基于流形覆盖的岩体宏细观破裂的颗粒离散元法

李树忱; 平洋; 李术才; 寇强; 马腾飞; 冯丙阳

doi:10.7498/aps.63.050202

摘要

本文基于流形覆盖的思想，结合颗粒接触模型，构造一种新的颗粒离散元数值方法即MPD（Manifold Particle Discrete），该方法可以从宏细观角度分析岩体破裂的全过程. 通过分析流形覆盖和球颗粒模型，构造三维流形覆盖的四面体单元，得到MPD模型的平衡方程和相容方程. 通过数值算例，验证了所提出的数值方法的正确性和分析岩石破裂的可行性.

关键词:

The rock mass can be assumed to be homogeneous material from the macroscopic view, but it is a heterogeneous material at a mesoscopic scale and its physico-mechanical properties are discontinuous in space. Therefore, it is necessary to research the generation and development of pre-peak micro cracks in rocks and frictional characteristics between post-peak mineral particles from macro-meso and multi-scale perspectives to know the substantive characteristics of rock failure and instability. This paper, based on the manifold cover concept, proposes a new discrete element numerical method (i.e. Manifold Particle Discrete) combining with the particle contact model, so as to introduce the concept of stress boundary. This method can be applied to the entire process of analyzing rock failure. By analyzing the manifold cover and ball particle model, this paper constitutes the ball unit cover function of three-dimensional manifold cover, establishes tetrahedron units, obtains the equilibrium equation and compatible equation of the MPD model. It also verifies the accuracy of the proposed numerical method and the feasibility of rock failure analysis through numerical examples.

Keywords:

作者及机构信息

1.
山东大学岩土与结构工程研究中心, 济南 250061

基金项目: 国家重点基础研究发展计划（973）项目（批准号：2010CB732002）、国家自然科学基金面上项目（批准号：51179098，51379113）、教育部高等学校博士学科点博导类专项科研基金（批准号：20120131110031）和新世纪优秀人才资助项目（批准号：NCET-12-2009）资助的课题.

Authors and contacts

1.
Geotechnical and Structural Engineering Research Center, Shandong University, Jinan 250061, China

Funds: Project supported by the National Basic Research Program of China(Grant No. 2010CB732002), the National Natural Science Foundation of China (Grant Nos. 51179098, 51379113), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120131110031), and the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-12-2009).

参考文献

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[2]	Chen Y Q, Zheng X P, Yao Z H 2002 Acta Mechanica Sinica 34 352 (in Chinese) [陈永强, 郑小平, 姚振汉 2002 力学学报 34 352]
[3]	Frantziskonis G, Renaudin P, Breysse D 1997 Eur. J. Mech. (A/Solids) 16 409
[4]	Blair S C, Cook N G 1998 Int. J. Rock Mech. Min. Sci. 35 837
[5]	Zhen H, Ge X Y, Li Z F 1999, Chinese Journal of Rock Mechanics and Engineering 16 8 (in Chinese) [郑宏, 葛修润, 李焯芬 1997 岩石力学与工程学报 16 8]
[6]	Zhao L L, Liu C S, Yan J X, Xu Z P 2010 Acta Phys. Sin. 59 1871 (in Chinese) [赵啦啦, 刘初升, 闫俊霞, 徐志鹏 2010 59 1871]
[7]	Xing J B, Yu L Q, Wang Y J 1999 Chinese Journal of Rock Mechanics and Engineering 16 627 (in Chinese) [邢纪波, 俞良群, 王泳嘉 1999 岩石力学与工程学报 16 627]
[8]	Xu J L, Tang Z P 2003 Chinese Journal of Computational Physics 20 477 (in Chinese) [胥建龙, 唐志平 2003 计算物理 20 477]
[9]	Cottrell M G, Yu J, Owen D R J 2003 International Journal of Impact Engineering 28 1017
[10]	Klerck P A, Sellers E J, Owen D R J 2004 Computer Methods in Applied Mechanics and Engineering 193 3035
[11]	Munjiza A, Owen D R J, Bicanic N 1995 International Journal of Computational Engineering Science 12 145
[12]	Munjiza A 2004 The Combined Finite-Discrete Element Method (New York: John Wiley &Sons) p300
[13]	Tang C A, Wang S H, Fu Y F 2003 (Beijing: Academic Press) p48 (in Chinese) [唐春安, 王述红, 傅宇方 2003 岩石破裂过程数值试验(北京: 科学出版社)第48页]
[14]	Tang C A, Liu H Y, Qin S Q 2000 Chinese J. Geophys. 43 116 (in Chinese) [唐春安, 刘红元, 秦四清 2000 地球 43 116]
[15]	Van Mier J G M 1997 CRCPress p364
[16]	Schlangen E, van Mier J G M 1991 Denver, Colorado, USA p513
[17]	Schlangen E, Garbocai E J 1997 Engng. Frac. Mech. 57 319
[18]	Bazant Z P, Tabbara M R 1990 Journal of Engineering Mechanics ASCE 116 1686
[19]	Shi G H 1997 Numerical manifold method and discontinuous deformation analysis (Beijing: Tsinghua University Press) p12 (in Chinese) [石根华 1997 数值流形方法与非连续变形分析(北京: 清华大学出版社)第12页]
[20]	Li S C, Cheng Y M 2005 Theor Appl Fract Mech. 44 234
[21]	Li S C, Cheng Y M, Li S C 2006 Acta Phys. Sin. 55 4760 (in Chinese) [李树忱, 程玉民, 李术才 2006 55 4760]
[22]	Cheng Y M, Wang J F, Bai F N 2012 Chin. Phys. B 21 090203
[23]	Cheng R J, Cheng Y M 2011 Acta Phys. Sin. 60 075206 (in Chinese) [程荣军, 程玉民 2011 60 075206]
[24]	Zhang H H, Li L X, An X M, Ma G W 2010 Eng Anal Boundary Elem. 34 41
[25]	Ma G W, An X M, Zhang H H, Li L X 2009 Int. J. Fract. 156 21
[26]	He L, Ma G W 2010 International Journal of Computational Methods 7 107
[27]	Jian Q H, Deng S S, Zhou C B 2006 Rock and Soil Mechanics 27 1472 (in Chinese) [姜清辉, 邓书申, 周创兵 2006 岩土力学 27 1472]
[28]	Cusatis G, Bazant Z P, Cedolin L 2003 J. Eng. Mech-ASCE 129 1439
[29]	Cusatis C, Pelessone D, Mencarelli A 2011 Cem. Concr. Compos. 33 925
[30]	Drucker D C, Prager W 1952 Quart Appl. Math. 10 157

