Technical Papers
Feb 10, 2021

Anisotropic Bounding Surface Plasticity Model for Porous Media

Publication: International Journal of Geomechanics
Volume 21, Issue 4

Abstract

An anisotropic plasticity model for the description of nonisotropic mechanical behaviors of porous media is presented. This model is developed using bounding surface plasticity theory within the critical state framework. The inherent and stress-induced anisotropy has been accounted for by an anisotropic variable, which is employed with the consideration of both irrecoverable deformation and stress state. The evolution of anisotropy has been described by both rotational and distortional hardening rules. The rotational hardening rule is proposed for the consideration of bounding surface inclination induced by inherent or induced anisotropy. The distortional hardening rule is developed to capture the varying shape of bounding surface associated with the accumulation of irrecoverable deformation and anisotropy. This model has been validated through modeling the stress–strain responses of porous media under various loading conditions, including triaxial drained/undrained compression/extension tests on both isotropically and anisotropically consolidated samples. Good agreement between model simulation and experimental results has been achieved for all cases taken into consideration, demonstrating the capability of the proposed model.

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Acknowledgments

This work is supported by Open Foundation of MOE Key Laboratory of Engineering Structures of Heavy Haul Railway (Central South University) (2020JZZ02), National Natural Science Foundation of China (NSFC, No. 51978677, 51708564 and 51678578), Guangdong Natural Science Foundation (GNSF, No. 2016A030313233), and Fundamental Research Funds for the Central Universities (FRFCU, No. 19lgzd42). The financial support is gratefully acknowledged.

