|
|
|
| The fabric-stress relationship and the equivalent stress method of granular materials |
| DONG Tong1，2，KONG Liang2，ZHENG Yingren1，WANG Xing2，LIU Yun3 |
(1. Chongqing Key Laboratory of Geomechanics and Geoenvironmental Protection，Army Logistics University of PLA，
Chongqing 401311，China；2. School of Sciences，Qingdao Technological University，Qingdao，Shandong 266033，China；
3. Chongqing Industry Polytechnic College，Chongqing 401120，China) |
|
|
|
|
Abstract The methods in establishing the existing anisotropic constitutive models are reviewed systematically. It is pointed out that the description of the fabric direction should be attributed to the coordinate transformation of fabric and stress. For anisotropic materials，the total stress needs to be allocated according to the actual bearing area of each component，because the effective bearing areas of soil skeleton in different directions are different. Therefore，by introducing the transformation matrix，the equivalent stress tensor is proposed to describe the anisotropy of granular materials，the true stress inside the material and the relationship between the fabric direction and the stress direction. Therefore，the material anisotropy in macro-scale can be regarded as the result of the application of anisotropic stress on an equivalent isotropic material in micro-scale. The equivalent stress tensor is used to describe the anisotropic stress and the existing isotropic model is used to describe the mechanical property of the equivalent isotropic material. A general method of transforming the existing isotropic failure criterion and constitutive model into anisotropic ones，named“Equivalent Stress Method”，is put forward from the perspective of stress. Finally，the SMP criterion is transformed into anisotropic one as an example. The comparison with the existing experimental results proves the rationality and validity of the anisotropic transformation.
|
|
|
|
|
|
| [1] 孙其诚，程晓辉，季顺迎，等. 岩土类颗粒物质宏–细观力学研究进展[J]. 力学进展，2011，41(3)：351–371.(SUN Qicheng，CHENG Xiaohui，JI Shunying，et al. Advances in the micro-macro mechanics of granular soil materials[J]. Advances in Mechanics，2011，41(3)：351–371.(in Chinese))
[2] ODA M. Mechanics of granular materials：an introduction[M]. Netherlands：A. A Balkema，1999：2–39.
[3] 董 彤，郑颖人，孔 亮，等. 考虑主应力方向的土体非线性弹性模型[J]. 岩土力学，2017，38(5)：1 373–1 378.(DONG Tong，ZHENG Yingren，KONG Liang，et al. Strength criterion and slipping plane of anisotropic sand considering the direction of the major principal stress[J]. Rock and Soil Mechanics，2017，38(5)：1 373– 1 378.(in Chinese))
[4] PIETRUSZCZAK S，MROZ Z. Formulation of anisotropic failure criteria incorporating a microstructure tensor[J]. Computers and Geotechnics，2000，26(2)：105–112.
[5] LADE P V. Failure criterion for cross-anisotropic soils[J]. Journal of Geotechnical and Geoenvironmental Engineering，2008，134(1)：117–124.
[6] 黄茂松. 土体稳定与承载特性的分析方法[J]. 岩土工程学报，2016，38(1)：1–34.(HUANG Maosong. Analysis methods for stability and bearing capacity of soils[J]. Chinese Journal of Geotechnical Engineering，2016，38(1)：1–34.(in Chinese))
[7] KONG Y，ZHAO J，YAO Y. A failure criterion for cross-anisotropic soils considering microstructure[J]. Acta Geotechnica，2013，8(6)：665–673.
[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.
[9] LI X S，DAFALIAS Y F. Anisotropic critical state theory：role of fabric[J]. Journal of Engineering Mechanics，2012，138(3)：263–275.
[10] DAFALIAS Y F，PAPADIMITRIOU A G，LI X S. Sand plasticity model accounting for inherent fabric anisotropy[J]. Journal of Engineering Mechanics，2004，130(11)：1 319–1 333.
[11] GAO Z，ZHAO J，YAO Y. A generalized anisotropic failure criterion for geomaterials[J]. International Journal of Solids and Structures，2010，47(22/23)：3 166–3 185.
[12] YAO Y P，KONG Y X. Extended UH model：three-dimensional unified hardening model for anisotropic clays[J]. Journal of Engineering Mechanics，2012，138(7)：853–866.
[13] ZHAO J，GUO N. Rotational resistance and shear-induced anisotropy in granular media[J]. Acta Mechanica Solida Sinica，2014，27(1)：1–14.
