Modeling of soils using isotropic and anisotropic models

Articles in Press

Document Type : Research Paper

Authors

1 Faculty of Engineering, Tarbiat Modares University, Tehran, Iran.

2 PoreLab, Department of Civil and Environmental Eng., Norwegian University of Science and Technology (NTNU), Trondheim, Norway.

10.22059/ijmge.2025.381819.595192

Abstract

In this study, two behavioral models—unified and multilaminate—are employed to simulate soil behavior. The unified model incorporates a non-associated flow rule along with the critical state concept. Additionally, the sub-loading surface concept is adopted to capture a smooth elastic-plastic transition. For numerical implementation, the implicit Euler method is used. The multilaminate model is based on a 13-plane framework, in which each plane exhibits elastic-plastic behavior. The overall soil response is obtained by integrating the elastoplastic responses of the individual planes oriented in various directions at a material point. A set of unconventional constitutive equations is applied to each plane. This model captures soil softening behavior more realistically due to the use of a non-classical plasticity approach. Moreover, it accounts for the effect of induced anisotropy. To evaluate the models, four clay samples subjected to monotonic loading—under both drained and undrained conditions—were analyzed using both the unified and multilaminate models and compared with experimental data. The results demonstrate that the unified model offers a more favorable representation of soil behavior.

