Generalized non-coaxial theory based on orthogonal decomposition of stress rate

WANG Xing; KONG Liang; LI Xue-feng

doi:10.11779/CJGE202112004

Volume 43 Issue 12

Dec 2022

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JOURNAL OF MECHANICAL ENGINEERING > 2021 > 43(12): 2180-2189.

WANG Xing, KONG Liang, LI Xue-feng. Generalized non-coaxial theory based on orthogonal decomposition of stress rate[J]. JOURNAL OF MECHANICAL ENGINEERING, 2021, 43(12): 2180-2189. doi: 10.11779/CJGE202112004

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WANG Xing, KONG Liang, LI Xue-feng. Generalized non-coaxial theory based on orthogonal decomposition of stress rate[J]. JOURNAL OF MECHANICAL ENGINEERING, 2021, 43(12): 2180-2189. doi: 10.11779/CJGE202112004

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Generalized non-coaxial theory based on orthogonal decomposition of stress rate

doi: 10.11779/CJGE202112004

WANG Xing^{1, 2
,},
KONG Liang^{1, 2,
,
,},
LI Xue-feng³

1.
School of Sciences, Qingdao University of Technology, Qingdao 266033, China
2.
School of Civil Engineering, Qingdao University of Technology, Qingdao 266033, China
3.
Solid Mechanics Institute, Ningxia University, Yinchuan 750021, China

Received Date: 26 Feb 2021
Available Online: 02 Dec 2022
Issue Publish Date: 01 Dec 2021

Abstract

Abstract

In the traditional non-coaxial theories, linear assumption is usually made between non-coaxial plastic strain rate and non-coaxial stress rate, and they are always in the same direction, which is inconsistent with the real non-coaxial deformation characteristics of soils. In order to make up for this defect, firstly, it is proved by the mathematical derivation that the total stress rate can be decomposed into the sum of the component stress rates in six orthogonal directions, and then it is revealed that the non-coaxial stress rate defined in the traditional non-coaxial theories is composed of multiple orthogonal components. For each orthogonal component of the non-coaxial stress rate, based on the generalized plastic mechanics, the corresponding nonlinear loading mechanism is established by defining the loading strength index, plastic modulus and plastic flow direction explicitly, and the total non-coaxial plastic deformation is regarded as the sum of the plastic deformation induced by each component, thus a generalized non-coaxial theory is established. The stress-strain relationship of elastoplastic model for soils based on the generalized non-coaxial theory is derived. The numerical tests for model evaluation show the rationality of the generalized non-coaxial theory, which preliminarily indicates that the new theory can provide a broader theoretical basis for the establishment of non-coaxial model for soils.
- traditional non-coaxial theory,
- orthogonal decomposition of stress rate,
- generalized non-coaxial theory,
- numerical test

