State-dependent non-orthogonal elastoplastic constitutive model for sand

LU Dechun; JIN Chenyi; LIANG Jingyu; LI Zehua; DU Xiuli

doi:10.11779/CJGE20211457

Volume 45 Issue 2

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Chinese Journal of Geotechnical Engineering > 2023 > 45(2): 221-231. > DOI: 10.11779/CJGE20211457

LU Dechun, JIN Chenyi, LIANG Jingyu, LI Zehua, DU Xiuli. State-dependent non-orthogonal elastoplastic constitutive model for sand[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(2): 221-231. DOI: 10.11779/CJGE20211457

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State-dependent non-orthogonal elastoplastic constitutive model for sand

1.
Key Lab of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China
2.
School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China

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Received Date: December 07, 2021
Available Online: February 23, 2023

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Abstract

Abstract

The mechanic characteristics of sand have obvious features of state dependence, which is mainly reflected by the fact that the deformation characteristics of sand in different stress and density states significantly differ. The reasonable description for the state-dependent hardening rule and dilatancy rule of sand is the basis to describe the state-dependent deformation characteristics of sand. A differential expression which can effectively describe the isotropic compression and critical state of sand is proposed. Based on the hardening rule under isotropic compression condition, a state-dependent hardening factor ω is proposed, and the state-dependent hardening parameter H is developed in order to reasonably decide the magnitude of plastic strain increment. In the process of determining the direction of plastic strain increment by adopting the non-orthogonal plastic flow rule, the influences of state parameter ψ on fractional order μ are introduced, and the state dependence of the direction of plastic strain increment is considered, thus reasonably describing the state-dependent dilatancy of sand. Furthermore, by introducing the state parameter into the Hooke's law, the elastic strain increment is obtained, and a non-orthogonal elastoplastic constitutive model which can describe the state dependence of sand is proposed. By reasonably predicting the results in triaxial drained and undrained tests on the Toyoura sand, it is proved that the established model can effectively capture the state-dependent mechanic characteristics of sand.
- sand,
- state dependence,
- constitutive model,
- non-orthogonal plastic flow rule,
- elastoplasticity

