Fractional Derivative Viscoelastic Response Model for Asphalt Binders
Publication: Journal of Materials in Civil Engineering
Volume 31, Issue 6
Abstract
The main goal of this paper is to establish an appropriate fractional derivative model with fewer parameters that can model all the viscoelastic characteristics of asphalt binders. Based on this, the fractional derivative model elements and combination types were selected by analyzing the dynamic viscoelastic data. The model consists of two Abel dashpots in series with a Maxwell element (the model is a fractional derivative model composed of four elements in series, called the FDM-4 model). It was validated by describing both the dynamic and static viscoelastic properties of asphalt binders and by comparison with classical viscoelastic models. The advantages and disadvantages of the models were analyzed. Finally, the fractional derivative model was applied to describe the viscoelastic characteristics of asphalt mastics, and it was proved that the model could well describe the viscoelastic characteristics of asphalt mastics. The results indicate that the elements (an elastic spring and Abel dashpot) connected in series with a linear dashpot are better than those connected in parallel from the perspective of model fitting precision. Increasing the number of Abel dashpots in series in the FDM-4 model has little effect on the fitting results. The FDM-4 model can accurately describe the dynamic viscoelastic behavior, static creep, and relaxation characteristics of asphalt binders and asphalt mastics.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was sponsored by the National Natural Science Foundation of China (51778195, U1633201, and 51478153).
References
Badami, J. V., and M. L. Greenfield. 2011. “Maxwell model analysis of bitumen rheological data.” J. Mater. Civ. Eng. 23 (10): 1387–1395. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000318.
Bagley, R. L., and P. J. Torvik. 1986. “On the fractional calculus model of viscoelastic behavior.” J. Rheol. 30 (1): 133–155. https://doi.org/10.1122/1.549887.
Chang, K. N. G., and J. N. Meegoda. 1997. “Micromechanical simulation of hot mix asphalt.” J. Eng. Mech. 123 (5): 495–503. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:5(495).
Chinese National Standards. 2004. Technical specification for construction of highway asphalt pavements. Penghu, China: National Standard of the People’s Republic of China.
Hoibery, A. J. 1959. Vol. 2 of Bituminous materials, 17–120. New York: Interscience Publishers.
Huet, C. 1963. “Etude par une méthode d’impédance du comportement viscoélastique des matériaux hydrocarbones.” Ph.D. thesis, Faculteédes Sciences, l’université de Paris.
Mun, S., and G. Zi. 2010. “Modeling the viscoelastic function of asphalt concrete using a spectrum method.” Mech. Time-Depend. Mater. 14 (2): 191–202. https://doi.org/10.1007/s11043-009-9102-0.
Olard, F., and H. Di Benedetto. 2003. “General ‘2S2P1D’ model and relation between the linear viscoelastic behaviours of bituminous binders and mixes.” Road. Mater. Pavement Des. 4 (2): 185–224.
Pronk, A. C. 2005. “The Huet-Sayegh model: A simple and excellent rheological model for master curves of asphaltic mixes.” In Proc., R. Lytton Symp. on Mechanics of Flexible Pavements, 73–82. Reston, VA: ASCE.
Shan, L. Y., Y. Q. Tan, H. Zhang, and Y. Xu. 2016a. “Analysis of linear viscoelastic response function model for asphalt binders.” J. Mater. Civ. Eng. 28 (6): 04016010. https://doi.org/10.1061/(ASCE)MT.1943-5533.0001497.
Shan, L. Y., Y. N. Xu, H. S. He, and N. Ren. 2016b. “Optimization criterion of viscoelastic response model for asphalt binders.” Constr. Build. Mater. 113: 553–560. https://doi.org/10.1016/j.conbuildmat.2016.02.184.
Shen, T., M. Gao, and B. H. Zhao. 1995. “Engineering methods for the transform inversion of stress relaxation modulus and complex modulus.” Acta Armamentar II 3: 40–44.
Williams, M. L., R. F. Landel, and J. D. Ferry. 1955. “The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids.” J. Am. Chem. Soc. 77 (14): 3701–3707. https://doi.org/10.1021/ja01619a008.
Woldekidan, M. F., M. Huurman, and A. C. Pronk. 2012. “A modified HS model: Numerical applications in modeling the response of bituminous materials.” Finite Elem. Anal. Des. 53: 37–47. https://doi.org/10.1016/j.finel.2012.01.003.
Zhan, X. L. 2007. “Research on the viscoelastic properties of asphalt using DMA.” Ph.D. thesis, Dept. of Highway and Railway Engineering, Harbin Institute of Technology.
Xu, Q., and M. Solaimanian. 2009. “Modelling linear viscoelastic properties of asphalt concrete by the Huet-Sayegh model.” Int. J. Pavement Eng. 10 (6): 401–422. https://doi.org/10.1080/10298430802524784.
Yin, Y. 2010. “Research on dynamic viscoelastic characteristics and shear modulus predicting methods for asphalt mixtures based on dynamic mechanical analysis (DMA) means.” Ph.D. thesis, Dept. of Highway Engineering, South China Univ. of Technology.
Zhu, H., J. W. Rish, and S. Batra. 2001. “A constitutive study of two-phase materials. Part II: Maxwell binder.” Comput. Geotech. 28 (5): 309–323. https://doi.org/10.1016/S0266-352X(01)00003-9.
Information & Authors
Information
Published In
Copyright
©2019 American Society of Civil Engineers.
History
Received: Aug 16, 2018
Accepted: Dec 3, 2018
Published online: Apr 6, 2019
Published in print: Jun 1, 2019
Discussion open until: Sep 6, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.