砼坝—地基破坏的离散元方法与断裂力学的耦合模型研究
|
摘要
本文研究结构从小变形损伤断裂到大变形渐进破坏的全过程仿真分析方法,期望实现从连续介质到非连续介质转化的数值模拟。据此,本文系统研究并初步实现了变形体离散单元法与弥散裂缝模型和分离裂缝模型两种非线性断裂力学模型的耦合,并应用于混凝土高坝的断裂与破坏过程的工程分析中,主要研究内容包括:
1.以三维刚体离散元为基础,采用在数值模型和实际结构之间建立的刚度等效、强度等效和荷载等效的原则,形成连续-非连续介质的统一模型——刚体弹簧元。应用这一方法研究了竖向横缝和水平施工缝等弱面组成的拱坝在强震条件下的整体性受损情况和破损机理。
2.提出了三维变形体离散元模拟连续介质和非连续介质时的分离界面刚度选取准则。应用三维变形体离散元对梅花拱坝沿坝基的上滑失稳溃决问题进行了仿真计算;指出在沿拱坝建基面存在不利的软弱面结构与两岸坝坡平缓时,需要认真研究拱坝沿坝基的上滑失稳问题,在拱坝设计中进行相应的稳定校核。
3.基于钝断裂带理论,推导了两种不同的非线性弥散断裂力学模型——固定裂缝模型和旋转裂缝模型的应力应变全量关系描述,将准脆性材料的开裂模型嵌入到变形体离散单元法的块体本构模型中,提出一种将损伤断裂模型与变形离散元结合的方法以研究连续-非连续耦合系统的破坏演化过程。
4.以变形体离散元的摩尔库仑接触模型和分离式裂缝模型为基础,建议了混凝土、岩石等准脆性材料Ⅰ/Ⅱ混合型开裂的拉剪分区开裂准则以及基于缝面法向张开度的刚度强度软化的裂缝扩展准则,提出了分离裂缝模型和变形体离散元的耦合模型并用于分析准脆性材料的受拉开裂和拉剪混合型开裂行为,模型初步实现了系统在外载作用下从小变形到完全破坏的全过程仿真。
5.采用本文提出的分离裂缝和变形体离散元的耦合模型分析了Koyna重力坝在动力荷载下的坝体开裂损伤行为,研究坝体在动力荷载下的稳定问题和强震下的大坝破坏模式以及再次经历相同地震时坝体的反应与累计残余变形,初步表明本文模型用于连续-断裂-非连续-破坏全过程的模拟具有可行性。
To build a numerical model for simulation of structural progressive collapse from small to large deformation and for numerical modeling of transition process from continua to discontinua is of theoretical and practical significance. Herein, the coupling method of deformable distinct elements with two nonlinear fracture mechanics models-smeared and discrete crack models is presented and applied to analyze the fracture and collapse of high concrete dam. The main contents are summarized as below:
1. Based on 3-D rigid distinct element method, a rigid body spring model is developed for simulation of continuum-discontinuum media by achieving the equivalence of the stiffness, strength and external load between the discrete model and the continuous structure. The model is then applied to analyze the failure mechanism of an arch dam with vertical and horizontal construction joints subjected to strong ground motion.
2. A rule for selecting the stiffness of discrete interface for deformable distinct element model is presented for simulating the unified model of continuous and discontinuous media. The upward-sliding failure along abutment interface of the Meihua arch dam is simulated by the deformable distinct element method. The results demonstrate that the instability of upward sliding near the dam-abutment interface is the cause of failure, indicating that the corresponding sliding stability analysis in the design of arch dam must be carefully performed when unfavorable weak joints exist and the abutments are relatively flat.
3. Based on the blunt crack band theory, systematic formulations of total relationship between stress and strain are deduced for the two nonlinear smeared crack models, i.e. fixed crack model and rotating crack model. The above-mentioned crack models of quasibrittle materials are then inserted in the constitutive models of 3-D deformable distinct element code. Thus, the method based on the coupling damage-crack model with distinct element method is developed to simulate the failure evolution process of continuous and discontinuous system.
1.以三维刚体离散元为基础,采用在数值模型和实际结构之间建立的刚度等效、强度等效和荷载等效的原则,形成连续-非连续介质的统一模型——刚体弹簧元。应用这一方法研究了竖向横缝和水平施工缝等弱面组成的拱坝在强震条件下的整体性受损情况和破损机理。
2.提出了三维变形体离散元模拟连续介质和非连续介质时的分离界面刚度选取准则。应用三维变形体离散元对梅花拱坝沿坝基的上滑失稳溃决问题进行了仿真计算;指出在沿拱坝建基面存在不利的软弱面结构与两岸坝坡平缓时,需要认真研究拱坝沿坝基的上滑失稳问题,在拱坝设计中进行相应的稳定校核。
3.基于钝断裂带理论,推导了两种不同的非线性弥散断裂力学模型——固定裂缝模型和旋转裂缝模型的应力应变全量关系描述,将准脆性材料的开裂模型嵌入到变形体离散单元法的块体本构模型中,提出一种将损伤断裂模型与变形离散元结合的方法以研究连续-非连续耦合系统的破坏演化过程。
4.以变形体离散元的摩尔库仑接触模型和分离式裂缝模型为基础,建议了混凝土、岩石等准脆性材料Ⅰ/Ⅱ混合型开裂的拉剪分区开裂准则以及基于缝面法向张开度的刚度强度软化的裂缝扩展准则,提出了分离裂缝模型和变形体离散元的耦合模型并用于分析准脆性材料的受拉开裂和拉剪混合型开裂行为,模型初步实现了系统在外载作用下从小变形到完全破坏的全过程仿真。
5.采用本文提出的分离裂缝和变形体离散元的耦合模型分析了Koyna重力坝在动力荷载下的坝体开裂损伤行为,研究坝体在动力荷载下的稳定问题和强震下的大坝破坏模式以及再次经历相同地震时坝体的反应与累计残余变形,初步表明本文模型用于连续-断裂-非连续-破坏全过程的模拟具有可行性。
To build a numerical model for simulation of structural progressive collapse from small to large deformation and for numerical modeling of transition process from continua to discontinua is of theoretical and practical significance. Herein, the coupling method of deformable distinct elements with two nonlinear fracture mechanics models-smeared and discrete crack models is presented and applied to analyze the fracture and collapse of high concrete dam. The main contents are summarized as below:
1. Based on 3-D rigid distinct element method, a rigid body spring model is developed for simulation of continuum-discontinuum media by achieving the equivalence of the stiffness, strength and external load between the discrete model and the continuous structure. The model is then applied to analyze the failure mechanism of an arch dam with vertical and horizontal construction joints subjected to strong ground motion.
2. A rule for selecting the stiffness of discrete interface for deformable distinct element model is presented for simulating the unified model of continuous and discontinuous media. The upward-sliding failure along abutment interface of the Meihua arch dam is simulated by the deformable distinct element method. The results demonstrate that the instability of upward sliding near the dam-abutment interface is the cause of failure, indicating that the corresponding sliding stability analysis in the design of arch dam must be carefully performed when unfavorable weak joints exist and the abutments are relatively flat.
3. Based on the blunt crack band theory, systematic formulations of total relationship between stress and strain are deduced for the two nonlinear smeared crack models, i.e. fixed crack model and rotating crack model. The above-mentioned crack models of quasibrittle materials are then inserted in the constitutive models of 3-D deformable distinct element code. Thus, the method based on the coupling damage-crack model with distinct element method is developed to simulate the failure evolution process of continuous and discontinuous system.
