Comparison of numerical interconversion methods for relaxation modulus of asphalt mixture
Article Text (Baidu Translation)
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摘要: 为了有效获取沥青混合料的松弛模量, 比较了分别由动态模量和蠕变柔量得到松弛模量的数值转换方法, 研究了沥青混合料线性黏弹性参数的转换原理; 对同种沥青混合料分别进行了动态模量和蠕变柔量测试, 拟合了试验数据主曲线, 获得了松弛模量函数, 分析了2种数值转换法存在差异的可能原因; 考虑了不同Maxwell单元数对松弛模量计算结果的影响, 比较了不同沥青混合料的松弛模量, 验证了2种方法对不同沥青混合料的适用性。研究结果表明: 表征沥青混合料松弛模量的Maxwell单元数越少, 其主曲线波动越大, 当单元数大于11时, 主曲线间差异小于5.26%, 建议选择11个单元左右以提高计算效率; 由动态模量和蠕变柔量转换得到的松弛模量符合材料的基本松弛特性, 2条松弛模量主曲线重合度较高, 且相关系数大于0.99;对于不同的沥青混合料, 2种转换方法同样适用, 在线性黏弹性范围内, 二者的差异主要出现在较低时间区域(10-8~10-4 s), 建议实际应用中采用2种方法的平均值以减少同种试验误差的干扰; 添加温拌剂在一定程度上会降低沥青混合料的松弛模量, 相比于普通热拌沥青混合料, 添加发泡温拌剂和Evotherm温拌剂的沥青混合料松弛模量分别降低了14.69%和13.61%, 从对松弛模量的影响程度来看, 2种温拌剂的使用效果相当。Abstract: In order to obtain the relaxation modulus of asphalt mixture effectively, the numerical interconversion methods from dynamic modulus and creep compliance to relaxation modulus were compared. The conversion principle between linear viscoelastic parameters of asphalt mixture was investigated. The dynamic modulus and creep compliance of the same asphalt mixture were tested, respectively, and the master curves of experimental data were fitted. The function of relaxation modulus was obtained, and the possible reasons for the difference between two numerical interconversion methods were analyzed. The effects of different Maxwell element numbers on the calculation results of relaxation modulus were considered. The relaxation moduli of different asphalt mixtures were compared, and the applicability of two methods to different asphalt mixtures was validated. Research result shows that the fewer the number of Maxwell elements characterizing the asphalt mixtures' relaxation modulus is, the larger the fluctuation of master curves are. When the number of elements is greater than 11, the difference between master curves is lower than 5.26%. It is suggested to select about 11 elements to improve the computational efficiency. The relaxation modulus obtained from the conversion of dynamic modulus and creep compliance accords with the basic relaxation characteristics of materials. The coincidence degree of two master curves of relaxation modulus is high, and the correlation coefficient is greater than 0.99. In terms of different asphalt mixtures, the two methods are also applicable. In the linear viscoelastic range, the main difference of two methods is found in the lower time region that is from 10-8 s to 10-4 s. It is suggested to adopt the average value of two methods in practice to avoid the errors caused by the same test. Adding warm mixing agent may reduce the relaxation modulus of asphalt mixture to some extent. Compared to hot mix asphalt, the relaxation moduli of asphalt mixtures with foam agent and Evotherm warm mixing agent reduce by 14.69% and 13.61%, respectively. According to the influence degree on the relaxation modulus, the two kinds of warm mixing agents have the equivalent effect.
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图 6 不同Maxwell单元数下的松弛模量主曲线
Figure 6. Relaxation modulus master murves under different Maxwell element numbers
图 8 温拌沥青混合料的松弛模量主曲线
Figure 8. Relaxation modulus master curves of warm mixed asphalt mixtures
图 9 三种沥青混合料的松弛模量主曲线
Figure 9. Relaxation modulus master curves of three asphalt mixtures
表 1 三种沥青混合料级配
Table 1. Gradations of three asphalt mixtures
筛孔尺寸/mm 19 12.5 9.5 4.75 2.36 1.18 0.6 0.3 0.15 0.075 HMA混合料级配/% 100 93.0 74.8 50.3 30.3 24.6 19.4 15.0 10.3 6.5 发泡温拌混合料级配/% 100 90.6 69.5 47.8 32.5 23.5 18.5 14.3 9.7 5.8 Evotherm温拌混合料级配/% 100 91.1 75.0 49.1 32.8 23.6 18.6 14.3 9.8 5.8 
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表 2 动态模量转换法得到的松弛模量Prony级数系数
Table 2. Prony series coefficients of relaxation modulus obtained by dynamic modulus interconversion method
单元个数 ρk/s Ek /MPa HMA 发泡温拌沥青混合料 Evotherm温拌沥青混合料 1 2.0×10-6 2 885.37 2 789.06 2 772.81 2 2.0×10-5 3 861.21 3 796.04 3 742.27 3 2.0×10-4 4 787.52 4 191.18 4 125.67 4 2.0×10-3 4 176.13 3 305.38 3 449.11 5 2.0×10-2 3 507.72 3 139.01 3 207.17 6 2.0×10-1 1 658.45 1 458.80 1 433.13 7 2.0×100 677.33 552.71 530.77 8 2.0×101 198.79 173.03 184.70 9 2.0×102 67.66 41.32 42.56 10 2.0×103 39.76 30.29 28.22 11 2.0×104 8.28 8.01 8.51
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表 3 蠕变柔量转换法得到的松弛模量Prony级数系数
Table 3. Prony series coefficients of relaxation modulus obtained by creep compliance interconversion method
单元个数 τj/s Ek/MPa HMA 发泡温拌沥青混合料 Evotherm温拌沥青混合料 1 2.0×10-6 2 828.84 2 627.85 2 759.64 2 2.0×10-5 7 949.18 7 475.12 7 364.29 3 2.0×10-4 7 385.47 7 158.08 7 128.25 4 2.0×10-3 6 211.09 5 515.92 5 818.92 5 2.0×10-2 4 239.35 3 351.35 3 462.57 6 2.0×10-1 2 250.29 1 968.26 2 080.35 7 2.0×100 825.64 688.14 695.87 8 2.0×101 216.26 194.71 217.45 9 2.0×102 76.19 59.27 58.26 10 2.0×103 37.56 25.57 32.71 11 2.0×104 8.45 7.32 7.81
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