三维块体系统接触检索算法与非连续变形分析
|
摘要
非连续变形分析(DDA)方法是一种模拟分析非连续介质(如块体或散粒体系统)的有效的数值方法。为了模拟离散系统的力学行为，不仅需要根据材料的物理和几何特性来给出各个物体的图形，而且需要准确地模拟物体之间的相互作用。DDA目前已经广泛的用在二维工程问题的非连续变形分析中，但对于三维问题，由于缺少一种可靠的三维块体间接触判断的方法而导致DDA方法迟迟不能用于三维工程问题的分析中。由三维不规则多面体组成的块体系统的接触检索目前不仅制约着3D-DDA方法的发展，同时也是所有分析非连续块体系统(尤其是岩体系统)的数值方法所共同面临的主要困难之一。接触检索算法的任务是判断和区分接触类型、定位接触位置、描述并跟踪接触状态的变化过程。在实际的数值计算中，接触检索可以通过接触判断和接触传递两个步骤来实现。
本文对已有的接触判断算法的优、缺点进行了分析，提出了建立正确接触判断算法所应该遵循的原则。同时提出了一种新的三维接触判断算法一切割体法，此方法结合了已有几种主要方法的优点。它对于块体的接触范围有明确的定义，而且将块体的接触范围分为4个区域。无论一个块体在何处与另外一个块体产生接触，这个块体上参与接触的部分一定落入这4个区域之中的某一个中。此方法通过将两个块体上参与接触的两个几何元素的类型组合而得到块体对之间的接触类型，同时建立了从块体的切割体信息集合到参与接触的几何元素类型集合之间的一一映射关系。
由于程序中采用分时步计算的方式来实现DDA分析，因此前后时步之间块体系统的接触信息的传递也非常重要，如果不能正确传递接触信息，便无法跟踪和更新块体系统中接触状态的变化。在罚方法和点接触模型的基础上，本文提出了接触传递的具体算法以实现在块体系统运动过程中将接触信息从当前时步传递到下一时步。此外，在计算技巧方面，由于确定接触点对位置时经常涉及到对细部范围内点、线、面各元素之间的相互关系及距离的精细计算，为了统一解决计算过程中的困难，以便准确地确定接触点位置，本文提出了环路搜索法。
对三维DDA理论中各项子矩阵和系统方程的推导和建立做了介绍和完善。基于Visual C~(++)平台，本文开发了三维DDA的可视化分析程序3DP DDA，程序中的接触算法即采用切割体法。此程序被设计在PC机上运行，它可以给出块体系统(如岩石块体系统)中各个块体运动过程的实时的可视化模拟结果，输出的数据结果中包括各块体的位移、变形、应力、应变，以及块体间的接触力、相对滑动和接触开合的位移值。
Discontinuous Deformation Analysis (DDA) is a powerful numerical method for simulating the discontinuous media composed of blocks or particles. To simulate and analysis the natural physical process of such systems, it needs not only to render realistic images according the material's physical and geometric properties, but also needs to model objects interactions precisely. DDA has been widely applied to the 2D analysis of discontinuous deformation of rock blocky systems in rock engineering, while for 3D problems, the lack of reliable 3D contact detection algorithms for polyhedron blocks turns out to be the main obstacle. Contact detection is a key problem, at present, encountered by all numerical methods during modeling and analyzing practical 3D blocky systems in rock engineering. A contact detection algorithm must judge and distinguish reliably and correctly the different contact types, find the locations and determine, update the states of contacts of blocky systems. During numerical modeling, the contact detection inludes the contact judge and the contact transfer.
Advantages and shortcomings of the existent contact judge schemes are discussed. The principle only according to which a correct contact judge algorithm be bring out is represented. And a new approach, namely Incision Body (IB) scheme is put forward, which combines the advantages of the existent methods. The scheme defined a contact scope for a block and, at the same time, divided the scope into four sections. No matter where a block contacts with another block, the contact part of the block must fall into one of four sections of another block. The contact type between two blocks is formed through combining the two geometry types of two contact components of the two blocks. The contact component of a block was determined by the information of incision body of the block, and a one-to-one mapping from the incision body to the contact component is established.
Contact transfer is very important when analyzing discontinuous media using a DDA computer program because the analysis is implemented step-by-step with several time increments. If the contact informations of a blocky system are transferred inaccuratly, the tracking and updating of contacts will be failed. Block contact constraints are enforced using the penalty method and the point-to-face model is adopted as contact model. Subsequently, a contact transfer algorithm is presented to fulfill the transfer of contact informations from current time step to next time step. Furthermore, there are numerous difficulties in
本文对已有的接触判断算法的优、缺点进行了分析，提出了建立正确接触判断算法所应该遵循的原则。同时提出了一种新的三维接触判断算法一切割体法，此方法结合了已有几种主要方法的优点。它对于块体的接触范围有明确的定义，而且将块体的接触范围分为4个区域。无论一个块体在何处与另外一个块体产生接触，这个块体上参与接触的部分一定落入这4个区域之中的某一个中。此方法通过将两个块体上参与接触的两个几何元素的类型组合而得到块体对之间的接触类型，同时建立了从块体的切割体信息集合到参与接触的几何元素类型集合之间的一一映射关系。
由于程序中采用分时步计算的方式来实现DDA分析，因此前后时步之间块体系统的接触信息的传递也非常重要，如果不能正确传递接触信息，便无法跟踪和更新块体系统中接触状态的变化。在罚方法和点接触模型的基础上，本文提出了接触传递的具体算法以实现在块体系统运动过程中将接触信息从当前时步传递到下一时步。此外，在计算技巧方面，由于确定接触点对位置时经常涉及到对细部范围内点、线、面各元素之间的相互关系及距离的精细计算，为了统一解决计算过程中的困难，以便准确地确定接触点位置，本文提出了环路搜索法。
对三维DDA理论中各项子矩阵和系统方程的推导和建立做了介绍和完善。基于Visual C~(++)平台，本文开发了三维DDA的可视化分析程序3DP DDA，程序中的接触算法即采用切割体法。此程序被设计在PC机上运行，它可以给出块体系统(如岩石块体系统)中各个块体运动过程的实时的可视化模拟结果，输出的数据结果中包括各块体的位移、变形、应力、应变，以及块体间的接触力、相对滑动和接触开合的位移值。
Discontinuous Deformation Analysis (DDA) is a powerful numerical method for simulating the discontinuous media composed of blocks or particles. To simulate and analysis the natural physical process of such systems, it needs not only to render realistic images according the material's physical and geometric properties, but also needs to model objects interactions precisely. DDA has been widely applied to the 2D analysis of discontinuous deformation of rock blocky systems in rock engineering, while for 3D problems, the lack of reliable 3D contact detection algorithms for polyhedron blocks turns out to be the main obstacle. Contact detection is a key problem, at present, encountered by all numerical methods during modeling and analyzing practical 3D blocky systems in rock engineering. A contact detection algorithm must judge and distinguish reliably and correctly the different contact types, find the locations and determine, update the states of contacts of blocky systems. During numerical modeling, the contact detection inludes the contact judge and the contact transfer.
Advantages and shortcomings of the existent contact judge schemes are discussed. The principle only according to which a correct contact judge algorithm be bring out is represented. And a new approach, namely Incision Body (IB) scheme is put forward, which combines the advantages of the existent methods. The scheme defined a contact scope for a block and, at the same time, divided the scope into four sections. No matter where a block contacts with another block, the contact part of the block must fall into one of four sections of another block. The contact type between two blocks is formed through combining the two geometry types of two contact components of the two blocks. The contact component of a block was determined by the information of incision body of the block, and a one-to-one mapping from the incision body to the contact component is established.
Contact transfer is very important when analyzing discontinuous media using a DDA computer program because the analysis is implemented step-by-step with several time increments. If the contact informations of a blocky system are transferred inaccuratly, the tracking and updating of contacts will be failed. Block contact constraints are enforced using the penalty method and the point-to-face model is adopted as contact model. Subsequently, a contact transfer algorithm is presented to fulfill the transfer of contact informations from current time step to next time step. Furthermore, there are numerous difficulties in
引文
[1] 孙广忠．岩体结构力学．北京：科学出版社，1988．
[2] Chappell B. A. Deformational response in discontinua, J. Rock. Mech. Min. Sci. & Geomech. Abstr., 1979, 16: 377～390.
[3] Chappell B. A. The effects of constrains on the reformational response of slip along planar joints. Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr., 1975, 12: 265～270.
[4] Chappell B. A. Stress distribution in anisotropic compliance of jointed rock. Geotech. Eng. (ASCE), 1986, 112: 682～700.
[5] Chappell B. A. Deformation control in excavating unstable slopes. J. Geotech. Eng. (ASCE), 1987, 113: 299～319.
[6] Sun J., Wang S. J. Rock mechanics and rock engineering in China: developments and current state-of-art. International Journal of Rock Mechanics & Mining Sciences. 2000, 37: 447～465.
[7] Jing L., Hudson J. A. Numerical methods in rock mechanics. International Journal of Rock Mechanics & Mining Sciences. 2002, 39: 409～427.
[8] 周维垣，杨强．岩石力学数值计算方法．北京：中国电力出版社，2005．
[9] Munjiza A., Latham J. P. Grand challenge of discontinuous deformation analysis. In: Hatzor Y. H. Proceedings of the 5th International Conference on Analysis of Discontinuous Deformation, BeerSheva, Israel: Balkema, 2002: 69～73.
[10] 刘君，孔宪京．三维连续与非连续变形分析．力学进展．2002，34(6)：941-948．
[11] 刘凯欣，高凌天．离散元法研究的评述．力学进展．2003，33(4)：483-490．
[12] 刘军，李仲奎．非连续变形分析(DDA)方法研究现状及发展趋势．岩石力学与工程学报．2004，23(5)：839-845．
[13] 陈文胜，王桂尧，刘辉等．岩石力学离散单元计算方法中的若干问题探讨．岩石力学与工程学报．2005．24(10)：1639-1644．
[14] Goodman R. E., Taylor R. L. and Brekke T. A model for the mechanics of jointed rock. J. Soil Mech. Found. Div. (A SCE), 1968, SM3: 637～659.
[15] Desai C. S., Zaman M. M., Lightner J. G.. et al. Thin-layer element for interface and joints. International Journal for Numerical and Analytical Methods in Geomechanics. 1984, 8(1): 19～43.
[16] Zaman M. M., Desai C. S. and Drumm E. C. Interface model for dynamic soil-structure interaction. Journal of Geotechnical Engineering. 1984, 110(9): 1257-1273.
[17] 雷晓燕，Swoboda G．，杜庆华．接触摩擦单元的理论及其应用．岩土工程学报．1994，16(3)：23～32．
[18] Lei X. Y., Swoboda G. and Zenz G.. Application of contact-friction interface element to tunnel excavation in faulted rock. Computers and Geotechnics. 1995, 17: 349～370.