引文
[1] 张楚汉主编. 水利水电工程科学前沿. 北京:清华大学出版社,2002
[2] 李瓒,陈兴华,郑建波,王光纶. 混凝土拱坝设计. 北京:中国电力出版社,2000
[3] 汝乃华,姜胜忠. 大坝事故与安全?拱坝. 北京:中国水利水电出版社,1995
[4] Osterreichische Draukraftwerke A G. Remedial Project of Kolnbrein Arch Dam Design and Construction. Klagenfurt: Carinthia, 1991
[5] Chopra A K, Chakrabarti P. The Koyna earthquake and the damage to Koyna dam. Bull. Seism. Soc. Am, 1973, 63(2): 381-397
[6] Londe P. The Malpasset Dam Failure. Proc. Int. Workshop on Dam Failure, Elsevier, 1987, 295-325
[7] Hansen K P, Roehm L H. The response of concrete dams to earthquake. Water Power and Dam Construction, 1979, 31(4): 27-31
[8] 张光斗,王光纶. 水工建筑物(上册). 北京:水利电力出版社,1992
[9] 吴媚玲. 水工建筑物. 北京:清华大学出版社,1991
[10] Forsythe G E, Wasow W R. 偏微分方程的有限差分方法(胡祖熾，吴文达，陈永和译）. 上海:上海科学技术出版社,1964
[11] 王磊,李家宝. 结构分析的有限差分法. 北京:人民交通出版社,1982
[12] Alterman Z S, Karal F C. Propagation of elastic waves in layered media by finite difference methods. Bull. Seism. Soc. Am. 1968, 58(1): 367-398
[13] Boore D M. Finite difference methods for seismic wave propagation in heterogeneous materials. In: Bolt B A, eds. Methods in Computational Physics. Academic Press, New York, 1972, 11
[14] Aki K, Larner K L. Surface motion of a layered medium having an irregular interface due to incident plane SH-waver. J. Geophysics Res, 1970, 75(5): 933-954
[15] Joyner W B. A method for calculating nonlinear seismic response in two dimensions. Bull. Seis. Soc. Am. 1975, 65: 1337-1357
[16] FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions), Version 2.1, User’s manual, Itasca Consulting Group, Inc. USA
[17] 李仲奎,梁海波. FLAC 程序基本原理及使用方法指南. 北京:清华大学水利水电工程系,1993
[18] 寇晓东,周维垣,杨若琼. FLAC-3D 进行三峡船闸高边坡稳定分析. 岩石力学与工程学报,2001,20(1):6-10
[19] 杨为民,陈卫忠,李术才,杨典森,李飞. 快速拉格朗日法分析巨型地下洞室群稳定性. 岩土工程学报,2005,27(2):230-234
[20] 张练,丁秀丽,付敬. 清江水布垭地下厂房围岩稳定三维数值分析. 岩土力学,2003,24(增 1):120-123
[21] 寇晓东,周维垣,杨若琼. 三维快速拉格朗日法进行小湾拱坝稳定分析. 水利学报,2000,9:8-14
[22] Zienkiewicz O C, Taylor R L. The finite element method. Boston: Butterworth-Heinemann, 2000
[23] 王勖成,劭敏. 有限单元法基本原理和数值方法. 北京:清华大学出版社,1997
[24] Goodman R E, Taylor R L, Brekke T L. A model for the mechanics of jointed rock. Journal of the Soil Mechanics and Foundations Division, ASCE, 1968, 94(SM3): 637-659
[25] Desai C S, Lightner J G, Siriwardane H J, et al. Thin-layer element for interfaces and joints. International Journal for Numerical Methods in Geomechanics, 1984, 8(1): 19-43
[26] Beer G. Application of numerical modeling to the analysis of excavation in jointed rock. In: Rossmanith H P, eds. Mechanics of jointed and faulted rock. Rotterdam: Balkema, 1990
[27] 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
[28] 陈厚群,李德玉,胡晓,侯顺载. 有横缝拱坝的非线性动力模型试验和计算分析研究.地震工程与工程振动,1995,15(4):10-26
[29] 陈健云,林皋. 小湾拱坝考虑横缝的非线性分析. 土木工程学报,1999,32(1):66-70
[30] 徐艳杰,张楚汉,王光纶,金峰. 小湾拱坝模拟实际横缝间距的非线性地震反应分析.水利学报,2001,4:68-74
[31] 张伯艳,陈厚群,涂劲. 基于动接触力法的拱坝坝肩抗震稳定有限元分析. 水利学报,2004,10:7-12
[32] 尹显俊. 岩体结构面循环加载本构模型研究及工程应用:[博士学位论文] . 北京:清华大学,2004
[33] 周元德. 混凝土非线性断裂力学模型与高拱坝开裂分析研究:[博士学位论文]. 北京:清华大学,2004
[34] 廖振鹏. 工程波动理论导论. 北京:科学出版社,2002
[35] Rizzo F J. An integral equation approach to boundary value problem of classical elastostatics. Q. Appl. Math., 1967, 25(1): 83-95
[36] Cruse T A, Rizzo F J. A direct formulation and numerical solution of the general transient elasto-dynamic problems. I. J. Math. Anal. Appl. 1968, 22: 244-295
[37] Gao X W, Davies T G. Boundary element programming in mechanics. Cambridge: Cambridge University Press, 2002
[38] Niwa Y, Kobayashi S, Azuma N. An analysis of transient stresses produced around cavities of arbitrary shape during the passage of traveling waves. Memoirs of Fac. Eng. Kyoto University, 1975, 37: 28-46
[39] Kobayashi S, Nishimura N. Dynamic analysis of underground structures by the integral equation method. Num. Meth. Goemechanics, Edmonton, Alberta, Can: Balkema A A, Rotterdam Ne, 1982. 401-409
[40] Manolis G D. A comparative study on three boundary element method approaches to problems in elastodynamics. Int. J. Numer. Meth. Eng., 1983, 19(1): 73-91
[41] Rice J M, Sadd M H. Propagation and scattering of SH waves in semi-infinite domains using a time-dependent boundary element method. J. Applied Mech., 1984, 51(3): 641-645
[42] Spyrakos C C, Beskos D E. Dynamic response of flexible strip foundations by boundary and finite element methods. Soil Dynamics and Earthquake Engineering, 1986, 5(2): 84-96
[43] Touhei T, Ohmachi T. FE-BE method for dynamic analysis of dam-foundation-reservoir systems in the time domain. Earthquake Engineering & Structural Dynamics, 1993, 22(3): 195-209
[44] Chuhan Zhang, Feng Jin, Pekau, O A. Time domain procedure of FE-BE-IBE coupling for seismic interaction of arch dams and canyons. Earthquake Engineering & Structural Dynamics, 1995, 24(12): 1651-1666
[45] 金峰. 结构-地基动力相互作用的 FE-BE-IBE 耦合模型及拱坝地震反应分析:[博士学位论文]. 北京:清华大学,1992
[46] 吴健,金峰,徐艳杰. 考虑辐射阻尼的拱坝随机振动分析. 水利学报,2005,36(1): 110-115
[47] Bettess P. Infinite element. International Journal for Numerical Methods in Engineering, 1977, 11(1): 53-64
[48] Bettess P, Zienkiewicz O C. Diffraction and reflection of surface waves using finite and infinite elements. International Journal for Numerical Methods in Engineering, 1977, 11(8): 1271-1290
[49] 葛修润,谷先荣,丰定祥. 三维无界元和节理无界元. 岩土工程学报,1986,8(5):9-20
[50] 赵崇斌,张楚汉,张光斗. 映射动力无穷元及其特性研究. 地震工程与工程振动,1987,7(3):1-15
[51] Zhang Chuhan, Zhao Chongbin. Coupling method of finite and infinite elements for strip foundation wave problems. Earthquake Engineering & Structural Dynamics, 1987, 15(7): 839-851
[52] Zhang Chuhan, Zhao Chongbin. Effect of canyon topography and geological conditions on strong ground motion. Earthquake Engineering & Structural Dynamics, 1988, 16(1): 81-97
[53] 燕柳斌,李国华,夏小舟. 地基基础-坝体体系动力特性及地震反应分析的有限元与无限元耦合法. 广西大学学报(自然科学版),2003,28(3):249-258
[54] 刘国华,刘西军. 无限单元法在坝体温度场分析中的尝试. 浙江大学学报(工学版), 2004,38(8):1009-1014
[55] Kim D K, Yun C B. Time-domain soil-structure interaction analysis in two-dimensional medium based on analytical frequency-dependent infinite elements. International Journal for Numerical Methods in Engineering, 2000, 47(7): 1241-1261
[56] Yerli H R, Temel B, Kiral E. Transient infinite elements for 2D soil-structure interaction analysis. Journal of Geotechnical and Geoenvironmental Engineering, 1998, 124(10): 976-988
[57] Nayroles B, Touzot G, Villon P. Generalizing the finite element method: Diffuse approximation and diffuse elements. Computational Mechanics, 1992, 10(5): 307-318
[58] Belytschko T. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229-256.
[59] 介玉新,高波,李广信. 无单元法在混凝土面板堆石坝应力分析中的应用. 清华大学学报(自然科学版),2003,43(8):1092-1095
[60] 周维垣,黄岩松,林鹏. 三维无单元伽辽金法及其在拱坝分析中的应用. 水利学报, 2005,36(6):644-649
[61] 寇晓东,杨若琼,沈大利,周维垣. 无单元法在小湾拱坝开裂计算中的应用. 云南水力发电,2000,16(1):71-76
[62] 张伯艳,陈厚群,杜修力,张艳红. 拱坝坝肩抗震稳定分析. 水利学报,2000,11:55-59
[63] 李瓒,龙云霄. 重力坝、拱坝基础岩体抗滑稳定分析中的一些问题的探讨. 水利学报, 2000,8:40-45
[64] 王瑞骏. 重力坝深层抗滑稳定性的空间刚体极限平衡分析. 西北水资源与水工程,1996,7(4):1-5
[65] 陈仲颐,周景星,王洪瑾. 土力学. 北京:清华大学出版社,1994
[66] Sarma K S. Stability analysis of embankments and slopes. J. Geotech. Am. Soc. Civ. Engrs, 1979, 105(12): 1511-1524
[67] 潘家铮. 建筑物抗滑稳定分析和滑坡分析. 北京:水利出版社,1980
[68] 陈祖煜. 建筑物抗滑稳定分析中“潘家铮最大最小原理”的证明. 清华大学学报,1998,1:6-13
[69] Donald I B, Chen Z Y. Slope stability analysis by the upper bound approach: fundamentals and methods. Canadian Geotechnical Journal, 1997, 34(6): 853-862
[70] 弥宏亮. 边坡稳定三维极限分析——方法?推广?应用:[博士学位论文]. 北京:清华大学,2003
[71] Kawai Tadahiko, Toi Yutaka. New element models in discrete structural analysis. Welding Journa(Miami, Fla), Soc of Nav Archit of Jpn, 1978, 16: 97-110
[72] 张建海,范景伟,胡定. 刚体弹簧元理论及应用. 成都:成都科技大学出版社,1997
[73] 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
[74] 卓家寿,邵国建,陈振雷. 工程稳定问题中确定滑坍面、滑向与安全度的干扰能量法.水利学报,1997,8:80-84
[75] Cundall P A. A computer model for simulating progressive large-scale movements in block rock systems, Proc. Symp. Int. Soci. Rock Mech., Nancy France, 1971
[76] Genhua Shi, Goodman R E. Two dimensional discontinuous deformation analysis. International Journal for Numerical and Analysis Methods in Geomechanics. 1985, 9(6): 541-556
[77] Genhua Shi, Goodman R E. Generalization of two-dimensional discontinuous deformation analysis for forward modeling. International Journal for Numerical and Analysis Methods in Geomechanics. 1989, 13(4): 359-380
[78] Lanru Jing. Formulation of discontinuous deformation analysis(DDA)- an implicit discrete element model for block systems. Engineering Geology, 1998, 49(3-4): 371-381
[79] 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,2004,23(1):10-14
[80] 张国新,武晓峰. 裂隙渗流对岩石边坡稳定的影响—渗流、变形耦合作用的 DDA 法.岩石力学与工程学报,2003,22(8):1269-1275
[81] 蔡永恩,罗纲,刘今朝,李青松,张伯艳,陈厚群. 不连续岩体-拱坝系统的动力过程数值模拟方法. 岩土力学,2004,25(Supp2):361-365
[82] 石根华. 数值流行方法与非连续变形分析. 裴觉民译. 北京:清华大学出版社,1997
[83] 张国新,王光纶,裴觉民. 基于流行方法的结构体破坏分析. 岩石力学与工程学报,2001,20(3):281-287
[84] 张国新,金峰,王光纶. 用基于流行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
[85] Tsuyoshi Ishida. Application of distinct element analysis to three simple block models aimed at practical application to toppling failure of fissured rock slopes. Computers and Geotechnics, 1990, 9(4): 341-353
[86] Bardet J P, Soctt R F. Seismic stability of fractured rock masses with the distinct element method. 26th US Symposium on Rock Mechanics, Rapid City, SD: Balkema A A, Rotterdam Neth, 1985. 26-28
[87] Ghaboussi J. Fully deformable discrete element analysis using a finite element approach. Computers and Geotechnics, 1988, 5(3): 175-195
[88] Williams J R, Jiocking G, Mustoe G G W. The theoretical basis of the discrete element method. Proceedings of the NUMETA’85 Conference, Swansea: Balkema A A, Rotterdam Neth, 1985. 897-906
[89] Williams J R, Mustoe G G W. Modal methods for the analysis of discrete system. Computers and Geotechnics, 1987, 4: 1-19
