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Generalization and implementation of hardening soil constitutive model in ABAQUS code

  • Bo Songa (School of Civil Engineering and Architecture, University of Jinan) ;
  • Jun-Yan Liu (School of Civil Engineering and Architecture, University of Jinan) ;
  • Yan Liu (School of Civil Engineering and Architecture, University of Jinan) ;
  • Ping Hu (School of Civil Engineering and Architecture, University of Jinan)
  • 투고 : 2023.08.13
  • 심사 : 2024.01.05
  • 발행 : 2024.02.25

초록

The original elastoplastic Hardening Soil model is formulated actually partly under hexagonal pyramidal Mohr-Coulomb failure criterion, and can be only used in specific stress paths. It must be completely generalized under Mohr-Coulomb criterion before its usage in engineering practice. A set of generalized constitutive equations under this criterion, including shear and volumetric yield surfaces and hardening laws, is proposed for Hardening Soil model in principal stress space. On the other hand, a Mohr-Coulumb type yield surface in principal stress space comprises six corners and an apex that make singularity for the normal integration approach of constitutive equations. With respect to the isotropic nature of the material, a technique for processing these singularities by means of Koiter's rule, along with a transforming approach between both stress spaces for both stress tensor and consistent stiffness matrix based on spectral decomposition method, is introduced to provide such an approach for developing generalized Hardening Soil model in finite element analysis code ABAQUS. The implemented model is verified in comparison with the results after the original simulations of oedometer and triaxial tests by means of this model, for volumetric and shear hardenings respectively. Results from the simulation of oedometer test show similar shape of primary loading curve to the original one, while maximum vertical strain is a little overestimated for about 0.5% probably due to the selection of relationships for cap parameters. In simulation of triaxial test, the stress-strain and dilation curves are both in very good agreement with the original curves as well as test data.

키워드

과제정보

The research work described herein was funded by the National Natural Science Foundation of China (Grant No. 51979122).

