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Journal of Applied Mathematics
Volume 2013, Article ID 537185, 15 pages
http://dx.doi.org/10.1155/2013/537185
Research Article

A Unified Elastoplastic Model of Unsaturated Soils Considering Capillary Hysteresis

1State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Xiaohongshan, Wuchang, Wuhan, Hubei 430071, China
2College of Civil and Architectural Engineering, Guilin University of Technology, Guilin, Guangxi 541004, China
3Department of Civil Engineering, Shanghai University, Shanghai 200072, China

Received 14 May 2013; Accepted 26 July 2013

Academic Editor: Pengcheng Fu

Copyright © 2013 Tiantian Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. J. Wheeler, “Inclusion of specific water volume within an elasto-plastic model for unsaturated soil,” Canadian Geotechnical Journal, vol. 33, no. 1, pp. 42–57, 1996. View at Publisher · View at Google Scholar · View at Scopus
  2. D. Sun, D. Sheng, and S. W. Sloan, “Elastoplastic modelling of hydraulic and stress-strain behaviour of unsaturated soils,” Mechanics of Materials, vol. 39, no. 3, pp. 212–221, 2007. View at Publisher · View at Google Scholar · View at Scopus
  3. C. W. W. Ng and Y. W. Pang, “Influence of stress state on soil-water characteristics and slope stability,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 126, no. 2, pp. 157–166, 2000. View at Publisher · View at Google Scholar · View at Scopus
  4. E. E. Alonso, A. Gens, and A. Josa, “A constitutive model for partially saturated soils,” Géotechnique, vol. 40, no. 3, pp. 405–430, 1990. View at Publisher · View at Google Scholar · View at Scopus
  5. S. J. Wheeler and V. Sivakumar, “An elasto-plastic critical state framework for unsaturated soil,” Géotechnique, vol. 45, no. 1, pp. 35–53, 1995. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Nuth, L. Laloui, and B. A. Schrefler, “Analysis of compaction phenomena due to water injection in reservoirs with a three-phase geomechanical model,” Journal of Petroleum Science and Engineering, vol. 73, no. 1-2, pp. 33–40, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. D. A. Sun and X. Li, “An elastoplastic hydro-mechanical model for unsaturated soils,” in Proceedings of the 7th International Conference on Computational Science (ICCS '07), pp. 1138–1145, Springer, Beijing, China, 2007.
  8. D. Sheng, A. Gens, D. G. Fredlund, and S. W. Sloan, “Unsaturated soils: from constitutive modelling to numerical algorithms,” Computers and Geotechnics, vol. 35, no. 6, pp. 810–824, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. F. D'Onza, D. Gallipoli, S. Wheeler et al., “Benchmark of constitutive models for unsaturated soils,” Géotechnique, vol. 61, no. 4, pp. 283–302, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. S. J. Wheeler, R. S. Sharma, and M. S. R. Buisson, “Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils,” Géotechnique, vol. 53, no. 1, pp. 41–54, 2003. View at Publisher · View at Google Scholar · View at Scopus
  11. G. Bolzon, B. A. Schrefler, and O. C. Zienkiewicz, “Elastoplastic soil constitutive laws generalized to partially saturated states,” Géotechnique, vol. 46, no. 2, pp. 279–289, 1996. View at Publisher · View at Google Scholar · View at Scopus
  12. Y. J. Cui and P. Delage, “Yielding and plastic behaviour of an unsaturated compacted silt,” Géotechnique, vol. 46, no. 2, pp. 291–311, 1996. View at Publisher · View at Google Scholar · View at Scopus
  13. M. Nuth, Constitutive modelling of unsaturated soils with hydro-geomechanical couplings [Ph.D. thesis], Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, 2009.
  14. N. Khalili, F. Geiser, and G. E. Blight, “Effective stress in unsaturated soils: review with new evidence,” International Journal of Geomechanics, vol. 4, no. 2, pp. 115–126, 2004. View at Publisher · View at Google Scholar · View at Scopus