[90] Cundall P A, Hart R D. Numerical modeling of discontinua. Engineering Computations, 1992, 9(2): 101-113
[91] Cundall P A. UDEC-A generalized distinct element program for modeling jointed rock. Peter Associates, European Research Office, U. S. Army, 1980
[92] Iofis I M, Maksimov A V, Mironov V V. Some practical aspects of numerical simulation of jointed rock mass by distinct element method. Proceedings of the International Conference on Mechanics of Jointed and Faulted Rock, 1990, 479-486
[93] Zhang Chuhan, Pekau O A, Jin Feng, Wang Guanglun. Application of distinct element method in dynamic analysis of high rock slopes and blocky structures. Soil Dynamics and Earthquake Engineering, 1997, 16(6): 385-394
[94] Lemos J V, Lorig L J. Hydromechanical modeling of jointed rock masses using the distinct element method. Proceedings of the International Conference on Mechanics of Jointed and Faulted Rock, 1990, 605-612
[95] 王洪涛. 裂隙网络渗流与离散元耦合分析充水岩质高边坡的稳定性. 水文地质工程地质,2000,2:30-33
[96] 周庆科,金峰,王恩志,徐艳杰. 离散单元法的饱和/非饱和渗流模型及其试验验证. 水力发电学报,2003,3:34-39
[97] 王刚. 离散元流变模型及其在三峡工程中的应用:[硕士学位论文] . 北京:清华大学, 2000
[98] Cundall P A, Hart R D. Development of generalized 2-D and 3-D distinct element programs for modelling jointed rock. ITASCA Consulting Group, Misc Paper SL-85-1, U. S. Army Corps of Engineers, 1985
[99] Cundall P A. Formulation of three-dimensional distinct element model, Part Ⅰ, A scheme to detect and represent contacts in system composed of many polyhedral blocks. Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr., 1988, 25(3): 107-116
[100] Hart R, Cundall P A, Lemos J. Formulation of three-dimensional distinct element model, Part Ⅱ,Mechanical calculation of a system composed of many polyhedral blocks. Int. J. Rock. Mech. Min. Sci.. & Geomech. Abstr., 1988, 25(3): 117-125
[101] Ghaboussi J, Barbosa R. Three-demensional discrete element method for granular materials. Int. J. Num. Analy. Methods Geomech., 1990, 14(7): 451-472
[102] Kremmer M,Favier J F. Calculating rotational motion in discrete element modeling of arbitrary shaped model objects. Engineering Computations, 2000, 17(6): 703-714
[103] Munjiza A, Latham J P, John N W M. 3D dynamics of discrete element systems comprising irregular discrete elements—integration solution for finite rotations in 3D. Int. J. Numer. Meth. Engng, 2003, 56(1): 35-55
[104] 鲁军. 离散单元法的数值模型研究及其工程应用:[博士学位论文] . 北京:清华大学, 1996
[105] 崔玉柱. 连续与非连续介质的数值模拟与拱坝-地基系统安全分析:[博士学位论文]. 北京:清华大学,2001
[106] Zhang Chuhan. Challenges of High Dam Construction to Computational Mechanics. 6th World Congress on Computational Mechanics in conjunction with Second Asian-Pacific Congress on Computational Mechanics. Beijing, China, 2004
[107] 王泳嘉,刘连峰. 三维离散单元法及其在边坡工程中的应用. 中国矿业,1996,5(1): 34-39
[108] 焦玉勇,葛修润,谷先荣. 三维离散元法中地下水及锚杆的模拟. 岩石力学与工程学报,1999,18(1):6-11
[109] 3DEC, 3 Dimensional distinct element code, Version 3.0, User’s manual, ITASCA Consulting Group, Inc. USA
[110] Psycharis I N, Lemos J V, Papastamatiou D Y, Zambas C, Papantonopoulos C. Numerical study of the seismic behaviour of a part of the Parthenon Pronaos. Earthquake Engineering and Structural Dynamics, 2003, 32(13): 2063-2084
[111] Papantonopoulos C, Psycharis I N, Papastamatiou D Y, Lemos J V, Mouzakis H P. Numerical prediction of the earthquake response of classical columns using the distinct element method. Earthquake Engineering and Structural Dynamics, 2002, 31(9): 1699-1717.
[112] 王涛,盛谦,陈晓玲. 基于直接法节理网络模拟的三维离散单元法计算. 岩石力学与工程学报,2005,24(10):1649-1653
[113] Lorig L J, Brady B H G, Cundall P A. Hybrid distinct element-boundary element analysis of jointed rock. Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr., 1986, 23, 303-312
[114] 金峰,贾伟伟,王光纶. 离散元-边界元动力耦合模型. 水利学报,2001,1:23-27
[115] 金峰,王光纶,贾伟伟. 离散元-边界元动力耦合模型在地下结构动力分析中的应用. 水利学报,2001,2:24-28
[116] Dowding C H, Belyschko T B, Yen H J. A coupled finite element-rigid block method for transient analysis of rock caverns. Int. J. Num. Analy. Methods Geomech, 1983, 7(1): 117-127
[117] Pan X D, Reed M B. A coupled distinct element-finite element method for large deformation analysis of rock masses. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1991, 28(1): 93-99
[118] Han K, Peric D, Crook A J L, Owen D R J. A combined finite/discrete element simulation of shot peening processes Part Ⅰ : Studies on 2D interaction laws. Engineering Computations, 2000, 17(5): 593-619
[119] Han K, Peric D, Owen D R J, Yu J. A combined finite/discrete element simulation of shot peening processes Part Ⅱ: 3D interaction laws. Engineering Computations, 2000, 17(6): 680-702
[120] Onate E, Rojek J. Combination of discrete element and finite element methods for dynamics analysis of geomechanics problems. Comput. Methods Appl. Mech. Engrg., 2004, 193(27-29): 3087-3128
[121] Munjiza A, Andrews K R F. Penalty function method for combined finite-discrete element systems comprising large number of separate bodies. Int. J. Numer. Meth. Engng. 2000, 49(11): 1377-1396
[122] Munjiza A. The combined finite-discrete element method. West Sussex: John Wiley & Sons, 2004
[123] Owen D R J, Feng Y T, Parallelised finite/discrete element simulation of multi-fracturing solids and discrete systems. Engineering Computations. 2001, 18(3-4): 557-576
[124] 徐秉业,刘信声. 应用弹塑性力学. 北京:中国建筑工业出版社,1998
[125] 过镇海,钢筋混凝土原理. 北京:清华大学出版社,1999
[126] 江见鲸. 混凝土结构工程学. 北京:中国建筑工业出版社,1998
[127] 金日光. 流变学进展. 北京:化学工业出版社,1996
[128] 黄克智,黄永刚. 固体本构关系. 北京:清华大学出版社,1999
[129] 余天庆,钱济成. 损伤理论及其应用. 北京:国防工业出版社,1993
[130] de Borst R. Fracture in quasi-brittle materials: a review of continuum damage-based approaches. Engineering Fracture Mechanics, 2002, 69(2): 95-112
[131] Lee J, Fenves G L. A plastic-damage concrete model for earthquake analysis of dams. Earthquake Engineering and Structural Dynamics. 1998, 27(9): 937-956
[132] Bazant Z P, Oh B H. Microplane model for fracture analysis of concrete structures. Symp. On Interaction of Non-Nuclear Munitions with Struct. Colorado Springs, US Air Force Academy, 1983, 49-53
[133] 张斌. 微平面模型研究与工程应用:[硕士学位论文]. 北京:清华大学,2005
[134] Ozbolt J, Reinhardt H W. Numerical study of mixed-mode fracture in concrete. International Journal of Fracture, 2002, 118(2): 145-161
[135] 丁遂栋,孙利民. 断裂力学. 北京:机械工业出版社,1997
[136] 唐春安,朱万成. 混凝土损伤与断裂—数值试验. 北京:科学出版社,2003
[137] Kaplan M F. Crack propagation and the fracture of concrete. American Concrete Institute Journal, 1961, 58: 591-610
[138] 潘家铮. 断裂力学在水工结构设计中的应用. 水利学报,1980,1:45-59
[139] Cotterell B, Mai Y W, Fracture mechanics of cementitious materials. New York: Blackie Academic & Professional, 1996
[140] 吴智敏,赵国藩. 混凝土断裂韧度的尺寸效应研究. 工业建筑,1995,25(4):20-22
[141] Pekau O A, Feng Lingmin, Zhang Chuhan. Seismic fracture of Koyna dam: case study. Earthquake Engineering and Structural Dynamics, 1995, 24(1): 15-33
[142] Feng Lingmin, Pekau O A, Zhang Chuhan. Cracking analysis of arch dams by 3-D boundary element method. Journal of Structural Engineering, 1996, 122(6): 691-699
[143] 黄云,金峰,王光纶,张楚汉. 高拱坝上游坝踵裂缝稳定性及其扩展. 清华大学学报(自然科学版),2002,42(4):555-559
[144] Jenq Y S, Shah S P. Two parameter fracture model for concrete. Journal of Engineering Mechanics, 1985, 111(10): 1227-1241
[145] 徐世烺,赵国藩. 混凝土结构裂缝扩展的双 K 断裂准则. 土木工程学报,1992,25(2):32-38
[146] Ngo D, Scordelis A C. Finite element analysis reinforced concrete beams. Journal of the American Concrete Institute, 1967, 67: 152-163
[147] Rashid Y R, Analysis of prestressed concrete pressure vessels. Nuclear Engineering and Design, 1968, 7: 334-344
[148] Berenblatthe G I. The formation of equilibrium cracks during brittle fracture. General ideas and hypothesis. Axially-symmetric cracks. Prikl. Matem. I mekham 1959, 23, 434-444
[149] Dugdale D S. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 1960, 8: 100-104
[150] Hillerborg A, Modeer M, Petersson P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 1976, 6(6): 773-782
[151] Needleman A. A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics, 1987, 54(3): 525-531
[152] Carpinteri A, Valents S V, Ferrara G, et al. Experimental and numerical fracture modeling of a gravity dam. Fracture Mechanics of Concrete Structures, Bazant Z P ed., Elsevier Applied Science, 1992, 351-360
[153] Feltrin G, Wepf D, Bachmann H. Seismic cracking of concrete gravity dams. Dam Engineering, 1990, 4(1): 279-289
[154] Jirasek M, Zimmermann T. Embedded crack model: Ⅰ Basic formulation. Int. J. Numer. Meth. Engng 2001, 50(6): 1269-1290
[155] de Borst R, Nauta P. Non-orthogonal cracks in smeared finite element model. Engrg. Comput., 1985, 2(1): 35-46
[156] Cope R J, Rao P V, Clark L A, Norris P. Modeling of reinforced concrete behavior for finite element analysis of bridge slabs. In: Taylor C, Hinton E, Owen D R J, editors. Numerical Methods for Nonlinear Problems. Swansea: Pineridge Press, 1980, 457-470
[157] Bazant Z P, Oh B H. Crack band theory for fracture of concrete. Material and Constructions, 1983, 16(93): 155-177
[158] Wang Guanglun, Pekau O A, Zhang Chuhan, Wang Shaomin. Seisimc fracture analysis of concrete gravity dams based on nonlinear fracture mechanics. Engineering Fracture Mechanics, 2000, 65(1): 67-87
[159] Vahid Lotfi, Radin Espandar. Seismic analysis of concrete arch dams by combined discrete crack and non-orthogonal smeared crack technique. Engineering Structures, 2004, 26(1): 27-37
[160] Mirzabozorg H, Ghaeniam M. Non-linear behavior of mass concrete in three-dimensional problems using a smeared crack approach. Earthquake Engng Struct. Dyn., 2005, 34(3): 247-269
[161] Bazant Z P, Planas J. Fracture and size effect in concrete and other quasibrittle materials. Boca Raton: CRC Press, 1998.