[19] Cundall P. A. A computer model for simulating progressive, large-scale movements in blocky rock systems. Proceedings of the International Symposium on Rock Fracture, Nancy, France, 1971: Ⅱ-8.
[20] Cundall P. A. and Strack O. D. L. A discrete numerical model for granular assemblies. Geotechnique. 1979, 29(1): 47～65.
[21] Cundall P. A. and Hart R. D. Numerical modeling of discontinua. Engineering Computations. 1992, 9: 101～113.
[22] Stewart I. J. A static relaxation method for the analysis of excavations in discontinuous rock. In: Brown E. T. and Hudson J. A. Design and performance of underground excavations. Cambridge U. K., 1984: 149～154.
[23] 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, lnt. J. Rock Mech. Min. Sci. & Geomech. Abstr. 1988, 25(3): 107-116.
[24] Hart R. D. and Cundall P. A. and Lemos J. Formulation of a three-dimensional distinct element model—Part Ⅱ. Mechanical calculations for motion and interaction of a system composed of many polyhedral blocks. 1988, 25(3): 117～125.
[25] 朱焕春，Andrieux Patrix，钟辉亚．节理岩体数值计算方法及其应用(二)：工程应用．岩石力学与工程学报．2005，24(1)：89～96．
[26] 王泳嘉．刑纪波．离散单元法及其在岩土力学中的应用．沈阳：东北工学院出版社，1991．
[27] 刑纪波．千泳嘉．离散单元法的改进及其在颗粒介质研究中的应用．岩士工程学报．1990．12(5)：51～57．
[28] 魏群．岩土工程中离散元的基本原理数值方法及试验研究：(博士学位论文)．北京：清华大学．1090．
[29] 王泳嘉，刘连峰．二维离散单元法软件系统TRUDEC的研制．岩石力学与工程学报．1996．15(3)：201～210．
[30] 朱浮声．王泳嘉，斯蒂芬森O．露天矿山高陡岩石边坡失稳的三维离散元分析．东北大学学报(自然科学版)．1997，18(3)：234～237．
[31] 麻凤海，于泳嘉．地层沉降控制的可变形离散单元模拟．岩石力学与工程学报．1999，18(2)：176～179．
[32] 王光纶，张楚汉，彭冈，陈昌伟．刚体动力试验与离散元法动力分析参数选择的研究．岩石力学与工程学报．1994，13(2)：124～133．
[33] 唐志平．二维离散元方法及其在冲击力学中的应用．中国科学(E辑)．2003，33(11)：989～998．
[34] 李世海，汪远年．三维离散元计算参数选取方法研究．岩石力学与工程学报．2004，23(21)：3642～3651．
[35] 徐冰，孙其诚，张凌等．颗粒离散元法研究进展．力学进展．2003，33(2)：251～260．
[36] 鲍鹏，姜忻良．离散元-无限元非线性耦合法．华中科技大学学报．2004，32(11)：91～93．
[37] 魏怀鹏，易大可，李世海等．基于连续介质模型的离散元方法中弹簧性质研究．岩石力学与工程学报．2006，25(6)：1159～1169．
[38] 雷卫东，Mohamed Hefny，赵坚等．岩石动力学中离散元程序处理波幅的新方法．中国矿业大学学报．2005，34(2)：170～174．
[39] 李世海．饶莹，赵满洪等．二维离散元块体—质点计算模型．见：中国土木工程学会第九届土力学及岩土工程学术会议论文集．北京，2003：1395～1399．
[40] 罗海宁，焦玉勇．对三维离散单元法中块体接触判断算法的改进．岩土力学 1999，20(2)：37～40．
[41] 鲁军．离散单元法的数学模型研究及其工程应用：(博土学位论文)．北京：清华大学，1996．
[42] 王为华，李夕兵，离散元发及其在岩土工程中的应用综述．岩土工程技术．2005，19(4)：177～181．
[43] 候艳丽，张冲，张楚汉等．拱坝沿建基面上滑溃决的可变形离散元仿真．岩土工程学报．2005，27(6)：657～661．
[44] 候艳丽，周元德，张楚汉．用非连续介质力学模型研究混凝土的l型断裂．清华大学学报．2006，46(3)：346～349．
[45] 张冲，候艳丽，金峰等．拱坝—坝肩三维可变形离散元整体稳定分析．岩石力学与工程学报．2006，25(6)：1226～1232．
[46] Morris J. P., Glenn L. A., Heuze F. E. Simulation of underground structures subjected to dynamic loading using the distinct element method. In: Hatzor Y. H. Proceedings of the 5th International Conference of Analysis on Discontinuous Deformation, B eerSheva, Israel: Balkema, 2002: 121～124.
[47] Potyondy D. O., Cundall P. A. A bonded-particle model for rock. International Journal of Rock Mechanics & Mining Sciences. 2004, 41: 1329-1364.
[48] Jing L. Block system construction for three-dimensional discrete element models of fractured rocks. International Journal of Rock Mechanics & Mining Sciences. 2000, 37: 645～659.
[49] Munjiza A., Latham J. P., Andrews K. R. F. Detonation gas model for combined finite-discrete element simulation of fracture and fragmentation. Int. J. Numer. Meth. Engng. 2000, 49: 1495～1520.
[50] Mishra B. K., Murty C. V. R. On the determination of contact parameters for realistic DEM simulations of ball mills. Powder Technology. 2001, 115: 290～297.
[51] Cleary P. W. DEM simulation of industrial particle flows: case studies of dragline excavators, mixing in tumblers and centrifugal mills. Powder Technology. 2000, 109: 83～104.
[52] Zhang Z. P., Liu L. F., Yuan Y. D., et al. A simulation study of the effect of dynamic variables on the packing of spheres. Powder Technology. 2001, 116: 23～32.
[53] Esaki T., Jiang Y., Bhattarai T. N., et al. Stability analysis and reinforcement system design in a progressively failed steep rock slope by the distinct element method. Int. J. Rock Mech. Min. Sci. 1998, (4/5): 664～666.
[54] Munjiza A. Combined single and smeared crack model in combined FEM/DEM. Int. J. Num. M. Eng. 1999, 44: 41～57.
[55] Kawai T. New discrete models and their application to seismic response analysis of structure. Nuclear Engineering and Design. 1978, 48: 207～229.
[56] 钱令希，张雄．结构分析中的刚性有限元法．计算结构力学及其应用．1991，8(1)：1～14．
[57] 钱令希，张雄．刚性有限元的参变量变分原理及有限元参数二次规划解．计算结构力学及其应用．1992，9(2)：117～123．
[58] 张雄．刚性有限元的数学理论基础及其在岩土工程中的应用：(博士学位论文)．大连：大连理工大学，1992．
[59] 卓家寿，赵宁．不连续介质静、动力分析的刚体—弹簧元法．河海大学学报．1993，21(5)：34～43．
[60] 赵宁，卓家寿．动力分析的刚体—界面元与有限元耦合法．河海大学学报．1994，22(6)：8～15．
[61] 赵宁，卓家寿．结构的三维非线性界面元分析．河海大学学报．1995，23(2)：23～31．
[62] 张建海，范景伟，何江达．用刚体弹簧元法求解边坡、坝基动力安全系数．岩石力学与工程学报．1999，18(4)：387～391．
[63] 任青文．块体单元法及其在岩体稳定分析中的应用．河海大学学报．1995，23(1)：1～7．
[64] Wang B. L.. Garga V. K. A numerical method for modeling large displacement of jointed rocks-Part Ⅰ: Fundaments. Canadin Geotechnical Journal. 1993, 30: 96～108.
[65] Garga V.K., Wang B. L. A numerical method for modeling large displacements of jointed rocks-Part Ⅱ: Modeling of rockbolts and groundwater and applications. Canadin Geotechnicai Journal. 1993, 30: 109～123.
[66] Hock E.. Bray J. W. Rock slope engineering (3rd edition). The lnsititue of Mining and Metallurgy, London, 1981.
[67] Sarma S. K. Stability analysis of embankments and slopes. J. Geomech. Am. Soi. Civ. Engrs. 1979. 105: 1511～1624.
[68] Donald．陈祖煜．边坡稳定分析的塑性力学上限解，第一部分：基本原理和方法．中国水利水电科学研究院．1994．
[69] Donald．陈祖煜．边坡稳定分析的塑性力学上限解，第二部分：论能量法和静力法的等效性．中国水利水电科学研究院．1994．
[70] Goodman R. E., Shi G. H. Block theory and its application. Geotechnique. 1995, 45(3): 383～423.
[71] 石根华．岩体稳定分析的赤平投影方法．中国科学．1977．3：260～271．
[72] Shi G. H., Goodman R. E. The key blocks of unrolled joint traces in developed maps of tunnel walls. International Journal for Numerical and Analytical Methods in Geomechanics. 1989, 13(1): 131～158.
[73] 张奇华．邬爱清．石根华．关键块体理论在百色水利枢纽地下厂房岩体稳定性分析中的应用．岩石力学与工程学报．2004，23(15)：2609～2614．
[74] Shi G. H., Goodman R. E. Two dimensional discontinuous deformation analysis. International Journal for Numerical and Analytical Methods in Geomechanics. 1985, 9: 541-556.
[75] Shi G. H. Discontinuous deformation analysis: A new numerical model for the statics and dynamics of block systems: (PhD Dissertation). Berkeley: University of California, Berkeley. U.S.A., 1988.
[76] Shi G. H., Goodman R. E. Generalization of two-dimensional discontinuous deformation analysis for forward modeling. International Journal for Numerical and Analytical Methods in Geomechanics. 1989. 13: 131～158.
[77] Shi G. H. Discontinuous deformation analysis: a new numerical model for the statics and dynamics of deformable block structures. Engineering Computations. 1992, 9: 157～168.
[78] 石根华．数值流形方法与非连续变形分析(裴觉民译)．北京：清华大学出版，1997．
[79] Shi G. H. Manifold method. In: M.Reza Salami and Don Banks. Proceedings of the 1st international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media. Berkeley, California. 1996. 52～204.
[80] 周维垣，杨若琼，剡公瑞．流形元法及其在工程中的应用．岩石力学与工程学报．1996，15(3)：211～218．
[81] 王芝银，王思敬，杨忐法．岩石大变形分析的流形元法．岩石力学与工程学报．1997，16(5)：399～404．
[82] 朱以文．曾又林，陈明详．岩石大变形分析的增量流形方法．岩石力学与工程学报．1999，18(1)：1～5．
[83] 王芝银，李运鹏．数值流形方法中的几点改进．岩土工程学报．1998，20(6)：33～36．
[84] 张湘伟，蔡永吕，廖林灿．数值流形方法物理覆盖系统的自动剖分，重庆大学学报(自然科学版)．2000，23(1)：29～31．
[85] 莫海鸿，陈尤雯．流形法在岩石力学研究中的应用．华南理工大学学报(自然科学版)．1998，26(9)：48～53．
[86] Shi G. H. Application of discontinuous deformation analysis and manifold method. 3rd International Conference on DDA. Colorado, USA, 1999, 3～15.
