Numerical Simulation of Viscoelastic Behavior of Asphalt Mixture Using Fractional Constitutive Model
Publication: Journal of Engineering Mechanics
Volume 147, Issue 5
Abstract
An innovative procedure was proposed to simulate the viscoelastic mechanical behavior of asphalt mixture. The existing fractional viscoelastic models were quantitatively analyzed, and the fractional Zener model was adopted. The model parameters were obtained by fitting the storage modulus and loss modulus simultaneously. The relaxation modulus of the fractional Zener model in the time domain was deduced using the Mittag-Leffler function. The numerical algorithm of the fractional Zener model was proposed and implemented into finite-element (FE) software ABAQUS version 6.9. Simulations of the relaxation test were conducted to verify the effectiveness of the numerical algorithm and the FE implementation. Then dynamic modulus tests were simulated, and the master curve of the storage and loss modulus was calculated. The simulation results indicated that the fractional Zener model can be effectively applied to FE analysis and accurately predict the storage modulus and loss modulus master curve of asphalt mixture in a wide frequency or temperature range.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The study is financially supported by the National Key Research and Development Project (No. 2020YFA0714302) and the National Natural Science Foundation of China (Nos. 51878164, 51922030, 52008101).
References
Atkinson, C., and A. Osseiran. 2011. “Rational solutions for the time-fractional diffusion equation.” SIAM J. Appl. Math. 71 (1): 92–106. https://doi.org/10.1137/100799307.
Baumgaertel, M., and H. H. Winter. 1989. “Determination of discrete relaxation and retardation time spectra from dynamic mechanical data.” Rheol. Acta 28 (6): 511–519. https://doi.org/10.1007/BF01332922.
Bologna, E., F. Graziano, L. Deseri, and M. Zingales. 2019. “Power-Laws hereditariness of biomimetic ceramics for cranioplasty neurosurgery.” Int. J. Non Linear Mech. 115 (Oct): 61–67. https://doi.org/10.1016/j.ijnonlinmec.2019.01.008.
Bradshaw, R. D., and L. C. Brinson. 1997. “A sign control method for fitting and interconverting material functions for linearly viscoelastic solids.” Mech. Time-Depend Mat. 1 (1):85–108. https://doi.org/10.1023/A:1009772018066.
Chen, T., Y. C. Luan, T. Ma, J. Q. Zhu, X. M. Huang, and S. J. Ma. 2020. “Mechanical and microstructural characteristics of different interfaces in cold recycled mixture containing cement and asphalt emulsion.” J. Cleaner Prod. 258 (Jun): 120674. https://doi.org/10.1016/j.jclepro.2020.120674.
China, M. O. T. O. 2011. Standard test methods of bitumen and bituminous mixtures for highway engineering. Beijing: China Communications Press.
Clauser, J. F., and W. G. Knauss. 1968. “On the numerical determination of relaxation and retardation spectra for linearly viscoelastic materials.” Trans. Soc. Rheol. 12 (1): 143–153. https://doi.org/10.1122/1.549103.
Cost, T. L., and E. B. Becker. 1970. “A multidata method of approximate Laplace transform inversion.” Int. J. Numer. Method Eng. 2 (2): 207–219. https://doi.org/10.1002/nme.1620020206.
Ding, X. H., T. Ma, L. H. Gu, and Y. Zhang. 2020. “Investigation of surface micro-crack growth behavior of asphalt mortar based on the designed innovative mesoscopic test.” Mater. Des. 185 (Jan): 108238. https://doi.org/10.1016/j.matdes.2019.108238.
Ding, X. M., L. C. Chen, T. Ma, H. X. Ma, L. H. Gu, T. Chen, and Y. Ma. 2019. “Laboratory investigation of the recycled asphalt concrete with stable crumb rubber asphalt binder.” Constr. Build. Mater. 203 (Apr): 552–557. https://doi.org/10.1016/j.conbuildmat.2019.01.114.
Di Paola, M., F. P. Pinnola, and M. Zingales. 2013. “A discrete mechanical model of fractional hereditary materials.” Meccanica 48 (7): 1573–1586. https://doi.org/10.1007/s11012-012-9685-4.
Di Paola, M., and M. Zingales. 2012. “Exact mechanical models of fractional hereditary materials.” J. Rheol. 56 (5): 983–1004. https://doi.org/10.1122/1.4717492.
Elster, C., and J. Honerkamp. 1991. “Modified maximum entropy method and its application to creep data.” Macromolecules 24 (1): 310–314. https://doi.org/10.1021/ma00001a047.
Emri, I., and N. W. Tschoegl. 1997. “Generating line spectra from experimental responses.” Rheol. Acta 36 (3): 303–306. https://doi.org/10.1007/BF00366671.
