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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.
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Keywords:
- rock failure /
- MPD model /
- stress-strain relation /
- manifold cover
[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 物理学报 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 地球物理学报 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 物理学报 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 物理学报 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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[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 物理学报 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 地球物理学报 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 物理学报 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 物理学报 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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