[87] 王水林，葛修润．流形元方法在模拟裂纹扩展中的应用．岩石力学与工程学报．1997，16(5)：405～410．
[88] 田荣．连续与非连续变形分析的有限覆盖无单元法及其应用研究：(博士学位论文)．大连：大连理工大学，2000．
[89] 田荣，栾茂田，杨庆．高阶流形方法及其应用．工程力学．2001，18(2)：21～26．
[90] Chen G., Ohnishi Y., Takahiro Ito. Development of high-order manifold method. International Journal for Numerical and Analytical Methods in Geomechanics. 1998, 43: 685～712.
[91] 张国新，王光纶，裴觉民．基于流形方法的结构体破坏分析．岩石力学与工程学报．2001，20(3)：281～287．
[92] 张国新，金峰，王光纶．用基于流形元的子域奇异边界元法模拟重力坝的地震破坏．工程力学．2001，18(4)：18～27．
[93] 张国新，彭静．二阶流形元法与结构变形分析．力学学报．2002，34(2)：261～269．
[94] Lu M. High-order manifold method with simplex integration. In: Hatzor Y. H. Proceedings of the 5th International Conference on Analysis of Discontinuous Deformation, BeerSheva, Israel: Balkema, 2002: 75～83.
[95] 董志宏，邬爱清，丁秀丽．数值流形方法中的锚固支护模拟及初步应用．岩石力学与工程学报．2005，24(20)：3754～3760．
[96] 姜清辉，王书法．锚固岩体的三维数值流形方法模拟．岩石力学与工程学报．2006，25(3)：528～532．
[97] 姜清辉，周创兵．四面体有限单元覆盖的三维数值流形方法．岩石力学与工程学报．2005，24(24)：4455～4460．
[98] Su H., Xie X. Preliminary research on solving large displacement problems by numerical manifold method with fixed mathematical. In: MacLaughlin M. and Sitar N. Proceedings of the 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 175～182.
[99] Lin S., Qi Y., Su H. Formulation of high-order numerical manifold method and fast simplex integration based on special matrix operations. In: MacLaughlin M. and Sitar N. Proceedings of the 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 183-190.
[100] Max Y．Ma．岩土工程中的非连续方法．见：计算机方法在岩石力学中的应用．武汉：武汉测绘科技大学出版社，1994．
[101] 裴觉民，吕祖衍．裂隙岩体非连续变形的静力和动力分析方法．岩土工程学报．1996，18(6)：46～54
[102] 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．岩石力学与工程学报．1997，16(5)：411～417．
[103] 王书法．朱维中，郑少河．节理岩体热戍力问题的非连续变形分析方法．岩石力学与工程学报．2000．19(5)：643～646．
[104] 张勇慧．关于DDA中推导热应力问题公式的讨论．岩石力学与工程学报．2001，20(2)：277～278．[热应力]
[105] 刘红岩，杨军，陈鹏万．爆破漏斗形成过程的DDA模拟分析．工程爆破．2004，10f2)：17～20．
[106] 张国新．金峰．重力坝抗滑稳定分析中DDA与有限元方法的比较．水力发电学报．2004，(1)：10～14．
[107] 黎勇，栾茂田．杨庆．非连续变形计算力学模型弹塑性分析方法在边坡稳定性分析中的应用．中国土木工程学会第九届土力学及岩土工程学术会议论文集．北京，2003
[108] 黎勇，栾茂田，冯夏庭．非连续变形计算力学模型的粘弹性分析方法Ⅰ：基本理论．计算力学学报．2004．21(4)：440～447．
[109] 黎勇．栾茂田，冯夏庭．非连续变形计算力学模型的粘弹性分析方法Ⅱ：算例分析计算力学学报．2004．21(4)：448～454．
[110] 姜清辉．朱传云．动力学问题的DDA方法及其在爆破抛掷过程中的应用．工程爆破．2004．10(3)：5～8．
[111] 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．岩石力学与工程学报．2006，25(1)：1～8．
[112] Yeung M. R., Goodman R. E. Muti block stability analysis using the DDA method. In: Myer, Cook, Goodman et al. Fractured and Jointed Rock Masses. Balkema, 1995, 701～707.
[113] Ohnishi Y., Yamamukai K., Chen G. Application of DDA in rock fall analysis. In: Aubertin, Hassani and Mitri. Rock Mechanics. Balkema, 1996, 2031～2037.
[114] Thomas PA. Discontinuous deformation analysis of particulate media: (PhD Dissertation). Berkeley: University of California, Berkeley, U.S.A.,1997.
[115] Koo C. Y., Chern J. C. Modificationof the DDA method for rigid block problem. Int. J. Rock Mech. Min. Sci. 1998, 35(6): 683～693.
[116] Arriaga M. C. S., Verduzco F. S. On the natural collapse of fractures in rocks with low fluid. International Journal of Rock Mechanics & Mining Sciences.1998, 35: 500-501.
[117] Chiou Y. J., Tzeng J. C., Liou Y. W. Experimental and analytical study of masonry infilled frames. Journal of Structural Engineering. 1999,125(10): 1109～1117.
[118] Mortazavi A. Modeling of rock blasting in jointed media using discontinuous deformation analysis: (PhD thesis) Kingston, Ontario, Canada: Queen's University, 1999.
[119] Pearce C. J., Thavalingam A., Liao Z. Computational aspects of the discontinuous deformation analysis framework for modeling concrete fracture. Engineering Fracture Mechanics. 2000, 65: 283～298.
[120] Doolin D. M., Sitar N. DDAML-discontinuous deformation analysis markup language. International Journal of Rock Mechanics & Mining Sciences. 2001, 38: 467～474.
[121] MacLaughlin M., Sitar N., Doolin D. et al. Investigation of slope-stability kinematics using discontinuous deformation analysis. International Journal of Rock Mechanics & Mining Sciences. 2001, 38: 753～762.
[122] Mortazavi A., Katsabanis P. D. Modelling burden size and strata dip effects on the surface blasting process. International Journal of Rock Mechanics & Mining Sciences. 2001, 38: 481～498.
[123] Jing L., Ma Y., Fang Z. Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method. International Journal of Rock Mechanics & Mining Sciences. 2001,38:343-355.
[124] Wu Y., Wang H., Zhou S. et al. Inverse DDA of a system of blocks in sphere coordinates. Journal of geodesy and geodynamics. 2003, 23(Supp): 30-33.
[125] Wang H., Zhang G., Wu Y. et al. The deformation of active tectonic blocks on the Chinese mainland and its relationship with seismic activity. Earthquake Research in China. 2004, 18(1): 54-66.
[126] Wu J.H., Ohnishi Y., Nishiyama S. Simulation of the mechanical behavior of inclined jointed rock masses during tunnel construction using Discontinuous Deformation Analysis (DDA). International Journal of Rock Mechanics & Mining Sciences. 2004, 41: 731-743.
[127] Hatzor Y.H., Arzi A.A., Zaslavsky Y. et al. Dynamic stability analysis of jointed rock slopes using the DDA method: King Herod's Palace, Masada, Israel. International Journal of Rock Mechanics & Mining Sciences. 2004,41:813-832.
[128] Sitar N., MacLaughlin M., Doolin D. Influence of kinematics on landslide mobility and failure mode. Journal of Geotechnical and Geoenvironmental Engineering. (ASCE) 2005,131(6):717-728.
[129] Wu A., Ding X., Li H. Numerical simulation of startup and the whole process characteristics of Qingjiangping landslide with DDA method. In: MacLaughlin M. and Sitar N. Proceedings of the 7th International Conference of the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 167-174.
[130] Moosavi M., Grayeli R. A model for cable bolt-rock mass interaction: Integration with discontinuous deformation analysis (DDA) algorithm. International Journal of Rock Mechanics & Mining Sciences. 2006, 43:661-670.
[131] Ke T.C., Goodman R.E. Discontinuous deformation analysis and the artificial joint concept. In: Nelson Laubach. Rock Mechanics. Balkema, 1994: 599-606.
[132] Ke T.C. Artificial joint-based DDA. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 326-333.
[133] Amadei B., Lin C.T., Sture S., et al. Modeling fracture of rock masses with the DDA method. In: Nelson Laubach. Rock Mechanics. Balkema, 1994: 583-590.
[134] Amadei B., Lin C, Dwyer J. Recent extensions to the DDA method. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulatio ns of Discontinuous Media. Berkeley, California, 1996: 1-30.
[135] Lin C, Amadei B., Jung J., et al. Extensions of discontinuous deformation analysis for jointed rock masses. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 1996, 33(7): 671-694.
[136] Cheng Y.M., Zhang Y.H. Rigid body rotation and block internal discretization in DDA analysis. International Journal for Numerical and Analytical Methods in Geomechanics. 2000,24: 567-578.
[137] Shyu K., Salami M.R. Stability of bartlett dam. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 440-445.
[138] Chang C.T. Nonlinear dynamic discontinuous deformation analysis with finite element meshed block system: (PhD thesis). Berkeley: University of California, 1994.
[139] Jing L. Formulation of discontinuous deformation analysis (DDA)-an implicit discrete element model for block systems. Engineering Geology. 1998, 43: 371～381.
[140] Koo C. Y., Chem J. C. The development of DDA with third order displacement function. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California. 1996: 342～349.
[141] Lin J. S., Hynes M. E. Seismic discontinuous deformation analysis. The Conference on Geotechnical Earthquake Engineering and Soil Dynamics Ⅲ. Part 1 (of 2), Seattle, USA, 1998, 790～799.
[142] Cai Y., Liang G. P., Shi G. H., et al. Studying an impact problem by using LDDA method. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 288～294.
[143] Liang G. P., Wang C. G. LDDA on the high speed catenary-pantograph system dynamics. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California. 1996: 350～356.
[144] 蔡永恩，梁国平，殷有泉．岩体滑坡动力过程的数值模拟新方法．见：第六届全国岩土力学数值分析与解析方法讨论会论文集．广州．1998：73～79．
[145] 黎勇．栾茂田．非连续变形计算力学模型的基本原理及其线性规划解．大连理工大学学报．2000，40(3)：351～357．
[146] 黎勇．非连续变形计算力学模型及其在岩土工程中的应用：(博士学位论文)．大连：大连理工大学，2000．
[147] 栾茂田，黎勇．杨庆．非连续变形计算力学模型在岩体边坡稳定性分析中的应用．岩石力学与工程学报．2000，19(3)：289～294．
[148] Chert G., Miki S., Ohnishi Y. Practical improvement on DDA. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 302～309.