참고문헌

  1. Abbo, A.J., Lyamin, A.V., Sloan, S.W. and Hambleton, J.P. (2011), "A C2 continuous approximation to the Mohr-Coulomb yield surface", Int. J. Solids Struct., 48, 3001-3010. https://doi.org/10.1016/j.ijsolstr.2011.06.021.
  2. Amat, S., Levin, D., Ruiz-Alvarez, J. and Yanez, D.F. (2023), "A new B-spline type approximation method for non-smooth functions", Appl. Math. Lett., 141, 108628. https://doi.org/10.1016/j.aml.2023.108628.
  3. Argani, L.P. and Gajo, A. (2021), "A new isotropic hyper-elasticity model for enhancing the rate of convergence of Mohr-Coulomb-like constitutive models and application to shallow foundations and trapdoors", Comput. Geotech., 132, 103957. https://doi.org/10.1016/j.compgeo.2020.103957.
  4. Bentley Systems Inc. (2022), PLAXIS CONNECT Edition V22.01 Material Models Manual, Bentley Systems Inc., Exton, PA, USA.
  5. Benz, T. (2007), "Small-strain stiffness of soils and its numerical consequences", Ph.D. Dissertation, Universitaet Stuttgart, Germany.
  6. Bolton, M.D. (1986), "The strength and dilatancy of sands", Geotechnique, 36(1), 65-78. https://doi.org/10.1680/geot.1986.36.1.65.
  7. Dassault Systemes Simulia Corp. (2019), SIMULIA User Assistance 2020. Dassault Systemes Simulia Corp., Johnston, RI, USA.
  8. De Souza Neto, E.A., Peric, D. and Owen, D.R.J. (2008), Computational Methods for Plasticity: Theory and Applications, John Wiley and Sons Ltd, Chichester, United Kingdom.
  9. Djedid, A. (1986), "Etude du comportement non-draine du sable", in Memoire de D.E.A., Institut de Mecanique de Grenoble, Grenoble, France. (in French)
  10. Jaky, J. (1944), "The coefficient of earth pressure at rest", J. Soc. Hungarian Architects Eng., 7, 355-358.
  11. Jia, S.P., Chen, W., Yang, J.P. and Chen, P.S. (2010), "An elastoplastic constitutive model based on modified Mohr-Coulomb criterion and its numerical implementation", Rock Soil Mech., 31(7), 2051-2058.
  12. Kawa, M., Pula, W. and Truty, A. (2021), "Probabilistic analysis of the diaphragm wall using the hardening soil-small (HSs) model", Eng. Struct., 232, 111869. https://doi.org/10.1016/j.engstruct.2021.111869.
  13. Koiter, W.T. (1953), "Stress-strain relations, uniqueness and variational theorems for elastoplastic materials with singular yield surface", Q. Appl. Math., 11, 350-354. https://doi.org/10.1090/qam/59769
  14. Lester, A.M. and Sloan, S.W. (2018), "A smooth hyperbolic approximation to the Generalised Classical yield function, including a true inner rounding of the Mohr-Coulomb deviatoric section", Comput. Geotech., 104, 331-357. https://doi.org/10.1016/j.compgeo.2017.12.002.
  15. Li, C., Li, C., Zhao, R. and Zhou, L. (2021a), "A strength criterion for rocks", Mech. Mater., 154, 103721. https://doi.org/10.1016/j.mechmat.2020.103721.
  16. Li, C., Li, C. and Zheng, H. (2021b), "Subspace tracking method for non-smooth yield surface", Comput. Math. Appl., 90, 125-134. https://doi.org/10.1016/j.camwa.2021.03.012.
  17. Mahetaji, M., Brahma, J. and Vij, R.K. (2023), "A new extended Mohr-Coulomb criterion in the space of three-dimensional stresses on the in-situ rock", Geomech. Eng., 32(1), 49-68. https://doi.org/10.12989/gae.2023.32.1.049.
  18. Matsuoka, H. and Nakai, T. (1985), "Relationship among Tresca, Mises, Mohr-Coulomb and Matsuoka-Nakai failure criteria", Soils Found., 25(4), 123-128. https://doi.org/10.3208/sandf1972.25.4_123.
  19. Menetrey, P. and Willam, K. (1995), "Triaxial failure criterion for concrete and its generalization", ACI Struct. J., 92(3), 311-318.
  20. Peric, D. and de Souza Neto, E.A. (1999), "A new computational model for Tresca plasticity at finite strains with an optimal parametrization in the principal space", Comput. Method. Appl. M., 171(3), 463-489. https://doi.org/10.1016/S0045-7825(98)00221-7.
  21. Pramthawee, P., Jongpradist, P. and Kongkitkul, W. (2011), "Evaluation of hardening soil model on numerical simulation of behaviors of high rockfill dams", Songklanakarin J. Sci. Technol., 33(3), 325-334.
  22. Pramthawee, P., Jongpradist, P. and Sukkarak, R. (2017), "Integration of creep into a modified hardening soil model for time-dependent analysis of a high rockfill dam", Comput. Geotech., 91, 104-116. http://dx.doi.org/10.1016/j.compgeo.2017.07.008.
  23. Schanz, T., Vermeer P.A. and Bonnier, P.G. (1999), "The hardening soil model: formulation and verification", Proceedings of the Beyond 2000 in Computational Geotechnics - 10 Years of PLAXIS, Balkema, Rotterdam, the Netherlands.
  24. Sui, C.Y., Shen, Y.S., Wen, Y.M. and Gao B. (2021), "Application of the modified Mohr-Coulomb yield criterion in seismic numerical simulation of tunnels", Shock Vib., article ID 9968935. https://doi.org/10.1155/2021/9968935.
  25. Sukkarak, R. Likitlersuang, S., Jongpradist, P. and Jamsawang, P. (2021), "Strength and stiffness parameters for hardening soil model of rockfill materials", Soils Found., 61, 1597-1614. https://doi.org/10.1016/j.sandf.2021.09.007.
  26. Surarak, C., Likitlersuang, S., Wanatowski, D., Balasubramaniam, A., Oh, E. and Guan, H. (2012), "Stiffness and strength parameters for hardening soil model of soft and stiff Bangkok clays", Soils Found., 52(4), 682-697. http://dx.doi.org/10.1016/j.sandf.2012.07.009.
  27. Sukkarak, R., Pramthawee, P. and Jongpradist, P. (2017), "A modified elasto-plastic model with double yield surfaces and considering particle breakage for the settlement analysis of high rockfill dams", KSCE J. Civil Eng., 21(3), 734-745. https://doi.org/10.1007/s12205-016-0867-9.
  28. Sukkarak, R., Pramthawee, P., Jongpradist, P., Kongkitkul, W. and Jamsawang, P. (2018), "Deformation analysis of high CFRD considering the scaling effects", Geomech. Eng., 14(3), 211-224. https://doi.org/10.12989/gae.2018.14.3.211.
  29. Wang, C., Ding, W. and Qiao, Y. (2014), "Development and application of hardening soil constitutive model in FLAC3D", Chinese J. Rock Mech. Eng., 33(1), 199-208. https://doi.org/10.13722/j.cnki.jrme.2014.01.015. (in Chinese)
  30. Wang, Z. (2020), "A modified Mohr-Coulomb criterion for rocks with smooth tension cutoff", Proceedings of the IOP Conf. Ser.: Earth Environ. Sci., 525, 012027. https://doi.org/10.1088/1755-1315/525/1/012027.
  31. Woo, S.I. (2023), "Critical state-based Mohr-Coulomb bounding surface model for sand under monotonic shearing", Adv. Civil Eng., article ID 8703610. https://doi.org/10.1155/2023/8703610.
  32. Wu, X. and Vanapalli, S.K. (2022), "Three-dimensional modeling of the mechanical behavior of a single pile in unsaturated expansive soils during infiltration", Comput. Geotech., 145, 104696. https://doi.org/10.1016/j.compgeo.2022.104696.
  33. Zhang, S., Wang, Q. and Zhou, W. (2019), "Implementation of the Tresca yield criterion in finite element analysis of burst capacity of pipelines", Int. J. Pressure Vessels Piping, 172, 180-187. https://doi.org/10.1016/j.ijpvp.2019.03.037.
  34. Zienkiewicz, O.C. and Pande, G.W. (1977). "Some useful forms of isotropic yield surfaces for soil and rock mechanics", Finite Element in Geomechanics, Balkema, Rotterdam, the Netherlands, 179-190.