Fractional-order plasticity model for sand-silt mixtures

SUN Zengchun; LIU Hanlong; XIAO Yang

doi:10.11779/CJGE20230666

Volume 46 Issue 8

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Chinese Journal of Geotechnical Engineering > 2024 > 46(8): 1596-1604. > DOI: 10.11779/CJGE20230666

SUN Zengchun, LIU Hanlong, XIAO Yang. Fractional-order plasticity model for sand-silt mixtures[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(8): 1596-1604. DOI: 10.11779/CJGE20230666

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SUN Zengchun, LIU Hanlong, XIAO Yang. Fractional-order plasticity model for sand-silt mixtures[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(8): 1596-1604. DOI: 10.11779/CJGE20230666

Citation:

SUN Zengchun, LIU Hanlong, XIAO Yang. Fractional-order plasticity model for sand-silt mixtures[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(8): 1596-1604. DOI: 10.11779/CJGE20230666

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Fractional-order plasticity model for sand-silt mixtures

SUN Zengchun^{1, 2,},
LIU Hanlong^{2, 3},
XIAO Yang^{2, 3, ,}

1.
College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, China
2.
School of Civil Engineering, Chongqing University, Chongqing 400045, China
3.
Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Chongqing 400045, China

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Received Date: July 12, 2023
Available Online: January 09, 2024

Graphical Abstract

Abstract

Abstract

The sand-silt mixtures, as common heterogeneous soils, are ubiquitous in nature and geotechnical engineering, and their particle contact state and mechanical properties are significantly affected by the factors such as density, stress level and fines content. In order to comprehensively describe the complex mechanical properties of the sand-silt mixtures within the fines content threshold (F_C $<$ F_Cthre), the plastic flow rules that can uniformly describe association and non-association are determined based on the fractional calculus theory. Using the concept of equivalent skeleton void ratio, the equivalent skeleton state parameter is embedded in the dilatancy equation and plastic modulus, and then a fractional-order plasticity model considering the fines content and state-dependent behavior is established. The comparison between the predicted results and the experimental data shows that the proposed fractional-order plasticity model can effectively reflect the strain-softening (strain-hardening) and dilatancy (contraction) behaviors of the sand-silt mixtures under drained conditions. Meanwhile, the key characteristics of undrained conditions, such as flow and non-flow behaviors, can also be reasonably described.
- sand-silt mixture,
- fines content,
- state-dependence,
- fractional calculus,
- constitutive model

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References (31)

