A Nonorthogonal Elastoplastic Model for Overconsolidated Clay
Publication: International Journal of Geomechanics
Volume 25, Issue 2
Abstract
The constitutive model in geotechnical engineering plays a critical role, driving the need for ongoing research and improvement. In this study, by utilizing a single yield curve and only one hardening parameter, a nonorthogonal elastoplastic (NOEP) constitutive model for the overconsolidated (OC) clay is established within the framework of the NOEP model. The nonorthogonal plastic flow rule, based on the Riemann–Liouville fractional derivative, was employed to determine the plastic flow direction, which is nonorthogonal to the improved yield curve. Furthermore, a novel hardening parameter is proposed to capture the magnitude of plastic strain increment for OC clays. This is achieved by comparing deformation behaviors in OC clays with two distinct degrees of overconsolidation. Additionally, it is further enhanced by the integration of a newly proposed potential stress ratio. The proposed model requires only eight parameters, and its performance is evaluated by its predictions with test results for OC clays subjected to drained or undrained triaxial stress conditions. This study is expected to offer valuable insights and a better approach toward understanding and capturing the deformation behaviors of OC clays.
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Data Availability Statement
Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This study was supported by the National Natural Science Foundation of China (Grant Nos. 52108294, 52278323, and 52025084), the Pyramid Talent Training Project of BUCEA (JDYC20220812), and the Post Graduate Innovation Project of BUCEA (PG2023037).
References
Asaoka, A., M. Nakano, and T. Noda. 2000. “Superloading yield surface concept for highly structured soil behavior.” Soils Found. 40 (2): 99–110. https://doi.org/10.3208/sandf.40.2_99.
Atkinson, J. 2007. “Peak strength of overconsolidated clays.” Géotechnique 57 (2): 127–135. https://doi.org/10.1680/geot.2007.57.2.127.
Collins, I. F., and G. T. Houlsby. 1997. “Application of thermomechanical principles to the modelling of geotechnical materials.” Proc. R. Soc. London, Ser. A 453 (1964): 1975–2001. https://doi.org/10.1098/rspa.1997.0107.
Dafalias, Y. F. 1986. “Bounding surface plasticity. I: Mathematical foundation and hypoplasticity.” J. Eng. Mech. 112 (9): 966–987. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:9(966).
Gao, Z. W., J. D. Zhao, and Z. Y. Yin. 2017. “Dilatancy relation for overconsolidated clay.” Int. J. Geomech. 17 (5): 06016035. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000793.
Gue, C. Y., M. J. Wilcock, M. M. Alhaddad, M. Z. E. B. Elshafie, K. Soga, and R. J. Mair. 2017. “Tunnelling close beneath an existing tunnel in clay—Perpendicular undercrossing.” Géotechnique 67 (9): 795–807. https://doi.org/10.1680/jgeot.SiP17.P.117.
Guo, R. P., and G. X. Li. 2008. “Elasto-plastic constitutive model for geotechnical materials with strain-softening behaviour.” Comput. Geosci. 34 (1): 14–23. https://doi.org/10.1016/j.cageo.2007.03.012.
Hashiguchi, K., and Z.-P. Chen. 1998. “Elastoplastic constitutive equation of soils with the subloading surface and the rotational hardening.” Int. J. Numer. Anal. Methods Geomech. 22: 197–227.https://doi.org/<197::AID-NAG914>3.0.CO;2-T.
Jocković, S., and M. Vukićević. 2017. “Bounding surface model for overconsolidated clays with new state parameter formulation of hardening rule.” Comput. Geotech. 83: 16–29. https://doi.org/10.1016/j.compgeo.2016.10.013.
Lade, P. V. 1990. “Single-hardening model with application to NC clay.” J. Geotech. Eng. 116 (3): 394–414. https://doi.org/10.1061/(ASCE)0733-9410(1990)116:3(394).
Li, X. S., and Y. F. Dafalias. 2000. “Dilatancy for cohesionless soils.” Géotechnique 50 (4): 449–460. https://doi.org/10.1680/geot.2000.50.4.449.