[149] Ke T. C. The issue of rigid-body rotation in DDA. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 318～325.
[150] MacLaughlin M., Sitar N. Rigid body rotation in DDA. In: M. Reza Salami and Don Banks. Proceedings of 1 st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 620～635.
[151] Thomas P. A., Bray J. D., Ke T. C. Discontinuous deformation analysis for soil mechanics. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 454～461.
[152] Ke T. C., Bray J. Modeling of particulate media using discontinuous deformation analysis. Journal of Engineering Mechanics. 1995, 121(11): 1234～1243.
[153] Ohnishi Y., Miki S. Development of circular and elliptic disc elements for DDA. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 44～51.
[154] Thomas P. A., Bray J. D. Capturing nonspherical shape of granular media with disk clusters. Journal of Geotechnical and Geoenvironmental Engineeing. 1999, 3: 169～178.
[155] Shyu K. , Salami R. Analysis of pile driving using DDA. In: Hassani A. and Mitri. Rock Mechanics. Balkema, 1996: 2009～2016.
[156] 张国新，李广信，郭瑞平．不连续变形分析与土的应力应变关系．清华大学学报(自然科学版)．2000，40(8)：102～105．
[157] Pei J. The effects of energy loss in block bumping on discontinuous deformation, in: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 401～406.
[158] Ohnishi Y. , Tanaka M. , Sasaki T. Modification of DDA for elasto-plastic analysis with illustrative generic problem. In: Cook M. , Goodman, Tsang. Fractured and Jointed Rock Masses. Balkema, 1995, 45～50.
[159] Kim Y-II. , Amadei B. , Pan E. Modeling the effect of water, excavation sequence and rock reinforcement with discontinuous deformation analysis. International Journal of Rock Mechanics & Mining Sciences. 1999, 36: 949～970.
[160] 郑榕明，张勇慧，王可钧．耦合算法原理及有限元与DDA的耦合．岩土工程学报．2000，22(6)：727～730．
[161] 刘君，陈键云，孔宪京．基于DDA和FEM耦合方法的碾压混凝土坝抗震安全性分析．大连理工大学学报．2003，43(6)：793～798．
[162] Cheng Y. M. Advancements and improvement in discontinuous deformation analysis. Computers and Geotechnics. 1998, 22 (2) : 153～163.
[163] Oh Y. N. , Jeng D. S. , Chen S. A parametric study using discontinuous deformation analysis to model wave-induced seabed response. In: Hatzor Y. H. Proceedings of 5th International Conference on Analysis of Discontinuous Deformation, BeerSheva, Israel: Balkema, 2002: 113～119.
[164] Doolin D. , Sitar N. Displacement accuracy of discontinuous deformation analysis method applied to sliding block. Journal of Engineering Mechanics. 2002, 128 (11) : 1158～1168 (ASCE).
[165] Tsesarsky M. , Hatzor Y. H. , Sitar N. Dynamic block displacement prediction—validation of DDA using analytical solutions and shaking table experiments. In: Hatzor Y. H. Proceedings of 5th International Conference on Analysis of Discontinuous Deformation, BeerSheva, Israel: Balkema, 2002: 195～203.
[166] Bangash T. , Munjiza A. Experimental validation of combined FEM/DEM simulation of R. C. beams under impact induced failure. In: Hatzor Y. H. Proceedings of 5th International Conference on Analysis of Discontinuous Deformation, BeerSheva, Israel: Balkema, 2002: 165～169.
[167] MacLaughlin M. M. , Hayes M. A. Validation of DDA block motions and failure modes using laboratory models. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 71～78.
[168] Wright C. A. , MacLaughlin M. M. , Donovan R. P. Comparison of the deformation of externally loaded DDA and UDEC blocks with an analytical solution. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 79～90.
[169] Osada M. , Taniyama H. Preliminary consideration for analyzing ground deformation due to fault movement. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 113～120.
[170] Sasaki T. , Hagiwara I. , Sasaki K. Earthquake response analysis of a rock-fall by discontinuous deformation analysis. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation. Honolulu, Hawaii, 2005: 137～146.
[171] Ishikawa T. , Miura S. , Ohnishi Y. Influence of input parameters on energy loss in free fall tests with DDA. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 147～158.
[172] Ohnishi Y. , Nishiyama S. , Sasaki T. The application of DDA to practical rock engineering problems: issues and recent insights. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 277～287.
[173] Hatzor YH. Feintuch A, The validity of dynamic block displacement prediction using DDA[J], International Journal of Rock Mechanics and Mining Sciences, 2001, 38: 599～606.
[174] 王书法．朱维申．考虑空间影响的两种非连续变形分析方法．岩石力学与工程学报．2000，19(3)：369～372．
[175] Shi G. H. Three dimensional discontinuous deformation analysis, ln: Elsworth D. et al, Proceedings of the 38th US Rock Mechanics Symposium. 2001, Washington D. C. , 1421～1428.
[176] 王如路．陈乃明．刘宝琛．三维块体不连续分析理论简析．岩石力学与工程学报．1996，15(3)：219～224．
[177] 姜清辉．三维非连续变形分析方法的研究：(博士学位论文)．武汉：中国科学院武汉岩土力学研究所．2000．
[178] 姜清辉．杨文柱，丰定详．三维块体系统非连续变形正分析模型．岩石力学与工程学报．2002，21(12)：1765～1769．
[179] 刘君．三维非连续变形分析与有限元耦合算法研究：(博士学位论文)．大连：大连理工大学，2001
[180] Liu Jun, Kong Xianjing, Lin Gao. Formulations of the three-dimensional discontinuous deformation analysis method. Acta Mechanica Sinica. 2004, 20 (3) : 270～282.
[181] 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．岩土工程学报．2006，28(8)：998～1001．
[182] 姜清辉，丰定详．三维非连续变形分析方法中角—面接触模型的研究．岩石力学与工程学报．2000，19(增)：930～935．
[183] Jiang Q. H. , Yeung M. R. A model of point-to-face contact for three-dimensional discontinuous deformation analysis. Rock Mechanics and Rock Engineering. 2003, 37: 95～116.
[184]: Wu J. H. , Juang C. H. , Lin H. M. Vertex-to-face contact searching algorithm for three-dimensional frictionless contact problems. International Journal for Numerical Methods in Engineering, 2005, 63, 876-897.
[185] 姜清辉．周创兵，罗先启．块状结构岩体在一般水压分布模式下的不连续变形分析．岩石力学与工程学报．2005，24(3)：401～405．
[186] Jang H. I. , Lee C. I. Development of a three-dimensional discontinuous deformation analysis technique and its application to toppling failure. In: Hatzor Y. H. Proceedings of 5th International Conference on the Analysis of Discontinuous Deformation. BeerSheva, Israel: Balkema, 2002: 225～229.
[187] 吴建宏，大西有三，石根华等．三维非连续变形分析(3D DDA)理论及其在岩石边坡失稳数值仿真中的应用．岩石力学与工程学报．2003，22(6)：937～942．
[188] Yang M. , Fukawa T. , Ohnishi Y. et al. The application of 3-dimensional DDA with a spherical rigid block for rockfali simulation. International Journal of Rock Mechanics & Mining Sciences. 2004, 41 (3), CD-ROM.
[189] Yeung M. R. , Sun N. , Jiang Q. H. Analysis of large block test data using three-dimensional discontinuous deformation analysis. Int. J. Rock Mech. Min. Sci. 2004, 41 (3), CD-ROM.
[190] Beyabanaki S. A. , Jafari A. Modified point-to-face frictionless contact constraints for three-dimensional discontinuous deformation analysis (3-D DDA). In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 25～36.
[191] Yeung M. R. , Jiang Q. H. , Sun N. Validation of block theory and three-dimensional discontinuous deformation analysis as wedge stability analysis methods. International Journal of Rock Mechanics & Mining Sciences. 2003, 40: 265～275.
[192] Moosavi M. , Jafari A. , Beyabanaki S. A. Dynamic three-dimensional discontinuous deformation analysis (3-D DDA) validation using analytical solutions. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 37～48.
[193] Shi G. H. Producing joint polygons, cutting rock blocks and finding removable blocks for general free surfaces using 3-D DDA. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 1～24.
[194] Ouadfel H. , Rothenburg L. An algorithm for detecting inter-ellipsoid contacts. Computers and Geotechnics. 1999, 24: 245～263.
[195] Potyondy D. O. , Cundall P. A. A bonded-particle model for rock. International Journal of Rock Mechanics & Mining Sciences, 2004, 41: 1329～1364.
[196] 陈文胜，郑宏，郑榕明等．岩石块体三维接触判断的侵入边法．岩石力学与工程学报．2004，23(4)：565～571．
[197] Shi G. H. Single and multiple block limit equilibrium of key block method and discontinuous deformation analysis. In: Hatzor Y. H. Proceedings of 5th International Conference on Analysis of Discontinuous Deformation. BeerSheva, Israel: Balkema, 2002: 3～43.
[198] Munjiza A. , Rougier E. , John N. W. M. MR linear contact detection algorithm. Int. J. Numer. Meth. Engng. 2006, 66: 46～71.
[199] Lemos J. V. The representation of contact in models of discrete elements. In: Fifth National Conference of Computational Mechanics. University of Minho, Guimaraes, Portugal, 1997: 20～22.
[200] Munjiza A. , Owen D. R. J. , Bicanic N. A combined finite-discrete method in transient dynamics of fracturing solids. Engineering Computations. 1995, 12: 145～174.
[201] Jimenez P. , Thomas F. , Torras C. , 3D collision detection: a survey. Preprint submitted to Elsevier Preprint, 13 April 2000.
[202] Schomer E. , Thiel C. Efficient collision detection for moving polyhedra.
[203]: Madhav K. , Ponamgi, Manocha D. , et al. Incremental algorithm for collision detection between polygonal models. IEEE Transactions on Visualization and Computer Graphics. 1997, 3 (1) : 51～64.
[204]: Moore M. , Wilhelms J. Collision detection and response for computer animation. Computer Graphics. 1988, 22 (4) : 289～298.
[205]: ThomasJ. , Klosowski. Efficient collision detection for interactive 3D graphics and virtual environments: (PhD thesis). New York: State University of New York at Stony Brook U. S. A. , 1998.
[206] 罗海宁、焦玉勇．对三维离散单元法中块体接触判断算法的改进．岩土力学．1999，20(2)：37～45．
[207] Nezami E. G. , Hashash Y. M. A. , Zhao D. , et al. A fast contact detection algorithm for 3-D discrete element method. Computers and Geotechnics. 2004, 31: 575～587.
[208] Liu X. L. , Lemos J. V. Procedure for contact detection in discrete element analysis. Advances in Engineering Software. 2001, 32: 409～415.
[209] Zong Z. H. , Nilsson L. A contact search algorithm for general 3-D contact-impact problems. Computers & Structures. 1990, 34 (2) : 327～335.
