基于显式时间积分的非连续变形分析方法

doi:10.13722/j.cnki.jrme.2016.0838

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摘要非连续变形分析(DDA)方法非常适合应用于模拟高度离散化的岩石块体系统的力学行为。然而，传统采取隐式时间积分方案的DDA方法，在运算过程中需要集成总体刚度矩阵和求解矩阵方程，这直接导致计算效率的降低，尤其在求解大规模非连续问题时。因此，提出一种基于显式时间积分的二维显式DDA方法。在求解过程中，不需要集成总体刚度矩阵和求解大型代数方程组。在求解加速度时，由于采用协调质量矩阵，可以分块求解，求解过程简单省时。仍沿用原DDA的开闭迭代算法，可确保块体间约束的准确施加，保证了求解精度。最后，通过几个典型算例，证实显式DDA的正确性和鲁棒性。

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	徐栋栋
	邬爱清

关键词 ：岩石力学, 非连续变形分析, 显式时间积分, 开闭迭代, 质量矩阵, 岩石块体系统

Abstract：Discontinuous deformation analysis method(DDA) is very suitable for modeling the mechanical behaviors of highly discrete rock block system. However，it need to integrate the global stiffness matrix and solve the matrix equation for the traditional DDA that adopts the implicit time integration scheme. This will result in the decrease of calculation efficiency，especially in solving the large-scale discontinuous problems. Therefore，an explicit version of two-dimensional DDA is proposed based on the explicit time integration scheme. There is no need to integrate the global stiffness matrix and solve the large-scale simultaneous algebraic equations in the solving process. Block elimination method is used to calculate the acceleration as the result of adoption of consistent mass matrix，which is simple and time-saving. The open-close iteration is still adopted to ensure the right arrangement of constraints. At last，the correctness and robustness of explicit DDA is confirmed by several classic numerical examples.

Key words： rock mechanics discontinuous deformation analysis(DDA) explicit time integration open-close iteration mass matrix rock block system

引用本文:

徐栋栋，邬爱清. 基于显式时间积分的非连续变形分析方法[J]. 岩石力学与工程学报, 2016, 35(S2): 3526-3534.
XU Dongdong，WU Aiqing. Discontinuous deformation analysis method based on the explicit time integration scheme. , 2016, 35(S2): 3526-3534.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2016.0838 或 https://rockmech.whrsm.ac.cn/CN/Y2016/V35/IS2/3526

[1] 徐志英. 岩石力学[M]. 3版. 北京：中国水利水电出版社，2007：1.(XU Zhiying. Rock mehcanics[M]. 3rd ed. Beijing：China Water and Power Press，2007：1.(in Chinese))

[2] CUNDALL P A. A computer model for simulating progressive large scale movements in blocky rock systems[C]// Proceedings of the Symposium of the International Society of Rock Mechanics. Rotterdam：A. A. Balkema，1971：11–18.

[3] CUNDALL P A：The measurement and analysis of acceleration on rock slopes[Ph. D. Thesis][D]. London：University of London，Imperial College of Science and Technology，1971.

[4] SHI G H，GOODMAN R E. Two-dimensional discontinuous deformation analysis[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1985，9(6)：541–556.

[5] SHI G H，GOODMAN R E. Generalization of two‐dimensional discontinuous deformation analysis for forward modelling[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1989，13(4)：359–380.

[6] CUNDALL P A. UDEC A. Generalized distinct element program for modelling jointed rock[R]. U. S. Army：[s.n.]，1980.

[7] CUNDALL P A. Formulation of a three-dimensional distinct element model—part I：a scheme to detect and represent contacts in a system composed of many polyhedral blocks[J]. International Journal of Rock Mechanics and Mining Sciences，1988，25(3)：107–116.

[8] CAI Y，LIANG G P，SHI G H，et al. Studying on impact problem by using LDDA method[C]// Proceedings of the First International Forum on Discontinuous Deformation Analysis(DDA) and Simulations of Discontinuous Media. Albuquerque：TSI Press，1996：288–294.

[9] BAO H，ZHAO Z，TIAN Q. On the implementation of augmented Lagrangian method in the two-dimensional discontinuous deformation Analysis[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2014，38(6)：551–571.

[10] ZHENG H，JIANG W. Discontinuous deformation analysis based on complementary theory[J]. Science in China Series E：Technological Sciences，2009，52(9)：2 547–2 554.

[11] TIAN Q，ZHAO Z，BAO H. Block fracturing analysis using nodal- based discontinuous deformation analysis with the double minimization procedure[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2014，38(9)：881–902.

[12] 焦玉勇，张秀丽，刘泉声，等. 用非连续变形分析方法模拟岩石裂纹扩展[J]. 岩石力学与工程学报，2007，26(4)：682–691.(JIAO Yuyong，ZHANG Xiuli，LIU Quansheng，et al. Simulation of rock crack propagation using discontinuous deformation analysis method[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(4)：682–691.(in Chinese))

[13] 王士民，朱合华，蔡永昌. 非连续子母块体理论模型研究(I)：基本理论[J]. 岩土力学，2010，31(7)：2 088–2 094.(WANG Shimin，ZHU Hehua，CAI Yongchang. A discontinuous sub-block model(I)：fundamentals[J]. Rock and Soil Mechanics，2010，31(7)：2 088–2 094. (in Chinese))

[14] CAI Y，ZHU H，ZHUANG X. A continuous/discontinuous deformation analysis(CDDA) method based on deformable blocks for fracture modeling[J]. Frontiers of Structural and Civil Engineering，2013，7(4)：369–378.