[162] 赵吉东. 岩土工程稳定破坏的应变梯度损伤局部化分岔模型及应用:[博士学位论文]. 北京:清华大学,2002
[163] Camacho G T, Ortiz M. Computational modeling of impact damage in brittle materials. International journal of Solids and Structures, 1996, 33(20-22): 2899-2938
[164] Espinosa H D, Zavattieri P D, Dwivedi S K. A finite deformation continuum/discrete model for the description of fragmentation and damage in brittle materials. J. Mech. Phys. Solids., 1998, 46(10): 1909-1942
[165] Prochazka P P. Application of discrete element methods to fracture mechanics of rock bursts. Engineering Fracture Mechanics, 2004, 71(4-6): 601-618
[166] Sebastien Hentz, Frederic V D, Laurent Daudeville. Discrete element modeling of concrete submitted to dynamic loading at high strain rates. Computers and Structures, 2004, 82(29-30): 2509-2524
[167] Munjiza A, Owen D R J, Bicanic N. A combined finite-discrete element method in transient dynamics of fracturing solids. Engineering Computations, 1995, 12(2): 145-174
[168] Munjiza A, John N W M. Mesh size sensitivity of the combined FEM/DEM fracture and fragmentation algorithms. Engineering Fracture Mechanics, 2002, 69(2): 281-295
[169] Klerck P A, Sellers E J, Owen D R J. Discrete fracture in quasi-brittle materials under compressive and tensile stress states. Comput. Methods. Appl. Mech. Engng. 2004, 193(27-29): 3035-3056
[170] 徐艳杰. 横缝配筋的拱坝地震非线性模型与无限地基影响研究:[博士学位论文]. 北京:清华大学,1999
[171] Munjiza A, Andrews K R F. NBS contact detection algorithm for bodies of similar size. Int. J. Numer. Meth. Engng., 1998, 43(1): 131-149
[172] Feng Y T, Owen D R J. An augmented spatial digital tree algorithm for contact detection in computational mechanics. Int. J. Numer. Meth. Engng., 2002, 55(2): 159-176
[173] Perkins E, Williams J R. A fast contact detection algorithm insensitive to object sizes. Engineering Computations, 2001, 18(1-2): 48-61
[174] Williams J R, O’Connor R. A linear complexity intersection algorithm for discrete element simulation of arbitrary geometries. Engineering Computations, 1995, 12(2): 185-201
[175] Liu X L, Lemos J V. Procedure for contact detection in discrete element analysis. Advances in engineering software, 2001, 32(5): 409-415
[176] Feng Y T, Owen D R J. An energy based corner to corner contact algorithm. 3rd Int. Conf. on discrete element method, Santa Fe, New Mexico, USA, 2002, 23-25
[177] Kremmer M, Favier J F. A method for representing boundaries in discrete element modeling-part Ⅰ: Geometry and contact detection. Int. J. Numer. Meth. Engng, 2001, 51(12): 1407-1421
[178] 王泳嘉,邢纪波. 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
[179] Amadei B, Goodman R E. A 3-D constitutive relation for fractured rock masses. Proc. Int. Symp. on the Mechanical Behavior of Structured Media, Ottawa, Canada, 1981, 249-268
[180] Fossum A F. Effective elastic properties for a randomly jointed rock mass. Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr,. 1985, 22(6): 467-470
[181] Kibok Min, Lanru Jing. Numerical determination of the equivalent elastic compliance tensor for fractured rock massed using the distinct element method. International Journal of Rock Mechanics & Mining Sciences, 2003, 40(6): 795-816
[182] Ting T C T. Anisotropic elasticity : theory and applications, Oxford: Oxford University Press, 1996
[183] 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
[184] Cundall P A. Adaptive density-scaling for time-explicit calculations. Proceedings of the Fourth International Conference on Numerical Methods in Geomechanics, Edmonton, 1982, 23-26
[185] 杜成斌,邱颖. 梅花周边缝拱坝的破坏形式分析. 水力发电,2002,5:61-63
[186] 崔玉柱,张楚汉,徐艳杰,金峰,王光纶. 用刚体弹簧元研究梅花拱坝的破坏机理. 清华大学学报,2002,42:88-92
[187] Suidan M, Schnobrich W C. Finite element analysis of reinforced concrete. ASCE J Struct Div, 1973, 99: 2109-2122
[188] Kolmar W, Mehlhorn G. Comparison of shear stiffness formulations for cracked reinforced concrete elements. In: Damjanic F, eds. Proceeding of International Conference on Computer Aided Analysis and Design of Concrete Structures, Part 1, Swansea: Pineridge Press, 1984, 133-147
[189] Bazant Z P. Instability, ductility and size effect in strain softening concrete. ASCE J Engng Mech, 1976, 102(2): 331-344
[190] Rots J G, Kusters G M A, Blaauwendraad J. The need for fracture mechanics options in finite element models for concrete structures. In: Damjanic F, eds. Proceeding of International Conference on Computer Aided Analysis and Design of Concrete Structures, Swansea: Pineridge Press, 1984, 19-32
[191] Rots J G. Smeared crack approach. In: Elfgren L, eds. Fracture Mechanics of Concrete Structures, London: Chapman and Hall, 1989, 138-146
[192] Rots J G. de Borst R. Analysis of mixed mode fracture in concrete. Journal of Engineering Mechanics, 1987, 113(11): 1739-1758
[193] de Borst R, Nauta P. Smeared crack analysis of reinforced concrete beams and slabs failing in shear. In: Damjanic F, eds. Proceeding of International Conference on Computer Aided Analysis and Design of Concrete Structures, Swansea: Pineridge Press, 1984, 261-273
[194] Feenstra P H, de Borst R. A plasticity model and algorithm for mode-Ⅰ cracking in concrete. International Journal Numerical Methods in Engineering, 1995, 38(15): 2509-2529
[195] de Borst R. Smeared cracking, plasticity, creep, and thermal loading- a unified approach. Computer Methods in Applied Mechanics and Engineering, 1987, 62(1): 89-110
[196] Willam K, Pramono E, Sture S. Fundamental issues of smeared crack models, SEM-RILEM International. Conference On Fracture of Concrete and Rock. Houston, Texas, Shah S P and Swartz S E, 1987, 192-207
[197] Milford R V, Schnobrich W C. Numerical model for cracked reinforced concrete. In: Damjanic F, eds. Proceeding of International Conference on Computer Aided Analysis and Design of Concrete Structures, Swansea: Pineridge Press, 1984, 71-84
[198] Jirasek M, Zimmermann T. Rotating crack model with transition to scalar damage. Engineering Mechanics, ASCE, 1998, 124(3): 277-284
[199] Petersson P E. Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials. TVBM-1006, Division of Building Materials, Lund Institute of Technology, 1981
[200] Arrea M, Ingraffea A R. Mixed-mode crack propagation in mortar and concrete. Report 81-13. Department of Structural Engineering, Cornell University, 1982
[201] Galvez J C, Elices M, Guinea G V, Planas J. Mixed mode fracture of concrete under proportional and nonproportional loading. International Journal of Fracture, 1998, 94(3): 267-284
[202] Nooru-Mohamed M B. Mixed mode fracture of concrete: an experimental approach, PhD thesis, Delft University of Technology, 1992
[203] Pivonka P, Ozbolt J, Lackner R, Mang H A. Comparative studies of 3D-constitutive models for concrete: application to mixed-mode fracture. International Journal for Numerical Methods in Engineering, 2004, 60(2): 549-570
[204] Cendon D A, Galvez J C, Elice M, Planas J. Modelling the fracture of concrete under mixed loading. International Jjournal of Fracture, 2000, 103(3): 293-310
[205] Prasad M V K V, Krishnamoorthy C S. Computational model for discrete crack growth in plain and reinforced concrete. Comput. Methods Appl. Mech. Engrg, 2002, 191(25-26): 2699-2725
[206] Galvez J C, Cervenka J, Cendon D A, Saouma V. A discrete crack approach to normal/shear cracking of concrete. Cement and concrete research. 2002, 32(10): 1567-1585
[207] Tin-Loi F, H. Li. Numerical simulations of quasibrittle fracture processes using the discrete cohesive crack model. International Journal of Mechanical Sciences, 2000, 42(2): 367-379
[208] Xu XP, Needleman A. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids, 1994, 42(9): 1397-1434
[209] Murphy N, Ivankovic A. The prediction of dynamic fracture evolution in PMMA using a cohesive zone model. Engineering Fracture Mechanics, 2005, 72: 861-875
[210] Elices M, Guinea G V, Gomez J, Planas J. The cohesive zone model: advantages, limitations and challenges. Engineering Fracture Mechanics, 2002, 69(2): 137-163
[211] Needleman A, An analysis of decohesion along an imperfect interface. International Journal of Fracture. 1990, 42: 21-40
[212] Xu X P, Needleman A. Void nucleation by inclusion debonding in a crystal matrix. Modelling and Simulation in Materials Science and Engineering, 1993, 1(2): 111-132
