一个基于微观力学分析的散粒体应力-剪胀关系

刘洋; 于鹏强; 张铎; 王肖肖

doi:10.11779/CJGE202110007

一个基于微观力学分析的散粒体应力-剪胀关系 English Version

1.
北京科技大学土木工程系,北京　100083
2.
中南建筑设计院地下空间工程技术中心,湖北　武汉　430071

基金项目:

国家自然科学基金项目 51178044

详细信息

作者简介:
刘洋(1979— ),男,江苏徐州人,博士,教授,主要从事土细观力学和砂土液化等方面的科研和教学工作。E-mail：yangliu@ustb.edu.cn

中图分类号: TU431
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出版历程
- 收稿日期: 2020-09-07
- 网络出版日期: 2022-12-02
- 刊出日期: 2021-09-30

Micromechanics-based stress-dilatancy relationship for granular materials

1.
Department of Civil Engineering, University of Science and Technology Beijing, Beijing100083, China
2.
Underground Space Engineering Technology Center, Central South Architectural Design Institute Co., Ltd., Wuhan 430071, China

摘要

摘要: 从微观力学角度出发,基于真应力张量推导了散体中平均接触力与平均接触位移的计算公式,并通过宏-微观能量守恒得到了考虑散体各向异性组构及其演化的应力-剪胀关系；详细分析了剪胀参数的物理意义及对剪胀性的影响,并与经典的剑桥流动法则、Rowe剪胀方程以及室内试验结果进行了比较分析。研究结果表明,提出的应力-剪胀关系宏微观物理意义明确,考虑了材料密实状态和微观各向异性组构及其演化对应力-剪胀关系的影响,可以很好地模拟散粒体的初始剪胀（缩）行为,并可反映峰值应力比滞后于最大剪胀比的现象。同时提出的应力-剪胀方程还可以描述材料在相变点处应力比不等于临界应力比的现象,与已有室内试验结果一致,能够较好地预测散体材料三轴条件下的各向异性应力-剪胀关系。
- 应力-剪胀关系 /
- 微观力学 /
- 组构演化 /
- 能量守恒
Abstract: From the perspective of micromechanics, the formulas for the average contact force and contact displacement in the granular are derived based on the true stress tensor, then the stress-shear dilatancy relationship considering the fabric anisotropy and its evolution is obtained through the macro-micro energy conservation. In addition, the physical meaning of dilatancy parameters and their influence on dilatancy are analyzed. Finally, the proposed formulation is compared with the classical Cambridge flow law, Rowe dilatancy equation and test results to calibrate its reasonableness and applicability. The proposed stress-dilatancy relationship with clear physical meaning can describe the initial dilatancy (contraction) behavior for granular materials, considering the anisotropic evolution of fabric and the influence of the density on the dilatancy. Moreover, the proposed stress-dilatancy equation can reflect that the stress ratio at the phase transition point is less than the critical stress ratio and the peak stress ratio emerges behind the maximum dilatancy ratio. It is in good agreement with the test results and can better predict the anisotropic stress-dilatancy relationship of granular materials.
- stress-dilatancy relationship /
- micromechanics /
- fabric evolution /
- energy conservation

HTML全文

图 1 全局和局部坐标系统

Figure 1. Global and local coordinate system

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图 2 $α$ 对试样应力比-剪胀比的影响

Figure 2. Effect of $α$ on stress-dilatancy relationship

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图 3 应力比-剪胀比关系示意图

Figure 3. Variation of dilatancy with stress ratio

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图 4 D₀对试样应力比-剪胀关系的影响

Figure 4. Effect of D₀ on stress-dilatancy relationship

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图 5 不同流动法则下应力比-剪胀比关系对比图

Figure 5. Comparison of different stress-dilatancy relationships

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图 6 Ottawa砂应力-剪胀关系的试验结果与预测结果对比图

Figure 6. Comparison of predicted and test results for Ottawa sand

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图 7 Toyoura砂应力-剪胀关系的试验与预测结果对比图

Figure 7. Comparison of predicted and test results for Toyoura sand

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参考文献(30)

