A practical constitutive theory based on egg-shaped function in elasto-plastic modeling for soft clay

Abstract

An exploratory discussion is presented on the application of egg-shaped function in elasto-plastic constitutive analysis for soft clay. Two main tasks of the paper are: 1) to propose a complete yield criterion based on egg-shaped function and supplement its definition in the deviatoric section, and then a yield criterion suitable for 3D stress conditions is obtained; 2) to elaborate its numerical implementation based on the drained triaxial tests. During the above discussion, a non-associated flow rule is proposed, in which the stress-dilatancy relationship in most classical theory is replaced by a linear dependence between the stress state parameter η and the rotation angle η of the plastic potential surface. Thereafter, isotropic and kinematic hardening behavior is considered by employing the hardening parameter H, which can be expressed as the function of plastic work Wp. Finally, comparisons between numerical results and test data on Taizhou soft clay are made to verify the effectiveness of the proposed model.

Keywords

egg-shaped function / elastoplasticity / yield criterion / non-associated flow

References

[1] ROSCOE K H, BURLAND J B. On the generalised stress-strain behaviour of ‘wet’ clay [C]// HEYMAN J, LECKIE F A. Engineering Plasticity. Cambridge University Press, 1968: 535–609. DOI: https://doi.org/10.1016/0022-4898(70)90160-6.

[2] McdowellG R, HauK W. A generalised modified Cam clay model for clay and sand incorporating kinematic hardening and bounding surface plasticity [J]. Granular Matter, 2004, 6(1): 11-16

[3] DafaliasY F, ManzariM T, PapadimitriouA G. SANICLAY: Simple anisotropic clay plasticity model [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30(12): 1231-1257

[4] YaoY-P, HouW, ZhouA-N. UH model: Three-dimensional unified hardening model for overconsolidated clays [J]. Géotechnique, 2009, 59(5): 452-469

[5] YanW M, LiX S. A model for natural soil with bonds [J]. Géotechnique, 2011, 61(2): 95-106

[6] YinZ-Y, XuQ, HicherP Y. A simple critical-state-based double-yield-surface model for clay behavior under complex loading [J]. Acta Geotechnica, 2013, 8(5): 509-523

[7] ZhongZ-H, YangG-H, FuX-D, WenY, ZhangY-C. Numerical verification of similar Cam-clay model based on generalized potential theory [J]. Journal of Central South University, 2014, 21(12): 4707-4713

[8] JockovicS, VukicevicM. Bounding surface model for overconsolidated clays with new state parameter formulation of hardening rule [J]. Computers and Geotechnics, 2017, 83: 16-29

[9] HanJ, LiangH, CaoC, BiZ, ZhuZ. A mechanical model for sheared joints based on Mohr-Coulomb material properties [J]. Géotechnique Letters, 2018, 8(2): 92-96

[10] YaoY-P, LiuL, LuoT, TianY, ZhangJ-M. Unified hardening (UH) model for clays and sands [J]. Computers and Geotechnics, 2019, 110: 326-343

[11] YinZ-Y, ChangC S, KarstunenM, HicherP Y. An anisotropic elastic-viscoplastic model for soft clays [J]. International Journal of Solids and Structures, 2010, 47(5): 665-677

[12] HammiY, StoneT W, PaliwalB, HorstemeyerM F, AllisonP G. Smooth yield surface constitutive modeling for granular materials [J]. ASME Journal of Engineering Materials and Technology, 2017, 139(1): 011010

[13] UedaK, LaiS. Constitutive modeling of inherent anisotropy in a strain space multiple mechanism model for granular materials [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2019, 433708-737

[14] JiangM-J. New paradigm for modern soil mechanics: Geomechanics from micro to macro [J]. Chinese Journal of Geotechnical Engineering, 2019, 41(2): 195-254(in Chinese)

[15] ZengT, ShaoJ-F, YaoY. A micromechanical-based elasto-viscoplastic model for the Callovo-Oxfordian argillite: Algorithms, validations, and applications [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2020, 44(2): 183-207

[16] PetalasA L, DafaliasY F, PapadimitriouA G. SANISAND-F: Sand constitutive model with evolving fabric anisotropy [J]. International Journal of Solids and Structures, 2020, 188–189: 12-31

