The optimization of pervious concrete ratios with spontaneous combustion gangue aggregates based on the RSM-BBD method
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摘要: 为了对自燃煤矸石骨料透水混凝土进行配比优化，采用BBD响应面法设计17组试验，研究骨灰比、水灰比和增强剂掺量对透水混凝土抗压强度、透水系数和孔隙率的影响，构建响应面模型，揭示各因素与响应值的相关关系，获得综合性能最优配比。研究结果表明：各因素与各响应值关系皆呈二次多项式模型，回归系数R2皆大于0.9，说明模型合理性和拟合性较好。水灰比和骨灰比对各响应值影响均非常显著，增强剂掺量只对抗压强度影响非常显著，骨灰比和增强剂掺量交互项对抗压强度影响显著，水灰比与增强剂掺量交互项对孔隙率影响显著。当骨灰比3.2、水灰比0.22、增强剂掺量4.5 % 时，混凝土28 d抗压强度为28.7 MPa、透水系数3.21 mm/s、孔隙率19.7 %，满足C20透水混凝土的工程要求。Abstract: In order to optimize the ratio of pervious concrete with spontaneous combustion coal gangue aggregate, 17 groups of experiments were designed by the BBD response surface method to study the effects of aggregate-cement ratio, water-cement ratio, and reinforcing agent on the compressive strength, permeability coefficient, and porosity of pervious concrete. The response surface model was constructed to reveal the correlation between various factors and response values and obtain the optimal ratio of comprehensive performance. The results show that each factor and each response value are quadratic polynomial models, and the regression coefficient R2 of each model is greater than 0.9, indicating that the model is reasonable and fitting. The influence of water-cement ratio and aggregate-cement ratio on each response value and reinforcing agent on compressive strength is very significant. The influence of the interaction of aggregate-cement ratio and water-cement ratio on compressive strength and the interaction of water-cement ratio and reinforcing agent on porosity is significant. When the ratio of aggregate-cement ratio is 3.2, the ratio of water-cement ratio is 0.22, and the dosage of the reinforcing agent is 4.5 %, the 28 d compressive strength of pervious concrete reaches 28.7 MPa, the permeability coefficient is 3.21 mm/s, and the porosity is 19.7 %, which meets the engineering requirements of C20 pervious concrete.
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图 1 自燃煤矸石外观和微观形貌
Figure 1. Appearance and microstructure of spontaneous combustion coal gangue
图 2 自燃煤矸石矿物组成及孔隙特征
Figure 2. Mineral composition and pore characteristics of spontaneous combustion coal gangue
图 5 骨灰比与水灰比交互作用对抗压强度、透水系数、孔隙率影响的响应曲面和等高线
Figure 5. Response surface and contour of the interaction between aggregate-cement ratio and water-cement ratio on compressive strength, permeability coefficient and porosity
图 6 骨灰比与增强剂掺量交互作用对抗压强度、透水系数、孔隙率影响的响应曲面和等高线
Figure 6. Response surface and contour of the interaction between aggregate-cement ratio and the dosage of the reinforcing agent on compressive strength, permeability coefficient and porosity
图 7 不同增强剂掺量下的透水混凝土28 d水化产物形貌
Figure 7. Morphology of 28 d hydration products of pervious concrete with different dosage of the reinforcing agent
图 8 水灰比与增强剂掺量交互作用对抗压强度、透水系数、孔隙率影响的响应曲面和等高线
Figure 8. Response surface and contour of the interaction between water-cement ratio and the dosage of the reinforcing agent on compressive strength, permeability coefficient and porosity
图 10 预测模型计算结果与试验结果对比
Figure 10. Comparison between the calculation results of the prediction model and the test results
图 11 不同倍数下掺量不同的增强剂透水混凝土微观形貌
Figure 11. The microstructure of pervious concrete with different reinforcing agent under different multiples
表 1 自燃煤矸石化学组成
Table 1. The chemical composition of spontaneous combustion coal gangue
组成 SiO2 Al2O3 Fe2O3 CaO MgO TiO2 Na2O K2O SO3 质量分数/% 59.34 25.28 4.66 4.50 2.00 1.70 1.15 0.53 0.25 
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表 2 自燃煤矸石骨料主要技术性质指标
Table 2. Main technical properties of spontaneous combustion coal gangue aggregate
品种 表观密度/(kg·m-3) 松堆密度/(kg·m-3) 压碎指标/% 空隙率/% 吸水率/% 自燃煤矸石 2 382 1 221 18 53.8 9.87 自燃煤矸石细骨料 2 357 1 030 — 56.3 11.70