[210] Munjiza A. , Andrews K. R. F. NBS contact detection algorithm for bodies of similar size. Int. J. Numer. Meth. Engng. 1998, 43: 131～149.
[211] Steve P. , Steve A. , Bruce H. et al. Parallel transient dynamics simulations: algorithms for contact detection and smoothed particle hydrodynamics. Journal of Parallel and Distributed Computing. 1998, 50: 104～122.
[212] Malone J. , Johnson N. A parallel finite element contact/impact algorithm for non-linear explicit transient analysis: part 1—the search algorithm and contact mechanics. International Journal for Numerical Methods in Engineering. 1994, 37: 559～590.
[213] Oldenburg M. , Nilsson L. The position code algorithm for contact searching. International Journal for Numerical Methods in Engineering. 1994, 37: 359～386.
[214] Ikegawa Y. , Hudson J. A. A novel automatic identification system for three-dimensional multi-block systems. Engineering Computations. 1992, 9: 169～179.
[215] Canny J. , Collision detection for moving polyhedra. IEEE Transactions on pattern analysis and Machine Intelligence. 1986, PAMI-8 (2) : 200～209.
[216] Krishnasamy J. , Jakiela M. J. A method to resolve ambiguities in comer-comer interactions between polygons in the context of motion simulations. Engineering Computations. 1995, 12: 135～144.
[217] 邬爱清．张奇华．岩石块体理论中三维随机块体几何搜索．水利学报．2005，36(4)：426～432．
[218] 张德海，刑纪波，朱浮声等．混凝土破坏过程的数值模拟．东北大学学报(自然科学版)．2004，25(2)：175～178．
[219] Munjiza A. , Andrews K. R. F. Penalty function method for combined finite-discrete element systems comprising large number of separate bodies. Int. J. Numer. Engng. 2000, 49: 1377～1396.
[220] 石丙飞，陈剑平，王清．块状结构岩体力学的回顾与展望．岩土力学．2003，24(增)．40～43．
[221] 陈剑平．岩体随机不连续面三维网络数值模拟技术．岩土工程学报．2001，23(4)：397～402．
[222] Rougier E. , Munjiza A. , John N. W. M. Numerical comparison of some explicit time integration schemes used in DEM, FEM/DEM and molecular dynamics. International Journal for Numerical Methods in Engineering. 2004, 61: 856～879.
[223] 陈祖煜．土质边坡稳定分析—原理．方法．程序．北京：中国水利水电出版社，2003
[224] Wang G. , Pekau O. A. , Zhang C. et al. Seismic fracture analysis of concrete gravity dams based on nonlinear fracture mechanics. 2000, 65: 67～87.
[225] Ozsan A., Karpuz C. Geotechnical rock-mass evaluation of the Anamur dam site, Turkey. Engineering Geology. 1996,42: 65-70.
[226] Zhang J.H., Jiang D.H., Fan J.W. Static and dynamic stability assessment of slopes or dam foundations using a rigid body-spring element method. International Journal of Rock Mechanics & Mining Sciences. 2001, 38: 1081-1090.
[227] Day R.A., Hight D.W., Potts D.M. Finite element analysis of construction stability of Thika Dam. Computers and Geotechnics. 1998, 23: 205-219.
[228] Liu J., Feng X.T., Ding X.L. et al, Stability assessment of the Three-Gorges Dam foundation, China, using physical and numerical modeling—Part I: physical model tests. International Journal of Rock Mechanics & Mining Sciences. 2003,40: 609-631.
[229] Liu J., Feng X.T., Ding X.L. Stability assessment of the Three-Gorges Dam foundation, China, using physical and numerical modeling—Part II: numerical modeling. International Journal of Rock Mechanics & Mining Sciences. 2003, 40: 633-652.
[230] M.M. MacLaughlin, D.M.Doolin. Review of validation of the discontinuous deformation analysis (DDA) method. International Journal for Numerical and Analytical Methods in Geomechanics. 2006, 30:271-305.
[2] Chappell B. A. Deformational response in discontinua, J. Rock. Mech. Min. Sci. & Geomech. Abstr., 1979, 16: 377～390.
[3] Chappell B. A. The effects of constrains on the reformational response of slip along planar joints. Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr., 1975, 12: 265～270.
[4] Chappell B. A. Stress distribution in anisotropic compliance of jointed rock. Geotech. Eng. (ASCE), 1986, 112: 682～700.
[5] Chappell B. A. Deformation control in excavating unstable slopes. J. Geotech. Eng. (ASCE), 1987, 113: 299～319.
[6] Sun J., Wang S. J. Rock mechanics and rock engineering in China: developments and current state-of-art. International Journal of Rock Mechanics & Mining Sciences. 2000, 37: 447～465.
[7] Jing L., Hudson J. A. Numerical methods in rock mechanics. International Journal of Rock Mechanics & Mining Sciences. 2002, 39: 409～427.
[8] 周维垣，杨强．岩石力学数值计算方法．北京：中国电力出版社，2005．
[9] Munjiza A., Latham J. P. Grand challenge of discontinuous deformation analysis. In: Hatzor Y. H. Proceedings of the 5th International Conference on Analysis of Discontinuous Deformation, BeerSheva, Israel: Balkema, 2002: 69～73.
[10] 刘君，孔宪京．三维连续与非连续变形分析．力学进展．2002，34(6)：941-948．
[11] 刘凯欣，高凌天．离散元法研究的评述．力学进展．2003，33(4)：483-490．
[12] 刘军，李仲奎．非连续变形分析(DDA)方法研究现状及发展趋势．岩石力学与工程学报．2004，23(5)：839-845．
[13] 陈文胜，王桂尧，刘辉等．岩石力学离散单元计算方法中的若干问题探讨．岩石力学与工程学报．2005．24(10)：1639-1644．
[14] Goodman R. E., Taylor R. L. and Brekke T. A model for the mechanics of jointed rock. J. Soil Mech. Found. Div. (A SCE), 1968, SM3: 637～659.
[15] Desai C. S., Zaman M. M., Lightner J. G.. et al. Thin-layer element for interface and joints. International Journal for Numerical and Analytical Methods in Geomechanics. 1984, 8(1): 19～43.
[16] Zaman M. M., Desai C. S. and Drumm E. C. Interface model for dynamic soil-structure interaction. Journal of Geotechnical Engineering. 1984, 110(9): 1257-1273.
[17] 雷晓燕，Swoboda G．，杜庆华．接触摩擦单元的理论及其应用．岩土工程学报．1994，16(3)：23～32．
[18] Lei X. Y., Swoboda G. and Zenz G.. Application of contact-friction interface element to tunnel excavation in faulted rock. Computers and Geotechnics. 1995, 17: 349～370.
[19] Cundall P. A. A computer model for simulating progressive, large-scale movements in blocky rock systems. Proceedings of the International Symposium on Rock Fracture, Nancy, France, 1971: Ⅱ-8.
[20] Cundall P. A. and Strack O. D. L. A discrete numerical model for granular assemblies. Geotechnique. 1979, 29(1): 47～65.
[21] Cundall P. A. and Hart R. D. Numerical modeling of discontinua. Engineering Computations. 1992, 9: 101～113.
[22] Stewart I. J. A static relaxation method for the analysis of excavations in discontinuous rock. In: Brown E. T. and Hudson J. A. Design and performance of underground excavations. Cambridge U. K., 1984: 149～154.
[23] 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, lnt. J. Rock Mech. Min. Sci. & Geomech. Abstr. 1988, 25(3): 107-116.
[24] Hart R. D. and Cundall P. A. and Lemos J. Formulation of a three-dimensional distinct element model—Part Ⅱ. Mechanical calculations for motion and interaction of a system composed of many polyhedral blocks. 1988, 25(3): 117～125.
[25] 朱焕春，Andrieux Patrix，钟辉亚．节理岩体数值计算方法及其应用(二)：工程应用．岩石力学与工程学报．2005，24(1)：89～96．
[26] 王泳嘉．刑纪波．离散单元法及其在岩土力学中的应用．沈阳：东北工学院出版社，1991．
[27] 刑纪波．千泳嘉．离散单元法的改进及其在颗粒介质研究中的应用．岩士工程学报．1990．12(5)：51～57．
[28] 魏群．岩土工程中离散元的基本原理数值方法及试验研究：(博士学位论文)．北京：清华大学．1090．
[29] 王泳嘉，刘连峰．二维离散单元法软件系统TRUDEC的研制．岩石力学与工程学报．1996．15(3)：201～210．
[30] 朱浮声．王泳嘉，斯蒂芬森O．露天矿山高陡岩石边坡失稳的三维离散元分析．东北大学学报(自然科学版)．1997，18(3)：234～237．
[31] 麻凤海，于泳嘉．地层沉降控制的可变形离散单元模拟．岩石力学与工程学报．1999，18(2)：176～179．
[32] 王光纶，张楚汉，彭冈，陈昌伟．刚体动力试验与离散元法动力分析参数选择的研究．岩石力学与工程学报．1994，13(2)：124～133．
[33] 唐志平．二维离散元方法及其在冲击力学中的应用．中国科学(E辑)．2003，33(11)：989～998．
[34] 李世海，汪远年．三维离散元计算参数选取方法研究．岩石力学与工程学报．2004，23(21)：3642～3651．
[35] 徐冰，孙其诚，张凌等．颗粒离散元法研究进展．力学进展．2003，33(2)：251～260．
[36] 鲍鹏，姜忻良．离散元-无限元非线性耦合法．华中科技大学学报．2004，32(11)：91～93．
[37] 魏怀鹏，易大可，李世海等．基于连续介质模型的离散元方法中弹簧性质研究．岩石力学与工程学报．2006，25(6)：1159～1169．
[38] 雷卫东，Mohamed Hefny，赵坚等．岩石动力学中离散元程序处理波幅的新方法．中国矿业大学学报．2005，34(2)：170～174．
[39] 李世海．饶莹，赵满洪等．二维离散元块体—质点计算模型．见：中国土木工程学会第九届土力学及岩土工程学术会议论文集．北京，2003：1395～1399．
[40] 罗海宁，焦玉勇．对三维离散单元法中块体接触判断算法的改进．岩土力学 1999，20(2)：37～40．
[41] 鲁军．离散单元法的数学模型研究及其工程应用：(博土学位论文)．北京：清华大学，1996．
[42] 王为华，李夕兵，离散元发及其在岩土工程中的应用综述．岩土工程技术．2005，19(4)：177～181．
[43] 候艳丽，张冲，张楚汉等．拱坝沿建基面上滑溃决的可变形离散元仿真．岩土工程学报．2005，27(6)：657～661．
[44] 候艳丽，周元德，张楚汉．用非连续介质力学模型研究混凝土的l型断裂．清华大学学报．2006，46(3)：346～349．
[45] 张冲，候艳丽，金峰等．拱坝—坝肩三维可变形离散元整体稳定分析．岩石力学与工程学报．2006，25(6)：1226～1232．
[46] Morris J. P., Glenn L. A., Heuze F. E. Simulation of underground structures subjected to dynamic loading using the distinct element method. In: Hatzor Y. H. Proceedings of the 5th International Conference of Analysis on Discontinuous Deformation, B eerSheva, Israel: Balkema, 2002: 121～124.