References

Anandarajah, A. 2000. “On influence of fabric anisotropy on the stress–strain behavior of clays.” Comput. Geotech. 27 (1): 1–17. https://doi.org/10.1016/S0266-352X(00)00005-7.
Anandarajah, A., and Y. F. Dafalias. 1986. “Bounding surface plasticity. III: Application to anisotropic cohesive soils.” J. Eng. Mech. 112 (12): 1292–1318. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:12(1292).
Anandarajah, A., N. Kuganenthira, and D. Zhao. 1996. “Variation of fabric anisotropy of kaolinite in triaxial loading.” J. Geotech. Eng. 122 (8): 633–640. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:8(633).
Banerjee, P. K., and A. S. Stipho. 1978. “Associated and non-associated constitutive relations for undrained behaviour of isotropic soft clays.” Int. J. Numer. Anal. Methods Geomech. 2 (1): 35–56. https://doi.org/10.1002/nag.1610020104.
Bardet, J. P. 1986. “Bounding surface plasticity model for sands.” J. Eng. Mech. 112 (11): 1198–1217. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:11(1198).
Burland, J. B. 1990. “On the compressibility and shear strength of natural clays.” Géotechnique 40 (3): 329–378. https://doi.org/10.1680/geot.1990.40.3.329.
Chen, Y., F. Marinelli, and G. Buscarnera. 2019. “A rotational hardening model capturing undrained failure in anisotropic soft clays.” Ind. Geotech. J. 49 (4): 369–380. https://doi.org/10.1007/s40098-018-0339-x.
Cheng, X., N. Li, and Z. Yang. 2020. “A simple anisotropic bounding surface model for saturated clay considering the cyclic degradation.” Eur. J. Environ. Civ. Eng. 24 (12): 2094–2115. https://doi.org/10.1080/19648189.2018.1549509.
Dafalias, Y. F. 1981. “A novel bounding surface constitutive law for the monotonic and cyclic hardening response of metals.” In Proc., 6th Int. Conf. SMiRT, Vol. 9P. Paris: North-Holland Publ Co, for Comm of the Eur Communities (Eur 7146).
Dafalias, Y. F. 1986. “An anisotropic critical state soil plasticity model.” Mech. Res. Commun. 13 (6): 341–347. https://doi.org/10.1016/0093-6413(86)90047-9.
Dafalias, Y. F., and L. Herrmann. 1986. “Bounding surface plasticity. II: Application to isotropic cohesive soils.” J. Eng. Mech. 112 (12): 1263–1291. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:12(1263).
Dafalias, Y. F., M. T. Manzari, and A. G. Papadimitriou. 2006. “SANICLAY: Simple anisotropic clay plasticity model.” Int. J. Numer. Anal. Methods Geomech. 30 (12): 1231–1257. https://doi.org/10.1002/nag.524.
Dafalias, Y. F., A. G. Papadimitriou, and X. S. Li. 2004. “Sand plasticity model accounting for inherent fabric anisotropy.” J. Eng. Mech. 130 (11): 1319–1333. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:11(1319).
Dafalias, Y. F., and E. P. Popov. 1975. “A model of nonlinearly hardening materials for complex loading.” Acta Mech. 21 (3): 173–192. https://doi.org/10.1007/BF01181053.
Dafalias, Y. F., and M. Taiebat. 2013. “Anatomy of rotational hardening in clay plasticity.” Géotechnique 63 (16): 1406–1418. https://doi.org/10.1680/geot.12.P.197.
Gajo, A., and D. Muir Wood. 1999. “A kinematic hardening constitutive model for sands: The multiaxial formulation.” Int. J. Numer. Anal. Methods Geomech. 23 (9): 925–965. https://doi.org/10.1002/(SICI)1096-9853(19990810)23:9%3C925::AID-NAG19%3E3.0.CO;2-M.
Gajo, A., and D. Muir Wood. 2001. “A new approach to anisotropic, bounding surface plasticity: General formulation and simulations of natural and reconstituted clay behaviour.” Int. J. Numer. Anal. Methods Geomech. 25 (3): 207–241. https://doi.org/10.1002/nag.126.
Gens, A. 1982. “Stress–strain and strength of a low plasticity clay.” Thesis, Faculty of Engineering, Univ. of London.
Graham, J., M. L. Noonan, and K. V. Lew. 1983. “Yield states and stress–strain relationships in a natural plastic clay.” Can. Geotech. J. 20 (3): 502–516. https://doi.org/10.1139/t83-058.
Habte, A. M. 2006. “Numerical and constitutive modeling of monotonic and cyclic loading in variably saturated soils.” Ph.D. thesis, School of Civil and Environmental Engineering, Univ. of New South Wales.
Hu, C., H. Liu, and W. Huang. 2012. “Anisotropic bounding-surface plasticity model for the cyclic shakedown and degradation of saturated clay.” Comput. Geotech. 44: 34–47. https://doi.org/10.1016/j.compgeo.2012.03.009.
Hwang, J.-J. 1996. “Critical state models for cyclic loading of K(o)-consolidated clay.” Master of science thesis, Microstructural Science, UMI.
Inel, S., and P. V. Lade. 1997. “Rotational kinematic hardening model for sand. Part II characteristic work hardening Law and predictions.” Comput. Geotech. 21 (3): 217–234. https://doi.org/10.1016/S0266-352X(97)00023-2.
Jiang, J., and H. I. Ling. 2010. “A framework of an anisotropic elastoplastic model for clays.” Mech. Res. Commun. 37 (4): 394–398. https://doi.org/10.1016/j.mechrescom.2010.04.004.
Jiang, J., H. I. Ling, and V. N. Kaliakin. 2012. “An associative and Non-associative anisotropic bounding surface model for clay.” J. Appl. Mech. 79 (3): 031010. https://doi.org/10.1115/1.4005958.
Jiang, J., H. I. Ling, V. N. Kaliakin, X. Zeng, and C. Hung. 2017. “Evaluation of an anisotropic elastoplastic–viscoplastic bounding surface model for clays.” Acta Geotech. 12 (2): 335–348. https://doi.org/10.1007/s11440-016-0471-7.
Khalili, N., M. A. Habte, and S. Valliappan. 2005. “A bounding surface plasticity model for cyclic loading of granular soils.” Int. J. Numer. Methods Eng. 63 (14): 1939–1960. https://doi.org/10.1002/nme.1351.
Khalili, N., M. A. Habte, and S. Zargarbashi. 2008. “A fully coupled flow deformation model for cyclic analysis of unsaturated soils including hydraulic and mechanical hystereses.” Comput. Geotech. 35 (6): 872–889. https://doi.org/10.1016/j.compgeo.2008.08.003.
Leroueil, S., D. Perret, and J. Locat. 1996. “Strain rate and structuring effects on compressibility of a young clay.” In Measuring and Modeling Time Dependent Soil Behavior, Geotechnical Special Publication 61, edited by T. C. Sheahan, and V. N. Kaliakin, 137–150. Reston, VA: ASCE.
Li, J., W. Gong, L. Li, and F. Liu. 2017. “Drained elastoplastic solution for cylindrical cavity expansion in K0-consolidated anisotropic soil.” J. Eng. Mech. 143 (11): 04017133. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001357.
Li, X. S., and Y. F. Dafalias. 2002. “Constitutive modeling of inherently anisotropic sand behavior.” J. Geotech. Geoenviron. Eng. 128 (10): 868–880. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:10(868).
Liang, R. Y., and F. Ma. 1992a. “Anisotropic Plasticity Model for Undrained Cyclic Behavior of Clays. I: Theory.” J. Geotech. Eng. 118 (2): 229–245. https://doi.org/10.1061/(ASCE)0733-9410(1992)118:2(229).
