An extension of the fractional model for construction of asphalt binder master curve

References

• AASHTO. (1998). Standard test method for determining the rheological properties of asphalt binder using a dynamic shear rheometer (DSR). Washington, DC: Author.
   Google Scholar
• Airey, G. D. (2002). Use of black diagrams to identify inconsistencies in rheological data. Road Materials and Pavement Design, 3, 403–424.10.1080/14680629.2002.9689933
   Google Scholar
• Airey, G., Hunter, A., & Rahimzadeh, B. (2002). The influence of geometry and sample preparation on dynamic shear rheometer testing. Proc Fourth Eur Symp Perform Bituminous Hydraul Mater Pavements, Nottingham, UK (pp. 3–12).
   Google Scholar
• Bagley, R. L., & Torvik, P. J. (1986). On the fractional calculus model of viscoelastic behavior. Journal of Rheology (1978-present), 30, 133–155.
   Web of Science ®Google Scholar
• Blair, G. W. S. (1949). A survey of general and applied rheology. London: Sir Isaac Pitman & Sons.
   Google Scholar
• Booij, H., & Thoone, G. (1982). Generalization of Kramers-Kronig transforms and some approximations of relations between viscoelastic quantities. Rheologica Acta, 21, 15–24.10.1007/BF01520701
   Web of Science ®Google Scholar
• Celauro, B., Celauro, C., Lo Presti, D., & Bevilacqua, A. (2012). Definition of a laboratory optimization protocol for road bitumen improved with recycled tire rubber. Construction and Building Materials, 37, 562–572. doi:10.1016/j.conbuildmat.2012.07.034
   Web of Science ®Google Scholar
• Celauro, C., Fecarotti, C., Pirrotta, A., & Collop, A. C. (2012). Experimental validation of a fractional model for creep/recovery testing of asphalt mixtures. Construction and Building Materials, 36, 458–466. doi:10.1016/j.conbuildmat.2012.04.028
   Web of Science ®Google Scholar
• 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 Materials and Pavement Design, 7(Suppl. 1), 75–92.10.1080/14680629.2006.9690059
   Google Scholar
• Christensen, R. (1982). Theory of viscoelasticity: An introduction. Amsterdam: Elsevier.
   Google Scholar
• Costa, L., Silva, H. M., Oliveira, J. R., & Fernandes, S. R. (2013). Incorporation of waste plastic in asphalt binders to improve their performance in the pavement. International Journal of Pavement Research & Technology, 6, 457–464.
   Google Scholar
• Di Paola, M., Failla, G., & Pirrotta, A. (2012). Stationary and non-stationary stochastic response of linear fractional viscoelastic systems. Probabilistic Engineering Mechanics, 28, 85–90.10.1016/j.probengmech.2011.08.017
   Web of Science ®Google Scholar
• Di Paola, M., Pirrotta, A., & Valenza, A. (2011). Visco-elastic behavior through fractional calculus: An easier method for best fitting experimental results. Mechanics of Materials, 43, 799–806.10.1016/j.mechmat.2011.08.016
   Web of Science ®Google Scholar
• Dondi, G., Vignali, V., Pettinari, M., Mazzotta, F., Simone, A., & Sangiorgi, C. (2014). Modeling the DSR complex shear modulus of asphalt binder using 3D discrete element approach. Construction and Building Materials, 54, 236–246.10.1016/j.conbuildmat.2013.12.005
   Web of Science ®Google Scholar
• Failla, G., & Pirrotta, A. (2012). On the stochastic response of a fractionally-damped Duffing oscillator. Communications in Nonlinear Science and Numerical Simulation, 17, 5131–5142.10.1016/j.cnsns.2012.03.033
   Web of Science ®Google Scholar
• Ferry, J. D. (1980). Viscoelastic properties of polymers. New York, NY: Wiley.
   Google Scholar
• Findley, W. N., & Davis, F. A. (2013). Creep and relaxation of nonlinear viscoelastic materials. New York, NY: Courier Dover Publications.
   Google Scholar
• Flugge, W. (1967). Viscoelasticity. New York, NY: Springer.
   Google Scholar
• García-Barruetabe, J., Cortés, F., Abete, J. M., Fernández, P., Lamela, M. J., & Fernández-Canteli, A. (2011). Experimental characterization and modelization of the relaxation and complex moduli of a flexible adhesive. Materials & Design, 32, 2783–2796. doi:10.1016/j.matdes.2011.01.005
   Web of Science ®Google Scholar
• Gorenflo, R., & Mainardi, F. (1997). Fractional calculus: Integral and differential equations of fractional order. New York, NY: Springer.