Liang, J. Y., D. C. Lu, X. L. Du, C. Ma, Z. W. Gao, and J. Y. Han. 2022. “A 3D non-orthogonal elastoplastic constitutive model for transversely isotropic soil.” Acta Geotech. 17: 19–36. https://doi.org/10.1007/s11440-020-01095-4.
Liang, J. Y., D. C. Lu, X. Zhou, X. L. Du, and W. Wu. 2019. “Non-orthogonal elastoplastic constitutive model with the critical state for clay.” Comput. Geotech. 116: 103200. https://doi.org/10.1016/j.compgeo.2019.103200.
Likitlersuang, S., and G. T. Houlsby. 2006. “Development of hyperplasticity models for soil mechanics.” Int. J. Numer. Anal. Methods Geomech. 30 (3): 229–254. https://doi.org/10.1002/nag.484.
Liu, E. L., and H. L. Xing. 2009. “A double hardening thermo-mechanical constitutive model for overconsolidated clays.” Acta Geotech. 4 (1): 1–6. https://doi.org/10.1007/s11440-008-0053-4.
Lu, D. C., J. Y. Liang, X. L. Du, C. Ma, and Z. W. Gao. 2019a. “Fractional elastoplastic constitutive model for soils based on a novel 3D fractional plastic flow rule.” Comput. Geotech. 105: 277–290. https://doi.org/10.1016/j.compgeo.2018.10.004.
Lu, D. C., X. Zhou, X. L. Du, and G. S. Wang. 2019b. “A 3D fractional elastoplastic constitutive model for concrete material.” Int. J. Solids Struct. 165: 160–175. https://doi.org/10.1016/j.ijsolstr.2019.02.004.
Marchi, M., G. Gottardi, and K. Soga. 2014. “Fracturing pressure in clay.” J. Geotech. Geoenviron. Eng. 140 (2): 04013008. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001019.
Mita, K. A., G. R. Dasari, and K. W. Lo. 2004. “Performance of a three-dimensional Hvorslev–modified Cam clay model for overconsolidated clay.” Int. J. Geomech. 4 (4): 296–309. https://doi.org/10.1061/(ASCE)1532-3641(2004)4:4(296).
Nakai, T., and M. Hinokio. 2004. “A simple elastoplastic model for normally and over consolidated soils with unified material parameters.” Soils Found. 44 (2): 53–70. https://doi.org/10.3208/sandf.44.2_53.
Nakano, M., K. Nakai, T. Noda, and A. Asaoka. 2005. “Simulation of shear and one-dimensional compression behavior of naturally deposited clays by super or subloading yield surface cam-clay model.” Soils Found. 45 (1): 141–151.
Pestana, J. M., A. J. Whittle, and A. Gens. 2002. “Evaluation of a constitutive model for clays and sands: Part II—Clay behaviour.” Int. J. Numer. Anal. Methods Geomech. 26 (11): 1123–1146. https://doi.org/10.1002/nag.238.
Roscoe, K. H., and J. B. Burland. 1968. “On the generalised stress-strain behaviour of ‘wet’ clay.” In Engineering plasticity, edited by J. Heyman and F. A. Leckie, 535–609. Cambridge, England: Cambridge University Press.
Shen, W. Q., S. Y. Liu, W. Y. Xu, and J. F. Shao. 2022. “An elastoplastic damage constitutive model for rock-like materials with a fractional plastic flow rule.” Int. J. Rock Mech. Min. Sci. 156: 105140. https://doi.org/10.1016/j.ijrmms.2022.105140.
Shi, X. S., I. Herle, and K. Bergholz. 2017. “A nonlinear Hvorslev surface for highly overconsolidated soils: Elastoplastic and hypoplastic implementations.” Acta Geotech. 12 (4): 809–823. https://doi.org/10.1007/s11440-016-0485-1.
Sun, Y. F., and W. Sumelka. 2019. “State-dependent fractional plasticity model for the true triaxial behaviour of granular soil.” Arch. Mech. 71 (1): 23–47.