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表 3 设计因素编码及水平
Table 3. Codes and levels of design factors
编码 因素 水平 -1 0 1 x1 mG/mC 2.8 3.1 3.4 x2 mW/mC 0.20 0.22 0.24 x3 wSR/% 3.0 4.5 6.0
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表 4 响应面试验设计与结果
Table 4. Design and results of response surface experiment
编号 因素 抗压强度y1/MPa 透水系数y2/(mm·s-1) 孔隙率y3/% mG/mC mW/mC wSR/% 试验值 预测值 试验值 预测值 试验值 预测值 1 2.8 0.24 4.5 41.2 42.0 0.22 0.17 5.8 4.3 2 3.4 0.22 3.0 28.4 29.9 2.31 2.31 18.5 18.3 3 2.8 0.22 3.0 32.4 31.1 0.87 1.00 10.4 11.2 4 3.4 0.22 6.0 32.2 33.5 2.02 1.89 16.3 15.6 5 2.8 0.22 6.0 47.5 46.1 0.58 0.58 8.4 8.6 6 3.4 0.24 4.5 40.5 38.6 0.97 0.72 12.1 11.5 7 2.8 0.20 4.5 26.0 27.9 1.86 2.11 15.4 16.0 8 3.4 0.20 4.5 18.5 17.7 3.45 3.84 21.3 22.8 9 3.1 0.22 4.5 29.8 30.5 1.84 1.72 13.9 14.0 10 3.1 0.22 4.5 29.6 30.5 1.42 1.72 14.2 14.0 11 3.1 0.22 4.5 30.7 30.5 1.62 1.72 12.7 14.0 12 3.1 0.22 4.5 33.0 30.5 1.76 1.72 13.4 14.0 13 3.1 0.22 4.5 29.3 30.5 1.97 1.72 15.7 14.0 14 3.1 0.20 6.0 26.8 26.3 3.87 3.62 21.8 21.0 15 3.1 0.24 6.0 45.2 45.8 1.12 1.50 11.8 13.1 16 3.1 0.24 3.0 34.0 34.5 1.08 1.33 11.4 12.2 17 3.1 0.20 3.0 19.6 19.0 5.00 4.62 28.6 27.3
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表 5 抗压强度多种模型综合分析结果
Table 5. Comprehensive analytical results of various models of compressive strength
模型 P值 R2 连续项 失拟项 校正值 预测值 线性模型 < 0.000 1 0.052 7 0.844 7 0.756 2 交互模型 0.180 2 0.065 8 0.873 5 0.678 1 二次模型 0.044 5 0.186 1 0.939 1 0.902 7
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表 6 透水系数多种模型综合分析结果
Table 6. Comprehensive analytical results of various models of permeability coefficient
模型 P值 R2 连续项 失拟项 校正值 预测值 线性模型 0.000 3 0.010 6 0.701 1 0.503 8 交互模型 0.808 8 0.006 4 0.645 8 -0.087 1 二次模型 0.007 4 0.050 0 0.909 8 0.905 0
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表 7 孔隙率多种模型综合分析结果
Table 7. Comprehensive analysis results of various models of porosity models
模型 P值 R2 连续项 失拟项 校正值 预测值 线性模型 < 0.000 1 0.028 7 0.747 5 0.587 6 交互模型 0.682 5 0.019 3 0.715 5 0.157 3 二次模型 0.006 8 0.158 0 0.922 0 0.905 7
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表 8 回归方程的方差分析结果
Table 8. Variance analytical results of regression equation
来源 df 均方差 F值 P值 y1 y2 y3 y1 y2 y3 y1 y2 y3 回归 9 109.03 2.57 51.03 28.39 16.96 22.03 0.000 1 0.000 6 0.000 2 x1 1 94.53 3.41 99.41 24.62 22.49 42.91 0.001 6 0.002 1 0.000 3 x2 1 612.50 14.55 264.50 159.50 96.08 114.16 <0.000 1 <0.000 1 <0.000 1 x3 1 173.91 0.35 14.04 45.29 2.30 6.06 0.000 3 0.173 0 0.053 3 x1 x2 1 11.56 0.18 0.04 3.01 1.16 0.02 0.126 3 0.316 3 0.899 2 x1 x3 1 31.92 0.00 0.00 8.31 0.00 0.00 0.023 5 1.000 0 0.949 5 x2 x3 1 4.00 0.34 12.96 1.04 2.26 5.59 0.341 4 0.176 5 0.048 0 x12 1 24.20 2.12 29.90 6.30 14.00 12.91 0.040 4 0.007 2 0.008 8 x22 1 7.42 1.58 22.96 1.93 10.44 9.91 0.207 1 0.014 4 0.016 2 x32 1 21.27 0.79 18.30 5.54 5.21 7.90 0.020 8 0.056 5 0.026 1 残差 7 3.84 0.15 2.32 — — — — — — 失拟值 3 5.95 0.29 3.74 2.64 6.59 3.00 0.186 1 0.051 0 0.158 0 纯误差 4 2.26 0.05 1.25 — — — — — —
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表 9 模型可信度检验分析结果
Table 9. Results of model credibility test and analysis
模型 标准偏差 均值 R2 R2校正值 R2预测值 残差平方和预测值 变异系数/% 信噪比 y1 1.96 32.04 0.973 3 0.939 1 0.902 7 299.75 6.12 18.888 y2 0.39 1.88 0.976 0 0.909 8 0.905 0 14.39 13.7 16.026 y3 1.52 14.81 0.965 9 0.922 0 0.905 7 187.47 10.28 19.702
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表 10 参数优化后预测值与实测值对比
Table 10. Comparison of predicted and measured values after parameter optimization
类别 骨灰比 水灰比 增强剂掺量/% 抗压强度 透水系数 孔隙率 预测值/MPa 实测值/MPa 误差/% 预测值/(mm·s-1) 实测值/(mm·s-1) 误差/% 预测值/% 实测值/% 误差/% 实验室试验值 3.2 0.22 4.5 28.7 29.3 2.09 3.21 3.29 2.49 19.7 18.9 4.06 现场试验路段实测值 3.2 0.22 4.5 28.7 30.2 5.23 3.21 3.11 3.12 19.7 19.2 2.54
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