沥青混合料动态黏弹性分数阶导数Zener模型Wicket方法

Wicket Method of Fractional Derivative Zener Model for Dynamic Viscoelastic of Asphalt Mixture

为了更好地将四参数分数阶导数模型(FDZ)应用于沥青混合料性能的表征,从FDZ模型微分方程出发,通过傅里叶变换,得到了FDZ模型损耗因子与存储模量之间与时间参数无关的函数关系(称为Wicket域),并建立FDZ模型的黏弹参数主曲线。采用两种不同的沥青混合料动态模量试验结果对Wicket方法进行了验证,并与Sigmoidal模型主曲线进行了对比分析。结果表明:Wicket方法首先获得了FDZ模型与特征时间无关的3个重要模型参数Ε_(0)、Ε_(∞)、α,然后基于时-温等效原理进一步确定FDZ模型参考温度下的特征时间与移位因子,相比直接法稳定性更好。对比Sigmoidal模型方法,采用Wicket图方法采用一套模型参数建立了沥青混合料FDZ模型所有黏弹参数(动态模量、相位角等)的主曲线,满足Kramers-Kronig关系。FDZ模型能够表征沥青混合料的黏弹力学特征,因此该模型可以考虑应用于沥青路面层状黏弹力学计算。

In order to better promote the application of the four-parameter fractional derivative model(FDZ)in the characterization of asphalt mixture performance,starting from the differential equation of the FDZ model,through Fourier transform,the time parameter independent functional relationship(called Wicket domain)between the loss factor and the storage modulus of the FDZ model is obtained,and the main curve of the viscoelastic parameters of the FDZ model is established.The Wicket method is validated by two different asphalt mixture dynamic modulus test results,and is compared with the main curve of Sigmoidal model.The results show that the Wicket method first obtains three important model parameters(Ε_(0)、Ε_(∞)、α)of the FDZ model that are independent of the characteristic time,then,based on the principle of time temperature equivalence,the characteristic time and shift factor of the FDZ model at the reference temperature are further determined,which is more stable than the direct method.Compared with the Sigmoidal model method,the Wicket diagram method is used to establish the master curve of all viscoelastic parameters(dynamic modulus,phase angle,etc.)of the asphalt mixture FDZ model with a set of model parameters,which meets the Kramers-Kronig relationship.FDZ model can characterize the viscoelastic mechanical behavior of asphalt mixture,so this model can be used in asphalt pavement layered viscoelastic calculation.