Keywords

Main Subjects

References

[1] Roscoe, K. H. (1963). Mechanical behaviour of an idealised 'wet clay'. In Proceedings of the 2nd European Conference on Soil Mechanics (pp. 47-54). http://www-civ.eng.cam.ac.uk/geotech_new/people/ans/wetclay.pdf
[2] Roscoe, K. H., Schofield, A., & Thurairajah, A. (1963). Yielding of clays in states wetter than critical. Geotechnique, 13(3), 211-240. Doi: https://doi.org/10.1680/GEOT.1963.13.3.211
[3] Pender, M. J. (1978). A model for the behaviour of overconsolidated soil. Geotechnique, 28(1), 1-25. Doi: https://doi.org/10.1680/geot.1978.28.1.1
[4] Chen, Y. N., & Yang, Z. X. (2017). A family of improved yield surfaces and their application in modeling of isotropically over-consolidated clays. Computers and Geotechnics, 90, 133-143. Doi: https://doi.org/10.1016/j.compgeo.2017.06.007
[5] Roscoe, K., & Burland, J. B. (1968). On the generalized stress-strain behaviour of wet clay. Doi: https://doi.org/10.1016/0022-4898(70)90160-6
[6] Naylor, D. J. (1985). A continuous plasticity version of the critical state model. International Journal for Numerical Methods in Engineering, 21(7), 1187-1204. Doi:  https://doi.org/10.1002/nme.1620210703
[7] Paston, M., Zienkiewicz, O. C., & Leung, K. H. (1985). Simple model for transient soil loading in earthquake analysis. II. Non-associative models for sands. International Journal for Numerical and Analytical Methods in Geomechanics, 9(5). Doi: https://doi.org/10.1002/nag.1610090506
[8] Been, K., & Jefferies, M. G. (1985). A state parameter for sands. Géotechnique, 35(2), 99-112. Doi: https://doi.org/10.1680/geot.1985.35.2.99
[9] Nova, R., & Wood, D. M. (1979). A constitutive model for sand in triaxial compression. International Journal for Numerical and Analytical Methods in Geomechanics, 3(3), 255-278. Doi: https://doi.org/10.1002/nag.1610030305
[10] Jefferies, M. G. (1993). Nor-Sand: a simple critical state model for sand. Géotechnique, 43(1), 91-103. Doi: https://doi.org/10.1680/geot.1993.43.1.91
[11] Wroth, C. P., & Bassett, R. H. (1965). A stress–strain relationship for the shearing behaviour of a sand. Géotechnique, 15(1), 32-56. Doi: https://doi.org/10.1680/geot.1965.15.1.32
[12] Jocković, S., & Vukićević, M. (2017). Bounding surface model for overconsolidated clays with new state parameter formulation of hardening rule. Computers and Geotechnics, 83, 16-29. Doi: https://doi.org/10.1016/j.compgeo.2016.10.013
[13] Jian, L. I., Chen, S., & Jiang, L. (2016). On implicit integration of the bounding surface model based on swell–shrink rules. Applied Mathematical Modelling, 40(19-20), 8671-8684.  Doi: https://doi.org/10.1016/j.apm.2016.05.014
[14] Khalili, N., Habte, M. A., & Valliappan, S. (2005). A bounding surface plasticity model for cyclic loading of granular soils. International Journal for Numerical Methods in Engineering, 63(14), 1939-1960. Doi: https://doi.org/10.1002/nme.1351
[15] Ling, H. I., & Yang, S. (2006). Unified sand model based on the critical state and generalized plasticity. Journal of Engineering Mechanics, 132(12), 1380-1391. Doi: https://doi.org/10.1061/(ASCE)0733-9399(2006)132:12(1380)
[16] Manzari, M. T., & Dafalias, Y. F. (1997). A critical state two-surface plasticity model for sands. Géotechnique, 47(2), 255-272. Doi: https://doi.org/10.1680/geot.1997.47.2.255
[17] da Fonseca, A. V., Molina-Gómez, F., Ferreira, C., & Quintero, J. (2023). Modelling the critical state behaviour of granular soils: Application of NorSand constitutive law to TP-Lisbon sand. Geomechanics and Engineering, 34(3), 317-328. Doi: https://doi.org/10.12989/gae.2023.34.3.317
[18] Yu, H. S. (1998). CASM: A unified state parameter model for clay and sand. International Journal for Numerical and Analytical Methods in Geomechanics, 22(8), 621-653. Doi: https://doi.org/10.1002/(SICI)1096-9853(199808)22:8<621::AID-NAG937>3.0.CO;2-8
[19] Yu, H. S., & Khong, C. D. (2003). Bounding surface formulation of a unified critical state model for clay and sand. In Deformation Characteristics of Geomaterials, IS Lyon 2003 (pp. 1111-1118). Doi: https://doi.org/10.1016/j.mechrescom.2006.06.010
[20] Fincato, R., & Tsutsumi, S. (2017). Closest-point projection method for the extended subloading surface model. Acta Mechanica, 228, 4213-4233. Doi: https://doi.org/10.1007/s00707-017-1926-0
[21] Hu, C., & Liu, H. (2014). Implicit and explicit integration schemes in the anisotropic bounding surface plasticity model for cyclic behaviours of saturated clay. Computers and Geotechnics, 55, 27-41. Doi:  https://doi.org/10.1016/j.compgeo.2013.07.012
[22] Rouainia, M., & Muir Wood, D. (2001). Implicit numerical integration for a kinematic hardening soil plasticity model. International Journal for Numerical and Analytical Methods in Geomechanics, 25(13), 1305-1325. Doi:  https://doi.org/10.1002/nag.179
[23] Manzari, M. T., & Nour, M. A. (1997). On implicit integration of bounding surface plasticity models. Computers & Structures, 63(3), 385-395.  Doi: https://doi.org/10.1016/S0045-7949(96)00373-2
[24] Moghadam, S. I., Taheri, E., Ahmadi, M., & Ghoreishian Amiri, S. A. (2022). Unified bounding surface model for monotonic and cyclic behaviour of clay and sand. Acta Geotechnica, 17(10), 4359-4375. Doi: https://doi.org/10.1007/s11440-022-01521-9
[25] Li, X. S., & Dafalias, Y. F. (2000). Dilatancy for cohesionless soils. Géotechnique, 50(4), 449-460. Doi: https://doi.org/10.1680/geot.2000.50.4.449
[26] Skempton, A. W., & Brown, J. D. (1961). A landslide in boulder clay at Selset, Yorkshire. Geotechnique, 11(4), 280-293. Doi: https://doi.org/10.1680/sposm.02050.0016
[27] Stark, T. D., Ebeling, R. M., & Vettel, J. J. (1994). Hyperbolic stress-strain parameters for silts. Journal of Geotechnical Engineering, 120(2), 420-441. Doi: https://doi.org/10.1061/(ASCE)0733-9410(1994)120:2(420)