[1]	SCHOFIELD A, WROTH P. Critical State Soil Mechanics[M]. London: McGraw-Hill, 1968.
[2]	NOVA R, WOOD D M. A constitutive model for sand in triaxial compression[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1979, 3(3): 255-278. doi: 10.1002/nag.1610030305
[3]	LAGIOIA R, PUZRIN A M, POTTS D M. A new versatile expression for yield and plastic potential surfaces[J]. Computers & Geotechnics, 1996, 19(3): 171-191.
[4]	ROWE P W. The stress-dilatancy relation for static equilibrium of an assembly of particles in contact[J]. Proceedings of the Royal Society of London, Series A. Mathematical and Physical Sciences, 1962, 269(1339): 500-527.
[5]	GUO P J, STOLLE D F. The extension of Rowe’s stress-dilatancy model to general stress condition[J]. Soils and Foundations, 2004, 44(4): 1-10. doi: 10.3208/sandf.44.4_1
[6]	蔡正银, 李相菘. 砂土的剪胀理论及其本构模型的发展[J]. 岩土工程学报, 2007, 29(8): 1122-1128. doi: 10.3321/j.issn:1000-4548.2007.08.002 CAI Zheng-yin, LI Xiang-song. Development of dilatancy theory and constitutive model of sand[J]. Chinese Journal of Geotechnical Engineering, 2007, 29(8): 1122-1128. (in Chinese) doi: 10.3321/j.issn:1000-4548.2007.08.002
[7]	WAN R, GUO P. A pressure and density dependent dilatancy model for granular materials[J]. Soils and Foundations, 1999, 39(6): 1-11. doi: 10.3208/sandf.39.6_1
[8]	LI X S, DAFALIAS Y F. Constitutive modeling of inherently anisotropic sand behavior[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(10): 868-880. doi: 10.1061/(ASCE)1090-0241(2002)128:10(868)
[9]	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
[10]	MANZARI M T, DAFALIAS Y F. A critical state two-surface plasticity model for sands[J]. Géotechnique, 1997, 47(2): 255-272. doi: 10.1680/geot.1997.47.2.255
[11]	GAJO A, MUIR WOOD D. Severn-Trent sand: a kinematic-hardening constitutive model: the qp formulation[J]. Géotechnique, 1999, 49(5): 595-614. doi: 10.1680/geot.1999.49.5.595
[12]	WANG R, DAFALIAS Y F, FU P, et al. Fabric evolution and dilatancy within anisotropic critical state theory guided and validated by DEM[J]. International Journal of Solids and Structures, 2019, 188-189(3): 210-222.
[13]	TOBITA Y. Fabric tensors in constitutive equations for granular materials[J]. Soils and Foundations, 1989, 29(4): 91-104. doi: 10.3208/sandf1972.29.4_91
[14]	ZHAO J, GUO N. Unique critical state characteristics in granular media considering fabric anisotropy[J]. Géotechnique, 2013, 63(8): 695-704. doi: 10.1680/geot.12.P.040
[15]	YIN Z Y, CHANG C S. Stress-dilatancy behavior for sand under loading and unloading conditions[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 2013, 37(8): 855-870.
[16]	LIU Y, CHANG C S. Relationship between element-level and contact-level parameters of micromechanical and upscaled plasticity models for granular soils[J]. Acta Geotechnica, 2020, 15(7): 1779-1798. doi: 10.1007/s11440-019-00895-7
[17]	XIAO Y, ASCE M, LONG L, et al. Effect of particle shape on stress-dilatancy responses of medium-dense sands[J]. Journal of Geotechnical & Geoenvironmental Engineering, 2018, 145(2): 04018105.
[18]	LIANG J, LU D, DU X, et al. A 3D non-orthogonal elastoplastic constitutive model for transversely isotropic soil[J]. Acta Geotechnica, 2021, in press.
[19]	TSEGAYE A B, BENZ T, NORDAL S. Formulation of non-coaxial plastic dissipation and stress-dilatancy relations for geomaterials[J]. Acta Geotechnica, 2020, 15(10): 2727-2739. doi: 10.1007/s11440-020-00968-y
[20]	杨骏堂, 刘元雪, 郑颖人, 等. 剪胀型土剪胀特性的大数据深度挖掘与模型研究[J]. 岩土工程学报, 2020, 42(3): 513-522. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202003018.htm YANG Jun-tang, LIU Yuan-xue, ZHENG Ying-ren et al. Deep mining of big data and model tests on dilatancy characteristics of dilatant soils[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(3): 513-522. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202003018.htm
[21]	LIAO C L, CHANG T P, YOUNG D H, et al. Stress-strain relationship for granular materials based on the hypothesis of best fit[J]. International Journal of Solids and Structures, 1997, 34(31/32): 4087-4100.
[22]	刘洋, CHANG C S, 张铎, 等. 散粒介质三维应力-组构解析与破坏分析[J]. 岩土工程学报, 2014, 36(3): 401-408. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201403002.htm LIU Yang, CHANG C S, ZHANG Duo, et al. Analytical solution of stress-fabric relationship and failure of granularmaterials in three dimensions[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(3): 401-408. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201403002.htm
[23]	CHANG C S, MISRA A. Packing structure and mechanical properties of granulates[J]. Journal of Engineering Mechanics, 1990, 116(5): 1077-1093. doi: 10.1061/(ASCE)0733-9399(1990)116:5(1077)
[24]	ODA M, KONISHI J, NEMAT-NASSER S. Some experimentally based fundamental results on the mechanical behaviour of granular materials[J]. Géotechnique, 1980, 30(4): 479-495. doi: 10.1680/geot.1980.30.4.479
[25]	ODA M, NEMAT-NASSER S, KONISHI J. Stress-induced anisotropy in granular masses[J]. Soils and Foundations, 1985, 25(3): 85-97. doi: 10.3208/sandf1972.25.3_85
[26]	WAN R G, GUO P J. Stress dilatancy and fabric dependencies on sand behavior[J]. Journal of Engineering Mechanics, 2004, 130(6): 635-645. doi: 10.1061/(ASCE)0733-9399(2004)130:6(635)
[27]	BEEN K, JEFFERIES M. Stress dilatancy in very loose sand[J]. Canadian Geotechnical Journal, 2004, 41(5): 972-989. doi: 10.1139/t04-038
[28]	LIU D Y, LOURENÇO S D N. Stress-dilatancy behaviour of a polymer-coated sand[J]. Acta Geotechnica, 2021, 16(2): 647-652. doi: 10.1007/s11440-020-01022-7
[29]	REGIER K. The stress-dilatancy behaviour of sands: pressure and density dependencies in both monotonic and cyclic loading regimes[M]. Calgary: University of Calgary, 1997.
[30]	PRADHAN T B, TATSUOKA F, SATO Y. Experimental stress-dilatancy relations of sand subjected to cyclic loading[J]. Soils and Foundations, 1989, 29(1): 45-64. doi: 10.3208/sandf1972.29.45

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