摘要
从分数阶导数的定义出发,提出采用分数阶微积分来描述沥青混合料的分数阶导数型粘弹性本构关系这一独特的新思路。通过对沥青混合料进行SPT动态模量试验测出沥青混合料的动态模量和相位角,并对试验结果分别采用经典Kelvin模型、Maxwell模型和三元件固体模型进行拟合。结果表明,经典粘弹性本构模型的拟合效果较差,不适宜用来模拟沥青混合料的动态粘弹性能。鉴于目前的本构关系不能很好的表证沥青混合料的动态粘弹性能,采用分数导数三元件固体模型对沥青混合料动态粘弹性进行研究,并对拟合效果进行分析。分数导数三元件固体模型的拟合效果较好,且确定模型实验参数少,得到的拟合参数具有一定的物理意义,分数导数的阶数α与相位角的相关性较好,很好的体现沥青混合料的粘弹比例,从而能够精确地描述沥青混合料的动态粘弹性能。
Based on the definition of fractional derivative, a unique and new idea was put forward that the fractional calculus was applied to describe the viscoelastic constitutive relation of asphalt mixture. According to the SPT test results, the dynamic modulus and phase angle of asphalt mixture were measured, and the test results were fitted with classic Kelvin model, Maxwell model and three - element solid model respeetively. It was indicated that the fitting effect of classic viscoelastic constitutive model was relatively bad, which was not suitable to simulate the dynamic mechanical properties of asphalt mixture. As the current constitutive relation could not describe the dynamic viscoelastic properties of asphalt mixture well, the three - element solid model with fractional derivative was applied to study the dynamic viscoelastic properties of asphalt mixture, and the fitting effect was analyzed. The results showed that the fitting effect of three - element solid model with fractional derivative was good and related model parameters were few, therefore the obtained fitting parameters had certain physical significance. The con＇elation between order number of fractional derivative and the phase angle was good, which reflected the the viscoelastic ratio of asphalt mixture very well so that the dynamic viscoelastic properties of asphalt mixture couht be described accurately.
出处
《森林工程》
2010年第2期77-82,共6页
Forest Engineering
关键词
沥青混合料
粘弹性
本构关系
动态模量
asphalt mixture
viscoelastic property
constitutive relation
dynamic modulus