  15. R. Tamagnini, “An extended Cam-clay model for unsaturated soils with hydraulic hysteresis,” Géotechnique, vol. 54, no. 3, pp. 223–228, 2004. View at Publisher · View at Google Scholar · View at Scopus
  16. C. Jommi, “Remarks on the constitutive modelling of unsaturated soils,” in Experimental Evidence and Theoretical Approaches in Unsaturated Soils. Proceedings of the International Workshop on Unsaturated Soils, A. Tarantino and C. Mancuso, Eds., pp. 139–153, Balkema, Rotterdam, The Netherlands, 2000. View at Google Scholar
  17. X. S. Li, “Thermodynamics-based constitutive framework for unsaturated soils. 2: a basic triaxial model,” Géotechnique, vol. 57, no. 5, pp. 423–435, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. C. Wei and M. M. Dewoolkar, “Formulation of capillary hysteresis with internal state variables,” Water Resources Research, vol. 42, no. 7, Article ID W07405, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. X. S. Li, “Modelling of hysteresis response for arbitrary wetting/drying paths,” Computers and Geotechnics, vol. 32, no. 2, pp. 133–137, 2005. View at Publisher · View at Google Scholar · View at Scopus
  20. Y. Mualem, “A conceptual model of hysteresis,” Water Resources Research, vol. 10, no. 3, pp. 514–520, 1974. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Y. Parlange, “Capillary hysteresis and the relationship between drying and wetting curves,” Water Resources Research, vol. 12, no. 2, pp. 224–228, 1976. View at Publisher · View at Google Scholar · View at Scopus
  22. L. Miao, F. Jing, and S. L. Houston, “Soil-water characteristic curve of remolded expansive soils,” in Proceedings of the 4th International Conference on Unsaturated Soils, pp. 997–1004, April 2006. View at Publisher · View at Google Scholar · View at Scopus
  23. D. Gallipoli, S. J. Wheeler, and M. Karstunen, “Modelling the variation of degree of saturation in a deformable unsaturated soil,” Géotechnique, vol. 53, no. 1, pp. 105–112, 2003. View at Publisher · View at Google Scholar · View at Scopus
  24. M. T. van Genuchten, “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils,” Soil Science Society of America Journal, vol. 44, no. 5, pp. 892–898, 1980. View at Publisher · View at Google Scholar · View at Scopus
  25. X. S. Li, “Thermodynamics-based constitutive framework for unsaturated soils. 1: theory,” Géotechnique, vol. 57, no. 5, pp. 411–422, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. G. T. Houlsby, “The work input to an unsaturated granular material,” Géotechnique, vol. 47, no. 1, pp. 193–196, 1997. View at Publisher · View at Google Scholar · View at Scopus
  27. A. W. Bishop, “The principle of effective stress bishop,” Teknisk Ukeblad, vol. 106, no. 39, pp. 113–143, 1959. View at Google Scholar
  28. N. Khalili and S. Zargarbashi, “Influence of hydraulic hysteresis on effective stress in unsaturated soils,” Géotechnique, vol. 60, no. 9, pp. 729–734, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. E. E. Alonso, J.-M. Pereira, J. Vaunat, and S. Olivella, “A microstructurally based effective stress for unsaturated soils,” Géotechnique, vol. 60, no. 12, pp. 913–925, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. J.-M. Pereira, O. Coussy, E. E. Alonso, J. Vaunat, and S. Olivella, “Is the degree of saturation a good candidate for Bishop’s parameter?” in Proceedings of the 5th International Conference on Unsaturated Soils, E. E. Alonso and A. Gens, Eds., pp. 913–919, CRC Press, Barcelona, Spain, September 2010. View at Publisher · View at Google Scholar · View at Scopus
  31. T. Cadoret, G. Mavko, and B. Zinszner, “Fluid distribution effect on sonic attenuation in partially saturated limestones,” Geophysics, vol. 63, no. 1, pp. 154–160, 1998. View at Publisher · View at Google Scholar · View at Scopus
