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

Abstract

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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References

  1. 1.

    Marateanu M, Anderson D (1996) Time-temperature dependency of asphalt binders—an improved model (with discussion). J Assoc Asphalt Paving Technol 65:408–448

    Google Scholar 

  2. 2.

    Shaw MT, MacKnight WJ (2018) Introduction to polymer viscoelasticity, 4th edn. Wiley, Hoboken

    Google Scholar 

  3. 3.

    Yusoff NIM, Shaw MT, Airey GD (2011) Modelling the linear viscoelastic rheological properties of bituminous binders. Constr Build Mater 25(5):2171–2189

    Article  Google Scholar 

  4. 4.

    Zeng M, Bahia HU, Zhai H, Anderson MR, Turner P (2001) Rheological modeling of modified asphalt binders and mixtures (with discussion). J Assoc Asphalt Paving Technol 70:403–441

    Google Scholar 

  5. 5.

    Christensen DW, Anderson DA (1992) Interpretation of dynamic mechanical test data for paving grade asphalt cements (with discussion). J Assoc Asphalt Paving Technol 61:67–116

    Google Scholar 

  6. 6.

    Marasteanu M, Anderson D (1999) Improved model for bitumen rheological characterization. Eurobitume workshop on performance related properties for bituminous binders. European Bitumen Association Brussels, Belgium, pp 1–4

    Google Scholar 

  7. 7.

    Stroup-Gardiner M (1996) The significance of phase angle measurements for asphalt cements (with discussion). J Assoc Asphalt Paving Technol 65:321–356

    Google Scholar 

  8. 8.

    Olidis C, Hein D (2004) Guide for the mechanistic-empirical design of new and rehabilitated pavement structures materials characterization: is your agency ready. In: 2004 annual conference of the transportation association of Canada, 2004

  9. 9.

    Rowe G, Baumgardner G, Sharrock M (2008) A generalized logistic function to describe the master curve stiffness properties of binder mastics and mixtures. In: 45th Petersen asphalt research conference, University of Wyoming, July 14–16, 2008

  10. 10.

    Rowe G, Baumgardner G, Sharrock M (2009) Functional forms for master curve analysis of bituminous materials. In: Advanced testing and characterization of bituminous materials, two volume set. CRC Press, pp 97–108

  11. 11.

    Booij H, Thoone G (1982) Generalization of Kramers–Kronig transforms and some approximations of relations between viscoelastic quantities. Rheol Acta 21(1):15–24

    Article  Google Scholar 

  12. 12.

    Elseifi MA, Al-Qadi IL, Flinstch GW, Masson J-F (2002) Viscoelastic modeling of straight run and modified binders using the matching function approach. Int J Pavement Eng 3(1):53–61

    Article  Google Scholar 

  13. 13.

    Anderson DA, Christensen DW, Bahia HU, Dongre R, Sharma M, Antle CE, Button J (1994) Binder characterization and evaluation, volume 3: physical characterization. Strategic Highway Research Program, National Research Council, report no. SHRP-A-369. Washington, DC, vol 3

  14. 14.

    Yusoff NIM, Hainin MR, Airey GD (2012) A comparative study of phase angle predictive equations using bituminous binder data. Arab J Sci Eng 37(6):1571–1583

    Article  Google Scholar 

  15. 15.

    Stastna J, Zanzotto L, Berti J (1997) How good are some rheological models of dynamic material functions of asphalt. J Assoc Asphalt Paving Technol 66:458–485

    Google Scholar 

  16. 16.

    Dickinson E, Witt H (1974) The dynamic shear modulus of paving asphalts as a function of frequency. Trans Soc Rheol 18(4):591–606

    Article  Google Scholar 

  17. 17.

    Chailleux E, Ramond G, Such C, de La Roche C (2006) A mathematical-based master-curve construction method applied to complex modulus of bituminous materials. Road Mater Pavement Des 7(sup1):75–92

    Article  Google Scholar 

  18. 18.

    Anderson DA, Christensen DW, Bahia H (1991) Physical properties of asphalt cement and the development of performance-related specifications. J Assoc Asphalt Paving Technol 60:437–475

    Google Scholar 

  19. 19.

