基于Cosserat理论的三维弹塑性模型及其在重力坝抗滑稳定分析中的应用

doi:10.13722/j.cnki.jrme.2020.1171

摘要
图/表
参考文献
相关文章 (15)

全文: PDF (2123 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要采用有限单元法模拟岩土工程中的应变局部化问题时，存在有限网格尺寸敏感性和网格锁定等问题，通过引入Cosserat连续体理论作为正则化机制，提出基于Cosserat连续体理论的三维Mohr-Coulomb弹塑性模型，采用Euler向后隐式应力更新算法，利用ABAQUS的二次开发功能进行数值实现，通过单轴压缩数值模拟验证模型和程序的可靠性及有效性，探究弯曲特征长度与剪切带宽度之间的关系，并建议材料弯曲特征长度的取值标准。分别采用经典弹塑性模型和基于Cosserat连续体理论的三维Mohr-Coulomb弹塑性模型进行重力坝三维抗滑稳定分析，经典弹塑性模型具有明显的网格依赖性，采用较疏的有限元网格计算会高估实际抗滑稳定性，而基于Cosserat理论的Mohr-Coulomb弹塑性模型在不同密度有限元网格上的抗滑稳定安全系数和滑移模式基本一致。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	唐嘉博1
	2
	马刚1
	2
	涂承义3
	曹学兴4
	周伟1
	2
	程勇刚1
	2

关键词 ：边坡工程, 应变局部化, Cosserat, Mohr-Coulomb, 重力坝, 三维抗滑稳定

Abstract：To solve the issues of finite mesh size sensitivity and mesh locking in applying finite element method to simulate strain localization in geotechnical engineering，a three-dimensional Mohr-Coulomb elastoplastic model was developed by introducing Cosserat continuum theory as a regularization mechanism. The secondary development function of ABAQUS and Euler backward implicit stress update algorithm were adopted to realize numerical simulation，and the reliability and effectiveness of the model and program were verified by numerical simulation of uniaxial compression. The relationship between the bending characteristic length and the shear band width was discussed，and the value standard of the bending characteristic length was proposed. The three-dimensional anti-sliding stability analysis of a gravity dam was carried out repectively by the classical elastic-plastic model and the proposed model. It is shown that the classical elastic-plastic model has obvious mesh dependence，more specifically，an overestimation of the actual anti-sliding stability resulted from sparse finite element mesh，while that the anti-sliding stability safety factor and the sliding mode by the developed model almost keep unchanged for different density finite element mesh.

Key words： slope engineering strain localization Cosserat Mohr-Coulomb gravity dam 3D anti-sliding stability

引用本文:

唐嘉博1，2，马刚1，2，涂承义3，曹学兴4，周伟1，2，程勇刚1，2. 基于Cosserat理论的三维弹塑性模型及其在重力坝抗滑稳定分析中的应用[J]. 岩石力学与工程学报, 2021, 40(8): 1702-1712.
TANG Jiabo1，2，MA Gang1，2，TU Chengyi3，CAO Xuexing4，ZHOU Wei1，2，CHENG Yonggang1，2. Three-dimensional elastic-plastic model based on Cosserat theory and its application in anti-sliding stability analysis of gravity dams. , 2021, 40(8): 1702-1712.

链接本文:

http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2020.1171 或 http://rockmech.whrsm.ac.cn/CN/Y2021/V40/I8/1702