Liang, R. Y., and F. G. Ma. 1992b. “An anisotropic plasticity model for undrained cyclic behavior of clays. II: Verification.” J. Geotech. Eng. 118 (2): 246–265. https://doi.org/10.1061/(ASCE)0733-9410(1992)118:2(246).
Ling, H. I., D. Yue, V. N. Kaliakin, and N. J. Themelis. 2002. “Anisotropic elastoplastic bounding surface model for cohesive soils.” J. Eng. Mech. 128 (7): 748–758. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:7(748).
Liu, M. D., and J. P. Carter. 2002. “A structured cam clay model.” Can. Geotech. J. 39 (6): 1313–1332. https://doi.org/10.1139/t02-069.
Lo, K. Y. 1965. “Stability of slopes in anisotropic soils.” J. Soil Mech. Found. Div. 90 (5): 133–155.
Ma, J. 2016. “An elastoplastic model for partially saturated collapsible rocks.” Rock Mech. Rock Eng. 49 (2): 455–465. https://doi.org/10.1007/s00603-015-0751-9.
Ma, J., G. Zhao, and N. Khalili. 2016a. “An elastoplastic damage model for fractured porous media.” Mech. Mater. 100: 41–54. https://doi.org/10.1016/j.mechmat.2016.06.006.
Ma, J., G. Zhao, and N. Khalili. 2016b. “A fully coupled flow deformation model for elasto-plastic damage analysis in saturated fractured porous media.” Int. J. Plast. 76: 29–50. https://doi.org/10.1016/j.ijplas.2015.07.011.
Martin, R. T., and C. C. Ladd. 1975. “Fabric of consolidated kaolinite.” Clays Clay Miner. 23 (1): 17–25. https://doi.org/10.1346/CCMN.1975.0230103.
Nieto Leal, A., V. N. Kaliakin, and M. Mashayekhi. 2018. “Improved rotational hardening rule for cohesive soils and definition of inherent anisotropy.” Int. J. Numer. Anal. Methods Geomech. 42 (3): 469–487. https://doi.org/10.1002/nag.2750.
Ohta, H., and A. Nishihara. 1985. “Anisotropy of undrained shear strength of clays under axi-symmetric loading conditions.” Soils Found. 25 (2): 73–86. https://doi.org/10.3208/sandf1972.25.2_73.
Pestana, J. M., and A. J. Whittle. 1999. “Formulation of a unified constitutive model for clays and sands.” Int. J. Numer. Anal. Methods Geomech. 23 (12): 1215–1243. https://doi.org/10.1002/(SICI)1096-9853(199910)23:12%3C1215::AID-NAG29%3E3.0.CO;2-F.
Rezania, M., M. Taiebat, and E. Poletti. 2016. “A viscoplastic SANICLAY model for natural soft soils.” Comput. Geotech. 73: 128–141. https://doi.org/10.1016/j.compgeo.2015.11.023.
Roscoe, K. H., and J. B. Burland. 1968. “On the generalised stress-strain behavior of wet clay.” In Engineering plasticity, edited by J. H. a. F. A. Leckie, 535–609. Cambridge, UK: Cambridge University Press.
Rowe, P. W. 1962. “The stress-dilatancy relation for static equilibrium of an assembly of particles in contact.” Proc. R. Soc. London, Ser. A 269 (1339): 500–527. https://doi.org/10.2307/2414551.
Schofield, A. N., and C. P. Worth. 1968. Critical state soil mechanics. New York: McGraw-Hill.
Sekiguchi, H., and H. Ohta. 1977. “Induced anisotropy and time dependency in clays.” In Proc., 9th Int. Conf. on Soil Mechanics and Foundation Engineering, 229–237. Washington, DC: The National Academies of Sciences, Engineering, and Medicine.
Sheng, D., S. W. Sloan, and H. S. Yu. 2000. “Aspects of finite element implementation of critical state models.” Comput. Mech. 26 (2): 185–196. https://doi.org/10.1007/s004660000166.
Sivakumar, V., I. G. Doran, J. Graham, and A. Johnson. 2001. “The effect of anisotropic elasticity on the yielding characteristics of overconsolidated natural clay.” Can. Geotech. J. 38 (1): 125–137. https://doi.org/10.1139/t00-074.
Stipho, A. S. 1978. “Experimental and theoretical investigation of the behaviour of anisotropically consolidated kaolin.” Ph.D. thesis, School of Engineering, Cardiff Univ.
Sun, D. A., H. Matsuoka, Y. P. Yao, and H. Ishii. 2004. “An anisotropic hardening elastoplastic model for clays and sands and its application to FE analysis.” Comput. Geotech. 31 (1): 37–46. https://doi.org/10.1016/j.compgeo.2003.11.003.
Wang, R., P. Fu, J.-M. Zhang, and Y. F. Dafalias. 2017. “Evolution of various fabric tensors for granular media toward the critical state.” J. Eng. Mech. 143 (10): 04017117. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001342.
Wensrich, C. M., J. Pineda, V. Luzin, L. Suwal, E. H. Kisi, and H. Allameh-Haery. 2018. “Deformation and fabric in compacted clay soils.” Phys. Rev. Appl 9 (5): 054003. https://doi.org/10.1103/PhysRevApplied.9.054003.
Wheeler, S. J., A. Näätänen, M. Karstunen, and M. Lojander. 2003. “An anisotropic elastoplastic model for soft clays.” Can. Geotech. J. 40 (2): 403–418. https://doi.org/10.1139/t02-119.
Xiao, Y., H. Liu, J. Zhu, W. Shi, and M. Liu. 2011. “A 3D bounding surface model for rockfill materials.” Sci. China Technol. Sci. 54 (11): 2904–2915. https://doi.org/10.1007/s11431-011-4554-2.
Xiao, Y., Z. Sun, A. W. Stuedlein, C. Wang, Z. Wu, and Z. Zhang. 2020. “Bounding surface plasticity model for stress-strain and grain-crushing behaviors of rockfill materials.” Geosci. Front. 11 (2): 495–510. https://doi.org/10.1016/j.gsf.2019.06.010.
Yang, C., J. P. Carter, and S. Yu. 2015a. “Comparison of model predictions of the anisotropic plasticity of lower cromer till.” Comput. Geotech. 69: 365–377. https://doi.org/10.1016/j.compgeo.2015.06.009.
Yang, C., D. Sheng, J. P. Carter, and S. W. Sloan. 2015b. “Modeling the plastic anisotropy of lower cromer till.” Comput. Geotech. 69: 22–37. https://doi.org/10.1016/j.compgeo.2015.04.013.
Yin, Z.-Y., C. S. Chang, M. Karstunen, and P.-Y. Hicher. 2010. “An anisotropic elastic–viscoplastic model for soft clays.” Int. J. Solids Struct. 47 (5): 665–677. https://doi.org/10.1016/j.ijsolstr.2009.11.004.
Zdravkovic, L., and J. Carter. 2008. “Contributions to géotechnique 1948–2008: Constitutive and numerical modeling.” Géotechnique 58 (5): 405–412. https://doi.org/10.1680/geot.2008.58.5.405.
Zdravković, L., D. M. Potts, and D. W. Hight. 2002. “The effect of strength anisotropy on the behaviour of embankments on soft ground.” Géotechnique 52 (6): 447–457. https://doi.org/10.1680/geot.2002.52.6.447.
Zhang, H., Q. Chen, J. Chen, and J. Wang. 2016. “Unified expression of rotational hardening in clay plasticity.” Int. J. Geomech. 16 (6): 06016004. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000647.
Zhou, C., S. Leroueil, M. Fafard, and S. Ghorbel. 2017. “Constitutive modeling of kinematic hardening behavior of saturated anisotropic soils.” Int. J. Geomech. 17 (3): 04016063. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000732.
Zhou, C., J. Yin, J. Zhu, and C. Cheng. 2005. “Elastic anisotropic viscoplastic modeling of the strain-rate-dependent stress–strain behavior of K0-consolidated natural marine clays in triaxial shear tests.” Int. J. Geomech. 5 (3): 218–232. https://doi.org/10.1061/(ASCE)1532-3641(2005)5:3(218).

