非连续变形方法是一种隐式求解的动力学计算方法, 且采用在块体界面加减刚硬弹簧的方式来满足块体界面无张拉和无嵌入的接触准则。基于建立的DDA块体接触分析模型, 推导了静力条件下块体的接触位移理论公式, 并且通过接触力的计算, 验证了该公式的正确性。运用此公式, 定量研究了块体变形模量、弹簧刚度、时间步长和接触位移之间的相互关系, 并绘出了当块体变形模量和弹簧刚度一定时, 接触位移随时间步长变化的关系曲线。通过建立简单的块体系统力学分析模型, 剖析DDA中开-闭迭代完整的实现过程, 证明了石根华博士在DDA计算中采用时间步长来调整和加快开-闭迭代收敛的策略是合理、高效的。该研究也揭示了DDA各参数取值应依据的基本规律, 可以推动DDA的实际工程应用。
Abstract
Discontinuous deformation analysis (DDA) is a dynamic calculation method implicitly solved, and the block kinematics is obtained by adding or subtracting stiff springs at the contact positions where no tension and no inter-penetration is required. On the basis of an analysis model for block contact iterations, the theoretical formula of the body contact displacement in static condition is deduced, and is verified by contact force calculation. According to the formula, the interrelation between deformation modulus, spring stiffness, time step and contact displacement is researched quantitatively. When deformation modulus and spring stiffness are certain, the variation of contact displacement with time step is obtained. By establishing a simple mechanics model of the block system, the process of the open-close iteration with DDA is analyzed. This research proves that the strategy of using time step to adjust and speed up the open-close iterative convergence proposed by Dr. Shi Genhua is reasonable and efficient. It also reveals the basic rule of determining DDA’s each parameter, and promotes the practical engineering application of DDA.
关键词
DDA /
接触力 /
时间步 /
弹簧刚度 /
变形模量 /
接触位移
Key words
DDA /
contact force /
time step /
spring stiffness /
deformation modulus /
contact displacement
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参考文献
[1] SHI Gen-hua. Discontinuous Deformation Analysis: A New Numerical Model for the Statics and Dynamics of Block System[D]. Berkeley: Department of Civil Engineering, University of California, 1988.
[2] 石根华. 数值流形方法与非连续变形分析[M]. 裴觉民, 译. 北京:清华大学出版社, 1997. (SHI Gen-hua. Numerical Manifold Method and Discontinuous Deformation Analysis [M]. Translated by PEI Jue-min. Beijing: Tsinghua University Press, 1997.(in Chinese))
[3] MACLAUGHLIN M M, BERGER E A. A Decade of DDA Validation[C]∥Proceedings of the 6th International Conference on Analysis of Discontinuous Deformation, Norway, October 5-8, 2003:13-32.
[4] OHNISHI Y, NISHIYAMA S, SAKAKI T, et al. The Application of DDA to Practical Rock Engineering Problems: Issues and Recent insights[C]∥Proceedings of the 7th International Conference on Analysis of Discontinuous Deformation, Hawaii, December 10-12, 2005: 277-287.
[5] WANG C Y, SHENG J, CHEN M H. Time Integration Theories for the DDA Method with Finite Element Meshes[C]∥Proceedings of the First International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, Albuquerque: TSI Press, June 12-14, 1996: 263-287.
[6] 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 Ai-qing, DING Xiu-li, CHEN Sheng-hong, 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))
[7] MACLAUGHLIN M, SITAR N, DOOLIN D, et al. Investigation of Slope-stability Kinematics Using Discontinuous Deformation Analysis[J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(5): 753-762.
[8] HATZOR Y H, FEINTUCH A. The Validity of Dynamic Block Displacement Prediction Using DDA[J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38: 599-606.
[9] 邬爱清. DDA方法块体稳定性验证及其在岩质边坡稳定性分析中的应用[J].岩石力学与工程学报, 2008, 27(4): 664-672. (WU Ai-qing. Validation for Rock Block Stability and Its Application to Rock Slope Stability Evaluation Using DDA Method[J]. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(4): 664-672.(in Chinese))
[10]邱宽红, 林绍忠, 黄 斌. 基于DDA的膨胀土边坡破坏过程模拟[J]. 长江科学院院报, 2009, 26(11):58-61. (QIU Kuan-hong, LIN Shao-zhong, HUANG Bin. Failure Simulation of Expansive Soil Slope Based on DDA [J]. Journal of Yangtze River Scientific Research Institute, 2009, 26(11): 58-61. (in Chinese))
[11]刘 军, 李仲奎. 非连续变形分析方法中一些控制参数的设置[J]. 成都理工大学学报(自然科学版), 2004, 31(5):522-526.(LIU Jun, LI Zhong-kui. Setting Some Control Parameters in the Discontinuous Deformation Analysis Method[J]. Journal of Chengdu University of Technology (Science & Technology Edition), 2004, 31(5): 522-526.(in Chinese))
基金
国家重点基础研究发展计划(973)项目(2011CB710600);国家自然科学基金资助项目(51179014)
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