[15] JIANG Q H，YEUNG M R. A model of point-to-face contact for three- dimensional discontinuous deformation analysis[J]. Rock Mechanics and Rock Engineering，2004，37(2)：95–116.

[16] WU J H，JUANG C H，LIN H M. Vertex‐to‐face contact searching algorithm for three‐dimensional frictionless contact problems[J]. International Journal for Numerical Methods in Engineering，2005，63(6)：876–897.

[17] LIU J，NAN Z，YI P. Validation and application of three-dimensional discontinuous deformation analysis with tetrahedron finite element meshed block[J]. Acta Mechanica Sinica，2012，28(6)：1 602–1 616.

[18] 姜清辉，周创兵，罗先启，等. 三维 DDA 与有限元的耦合分析方法及其应用[J]. 岩土工程学报，2006，28(8)：998–1 001.(JIANG Qinghui，ZHOU Chuangbing，LUO Xianqi，et al. Coupling method of three-dimensional DDA-FEM and its application[J]. Chinese Journal of Geotechnical Engineering，2006，28(8)：998–1 001.(in Chinese))

[19] 张杨，邬爱清，林绍忠. 三维高阶 DDA 方法的静力分析研究[J]. 岩石力学与工程学报，2010，29(3)：558–564.(ZHANG Yang，WU Aiqing，LIN Shaozhong. Study of static analysis of 3D high-order DDA[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(3)：558–564.(in Chinese))

[20] 李海枫，张国新，石根华，等. 流形切割及有限元网格覆盖下的三维流形单元生成[J]. 岩石力学与工程学报，2010，29(4)：731–742.(LI Haifeng，ZHANG Guoxin，SHI Genhua，et al. Manifold cut and generation of three-dimensional manifold element under fe mesh cover[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(4)：731–742.(in Chinese))

[21] 邬爱清，任放，董学晟. DDA 数值模型及其在岩体工程上的初步应用研究[J]. 岩石力学与工程学报，1997，16(5)：411–417.(WU Aiqing，REN Fang，DONG Xuecheng. A study on the numerical model of DDA and its preliminary application to rock engineering[J]. Chinese Journal of Rock Mechanics and Engineering，1997，16(5)：411–417.(in Chinese))

[22] 邬爱清，丁秀丽，陈胜宏，等. DDA 方法在复杂地质条件下地下厂房围岩变形与破坏特征分析中的应用研究[J]. 岩石力学与工程学报，2006，25(1)：1–8.(WU Aiqing，DING Xiuli，CHEN Shenghong，et al. Researches on deformation and failure characteristics of an underground powerhouse with complicated geological conditions by DDA method[J]. Chinese Journal of Rock Mechanics and Engineering，2006，25(1)：1–8.(in Chinese))

[23] MIKOLA R G，SITAR N. Explicit three dimensional discontinuous deformation analysis for blocky system[C]// Proceedings of the 47th US Rock Mechanics/Geomechanics Symposium. [S.l.]：American Rock Mechanics Association，2013.

[24] SHI G H. Manifold method of material analysis[C]// Transactions of the 9th Army Conference on Applied Mathematics and Computing. Minneapolis M N：U.S. Army Research Office，1991：57–76.

[25] 姜清辉，周创兵，漆祖芳. 基于Newmark积分方案的DDA方法[J]. 岩石力学与工程学报，2009，28(增1)：2 778–2 783.(JIANG Qinghui，ZHOU Chuangbing，QI Zufang. Discontinuous deformation analysis method based on Newmark integration algorithm[J]. Chinese Journal of Rock Mechanics and Engineering，2009，28(Supp.1)：2 778–2 783.(in Chinese))

[26] DOOLIN D M，SITAR N. Time integration in discontinuous deformation analysis[J]. Journal of Engineering Mechanics，2004，130(3)：249–258.

[27] QU X L，FU G Y，MA G W. An explicit time integration scheme of numerical manifold method[J]. Engineering Analysis with Boundary Elements，2014，48：53–62.

[28] 朱伯芳. 有限单元法原理与应用[M]. 2版. 北京：中国水利水电出版社，1998：425–426.(ZHU Bofang. The finite element method theory and applications[M]. 2nd ed. Beijing：China Water and Power Press，1998：425–426.(in Chinese))

[29] 石根华. 数值流形方法与非连续变形分析[M]. 裴觉民译. 北京：淸华大学出版社，1997：118–130.(SHI Genhua. Numerical manifold method and discontinuous deformation analysis[M]. Translated by PEI Juemin. Beijing：Tsinghua University Press，1997：118–130.(in Chinese))

[30] LIN S Z，XIE Z Q. Performance of DDA time integration[J]. Science China Technological Sciences，2015，58(9)：1 558–1 566.

[31] 付晓东，盛谦，张勇慧. 基于OpenMP的非连续变形分析并行计算方法[J]. 岩土力学，2014，35(8)：2 401–2 407.(FU Xiaodong，SHENG Qian，ZHANG Yonghui. Parallel computing method for discontinuous deformation analysis using OpenMP[J]. Rock and Soil Mechanics，2014，35(8)：2 401–2 407.(in Chinese))

[32] 刘凯欣，高凌天. 离散元法研究的评述[J]. 力学进展，2003，33(4)：483–490.(LIU Kaixin，GAO Lingtian. A review on the discrete element method[J]. Advances in Mechanics，2003，33(4)：483–490.(in Chinese))