Elastoplastic Model of Sand Based on Double-State Parameters under Complex Loading Conditions
Publication: International Journal of Geomechanics
Volume 21, Issue 2
Abstract
Based on the existing unified hardening model, the double-state parameters unified hardening (DPUH) model is proposed, which can take into account the initial density and confining pressure dependent characteristics and stress-induced anisotropy of geotechnical materials. The DPUH model uses 11 material parameters, whose physical significance is clear. It has the following characteristics: (1) the state parameter χ is introduced to reflect the effect of initial density on deformation and shear strength under monotonic loading; (2) the stress state parameter R is used to reflect the influence of stress history on the current elastoplastic modulus and strength; (3) in order to reflect the influence of stress-induced anisotropy on the stress–strain relationship, the rotational hardening rules are introduced to establish the mixed hardening parameters that meet the critical state condition and take into account the isotropic compression and rotation-hardening characteristics; (4) the double-state parameters model can be used to describe the cyclic mobility phenomenon under cyclic loading conditions. By comparing the test data with prediction results of sand, it can be adopted to simulate the stress–strain relationship for sand with a different initial density and confining pressure under complex loading conditions.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
This work is supported by the National Natural Science Foundation of China (NSFC) (Project No. 11402260).
References
Asaoka, A., T. Noda, and E. Yamada. 2002. “An elasto-plastic description of two distinct volume change mechanisms of soils.” Soils Found. 42 (5): 47–57. https://doi.org/10.3208/sandf.42.5_47.
Been, K., M. G. Jefferies, and J. Hachey. 1991. “The critical state of sands.” Géotechnique 41 (3): 365–381. https://doi.org/10.1680/geot.1991.41.3.365.
Chowdhury, E. Q., T. Nakai, M. Tawada, and S. Yamada. 1999. “A model for clay using modified stress under various loading conditions with the application of subloading concept.” Soils Found. 39 (6): 103–116. https://doi.org/10.3208/sandf.39.6_103.
Dafalias, Y. F., D. E. Panayotounakos, and Z. Pitouras. 2008. “Stress field due to elastic mass growth on spherical and cylindrical.” Int. J. Solids Struct. 45: 4629–4647.
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 L. R. Herrmann. 1986a. “Bounding surface plasticity. I: Mathematical foundation and hypoplasticity.” J. Eng. Mech. 112: 966–987. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:9(966).
Dafalias, Y. F., and L. R. Herrmann. 1986b. “Bounding surface plasticity. II: Application to isotropic cohesive soils.” J. Eng. Mech. 112: 1263–1291. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:12(1263).
Dafalias, Y. F. 2016. “Must critical state theory be revisited to include fabric effects?” Acta Geotech. 11 (3): 479–491. https://doi.org/10.1007/s11440-016-0441-0.
Elgamal, A., Z. H. Yang, E. Parra, and A. Ragheb. 2003. “Modeling of cyclic mobility in saturated cohesionless soils.” Int. J. Plast. 19 (6): 883–905. https://doi.org/10.1016/S0749-6419(02)00010-4.
Fu, P., and Y. F. Dafalias. 2015. “Relationship between void- and contact normal-based fabric tensors for 2D idealized granular materials.” Int. J. Solids Struct. 63: 68–81. https://doi.org/10.1016/j.ijsolstr.2015.02.041.
Gao, Z. W., J. D. Zhao, and Z. Y. Yin. 2016. “Dilatancy relation for overconsolidated clay.” Int. J. Geomech. 17: 06016035. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000793.
Hashiguchi, K. 1995. “On the linear relations of V-lnp and lnv-lnp for isotropic consolidation of soils.” Int. J. Numer. Anal. Methods Geomech. 19: 367–376. https://doi.org/10.1002/nag.1610190505.
Hashiguchi, K., and T. Okayasu. 2000. “Time-dependent elastoplastic constitutive equation based on the subloading surface model and its application to soils.” Soils Found. 40 (4): 19–36. https://doi.org/10.3208/sandf.40.4_19.
Ishihara, K., F. Tatsuoka, and S. Yasuda. 1975. “Undrained deformation and liquefaction of sand under cyclic stresses.” Soils Found. 15: 29–44. https://doi.org/10.3208/sandf1972.15.29.
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.
Li, X. S., and Y. F. Dafalias. 2004. “A constitutive framework for anisotropic sand including non-proportional loading.” Géotechnique 54 (1): 41–55.
Li, X. S., and Y. Wang. 1998. “Linear representation of steady-state line for sand.” J. Geotech. Geoenviron. Eng. 124 (12): 1215–1217. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:12(1215).
Li, X., and H.-S. Yu. 2015. “Particle-scale insight into deformation noncoaxiality of granular materials.” Int. J. Geomech. 15 (4): 04014061. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000338.
Nakai, T. 1989. “An isotropic hardening elastoplastic model for sand considering the stress path dependency in three-dimensional stresses.” Soils Found. 29: 119–137. https://doi.org/10.3208/sandf1972.29.119.
Nakai, T., and M. Hinokio. 2004. “A simple elastoplastic model for normally and over consolidated soils with unified material parameters.” Soils Found. 44: 53–70. https://doi.org/10.3208/sandf.44.2_53.