[213] Carol I, Pere C P, Carlos M L. Normal/shear cracking model: application to discrete crack analysis. Journal of Engineering Mechanics, 1997, 23(8): 765-773
[214] Galvez J C, Cendon D A, Planas J. Influence of shear parameters on mixed-mode fracture of concrete, International Journal of Fracture, 2002, 118(2): 163-189
[215] Margolin L D. A generalized Griffith criterion for crack propagation. Engng Fract. Mech. 1984, 19(3): 539-545
[216] Wells G N, Sluys L J. A new method for modeling cohesive cracks using finite elements. Int. J. Numer. Meth. Engng, 2001, 50(12): 2667-2682
[217] Sujan Malla, Martin Wieland. Simple model for safety assessment of cracked concrete dams subjected to strong ground shaking. Commission International Des Grands Barrages 2003, 151-168
[218] Chorpa A K, Chakrabarti P. The earthquake experience at Koyna Dam and stress in concrete gravity dams. Earthquake Engineering and Structural Dynamics, 1972, 1: 151-164
[219] Hall F J, The dynamic and earthquake behavior of concrete dams: review of experimental behavior and observational evidence. Soil. Dyn. Earthquake Eng., 1988, 7(2): 58-121
[220] Skrikerud P E, Bachmann H. Discrete crack modeling for dynamically loaded, unreinforced concrete structures. Earthquake Engineering and Structural Dynamics, 1986, 14(2): 297-315
[221] Ayari L M, Saouma V E. A fracture mechanics based seismic analysis of concrete gravity dams using discrete cracks. Engineering Fracture Mechanics, 1990, 35(1-3): 587-598
[222] Bhattacharjee S S, Leger P. Seismic cracking and energy dissipation in concrete gravity dams. Earthquake Engineering and Structural Dynamics, 1993, 22(11): 991-1007
[223] Yusuf Calayir, Muhammet Karaton. Seismic fracture analysis of concrete gravity dams including dam-reservoir interaction. Computer and Structures, 2005, 83(19-20): 1595-1606
[2] 李瓒,陈兴华,郑建波,王光纶. 混凝土拱坝设计. 北京:中国电力出版社,2000
[3] 汝乃华,姜胜忠. 大坝事故与安全?拱坝. 北京:中国水利水电出版社,1995
[4] Osterreichische Draukraftwerke A G. Remedial Project of Kolnbrein Arch Dam Design and Construction. Klagenfurt: Carinthia, 1991
[5] Chopra A K, Chakrabarti P. The Koyna earthquake and the damage to Koyna dam. Bull. Seism. Soc. Am, 1973, 63(2): 381-397
[6] Londe P. The Malpasset Dam Failure. Proc. Int. Workshop on Dam Failure, Elsevier, 1987, 295-325
[7] Hansen K P, Roehm L H. The response of concrete dams to earthquake. Water Power and Dam Construction, 1979, 31(4): 27-31
[8] 张光斗,王光纶. 水工建筑物(上册). 北京:水利电力出版社,1992
[9] 吴媚玲. 水工建筑物. 北京:清华大学出版社,1991
[10] Forsythe G E, Wasow W R. 偏微分方程的有限差分方法(胡祖熾，吴文达，陈永和译）. 上海:上海科学技术出版社,1964
[11] 王磊,李家宝. 结构分析的有限差分法. 北京:人民交通出版社,1982
[12] Alterman Z S, Karal F C. Propagation of elastic waves in layered media by finite difference methods. Bull. Seism. Soc. Am. 1968, 58(1): 367-398
[13] Boore D M. Finite difference methods for seismic wave propagation in heterogeneous materials. In: Bolt B A, eds. Methods in Computational Physics. Academic Press, New York, 1972, 11
[14] Aki K, Larner K L. Surface motion of a layered medium having an irregular interface due to incident plane SH-waver. J. Geophysics Res, 1970, 75(5): 933-954
[15] Joyner W B. A method for calculating nonlinear seismic response in two dimensions. Bull. Seis. Soc. Am. 1975, 65: 1337-1357
[16] FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions), Version 2.1, User’s manual, Itasca Consulting Group, Inc. USA
[17] 李仲奎,梁海波. FLAC 程序基本原理及使用方法指南. 北京:清华大学水利水电工程系,1993
[18] 寇晓东,周维垣,杨若琼. FLAC-3D 进行三峡船闸高边坡稳定分析. 岩石力学与工程学报,2001,20(1):6-10
[19] 杨为民,陈卫忠,李术才,杨典森,李飞. 快速拉格朗日法分析巨型地下洞室群稳定性. 岩土工程学报,2005,27(2):230-234
[20] 张练,丁秀丽,付敬. 清江水布垭地下厂房围岩稳定三维数值分析. 岩土力学,2003,24(增 1):120-123
[21] 寇晓东,周维垣,杨若琼. 三维快速拉格朗日法进行小湾拱坝稳定分析. 水利学报,2000,9:8-14
[22] Zienkiewicz O C, Taylor R L. The finite element method. Boston: Butterworth-Heinemann, 2000
[23] 王勖成,劭敏. 有限单元法基本原理和数值方法. 北京:清华大学出版社,1997
[24] Goodman R E, Taylor R L, Brekke T L. A model for the mechanics of jointed rock. Journal of the Soil Mechanics and Foundations Division, ASCE, 1968, 94(SM3): 637-659
[25] Desai C S, Lightner J G, Siriwardane H J, et al. Thin-layer element for interfaces and joints. International Journal for Numerical Methods in Geomechanics, 1984, 8(1): 19-43
[26] Beer G. Application of numerical modeling to the analysis of excavation in jointed rock. In: Rossmanith H P, eds. Mechanics of jointed and faulted rock. Rotterdam: Balkema, 1990
[27] 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
[28] 陈厚群,李德玉,胡晓,侯顺载. 有横缝拱坝的非线性动力模型试验和计算分析研究.地震工程与工程振动,1995,15(4):10-26
[29] 陈健云,林皋. 小湾拱坝考虑横缝的非线性分析. 土木工程学报,1999,32(1):66-70
[30] 徐艳杰,张楚汉,王光纶,金峰. 小湾拱坝模拟实际横缝间距的非线性地震反应分析.水利学报,2001,4:68-74
[31] 张伯艳,陈厚群,涂劲. 基于动接触力法的拱坝坝肩抗震稳定有限元分析. 水利学报,2004,10:7-12
[32] 尹显俊. 岩体结构面循环加载本构模型研究及工程应用:[博士学位论文] . 北京:清华大学,2004
[33] 周元德. 混凝土非线性断裂力学模型与高拱坝开裂分析研究:[博士学位论文]. 北京:清华大学,2004
[34] 廖振鹏. 工程波动理论导论. 北京:科学出版社,2002
[35] Rizzo F J. An integral equation approach to boundary value problem of classical elastostatics. Q. Appl. Math., 1967, 25(1): 83-95
[36] Cruse T A, Rizzo F J. A direct formulation and numerical solution of the general transient elasto-dynamic problems. I. J. Math. Anal. Appl. 1968, 22: 244-295
[37] Gao X W, Davies T G. Boundary element programming in mechanics. Cambridge: Cambridge University Press, 2002
[38] Niwa Y, Kobayashi S, Azuma N. An analysis of transient stresses produced around cavities of arbitrary shape during the passage of traveling waves. Memoirs of Fac. Eng. Kyoto University, 1975, 37: 28-46
[39] Kobayashi S, Nishimura N. Dynamic analysis of underground structures by the integral equation method. Num. Meth. Goemechanics, Edmonton, Alberta, Can: Balkema A A, Rotterdam Ne, 1982. 401-409
[40] Manolis G D. A comparative study on three boundary element method approaches to problems in elastodynamics. Int. J. Numer. Meth. Eng., 1983, 19(1): 73-91
[41] Rice J M, Sadd M H. Propagation and scattering of SH waves in semi-infinite domains using a time-dependent boundary element method. J. Applied Mech., 1984, 51(3): 641-645
[42] Spyrakos C C, Beskos D E. Dynamic response of flexible strip foundations by boundary and finite element methods. Soil Dynamics and Earthquake Engineering, 1986, 5(2): 84-96
[43] Touhei T, Ohmachi T. FE-BE method for dynamic analysis of dam-foundation-reservoir systems in the time domain. Earthquake Engineering & Structural Dynamics, 1993, 22(3): 195-209
[44] Chuhan Zhang, Feng Jin, Pekau, O A. Time domain procedure of FE-BE-IBE coupling for seismic interaction of arch dams and canyons. Earthquake Engineering & Structural Dynamics, 1995, 24(12): 1651-1666
[45] 金峰. 结构-地基动力相互作用的 FE-BE-IBE 耦合模型及拱坝地震反应分析:[博士学位论文]. 北京:清华大学,1992
[46] 吴健,金峰,徐艳杰. 考虑辐射阻尼的拱坝随机振动分析. 水利学报,2005,36(1): 110-115
[47] Bettess P. Infinite element. International Journal for Numerical Methods in Engineering, 1977, 11(1): 53-64
[48] Bettess P, Zienkiewicz O C. Diffraction and reflection of surface waves using finite and infinite elements. International Journal for Numerical Methods in Engineering, 1977, 11(8): 1271-1290
[49] 葛修润,谷先荣,丰定祥. 三维无界元和节理无界元. 岩土工程学报,1986,8(5):9-20
[50] 赵崇斌,张楚汉,张光斗. 映射动力无穷元及其特性研究. 地震工程与工程振动,1987,7(3):1-15
[51] Zhang Chuhan, Zhao Chongbin. Coupling method of finite and infinite elements for strip foundation wave problems. Earthquake Engineering & Structural Dynamics, 1987, 15(7): 839-851
[52] Zhang Chuhan, Zhao Chongbin. Effect of canyon topography and geological conditions on strong ground motion. Earthquake Engineering & Structural Dynamics, 1988, 16(1): 81-97
[53] 燕柳斌,李国华,夏小舟. 地基基础-坝体体系动力特性及地震反应分析的有限元与无限元耦合法. 广西大学学报(自然科学版),2003,28(3):249-258
[54] 刘国华,刘西军. 无限单元法在坝体温度场分析中的尝试. 浙江大学学报(工学版), 2004,38(8):1009-1014
[55] Kim D K, Yun C B. Time-domain soil-structure interaction analysis in two-dimensional medium based on analytical frequency-dependent infinite elements. International Journal for Numerical Methods in Engineering, 2000, 47(7): 1241-1261
[56] Yerli H R, Temel B, Kiral E. Transient infinite elements for 2D soil-structure interaction analysis. Journal of Geotechnical and Geoenvironmental Engineering, 1998, 124(10): 976-988
[57] Nayroles B, Touzot G, Villon P. Generalizing the finite element method: Diffuse approximation and diffuse elements. Computational Mechanics, 1992, 10(5): 307-318
[58] Belytschko T. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229-256.
