Stochastic Identification of Linear-Viscoelastic Models of Aged and Unaged Asphalt Mixtures
Publication: Journal of Materials in Civil Engineering
Volume 27, Issue 4
Abstract
The behavior of asphalt mixtures is typically described using linear viscoelastic models at low-strain applications. The time and temperature dependency of asphalt mixture properties is described by forming a master curve that includes three components: time-temperature shift factors, and storage and loss moduli (or compliances). Mathematical models are needed to describe the master curve, which are used in calculating asphalt pavement responses to load and also to compare the overall properties of various mixtures at a wide range of temperatures. This paper proposes a rigorous approach to mathematically describe the master curves using stochastic identification techniques. These techniques have the advantage over current deterministic methods in their ability to account for the uncertainty associated with the constructed models, which could be contributed to variation in the material properties of the asphalt mixture phases as well as their spatial distribution, measurement errors, modeling errors, and inadequate available information. Consequently, uncertainty can be accounted for in the analysis and design of asphalt pavements. The stochastic approach is used successfully in this paper to identify the linear viscoelastic master curve for asphalt mixtures that have been aged to different time durations.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was made possible by NPRP Grant # 4-789-2–293 from the Qatar National Research Fund (a member of Qatar Foundation). The authors would like to acknowledge the information provided by Eisa Rahmani on his work on deterministic model updating of a Prony-series type models. The statements made herein are solely the responsibility of the authors.
References
AASHTO. (2002). “Preparing and determining the density of hot-mix asphalt (HMA) specimens by means of the superpave gyratory compactor.” AASHTO T 312, Washington, DC.
AASHTO. (2003). “Standard method of test for determining dynamic modulus of hot-mix asphalt concrete mixtures.” AASHTO TP 62, Washington, DC.
Bayes, T. (1763). “An essay towards solving a problem in the doctrine of chances.” Phylosophical Trans. R. Soc. London, 53, 370–418.
Bonaquist, R., and Christensen, D. W. (2005). “Practical procedure for developing dynamic modulus master curves for pavement structural design.” Transportation Research Record 1929, Transportation Research Board, Washington, DC, 208–217.
Christensen, D. W., and Anderson, D. A. (1992). “Interpretation of dynamic mechanical test mata for paving grade asphalt cements (with discussion).” J. Assoc. Asphalt Paving Technol., 61, 67–116.
Garcia, G., and Thompson, M. (2005). “HMA dynamic modulus predictive models: A review.”, Illinois Center for Transportation, Univ. of Illinois, Urbana, IL.
Glover, C. J., et al. (2005). “Development of new method for assessing asphalt binder durability with field validation.”, Texas Transportation Institute, College Station, TX.
Kennedy, M. C., and O’Hagan, A. (2001). “Bayesian calibration of computer models.” J. R. Stat. Soc., 63(3), 425–450.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E. (1953). “Equation of state calculations by fast computing machines.” J. Chem. Phys., 21(6), 1087–1092.
Park, S. W., and Schapery, R. A. (1999). “Methods of interconversion between linear viscoelastic material functions. Part I—A numerical method based on Prony series.” Int. J. Solid. Struct., 36(11), 1653–1675.
Pellinen, T., Witczak, M., and Bonaquist, R. (2003). “Asphalt mix master curve construction using sigmoidal fitting function with non-linear least squares optimization.” Recent advances in materials characterization and modeling of pavement systems, ASCE, Reston, VA, 83–101.
Robert, P. C., and Casella, G. (2004). Monte Carlo statistical methods.
Schwartz, C. W. (2005). “Evaluation of the Witczak dynamic modulus prediction model.” Proc., 84th Annual Meeting of the Transportation Research Board, Transportation Research Board, Washington, DC.
Texas Department of Transportation (TxDOT). (2004). “Standard specifications for constructions and maintenence of highways, streets, and bridges.” Austin, TX.
Yusoff, N. I. M., Airey, G. D., and Hainin, M. R. (2010). “Predictability of complex modulus using rheological models.” Asian J. Sci. Res., 3(1), 18–30.
Information & Authors
Information
Published In
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jul 27, 2013
Accepted: Apr 11, 2014
Published online: Jul 24, 2014
Discussion open until: Dec 24, 2014
Published in print: Apr 1, 2015
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.