[47] Potyondy D. O., Cundall P. A. A bonded-particle model for rock. International Journal of Rock Mechanics & Mining Sciences. 2004, 41: 1329-1364.
[48] Jing L. Block system construction for three-dimensional discrete element models of fractured rocks. International Journal of Rock Mechanics & Mining Sciences. 2000, 37: 645～659.
[49] Munjiza A., Latham J. P., Andrews K. R. F. Detonation gas model for combined finite-discrete element simulation of fracture and fragmentation. Int. J. Numer. Meth. Engng. 2000, 49: 1495～1520.
[50] Mishra B. K., Murty C. V. R. On the determination of contact parameters for realistic DEM simulations of ball mills. Powder Technology. 2001, 115: 290～297.
[51] Cleary P. W. DEM simulation of industrial particle flows: case studies of dragline excavators, mixing in tumblers and centrifugal mills. Powder Technology. 2000, 109: 83～104.
[52] Zhang Z. P., Liu L. F., Yuan Y. D., et al. A simulation study of the effect of dynamic variables on the packing of spheres. Powder Technology. 2001, 116: 23～32.
[53] Esaki T., Jiang Y., Bhattarai T. N., et al. Stability analysis and reinforcement system design in a progressively failed steep rock slope by the distinct element method. Int. J. Rock Mech. Min. Sci. 1998, (4/5): 664～666.
[54] Munjiza A. Combined single and smeared crack model in combined FEM/DEM. Int. J. Num. M. Eng. 1999, 44: 41～57.
[55] Kawai T. New discrete models and their application to seismic response analysis of structure. Nuclear Engineering and Design. 1978, 48: 207～229.
[56] 钱令希，张雄．结构分析中的刚性有限元法．计算结构力学及其应用．1991，8(1)：1～14．
[57] 钱令希，张雄．刚性有限元的参变量变分原理及有限元参数二次规划解．计算结构力学及其应用．1992，9(2)：117～123．
[58] 张雄．刚性有限元的数学理论基础及其在岩土工程中的应用：(博士学位论文)．大连：大连理工大学，1992．
[59] 卓家寿，赵宁．不连续介质静、动力分析的刚体—弹簧元法．河海大学学报．1993，21(5)：34～43．
[60] 赵宁，卓家寿．动力分析的刚体—界面元与有限元耦合法．河海大学学报．1994，22(6)：8～15．
[61] 赵宁，卓家寿．结构的三维非线性界面元分析．河海大学学报．1995，23(2)：23～31．
[62] 张建海，范景伟，何江达．用刚体弹簧元法求解边坡、坝基动力安全系数．岩石力学与工程学报．1999，18(4)：387～391．
[63] 任青文．块体单元法及其在岩体稳定分析中的应用．河海大学学报．1995，23(1)：1～7．
[64] Wang B. L.. Garga V. K. A numerical method for modeling large displacement of jointed rocks-Part Ⅰ: Fundaments. Canadin Geotechnical Journal. 1993, 30: 96～108.
[65] Garga V.K., Wang B. L. A numerical method for modeling large displacements of jointed rocks-Part Ⅱ: Modeling of rockbolts and groundwater and applications. Canadin Geotechnicai Journal. 1993, 30: 109～123.
[66] Hock E.. Bray J. W. Rock slope engineering (3rd edition). The lnsititue of Mining and Metallurgy, London, 1981.
[67] Sarma S. K. Stability analysis of embankments and slopes. J. Geomech. Am. Soi. Civ. Engrs. 1979. 105: 1511～1624.
[68] Donald．陈祖煜．边坡稳定分析的塑性力学上限解，第一部分：基本原理和方法．中国水利水电科学研究院．1994．
[69] Donald．陈祖煜．边坡稳定分析的塑性力学上限解，第二部分：论能量法和静力法的等效性．中国水利水电科学研究院．1994．
[70] Goodman R. E., Shi G. H. Block theory and its application. Geotechnique. 1995, 45(3): 383～423.
[71] 石根华．岩体稳定分析的赤平投影方法．中国科学．1977．3：260～271．
[72] Shi G. H., Goodman R. E. The key blocks of unrolled joint traces in developed maps of tunnel walls. International Journal for Numerical and Analytical Methods in Geomechanics. 1989, 13(1): 131～158.
[73] 张奇华．邬爱清．石根华．关键块体理论在百色水利枢纽地下厂房岩体稳定性分析中的应用．岩石力学与工程学报．2004，23(15)：2609～2614．
[74] Shi G. H., Goodman R. E. Two dimensional discontinuous deformation analysis. International Journal for Numerical and Analytical Methods in Geomechanics. 1985, 9: 541-556.
[75] Shi G. H. Discontinuous deformation analysis: A new numerical model for the statics and dynamics of block systems: (PhD Dissertation). Berkeley: University of California, Berkeley. U.S.A., 1988.
[76] Shi G. H., Goodman R. E. Generalization of two-dimensional discontinuous deformation analysis for forward modeling. International Journal for Numerical and Analytical Methods in Geomechanics. 1989. 13: 131～158.
[77] Shi G. H. Discontinuous deformation analysis: a new numerical model for the statics and dynamics of deformable block structures. Engineering Computations. 1992, 9: 157～168.
[78] 石根华．数值流形方法与非连续变形分析(裴觉民译)．北京：清华大学出版，1997．
[79] Shi G. H. Manifold method. In: M.Reza Salami and Don Banks. Proceedings of the 1st international forum on discontinuous deformation analysis (DDA) and simulations of discontinuous media. Berkeley, California. 1996. 52～204.
[80] 周维垣，杨若琼，剡公瑞．流形元法及其在工程中的应用．岩石力学与工程学报．1996，15(3)：211～218．
[81] 王芝银，王思敬，杨忐法．岩石大变形分析的流形元法．岩石力学与工程学报．1997，16(5)：399～404．
[82] 朱以文．曾又林，陈明详．岩石大变形分析的增量流形方法．岩石力学与工程学报．1999，18(1)：1～5．
[83] 王芝银，李运鹏．数值流形方法中的几点改进．岩土工程学报．1998，20(6)：33～36．
[84] 张湘伟，蔡永吕，廖林灿．数值流形方法物理覆盖系统的自动剖分，重庆大学学报(自然科学版)．2000，23(1)：29～31．
[85] 莫海鸿，陈尤雯．流形法在岩石力学研究中的应用．华南理工大学学报(自然科学版)．1998，26(9)：48～53．
[86] Shi G. H. Application of discontinuous deformation analysis and manifold method. 3rd International Conference on DDA. Colorado, USA, 1999, 3～15.
[87] 王水林，葛修润．流形元方法在模拟裂纹扩展中的应用．岩石力学与工程学报．1997，16(5)：405～410．
[88] 田荣．连续与非连续变形分析的有限覆盖无单元法及其应用研究：(博士学位论文)．大连：大连理工大学，2000．
[89] 田荣，栾茂田，杨庆．高阶流形方法及其应用．工程力学．2001，18(2)：21～26．
[90] Chen G., Ohnishi Y., Takahiro Ito. Development of high-order manifold method. International Journal for Numerical and Analytical Methods in Geomechanics. 1998, 43: 685～712.
[91] 张国新，王光纶，裴觉民．基于流形方法的结构体破坏分析．岩石力学与工程学报．2001，20(3)：281～287．
[92] 张国新，金峰，王光纶．用基于流形元的子域奇异边界元法模拟重力坝的地震破坏．工程力学．2001，18(4)：18～27．
[93] 张国新，彭静．二阶流形元法与结构变形分析．力学学报．2002，34(2)：261～269．
[94] Lu M. High-order manifold method with simplex integration. In: Hatzor Y. H. Proceedings of the 5th International Conference on Analysis of Discontinuous Deformation, BeerSheva, Israel: Balkema, 2002: 75～83.
[95] 董志宏，邬爱清，丁秀丽．数值流形方法中的锚固支护模拟及初步应用．岩石力学与工程学报．2005，24(20)：3754～3760．
[96] 姜清辉，王书法．锚固岩体的三维数值流形方法模拟．岩石力学与工程学报．2006，25(3)：528～532．
[97] 姜清辉，周创兵．四面体有限单元覆盖的三维数值流形方法．岩石力学与工程学报．2005，24(24)：4455～4460．
[98] Su H., Xie X. Preliminary research on solving large displacement problems by numerical manifold method with fixed mathematical. In: MacLaughlin M. and Sitar N. Proceedings of the 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 175～182.
[99] Lin S., Qi Y., Su H. Formulation of high-order numerical manifold method and fast simplex integration based on special matrix operations. In: MacLaughlin M. and Sitar N. Proceedings of the 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 183-190.
[100] Max Y．Ma．岩土工程中的非连续方法．见：计算机方法在岩石力学中的应用．武汉：武汉测绘科技大学出版社，1994．
[101] 裴觉民，吕祖衍．裂隙岩体非连续变形的静力和动力分析方法．岩土工程学报．1996，18(6)：46～54
[102] 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．岩石力学与工程学报．1997，16(5)：411～417．
[103] 王书法．朱维中，郑少河．节理岩体热戍力问题的非连续变形分析方法．岩石力学与工程学报．2000．19(5)：643～646．
[104] 张勇慧．关于DDA中推导热应力问题公式的讨论．岩石力学与工程学报．2001，20(2)：277～278．[热应力]
[105] 刘红岩，杨军，陈鹏万．爆破漏斗形成过程的DDA模拟分析．工程爆破．2004，10f2)：17～20．
[106] 张国新．金峰．重力坝抗滑稳定分析中DDA与有限元方法的比较．水力发电学报．2004，(1)：10～14．
[107] 黎勇，栾茂田．杨庆．非连续变形计算力学模型弹塑性分析方法在边坡稳定性分析中的应用．中国土木工程学会第九届土力学及岩土工程学术会议论文集．北京，2003
[108] 黎勇，栾茂田，冯夏庭．非连续变形计算力学模型的粘弹性分析方法Ⅰ：基本理论．计算力学学报．2004．21(4)：440～447．
[109] 黎勇．栾茂田，冯夏庭．非连续变形计算力学模型的粘弹性分析方法Ⅱ：算例分析计算力学学报．2004．21(4)：448～454．
[110] 姜清辉．朱传云．动力学问题的DDA方法及其在爆破抛掷过程中的应用．工程爆破．2004．10(3)：5～8．
[111] 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．岩石力学与工程学报．2006，25(1)：1～8．
[112] Yeung M. R., Goodman R. E. Muti block stability analysis using the DDA method. In: Myer, Cook, Goodman et al. Fractured and Jointed Rock Masses. Balkema, 1995, 701～707.