[59] 介玉新,高波,李广信. 无单元法在混凝土面板堆石坝应力分析中的应用. 清华大学学报(自然科学版),2003,43(8):1092-1095
[60] 周维垣,黄岩松,林鹏. 三维无单元伽辽金法及其在拱坝分析中的应用. 水利学报, 2005,36(6):644-649
[61] 寇晓东,杨若琼,沈大利,周维垣. 无单元法在小湾拱坝开裂计算中的应用. 云南水力发电,2000,16(1):71-76
[62] 张伯艳,陈厚群,杜修力,张艳红. 拱坝坝肩抗震稳定分析. 水利学报,2000,11:55-59
[63] 李瓒,龙云霄. 重力坝、拱坝基础岩体抗滑稳定分析中的一些问题的探讨. 水利学报, 2000,8:40-45
[64] 王瑞骏. 重力坝深层抗滑稳定性的空间刚体极限平衡分析. 西北水资源与水工程,1996,7(4):1-5
[65] 陈仲颐,周景星,王洪瑾. 土力学. 北京:清华大学出版社,1994
[66] Sarma K S. Stability analysis of embankments and slopes. J. Geotech. Am. Soc. Civ. Engrs, 1979, 105(12): 1511-1524
[67] 潘家铮. 建筑物抗滑稳定分析和滑坡分析. 北京:水利出版社,1980
[68] 陈祖煜. 建筑物抗滑稳定分析中“潘家铮最大最小原理”的证明. 清华大学学报,1998,1:6-13
[69] Donald I B, Chen Z Y. Slope stability analysis by the upper bound approach: fundamentals and methods. Canadian Geotechnical Journal, 1997, 34(6): 853-862
[70] 弥宏亮. 边坡稳定三维极限分析——方法?推广?应用:[博士学位论文]. 北京:清华大学,2003
[71] Kawai Tadahiko, Toi Yutaka. New element models in discrete structural analysis. Welding Journa(Miami, Fla), Soc of Nav Archit of Jpn, 1978, 16: 97-110
[72] 张建海,范景伟,胡定. 刚体弹簧元理论及应用. 成都:成都科技大学出版社,1997
[73] 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
[74] 卓家寿,邵国建,陈振雷. 工程稳定问题中确定滑坍面、滑向与安全度的干扰能量法.水利学报,1997,8:80-84
[75] Cundall P A. A computer model for simulating progressive large-scale movements in block rock systems, Proc. Symp. Int. Soci. Rock Mech., Nancy France, 1971
[76] Genhua Shi, Goodman R E. Two dimensional discontinuous deformation analysis. International Journal for Numerical and Analysis Methods in Geomechanics. 1985, 9(6): 541-556
[77] Genhua Shi, Goodman R E. Generalization of two-dimensional discontinuous deformation analysis for forward modeling. International Journal for Numerical and Analysis Methods in Geomechanics. 1989, 13(4): 359-380
[78] Lanru Jing. Formulation of discontinuous deformation analysis(DDA)- an implicit discrete element model for block systems. Engineering Geology, 1998, 49(3-4): 371-381
[79] 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,2004,23(1):10-14
[80] 张国新,武晓峰. 裂隙渗流对岩石边坡稳定的影响—渗流、变形耦合作用的 DDA 法.岩石力学与工程学报,2003,22(8):1269-1275
[81] 蔡永恩,罗纲,刘今朝,李青松,张伯艳,陈厚群. 不连续岩体-拱坝系统的动力过程数值模拟方法. 岩土力学,2004,25(Supp2):361-365
[82] 石根华. 数值流行方法与非连续变形分析. 裴觉民译. 北京:清华大学出版社,1997
[83] 张国新,王光纶,裴觉民. 基于流行方法的结构体破坏分析. 岩石力学与工程学报,2001,20(3):281-287
[84] 张国新,金峰,王光纶. 用基于流行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
[85] Tsuyoshi Ishida. Application of distinct element analysis to three simple block models aimed at practical application to toppling failure of fissured rock slopes. Computers and Geotechnics, 1990, 9(4): 341-353
[86] Bardet J P, Soctt R F. Seismic stability of fractured rock masses with the distinct element method. 26th US Symposium on Rock Mechanics, Rapid City, SD: Balkema A A, Rotterdam Neth, 1985. 26-28
[87] Ghaboussi J. Fully deformable discrete element analysis using a finite element approach. Computers and Geotechnics, 1988, 5(3): 175-195
[88] Williams J R, Jiocking G, Mustoe G G W. The theoretical basis of the discrete element method. Proceedings of the NUMETA’85 Conference, Swansea: Balkema A A, Rotterdam Neth, 1985. 897-906
[89] Williams J R, Mustoe G G W. Modal methods for the analysis of discrete system. Computers and Geotechnics, 1987, 4: 1-19
[90] Cundall P A, Hart R D. Numerical modeling of discontinua. Engineering Computations, 1992, 9(2): 101-113
[91] Cundall P A. UDEC-A generalized distinct element program for modeling jointed rock. Peter Associates, European Research Office, U. S. Army, 1980
[92] Iofis I M, Maksimov A V, Mironov V V. Some practical aspects of numerical simulation of jointed rock mass by distinct element method. Proceedings of the International Conference on Mechanics of Jointed and Faulted Rock, 1990, 479-486
[93] Zhang Chuhan, Pekau O A, Jin Feng, Wang Guanglun. Application of distinct element method in dynamic analysis of high rock slopes and blocky structures. Soil Dynamics and Earthquake Engineering, 1997, 16(6): 385-394
[94] Lemos J V, Lorig L J. Hydromechanical modeling of jointed rock masses using the distinct element method. Proceedings of the International Conference on Mechanics of Jointed and Faulted Rock, 1990, 605-612
[95] 王洪涛. 裂隙网络渗流与离散元耦合分析充水岩质高边坡的稳定性. 水文地质工程地质,2000,2:30-33
[96] 周庆科,金峰,王恩志,徐艳杰. 离散单元法的饱和/非饱和渗流模型及其试验验证. 水力发电学报,2003,3:34-39
[97] 王刚. 离散元流变模型及其在三峡工程中的应用:[硕士学位论文] . 北京:清华大学, 2000
[98] Cundall P A, Hart R D. Development of generalized 2-D and 3-D distinct element programs for modelling jointed rock. ITASCA Consulting Group, Misc Paper SL-85-1, U. S. Army Corps of Engineers, 1985
[99] Cundall P A. Formulation of three-dimensional distinct element model, Part Ⅰ, A scheme to detect and represent contacts in system composed of many polyhedral blocks. Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr., 1988, 25(3): 107-116
[100] Hart R, Cundall P A, Lemos J. Formulation of three-dimensional distinct element model, Part Ⅱ,Mechanical calculation of a system composed of many polyhedral blocks. Int. J. Rock. Mech. Min. Sci.. & Geomech. Abstr., 1988, 25(3): 117-125
[101] Ghaboussi J, Barbosa R. Three-demensional discrete element method for granular materials. Int. J. Num. Analy. Methods Geomech., 1990, 14(7): 451-472
[102] Kremmer M,Favier J F. Calculating rotational motion in discrete element modeling of arbitrary shaped model objects. Engineering Computations, 2000, 17(6): 703-714
[103] Munjiza A, Latham J P, John N W M. 3D dynamics of discrete element systems comprising irregular discrete elements—integration solution for finite rotations in 3D. Int. J. Numer. Meth. Engng, 2003, 56(1): 35-55
[104] 鲁军. 离散单元法的数值模型研究及其工程应用:[博士学位论文] . 北京:清华大学, 1996
[105] 崔玉柱. 连续与非连续介质的数值模拟与拱坝-地基系统安全分析:[博士学位论文]. 北京:清华大学,2001
[106] Zhang Chuhan. Challenges of High Dam Construction to Computational Mechanics. 6th World Congress on Computational Mechanics in conjunction with Second Asian-Pacific Congress on Computational Mechanics. Beijing, China, 2004
[107] 王泳嘉,刘连峰. 三维离散单元法及其在边坡工程中的应用. 中国矿业,1996,5(1): 34-39
[108] 焦玉勇,葛修润,谷先荣. 三维离散元法中地下水及锚杆的模拟. 岩石力学与工程学报,1999,18(1):6-11
[109] 3DEC, 3 Dimensional distinct element code, Version 3.0, User’s manual, ITASCA Consulting Group, Inc. USA
[110] Psycharis I N, Lemos J V, Papastamatiou D Y, Zambas C, Papantonopoulos C. Numerical study of the seismic behaviour of a part of the Parthenon Pronaos. Earthquake Engineering and Structural Dynamics, 2003, 32(13): 2063-2084
[111] Papantonopoulos C, Psycharis I N, Papastamatiou D Y, Lemos J V, Mouzakis H P. Numerical prediction of the earthquake response of classical columns using the distinct element method. Earthquake Engineering and Structural Dynamics, 2002, 31(9): 1699-1717.