施引文献

[1]	Xie H P 1990 (Xuzhou: CUM T Publishing Press) p41 (in Chinese) [谢和平 1990 岩石混凝土损伤力学 (徐州: 中国矿业大学出版社) 第41页]
[2]	Chen Y Q, Zheng X P, Yao Z H 2002 Acta Mechanica Sinica 34 352 (in Chinese) [陈永强, 郑小平, 姚振汉 2002 力学学报 34 352]
[3]	Frantziskonis G, Renaudin P, Breysse D 1997 Eur. J. Mech. (A/Solids) 16 409
[4]	Blair S C, Cook N G 1998 Int. J. Rock Mech. Min. Sci. 35 837
[5]	Zhen H, Ge X Y, Li Z F 1999, Chinese Journal of Rock Mechanics and Engineering 16 8 (in Chinese) [郑宏, 葛修润, 李焯芬 1997 岩石力学与工程学报 16 8]
[6]	Zhao L L, Liu C S, Yan J X, Xu Z P 2010 Acta Phys. Sin. 59 1871 (in Chinese) [赵啦啦, 刘初升, 闫俊霞, 徐志鹏 2010 59 1871]
[7]	Xing J B, Yu L Q, Wang Y J 1999 Chinese Journal of Rock Mechanics and Engineering 16 627 (in Chinese) [邢纪波, 俞良群, 王泳嘉 1999 岩石力学与工程学报 16 627]
[8]	Xu J L, Tang Z P 2003 Chinese Journal of Computational Physics 20 477 (in Chinese) [胥建龙, 唐志平 2003 计算物理 20 477]
[9]	Cottrell M G, Yu J, Owen D R J 2003 International Journal of Impact Engineering 28 1017
[10]	Klerck P A, Sellers E J, Owen D R J 2004 Computer Methods in Applied Mechanics and Engineering 193 3035
[11]	Munjiza A, Owen D R J, Bicanic N 1995 International Journal of Computational Engineering Science 12 145
[12]	Munjiza A 2004 The Combined Finite-Discrete Element Method (New York: John Wiley &Sons) p300
[13]	Tang C A, Wang S H, Fu Y F 2003 (Beijing: Academic Press) p48 (in Chinese) [唐春安, 王述红, 傅宇方 2003 岩石破裂过程数值试验(北京: 科学出版社)第48页]
[14]	Tang C A, Liu H Y, Qin S Q 2000 Chinese J. Geophys. 43 116 (in Chinese) [唐春安, 刘红元, 秦四清 2000 地球 43 116]
[15]	Van Mier J G M 1997 CRCPress p364
[16]	Schlangen E, van Mier J G M 1991 Denver, Colorado, USA p513
[17]	Schlangen E, Garbocai E J 1997 Engng. Frac. Mech. 57 319
[18]	Bazant Z P, Tabbara M R 1990 Journal of Engineering Mechanics ASCE 116 1686
[19]	Shi G H 1997 Numerical manifold method and discontinuous deformation analysis (Beijing: Tsinghua University Press) p12 (in Chinese) [石根华 1997 数值流形方法与非连续变形分析(北京: 清华大学出版社)第12页]
[20]	Li S C, Cheng Y M 2005 Theor Appl Fract Mech. 44 234
[21]	Li S C, Cheng Y M, Li S C 2006 Acta Phys. Sin. 55 4760 (in Chinese) [李树忱, 程玉民, 李术才 2006 55 4760]
[22]	Cheng Y M, Wang J F, Bai F N 2012 Chin. Phys. B 21 090203
[23]	Cheng R J, Cheng Y M 2011 Acta Phys. Sin. 60 075206 (in Chinese) [程荣军, 程玉民 2011 60 075206]
[24]	Zhang H H, Li L X, An X M, Ma G W 2010 Eng Anal Boundary Elem. 34 41
[25]	Ma G W, An X M, Zhang H H, Li L X 2009 Int. J. Fract. 156 21
[26]	He L, Ma G W 2010 International Journal of Computational Methods 7 107
[27]	Jian Q H, Deng S S, Zhou C B 2006 Rock and Soil Mechanics 27 1472 (in Chinese) [姜清辉, 邓书申, 周创兵 2006 岩土力学 27 1472]
[28]	Cusatis G, Bazant Z P, Cedolin L 2003 J. Eng. Mech-ASCE 129 1439
[29]	Cusatis C, Pelessone D, Mencarelli A 2011 Cem. Concr. Compos. 33 925
[30]	Drucker D C, Prager W 1952 Quart Appl. Math. 10 157

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