    Li X, Zofka A, Marasteanu M, Clyne TR (2006) Evaluation of field aging effects on asphalt binder properties. Road Mater Pavement Des 7(sup1):57–73

    Article  Google Scholar 

  20. 20.

    Pellinen TK, Witczak MW, Bonaquist RF (2004) Asphalt mix master curve construction using sigmoidal fitting function with non-linear least squares optimization. In: Paper presented at the proceedings of 15th ASCE engineering mechanics conference, Columbia University, New York, United States

  21. 21.

    Pellinen TK, Witczak MW (2002) Stress dependent master curve construction for dynamic (complex) modulus (with discussion). J Assoc Asphalt Paving Technol 71:281–309

    Google Scholar 

  22. 22.

    Bonaquist R (1929) Christensen DW (2005) Practical procedure for developing dynamic modulus master curves for pavement structural design. Transp Res Rec 1:208–217

    Google Scholar 

  23. 23.

    Medani T, Huurman M (2003) Constructing the stiffness master curves for asphaltic mixes. Report 7-01-127-3. Delft University and Technology

  24. 24.

    Medani T, Huurman M, Molenaar A (2004) On the computation of master curves for bituminous mixes. In: Proceedings of the 3rd asphalt and bitumen congress, Vienna, Austria, May 2004, pp 1–9

  25. 25.

    Biswas KG, Pellinen TK (2007) Practical methodology of determining the in situ dynamic (complex) moduli for engineering analysis. J Mater Civ Eng 19(6):508–514

    Article  Google Scholar 

  26. 26.

    Tran N, Hall K (2005) Evaluating the predictive equation in determining dynamic moduli of typical asphalt mixtures used in Arkansas. J Assoc Asphalt Paving Technol 74:1–17

    Google Scholar 

  27. 27.

    Baosheng W, Van Maren D, Lingyun L (2008) Predictability of sediment transport in the Yellow River using selected transport formulas. Int J Sedim Res 23(4):283–298

    Article  Google Scholar 

  28. 28.

    Al-Mehthel M, Al-Abdul Wahhab H, Al-Idi SH, Baig MG (2010) Sulfur-extended Asphalt as a major outlet for sulfur that outperformed other asphalt mixes in the gulf. In: Sulfur world symposium, Qatar

  29. 29.

    Eisa M, Basiouny M, Elbasomy O (2019) Evaluating hot asphalt mixtures of poor quality aggregate with sulphur extended asphalt. Innov Infrastruct Solut 4(1):e56

    Article  Google Scholar 

  30. 30.

    Strickland D, Colange J, Martin M, Deme I (2008) Performance properties of sulphur extended asphalt mixtures with modified sulphur pellets. In: Proceedings of the international society for asphalt pavements

  31. 31.

    Alghrafy YM, Abd Alla E-SM, El-Badawy SM (2020) Rheological properties and aging performance of sulfur extended asphalt modified with recycled polyethylene waste. Constr Build Mater. https://doi.org/10.1016/j.conbuildmat.2020.121771

    Article  Google Scholar 

  32. 32.

    Airey GD (1997) Rheological characteristics of polymer modified and aged bitumens. University of Nottingham, Nottingham

    Google Scholar 

  33. 33.

    AASHTO T240 (2013) Standard method of test for effect of heat and air on a moving film of asphalt binder (rolling thin-film oven test). American Association of State and Highway Transportation Officials, Washington, DC

    Google Scholar 

  34. 34.

    AASHTO R 28–12 (2009) Standard practice for accelerated aging of asphalt binder using a pressurized aging vessel (PAV). American Association of State and Highway Transportation Officials, Washington, DC

    Google Scholar 

  35. 35.

    Morrison FA (2005) Using the solver add-in in microsoft excel®. Michigan Technological University, Michigan

    Google Scholar 

  36. 36.

    Kemmer G, Keller S (2010) Nonlinear least-squares data fitting in Excel spreadsheets. Nat Protoc 5(2):267–281. https://doi.org/10.1038/nprot.2009.182

    Article  Google Scholar 

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Acknowledgements

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

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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). https://doi.org/10.1007/s41062-021-00459-3

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Keywords

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