The master curve of a viscoelastic variable is of significance due to its capability of characterizing the linear viscoelastic (LVE) property in an extended time or frequency range. However, the master curves constructed using the traditional approach fail to strictly comply with the LVE theory, leading to inaccurate predictions in the extended range. In order to address this issue, a framework was developed for the LVE characterization of asphalt mixtures. The generalized logistic sigmoidal model was adopted as the master curve model of storage modulus. A numerical model of loss modulus was established in relation to the continuous relaxation spectrum, whose mathematical model was derived in light of its relationship with the storage modulus. The model parameters determined using the storage modulus and loss modulus test data were employed to construct the master curves of storage modulus, loss modulus, dynamic modulus and phase angle. Then the relaxation modulus master curve was generated by establishing a numerical model. Afterwards, the continuous retardation spectrum was solved numerically based on its relationship with the continuous relaxation spectrum. The master curves of storage compliance, loss compliance and creep compliance were obtained using the corresponding numerical models that were established with respect to the continuous retardation spectrum. The interrelationship among the viscoelastic variables was then employed to obtain the dynamic compliance and phase angle master curves. It was demonstrated that the developed framework ensured the master curves of all viscoelastic variables complied with the LVE theory.

中文翻译：

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沥青混合料线性粘弹性表征的框架

粘弹性变量的主曲线很重要，因为它能够在扩展的时间或频率范围内表征线性粘弹性 (LVE) 特性。然而，使用传统方法构建的主曲线未能严格遵守 LVE 理论，导致扩展范围内的预测不准确。为了解决这个问题，开发了一个用于沥青混合料 LVE 表征的框架。采用广义logistic sigmoidal模型作为储能模量的主曲线模型。建立了与连续弛豫谱相关的损耗模量数值模型，并根据其与储能模量的关系推导出其数学模型。利用储能模量和损耗模量试验数据确定的模型参数构建储能模量、损耗模量、动态模量和相角的主曲线。然后通过建立数值模型生成松弛模量主曲线。然后，根据其与连续弛豫光谱的关系，对连续延迟光谱进行数值求解。使用相对于连续延迟谱建立的相应数值模型获得存储柔量、损失柔量和蠕变柔量的主曲线。然后使用粘弹性变量之间的相互关系来获得动态柔量和相位角主曲线。