  32. C. Wei and K. K. Muraleetharan, “Linear viscoelastic behavior of porous media with non-uniform saturation,” International Journal of Engineering Science, vol. 45, no. 2–8, pp. 698–715, 2007. View at Publisher · View at Google Scholar · View at Scopus
  33. S. K. Vanapalli, D. G. Fredlund, and D. E. Pufahl, “The influence of soil structure and stress history on the soil-water characteristics of a compacted till,” Géotechnique, vol. 49, no. 2, pp. 143–159, 1999. View at Google Scholar · View at Scopus
  34. D. Sun, D. Sheng, and Y. Xu, “Collapse behaviour of unsaturated compacted soil with different initial densities,” Canadian Geotechnical Journal, vol. 44, no. 6, pp. 673–686, 2007. View at Publisher · View at Google Scholar · View at Scopus
  35. D. A. Sun, D. C. Sheng, H. B. Cui, and S. W. Sloan, “A density-dependent elastoplastic hydro-mechanical model for unsaturated compacted soils,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 31, no. 11, pp. 1257–1279, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  36. T. Cadoret, D. Marion, and B. Zinszner, “Influence of frequency and fluid distribution on elastic wave velocities in partially saturated limestones,” Journal of Geophysical Research, vol. 100, no. 6, pp. 9789–9803, 1995. View at Publisher · View at Google Scholar · View at Scopus
  37. R. Knight and R. Nolen-Hoeksema, “A laboratory study of the dependence of elastic wave velocities on pore scale fluid distribution,” Geophysical Research Letters, vol. 17, no. 10, pp. 1529–1532, 1990. View at Publisher · View at Google Scholar · View at Scopus
  38. M. Le Ravalec, Y. Guéguen, and T. Chelidze, “Elastic wave velocities in partially saturated rocks: saturation hysteresis,” Journal of Geophysical Research B, vol. 101, no. 1, pp. 837–844, 1996. View at Publisher · View at Google Scholar · View at Scopus
  39. J. R. Rice, “Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity,” Journal of the Mechanics and Physics of Solids, vol. 19, no. 6, pp. 433–455, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  40. K. H. Roscoe and J. B. Burland, “On the generalized stress-strain behavior of ‘wet’ clay,” in Engineering Plasticity, pp. 535–609, Cambridge University Press, Cambridge, UK, 1968. View at Google Scholar
  41. L. Luckner, M. T. van Genuchten, and D. R. Nielsen, “A consistent set of parametric models for the two-phase flow of immiscible fluids in the subsurface,” Water Resources Research, vol. 25, no. 10, pp. 2187–2193, 1989. View at Publisher · View at Google Scholar · View at Scopus
  42. W. S. Sillers, The mathematical representation of the soil-water characteristic curve [Ph.D. thesis], University of Saskatchewan, Saskatchewan, Canada, 1997.
  43. D. Gallipoli, A. Gens, R. Sharma, and J. Vaunat, “An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour,” Géotechnique, vol. 53, no. 1, pp. 123–135, 2003. View at Publisher · View at Google Scholar · View at Scopus
  44. R. A. Fisher, “On the capillary forces in an ideal soil; correction of formulae given by W. B. Haines,” Journal of Agricultural Science, vol. 16, no. 3, pp. 492–505, 1926. View at Publisher · View at Google Scholar
  45. N. Lu and W. J. Likos, “Suction stress characteristic curve for unsaturated soil,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 132, no. 2, pp. 131–142, 2006. View at Publisher · View at Google Scholar · View at Scopus
  46. A. Raveendiraraj, Coupling of mechanical behaviour and water retention behaviour in unsaturated soils [Ph.D. thesis], University of Glasgow, Glasgow, UK, 2009.
  47. M. Feng and D. G. Frelund, “Hysteresis influence associated with thermal conductivity sensor measurements,” in Proceedings of the 52nd Canadian Geotechnical Conference and Unsaturated Soil Group, Proceeding from Theory to the Practice of Unsaturated Soil Mechanics, pp. 651–657, Regina, Canada, 1999.
  48. R. S. Sharma, Mechanical behavior of an unsaturated highly expansive clays [Ph.D. thesis], University of Oxford, Oxford, UK, 1998.