[112] 王涛,盛谦,陈晓玲. 基于直接法节理网络模拟的三维离散单元法计算. 岩石力学与工程学报,2005,24(10):1649-1653
[113] Lorig L J, Brady B H G, Cundall P A. Hybrid distinct element-boundary element analysis of jointed rock. Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr., 1986, 23, 303-312
[114] 金峰,贾伟伟,王光纶. 离散元-边界元动力耦合模型. 水利学报,2001,1:23-27
[115] 金峰,王光纶,贾伟伟. 离散元-边界元动力耦合模型在地下结构动力分析中的应用. 水利学报,2001,2:24-28
[116] Dowding C H, Belyschko T B, Yen H J. A coupled finite element-rigid block method for transient analysis of rock caverns. Int. J. Num. Analy. Methods Geomech, 1983, 7(1): 117-127
[117] Pan X D, Reed M B. A coupled distinct element-finite element method for large deformation analysis of rock masses. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1991, 28(1): 93-99
[118] Han K, Peric D, Crook A J L, Owen D R J. A combined finite/discrete element simulation of shot peening processes Part Ⅰ : Studies on 2D interaction laws. Engineering Computations, 2000, 17(5): 593-619
[119] Han K, Peric D, Owen D R J, Yu J. A combined finite/discrete element simulation of shot peening processes Part Ⅱ: 3D interaction laws. Engineering Computations, 2000, 17(6): 680-702
[120] Onate E, Rojek J. Combination of discrete element and finite element methods for dynamics analysis of geomechanics problems. Comput. Methods Appl. Mech. Engrg., 2004, 193(27-29): 3087-3128
[121] Munjiza A, Andrews K R F. Penalty function method for combined finite-discrete element systems comprising large number of separate bodies. Int. J. Numer. Meth. Engng. 2000, 49(11): 1377-1396
[122] Munjiza A. The combined finite-discrete element method. West Sussex: John Wiley & Sons, 2004
[123] Owen D R J, Feng Y T, Parallelised finite/discrete element simulation of multi-fracturing solids and discrete systems. Engineering Computations. 2001, 18(3-4): 557-576
[124] 徐秉业,刘信声. 应用弹塑性力学. 北京:中国建筑工业出版社,1998
[125] 过镇海,钢筋混凝土原理. 北京:清华大学出版社,1999
[126] 江见鲸. 混凝土结构工程学. 北京:中国建筑工业出版社,1998
[127] 金日光. 流变学进展. 北京:化学工业出版社,1996
[128] 黄克智,黄永刚. 固体本构关系. 北京:清华大学出版社,1999
[129] 余天庆,钱济成. 损伤理论及其应用. 北京:国防工业出版社,1993
[130] de Borst R. Fracture in quasi-brittle materials: a review of continuum damage-based approaches. Engineering Fracture Mechanics, 2002, 69(2): 95-112
[131] Lee J, Fenves G L. A plastic-damage concrete model for earthquake analysis of dams. Earthquake Engineering and Structural Dynamics. 1998, 27(9): 937-956
[132] Bazant Z P, Oh B H. Microplane model for fracture analysis of concrete structures. Symp. On Interaction of Non-Nuclear Munitions with Struct. Colorado Springs, US Air Force Academy, 1983, 49-53
[133] 张斌. 微平面模型研究与工程应用:[硕士学位论文]. 北京:清华大学,2005
[134] Ozbolt J, Reinhardt H W. Numerical study of mixed-mode fracture in concrete. International Journal of Fracture, 2002, 118(2): 145-161
[135] 丁遂栋,孙利民. 断裂力学. 北京:机械工业出版社,1997
[136] 唐春安,朱万成. 混凝土损伤与断裂—数值试验. 北京:科学出版社,2003
[137] Kaplan M F. Crack propagation and the fracture of concrete. American Concrete Institute Journal, 1961, 58: 591-610
[138] 潘家铮. 断裂力学在水工结构设计中的应用. 水利学报,1980,1:45-59
[139] Cotterell B, Mai Y W, Fracture mechanics of cementitious materials. New York: Blackie Academic & Professional, 1996
[140] 吴智敏,赵国藩. 混凝土断裂韧度的尺寸效应研究. 工业建筑,1995,25(4):20-22
[141] Pekau O A, Feng Lingmin, Zhang Chuhan. Seismic fracture of Koyna dam: case study. Earthquake Engineering and Structural Dynamics, 1995, 24(1): 15-33
[142] Feng Lingmin, Pekau O A, Zhang Chuhan. Cracking analysis of arch dams by 3-D boundary element method. Journal of Structural Engineering, 1996, 122(6): 691-699
[143] 黄云,金峰,王光纶,张楚汉. 高拱坝上游坝踵裂缝稳定性及其扩展. 清华大学学报(自然科学版),2002,42(4):555-559
[144] Jenq Y S, Shah S P. Two parameter fracture model for concrete. Journal of Engineering Mechanics, 1985, 111(10): 1227-1241
[145] 徐世烺,赵国藩. 混凝土结构裂缝扩展的双 K 断裂准则. 土木工程学报,1992,25(2):32-38
[146] Ngo D, Scordelis A C. Finite element analysis reinforced concrete beams. Journal of the American Concrete Institute, 1967, 67: 152-163
[147] Rashid Y R, Analysis of prestressed concrete pressure vessels. Nuclear Engineering and Design, 1968, 7: 334-344
[148] Berenblatthe G I. The formation of equilibrium cracks during brittle fracture. General ideas and hypothesis. Axially-symmetric cracks. Prikl. Matem. I mekham 1959, 23, 434-444
[149] Dugdale D S. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 1960, 8: 100-104
[150] Hillerborg A, Modeer M, Petersson P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 1976, 6(6): 773-782
[151] Needleman A. A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics, 1987, 54(3): 525-531
[152] Carpinteri A, Valents S V, Ferrara G, et al. Experimental and numerical fracture modeling of a gravity dam. Fracture Mechanics of Concrete Structures, Bazant Z P ed., Elsevier Applied Science, 1992, 351-360
[153] Feltrin G, Wepf D, Bachmann H. Seismic cracking of concrete gravity dams. Dam Engineering, 1990, 4(1): 279-289
[154] Jirasek M, Zimmermann T. Embedded crack model: Ⅰ Basic formulation. Int. J. Numer. Meth. Engng 2001, 50(6): 1269-1290
[155] de Borst R, Nauta P. Non-orthogonal cracks in smeared finite element model. Engrg. Comput., 1985, 2(1): 35-46
[156] Cope R J, Rao P V, Clark L A, Norris P. Modeling of reinforced concrete behavior for finite element analysis of bridge slabs. In: Taylor C, Hinton E, Owen D R J, editors. Numerical Methods for Nonlinear Problems. Swansea: Pineridge Press, 1980, 457-470
[157] Bazant Z P, Oh B H. Crack band theory for fracture of concrete. Material and Constructions, 1983, 16(93): 155-177
[158] Wang Guanglun, Pekau O A, Zhang Chuhan, Wang Shaomin. Seisimc fracture analysis of concrete gravity dams based on nonlinear fracture mechanics. Engineering Fracture Mechanics, 2000, 65(1): 67-87
[159] Vahid Lotfi, Radin Espandar. Seismic analysis of concrete arch dams by combined discrete crack and non-orthogonal smeared crack technique. Engineering Structures, 2004, 26(1): 27-37
[160] Mirzabozorg H, Ghaeniam M. Non-linear behavior of mass concrete in three-dimensional problems using a smeared crack approach. Earthquake Engng Struct. Dyn., 2005, 34(3): 247-269
[161] Bazant Z P, Planas J. Fracture and size effect in concrete and other quasibrittle materials. Boca Raton: CRC Press, 1998.