[14] 李学丰，孔 亮，袁 琪，等. 宏细观结合各向异性砂土的变形特性模拟[J]. 同济大学学报：自然科学版，2016，44(2)；173–179.(LI Xuefeng，KONG Liang，YUAN Qi，et al. Deformation analysis of anisotropic sand using the method of macro-meso incorporation[J]. Journal of Tongji University：Natural Science，2016，44(2)：173–179.(in Chinese))
[15] 曹 威，王 睿，张建民. 横观各向同性砂土的强度准则[J]. 岩土工程学报，2016，38(11)：2 026–2 032.(CAO Wei，WANG Rui，ZHANG Jianmin. New strength criterion for sand with cross-anisotropy[J]. Chinese Journal of Geotechnical Engineering，2016，38(11)：2 026–
2 032.(in Chinese))
[16] 董 彤，郑颖人，孔 亮，等. 考虑主应力轴方向的土体各向异性强度准则与滑动面研究[J]. 岩土工程学报，2018，40(4)：736–742. (DONG Tong，ZHENG Yingren，KONG Liang，et al. Mechanical mechanism of the non-coaxiality of geomaterials[J]. Chinese Journal of Geotechnical Engineering，2018，40(4)：736–742.(in Chinese))
[17] TOBITA Y. Fabric tensors in constitutive equations for granular materials[J]. Soils and Foundations，1989，29(4)：91–104.
[18] ODA M. Inherent and induced anisotropy in plasticity theory of granular soils[J]. Mechanics of Materials，1993，16(1)：35–45.
[19] CHANG C S，LIU Y. Stress and fabric in granular material[J]. Theoretical and Applied Mechanics Letters，2013：3(2)：10–15.
[20] YAO Y，TIAN Y，GAO Z. Anisotropic UH model for soils based on a simple transformed stress method[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2017，41(1)：54–78.
[21] DONG T，KONG L. Equivalent stress tensor and anisotropic failure criterion of soils[C]// International Conference on Transportation Infrastructure and Materials. Lancaster Pennsylvania：DEStech Publication，Inc，U S A.，2017：644–652.
[22] 姚仰平，孔玉侠. 横观各向同性土强度与破坏准则的研究[J]. 水利学报，2012，42(1)：43–50.(YAO Yangping，KONG Yuxia. Study on strength and failure criterion of cross-anisotropic soil[J]. Journal of Hydraulic Engineering，2012，42(1)：43–50.(in Chinese))
[23] MUHUNTHAN B，CHAMEAU J L，MASAD E. Fabric Effects on the Yield Behavior of Soils[J]. Soils and Foundations，1996，36(3)：85–97.
[24] LI X，YU H S. Tensorial characterisation of directional data in micromechanics[J]. International Journal of Solids and Structures，2011，48(14/15)：2 167–2 176.
[25] DAFALIAS Y F，PAPADIMITRIOU A G，LI X S. Sand plasticity model accounting for inherent fabric anisotropy[J]. Journal of Engineering Mechanics，2004，130(11)：1 319–1 333.
[26] BATHURST R J，ROTHENBURG L. Observations on stress-force- fabric relationships in idealized granular materials[J]. Mechanics of Materials，1990，9(1)：65–80.
[27] EMERIAULT F，CHANG C S. Interparticle forces and displacements in Granular Materials[J]. Computers and Geotechnics，1997，20(3/4)：223–244.
[28] 李建红，沈珠江. 结构性土的微观破损机理研究[J]. 岩土力学，2007，28(8)：1 525–1 532.(LI Jianhong，SHEN Zhujiang. Study on mechanism of micro-failure of structured soils[J]. Rock and Soil Mechanics，2007，28(8)：1 525–1 532.(in Chinese))
[29] 董 彤，孔 亮，郑颖人，等. 考虑岩土材料各向异性与应力方向性的等效非线性模型[J]. 岩石力学与工程学报，2018，37(2)：506–512.(DONG Tong，KONG Liang，ZHENG Yingren，et al. Equivalent nonlinear model considering the anisotropy and the stress directionality of geomaterials[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(2)：506–512.(in Chinese))
[30] ABELEV A V，LADE P V. Effects of cross anisotropy on three-dimensional behavior of sand. I：stress-strain behavior and shear banding[J]. Journal of Engineering Mechanics，2003，129(2)：160–165.
[31] LADE P V，RODRIGUEZ N M，DYCK E J V. Effects of principal stress directions on 3d failure conditions in cross-anisotropic sand[J]. Journal of Geotechnical and Geoenvironmental Engineering，2014，140(2)：04013001. |
|
|
|
2018, Vol. 37 
