General Viscoelastic Solutions for Multilayered Systems Subjected to Static and Moving Loads
Publication: Journal of Materials in Civil Engineering
Volume 23, Issue 7
Abstract
Since the linear elastic layer solution for the layered systems was developed in the 1940s, the linear elastic layer analysis has been systemized and widely used for the designs of roadway pavements as a tool for evaluating the structural soundness of pavements. The primary assumption made in the analysis is that the layered system consisting of materials that are linear elastic; and hence, an application of the elastic layer analysis to asphalt mixtures, which is a well-known viscoelastic material, has been limited. Therefore, the intention of the study was to derive a viscoelastic solution able to take into account the time- and rate-dependent nature of the viscoelastic materials in the multilayered system. In this paper, a linear viscoelastic solution for the multilayered system subjected to a cylindrical unit step (static) load was derived from the elastic solution by using the principle of elastic-viscoelastic correspondence and the numerical inversion of Laplace transforms. The solution was then extended to simulating pavement responses subjected to a moving load by employing the Boltzmann’s superposition principle. The soundness of output from the viscoelastic solution was confirmed by comparing them to those of the finite-element analysis (FEA). Compared to the time and effort required in FEA, the analysis based on the viscoelastic solution was much faster. Therefore, it is expected that the viscoelastic solutions derived in this study will be an effective tool for the design of flexible pavements.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The author is very thankful to anonymous reviewers for their very helpful suggestions and comments that improved the content and presentation of the paper.
References
Abate, J., and Valko, P. P. (2004). “Multi-precision Laplace transform inversion.” Int. J. Numer. Methods Eng., 60(5), 979–993.
Adina R&D, Inc. (2008). ADINA user’s manual, Version 8.5, Watertown, MA.
Al-Qadi, I. L., Yoo, P. J., Elseifi, M. A., and Janajreh, I. (2005). “Effects of tire configurations on pavement damage.” J. Assoc. Asphalt Paving Technol., 74, 921–962.
Boltzmann, L. (1878). “Zur theorie der elastischen nachwirkung.” Ann. Phys. (Leipzig), 241(11), 430–432.
Burmister, D. M. (1945). “The general theory of stresses and displacements in layered soil systems.” J. Appl. Phys., 16, 296–302, 89–94, 126–127.
Chou, Y. T. (1969). “General theory of stresses and displacements in elastic and viscoelastic layered systems.” Final Rep., WESMPM698, Army Engineer Waterways Experiment Station, Vicksburg, MS.
De Jong, D. L., Peatz, M. G. F., and Korswagen, A. R. (1973). “Computer program BISAR, layered systems under normal and tangential loads.” External Rep. AMSR.0006.73, Koninklijke/Shell-Laboratorium, Amsterdam, Netherlands.
Elseifi, M. A., Al-Qadi, I. L., and Yoo, P. J. (2006). “Viscoelastic modeling and field validation of flexible pavements.” J. Eng. Mech., 132(2), 172–178.
Findley, W. N., Lai, J. S., and Onaran, K. (1976). Creep and relaxation of nonlinear viscoelastic materials, Dover, Mineola, NY.
Huang, Y. H. (1993). Pavement analysis and design, Prentice-Hall, Upper Saddle River, NJ.
Kim, J., Byron, T., Sholar, G. A., and Kim, S. (2007). “Comparison of a three-dimensional viscoelastic pavement model to full-scale field tests.” Proc., 86th Annual Transportation Research Board, Washington, DC.
Kim, J., Lee, H., and Kim, N. (2010). “Determination of shear and bulk moduli of viscoelastic solids from the indirect tension creep test.” J. Eng. Mech., 136(9), 1067–1075.
Kim, J., Roque, R., and Byron, T. (2009). “Viscoelastic analysis of flexible pavements and its reological effects on top-down cracking.” J. Mater. Civ. Eng., 21(7), 324–332.
Kim, J., Sholar, G., and Kim, S. (2008). “Determination of accurate creep compliance and relaxation modulus at a single temperature for viscoelastic solids.” J. Mater. Civ. Eng., 20(2), 147–156.
Kim, J., and West, R. C. (2010). “Application of the viscoelastic continuum damage model to the indirect tension test at a single temperature.” J. Eng. Mech., 136(4), 496–505.
Lee, H., and Kim, J. (2009). “Determination of viscoelastic Poisson’s ratio and creep compliance from the indirect tension test.” J. Mater. Civ. Eng., 21(8), 416–425.
Love, A. E. H. (1927). Treatise on the mathematical theory of elasticity, Dover Publications, Inc., Mineola, NY.
National Cooperative Highway Research Program (NCHRP), and ARA. (2004). “Guide for mechanistic-empirical design of new and rehabilitated pavement structures.” NCHRP 1-37A, Transportation Research Board, National Research Council, Washington, DC.
Roque, R., Buttlar, W. G., Ruth, B. E., Tia, M., Dickison, S. W., and Reid, B. (1997). “Evaluation of SHRP indirect tension tester to mitigate cracking in asphalt concrete pavements and overlays.” Final Rep., FDOT B-9885, Univ. of Florida, Gainesville, FL.
Talbot, A. (1979). “The accurate numerical inversion of Laplace transforms.” J. Inst. Math. Appl., 23, 97–120.
Thompson, M. R. (1982). ILLI-PAVE, user’s manual, Transportation Facilities Group, Dept. of Civil Engineering, Univ. of Illinois, Urbana, IL.
Tschoegl, N. W. (1989). The phenomenological theory of linear viscoelastic behavior: An introduction, Springer-Verlag, New York.
Information & Authors
Information
Published In
Journal of Materials in Civil Engineering
Volume 23 • Issue 7 • July 2011
Pages: 1007 - 1016
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Apr 2, 2010
Accepted: Jan 7, 2011
Published online: Jan 10, 2011
Published in print: Jul 1, 2011
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.