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摘要: 为减少半刚性基层材料路用性能评价指标, 合理评价材料性能, 提出基于灰色关联聚类、主成分分析和熵权法的半刚性基层材料路用性能综合评价方法。对多指标进行灰色聚类分析, 对同类指标进行主成分分析, 得到每类指标的主成分集合, 采用熵权法确定每类指标的权重, 综合形成既反映全体指标信息又体现指标差异性的综合指标。选择四川广巴高速公路沿线A、B、C、D、E共5种砂岩成型半刚性基层材料, 并选择11个路用性能指标评价5种材料的路用性能。评价结果表明: 5种材料的性能从优到劣排序为A、B、D、C、E, 与灰色关联度评价结果一致, 因此, 采用综合评价方法易判断材料性能优劣及材料性能间的差异。Abstract: In order to decrease the evaluation indexes of semi-rigid base mixture's pavement performance and evaluate the performance rationally, a comprehensive evaluation method of pavement performance was presented based on grey correlation clustering analysis, principal component analysis and entropy weight method. The multi indexes were classed according to grey clustering analysis, each cluster was conducted according to principal component analysis, and principal components assemble was decided. The weight of each cluster was decided according to entropy weight method. The comprehensive index was decided to reflect all the indexes' informations and differences. The cement stabilized sandstone mixture's pavement performances of 5 samples as A, B, C, D, E were tested, which were sampled from Sichuan Guangba Expressway. The eleven performance indexes were chosen to evaluate the mixture's performance. Evaluation result shows that the order from superior to inferior of pavement perfromances is as follows A, B, D, C, E, and the result is consistent with the evalutation result of grey correlation degree, so the comprehensive evaluation method is easier to differentiate the mixtures' performances.
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表 1 砂岩的物理力学指标
Table 1. Physical and mechanical properties of sandstones
砂岩样品 A B C D E 毛体积密度/ (g·cm-3) 2.558 2.392 2.424 2.448 2.389 饱水抗压强度/MPa 80.2 70.5 60.7 54.9 29.6 压碎值/% 20.7 22.4 25.5 26.0 28.4 
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表 2 普通硅酸盐水泥技术性能
Table 2. Technical properties of common silicate cement
细度筛余量/% (80 μm方孔筛) 初凝时间/min 终凝时间/min 3 d强度/MPa 抗压强度 抗折强度 7.1 170 203 27.1 5.7
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表 3 混合料路用性能试验结果
Table 3. Test results of mixtures' pavement performances
试验指标 代号 龄期/d 砂岩 最优值 A B C D E 无侧限抗压强度/MPa y1 7 3.56 3.62 3.32 3.54 2.97 3.62 y2 28 4.64 4.40 4.15 4.29 3.84 4.64 y3 90 5.20 5.03 4.56 4.75 4.01 5.20 劈裂强度/MPa y4 28 0.42 0.34 0.34 0.30 0.26 0.42 y5 90 0.45 0.42 0.38 0.41 0.36 0.45 抗压回弹模量/MPa y6 28 1 214 1 220 795 1 035 461 1 220 y7 90 1 312 1 259 975 1 127 631 1 312 抗弯拉强度/MPa y8 28 0.54 0.41 0.35 0.46 0.26 0.54 y9 90 0.83 0.64 0.63 0.77 0.47 0.83 冻融系数/% y10 90 0.92 0.87 0.73 0.80 0.71 0.92 冲刷量/g y11 28 12.9 11.2 16.8 13.0 19.7 11.2
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表 4 Y1的特征值与对应的贡献率
Table 4. Characteristic values and correspondence contribution rates of Y1
主成分 特征值 贡献率/% 累计贡献率/% z11 7.174 89.674 89.674 z12 0.366 4.581 94.255 z13 0.297 3.708 97.963 z14 0.163 2.037 100.000 z15 0.000 0.000 100.000 z16 0.000 0.000 100.000 z17 0.000 0.000 100.000 z18 0.000 0.000 100.000
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表 5 Y2的特征值与对应的贡献率
Table 5. Characteristic values and correspondence contribution rates of Y2
主成分 特征值 贡献率% 累计贡献率/% z21 2.946 98.195 98.195 z22 0.053 1.757 99.952 z23 0.001 0.048 100.000
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表 6 两类指标的得分值
Table 6. Values of two indexes
砂岩样品 A B C D E F1 3.329 1.116 -1.149 0.544 -3.841 F2 1.319 1.500 -0.798 0.588 -2.610
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表 7 两类指标的熵权
Table 7. Entropy weights of two indexes
指标类 熵值 熵权ωi Y1 0.826 0.512 8 Y2 0.835 0.487 2
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表 8 混合料综合得分值
Table 8. Mixtures' comprehensive values
砂岩样品 A B C D E 综合得分 2.350 1.303 -0.978 0.565 -3.241
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表 9 灰色关联度
Table 9. Grey correlation degrees
砂岩样品 A B C D E 灰色关联度 0.999 0.989 0.849 0.927 0.715
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