Acta Mechanica Solida Sinica

, Volume 28, Issue 6, pp 647–658 | Cite as

Fractional Order Modelling of the Cumulative Deformation of Granular Soils Under Cyclic Loading

Article

Abstract

To model the cumulative deformation of granular soils under cyclic loading, a mathematical model was proposed. The power law connection between the shear strain and loading cycle was represented by using fractional derivative approach. The volumetric strain was characterized by a modified cyclic flow rule which considered the effect of particle breakage. All model parameters were obtained by the cyclic and static triaxial tests. Predictions of the test results were provided to validate the proposed model. Comparison with an existing cumulative model was also made to show the advantage of the proposed model.

Key Words

cumulative deformation cyclic stress cyclic flow rule fractional derivative granular soil 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Miura, N., Fujikawa, K., Sakai, A. and Hara, K., Field measurement of settlement in saga airport highway subjected to trafficload. Tsuchi-to-Kiso, 1995, 43–6(449): 49–51.Google Scholar
  2. 2.
    Ren, X.W., Tang, Y.Q., Li, J. and Yang, Q., A prediction method using grey model for cumulative plastic deformation under cyclic loads. Natural Hazards, 2012, 64(1): 441–457.CrossRefGoogle Scholar
  3. 3.
    Li, D.Q. and Selig, E.T., Cumulative plastic deformation for tine grained subgrade soils. Journal of Geotechnical Engineeing ASCE, 1996, 122(12): 1006–1013.CrossRefGoogle Scholar
  4. 4.
    Chai, J.C. and Miura, N., Traffic-load-induced permanent deformation of road on soft subsoil. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(11): 907–916.CrossRefGoogle Scholar
  5. 5.
    Bouckovalas, G., Whitman, R.V. and Marr, W.A., Permanent displacement of sand with cyclic loading. Journal of Geotechnical Engineeing ASCE, 1984, 110(11): 1606–1623.CrossRefGoogle Scholar
  6. 6.
    Suiker, A.S. J. and de, Borst, R., A numerical model for the cyclic deterioration of railway tracks. International Journal for Numerical Methods in Engineering, 2003, 57(4), 441–470.CrossRefGoogle Scholar
  7. 7.
    Khalili, N., Habte, M. and Valliappan, S., A bounding surface plasticity model for cyclic loading of granular soils. International Journal for Numerical Methods in Engineering, 2005, 63(14): 1939–1960.CrossRefGoogle Scholar
  8. 8.
    Niemunis, A., Wichtmann, T. and Triantafyllidis, T.H., A high-cycle accumulation model for sand. Computer and Geotechnics, 2005, 32(4): 245–263.CrossRefGoogle Scholar
  9. 9.
    Wichtmann, T., Niemunis, A. and Triantafyllidis, T.H., Experimental evidence of a unique flow rule of non-cohesive soils under high-cyclic loading. Acta Geotechnica, 2006, 1(1): 59–73.CrossRefGoogle Scholar
  10. 10.
    Wichtmann, T., Niemunis, A. and Triantafyllidis, T.H., Validation and calibration of a high-cycle accumulation model based on cyclic triaxial tests on eight sands. Soils and Foundations, 2009, 49(5): 711–728.CrossRefGoogle Scholar
  11. 11.
    Li, S. and Huang, M., Undrained long-term cyclic degradation characteristics of offshore soft clay. In: Proceedings of the GeoShanghai 2010 International Conference, Shanghai, China. Huang, M.S., Yu, X. and Huang, Y. eds., 2010: 263–271.Google Scholar
  12. 12.
    Li, L.L., Dan, H.B. and Wang, L.Z., Undrained behavior of natural marine clay under cyclic loading. Ocean Engineering, 2011, 38(16): 1792–1805.CrossRefGoogle Scholar
  13. 13.
    Karim, M.R., Oka, F., Krabbenhoft, K., Leroueil, S. and Kimoto, S., Simulation of long-term consolidation behavior of soft sensitive clay using an elasto-viscoplastic constitutive model. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(16): 2801–2824.Google Scholar
  14. 14.
    Liu, H., Zou, D. and Liu, J., Constitutive modeling of dense gravelly soils subjected to cyclic loading. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, DOI: 10.1002/nag.2269.CrossRefGoogle Scholar
  15. 15.
