Elasto-Plastic Finite Element Evaluation of Flexible Pavements Based on Shakedown Concept

Document Type: Research Paper


1 Assistant Professor, Civil Engineering Department, Fasa University

2 Master of Science in Geotechnical Engineering


In this paper, three-dimensional elasto-plastic finite element analysis was performed on flexible pavements under vertical repeated traffic loads to evaluate their shakedown behavior. Six different pavements with different structural number (SN) were modeled and subjected to a wide range of cyclic vehicle loads. Shakedown limits were obtained considering both failure and serviceability restraints. Results indicate that shakedown coefficient and shakedown bearing capacity increase with a rise in SN for all load types. Lower limit of shakedown bearing capacity versus SN can be regarded as a criterion for pavement design. Besides, shakedown failure-displacement factor (SFDF) was introduced as an index which is able to include both failure and serviceability criteria to compare pavements in terms of their shakedown behavior. Results suggest increase in SFDF with increasing SN, particularly for light loads. Furthermore, results indicate that increase in asphalt layer thickness always improves shakedown bearing capacity, while increase in base and subbase layer thickness is not only ineffective beyond an effective thickness but may also be damaging. In addition, the results of the present study were compared to lower bound and upper bound shakedown analysis for verification and showed reasonable agreement.


-AASHTO (1993) “AASHTO Guide for design of pavement structures, USA: AASHTO.

Arvin, M. R., Askari, F. and Farzaneh, O. (2012) “Seismic behavior of slopes by lower bound dynamic shakedown theory”, Computers and Geotechnics, Vol. 39, pp. 107-115.

 Askari, F., Arvin, M. R. and Farzaneh, O. (2013) “Shakedown method versus pseudostatic method for seismic slope stability”, International Journal of Civil Engineering, Transaction B: Geotechnical Engineering, Vol. 11, No. 2, pp. 133-140.

-Bleich, H. (1932) “Über die Bemessung statish unbestimmter Stahl tragwerke unter der Berücksichtigung des elastisch-plastischen Verhaltens des Baustoffes”, Bauingenieur; pp. 13, 261.

-Cerni, G., Cardone, F., Virgili, A. and Camilli, S. (2012) “Characterization of permanent deformation behaviour of unbound granular materials under repeated triaxial loading”, Construction Building Materials, Vol. 28, No. 2, pp. 79–87.

-Chazallon, C., Koval, G., Hornych, P., Allou, F. and Mouhoubi, S. (2009) “Modelling of rutting of two flexible pavements with the shakedown theory and the finite element method”, Computers and Geotechnics, Vol. 36, pp. 798–809.

-Christopher, B. R., Schwartz, C. and Boudreau, R. (2006) “Geotechnical aspects of pavements”, Publication No. FHWA NHI-05-037.

-Collins, I. F. and Boulbibane, M. (2000 a) “Geomechanical analysis of unbound pavements based on shakedown theory”, Journal of Geotechnical and Geo-environmental Engineering, ASCE, Vol. 126, No. 1, pp. 50-59.

-Collins, I. F. and Boulbibane, M. (2000 b) “Shakedown under moving loads with applications to pavement design and wear”, Proceedings of the John Booker Memorial Symposium, edited by D. W. Smith and J. P. Carter, University of Sydney, NSW, Australia.

-Collins, I. F. and Cliffe, P. F. (1987) “Shakedown in frictional materials under moving surface loads”, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 11, pp. 409-420.

-Collins, I. F., Wang, A. P. and Saunders, L. R. (1993 a) “Shakedown in layered pavements under moving surface loads”, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 17, pp. 165-174.

-Collins, I. F., Wang, A. P. and Saunders, L. R. (1993 b) “Shakedown theory and the design of unbound pavements”, Road and Transport Research, Vol. 2, No. 4, pp. 29-38.

-Ghadimi, B., Nikraz, H. and Rosano, M. (2016) “Dynamic simulation of a flexible pavement layers considering shakedown effects and soil-asphalt interaction”, Transportation Geotechnics, Vol. 7, pp. 40-58.

-Habiballah, T. and Chazallon, C. (2005) “An elasto-plastic model based on the shakedown concept for flexible pavements unbound granular materials”, International Journal of Numerical and Analytical Methods in Geomechanics, Vol. 29, pp. 577–596.

-Haldar, A. K., Reddy, D. V. and Arockiasamy, M. (1990) “Foundation shakedown of offshore platforms”, Computers and Geomechanics, Vol 10, pp. 231-245.

-Huang, Y. H. (2004) “Pavement analysis and design”, Pearson Education Inc. Second Edition.

-Iran Highway Asphalt Paving Code  (2011) No. 234, First Edition, Tehran, Bureau of Planning and Management

-Jupsi, S. (2007) “Experimental validation of the shakedown concept for pavement analysis and design”, Ph.D. Dissertation, University of Nottingham.

-Melan, E.  (1938) “Der Spanning Zustand Eines “MisesHenckyschen”, Kontinuums Bei Verändlichen Belastung, Sitz. Ber. Akad. Wiss. Wien, Abt. Lla, pp. 147, 73.

-Midas GTS NX 2014 ver.1.22 . (2014).

-Raad, L. and Minassian, G. (2005) “The influence of granular base characteristics on upper bound shakedown of pavement structures”, Road Materials and Pavement Design, Vol. 6, No. 1, pp. 53–79.

-Raad, L., Weichert, D. and Haidar, A. (1989), “Analysis of full-depth asphalt concrete pavements using shakedown theory” Transportation Research Record. No.1227, pp. 53-65.

-Raad, L., Weichert, D. and Najm, W. (1988) “Stability of multilayer systems under repeated loads”, Transportation Research Record, No. 1207, pp.181-186.

-Rahman, M. S. and Erlingsson, S. (2015) “Predicting permanent deformation behaviour of unbound

granular materials”, International Journal of Pavement Engineering, Vol. 16, No. 7, pp. 587-601.

-Ravindra, P.S. and Small, J.C. (2008) “Shakedown analysis of road pavements”, The 12th International Conference of International Association for Computer Methods and Advances in Geomechanics Goa, India. pp. 4432-4438.

-Ravindra, P. S. (2008) “Shakedown analysis of road pavements-an experimental point of view”, Ph.D. Dissertation, University of Sydney, NSW, Australia.

-Sharp, R. W. and Booker, J. R. (1984) “Shakedown of pavements under moving surface loads”, Journal of Transport Engineering, ASCE, Vol. 110, No. 1, pp. 1-14.

-Shiau, S. H. (2001) “Numerical methods for shakedown analysis of pavements under moving surface loads”, PhD Dissertation, The University of Newcastle, Australia.

-Taherkhani, H. and Valizadeh, M., (2015) “An investigation on the effects of aggregates properties on the performance of unbound aggregate base layer”, International Journal of Transportation Engineering,Vol. 3, No. 2, pp. 151-164.

-The Asphalt Institute (1984) “Mix design methods for asphalt concrete and other hot mix types”, The Asphalt Institute MS-2.

-Wang, J. (2011) “Shakedown analysis and design of flexible road pavements under moving surface loads” PhD Dissertation, University of Nottingham, UK.

-Yu, H. S. and Hossain, M. Z. (1998) “Lower bound shakedown analysis of layered pavements using discontinuous stress fields”, Computer Methods in Applied Mechanics and Engineering,  Vol. 167, pp. 209-222