Stability of Pavement Structures Under Long Term Repeated Loading

  • Lutfi Raad
  • Dieter Weichert
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 36)


This paper addresses the stability of pavement structures under long term repeated loading using the shakedown theory. The accumulation of plastic strains in a given system may increase under repeated load applications, leading to incremental collapse, or plastic strains may cease to increase with time, resulting in a stable response or shakedown. An improved numerical method using finite element formulation coupled with an optimization technique is introduced. The method takes into consideration the variable elastic coefficients of both the coarse-grained and fine-grained layers in the pavement structure through the application of an extension of the classical shakedown theorem. The proposed method is used to illustrate the influence of layer properties on the shakedown behavior of general pavement systems.


Pavement Structure Pavement Temperature Pavement System Shakedown Analysis Load Multiplier 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1936 Melan, E, “Theorie Statisch unbestimmter Systeme aus ideal-plastischem Baustoff', Sitzungsber. Akad. der Wissenschaften in Wien, IIa, pp. 145–195.Google Scholar
  2. 1960 Koiter, W.T., “General Theorems for Elastic-Plastic Solids”, in: Sneddon, I.N And Hill, R. (eds), Progress in Solid Mechanics, North Holland, Amsterdam, pp. 165–221.Google Scholar
  3. 1961 Hooke, R. and Jeeves, T.A., “Direct Search Solution of Numerical and Statistical Problems”, J. Ass. Comp. Mach., 8, 212.Google Scholar
  4. 1969 König, J.A., “Shakedown Theory of Plates”, Archiwum Mechaniki Stosowanej, 21, 5, 623.Google Scholar
  5. 1972 Belytschko, T., “Plane Stress Shakedown Analysis by Finite Elements”, Int. J. Mech Sci. 14, 619.Google Scholar
  6. 1970 Monismith, C.L. et al., Asphalt Mixture Behavior In Repeated Flexure, Report No. TE-70-5, University of California, Berkeley, U.S.A.Google Scholar
  7. 1971 Salam, Y.S. “Characterization of Deformation and Fracture of Asphalt Concrete”, Ph.D. dissertation, University of California, Berkeley, U.S.A.Google Scholar
  8. 1974 Maier, G. and CORRADI, L., “Upper Bounds on Dynamical Deformations of Elastoplastic Continua”, Meccanica, IX, 30.Google Scholar
  9. 1977 Knutson, MR. et al., Materials Foundation Study — Ballast and Foundation Materials Research Program, Tech. Rep FRA-OR&D-77-02, Federal Railroad Administration, Washington, DC, U.S.A.Google Scholar
  10. 1978 Shell International Company Limited, Shell Pavement Design Manual-Asphalt Pavements and Overlays for Road Traffic, London, U.K.Google Scholar
  11. 1979 Figueroa, J. “Resilient Based Flexible Design Procedures for Secondary Roads”, PhD dissertation, University of Illinois at Urbana-Champaign, U.S.A.Google Scholar
  12. 1979 Thompson, M.R. and ROBNETT, Q.L., “Resilient Properties of Subgrade Soils”, J. Trans. Engg., ASCE, 105, TE1, 71.Google Scholar
  13. 1980 Aboustit, B.L. and REDDY, D.V., “Finite Element Linear Programming Approach to Foundation Shakedown”, in: Proc., Intern. Symp. on Soils Under Cyclic and Transient Loading, Swansea, U.K., pp. 727–738.Google Scholar
  14. 1980 Alwis, W.M. and Grundy, P., ”Shakedown of Plates under Moving Loads”, in: Proc, 7th Australian Conference on Mechanics of Structures and Materials, 1980, pp. 191–196.Google Scholar
  15. 1980 Pande, G.N., Abdullah, W.S. and Davis, E.H., “Shakedown of Elasto-Plastic Continua with Special Reference to Soil-Rock Structures”, in: Proc. Int. Symp. on Soils Under Cyclic and Transient Loading, Swansea, U.K., pp.39–74.Google Scholar
  16. 1980 Raad, L. and Figueroa, J., “Load Response of Transportation Support systems”. J. Trans. Engg., ASCE, 106, TE1, 111.Google Scholar
  17. 1984 Sharp, R.W. and Booker, J.R., “Shakedown of Pavements Under Moving Surface Loads”, J. Trans. Eng., ASCE, 110, TE1, 1.Google Scholar
  18. 1985 Sharp, R.W., “Pavement Design Based on Shakedown Analysis”, in: Transportation Research Record 1022, TRB, National Research Council, Washington, D.C., U.S.A., pp. 99–107.Google Scholar
  19. 1987 Maier, G., “A Generalization to Non-Linear Hardening of the First Shakedown Theorem for Discrete Elastic-Plastic Structural Models”, Atti Acc. Lincei Ren. fis. 8, LXXXI, 161Google Scholar
  20. 1988 Raad, L., Weichert, D. and W. Najm, W., “Stability of Multilayer Systems Under Repeated Loads”, in: Transportation Research Record 1207, TRB, National Research Council, Washington, D.C., U.S.A., pp. 181–186.Google Scholar
  21. 1988 Weichert, D. and GROSS-WEEGE, J, “The Numerical Assessment of Elastic-Plastic Sheets under Variable Mechanical and Thermal Loads Using A simplified Two-Yield Condition”, In. J. Mech. Sc., 30, 10, 757.Google Scholar
  22. 1989 Raad, L., Weichert, D. and Haidar, A., “Shakedown and Fatigue of Pavements with Granular Bases” in: Transportation Research Record 1227, National Research Council, Washington, D.C., U.S.A., pp. 159–172.Google Scholar
  23. 1989 Raad, L., Weichert, D. and Haidar, A., “Analysis of Full-Depth Asphalt Concrete Pavements Using Shakedown Theory” in Transportation Research Record 1227 National Research Council, Washington, D.C., U.S.A., pp. 53–65.Google Scholar
  24. 1990 Stein, E, Zhang, G. and König, J.A., “Michromechanical Modelling and Computation of Shakedown with Nonlinear Kinematic Hardening Including Examples for 2-D Problems”, in: AXELRAD, D.R. and MUSCHIK, W. (eds), Recent Developments Micromechanics, Springer Verlag, Berlin.Google Scholar
  25. 1992 Weichert, D. and Raad, L, “Extension of the Shakedown Theorem to a Certain Class of Materials with Variable Elastic Coefficients”, Mech. Res. Com., 19, 6, 511.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Lutfi Raad
    • 1
  • Dieter Weichert
    • 2
  1. 1.Transportation Research CenterUniversity of Alaska FairbanksFairbanksUSA
  2. 2.L.M.L (EUDIL)-CNRS URA 1441Université des Sciences et Technologies de LilleVilleneuve d’AscqFrance

Personalised recommendations