Havriliak, S., and S. Negami. 1966. “A complex plane analysis of -dispersions in some polymer systems.” J. Polym. Sci. Part C: Polym. Symp. 14 (1): 99–117. https://doi.org/10.1002/polc.5070140111.
Honerkamp, J., and J. Weese. 1989. “Determination of the relaxation spectrum by a regularization method.” Macromolecules 22 (11): 4372–4377. https://doi.org/10.1021/ma00201a036.
Huet, C. 1965. “Etude par une méthode d’impédance du comportement viscoélastique des matériaux hydrocarbonés.” Thèse de doctorat d’ingénieur, Faculté des Sciences de l’université de Paris.
Kaschta, J. 1992. On the calculation of discrete retardation and relaxation spectra, theoretical and applied rheology, 155. Amsterdam, Netherlands: Elsevier.
Kaschta, J., and R. R. Schwarzl. 1994. “Calculation of discrete retardation spectra from creep data—I. Method.” Rheol. Acta 33 (6): 517–529. https://doi.org/10.1007/BF00366336.
Koeller, R. C. 1984. “Applications of fractional calculus to the theory of viscoelasticity.” J. Appl. Mech. 51 (2): 299–307. https://doi.org/10.1115/1.3167616.
Liu, Y. 1999. “Calculation of discrete relaxation modulus and creep compliance.” Rheol. Acta 38 (4): 357–364. https://doi.org/10.1007/s003970050186.
Lundström, R. 2002. “Rheological and fatigue characterisation of asphalt concrete mixtures using uniaxial testing.” Licentiate thesis, Dept. of Civil and Architectural Engineering, KTH.
Neifar, M. 1997. Comportement thermomécanique des enrobés bitumineux: Expérimentation et modélisation. Villeurbanne, France: INSA-Lyon.
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. https://doi.org/10.1080/14680629.2003.9689946.
Park, S. W., and Y. R. Kim. 2001. “Fitting Prony-series viscoelastic models with power-law presmoothing.” J. Mater. Civ. Eng. 13 (1): 26–32. https://doi.org/10.1061/(ASCE)0899-1561(2001)13:1(26).
Ramkumar, D., J. M. Caruthers, H. Mavridis, and R. Shroff. 1997. “Computation of the linear viscoelastic relaxation spectrum from experimental data.” J. Appl. Polym. Sci. 64 (11): 2177–2189. https://doi.org/10.1002/(SICI)1097-4628(19970613)64:11%3C2177::AID-APP14%3E3.0.CO;2-1.
Sayegh, G. 1965. Variations des modules de quelques bitumes purs et enrobés bitumineux [Modulus variations of some pure bitumens and bituminous mixtures]. Paris: Université de Paris.
Schapery, R. A. 1962. A simple collocation method for fitting viscoelastic models to experimental data. Pasadena, CA: California Institute of Technology.
Sun, Y., J. Chen, and B. Huang. 2015a. “Characterization of asphalt concrete linear viscoelastic behavior utilizing Havriliak–Negami complex modulus model.” Constr. Build. Mater. 99 (Nov): 226–234. https://doi.org/10.1016/j.conbuildmat.2015.09.016.
Sun, Y., B. Huang, and J. Chen. 2015b. “A unified procedure for rapidly determining asphalt concrete discrete relaxation and retardation spectra.” Constr. Build. Mater. 93 (Sep): 35–48. https://doi.org/10.1016/j.conbuildmat.2015.04.055.
Tschoegl, N. W. 2012. The phenomenological theory of linear viscoelastic behavior: An introduction. Berlin: Springer.
Winitzki, S. 2003. “Uniform approximations for transcendental functions.” In Proc., Int. Conf. on Computational Science and Its Applications, 780–789. Berlin: Springer.
Zeng, C., and Y. Q. Chen. 2015. “Global Padé approximations of the generalized Mittag-Leffler function and its inverse.” Fract. Calc. Appl. Anal. 18 (6): 1492–1506. https://doi.org/10.1515/fca-2015-0086.
Zeng, M., H. U. Bahia, H. Zhai, M. R. Anderson, and P. Turner. 2001. “Rheological modeling of modified asphalt binders and mixtures.” Asphalt Paving Technol. 70 (1): 403–441.
Zhao, Y., H. Liu, L. Bai, and Y. Tan. 2012. “Characterization of linear viscoelastic behavior of asphalt concrete using complex modulus model.” J. Mater. Civ. Eng. 25 (10): 1543–1548. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000688.
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Published In
Journal of Engineering Mechanics
Volume 147 • Issue 5 • May 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jan 27, 2019
Accepted: Jan 6, 2021
Published online: Mar 13, 2021
Published in print: May 1, 2021
Discussion open until: Aug 13, 2021
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