[162] 赵吉东. 岩土工程稳定破坏的应变梯度损伤局部化分岔模型及应用:[博士学位论文]. 北京:清华大学,2002
[163] Camacho G T, Ortiz M. Computational modeling of impact damage in brittle materials. International journal of Solids and Structures, 1996, 33(20-22): 2899-2938
[164] Espinosa H D, Zavattieri P D, Dwivedi S K. A finite deformation continuum/discrete model for the description of fragmentation and damage in brittle materials. J. Mech. Phys. Solids., 1998, 46(10): 1909-1942
[165] Prochazka P P. Application of discrete element methods to fracture mechanics of rock bursts. Engineering Fracture Mechanics, 2004, 71(4-6): 601-618
[166] Sebastien Hentz, Frederic V D, Laurent Daudeville. Discrete element modeling of concrete submitted to dynamic loading at high strain rates. Computers and Structures, 2004, 82(29-30): 2509-2524
[167] Munjiza A, Owen D R J, Bicanic N. A combined finite-discrete element method in transient dynamics of fracturing solids. Engineering Computations, 1995, 12(2): 145-174
[168] Munjiza A, John N W M. Mesh size sensitivity of the combined FEM/DEM fracture and fragmentation algorithms. Engineering Fracture Mechanics, 2002, 69(2): 281-295
[169] Klerck P A, Sellers E J, Owen D R J. Discrete fracture in quasi-brittle materials under compressive and tensile stress states. Comput. Methods. Appl. Mech. Engng. 2004, 193(27-29): 3035-3056
[170] 徐艳杰. 横缝配筋的拱坝地震非线性模型与无限地基影响研究:[博士学位论文]. 北京:清华大学,1999
[171] Munjiza A, Andrews K R F. NBS contact detection algorithm for bodies of similar size. Int. J. Numer. Meth. Engng., 1998, 43(1): 131-149
[172] Feng Y T, Owen D R J. An augmented spatial digital tree algorithm for contact detection in computational mechanics. Int. J. Numer. Meth. Engng., 2002, 55(2): 159-176
[173] Perkins E, Williams J R. A fast contact detection algorithm insensitive to object sizes. Engineering Computations, 2001, 18(1-2): 48-61
[174] Williams J R, O’Connor R. A linear complexity intersection algorithm for discrete element simulation of arbitrary geometries. Engineering Computations, 1995, 12(2): 185-201
[175] Liu X L, Lemos J V. Procedure for contact detection in discrete element analysis. Advances in engineering software, 2001, 32(5): 409-415
[176] Feng Y T, Owen D R J. An energy based corner to corner contact algorithm. 3rd Int. Conf. on discrete element method, Santa Fe, New Mexico, USA, 2002, 23-25
[177] Kremmer M, Favier J F. A method for representing boundaries in discrete element modeling-part Ⅰ: Geometry and contact detection. Int. J. Numer. Meth. Engng, 2001, 51(12): 1407-1421
[178] 王泳嘉,邢纪波. 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
[179] Amadei B, Goodman R E. A 3-D constitutive relation for fractured rock masses. Proc. Int. Symp. on the Mechanical Behavior of Structured Media, Ottawa, Canada, 1981, 249-268
[180] Fossum A F. Effective elastic properties for a randomly jointed rock mass. Int. J. Rock. Mech. Min. Sci. & Geomech. Abstr,. 1985, 22(6): 467-470
[181] Kibok Min, Lanru Jing. Numerical determination of the equivalent elastic compliance tensor for fractured rock massed using the distinct element method. International Journal of Rock Mechanics & Mining Sciences, 2003, 40(6): 795-816
[182] Ting T C T. Anisotropic elasticity : theory and applications, Oxford: Oxford University Press, 1996
[183] 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
[184] Cundall P A. Adaptive density-scaling for time-explicit calculations. Proceedings of the Fourth International Conference on Numerical Methods in Geomechanics, Edmonton, 1982, 23-26
[185] 杜成斌,邱颖. 梅花周边缝拱坝的破坏形式分析. 水力发电,2002,5:61-63
[186] 崔玉柱,张楚汉,徐艳杰,金峰,王光纶. 用刚体弹簧元研究梅花拱坝的破坏机理. 清华大学学报,2002,42:88-92
[187] Suidan M, Schnobrich W C. Finite element analysis of reinforced concrete. ASCE J Struct Div, 1973, 99: 2109-2122
[188] Kolmar W, Mehlhorn G. Comparison of shear stiffness formulations for cracked reinforced concrete elements. In: Damjanic F, eds. Proceeding of International Conference on Computer Aided Analysis and Design of Concrete Structures, Part 1, Swansea: Pineridge Press, 1984, 133-147
[189] Bazant Z P. Instability, ductility and size effect in strain softening concrete. ASCE J Engng Mech, 1976, 102(2): 331-344
[190] Rots J G, Kusters G M A, Blaauwendraad J. The need for fracture mechanics options in finite element models for concrete structures. In: Damjanic F, eds. Proceeding of International Conference on Computer Aided Analysis and Design of Concrete Structures, Swansea: Pineridge Press, 1984, 19-32
[191] Rots J G. Smeared crack approach. In: Elfgren L, eds. Fracture Mechanics of Concrete Structures, London: Chapman and Hall, 1989, 138-146
[192] Rots J G. de Borst R. Analysis of mixed mode fracture in concrete. Journal of Engineering Mechanics, 1987, 113(11): 1739-1758
[193] de Borst R, Nauta P. Smeared crack analysis of reinforced concrete beams and slabs failing in shear. In: Damjanic F, eds. Proceeding of International Conference on Computer Aided Analysis and Design of Concrete Structures, Swansea: Pineridge Press, 1984, 261-273
[194] Feenstra P H, de Borst R. A plasticity model and algorithm for mode-Ⅰ cracking in concrete. International Journal Numerical Methods in Engineering, 1995, 38(15): 2509-2529
[195] de Borst R. Smeared cracking, plasticity, creep, and thermal loading- a unified approach. Computer Methods in Applied Mechanics and Engineering, 1987, 62(1): 89-110
[196] Willam K, Pramono E, Sture S. Fundamental issues of smeared crack models, SEM-RILEM International. Conference On Fracture of Concrete and Rock. Houston, Texas, Shah S P and Swartz S E, 1987, 192-207
[197] Milford R V, Schnobrich W C. Numerical model for cracked reinforced concrete. In: Damjanic F, eds. Proceeding of International Conference on Computer Aided Analysis and Design of Concrete Structures, Swansea: Pineridge Press, 1984, 71-84
[198] Jirasek M, Zimmermann T. Rotating crack model with transition to scalar damage. Engineering Mechanics, ASCE, 1998, 124(3): 277-284
[199] Petersson P E. Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials. TVBM-1006, Division of Building Materials, Lund Institute of Technology, 1981
[200] Arrea M, Ingraffea A R. Mixed-mode crack propagation in mortar and concrete. Report 81-13. Department of Structural Engineering, Cornell University, 1982
[201] Galvez J C, Elices M, Guinea G V, Planas J. Mixed mode fracture of concrete under proportional and nonproportional loading. International Journal of Fracture, 1998, 94(3): 267-284
[202] Nooru-Mohamed M B. Mixed mode fracture of concrete: an experimental approach, PhD thesis, Delft University of Technology, 1992
[203] Pivonka P, Ozbolt J, Lackner R, Mang H A. Comparative studies of 3D-constitutive models for concrete: application to mixed-mode fracture. International Journal for Numerical Methods in Engineering, 2004, 60(2): 549-570
[204] Cendon D A, Galvez J C, Elice M, Planas J. Modelling the fracture of concrete under mixed loading. International Jjournal of Fracture, 2000, 103(3): 293-310
[205] Prasad M V K V, Krishnamoorthy C S. Computational model for discrete crack growth in plain and reinforced concrete. Comput. Methods Appl. Mech. Engrg, 2002, 191(25-26): 2699-2725
[206] Galvez J C, Cervenka J, Cendon D A, Saouma V. A discrete crack approach to normal/shear cracking of concrete. Cement and concrete research. 2002, 32(10): 1567-1585
[207] Tin-Loi F, H. Li. Numerical simulations of quasibrittle fracture processes using the discrete cohesive crack model. International Journal of Mechanical Sciences, 2000, 42(2): 367-379
[208] Xu XP, Needleman A. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids, 1994, 42(9): 1397-1434
[209] Murphy N, Ivankovic A. The prediction of dynamic fracture evolution in PMMA using a cohesive zone model. Engineering Fracture Mechanics, 2005, 72: 861-875
[210] Elices M, Guinea G V, Gomez J, Planas J. The cohesive zone model: advantages, limitations and challenges. Engineering Fracture Mechanics, 2002, 69(2): 137-163
[211] Needleman A, An analysis of decohesion along an imperfect interface. International Journal of Fracture. 1990, 42: 21-40
[212] Xu X P, Needleman A. Void nucleation by inclusion debonding in a crystal matrix. Modelling and Simulation in Materials Science and Engineering, 1993, 1(2): 111-132
[213] Carol I, Pere C P, Carlos M L. Normal/shear cracking model: application to discrete crack analysis. Journal of Engineering Mechanics, 1997, 23(8): 765-773
[214] Galvez J C, Cendon D A, Planas J. Influence of shear parameters on mixed-mode fracture of concrete, International Journal of Fracture, 2002, 118(2): 163-189
[215] Margolin L D. A generalized Griffith criterion for crack propagation. Engng Fract. Mech. 1984, 19(3): 539-545
[216] Wells G N, Sluys L J. A new method for modeling cohesive cracks using finite elements. Int. J. Numer. Meth. Engng, 2001, 50(12): 2667-2682
[217] Sujan Malla, Martin Wieland. Simple model for safety assessment of cracked concrete dams subjected to strong ground shaking. Commission International Des Grands Barrages 2003, 151-168
[218] Chorpa A K, Chakrabarti P. The earthquake experience at Koyna Dam and stress in concrete gravity dams. Earthquake Engineering and Structural Dynamics, 1972, 1: 151-164
[219] Hall F J, The dynamic and earthquake behavior of concrete dams: review of experimental behavior and observational evidence. Soil. Dyn. Earthquake Eng., 1988, 7(2): 58-121
[220] Skrikerud P E, Bachmann H. Discrete crack modeling for dynamically loaded, unreinforced concrete structures. Earthquake Engineering and Structural Dynamics, 1986, 14(2): 297-315
[221] Ayari L M, Saouma V E. A fracture mechanics based seismic analysis of concrete gravity dams using discrete cracks. Engineering Fracture Mechanics, 1990, 35(1-3): 587-598
[222] Bhattacharjee S S, Leger P. Seismic cracking and energy dissipation in concrete gravity dams. Earthquake Engineering and Structural Dynamics, 1993, 22(11): 991-1007
[223] Yusuf Calayir, Muhammet Karaton. Seismic fracture analysis of concrete gravity dams including dam-reservoir interaction. Computer and Structures, 2005, 83(19-20): 1595-1606