Sun, Y. F., and W. Sumelka. 2021. “Multiaxial stress-fractional plasticity model for anisotropically overconsolidated clay.” Int. J. Mech. Sci. 205: 106598. https://doi.org/10.1016/j.ijmecsci.2021.106598.
Tong, C. X., H. W. Liu, and H. C. Li. 2022. “Constitutive modeling of normally and over-consolidated clay with a high-order yield function.” Mathematics 10 (9): 1376. https://doi.org/10.3390/math10091376.
Wan, Z., C. C. Song, S. T. Xue, and L. Y. Xie. 2021. “Elastoplastic constitutive model describing dilatancy behavior of overconsolidated clay.” Int. J. Geomech. 21 (3): 04021008. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001947.
Wang, G. S., D. C. Lu, X. Zhou, Y. F. Wu, X. L. Du, and Y. Xiao. 2020. “A stress-path-independent damage variable for concrete under multiaxial stress conditions.” Int. J. Solids Struct. 206: 59–74. https://doi.org/10.1016/j.ijsolstr.2020.09.012.
Wang, S., and W. Wu. 2021. “Validation of a simple hypoplastic constitutive model for overconsolidated clays.” Acta Geotech. 16 (1): 31–41. https://doi.org/10.1007/s11440-020-01105-5.
Xiao, Y., and C. S. Desai. 2019. “Constitutive modeling for overconsolidated clays based on disturbed state concept. I: Theory.” Int. J. Geomech. 19 (9): 04019101. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001474.
Xiao, Y., Y. F. Sun, F. Yin, H. L. Liu, and J. Xiang. 2017. “Constitutive modeling for transparent granular soils.” Int. J. Geomech. 17 (7): 0000857. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000857.
Yao, Y. P., Z. W. Gao, J. D. Zhao, and Z. Wan. 2012. “Modified UH model: Constitutive modeling of overconsolidated clays based on a parabolic Hvorslev envelope.” J. Geotech. Geoenviron. Eng. 138 (7): 860–868. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000649.
Yao, Y.-P., W. Hou, and A.-N. Zhou. 2009. “UH model: Three-dimensional unified hardening model for overconsolidated clays.” Géotechnique 59 (5): 451–469. https://doi.org/10.1680/geot.2007.00029.
Yao, Y. P., D. A. Sun, and H. Matsuoka. 2008. “A unified constitutive model for both clay and sand with hardening parameter independent on stress path.” Comput. Geotech. 35 (2): 210–222. https://doi.org/10.1016/j.compgeo.2007.04.003.
Yin, Z.-Y., Q. Xu, and P.-Y. Hicher. 2013. “A simple critical-state-based double-yield-surface model for clay behavior under complex loading.” Acta Geotech. 8 (5): 509–523. https://doi.org/10.1007/s11440-013-0206-y.
Zhang, J. R., L. Li, and D. A. Sun. 2020. “Similarity solution for undrained cylindrical cavity contraction in anisotropic modified Cam-clay model soils.” Comput. Geotech. 120: 103405. https://doi.org/10.1016/j.compgeo.2019.103405.
Zhang, S., G. L. Ye, and J. H. Wang. 2018. “Elastoplastic model for overconsolidated clays with focus on volume change under general loading conditions.” Int. J. Geomech. 18 (3): 04018005. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001101.
Zhou, A. N., and Y. P. Yao. 2018. “Revising the unified hardening model by using a smoothed Hvorslev envelope.” J. Rock Mech. Geotech. Eng. 10 (2018): 778–790. https://doi.org/10.1016/j.jrmge.2017.10.008.
Zhou, F. X., L. Y. Wang, and H. B. Liu. 2021. “A fractional elasto-viscoplastic model for describing creep behavior of soft soil.” Acta Geotech. 16: 67–76. https://doi.org/10.1007/s11440-020-01008-5.
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Published In
International Journal of Geomechanics
Volume 25 • Issue 2 • February 2025
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jan 18, 2024
Accepted: Aug 16, 2024
Published online: Dec 5, 2024
Published in print: Feb 1, 2025
Discussion open until: May 5, 2025
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