[17] JiangM-J, YuH-S, LeroueilS. A simple and effcient approach to capturing bonding effect in naturally microstrucutred sands by discrete element method [J]. International Journal for Numerical Methods in Engineering, 2007, 69(6): 1158-1193

[18] YinZ-Y, ChangC S. Microstructural modelling of stress-dependent behaviour of clay [J]. International Journal of Solids and Structures, 2009, 46(6): 1373-1388

[19] YinZ-Y, HattabM, HicherP Y. Multiscale modeling of a sensitive marine clay [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2011, 35(15): 1682-1702

[20] YaoY-P, LuD-C, ZhouA-N, ZouB. Generalized non-linear strength theory and transformed stress space [J]. Science in China, Series E: Technological Sciences, 2004, 47(6): 691-709

[21] MatsuokaH, NakaiT. Stress-deformation and strength characteristics of soil under three different principal stresses [J]. Proceedings of the Japan Society of Civil Engineers, 1974, 232: 59-70

[22] NakaiT, MatsuokaH. A generalised elastoplastic constitutive model for clay in three dimensional stresses [J]. Soils and Foundations, 1986, 26(4): 81-98

[23] MitsutoshiYLadeP V, NakaiT. 3-D Coulomb’s failure criterion for various geomaterials [C]. Geomechanics II: Testing, Modeling, and Simulation, 2005, Resyon, VA, ASCE, 7186

[24] NakaiT, HinokioM. A simple elastoplastic model for normally and over consolidated soils with unified material parameters [J]. Soils and Foundations, 2004, 44(2): 53-70

[25] MortaraG. A new yield and failure criterion for geomaterials [J]. Géotechnique, 2008, 58(2): 125-132

[26] MortaraG. A hierarchical single yield surface for frictional materials [J]. Computers and Geotechnics, 2009, 36(6): 960-967

[27] MortaraG. A constitutive framework for the elastoplastic modelling of geomaterials [J]. International Journal of Solids and Structures, 2015, 63: 139-152

[28] LuD-C, MaC, DuX-L, JinL, GongQ-M. Development of a new nonlinear unified strength theory for geomaterials based on thr characteristic stress concept [J]. International Journal of Geomechanics, ASCE, 2017, 17(2): 4016058

[29] BardetJ P. Lode dependences for isotropic pressure-sensitive elastoplastic materials [J]. ASME Journal of Applied Mechanics, 1990, 573498-506

[30] ShaoJ F, ZhuQ Z, SuK. Modeling of creep in rock materials in terms of material degradation [J]. Computers and Geotechnics, 2003, 30(7): 549-555

[31] LagioiaR, PanteghiniA. On the existence of a unique class of yield and failure criteria comprising Tresca, Von-Mises, Drucker-Prager, Mohr-Coulomb, Galileo-Rankine, Matsuoka-Nakai and Lade-Duncan [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2016, 472(2185): 20150713

[32] JiangH. Three-dimensional failure criteria for rocks based on the Hoek-Brown criterion and a general Lode dependence [J]. International Journal of Geomechanics, 2017, 17804017023

[33] YaoY-P, WangN-D. Transformed stress method for generalizing soil constitutive models [J]. ASCE Journal of Engineering Mechanics, 2014, 1403614-629

[34] LuD-C, LiX-Q, DuX-L, LiangJ-Y. A simple 3D elastoplastic constitutive model for soils based on the characteristic stress [J]. Computers and Geotechnics, 2019, 109: 229-247

[35] ChenH-H, LiL, LiJ-P, WangH. Stress transform method to undrained and drained expansion of a cylindrical cavity in anisotropic modified cam-clay soils [J]. Computers and Geotechnics, 2019, 106: 128-142

[36] WanZ, SongC-C, MengD. A nonlinear strength criterion and transformation stress method [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1210-1222(in Chinese)

[37] RenF, ShengQ, ChangY-T. Egg-shaped yield function for geotechnical engineering materials [J]. Chinese Journal of Geotechnical Engineering, 1993, 13(4): 33-39(in Chinese)