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International Journal of Geomechanics
Volume 21Issue 4April 2021

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Received: Apr 18, 2020
Accepted: Nov 9, 2020
Published online: Feb 10, 2021
Published in print: Apr 1, 2021
Discussion open until: Jul 10, 2021

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Jianjun Ma
Associate Professor, School of Civil Engineering, Sun Yat-Sen Univ., Guangzhou 510275, China; Southern Marine Science and Engineering Guangdong Laboratory (Zhuahai), Guangdong Key Laboratory of Oceanic Civil Engineering, Guangdong Research Center for Underground Space Exploitation Technology, Zhuhai 519082, China; MOE Key Laboratory of Engineering Structures of Heavy Haul Railway, Central South Univ., Changsha 410075, China.
Junwei Guan
Postgraduate Researcher, School of Civil Engineering, Sun Yat-Sen Univ., Guangzhou 510275, China.
Senior Lecturer, School of Civil and Environmental Engineering, Queensland Univ. of Technology, Brisbane, QLD 4000, Australia. ORCID: https://orcid.org/0000-0003-3439-3888.
Professor, School of Aeronautics and Astronautics, Sun Yat-Sen Univ., Shenzhen/Guangzhou 510006, China (corresponding author). ORCID: https://orcid.org/0000-0002-0122-6226. Email: [email protected]

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