    Seidalinov, G. and Taiebat, M. Bounding surface SANICLAY plasticity model for cyclic clay behavior. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, 38(7): 702–724.CrossRefGoogle Scholar
  16. 16.
    Ishikawa, T., Sekine, E. and Miura, S., Cyclic deformation of granular material subjected to moving-wheel loads. Canadian Geotechnical Journal, 2011, 48(5): 691–703.CrossRefGoogle Scholar
  17. 17.
    Suiker, A.S.J, Selig, E.T. and Frenkel, R., Static and cyclic triaxial testing of ballast and subballast. Journal of Geotechnical and Geoenvironmental Engineering, 2005, 131(6): 771–782.CrossRefGoogle Scholar
  18. 18.
    Indraratna, B., Lackenby, J. and Christie, D., Effect of confining pressure on the degradation of ballast under cyclic loading. Géotechnique, 2005, 55(4): 325–328.CrossRefGoogle Scholar
  19. 19.
    Lackenby, J., Indraratna, B., McDowell, G. and Christie, D., Effect of confining pressure on ballast degradation and deformation under cyclic triaxial loading. Géotechnique, 2007, 57(6): 527–536.CrossRefGoogle Scholar
  20. 20.
    Indraratna, B., Thakur, P.K. and Vinod, J.S., Experimental and numerical study of railway ballast behavior under cyclic loading. International Journal of Geomechanics, 2009, 10(4): 136–144.CrossRefGoogle Scholar
  21. 21.
    Xiao, Y., Liu, H., Chen, Y. and Jiang, J., Bounding surface model for rockfill materials dependent on density and pressure under triaxial stress conditions. Journal of Engineering Mechanics, 2014, 140(4), 04014002. Doi: 10.1061/(ASCE)EM.1943-7889.0000702.CrossRefGoogle Scholar
  22. 22.
    Fu, Z., Chen, S. and Peng, C., Modeling cyclic behavior of rockfill materials in a framework of generalized plasticity. International Journal of Geomechanics, 2014, 14(2): 191–204.CrossRefGoogle Scholar
  23. 23.
    Ling, H.I. and Yang, S., Unified sand model based on the critical state and generalized plasticity. Journal of Engineering Mechanics, 2006, 132(12): 1380–1391.CrossRefGoogle Scholar
  24. 24.
    Indraratna, B., Thakur, P.K., Vinod, J.S. and Salim, W., Semi-empirical cyclic densification model for ballast incorporating particle breakage. International Journal of Geomechanics, 2012, 12(3): 260–271.CrossRefGoogle Scholar
  25. 25.
    Chrismer, S. and Selig, E.T., Computer model for ballast maintenance planning. In: Proceedings of 5th International Heavy Haul Railway Conference, Beijing, China, 1993: 223–227.Google Scholar
  26. 26.
    Indraratna, B., Salim, W., Ionescue, D. and Christie, D., Stress-strain and degradation behavior of railway ballast under static and dynamic loading, based on large-scale triaxial testing. In: Proceedings of 15th international conference on soil mechanics and geotechnical engineering, Istanbul, Turkey, 2001: 2093–2096.Google Scholar
  27. 27.
    Sun, H.G., Chen, W. and Chen, Y.Q., Variable-order fractional differential operators in anomalous diffusion modeling, Physica A, 2009, 388(21): 4586–4592.CrossRefGoogle Scholar
  28. 28.
    Sun, Y., Liu, H., Xiao, Y. Gao, H. and Cui, Y., Modeling of rheological behavior of geomaterials based on fractional viscoelastic equation with variable parameters. In: Proceedings of GeoHunan international conference 2011, Hunan, China. Ge, L., Zhang, X., Wu, J. and Correia, A.G. eds., 2011: 107–114.Google Scholar
  29. 29.
    Yin, D., Wu, H., Cheng, C. and Chen, Y.Q., Fractional order constitutive model of geomaterials under the condition of triaxial test. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(8): 961–972.CrossRefGoogle Scholar
  30. 30.
    Yin, D., Duan, X. and Zhou, X., Fractional time-dependent deformation component models for characterizing viscoelastic Poisson’s ratio. European Journal of Mechanics A/Solids, 2013, 42: 422–429.CrossRefGoogle Scholar
  31. 31.
    Kilbas, A.A.A, Srivastava, H.M. and Trujillo, J.J., Theory and applications of fractional differential equations. Elsevier Science Limited, 2006: 91–99.Google Scholar
  32. 32.
    Rowe, P.W., The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proceedings of Royal Society of London A Mathematical and Physical Science, 1962, 269(1339): 500–527.CrossRefGoogle Scholar
  33. 33.
