Phase angle master curves of sulfur-extended asphalt modified with recycled polyethylene waste


Master curves (MC) of mixtures and asphalt binders are typically implemented in the linear viscoelastic range for assessing their rheological behavior. Although there are several theoretical models to represent the MC of mixtures and asphalt binders, their performance is variable. The use of MC to model the binder’s phase angle has received less attention compared to the MC of the complex modulus. Thus, this paper investigates the possibility of using several predictive equations to represent the phase angle (δ) of neat asphalt (virgin asphalt and sulfur-extended asphalt, SEA) and modified asphalt [recycled polyethylene-modified asphalt and recycled polyethylene-modified SEA (PMSEA)]. The investigated models include the standard sigmoidal (SS) model, generalized logistic sigmoidal (GLS) model, Christensen (CA) model, and Anderson and Marasteanu (CAM) model. The viscoelastic properties of these binders are determined through a dynamic shear rheometer spanning a broad variety of temperatures and frequencies using dynamic mechanical analysis (DMA). The results show that most of the investigated models can reasonably predict neat asphalts’ viscoelastic behavior in terms of δ. However, the accuracy of the investigated models becomes relatively lower for the modified binders, especially in the long-term aged condition. The goodness-of-fit statistics of the investigated models show that the GLS model is the most accurate mode, followed by the SS, CAM, and then the CA model.

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The authors acknowledge the support provided by Assiut and Mansoura University, Egypt, in carrying out this research.


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Author information




YMA participated in laboratory work, investigation, writing of the original draft, and resources. SME-B involved in conceptualization, methodology, visualization, validation, review, and editing. E-SMAA involved in conceptualization, methodology, supervision of laboratory work, and writing of the original draft, review and editing.

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Correspondence to Yasser M. Alghrafy.

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Alghrafy, Y.M., Abd Alla, ES.M. & El-Badawy, S.M. Phase angle master curves of sulfur-extended asphalt modified with recycled polyethylene waste. Innov. Infrastruct. Solut. 6, 84 (2021).

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  • Sulfur-extended asphalt
  • Recycled polyethylene
  • Modeling
  • Linear viscoelastic
  • Phase angle
  • Dynamic mechanical analysis