[38] XuR-Q, YangL-D, GongX-N. Stress-strain constitutive relationship of boundary surface of soils [J]. Jounal of Tongji University (Nature & Science), 1997, 25(1): 29-33(in Chinese)

[39] XuR-Q, WangX-C, RongX-N. Marco- and meso-scale parametric analysis of egg-shaped yield surface of structural soil [J]. International Journal of Offshore and Polar Engineering, 2014, 24(4): 301-308

[40] ZienkiewiczO C, PandeG NGudehusG. Some useful forms of isotropic yield surfaces for soil and rock mechanics [C]. Finite Element in Geomechanics, 1977, London, John Wiley & Sons Ltd, 179190

[41] YuH S. CASM: A unified state parameter model for clay and sand [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1998, 22(8): 621-653

[42] PanteghiniA, LagioiaR. An extended modified Cam-Clay yield surface for arbitrary meridional and deviatoric shapes retaining full convexity and double homothety [J]. Géotechnique, 2018, 68(7): 590-601

[43] ArgyrisJ H, FaustG, SzimmatJ, WarnkeE P, WillamK J. Recent developments in the finite element analysis of prestressed concrete reactor vessels [J]. Nuclear Engineering and Design, 1974, 28(1): 42-75

[44] WillamK, WarnkeE P. Constitutive model for the triaxial behavior of concrete [C]. Seminar on Concrete Structure Subjected to Triaxial Stresses, 1975, Bergamo, Italy, ISMES, 1719

[45] van EekelenH A M. Isotropic yield surface in three dimensions for use in soil mechanics [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1980, 4(1): 89-101

[46] LinF-B, BazantZ P. Convexity of smooth yield surface of frictional material [J]. ASCE Journal of Engineering Mechanics, 1986, 112(11): 1259-1262

[47] ShengD, SloanS W, YuH S. Aspects of finite element implementation of critical state models [J]. Computational Mechanics, 2000, 26(2): 185-196

[48] HashiguchiK. A proposal of the simplest convex-conical surface for soils [J]. Soils and Foundations, 2002, 42(3): 107-113

[49] GuoR-P, LiG-X. Elasto-plastic model of soil with a function of plastic work as the hardening function [J]. Journal of Tsinghua University (Science and Technology), 2000, 40(5): 125-127(in Chinese)

[50] LiuX-R, ZhongZ-L, ZhangY-X, WangJ-M. Elastoplastic modeling of unsaturated intact Q2 loess with plastic work as hardening parameter [J]. Rock and Soil Mechanics, 2009, 30(5): 1215-1220(in Chinese)

[51] RoscoeK H, PoorooshasbH B. A theoretical and experimental study of strains in triaxial tests on normally consolidated clays [J]. Géotechnique, 1963, 13(1): 12-38

[52] PoorooshasbH B, HolubecI, SherbourneA N. Yielding and flow of sand in triaxial compression: Part I [J]. Canadian Geotechnical Journal, 1966, 3(4): 179-190

[53] LadeP V, DuncanJ M. Stress-path dependent behavior of cohesionless soil [J]. ASCE Journal of Geotechnical Engineering, 1976, 102(1): 51-68

[54] ZhouC, LeroueilS, FafardM, GhorbelS. Constitutive modeling of kinematic hardening behavior of saturated anisotropic soils [J]. ASCE International Journal of Geomechanics, 2017, 17(3): 04016063

[55] HuangW-X. Theory of elastoplastic stress-strain model for soil [J]. Rock and Soil Mechanics, 1979, 111-20(in Chinese)

[56] SultanN, CuiY J, DelageP. Yielding and plastic behavior of Boom clay [J]. Géotechnique, 2010, 60(9): 657-666

[57] SchofieldA N, WorthC PCritical state soil mechanics [M], 1968, New York, McGraw-Hill

[58] JinY-F, YinZ-Y, ShenS-L, HicherP Y. Investigation into MOGA for identifying parameters of a critical-state-based sand model and parameters correlation by factor analysis [J]. Acta Geotechnica, 2016, 11(5): 1311-1145

[59] JinY-F, WuZ-X, YinZ-Y, ShenS-L. Estimation of critical state-related formula in advanced constitutive modeling of granular material [J]. Acta Geotechnica, 2017, 12(6): 1329-1351