[9]	ERINGEN A C，KIM B S. Stress concentration at the tip of crack[J]. Mechanics Research Communications，1974，1(4)：233-237.
[5]	王小平，徐卫亚. 应变局部化问题中的正则化机制探讨[J]. 岩土力学，2008，29(11)：2 997-3 002.(WANG Xiaoping，XU Weiya. Discussion on regularizatin mechanism in strain localization problems[J]. Rock and Soil Mechanics，2008，29(11)：2 997-3 002.(in Chinese))
[38]	ABAQUS I. Abaqus documentation[M]. [S. l.]：[s. n.]，2014：1-5.
[8]	ERINGEN A C，EDELEN D G B. On nonlocal elasticity[J]. International Journal of Engineering Ence，1972，10(3)：233-248.
[33]	钱建固，黄茂松. 土体应变局部化现象的理论解析[J]. 岩土力学，2005，26(3)：432-436.(QIAN Jiangu，HUANG Maosong. An analytical solution for criterion of onset of strain localization of soils[J]. Rock and Soil Mechanics，2005，26(3)：432-436.(in Chinese))
[14]	VARDOULAKIS I，MÜHLHAUS H B. The thickness of shear bands in granular materials[J]. Geotechnique，1987，37(3)：271-283.
[23]	RATTEZ H，STEFANOU I，SULEM J，et al. Numerical analysis of strain localization in rocks with thermo-hydro-mechanical couplings using cosserat continuum[J]. Rock Mechanics and Rock Engineering，2018，51(10)：3 295-3 311.
[25]	COLLINS-CRAFT N A，STEFANOU I，SULEM J，et al. A Cosserat Breakage Mechanics model for brittle granular media[J]. Journal of the Mechanics and Physics of Solids，2020：103 975.
[27]	MA G，ZHOU W，CHANG X L，et al. Formation of shear bands in crushable and irregularly shaped granular materials and the associated microstructural evolution[J]. Powder Technology，2016，301：118-130.
[29]	GANG M，REGUEIRO R A，WEI Z，et al. Spatiotemporal analysis of strain localization in dense granular materials[J]. Acta Geotechnica，2018，14(4)：1-18.
[31]	TORNABENE F，FANTUZZI N，BACCIOCCHI M. Mechanical behaviour of composite Cosserat solids in elastic problems with holes and discontinuities[J]. Composite Structures，2017，179(Supp.)：468-481.
[34]	李培基. 重力坝深层抗滑稳定问题浅析[J]. 水利水电工程设计. 2000，(1)：49-52.(LI Peiji. A brief analysis of deep anti-sliding stability of gravity dams[J]. Water Conservancy and Hydropower Engineering Design，2000，(1)：49-52.(in Chinese))
[36]	马刚，涂承义，常晓林，等. 基于Cosserat连续体理论的重力坝深层抗滑稳定分析[J]. 四川大学学报：工程科学版，2012，44(5)：57-63.(MA Gang，TU Chengyi，CHANG Xiaolin，et al. Analysis of deep anti-sliding stability of gravity dam based on Cosserat continuum theory[J]. Journal of Sichuan University：Engineering Science，2012，44(5)：57-63.(in Chinese))
[40]	RUEDEN C T，SCHINDELIN J，HINER M C，et al. ImageJ2： ImageJ for the next generation of scientific image data[J]. Bmc Bioinformatics，2017，18(1)：1-26.
[4]	VALANIS K C，PETERS J F. Ill-posedness of the initial and boundary value problems in non-associative plasticity[J]. Acta Mechanica. 1996，114(1/4)：1-25.
[6]	BAZANT Z P，JIRÁSEK M. Nonlocal integral formulations of plasticity and damage：survey of progress[J]. Journal of Engineering Mechanics. 2002，128(11)：1 129-1 239.
[10]	BAZANT Z P，PIJAUDIER-CABOT G. Nonlocal continuum damage，localization instability and convergence[J]. Journal of Applied Mechanics，1988，55(2)：287-293.
[2]	TANG H，DONG Y，WANG T，et al. Simulation of strain localization with discrete element-Cosserat continuum finite element two scale method for granular materials[J]. Journal of the Mechanics and Physics of Solids，2018，122：450-471.
[13]	王小平，孟国涛. 非局部化弹塑性理论及其应用[J]. 岩石力学与工程学报，2007，26(增 1)：2 964-2 967.(WANG Xiaoping，MENG Guotao. Nonlocal elastoplastic theory and its application[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(Supp.1)：2 964-2 967.(in Chinese))
[15]	MÜHLHAUS H B. Application of Cosserat theory in numerical solutions of limit load problems[J]. Ingenieur-Archiv，1989，59(2)：124-137.
[17]	BORST R D. Simulation of strain localization：a reappraisal of the Cosserat continuum[J]. Engineering Computations，1991，8(4)：317-332.
[19]	TANG H，DONG Y，WANG T，et al. Simulation of strain localization with discrete element-Cosserat continuum finite element two scale method for granular materials[J]. Journal of the Mechanics and Physics of Solids，2018，122：450-471.
[21]	唐洪祥，李锡夔. 基于Cosserat连续体的CAP弹塑性模型与应变局部化有限元模拟[J]. 岩石力学与工程学报，2008，27(5)：960-970. (TANG Hongxiang，LI Xikui. CAP elastoplastic cosserat continuum model and finite element simulation of strain localization[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(5)：960-970. (in Chinese))