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References

[1]	郑颖人, 孔亮. 岩土塑性力学[M]. 2版. 北京: 中国建筑工业出版社, 2019. ZHENG Ying-ren, KONG Liang. Geotechnical Plastic Mechanics[M]. 2nd ed. Beijing: China Architecture and Building Press, 2019. (in Chinese)
[2]	王兴, 孔亮, 李学丰. 砂土非共轴本构模型及其在地基承载力方面的应用[J]. 岩土工程学报, 2020, 42(5): 892-899. WANG Xing, KONG Liang, LI Xue-feng. Three-dimensional non-coaxial constitutive model for sand and its application in bearing capacity of foundation[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(5): 892-899. (in Chinese)
[3]	王兴, 孔亮, 李学丰. 基于改进角点理论的砂土非共轴模型及其应用[J]. 岩土工程学报, 2021, 43(2): 254-262. WANG Xing, KONG Liang, LI Xue-feng. Non-coaxial sand model based on improved vertex theory and its application[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(2): 254-262. (in Chinese)
[4]	TIAN Y, YAO Y P. Constitutive modeling of principal stress rotation by considering inherent and induced anisotropy of soils[J]. Acta Geotechnica, 2018, 13(6): 1299-1311.
[5]	TIAN Y, YAO Y P. Modelling the non-coaxiality of soils from the view of cross-anisotropy[J]. Computers and Geotechnics, 2017, 86: 219-229.
[6]	田雨, 姚仰平, 罗汀. 从各向异性的角度解释和模拟土的非共轴特性[J]. 岩土力学, 2018, 39(6): 2035-2042. TIAN Yu, YAO Yang-ping, LUO Ting. Explanation and modeling of non-coaxiality of soils from anisotropy[J]. Rock and Soil Mechanics, 2018, 39(6): 2035-2042. (in Chinese).
[7]	GAO Z W, ZHAO J D. A non-coaxial critical-state model for sand accounting for fabric anisotropy and fabric evolution[J]. International Journal of Solids and Structures, 2017(106/107): 200-212.
[8]	PETALAS A L, DAFALIAS Y F, PAPADIMITRIOU A G. SANISAND-FN: an evolving fabric-based sand model accounting for stress principal axes rotation[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2019, 43(1): 97-123.
[9]	HU N, YU H S, YANG D S, et al. Constitutive modelling of granular materials using a contact normal-based fabric tensor[J]. Acta Geotechnica, 2020, 15(5): 1125-1151.
[10]	LI X S, DAFALIAS Y F. A constitutive framework for anisotropic sand including non-proportional loading[J]. Géotechnique, 2004, 54(1): 41-55.
[11]	袁冉, 杨文波, 余海岁, 等. 土体非共轴各向异性对城市浅埋土质隧道诱发地表沉降的影响[J]. 岩土工程学报, 2018, 40(4): 673-680. YUAN Ran, YANG Wen-bo, YU Hai-sui, et al. Effects of non-coaxiality and soil anisotropy on tunneling-induced subsurface settlements[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(4): 673-680. (in Chinese)
[12]	吕玺琳, 黄茂松, 钱建固. 基于非共轴本构模型的砂土真三轴试验分叉分析[J]. 岩土工程学报, 2008, 30(5): 646-651. LÜ Xi-lin, HUANG Mao-song, QIAN Jian-gu. Bifurcation analysis in true traxial tests on sands based on non-coaxial elasto-plasticity model[J]. Chinese Journal of Geotechnical Engineering, 2008, 30(5): 646-651. (in Chinese)
[13]	刘元雪, 郑颖人. 考虑主应力轴旋转对土体应力-应变关系影响的一种新方法[J]. 岩土工程学报, 1998, 20(2): 45-47. LIU Yuan-xue, ZHENG Ying-ren. A new method to analyze the influence of principal stress axes rotation on the stress strain relation of soils[J]. Chinese Journal of Geotechnical Engineering, 1998, 20(2): 45-47. (in Chinese)
[14]	RUDNICKI J W, RICE J R. Conditions for the localization of deformation in pressure-sensitive dilatant materials[J]. Journal of the Mechanics and Physics of Solids, 1975, 23(6): 371-394.
[15]	HASHIGUCHI K, TSUTSUMI S. Shear band formation analysis in soils by the subloading surface model with tangential stress rate effect[J]. International Journal of Plasticity, 2003, 19(10): 1651-1677.
[16]	钱建固, 黄茂松, 杨峻. 真三维应力状态下土体应变局部化的非共轴理论[J]. 岩土工程学报, 2006, 28(4): 510-515. QIAN Jian-gu, HUANG Mao-song, YANG Jun. Effect of non-coaxial plasticity on onset strain localization in soils under 3D stress condition[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(4): 510-515. (in Chinese)
[17]	李学丰, 黄茂松, 钱建固. 宏-细观结合的砂土单剪试验非共轴特性分析[J]. 岩土力学, 2013, 34(12): 3417-3424. LI Xue-feng, HUANG Mao-song, QIAN Jian-gu. Analysis of non-coaxial characters of sand for simple shear test with the method of macro-meso-incorporation[J]. Rock and Soil Mechanics, 2013, 34(12): 3417-3424. (in Chinese)
[18]	陈洲泉, 黄茂松. 砂土各向异性与非共轴特性的本构模拟[J]. 岩土工程学报, 2018, 40(2): 243-251. CHEN Zhou-quan, HUANG Mao-song. Constitutive modeling of anisotropic and non-coaxial behaviors of sand[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(2): 243-251. (in Chinese)
[19]	LI X S, DAFALIAS Y F. Noncoaxiality between two tensors with application to stress rate decomposition and fabric anisotropy variable[J]. Journal of Engineering Mechanics, 2020, 146(3): 4020004.
[20]	ZIENKIEWICZ O C. Generalized plasticity and some models for geomechanics[J]. Applied Mathematics and Mechanics, 1982, 3(3): 303-318.
[21]	DAFALIAS Y F. An anisotropic critical state soil plasticity model[J]. Mechanics Research Communications, 1986, 13(6): 341-347.
[22]	GUTIERREZ M, ISHIHARA K, TOWHATA I. Flow theory for sand during rotation of principal stress direction[J]. Soils and Foundations, 1991, 31(4): 121-132.
[23]	蔡燕燕, 俞缙, 余海岁, 等. 加载路径对粗粒土非共轴性影响的试验研究[J]. 岩土工程学报, 2012, 34(6): 1117-1122. CAI Yan-yan, YU Jin, YU Hai-sui, et al. Experimental study on effect of loading path on non-coaxiality of granular materials[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(6): 1117-1122. (in Chinese)
[24]	YAMADA Y, ISHIHARA K. Undrained deformation characteristics of sand in multi-directional shear[J]. Soils and Foundations, 1983, 23(1): 61-79.
[25]	NAKATA Y, HYODO M, MURATA H, et al. Flow deformation of sands subjected to principal stress rotation[J]. Soils and Foundations, 1998, 38(2): 115-128.
[26]	童朝霞, 张建民, 于艺林, 等. 中主应力系数对应力主轴循环旋转条件下砂土变形特性的影响[J]. 岩土工程学报, 2009, 31(6): 946-952. TONG Zhao-xia, ZHANG Jian-min, YU Yi-lin, et al. Effects of intermediate principal stress parameter on deformation behavior of sands under cyclic rotation of principal stress axes[J]. Chinese Journal of Geotechnical Engineering, 2009, 31(6): 946-952. (in Chinese)
[27]	LI X S, DAFALIAS Y F. Dilatancy for cohesionless soils[J]. Géotechnique, 2000, 50(4): 449-460.
[28]	GUDEHUS G. A comparison of some constitutive laws for soils under radially symmetric loading and unloading[C]//Proceedings of the 3th Conference on Numerical Methods in Geomechanics, 1979, Aachen.

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Generalized non-coaxial theory based on orthogonal decomposition of stress rate

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