ABSTRACT

The master curves of complex shear modulus $|G^{\ast }(\omega )|$ and phase angle $\delta (\omega )$ of asphalt binder provide its important rheological information. Although many studies have been performed to develop prediction models of $|G^{\ast }(\omega )|$, the determination methods often focus on fitting them with experimental data of the modulus. The intrinsic relationships between $|G^{\ast }(\omega )|$, $\delta (\omega )$, relaxation spectrum $H(\tau )$ and relaxation modulus $G(t)$ are seldom considered. Consequently, defects of the fitting arise naturally, due to overfitting issues from experimental errors and underfitting issues from bias in the approximation/empirical models. The mismatched master curves of $|G^{\ast }(\omega )|$, and $\delta (\omega )$ often lead to inconsistent $H(\tau )$ deduced from storage modulus $G^{\mathrm{\prime }}(\omega )$ and loss modulus $G^{\mathrm{\prime }\mathrm{\prime }}(\omega )$, and also inaccurate $G(t)$ calculated from the resultant $H(\tau )$. This study proposes a new method to determine the master curves of $|G^{\ast }(\omega )|$ and $\delta (\omega )$, which uses a joint optimisation to simultaneously minimise errors between the data and the models of $|G^{\ast }(\omega )|$ and $\delta (\omega )$, together with the differences between $H(\tau )$’s obtained from $G^{\mathrm{\prime }}(\omega )$ and $G^{\mathrm{\prime }\mathrm{\prime }}(\omega )$ as a penalty of the loss function. Two asphalt binders are used to assess the newly developed method and existing ones. Cross-validation based on stress-relaxation test indicates that the new method is more robust and accurate.

摘要

复剪切模量主曲线$|G^{*}(\omega )|$和相位角$\delta (\omega )$沥青结合料的含量提供了其重要的流变学信息。尽管已经进行了许多研究来开发预测模型$|G^{*}(\omega )|$, 确定方法往往侧重于将它们与模量的实验数据拟合。之间的内在关系$|G^{*}(\omega )|$,$\delta (\omega )$, 弛豫谱$H(\tau )$和松弛模量$G(吨)$很少考虑。因此，由于实验误差的过拟合问题和近似/经验模型中的偏差导致的欠拟合问题，拟合的缺陷自然而然地出现。主曲线不匹配$|G^{*}(\omega )|$， 和$\delta (\omega )$经常导致不一致$H(\tau )$从储能模量推导出来$G^{\mathrm{\text{'}}}(\omega )$和损耗模量$G^{\mathrm{\text{'}}\mathrm{\text{'}}}(\omega )$，而且也不准确$G(吨)$从结果计算$H(\tau )$. 本研究提出了一种新的方法来确定主曲线$|G^{*}(\omega )|$和$\delta (\omega )$，它使用联合优化来同时最小化数据和模型之间的误差$|G^{*}(\omega )|$和$\delta (\omega )$, 以及两者之间的差异$H(\tau )$来自$G^{\mathrm{\text{'}}}(\omega )$和$G^{\mathrm{\text{'}}\mathrm{\text{'}}}(\omega )$作为损失函数的惩罚。两种沥青粘合剂用于评估新开发的方法和现有方法。基于应力松弛测试的交叉验证表明新方法更加稳健和准确。