[24]	WANG D，CHEN X，LYU Y，et al. Geotechnical localization analysis based on Cosserat continuum theory and second-order cone programming optimized finite element method[J]. Computers and Geotechnics，2019，114：103 118.
[26]	ZHOU W，YANG L，MA G，et al. DEM modeling of shear bands in crushable and irregularly shaped granular materials[J]. Granular Matter，2017，19(2)：25.
[28]	MA G，REGUEIRO R A，ZHOU W，et al. Role of particle crushing on particle kinematics and shear banding in granular materials[J]. Acta Geotechnica，2018，13(3)：601-618.
[30]	SADOVSKII V M，GUZEV M A，SADOVSKAYA O V，et al. Modeling of Plastic Deformation Based on the Theory of an Orthotropic Cosserat Continuum[J]. Physical Mesomechanics，2020，23(3)：223-230.
[32]	STEFANOU I，SULEM J. Strain localization with rate dependent models versus cosserat continuum：an illustrative example[C]// International Workshop on Bifurcation and Degradation in Geomaterials. Springer，Cham：[s. n.]，2017：557-562.
[1]	TANG H，FENG Z，YANG D，et al. Numerical simulation of strain localization based on Cosserat continuum theory and isogeometric analysis[J]. Computers and Geotechnics，2021，129：103874.
[3]	RUDNICKI J W，RICE J R. Conditions for the localization of deformation in pressure-sensitive dilatant materials[J]. Journal of Mechanics Physics of Solids，1975，23(6)：371-394.
[7]	SHAHIN G，MARINELLI F，BUSCARNERA G. Viscoplastic interpretation of localized compaction creep in porous rock[J]. Journal of Geophysical Research：Solid Earth，2019，124(10)：10 180-10 196.
[11]	KENAWY M，KUNNATH S，KOLWANKAR S，et al. Concrete uniaxial nonlocal damage-plasticity model for simulating post-peak response of reinforced concrete beam-columns under cyclic loading[J]. Journal of Structural Engineering，2020，146(5)：4 020 051-4 020 052.
[12]	冯吉利，温科伟，田晓燕，等. 岩土工程开挖模拟的非局部软化模型[J]. 工程力学，1999，16(6)：36.(FENG Jili，WEN Kewei，TIAN Xiaoyan，et al. Non-local softening model for excavation simulation in geotechnical engineering[J]. Engineering Mechanics，1999，16(6)：36.(in Chinese))
[16]	BORST R D，SLUYS L J. Localisation in a Cosserat continuum under static and dynamic loading conditions[J]. Computer Methods in Applied Mechanics and Engineering，1991，90(1/3)：805-827.
[18]	BORST R D. A generalisation of J2-flow theory for polar continua[J]. Computer Methods in Applied Mechanics and Engineering，1993，103(3)：347-362.
[20]	李锡夔，唐洪祥. 压力相关弹塑性Cosserat连续体模型与应变局部化有限元模拟[J]. 岩石力学与工程学报，2005，24(9)：1 497-1 505. (LI Xikui，TANG Hongxiang. Pressure-dependent elasto-plastic cosserat continuum modeland finite element simulation of strain localization[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(9)：1 497-1 505.(in Chinese))
[22]	唐洪祥，李锡夔. 地基渐进破坏及极限承载力的Cosserat连续体有限元分析[J]. 岩土力学，2007，28(11)：2 259-2 264.(TANG Hongxiang，LI Xikui. Finite element analysis of Cosserat continuum for progressive failure and limit bearing capacity of soil foundation[J]. Rock and Soil Mechanics，2007，28(11)：2 259-2 264.(in Chinese))
[35]	马刚，常晓林，周伟，等. 基于Cosserat理论的重力坝深层抗滑稳定分析[J]. 岩土力学，2012，33(5)：1 505-1 512.(MA Gang，CHANG Xiaolin，ZHOU Wei，et al. Deep anti-sliding stability analysis of gravity dam based on Cosserat continuum theory[J]. Rock and Soil Mechanics，2012，33(5)：1 505-1 512.(in Chinese))
[37]	涂承义，马刚. Cosserat连续体的本构参数对重力坝深层抗滑稳定的影响[J]. 中国农村水利水电，2017，(4)：158-163.(TU Chengyi，MA Gang. The effects of constitutive parameters in Cosserat continuum model on the deep anti-sliding stability of gravity dams[J]. Water Conservancy and Hydropower in China¢s Countryside，2017，(4)：158-163.(in Chinese))
[39]	彼莱奇科，庄茁，廖荣锦，等. 连续体和结构的非线性有限元[M]. 北京：清华大学出版社，2002.(BELYTSCHKO T，ZHUANG Zhuo，MORAN B，et al. Nonlinear finite elements for continua and structures[M]. Beijing： Tsinghua University Press，2002.(in Chinese))
[41]	常晓林，王辉，周伟，等. 重力坝两种滑移失稳机理及安全度评价方法[J]. 水利学报，2009，40(10)：1 189-1 195.(CHANG Xiaolin，WANG Hui，ZHOU Wei，et al. Two slip instability mechanisms and safety evaluation methods for gravity dams[J]. Journal of Hydraulic Engineering，2009，40(10)：1 189-1 195.(in Chinese))
[42]	周伟，常晓林，徐建强. 基于分项系数法的重力坝深层抗滑稳定分析[J]. 岩土力学，2007，28(2)：315-320.(ZHOU Wei，CHANG Xiaolin，XU Jianqiang. Analysis of anti-sliding stability in deep foundation of gravity dam based on partial coefficient[J]. Rock and Soil Mechanics，2007，28(2)：315-320.(in Chinese))