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| A non-orthogonal single yield surface model for clays and sands based on a two-parameter yield function |
| LI Haichao1，TONG Chenxi1，MA Bo1，ZHANG Sheng1，2 |
| (1. School of Civil Engineering，Central South University，Changsha，Hunan 410075，China；2. National Engineering Laboratory for High Speed Railway Construction，Central South University，Changsha，Hunan 410075，China) |
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Abstract A non-orthogonal single yield surface model for clays and sands is proposed based on the critical state soil mechanics，while，and a state-dependent hardening rule including parameters of and is developed for the sub-loading surface by considering the effects of the stress level and the relative density. The proposed model is quite simple in the formula and is capable of describing the strain-softening and dilative features of over consolidated clays and dense sands. In the plane，the relative position between the current mean effective stress and the critical state mean effective stress is represented by the pressure state parameter，while the void difference between the current and critical states in the plane is captured by the density state parameter. Both and will approach zero once the material enters the critical state due to yielding. On the other hand，the generalized plastic potential function adopted in the proposed model is integrated by a high-order dilatancy rule，which is extended from the modified Cam-clay dilatancy rule. The plastic potential function contains a dilatancy related parameter a，whose value can be determined by fitting dilatancy curves with the high-order dilatancy rule. Besides，a two-parameter yield function can be developed by introducing an extra parameter into the proposed plastic potential function. Adjusting the value of d，both associated() and non-associated() plastic flow rules can be obtained. The deviation between the plastic flow direction() and the loading direction() increases as the parameter d increases，and at the same time，the strain vector is not normal to the yield surface. With the two-parameter yield function，the proposed model can consider the effect of the yield surface shape on the model prediction. Comparisons between the calculation results by the proposed model and drained triaxial test results of clays and sands show that the developed model can uniformly describe the behaviors of clays and sands. Moreover，adjusting the yield function shape can improve the accuracy of model prediction significantly.
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[1] ROSCOE K H，BURLAND J B. On the generalized stress-strain behaviour of wet clay[J]. Géotechnique，1968，10：535–609.
[2] YAO Y P，HOU W，ZHOU A N. UH model：Three-dimensional unified hardening model for overconsolidated clays[J]. Géotechnique，2009，59(5)：451–469.
[3] HASHIGUCHI K. Subloading surface model in unconventional plasticity[J]. International Journal of Solids and Structures，1989，25(8)：917–945.
[4] YAMAKAWA Y，HASHIGUCHI K，IKEDA K. Implicit stress- update algorithm for isotropic Cam-clay model based on the subloading surface concept at finite strains[J]. International Journal of Plasticity，2010，26(5)：634–658.
[5] HASHIGUCHI K. Foundations of elastoplasticity：subloading surface model[M]. New York：Springer，2017：330–340.
[6] NAKAI T，HINOKIO M. A simple elastoplastic model for normally and over consolidated soils with unified material parameters[J]. Soils and foundations，2004，44(2)：53–70.
[7] BEEN K，JEFFERIES M G. A state parameter for sands[J]. Géotechnique，1985，35(2)：99–112.
[8] JEFFERIES M G. Nor-Sand：a simle critical state model for sand[J]. Géotechnique，1993，43(1)：91–103.
[9] DAFALIAS Y F. Bounding surface plasticity. I：Mathematical foundation and hypoplasticity[J]. Journal of Engineering Mechanics，1986，112(9)：966–987.
[10] XIAO Y，LIU H，CHEN Y，et al. Bounding surface plasticity model incorporating the state pressure index for rockfill materials[J]. Journal of Engineering Mechanics，2014，140(11)：04014087.
[11] 刘斯宏，沈超敏，毛航宇，等. 堆石料状态相关弹塑性本构模型[J]. 岩土力学，2019，40(8)：2 891–2 898.(LIU Sihong，SHEN Chaomin，MAO Hangyu，et al. State-dependent elastoplastic constitutive model for rockfill materials[J]. Rock and Soil Mechanics，2019，40(8)：2 891–2 898.(in Chinese))
[12] YU H 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.
[13] YAO Y P，LIU L，LUO T，et al. Unified hardening (UH) model for clays and sands[J]. Computers and Geotechnics，2019，110：326–343.