   Google Scholar
• Grzesikiewicz, W., Wakulicz, A., & Zbiciak, A. (2013). Non-linear problems of fractional calculus in modeling of mechanical systems. International Journal of Mechanical Sciences, 70, 90–98.10.1016/j.ijmecsci.2013.02.007
   Web of Science ®Google Scholar
• Hajikarimi, P., Aflaki, S., & Hoseini, A. S. (2013). Implementing fractional viscoelastic model to evaluate low temperature characteristics of crumb rubber and gilsonite modified asphalt binders. Construction and Building Materials, 49, 682–687.10.1016/j.conbuildmat.2013.09.001
   Web of Science ®Google Scholar
• Hernández-Jimánde, A., Hernández-Santiago, J., Macias-Garcsag, A., & Sánchez-González, J. (2002). Relaxation modulus in PMMA and PTFE fitting by fractional Maxwell model. Polymer Testing, 21, 325–331. doi:10.1016/S0142-9418(01)00092-7
   Web of Science ®Google Scholar
• Heymans, N., & Podlubny, I. (2006). Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta, 45, 765–771. doi:10.1007/s00397-005-0043-5
   Web of Science ®Google Scholar
• Huet, C. (1965). Etude par une méthode d'impédance du comportement viscoélastique des matériaux hydrocarbonés [Study of the viscoelastic behavior of bituminous mixes by method of impedance] ( Doctoral thesis). Université de Paris, Paris.
   Google Scholar
• Katicha, S., & Flintsch, G. W. (2012). Fractional viscoelastic models: Master curve construction, interconversion, and numerical approximation. Rheologica Acta, 51, 675–689. doi:10.1007/s00397-012-0625-y
   Web of Science ®Google Scholar
• Koeller, R. (1984). Applications of fractional calculus to the theory of viscoelasticity. Journal of Applied Mechanics, 51, 299–307.10.1115/1.3167616
   Web of Science ®Google Scholar
• Nguyen, H. M., Pouget, S., Di Benedetto, H., & Sauzéat, C. (2009). Time–temperature superposition principle for bituminous mixtures. European Journal of Environmental and Civil Engineering, 13, 1095–1107. doi:10.1080/19648189.2009.9693176
   Web of Science ®Google Scholar
• Nutting, P. (1921). A new general law of deformation. Journal of the Franklin Institute, 191, 679–685.10.1016/S0016-0032(21)90171-6
   Google Scholar
• Oeser, M., Pellinen, T., Scarpas, T., & Kasbergen, C. (2008). Studies on creep and recovery of rheological bodies based upon conventional and fractional formulations and their application on asphalt mixture. International Journal of Pavement Engineering, 9, 373–386.10.1080/10298430802068923
   Google Scholar
• Olard, F., & Di Benedetto, H. (2003). General “2S2P1D” model and relation between the linear viscoelastic behaviours of bituminous binders and mixes. Road Materials and Pavement Design, 4, 185–224.
   Google Scholar
• Podlubny, I. (1998). Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (Vol. 198). Academic Press.
   Google Scholar
• Pronk, A. (2003a). Revival of the Huet-Sayegh response model-Notes on the Huet-Sayegh rheological model. Report. n. DWW-2003-29, DWW, Delft.
   Google Scholar
• Pronk, A. (2003b). The variable dashpot. Report. n. DWW-2003-30, DWW, Delft.
   Google Scholar
• Rouleau, L., Deü, J.-F., Legay, A., & Le Lay, F. (2013). Application of Kramers-Kronig relations to time–temperature superposition for viscoelastic materials. Mechanics of Materials, 65, 66–75.10.1016/j.mechmat.2013.06.001
   Web of Science ®Google Scholar
• Samko, S. G., Kilbas, A. A., & Maričev, O. I. (1993). Fractional integrals and derivatives. Yverdon: Gordon and Breach Science Publ.
   Google Scholar
• Such, C. (1983). Analyse du comportement visqueux des bitumes [Analysis of viscous behaviour of bitumens]. Bull Liaison Lab Ponts Chauss, 127, 25–35.
   Google Scholar
• Tschoegl, N. W. (1989). The phenomenological theory of linear viscoelastic behavior: An introduction. Berlin: Springer-Verlag.10.1007/978-3-642-73602-5
   Google Scholar
• Vaiana, R., Iuele, T., Gallelli, V., & Tighe, S. (2013). Warm mix asphalt by water-containing methodology: A laboratory study on workability properties versus micro-foaming time. Canadian Journal of Civil Engineering, 41, 183–190.
   Web of Science ®Google Scholar
• Williams, M. L., Landel, R. F., & Ferry, J. D. (1955). The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. Journal of the American Chemical Society, 77, 3701–3707.10.1021/ja01619a008
   Web of Science ®Google Scholar
• Woldekidan, M., Huurman, M., & Pronk, A. (2012). A modified HS model: Numerical applications in modeling the response of bituminous materials. Finite Elements in Analysis and Design, 53, 37–47.10.1016/j.finel.2012.01.003
   Web of Science ®Google Scholar
• Yusoff, N. I. M., Jakarni, F. M., Nguyen, V. H., Hainin, M. R., & Airey, G. D. (2013). Modelling the rheological properties of bituminous binders using mathematical equations. Construction and Building Materials, 40, 174–188.10.1016/j.conbuildmat.2012.09.105
   Web of Science ®Google Scholar