[28] Bishop, A. W., Webb, D. L., & Lewin, P. I. (1965). Undisturbed samples of London Clay from the Ashford Common shaft: strength–effective stress relationships. Geotechnique, 15(1), 1-31. Doi: https://doi.org/10.1680/geot.1965.15.1.1
[29] Wesley, L. D. (1990). Influence of structure and composition on residual soils. Journal of geotechnical engineering, 116(4), 589-603.‏ Doi: https://doi.org/10.1061/(ASCE)0733-9410(1990)116:4(589)
[30] Jeong, S., Ko, J., Song, S., & Kim, J. (2024). The behaviors of a Korean weathered soil under monotonic loadings. Geomechanics and Engineering, 38(2), 157-164. Doi: . https://doi.org/10.12989/gae.2024.38.2.157
[31] Bella, G., & Musso, G. (2024). Liquefaction susceptibility of silty tailings under monotonic triaxial tests in nearly saturated conditions. Geomechanics and Engineering: An International Journal, 36(3), 247-258. Doi: https://doi.org/10.12989/gae.2024.36.3.247
[32] Yu, H. S. (2007). Plasticity and Geotechnics (Vol. 13). Springer Science & Business Media. Doi: https://doi.org/10.1007/978-0-387-33599-5
[33] Schofield, A. N., & Wroth, P. (1968). Critical state soil mechanics (Vol. 310). London: McGraw-Hill.  Doi: http://www-civ.eng.cam.ac.uk/geotech_new/publications/schofield_wroth_1968.pdf
[34] Yu, H. S., Khong, C., & Wang, J. (2007). A unified plasticity model for cyclic behaviour of clay and sand. Mechanics Research Communications, 34(2), 97-114.  Doi: . https://doi.org/10.1016/j.mechrescom.2006.06.010
[35] Hashiguchi, K. (2017). Foundations of elastoplasticity: subloading surface model. New York: Springer. Doi: https://doi.org/10.1007/978-3-030-93138-4
[36] Dafalias, Y. F., & Popov, E. P. (1975). A model of nonlinearly hardening materials for complex loading. Acta Mechanica, 21(3), 173-192. Doi: https://doi.org/10.1007/BF01181053
[37] Hashiguchi, K., Ueno, M., & Chen, Z. P. (1996). Elastoplastic constitutive equation of soils based on the concepts of subloading surface and rotational hardening. Doboku Gakkai Ronbunshu, 1996(547), 127-144.  Doi: https://doi.org/10.1002/(SICI)10969853(199803)22:3<197::AID-NAG914>3.0.CO;2-T
[38] Hashiguchi, K. (1989). Subloading surface model in unconventional plasticity. International Journal of Solids and Structures, 25(8), 917-945. Doi: https://doi.org/10.1016/0020-7683(89)90038-3
[39] Dafalias, Y. F. (1981). The concept and application of the bounding surface in plasticity theory. In Physical Non-Linearities in Structural Analysis: Symposium Senlis, France May 27–30, 1980 (pp. 56-63). Berlin, Heidelberg: Springer Berlin Heidelberg. Doi: https://doi.org/10.1007/978-3-642-81582-9_9
[40] Hu, C., & Liu, H. (2015). A new bounding-surface plasticity model for cyclic behaviors of saturated clay. Communications in Nonlinear Science and Numerical Simulation, 22(1-3), 101-119. Doi: https://doi.org/10.1016/j.cnsns.2014.10.023
[41] Dafalias, Y. F., & Herrmann, L. R. (1986). Bounding surface plasticity. II: Application to isotropic cohesive soils. Journal of Engineering Mechanics, 112(12), 1263-1291. Doi: https://doi.org/10.1061/(ASCE)0733-9399(1986)112:12(1263)
[42] Lu, Y., Zhu, W. X., Ye, G. L., & Zhang, F. (2021). A unified constitutive model for cemented/non-cemented soils under monotonic and cyclic loading. Acta Geotechnica, 16(1), 1-19.  Doi: https://doi.org/10.1007/s11440-021-01348-w
[43] Wang, R., Cao, W., Xue, L., & Zhang, J. M. (2021). An anisotropic plasticity model incorporating fabric evolution for monotonic and cyclic behavior of sand. Acta Geotechnica, 16(1), 43–65. Doi: https://doi.org/10.1007/s11440-020-00984-y
[44] Rezania, M., & Dejaloud, H. (2021). BS-CLAY1: Anisotropic bounding surface constitutive model for natural clays. Computers and Geotechnics, 135, 104099.  Doi: https://doi.org/10.1016/j.compgeo.2021.104099
[45] Rezania, M., Dejaloud, H.  (2022). A bounding surface constitutive model with a moving projection centre for highly overconsolidated clays. 
[46] Gao, Z., Zhao, J., & Yin, Z. Y. (2017). Dilatancy relation for overconsolidated clay. International Journal of Geomechanics, 17(5), 06016035. Doi: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000793
[47] Verbrugge, J. C., & Schroeder, C. (2018). Geotechnical Correlations for Soils and Rocks. John Wiley & Sons. Doi:10.1002/9781119482819
[48] Schuller, H., & Schweiger, H. F. (2002). Application of a multilaminate model to simulation of shear band formation in NATM-tunnelling. Computers and Geotechnics, 29(7), 501-524. Doi: https://doi.org/10.1016/S0266-352X(02)00013-7
[49] Dashti, H., Sadrnejad, S. A., & Ganjian, N. (2017). Modification of a constitutive model in the framework of a multilaminate method for post-liquefaction sand. Latin American Journal of Solids and Structures, 14, 1569-1593. Doi: https://doi.org/10.1590/1679-78253841
[50] Dashti, H., Sadrnejad, S. A., & Ganjian, N. (2019). A novel semi-micro multilaminate elasto-plastic model for the liquefaction of sand. Soil Dynamics and Earthquake Engineering, 124, 121-135. Doi: https://doi.org/10.1016/j.soildyn.2019.05.031
[51] Sadrnejad, S. A., & Hoseinzadeh, M. R. (2019). Multi-laminate rate-dependent modelling of static and dynamic concrete behaviors through damage formulation. Scientia Iranica, 26(3), 1194-1205. Doi: 20.1001.1.10263098.2019.26.3.9.2
[52] Peyman, F., & Sadrnejad, S. A. (2019). Numerical Analysis of Sand Behavior based on Modified Multi-laminate Model. International Journal of New Technology and Research, 2(8), 263445.  
[53] Sadrnejad, S., & Ghoreyshian, A. S. (2010). A simple unconventional plasticity model within the multilaminate framework. http://ijce.iust.ac.ir/article-1-456-en.html
[54] Ghoreishian Amiri, S. A. (2014). Application of the multi-laminate sub-loading surface model in the simulation of a pipe-jacking operation. Numerical Methods in Civil Engineering, 1(2), 41-47.  Doi: https://doi.org/10.29252/NMCE.1.2.41
 
International Journal of Mining and Geo-Engineering

Articles in Press, Accepted Manuscript
Available Online from 08 July 2025

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