[113] Ohnishi Y., Yamamukai K., Chen G. Application of DDA in rock fall analysis. In: Aubertin, Hassani and Mitri. Rock Mechanics. Balkema, 1996, 2031～2037.
[114] Thomas PA. Discontinuous deformation analysis of particulate media: (PhD Dissertation). Berkeley: University of California, Berkeley, U.S.A.,1997.
[115] Koo C. Y., Chern J. C. Modificationof the DDA method for rigid block problem. Int. J. Rock Mech. Min. Sci. 1998, 35(6): 683～693.
[116] Arriaga M. C. S., Verduzco F. S. On the natural collapse of fractures in rocks with low fluid. International Journal of Rock Mechanics & Mining Sciences.1998, 35: 500-501.
[117] Chiou Y. J., Tzeng J. C., Liou Y. W. Experimental and analytical study of masonry infilled frames. Journal of Structural Engineering. 1999,125(10): 1109～1117.
[118] Mortazavi A. Modeling of rock blasting in jointed media using discontinuous deformation analysis: (PhD thesis) Kingston, Ontario, Canada: Queen's University, 1999.
[119] Pearce C. J., Thavalingam A., Liao Z. Computational aspects of the discontinuous deformation analysis framework for modeling concrete fracture. Engineering Fracture Mechanics. 2000, 65: 283～298.
[120] Doolin D. M., Sitar N. DDAML-discontinuous deformation analysis markup language. International Journal of Rock Mechanics & Mining Sciences. 2001, 38: 467～474.
[121] MacLaughlin M., Sitar N., Doolin D. et al. Investigation of slope-stability kinematics using discontinuous deformation analysis. International Journal of Rock Mechanics & Mining Sciences. 2001, 38: 753～762.
[122] Mortazavi A., Katsabanis P. D. Modelling burden size and strata dip effects on the surface blasting process. International Journal of Rock Mechanics & Mining Sciences. 2001, 38: 481～498.
[123] Jing L., Ma Y., Fang Z. Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method. International Journal of Rock Mechanics & Mining Sciences. 2001,38:343-355.
[124] Wu Y., Wang H., Zhou S. et al. Inverse DDA of a system of blocks in sphere coordinates. Journal of geodesy and geodynamics. 2003, 23(Supp): 30-33.
[125] Wang H., Zhang G., Wu Y. et al. The deformation of active tectonic blocks on the Chinese mainland and its relationship with seismic activity. Earthquake Research in China. 2004, 18(1): 54-66.
[126] Wu J.H., Ohnishi Y., Nishiyama S. Simulation of the mechanical behavior of inclined jointed rock masses during tunnel construction using Discontinuous Deformation Analysis (DDA). International Journal of Rock Mechanics & Mining Sciences. 2004, 41: 731-743.
[127] Hatzor Y.H., Arzi A.A., Zaslavsky Y. et al. Dynamic stability analysis of jointed rock slopes using the DDA method: King Herod's Palace, Masada, Israel. International Journal of Rock Mechanics & Mining Sciences. 2004,41:813-832.
[128] Sitar N., MacLaughlin M., Doolin D. Influence of kinematics on landslide mobility and failure mode. Journal of Geotechnical and Geoenvironmental Engineering. (ASCE) 2005,131(6):717-728.
[129] Wu A., Ding X., Li H. Numerical simulation of startup and the whole process characteristics of Qingjiangping landslide with DDA method. In: MacLaughlin M. and Sitar N. Proceedings of the 7th International Conference of the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 167-174.
[130] Moosavi M., Grayeli R. A model for cable bolt-rock mass interaction: Integration with discontinuous deformation analysis (DDA) algorithm. International Journal of Rock Mechanics & Mining Sciences. 2006, 43:661-670.
[131] Ke T.C., Goodman R.E. Discontinuous deformation analysis and the artificial joint concept. In: Nelson Laubach. Rock Mechanics. Balkema, 1994: 599-606.
[132] Ke T.C. Artificial joint-based DDA. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 326-333.
[133] Amadei B., Lin C.T., Sture S., et al. Modeling fracture of rock masses with the DDA method. In: Nelson Laubach. Rock Mechanics. Balkema, 1994: 583-590.
[134] Amadei B., Lin C, Dwyer J. Recent extensions to the DDA method. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulatio ns of Discontinuous Media. Berkeley, California, 1996: 1-30.
[135] Lin C, Amadei B., Jung J., et al. Extensions of discontinuous deformation analysis for jointed rock masses. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 1996, 33(7): 671-694.
[136] Cheng Y.M., Zhang Y.H. Rigid body rotation and block internal discretization in DDA analysis. International Journal for Numerical and Analytical Methods in Geomechanics. 2000,24: 567-578.
[137] Shyu K., Salami M.R. Stability of bartlett dam. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 440-445.
[138] Chang C.T. Nonlinear dynamic discontinuous deformation analysis with finite element meshed block system: (PhD thesis). Berkeley: University of California, 1994.
[139] Jing L. Formulation of discontinuous deformation analysis (DDA)-an implicit discrete element model for block systems. Engineering Geology. 1998, 43: 371～381.
[140] Koo C. Y., Chem J. C. The development of DDA with third order displacement function. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California. 1996: 342～349.
[141] Lin J. S., Hynes M. E. Seismic discontinuous deformation analysis. The Conference on Geotechnical Earthquake Engineering and Soil Dynamics Ⅲ. Part 1 (of 2), Seattle, USA, 1998, 790～799.
[142] Cai Y., Liang G. P., Shi G. H., et al. Studying an impact problem by using LDDA method. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 288～294.
[143] Liang G. P., Wang C. G. LDDA on the high speed catenary-pantograph system dynamics. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California. 1996: 350～356.
[144] 蔡永恩，梁国平，殷有泉．岩体滑坡动力过程的数值模拟新方法．见：第六届全国岩土力学数值分析与解析方法讨论会论文集．广州．1998：73～79．
[145] 黎勇．栾茂田．非连续变形计算力学模型的基本原理及其线性规划解．大连理工大学学报．2000，40(3)：351～357．
[146] 黎勇．非连续变形计算力学模型及其在岩土工程中的应用：(博士学位论文)．大连：大连理工大学，2000．
[147] 栾茂田，黎勇．杨庆．非连续变形计算力学模型在岩体边坡稳定性分析中的应用．岩石力学与工程学报．2000，19(3)：289～294．
[148] Chert G., Miki S., Ohnishi Y. Practical improvement on DDA. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 302～309.
[149] Ke T. C. The issue of rigid-body rotation in DDA. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 318～325.
[150] MacLaughlin M., Sitar N. Rigid body rotation in DDA. In: M. Reza Salami and Don Banks. Proceedings of 1 st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 620～635.
[151] Thomas P. A., Bray J. D., Ke T. C. Discontinuous deformation analysis for soil mechanics. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 454～461.
[152] Ke T. C., Bray J. Modeling of particulate media using discontinuous deformation analysis. Journal of Engineering Mechanics. 1995, 121(11): 1234～1243.
[153] Ohnishi Y., Miki S. Development of circular and elliptic disc elements for DDA. In: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 44～51.
[154] Thomas P. A., Bray J. D. Capturing nonspherical shape of granular media with disk clusters. Journal of Geotechnical and Geoenvironmental Engineeing. 1999, 3: 169～178.
[155] Shyu K. , Salami R. Analysis of pile driving using DDA. In: Hassani A. and Mitri. Rock Mechanics. Balkema, 1996: 2009～2016.
[156] 张国新，李广信，郭瑞平．不连续变形分析与土的应力应变关系．清华大学学报(自然科学版)．2000，40(8)：102～105．
[157] Pei J. The effects of energy loss in block bumping on discontinuous deformation, in: M. Reza Salami and Don Banks. Proceedings of 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Berkeley, California, 1996: 401～406.
[158] Ohnishi Y. , Tanaka M. , Sasaki T. Modification of DDA for elasto-plastic analysis with illustrative generic problem. In: Cook M. , Goodman, Tsang. Fractured and Jointed Rock Masses. Balkema, 1995, 45～50.
[159] Kim Y-II. , Amadei B. , Pan E. Modeling the effect of water, excavation sequence and rock reinforcement with discontinuous deformation analysis. International Journal of Rock Mechanics & Mining Sciences. 1999, 36: 949～970.
[160] 郑榕明，张勇慧，王可钧．耦合算法原理及有限元与DDA的耦合．岩土工程学报．2000，22(6)：727～730．
[161] 刘君，陈键云，孔宪京．基于DDA和FEM耦合方法的碾压混凝土坝抗震安全性分析．大连理工大学学报．2003，43(6)：793～798．
[162] Cheng Y. M. Advancements and improvement in discontinuous deformation analysis. Computers and Geotechnics. 1998, 22 (2) : 153～163.
[163] Oh Y. N. , Jeng D. S. , Chen S. A parametric study using discontinuous deformation analysis to model wave-induced seabed response. In: Hatzor Y. H. Proceedings of 5th International Conference on Analysis of Discontinuous Deformation, BeerSheva, Israel: Balkema, 2002: 113～119.
[164] Doolin D. , Sitar N. Displacement accuracy of discontinuous deformation analysis method applied to sliding block. Journal of Engineering Mechanics. 2002, 128 (11) : 1158～1168 (ASCE).
[165] Tsesarsky M. , Hatzor Y. H. , Sitar N. Dynamic block displacement prediction—validation of DDA using analytical solutions and shaking table experiments. In: Hatzor Y. H. Proceedings of 5th International Conference on Analysis of Discontinuous Deformation, BeerSheva, Israel: Balkema, 2002: 195～203.
[166] Bangash T. , Munjiza A. Experimental validation of combined FEM/DEM simulation of R. C. beams under impact induced failure. In: Hatzor Y. H. Proceedings of 5th International Conference on Analysis of Discontinuous Deformation, BeerSheva, Israel: Balkema, 2002: 165～169.
[167] MacLaughlin M. M. , Hayes M. A. Validation of DDA block motions and failure modes using laboratory models. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 71～78.
[168] Wright C. A. , MacLaughlin M. M. , Donovan R. P. Comparison of the deformation of externally loaded DDA and UDEC blocks with an analytical solution. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 79～90.
[169] Osada M. , Taniyama H. Preliminary consideration for analyzing ground deformation due to fault movement. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 113～120.
[170] Sasaki T. , Hagiwara I. , Sasaki K. Earthquake response analysis of a rock-fall by discontinuous deformation analysis. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation. Honolulu, Hawaii, 2005: 137～146.
[171] Ishikawa T. , Miura S. , Ohnishi Y. Influence of input parameters on energy loss in free fall tests with DDA. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 147～158.