[14] PESTANA J M，WHITTLE A J. Formulation of a unified constitutive model for clays and sands[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1999，23(12)：1 215–1 243.
[15] ALONSO E E，ROMERO E E，ORTEGA E. Yielding of rockfill in relative humidity-controlled triaxial experiments[J]. Acta Geotechnica，2016，11(3)：455–477.
[16] COLLINS I F，KELLY P A. A thermomechanical analysis of a family of soil models[J]. Géotechnique，2002，52(7)：507–518.
[17] GAO Z，ZHAO J，YIN Z Y. Dilatancy relation for overconsolidated clay[J]. International Journal of Geomechanics，2017，17(5)：06016035.
[18] PANTEGHINI A，LAGIOIA R. 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.
[19] 李海潮，张 升，沈 远. 考虑温度影响的岩土材料高阶屈服函数[J]. 岩石力学与工程学报，2018，37(12)：2 795–2 803.(LI Haichao，ZHANG Sheng，SHEN Yuan. A high order yield function for geo-materials considering the effect of temperature[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(12)：2 795– 2 803.(in Chinese))
[20] 姚仰平，刘 林，罗 汀. 砂土的 UH 模型[J]. 岩土工程学报，2016，38(12)：2 147–2 153.(YAO Yangping，LIU Lin，LUO Ting. UH model for sands[J]. Chinese Journal of Geotechnical Engineering，2016，38(12)：2 147–2 153.(in Chinese))
[21] MORTARA G. A new yield criterion for soils with embedded tension cut-off[J]. Meccanica，2019，54(4/5)：683–696.
[22] BOUSSHINE L，CHAABA A，DE SAXCE G. Softening in stress-strain curve for Drucker-Prager non-associated plasticity[J]. International Journal of Plasticity，2001，17(1)：21–46.
[23] KASAMA K，OCHIAI H，YASUFUKU N. On the stress-strain behaviour of lightly cemented clay based on an extended critical state concept[J]. Soils and Foundations，2000，40(5)：37–47.
[24] NGUYEN L D，FATAHI B，KHABBAZ H. A constitutive model for cemented clays capturing cementation degradation[J]. International Journal of Plasticity，2014，56(5)：1–18.
[25] SUN Y，GAO Y，ZHU Q. Fractional order plasticity modelling of state-dependent behaviour of granular soils without using plastic potential[J]. International Journal of Plasticity，2018，102(3)：53–69.
[26] 孙逸飞，高玉峰，鞠 雯. 分数阶塑性力学及其砂土本构模型[J].岩土工程学报，2018，40(8)：1 535–1 541.(SUN Yifei，GAO Yufeng，JU Wen. Fractional plasticity and its application in constitutive model for sands[J]. Chinese Journal of Geotechnical Engineering，2018，40(8)：1 535–1 541.(in Chinese))
[27] LU D，LIANG J，DU X，et al. Fractional elastoplastic constitutive model for soils based on a novel 3D fractional plastic flow rule[J]. Computers and Geotechnics，2019，105(2)：277–290.
[28] 张 锋. 计算土力学[M]. 北京：人民交通出版社，2007：31.(ZHANG Feng. Computational soil mechanics[M]. Beijing：China Communications Press，2007：31.(in Chinese))
[29] SULTAN N，CUI Y J，DELAGE P. Yielding and plastic behaviour of Boom clay[J]. Géotechnique，2010，60(9)：657–666.
[30] ELLIOTT G M. An investigation of a yield criterion for porous rock [Ph. D. Thesis][D]. London：University of London，1983.
[31] PETALAS A L，DAFALIAS Y F. Implicit integration of incrementally non-linear，zero-elastic range，bounding surface plasticity[J]. Computers and Geotechnics，2019，112：386–402.
[32] WANG Z L，DAFALIAS Y F，LI X S，et al. State pressure index for modeling sand behavior[J]. Journal of geotechnical and geoenvironmental engineering，2002，128(6)：511–519.
[33] ZERVOYANNIS C. Etude synthétique des propriétés mécaniques des argiles saturées et des sables sur chemin œdométrique et triaxial de révolution[Ph. D. Thesis][D]. Chatenay-Malabry：Ecole Centrale Paris Chatenay- Malabry，1982. |
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2020, Vol. 39 
