基于近似Kramers-Kronig关系的动态模量Sigmoidal模型力学演进研究

Study on Mechanical Evolution of Dynamic Modulus Sigmoidal Model Based on Approximate Kramers-Kronig Relation

为了更好地描述沥青混合料的时间和温度依赖性,优选表征动态力学性质的黏弹力学模型,推广黏弹性动态力学设计方法。基于线性黏弹性Kramers-Kronig近似解析式,通过对存储模量Sigmoidal函数解析式求导后,得到损失模量解析式,称为SigmoidalⅡ类模型。应用黏弹性材料时-温等效原理,通过构造不同目标函数,建立了上述模型黏弹函数主曲线,并与SigmoidalⅠ-Ⅰ模型、SigmoidalⅠ-Ⅱ模型进行了对比分析。结果表明:3个模型均能应用时-温等效原理建立黏弹函数(动态模量和相位角)的主曲线,与AASHTO R 62-131规范对比,3个模型均提出了相位角主曲线解析式,目标函数构造时,黏弹参数的选择影响Sigmoidal模型的拟合效果。对比另外2个模型,SigmoidalⅡ模型仅采用一个黏弹参数(动态模量)构造目标函数即可建立所有黏弹参数主曲线及Cole-Cole曲线,且黏弹函数测试值与预测值吻合较好,其中,动态模量和相位角曲线的拟合优度均在0.95以上,说明该模型能更好地描述沥青混合料的动态黏弹参数。SigmoidalⅡ模型存储模量和损失模量(动态模量和相位角)共用一套模型参数,黏弹参数之间满足线性黏弹性因果关系且符合力学模型的要求。SigmoidalⅡ模型可为沥青混合料设计和沥青路面层状黏弹动力学计算提供新的参考。

In order to better describe the dependence of asphalt mixtures on time and temperature,the viscoelastic mechanical model that characterizes dynamic mechanical properties is optimized,and the viscoelastic dynamic mechanical design method is promoted.Based on the linear viscoelastic Kramers-Kronig approximate analytical formula,the loss modulus analytical formula is obtained by deriving the storage modulus Sigmoid function analytical formula,which is called the Sigmoid II model.Based on the timetemperature equivalence principle of viscoelastic materials,the master curves of the viscoelastic function of the above models are established by constructing different objective functions,and compared with the Sigmoid I-I model and Sigmoid I-II model.The research results show that the 3 models can apply the time-temperature equivalence principle to establish the master curve of the viscoelastic function(dynamic modulus and phase angle).Compared with the AASHTO R 62-131 specification,the 3 models have put forward the analytical formula of the master curve of the phase angle.When constructing the objective function,the selection of viscoelastic parameters affects the fitting performance of the sigmoid model.Compared with the other 2 models,Sigmoidal II model can establish the master curves and Cole-Cole curve for all viscoelastic parameters by using only one viscoelastic parameter(dynamic modulus)to construct the objective function,and the test value of viscoelastic function is in good agreement with the predicted value.Among them,the goodness of fit of dynamic modulus and phase angle curve are both above 0.95,indicating that the model can better describe the dynamic viscoelastic parameters of asphalt mixture.Finally,the Sigmoid II model shares a set of model parameters for storage modulus and loss modulus(dynamic modulus and phase angle),and the viscoelastic parameters satisfy a linear viscoelastic causal relationship and meet the requirements of the mechanical model.SigmoidalⅡmodel can provide a new reference for asphalt mixtures design and the calculation of layered viscoelastic dynamics of asphalt pavement.