Material optimization and cross-scale enhancement mechanism of porous concrete based on response surface method
Article Text (Baidu Translation)
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摘要: 为提升多孔混凝土(PC)的力学性能和耐久性，系统研究了玄武岩纤维(BF)、纳米SiO2(NS)和纳米CaCO3(NC)对PC的增强作用。通过单因素试验确定3种增强材料的掺量范围，并基于响应面法(RSM)，以3种增强材料的掺量作为变量因素，以PC透水系数、抗压强度和抗折强度为响应指标，设计试验并建立回归模型；通过统计分析和模型优化，研究3种增强材料的交互效应，结合渴求函数确定了最佳掺量比例；进一步通过宏观性能与微观结构对比分析，揭示了其跨尺度协同增强机制。研究结果表明：单掺BF、NS和NC均能在一定范围内提升PC的抗压强度和透水系数；3种材料的增强作用并非简单的线性叠加，而是表现出显著的交互效应，RSM优化出BF的最佳体积分数为0.34%，NS和NC的最佳质量分数分别为0.38%和0.47%；相比增强前，优化后的PC透水系数、抗压强度和抗折强度分别提升了72.9%、63.6%和96.6%，且具有良好的抗冻融性能；BF主要通过介观尺度上的“桥联”效应提升PC的韧性，而NS和NC则通过微观尺度上的火山灰效应、成核效应和填充效应，促进水化产物的生成，改善基体和界面过渡区的致密性，从而增强PC的力学性能和耐久性；基于RSM进行纤维-活性纳米材料优化设计，可显著提升PC综合性能，为PC的性能优化和工程应用提供理论依据和试验基础。Abstract: To enhance the mechanical properties and durability of porous concrete (PC), the enhancement effect of basalt fiber (BF), nano-SiO2 (NS), and nano-CaCO3 (NC) on PC was systematically investigated. The appropriate dosage ranges of the three enhancement materials were determined through the single-factor test. Based on response surface method (RSM), with the dosages of these materials as variables, and the permeability coefficient, compressive strength, and flexural strength of PC as response objectives, an experiment was designed, and a regression model was established. The interaction effect of the three enhancement materials was studied using statistical analysis and model optimization, with the optimal dosages determined via desirability function. Further, the cross-scale synergistic enhancement mechanism was revealed through a comparative analysis of macroscopic performance and microscopic structure. Analysis results indicate that individual incorporation of BF, NS, and NC can enhance the compressive strength and permeability coefficient of PC within a certain range. The effect of the three enhancement materials is not merely a simple linear combination, but exhibits significant interactions. The optimal volume fraction of BF optimized by RSM is 0.34%, and the optimal mass fractions of NS and NC are 0.38% and 0.47%, respectively. Compared to the unenhanced PC, the optimized one is 72.9%, 63.6%, and 96.6% higher in permeability coefficient, compressive strength, and flexural strength, respectively, with excellent freeze-thaw resistance. BF primarily enhances the toughness of PC through the 'bridging' effect at the mesoscopic scale, while NS and NC promote the formation of hydration products and improve the density of the matrix and interfacial transition zone through pozzolanic, nucleation, and filling effects at the microscopic scale, thereby enhancing the mechanical properties and durability of PC. Optimized design of fiber-activated nanomaterials based on RSM can significantly enhance the overall performance of PC and provide a theoretical basis and experimental foundation for its performance optimization and engineering applications.
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图 1 水泥、矿粉及活性纳米材料的粒径分布
Figure 1. Particle size distribution of cement, mineral powders and activated nanomaterials
图 3 单因素对PC抗压强度和透水系数的影响
Figure 3. Effect of single factor on compressive strength and permeability coefficient of PC
图 4 透水系数响应面及等值线
Figure 4. Response surface and contour diagram of permeability coefficient
图 5 抗压强度响应面及等值线
Figure 5. Response surface and contour diagram of compressive strength
表 1 水泥、矿粉及活性纳米材料化学成分
Table 1. Chemical composition of cement, mineral powders and active nanomaterials
% 类型 SiO2 Al2O3 Fe2O3 CaO MgO Na2O SO3 烧失量 水泥 21.59 4.07 5.01 64.15 1.98 0.11 2.19 0.90 矿粉 34.10 15.23 0.32 39.71 6.51 0.23 2.29 1.24 NS 97.74 0.39 0.08 0.20 0.15 0.09 1.35 NC 0.12 0.09 0.25 54.77 0.18 0.06 1.23 43.30 