Pradhan, T., F. Tatsuoka, and Y. Sato. 1989. “Experimental stress–dilatancy relations of sand subjected to cyclic loading.” Soils Found. 29: 45–64. https://doi.org/10.3208/sandf1972.29.45.
Rodriguez, N. M., and P. V. Lade. 2014. “Non-coaxiality of strain increment and stress directions in cross-anisotropic sand.” Int. J. Solids Struct. 51 (5): 1103–1114. https://doi.org/10.1016/j.ijsolstr.2013.12.003.
Saada, A. S., and G. Bianchini (eds) 1989. “Constitutive equations for granular non-cohesive soils.” In Proc. Int. Workshop on Constitutive Equations for Granular Non-Cohesive Soils, 450–489. Rotterdam, Netherlands: Balkema.
Sheng, D., Y. Yao, and J. P. Carter. 2008. “A volume-stress model for sands under isotropic and critical stress states.” Can. Geotech. J. 45 (11): 1639–1645. https://doi.org/10.1139/T08-085.
Shi, X. S., J. D. Zhao, J. H. Yin, and Z. J. Yu. 2019. “An elastoplastic model for gap-graded soils based on homogenization theory.” Int. J. Solids Struct. 163 (5): 1–14. https://doi.org/10.1016/j.ijsolstr.2018.12.017.
Sun, D. A., W. X. Huang, D. C. Sheng, and H. Yamamoto. 2007. “An elastoplastic model for granular materials exhibiting particle crushing.” Key Eng. Mater. 340-341: 1273–1278. https://doi.org/10.4028/www.scientific.net/KEM.340-341.1273.
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: 37–46. https://doi.org/10.1016/j.compgeo.2003.11.003.
Taiebat, M., and Y. F. Dafalias. 2008. “SANISAND: Simple anisotropic sand plasticity model.” Int. J. Numer. Anal. Methods Geomech. 32: 915–948. https://doi.org/10.1002/nag.651.
Tatsuoka, F., and K. Ishihara. 1974. “Drained deformation of sand under cyclic stresses reversing direction.” Soils Found. 14: 51–65. https://doi.org/10.3208/sandf1972.14.3_51.
Verdugo, R., and K. Ishihara. 1996. “The steady state of sandy soils.” Soils Found. 36: 81–91. https://doi.org/10.3208/sandf.36.2_81.
Yamamuro, J. A., and P. V. Lade. 1996. “Drained sand behavior in axisymmetric tests at high pressures.” J. Geotech. Eng. 122: 109–119. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:2(109).
Yang, Y., W. Fei, H. S. Yu, J. Ooi, and M. Rotter. 2015. “Experimental study of anisotropy and non-coaxiality of granular solids.” Granular Matter 17: 189–196. https://doi.org/10.1007/s10035-015-0551-7.
Yao, Y.-P., W. Hou, and A.-N. Zhou. 2009. “UH model: Three-dimensional unified hardening model for overconsolidated clays.” Géotechnique 59: 451–469. https://doi.org/10.1680/geot.2007.00029.
Yao, Y.-P., L. M. Kong, A. N. Zhou, and J. H. Yin. 2014. “Time-dependent unified hardening model: Three-dimensional elastoviscoplastic constitutive model for clays.” J. Eng. Mech. 141 (6): 04014162. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000885.
Yao, Y.-P., D. A. Sun, and T. Luo. 2004. “A critical state model for sands dependent on stress and density.” Int. J. Numer. Anal. Methods Geomech. 28: 323–337. https://doi.org/10.1002/nag.340.
Yao, Y.-P., and N.-D. Wang. 2014. “Transformed stress method for generalizing soil constitutive models.” J. Eng. Mech. 140 (3): 614–629. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000685.
Yao, Y.-P., H. Yamamoto, and N.-D. Wang. 2008. “Constitutive model considering sand crushing.” Soils Found. 48 (4): 603–608. https://doi.org/10.3208/sandf.48.603.
Zhang, J. M., Y. Shamoto, and K. Tokimatsu. 1997. “Moving critical and phase-transformation stress state lines of saturated sand during undrained cyclic shear.” Soils Found. 37: 51–59. https://doi.org/10.3208/sandf.37.2_51.
Zhao, J., and N. Guo. 2015. “The interplay between anisotropy and strain localisation in granular soils: A multiscale insight.” Géotechnique 65 (8): 642–656. https://doi.org/10.1680/geot.14.P.184.
Zhao, J., and Z. Gao. 2016. “Unified anisotropic elasto-plastic model for sand.” J. Eng. Mech. 142 (1): 04015056. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000962.
Zhu, F., and J. Zhao. 2019. “A peridynamic investigation on crushing of sand particles.” Géotechnique 69 (6): 526–540. https://doi.org/10.1680/jgeot.17.P.274.
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© 2020 American Society of Civil Engineers.
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Received: Jun 21, 2019
Accepted: Sep 14, 2020
Published online: Dec 10, 2020
Published in print: Feb 1, 2021
Discussion open until: May 10, 2021
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