Skip to main content

Use of linear viscoelastic theory to predict resilient behavior of unbound granular materials


This paper presents a methodology to estimate the stress-strain relationship of an unbound aggregate base using linear viscoelastic theory. Current Mechanistic-Empirical (ME) pavement design procedure adopts the resilient modulus concept to explain the behavior of granular materials for flexible pavement design. The resilient modulus is a stress dependent material property of granular materials that is different from strength. Although California Bearing Ratio (CBR) test results (i.e., stress and strain) can be used to estimate the strength of a granular material, it is not possible to estimate the resilient modulus directly. Therefore, it is necessary to estimate stress along with strain changes. The convolution integral enables the stress to be estimated from the given strain changes only if the relaxation modulus is measured. Aggregate specimens prepared from two different sources in Georgia were subjected to the relaxation modulus test. From the test data, the time-dependent stress due to a known strain rate was computed as a convolution integral of the strain. The computed stress-strain relationship was compared with that from the resilient modulus (M R ) test. The results indicate that the stress-strain relationships from the M R test and the convolution integral are similar with nearly the same slopes when horizontal stress is assumed to be approximately 45% of vertical stress. This observation supports the use of the proposed methodology by state highway agencies to validate the M R test results for quality control and quality assurance of aggregate base material selection for pavement design and construction.

This is a preview of subscription content, access via your institution.


  • Al-Rousan, T., Masad, E., Tutumluer, E., and Pan, T. (2007). “Evaluation of image analysis techniques for quantifying aggregate shape characteristics.” Journal of Construction and Building Materials, Vol. 21, Issue 5, pp. 978–990, DOI: 10.1016/jconbuildmat.2006.03.005.

    Article  Google Scholar 

  • Findley, W., Lai, J., and Onaran, K. (1976). Creep and Relaxation of Nonlinear Viscoelastic Materials, North-Holland Publishing Company, Amsterdam.

    MATH  Google Scholar 

  • Funahashi, K. (1989). “On the approximate realization of continuous mappings by neural networks.” Neural Networks, Vol. 2, No. 3, pp. 183–192, DOI: 10.1016/0893-6080(89)90003-8.

    Article  Google Scholar 

  • Hornik, K., Stinchcombe, M., and White, H. (1989). “Multilayer feedforward networks are universal approximators.” Neural Networks, Vol. 2, No. 5, pp. 359–366, DOI: 10.1016/0893-6080(89)90020-8.

    Article  Google Scholar 

  • Jang, J., Sun, C., and Mitzutani, E. (1997). Neuro-Fuzzy and Soft Computing, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Kim, S., Tutumluer, E., and Little, D. (2007). “Effect of gradation on nonlinear stress-dependent behavior of a sandy flexible pavement subgrade.” Journal of Transportation Engineering, American Society of Civil Engineering, Vol. 133, No. 10, pp. 582–589, DOI: 10.1061/(ASCE)0733-947X(2007)133:10(582).

    Google Scholar 

  • Kim, S. (2013). Measurements of dynamic and resilient moduli for roadway test sections, Final Report, GDOT Research Project No. 12-07.

    Google Scholar 

  • MacKay D. J. C. (199). “A practical bayesian framework for backpropogation Networks.” Neural Computation, Vol. 4, No. 3, pp. 448-472, DOI: 10.1162/neco.1992.4.3.448.

  • McFall, K. and Mahan, J. R. (2009). “Artificial neural network method for solution of boundary value problems with exact satisfaction of arbitrary boundary conditions.” IEEE Transactions on Neural Networks, Vol. 20, No. 8, pp. 1221–1233, DOI: 10.1109/TNN.2009.2020735.

    Article  Google Scholar 

  • NeuroShell 2, Software by Ward Systems Group, Inc., Frederick, MD.

  • Xiao, Y., Tutumluer, E., and Siekmeier, J. (2011). Resilient Modulus Behavior Estimated from Aggregate Source Properties. Proceedings of the ASCE Geo-Frontiers 2011 Conference, Dallas, Texas, pp. 4843–4852.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Jin-Hoon Jeong.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, SH., McFall, K., Kwon, J. et al. Use of linear viscoelastic theory to predict resilient behavior of unbound granular materials. KSCE J Civ Eng 20, 1806–1812 (2016).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: