基于应力率正交分解的广义非共轴理论

王兴; 孔亮; 李学丰

doi:10.11779/CJGE202112004

基于应力率正交分解的广义非共轴理论 English Version

王兴^{1, 2,},
孔亮^{1, 2, ,},
李学丰³

1.
青岛理工大学理学院,山东　青岛　266033
2.
青岛理工大学土木工程学院,山东　青岛　266033
3.
宁夏大学固体力学研究所,宁夏　银川　750021

基金项目:

国家自然科学基金项目 51778311

宁夏重点研发项目 2018DWHZ0084

宁夏科技创新领军人才计划 KJT2019001

详细信息

作者简介:
王兴(1988— ),男,博士研究生,主要从事岩土本构关系方面的研究。E-mail：1306825892@qq.com

通讯作者:
孔亮, E-mail：qdkongliang@163.com

中图分类号: TU43
计量
- 文章访问数: 231
- HTML全文浏览量: 27
- PDF下载量: 114
出版历程
- 收稿日期: 2021-02-25
- 网络出版日期: 2022-11-30
- 刊出日期: 2021-11-30

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

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

摘要

摘要: 传统非共轴理论中非共轴塑性应变率与非共轴应力率之间通常采用线性假设并且二者始终同向,这与土体实际的非共轴变形特性不相符。为了弥补这一缺陷,首先基于数学推导证明了总应力率可以分解为6个正交方向上的分量应力率之和,由此揭示出传统非共轴理论中定义的非共轴应力率是由多项正交分量所构成。针对非共轴应力率中的每一正交分量,基于广义塑性力学,通过直接定义加载强度指标、塑性模量和塑性流动方向建立相应的非线性加载机制描述其所诱发的塑性变形。将总的非共轴塑性变形视为每一分量诱发的塑性变形之和,从而建立了一种广义形式的非共轴理论。推导了基于广义非共轴理论建立土体弹塑性模型时的应力应变关系式。针对模型评估的数值试验显示了广义非共轴理论的合理性,从而表明了新建理论能够为土体非共轴模型的建立提供更为广泛的理论基础。
- 传统非共轴理论 /
- 应力率正交分解 /
- 广义非共轴理论 /
- 数值试验
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

HTML全文

图 1 传统的非共轴理论^[14]

Figure 1. Traditional non-coaxial theory by Ref. [14]

下载: 全尺寸图片幻灯片

图 2 传统的非共轴理论^[15]

Figure 2. Traditional non-coaxial theory by Ref. [15]

下载: 全尺寸图片幻灯片

图 3 传统的非共轴理论^[16]

Figure 3. Traditional non-coaxial theory by Ref. [16]

下载: 全尺寸图片幻灯片

图 4 塑性流动方向^[22]

Figure 4. Plastic flow direction by Ref [22]

下载: 全尺寸图片幻灯片

图 5 几何映射方法示意图

Figure 5. Schematic diagram of geometric mapping method

下载: 全尺寸图片幻灯片

图 6 插值系数法示意图

Figure 6. Schematic diagram of interpolation coefficient method

下载: 全尺寸图片幻灯片

图 7 加载与反向加载

Figure 7. Loading and reverse loading

下载: 全尺寸图片幻灯片

图 8 第二类非共轴加载

Figure 8. Second kind of non-coaxial loading

下载: 全尺寸图片幻灯片

图 9 应力探测示意图

Figure 9. Schematic diagram of stress probe tests

下载: 全尺寸图片幻灯片

图 10 应变探测示意图

Figure 10. Schematic diagram of stress probe tests

下载: 全尺寸图片幻灯片

图 11 应力率响应包络线

Figure 11. Response envelopes of stress rate

下载: 全尺寸图片幻灯片

参考文献(28)

[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. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202005016.htm 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) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202005016.htm
[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. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202102007.htm 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) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202102007.htm
[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. doi: 10.1007/s11440-018-0680-3
[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. doi: 10.1016/j.compgeo.2017.01.013
[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. doi: 10.16285/j.rsm.2016.2030 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). doi: 10.16285/j.rsm.2016.2030
[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. doi: 10.1002/nag.2855
[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. doi: 10.1007/s11440-019-00811-z
[10]	LI X S, DAFALIAS Y F. A constitutive framework for anisotropic sand including non-proportional loading[J]. Géotechnique, 2004, 54(1): 41-55. doi: 10.1680/geot.2004.54.1.41
[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. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201804017.htm 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) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201804017.htm
[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. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200805005.htm 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) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200805005.htm
[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. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC802.012.htm 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) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC802.012.htm
[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. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200604015.htm 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) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200604015.htm
[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. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201312012.htm 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) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201312012.htm
[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. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201802005.htm 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) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201802005.htm
[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. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201206025.htm 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) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201206025.htm
[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. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200906025.htm 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) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200906025.htm
[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.

