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A cyclic elastoplastic constitutive model and effect of non-associativity on the response of liquefiable sandy soils

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Abstract

A large number of constitutive models for geomaterials, such as soils and rocks, have been proposed over the last three decades. Those models have been implemented into computer codes and have been successfully used to solve practical engineering problems particularly under monotonic loading conditions. Compared with the models for monotonic loadings, more improvements for cyclic models are necessary in order to obtain more accurate predictions for the dynamic behavior of geomaterials, e.g., the behavior during earthquakes. A cyclic elastoplastic model has been developed in this study for sandy soils; it is based on the kinematical hardening rule with a yield function that includes the changes in the stress ratio and the mean effective stress considering the degradation of the yield surface. From a simulation with the present model, it has been found that strong non-associativity leads to a large decrease in the mean effective stress during cyclic deformations under undrained conditions, while the model with the associated flow rule does not. This result is quite important because the mean effective stress becomes almost zero at the state of full liquefaction. Compared with the experimental results, the model can accurately reproduce the cyclic behavior of soil.

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References

  1. Adachi T, Oka F (1982) Constitutive equations for sands and overconsolidated clays and assigned works for sand. In: Gudehus G, Darve F, Vardoulakis I (eds) Results of the international workshop on constitutive relations for soils. Balkema, pp 141–157

  2. Armstrong PJ, Frederick CO (1966) A mathematical representation of the multiaxial Bauschinger effect. Berkeley Nuclear Laboratories. Technical report RD/B/N 731

  3. Asaoka A, Noda T, Yamada E, Kaneda K, Nakano M (2002) An elasto-plastic description of two distinct volume change mechanism of soils. Soils Found 42(5):47–57

    Article  Google Scholar 

  4. Bauer E, Wu W (1993) A hypoplastic models for granular soils under cyclic loading. In: Kolymbas D (eds) Proceedings of the international workshop on modern approaches to plasticity. Elsevier, pp 247–258

  5. Bauer E (1996) Calibration of a comprehensive hypoplastic model for granular material. Soils Found 36(1):13–26

    Article  MathSciNet  Google Scholar 

  6. Been K, Jeffries FK (1985) A state parameter for sands. Geotechnique 35(2):99–112

    Article  Google Scholar 

  7. Chiaro C, Koseki J, De Silva LN (2013) An elasto-plastic model for liquefiable sands subjected to torsional shear loadings. In: Yang Q, Zhang J-M, Zheng H, Yao Y (eds) Constitutive modeling of geomaterials. Springer, Berlin, pp 519–526

    Chapter  Google Scholar 

  8. Dafalias YF, Herrman LR, Anandarajah A (1981) Cyclic loading response of cohesive soils using a bounding surface plasticity model. In: International conferences on recent advances in geotechnical earthquake engineering and soil dynamics. Paper no. 16, pp 139–144

  9. Fahey M (1992) Shear modulus of cohesionless soil: variation of stress-strain level. Can Geotech J 29(1):157–161

    Article  Google Scholar 

  10. Furuya K, Oka F, Sunami S, Hioki K (2003) An elasto-plastic constitutive model for sand considering the structure and application to the improved sand by compaction sand pile. In: Proceedings of the 38th annual meeting of the Japanese Geotechnical Society, pp 1097–1098 (in Japanese)

  11. Ghaboussi J, Momen H (1979) Plasticity model for cyclic behaviour of sands. In: Wittke W (ed) 3rd international conference on numerical methods in geomechanics, Aachen. Balkema, pp 423–434

  12. Gudehus G (1979) A comparison of some constitutive laws for soils under radially symmetric loading and unloading. In: Wittke W (ed) Proceedings of the 3rd international conference numerical methods in geomechanics. Balkema, Rotterdam, pp 1309–1323

  13. Hardin BO, Drnevich VP (1972) Shear modulus and damping in soils: design equation and curves. J Soil Mech Found ASCE 98(SM7):667–692

    Google Scholar 

  14. Hashiguchi K, Chen Z-P (1998) Elastoplastic constitutive equations of soils with subloading surface and the rotational hardening. Int J Numer Anal Methods Geomech 22:197–227

    Article  Google Scholar 

  15. Hashiguchi K (2009) Elastoplasticity theory. Springer, Berlin

    Book  Google Scholar 

  16. Ishihara K (1993) Liquefaction and flow failure during earthquakes. Geotechnique 43(3):351–415

    Article  Google Scholar 

  17. Ishihara K, Kabilamany K (1990) Stress dilatancy and hardening laws for rigid granular model of sand. Soil Dyn Earthq Eng 9(2):66–77

    Article  Google Scholar 

  18. Kimoto S, Oka F (2005) An elasto-viscoplastic model for clay considering destructuralization and consolidation analysis of unstable behavior. Soils Found 45(2):29–42

    Article  Google Scholar 

  19. Kimoto S, Khan BS, Mirjalili M, Oka F (2015) A cyclic elasto-viscoplastic constitutive model for clay considering the nonlinear kinematic hardening rules and the structural degradation. Int J Geomech ASCE 15(5):A4014005-14