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References

[1]	VERDUGO R, ISHIHARA K. The steady state of sandy soils[J]. Soils and Foundations, 1996, 36(2): 81-91. doi: 10.3208/sandf.36.2_81
[2]	CAI Z Y, LI X S. Deformation characteristics and critical state of sand[J]. Chinese Journal of Geotechnical Engineering. 2004, 26(5): 697-701. doi: 10.3321/j.issn:1000-4548.2004.05.025
[3]	BEEN K, JEFFERIES M G. A state parameter for sands[J]. Géotechnique, 1985, 35(2): 99-112. doi: 10.1680/geot.1985.35.2.99
[4]	ASAOKA A. Consolidation of clay and compaction of sand-an elasto-plastic description[C]// 12Asian Regional Conference on Soil Mechanics and Geotechnical Engineering. Singapore: World Scientific Publishing Company, 2004: 1157-1195.
[5]	ZHANG F, YE B, NODA T, et al. Explanation of cyclic mobility of soils: approach by stress-induced anisotropy[J]. Soils and Foundations, 2007, 47(4): 635-648. doi: 10.3208/sandf.47.635
[6]	NAKAI T R. An isotropic hardening elastoplastic model for sand considering the stress path dependency in three-dimensional stresses[J]. Soils and Foundations, 1989, 29(1): 119-137. doi: 10.3208/sandf1972.29.119
[7]	WOOD D M, BELKHEIR K. Strain softening and state parameter for sand modelling[J]. Géotechnique, 1994, 44(2): 335-339. doi: 10.1680/geot.1994.44.2.335
[8]	BOLTON M D. The strength and dilatancy of sands[J]. Géotechnique, 1986, 36(1): 65-78. doi: 10.1680/geot.1986.36.1.65
[9]	ISHIHARA K. Liquefaction and flow failure during earthquakes[J]. Géotechnique, 1993, 43(3): 351-451. doi: 10.1680/geot.1993.43.3.351
[10]	姚仰平, 刘林, 罗汀. 砂土的UH模型[J]. 岩土工程学报, 2016, 38(12): 2147-2153. doi: 10.11779/CJGE201612002 YAO Yangping, LIU Lin, LUO Ting. UH model for sands[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(12): 2147-2153. (in Chinese) doi: 10.11779/CJGE201612002
[11]	姚仰平, 张民生, 万征, 等. 基于临界状态的砂土本构模型研究[J]. 力学学报, 2018, 50(3): 589-598. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201803015.htm YAO Yangping, ZHANG Minsheng, WAN Zheng, et al. Constitutive model for sand based on the critical state[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 589-598. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201803015.htm
[12]	LI X S, DAFALIAS Y F. Dilatancy for cohesionless soils[J]. Géotechnique, 2000, 50(4): 449-460. doi: 10.1680/geot.2000.50.4.449
[13]	YANG J, LI X S. State-dependent strength of sands from the perspective of unified modeling[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2004, 130(2): 186-198. doi: 10.1061/(ASCE)1090-0241(2004)130:2(186)
[14]	张卫华, 赵成刚, 傅方. 基于相变状态的砂土本构模型的研究[J]. 工程地质学报, 2013, 21(3): 337-344. doi: 10.3969/j.issn.1004-9665.2013.03.001 ZHANG Weihua, ZHAO Chenggang, FU Fang. Phase transformation state based constitutive model for sands[J]. Journal of Engineering Geology, 2013, 21(3): 337-344. (in Chinese) doi: 10.3969/j.issn.1004-9665.2013.03.001
[15]	迟明杰, 赵成刚, 李小军. 剪胀性砂土本构模型的研究[J]. 岩土力学, 2008, 29(11): 2939-2944. doi: 10.16285/j.rsm.2008.11.021 CHI Mingjie, ZHAO Chenggang, LI Xiaojun. Research on constitutive model for dilatant sand[J]. Rock and Soil Mechanics, 2008, 29(11): 2939-2944. (in Chinese) doi: 10.16285/j.rsm.2008.11.021
[16]	SUN Y F, NIMBALKAR S. Stress-fractional soil model with reduced elastic region[J]. Soils and Foundations, 2019, 59(6): 2007-2023. doi: 10.1016/j.sandf.2019.10.001
[17]	李海潮, 童晨曦, 马博, 等. 基于双参数屈服函数的黏土和砂土非正交单屈服面模型[J]. 岩石力学与工程学报, 2020, 39(11): 2319-2327. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX202011015.htm LI Haichao, TONG Chenxi, MA Bo, et al. A non-orthogonal single yield surface model for clays and sands based on a two-parameter yield function[J]. Chinese Journal of Rock Mechanics and Engineering, 2020, 39(11): 2319-2327. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX202011015.htm
[18]	李海潮, 马博, 张升. 适用于堆石料的分数阶下加载面模型[J]. 岩土力学, 2021, 42(1): 68-76. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202101008.htm LI Haichao, MA Bo, ZHANG Sheng. A fractional sub-loading surface model for rockfill[J]. Rock and Soil Mechanics, 2021, 42(1): 68-76. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202101008.htm
[19]	LADE P V, NELSON R B, ITO Y M. Nonassociated flow and stability of granular materials[J]. Journal of Engineering Mechanics, 1987, 113(9): 1302-1318. doi: 10.1061/(ASCE)0733-9399(1987)113:9(1302)
[20]	WAN R, PINHEIRO M. On the validity of the flow rule postulate for geomaterials[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, 38(8): 863-880. doi: 10.1002/nag.2242
[21]	LU D C, LIANG J Y, DU X L, et al. Fractional elastoplastic constitutive model for soils based on a novel 3D fractional plastic flow rule[J]. Computers and Geotechnics, 2019, 105: 277-290. doi: 10.1016/j.compgeo.2018.10.004
[22]	QU P F, ZHU Q Z. A novel fractional plastic damage model for quasi-brittle materials[J]. Acta Mechanica Solida Sinica, 2021, 34(5): 706-717. doi: 10.1007/s10338-021-00240-0
[23]	ZHOU F X, WANG L Y, LIU H B. A fractional elasto-viscoplastic model for describing creep behavior of soft soil[J]. Acta Geotechnica, 2021, 16(1): 67-76. doi: 10.1007/s11440-020-01008-5
[24]	LU D C, ZHOU X, DU X L, et al. A 3D fractional elastoplastic constitutive model for concrete material[J]. International Journal of Solids and Structures, 2019, 165: 160-175. doi: 10.1016/j.ijsolstr.2019.02.004
[25]	LIANG J Y, LU D C, DU X L, et al. A 3D non-orthogonal elastoplastic constitutive model for transversely isotropic soil[J]. Acta Geotechnica, 2022, 17(1): 19-36.
[26]	LADE P, BOPP P A. Relative density effects on drained sand behavior at high pressures[J]. Soils and Foundations, 2005, 45(1): 1-13.
[27]	YAO Y P, SUN D A, MATSUOKA H. A unified constitutive model for both clay and sand with hardening parameter independent on stress path[J]. Computers and Geotechnics, 2008, 35(2): 210-222.
[28]	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.
[29]	ROSCOE K H, BURLAND J B. On the generalised stress-strain behaviour of 'wet' clay[J]. Engineering Plasticity. 1968: 535-609.
[30]	LIANG J Y, LU D C, ZHOU X, et al. Non-orthogonal elastoplastic constitutive model with the critical state for clay[J]. Computers and Geotechnics, 2019, 116: 103200.