[172] Ohnishi Y. , Nishiyama S. , Sasaki T. The application of DDA to practical rock engineering problems: issues and recent insights. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 277～287.
[173] Hatzor YH. Feintuch A, The validity of dynamic block displacement prediction using DDA[J], International Journal of Rock Mechanics and Mining Sciences, 2001, 38: 599～606.
[174] 王书法．朱维申．考虑空间影响的两种非连续变形分析方法．岩石力学与工程学报．2000，19(3)：369～372．
[175] Shi G. H. Three dimensional discontinuous deformation analysis, ln: Elsworth D. et al, Proceedings of the 38th US Rock Mechanics Symposium. 2001, Washington D. C. , 1421～1428.
[176] 王如路．陈乃明．刘宝琛．三维块体不连续分析理论简析．岩石力学与工程学报．1996，15(3)：219～224．
[177] 姜清辉．三维非连续变形分析方法的研究：(博士学位论文)．武汉：中国科学院武汉岩土力学研究所．2000．
[178] 姜清辉．杨文柱，丰定详．三维块体系统非连续变形正分析模型．岩石力学与工程学报．2002，21(12)：1765～1769．
[179] 刘君．三维非连续变形分析与有限元耦合算法研究：(博士学位论文)．大连：大连理工大学，2001
[180] Liu Jun, Kong Xianjing, Lin Gao. Formulations of the three-dimensional discontinuous deformation analysis method. Acta Mechanica Sinica. 2004, 20 (3) : 270～282.
[181] 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．岩土工程学报．2006，28(8)：998～1001．
[182] 姜清辉，丰定详．三维非连续变形分析方法中角—面接触模型的研究．岩石力学与工程学报．2000，19(增)：930～935．
[183] Jiang Q. H. , Yeung M. R. A model of point-to-face contact for three-dimensional discontinuous deformation analysis. Rock Mechanics and Rock Engineering. 2003, 37: 95～116.
[184]: Wu J. H. , Juang C. H. , Lin H. M. Vertex-to-face contact searching algorithm for three-dimensional frictionless contact problems. International Journal for Numerical Methods in Engineering, 2005, 63, 876-897.
[185] 姜清辉．周创兵，罗先启．块状结构岩体在一般水压分布模式下的不连续变形分析．岩石力学与工程学报．2005，24(3)：401～405．
[186] Jang H. I. , Lee C. I. Development of a three-dimensional discontinuous deformation analysis technique and its application to toppling failure. In: Hatzor Y. H. Proceedings of 5th International Conference on the Analysis of Discontinuous Deformation. BeerSheva, Israel: Balkema, 2002: 225～229.
[187] 吴建宏，大西有三，石根华等．三维非连续变形分析(3D DDA)理论及其在岩石边坡失稳数值仿真中的应用．岩石力学与工程学报．2003，22(6)：937～942．
[188] Yang M. , Fukawa T. , Ohnishi Y. et al. The application of 3-dimensional DDA with a spherical rigid block for rockfali simulation. International Journal of Rock Mechanics & Mining Sciences. 2004, 41 (3), CD-ROM.
[189] Yeung M. R. , Sun N. , Jiang Q. H. Analysis of large block test data using three-dimensional discontinuous deformation analysis. Int. J. Rock Mech. Min. Sci. 2004, 41 (3), CD-ROM.
[190] Beyabanaki S. A. , Jafari A. Modified point-to-face frictionless contact constraints for three-dimensional discontinuous deformation analysis (3-D DDA). In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 25～36.
[191] Yeung M. R. , Jiang Q. H. , Sun N. Validation of block theory and three-dimensional discontinuous deformation analysis as wedge stability analysis methods. International Journal of Rock Mechanics & Mining Sciences. 2003, 40: 265～275.
[192] Moosavi M. , Jafari A. , Beyabanaki S. A. Dynamic three-dimensional discontinuous deformation analysis (3-D DDA) validation using analytical solutions. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 37～48.
[193] Shi G. H. Producing joint polygons, cutting rock blocks and finding removable blocks for general free surfaces using 3-D DDA. In: MacLaughlin M. and Sitar N. Proceedings of 7th International Conference on the Analysis of Discontinuous Deformation, Honolulu, Hawaii, 2005: 1～24.
[194] Ouadfel H. , Rothenburg L. An algorithm for detecting inter-ellipsoid contacts. Computers and Geotechnics. 1999, 24: 245～263.
[195] Potyondy D. O. , Cundall P. A. A bonded-particle model for rock. International Journal of Rock Mechanics & Mining Sciences, 2004, 41: 1329～1364.
[196] 陈文胜，郑宏，郑榕明等．岩石块体三维接触判断的侵入边法．岩石力学与工程学报．2004，23(4)：565～571．
[197] Shi G. H. Single and multiple block limit equilibrium of key block method and discontinuous deformation analysis. In: Hatzor Y. H. Proceedings of 5th International Conference on Analysis of Discontinuous Deformation. BeerSheva, Israel: Balkema, 2002: 3～43.
[198] Munjiza A. , Rougier E. , John N. W. M. MR linear contact detection algorithm. Int. J. Numer. Meth. Engng. 2006, 66: 46～71.
[199] Lemos J. V. The representation of contact in models of discrete elements. In: Fifth National Conference of Computational Mechanics. University of Minho, Guimaraes, Portugal, 1997: 20～22.
[200] Munjiza A. , Owen D. R. J. , Bicanic N. A combined finite-discrete method in transient dynamics of fracturing solids. Engineering Computations. 1995, 12: 145～174.
[201] Jimenez P. , Thomas F. , Torras C. , 3D collision detection: a survey. Preprint submitted to Elsevier Preprint, 13 April 2000.
[202] Schomer E. , Thiel C. Efficient collision detection for moving polyhedra.
[203]: Madhav K. , Ponamgi, Manocha D. , et al. Incremental algorithm for collision detection between polygonal models. IEEE Transactions on Visualization and Computer Graphics. 1997, 3 (1) : 51～64.
[204]: Moore M. , Wilhelms J. Collision detection and response for computer animation. Computer Graphics. 1988, 22 (4) : 289～298.
[205]: ThomasJ. , Klosowski. Efficient collision detection for interactive 3D graphics and virtual environments: (PhD thesis). New York: State University of New York at Stony Brook U. S. A. , 1998.
[206] 罗海宁、焦玉勇．对三维离散单元法中块体接触判断算法的改进．岩土力学．1999，20(2)：37～45．
[207] Nezami E. G. , Hashash Y. M. A. , Zhao D. , et al. A fast contact detection algorithm for 3-D discrete element method. Computers and Geotechnics. 2004, 31: 575～587.
[208] Liu X. L. , Lemos J. V. Procedure for contact detection in discrete element analysis. Advances in Engineering Software. 2001, 32: 409～415.
[209] Zong Z. H. , Nilsson L. A contact search algorithm for general 3-D contact-impact problems. Computers & Structures. 1990, 34 (2) : 327～335.
[210] Munjiza A. , Andrews K. R. F. NBS contact detection algorithm for bodies of similar size. Int. J. Numer. Meth. Engng. 1998, 43: 131～149.
[211] Steve P. , Steve A. , Bruce H. et al. Parallel transient dynamics simulations: algorithms for contact detection and smoothed particle hydrodynamics. Journal of Parallel and Distributed Computing. 1998, 50: 104～122.
[212] Malone J. , Johnson N. A parallel finite element contact/impact algorithm for non-linear explicit transient analysis: part 1—the search algorithm and contact mechanics. International Journal for Numerical Methods in Engineering. 1994, 37: 559～590.
[213] Oldenburg M. , Nilsson L. The position code algorithm for contact searching. International Journal for Numerical Methods in Engineering. 1994, 37: 359～386.
[214] Ikegawa Y. , Hudson J. A. A novel automatic identification system for three-dimensional multi-block systems. Engineering Computations. 1992, 9: 169～179.
[215] Canny J. , Collision detection for moving polyhedra. IEEE Transactions on pattern analysis and Machine Intelligence. 1986, PAMI-8 (2) : 200～209.
[216] Krishnasamy J. , Jakiela M. J. A method to resolve ambiguities in comer-comer interactions between polygons in the context of motion simulations. Engineering Computations. 1995, 12: 135～144.
[217] 邬爱清．张奇华．岩石块体理论中三维随机块体几何搜索．水利学报．2005，36(4)：426～432．
[218] 张德海，刑纪波，朱浮声等．混凝土破坏过程的数值模拟．东北大学学报(自然科学版)．2004，25(2)：175～178．
[219] Munjiza A. , Andrews K. R. F. Penalty function method for combined finite-discrete element systems comprising large number of separate bodies. Int. J. Numer. Engng. 2000, 49: 1377～1396.
[220] 石丙飞，陈剑平，王清．块状结构岩体力学的回顾与展望．岩土力学．2003，24(增)．40～43．
[221] 陈剑平．岩体随机不连续面三维网络数值模拟技术．岩土工程学报．2001，23(4)：397～402．
[222] Rougier E. , Munjiza A. , John N. W. M. Numerical comparison of some explicit time integration schemes used in DEM, FEM/DEM and molecular dynamics. International Journal for Numerical Methods in Engineering. 2004, 61: 856～879.
[223] 陈祖煜．土质边坡稳定分析—原理．方法．程序．北京：中国水利水电出版社，2003
[224] Wang G. , Pekau O. A. , Zhang C. et al. Seismic fracture analysis of concrete gravity dams based on nonlinear fracture mechanics. 2000, 65: 67～87.
[225] Ozsan A., Karpuz C. Geotechnical rock-mass evaluation of the Anamur dam site, Turkey. Engineering Geology. 1996,42: 65-70.
[226] Zhang J.H., Jiang D.H., Fan J.W. Static and dynamic stability assessment of slopes or dam foundations using a rigid body-spring element method. International Journal of Rock Mechanics & Mining Sciences. 2001, 38: 1081-1090.
[227] Day R.A., Hight D.W., Potts D.M. Finite element analysis of construction stability of Thika Dam. Computers and Geotechnics. 1998, 23: 205-219.
[228] Liu J., Feng X.T., Ding X.L. et al, Stability assessment of the Three-Gorges Dam foundation, China, using physical and numerical modeling—Part I: physical model tests. International Journal of Rock Mechanics & Mining Sciences. 2003,40: 609-631.
[229] Liu J., Feng X.T., Ding X.L. Stability assessment of the Three-Gorges Dam foundation, China, using physical and numerical modeling—Part II: numerical modeling. International Journal of Rock Mechanics & Mining Sciences. 2003, 40: 633-652.
[230] M.M. MacLaughlin, D.M.Doolin. Review of validation of the discontinuous deformation analysis (DDA) method. International Journal for Numerical and Analytical Methods in Geomechanics. 2006, 30:271-305.