型显著性的参数。
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表 6 优化模型验证试验结果比较
Table 6. Optimization model validation test results ratio
龄期 3 d 7 d 28 d 预测值/MPa 1.14 1.81 5.06 实测值/MPa 1.1 1.6 5.0 1.1 1.8 5.1 1.2 1.9 5.1 平均值/MPa 1.13 1.77 5.07 误差/% 0.8% 2.34% 0.14 %
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