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表 2 玄武岩纤维基本物理技术指标
Table 2. Basic performance parameters of basalt fiber
指标 密度/ (g·cm-3) 平均直径/μm 长度/ mm 拉伸强度/ MPa 弹性模量/ GPa 玄武岩纤维 2.65 16 6~10 3 300~4 500 95~115
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表 4 响应面因素与水平
Table 4. Factors and levels of RSM
% 水平设置 体积分数 质量分数 BF NS NC - 0.2 0.1 0.3 0 0.4 0.3 0.5 + 0.6 0.5 0.7
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表 5 响应面试验设计
Table 5. Experimental design based on RSM
% 编号 编码 体积分数 质量分数 BF NS NC 1 000 0.4 0.3 0.5 2 0++ 0.4 0.5 0.7 3 -0- 0.2 0.3 0.3 4 +0+ 0.6 0.3 0.7 5 0-- 0.4 0.1 0.3 6 000 0.4 0.3 0.5 7 0-+ 0.4 0.1 0.7 8 000 0.4 0.3 0.5 9 --0 0.2 0.1 0.5 10 0+- 0.4 0.5 0.3 11 000 0.4 0.3 0.5 12 -+0 0.2 0.5 0.5 13 +0- 0.6 0.3 0.3 14 000 0.4 0.3 0.5 15 -0+ 0.2 0.3 0.7 16 ++0 0.6 0.5 0.5 17 +-0 0.6 0.1 0.5
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表 6 RSM试验结果
Table 6. RSM results
编号 编码 响应指标 透水系数/(mm·s-1) 抗压强度/MPa 抗折强度/MPa 1 000 11.01 32.80 5.26 2 0++ 9.89 27.87 4.51 3 -0- 10.29 29.74 4.26 4 +0+ 3.83 21.64 3.65 5 0-- 9.21 29.11 4.33 6 000 12.01 32.51 5.22 7 0-+ 8.19 25.28 4.55 8 000 11.84 31.67 5.36 9 --0 9.27 24.12 4.04 10 0+- 12.29 28.42 5.16 11 000 12.17 32.56 5.28 12 -+0 10.32 29.87 4.69 13 +0- 6.25 20.52 3.02 14 000 12.21 33.03 4.99 15 -0+ 8.31 27.42 4.11 16 ++0 5.78 16.63 3.45 17 +-0 3.93 23.42 3.87
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表 7 透水系数回归模型方差分析
Table 7. ANOVA of permeability coefficient regression model
方差来源 平方和 自由度 均方 F值 P值 显著性 Y1 125.46 9 13.94 55.43 ＜0.000 1 是 A 42.26 1 42.26 168.03 ＜0.000 1 是 B 7.38 1 7.38 29.33 0.001 0 是 C 7.66 1 7.66 30.44 0.000 9 是 AB 0.16 1 0.16 0.64 0.450 2 否 AC 0.05 1 0.05 0.19 0.676 9 否 BC 0.47 1 0.45 1.87 0.214 2 否 A2 55.28 1 55.28 219.80 ＜0.000 1 是 B2 3.40 1 3.40 13.52 0.007 9 是 C2 4.68 1 4.68 18.59 0.003 5 是 残差 1.76 7 0.25 失拟项 0.79 3 0.26 1.09 0.450 6 否 绝对误差 0.97 4 0.24 总离差 127.23 16
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表 8 抗压强度回归模型方差分析
Table 8. ANOVA of compressive strength regression model
方差来源 平方和 自由度 均方 F值 P值 显著性 Y2 371.60 9 41.29 81.47 ＜0.000 1 是 A 104.69 1 104.69 206.58 ＜0.000 1 是 B 0.092 4 1 0.092 4 0.182 4 0.682 1 否 C 3.89 1 3.89 7.68 0.027 6 是 AB 39.31 1 39.31 77.57 ＜0.000 1 是 AC 2.96 1 2.96 5.84 0.046 4 是 BC 2.69 1 2.69 5.31 0.054 7 否 A2 147.66 1 147.66 291.38 ＜0.000 1 是 B2 39.99 1 39.99 78.92 ＜0.000 1 是 C2 13.07 1 13.07 25.79 0.001 4 是 残差 3.55 7 0.506 8 失拟项 2.48 3 0.828 3 3.12 0.150 3 否 绝对误差 1.06 4 0.265 6 总离差 375.15 16
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表 9 抗折强度回归模型方差分析
Table 9. ANOVA of flexural strength regression model
方差来源 平方和 自由度 均方 F值 P值 显著性 Y3 7.76 9 0.861 9 26.13 0.000 1 是 A 1.21 1 1.21 36.65 0.000 5 是 B 0.130 0 1 0.130 0 3.94 0.087 5 否 C 0.000 3 1 0.000 3 0.009 5 0.925 2 否 AB 0.286 2 1 0.286 2 8.68 0.021 5 是 AC 0.152 1 1 0.152 1 4.61 0.068 9 否 BC 0.189 2 1 0.189 2 5.74 0.047 8 是 A2 4.58 1 4.58 138.99 ＜0.000 1 是 B2 0.116 0 1 0.116 0 3.52 0.102 8 否 C2 0.737 4 1 0.737 4 22.36 0.002 1 是 残差 0.230 9 7 0.033 0 失拟项 0.153 2 3 0.051 1 2.63 0.186 7 否 绝对误差 0.077 7 4 0.019 4 总离差 7.99 16
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表 10 响应指标的目标值与权重
Table 10. Target values and weights of response indicators
响应指标 指标权重 上限值 下限值 目标值 透水系数/(mm·s-1) 1 3.8 12.3 最大值 28 d抗压强度/MPa 1 16.6 33.0 最大值 28 d抗折强度/MPa 1 3.0 5.36 最大值
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表 11 最优设计结果与试验验证
Table 11. Optimal design results and experimental validation
最优解 透水系数 抗压强度 抗折强度 A: 体积分数为0.34%
B: 质量分数为0.38%
C: 质量分数为0.47%预测值/(mm·s-1) 实测值/(mm·s-1) 相对误差/% 预测值/MPa 实测值/MPa 相对误差/% 预测值/MPa 实测值/MPa 相对误差/% 12.58 12.29 2.3 33.03 34.12 3.3 5.31 5.17 2.5
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