    Indraratna, B. and Salim, W., Modelling of particle breakage of coarse aggregates incorporating strength and dilatancy. Proceedings of ICE Geotechnical Engineering, 2002, 155(4): 243–252.CrossRefGoogle Scholar
  34. 34.
    Sun, Y., Liu, H. and Yang, G., Yielding function for coarse aggregates considering gradation evolution induced by particle breakage. Rock and Soil Mechanics, 2013, 34(12): 3479–3484.Google Scholar
  35. 35.
    Liu, H., Sun, Y., Yang, G. and Chen, Y., A review of particle breakage characteristics of coarse aggregates. Journal of Hohai University (Natural Sciences), 2012, 40(4): 361–369 (in Chinese).Google Scholar
  36. 36.
    McDowell, G.R., A family of yield loci based on micro mechanics. Soils and Foundations, 2000, 40(6): 133–137.CrossRefGoogle Scholar
  37. 37.
    Chang, C.S and Whitman, R.V., Drained permanent deformation of sand due to cyclic loading. Journal of Geotechnical Engineeing ASCE, 1988, 114(10): 1164–1180.CrossRefGoogle Scholar
  38. 38.
    Wichtmann, T., Niemunis, A. and Triantafyllidis, T.H., Flow rule in a high-cycle accumulation model backed by cyclic test data of 22 sands. Acta Geotechnica, 2014: 1–15.Google Scholar
  39. 39.
    Richart, F.E. Jr, Hall, J.R. and Woods, R.D., Vibrations of Soils and Foundations. Englewood Cliffs, NJ: Prentice-Hall, 1970.Google Scholar
  40. 40.
    Li, X. and Dafalias, Y., Dilatancy for cohesionless soils. Géotechnique, 2000, 50(4), 449–460.CrossRefGoogle Scholar
  41. 41.
    Li, D. and Selig, E.T., Cumulative plastic deformation for fine-grained subgrade soils. Journal of Geotechnical Engineeing ASCE, 1996, 122(12): 1006–1013.CrossRefGoogle Scholar
  42. 42.
    Lackenby, J., Triaxial behaviour of ballast and the role of confining pressure under cyclic loading. Dissertation for the Doctoral Degree. Wollongong: University of Wollongong, 2006: 89–91.Google Scholar
  43. 43.
    Xiao, Y., Liu, H., Chen, Y., Jiang, J. and Zhang, W., State-dependent constitutive model for rockfill materials. International Journal of Geomechanics, 2014, 04014075. Doi: 10.1061/(ASCE)GM.1943-5622.0000421.CrossRefGoogle Scholar
  44. 44.
    Indraratna, B., Wijewardena, L.S.S. and Balasubramaniam, A.S., Large-scale triaxial testing of greywacke rockfill. Géotechnique, 1993, 43(1): 37–51.CrossRefGoogle Scholar
  45. 45.
    Frossard, E., Dano, C., Hu, W. and Hicher, P.Y., Rockfill shear strength evaluation: a rational method based on size effects. Géotechnique, 2012, 62(5): 415–427.CrossRefGoogle Scholar
  46. 46.
    Xiao, Y., Liu, H., Chen, Y. and Jiang, J., Bounding Surface Plasticity Model Incorporating the State Pressure Index for Rockfill Materials. Journal of Engineering Mechanics, 2014, 140(11), 04014087. doi: 10.1061/(ASCE)EM.1943-7889.0000802.CrossRefGoogle Scholar
  47. 47.
    Xiao, Y., Liu, H., Chen, Y., Jiang, J. and Zhang, W., Testing and modeling of the state-dependent behaviors of rockfill material. Computers and Geotechnics, 61(9): 153–165.CrossRefGoogle Scholar
  48. 48.
    Xiao, Y., Sun, Y. and Hanif, F., A particle-breakage critical state model for rockfill material. Science China Technological Sciences, 2015, 58(7): 1125–1136.CrossRefGoogle Scholar
  49. 49.
    François, S., Karg, C., Haegeman, W. and Degrande, G., A numerical model for foundation settlements due to deformation accumulation in granular soils under repeated small amplitude dynamic loading. International Journal for Numerical and Analytical Methods in Geomechanics, 2010, 34(3): 273–296.MATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2015

Authors and Affiliations

  1. 1.Institute for Mathematics and Its ApplicationsUniversity of WollongongWollongongAustralia
  2. 2.State Key Laboratory of Coal Mine Disaster Dynamics and ControlChongqing UniversityChongqingChina
  3. 3.Key Laboratory of New Technology for Construction of Cities in Mountain AreaChongqing UniversityChongqingChina
  4. 4.College of Civil EngineeringChongqing UniversityChongqingChina
  5. 5.Faculty of Engineering, Computing and MathematicsUniversity of Western AustraliaPerthAustralia

Personalised recommendations