References

[1]	吴琪, 陈国兴, 周正龙, 等. 基于颗粒接触状态理论的粗细粒混合料液化强度试验研究[J]. 岩土工程学报, 2018, 40(6): 475-485. doi: 10.11779/CJGE201803011 WU Qi, CHEN Guoxing, ZHOU Zhenglong, et al. Experimental investigation on liquefaction resistance of fine-coarse-grained soil mixtures based on theory of intergrain contact state[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(6): 475-485. (in Chinese) doi: 10.11779/CJGE201803011
[2]	李涛, 赵洪扬, 翁勃航, 等. 细颗粒形状和含量对钙质混合砂强度的影响试验研究[J]. 岩土工程学报, 2023, 45(7): 1517-1525. doi: 10.11779/CJGE20220535 LI Tao, ZHAO Hongyang, WENG Bohang, et al. Experimental study on effects of shape and content of fine particles on strength of calcareous mixed sand[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(7): 1517-1525. (in Chinese) doi: 10.11779/CJGE20220535
[3]	YILMAZ Y, DENG Y, CHANG CS, et al. Strength-dilatancy and critical state behaviours of binary mixtures of graded sands influenced by particle size ratio and fines content[J]. Géotechnique, 2023, 73(3): 202-217. doi: 10.1680/jgeot.20.P.320
[4]	LADE P V, YAMAMURO J A. Effects of nonplastic fines on static liquefaction of sands[J]. Canadian Geotechnical Journal, 1997, 34(6): 918-928. doi: 10.1139/t97-052
[5]	RAHMAN M M, LO S R, BAKI MAL. Equivalent granular state parameter and undrained behaviour of sand-fines mixtures[J]. Acta Geotechnica, 2011, 6(4): 183-194. doi: 10.1007/s11440-011-0145-4
[6]	MONKUL M M, ETMINAN E, ŞENOL A. Coupled influence of content, gradation and shape characteristics of silts on static liquefaction of loose silty sands[J]. Soil Dynamics and Earthquake Engineering, 2017, 101: 12-26. doi: 10.1016/j.soildyn.2017.06.023
[7]	GOBBI S, SANTISI D M P, LENTI L, et al. Effect of active plastic fine fraction on undrained behavior of binary granular mixtures[J]. International Journal of Geomechanics, 2022, 22(1): 06021035. doi: 10.1061/(ASCE)GM.1943-5622.0002242
[8]	CHANG C S, YIN Z Y. Micromechanical modeling for behavior of silty sand with influence of fine content[J]. International Journal of Solids and Structures, 2011, 48(19): 2655-2667. doi: 10.1016/j.ijsolstr.2011.05.014
[9]	RAHMAN M M, LO S R, DAFALIAS Y F. Modelling the static liquefaction of sand with low-plasticity fines[J]. Géotechnique, 2014, 64(11): 881-894. doi: 10.1680/geot.14.P.079
[10]	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
[11]	XU L Y, ZHANG J Z, CAI F, et al. Constitutive modeling the undrained behaviors of sands with non-plastic fines under monotonic and cyclic loading[J]. Soil Dynamics and Earthquake Engineering, 2019, 123: 413-424. doi: 10.1016/j.soildyn.2019.05.021
[12]	WEI X, YANG J. A critical state constitutive model for clean and silty sand[J]. Acta Geotechnica, 2019, 14(2): 329-345.
[13]	SUN Z C, CHU J, XIAO Y. Formulation and implementation of an elastoplastic constitutive model for sand-fines mixtures[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2021, 45(18): 2682-2708. doi: 10.1002/nag.3282
[14]	李晓强, 梁靖宇, 路德春, 等. 非饱和土的非正交弹塑性本构模型[J]. 中国科学: 技术科学, 2022, 52(7): 1048-1064. https://www.cnki.com.cn/Article/CJFDTOTAL-JEXK202207006.htm LI Xiaoqiang, LIANG Jingyu, LU Dechun, et al. Non- orthogonal elastoplastic constitutive model for unsaturated soil[J]. SCIENTIA SINICA Technologica, 2022, 52(7): 1048-1064. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JEXK202207006.htm
[15]	YAO Y P, HE G, LUO T. Study on determining the plastic flow direction of soils with dilatancy[J]. Acta Geotechnica, 2023, 18(5): 2411-2425. doi: 10.1007/s11440-022-01770-8
[16]	SUN Y F, SHEN Y. Constitutive model of granular soils using fractional-order plastic-flow rule[J]. International Journal of Geomechanics, 2017, 17(8): 04017025. doi: 10.1061/(ASCE)GM.1943-5622.0000904
[17]	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
[18]	路德春, 金辰逸, 梁靖宇, 等. 考虑状态相关的砂土非正交弹塑性本构模型[J]. 岩土工程学报, 2023, 45(2): 221-231. doi: 10.11779/CJGE20211457 (LU Dechun, JIN Chenyi, LIANG Jingyu, et al. State-dependent non-orthogonal elastoplastic constitutive model for sand[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(2): 221-231. doi: 10.11779/CJGE20211457
[19]	汪成贵, 束善治, 肖杨, 等. 考虑钙质砂颗粒破碎的分数阶边界面本构模型[J]. 岩土工程学报, 2023, 45(6): 1162-1170. doi: 10.11779/CJGE20220229 WANG Chenggui, SHU Shanzhi, XIAO Yang, et al. Fractional-order bounding surface model considering breakage of calcareous sand[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(6): 1162-1170. (in Chinese) doi: 10.11779/CJGE20220229
[20]	THEVANAYAGAM S, SHENTHAN T, MOHAN S, et al. Undrained fragility of clean sands, silty sands, and sandy silts[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(10): 849-859. doi: 10.1061/(ASCE)1090-0241(2002)128:10(849)
[21]	CHANG C S, DENG Y. Revisiting the concept of inter- granular void ratio in view of particle packing theory[J]. Géotechnique Letters, 2019, 9(2): 121-129. doi: 10.1680/jgele.18.00175
[22]	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
[23]	MURTHY T G, LOUKIDIS D, CARRARO J A H, et al. Undrained monotonic response of clean and silty sands[J]. Géotechnique, 2007, 57(3): 273-288. doi: 10.1680/geot.2007.57.3.273
[24]	GOUDARZY M, SARKAR D, LIESKE W, et al. Influence of plastic fines content on the liquefaction susceptibility of sands: monotonic loading[J]. Acta Geotechnica, 2022, 17(5): 1719-1737. doi: 10.1007/s11440-021-01283-w
[25]	ZHU Z H, DUPLA J C, CANOU J, et al. Experimental study of liquefaction resistance: effect of non-plastic silt content on sand matrix[J]. European Journal of Environmental and Civil Engineering, 2022, 26(7): 2671-2689. doi: 10.1080/19648189.2020.1765198
[26]	LÜ X L, XUE D W, ZHANG B, et al. Experimental studies and constitutive modeling of static liquefaction instability in sand-clay mixtures[J]. International Journal of Geomechanics, 2022, 22(9): 04022149. doi: 10.1061/(ASCE)GM.1943-5622.0002472
[27]	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. doi: 10.1680/geot.2007.00029
[28]	GOUDARZY M, RAHEMI N, RAHMAN M M, et al. Predicting the maximum shear modulus of sands containing nonplastic fines[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2017, 143(9): 06017013. doi: 10.1061/(ASCE)GT.1943-5606.0001760
[29]	孙增春, 汪成贵, 刘汉龙, 等. 粗粒土边界面塑性模型及其积分算法[J]. 岩土力学, 2020, 41(12): 3957-3967. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202012015.htm SUN Zengchun, WANG Chenggui, LIU Hanlong, et al. Bounding surface plasticity model for granular soil and its integration algorithm[J]. Rock and Soil Mechanics, 2020, 41(12): 3957-3967. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202012015.htm
[30]	XIAO Y, SUN Y F, LIU H L, et al. Model predictions for behaviors of sand-nonplastic-fines mixtures using equivalent- skeleton void-ratio state index[J]. Science China Technological Sciences, 2017, 60(6): 878-892. doi: 10.1007/s11431-016-9024-9
[31]	XIAO Y, LIU H L, CHEN Y M, et al. Bounding surface model for rockfill materials dependent on density and pressure under triaxial stress conditions[J]. Journal of Engineering Mechanics, 2014, 140(4): 04014002. doi: 10.1061/(ASCE)EM.1943-7889.0000702