施引文献(29)

期刊类型引用(18)

1.	倪小东，张宇科，陆江发，崔允亮. 地层局部沉陷诱发有压管道渗透侵蚀机制研究. 华中科技大学学报(自然科学版). 2025(02): 17-24 . 百度学术
2.	王晓璞，赵海龙，任玲玲，高岩岩，薛东兴，山河，王斌，姚传进，赵建，白英睿. 结合人工智能图像识别的微塑料运移与滞留微观可视化实验方法. 实验技术与管理. 2025(04): 14-19 . 百度学术
3.	梁越，冉裕星，许彬，张鑫强，何慧汝. 细颗粒含量影响渗流侵蚀规律的细观机理研究. 岩土工程学报. 2025(05): 1099-1106 . 本站查看
4.	施静怡，吴能森，刘强. 静压桩在成层地基中挤土效应的可视化研究. 河南城建学院学报. 2024(02): 20-26 . 百度学术
5.	刘江涛，李存军，于江华，张彦红，张春彬，孔纲强. 施工顺序对微型钢管桩加固既有基础变形的影响试验研究. 土木与环境工程学报(中英文). 2024(04): 100-108 . 百度学术
6.	梁越，何慧汝，许彬，张鑫强，冉裕星. 基于透明土的水力梯度对渗流侵蚀影响试验研究. 河海大学学报(自然科学版). 2024(05): 60-66 . 百度学术
7.	徐春瑞，郭畅，黄博. 孔隙率对砂土渗透稳定性影响的内部可视化研究. 地基处理. 2024(05): 451-462 . 百度学术
8.	王宇，陈从建，钱声源，段祥宝，谷艳昌. 可视化渗透破坏实验装置研发及土力学实践探索. 力学与实践. 2023(01): 193-199 . 百度学术
9.	周峙，罗易，张家铭，孙狂飙. 考虑裂隙面积率的裂隙性黏土优势流双域入渗规律研究. 安全与环境工程. 2023(02): 109-118 . 百度学术
10.	李敏，齐振霄，姚昕妤，赵博华，李琦. 基于可视角度下重金属污染物在介质中的迁移规律. 环境工程学报. 2023(04): 1303-1312 . 百度学术
11.	马朝阳，任杰，南胜豪，徐松. 土石堤坝渗漏病险试验装置的研制及初步应用. 岩土工程学报. 2023(11): 2268-2277 . 本站查看
12.	侯娟，滕宇阳，李昊，刘磊. 多孔介质曲折度对膨润土衬垫渗透性能的影响. 湖南大学学报(自然科学版). 2022(01): 155-164 . 百度学术
13.	梁越，代磊，魏琦. 基于透明土和粒子示踪技术的渗流侵蚀试验研究. 岩土工程学报. 2022(06): 1133-1140 . 本站查看
14.	顾展飞，田光辉，王栩硕，于文搏. 地下管线渗漏对粉土地面塌陷过程的影响及实验研究. 科技创新与应用. 2022(25): 61-64 . 百度学术
15.	杜建明，房倩，刘翔，海路. 透明土物理模拟试验技术现状与趋势. 科学技术与工程. 2021(03): 852-861 . 百度学术
16.	谷敬云，罗玉龙，张兴杰，詹美礼，王媛，盛金昌. 基于平面激光诱导荧光的潜蚀可视化试验装置及其初步应用. 岩石力学与工程学报. 2021(06): 1287-1296 . 百度学术
17.	冷先伦，王川，庞荣，盛谦. 透明胶结土材料强度特性的试验研究. 岩土力学. 2021(08): 2059-2068+2077 . 百度学术
18.	赵宽耀，许强，刘方洲，张先林. 黄土中优势通道渗流特征研究. 岩土工程学报. 2020(05): 941-950 . 本站查看