    Article  Google Scholar 

  20. Lade PV (1975) Elastoplastic stress-strain theory for cohesionless soil. J Geotech Eng ASCE. 101(10):1037–1053

    Google Scholar 

  21. Lade PV (1992) Static instability and liquefaction on loose fine sandy slopes. J Geotech Eng ASCE 118(1):51–71

    Article  Google Scholar 

  22. Matsuoka H, Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. Proc JSCE 232:59–70

    Google Scholar 

  23. Morio B, Kusakabe S, Yasufuku N, Hyodo M (1994) Evaluation of undrained behavior of anisotropic sand based on elastoplastic constitutive model. Proc JSCE 505(III-29):287–296 (in Japanese)

    Google Scholar 

  24. Niemunis A, Herle I (1997) Hypoplastic model for cohesionless soils with elastic range. Mech Cohes Mater 2:279–299

    Article  Google Scholar 

  25. Oka F (1992) A cyclic elasto-viscoplastic constitutive model for clay based on the non-linear-hardening rule. In: Pande GN, Pietruszczak S (eds) Proceedings of the 4th international symposium on numerical models in geomechanics, Swansea, vol 1. Balkema, pp 105–114

  26. Oka F, Yashima A, Tateishi A, Taguchi Y, Yamashita S (1999) A cyclic elasto-plastic constitutive model for sand considering a plastic-strain dependence of the shear modulus. Geotechnique 49(5):661–680

    Article  Google Scholar 

  27. Oka F, Kodaka T, Yamada H (2000) A study on the constitutive model for sands considering the steady state. In: Proceedings of the 55th annual meeting of Japanese Society for Civil Engineers, no. III-A15, pp 30–31 (in Japanese)

  28. Oka F, Kimoto S (2016) Effect of the non-associativity of plasticity model on the cyclic behavior of geomaterials, key engineering. In: Proceedings of the 13th Asia-Pacific symposium on engineering plasticity and its applications, 4–8 Dec, vol 725, pp 322–326

    Article  Google Scholar 

  29. Pastro M, Zienkiewicz OC, Chan AHC (1990) Generalized plasticity and the modeling of soil behavior. Int J Numer Anal Methods Geomech 14(3):151–190

    Article  Google Scholar 

  30. Pestana JM, Whittle AJ (1999) Formulation for unified constitutive model for clays and sands. Int J Numer Anal Methods Geomech 23:1215–1243

    Article  Google Scholar 

  31. Prevost JH (1978) Plasticity theory for soils stress-strain behavior. J Eng Mech ASCE 104(5):1177–1194

    Google Scholar 

  32. Shao C, Desai CS (2000) Implementation of DSC model and application of analysis of field pile load tests under cyclic loading. Int J Numer Anal Methods Geomech 44(6):601–624

    Article  Google Scholar 

  33. Valanis KC, Read HE (1982) A new endochronic plasticity model for soils. In: Pande GN, Zienkiewicz OC (eds) Soil mechanics-transient and cyclic loads. Wiley, New Work, pp 375–417

    Google Scholar 

  34. Wan R (2010) Failure analysis using elastoplastic micromechanical model. In: Nico F, Wan R (eds) Micromechanics of failure in granular geomaterials. Wiley, New York, pp 105–139

    Google Scholar 

  35. Wichtmann T, Triantafyllidis T (2016) An experimental data base for the development, calibration and verification of constitutive models for sand with focus to cyclic loading. Part II: tests with strain cycles and combined loading. Acta Geotech 11(4):763–774. https://doi.org/10.1007/s11440-015-0412-x

    Article  Google Scholar 

  36. Wu W, Bauer, E (1993) A hypoplastic model for barotropy and pyknotropy of granular soils. In: Kolymbas D (eds) Proceedings of the international workshop on modern approaches to plasticity. Elsevier, pp 225–245

  37. Yamada Y, Ishihara K (1979) Anisotropic deformation characteristics of sand under three dimensional stress conditions. Soils Found 19(2):79–94

    Article  Google Scholar 

  38. Yasufuku N (1990) Yielding characteristics of anisotropically consolidated sand in the wide range of stress level and elastoplastic constitutive equation. Dr Thesis of Kyushu University (in Japanese)

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Acknowledgements

The authors express their thanks to Mr. H. Uno of LIQCA Liquefaction Geo Institute for his support in performing the calculations and to the reviewers for their helpful and constructive comments.

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Authors and Affiliations

  1. Professor Emeritus of Kyoto University, Association for Disaster Prevention Research Lab.3, 138-1,Tanakaasukai-cho, Sakyo-ku, Kyoto, 606-8226, Japan

    Fusao Oka

  2. Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto, 615-8540, Japan

    Sayuri Kimoto

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  1. Fusao Oka
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  2. Sayuri Kimoto
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Correspondence to Fusao Oka.

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Oka, F., Kimoto, S. A cyclic elastoplastic constitutive model and effect of non-associativity on the response of liquefiable sandy soils. Acta Geotech. 13, 1283–1297 (2018). https://doi.org/10.1007/s11440-018-0659-0

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