混凝土坝裂缝的混沌特性及分析理论和方法
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摘要
本文应用混沌理论、分形理论、人工神经网络、灰色系统理论、运动稳定性理论、突变理论等理论和方法，对大坝安全监测中有关裂缝稳定性的相关问题进行研究。主要内容如下：
(1)研究了裂缝动力系统的相空间重构方法以及裂缝相空间重构参数的确定方法，计算了裂缝动力系统混沌特征量—关联维数D_2、最大Lyapunov指数和Kolmogorov熵，计算结果表明裂缝时间序列具有混沌特性。
(2)传统的裂缝开度统计模型的预测精度较低，提出了三种预测精度更高的统计与混沌混合预测模型。针对CTOD准则在混凝土坝裂缝失稳扩展分析中的不足，提出了一种裂缝失稳扩展新判据。
(3)采用灰色系统理论、运动稳定性理论和突变理论，研究了混凝土坝裂缝亚临界扩展识别方法，给出了三个裂缝亚临界扩展判据。
(4)用断裂力学有限元计算应力强度因子不能满足对混凝土坝裂缝实时监测、实时分析中的要求，提出了利用遗传算法和混沌优化算法改进的四层神经网络的解决方法，实例分析表明，本文提出的四层优化神经网络计算的应力强度因子接近于用断裂力学有限元计算的应力强度因子。
(5)针对实际断裂面或裂缝的不规则性，利用Griffith能量平衡原理及分形几何，推导了裂缝尖端实际应力场和位移场的表达式，研究发现，裂缝的分形性减小了裂缝尖端应力的奇异性。
Some problems related to crack stability of concrete dams in the field of dam monitoring are studied in this dissertation using theories and mathematics such as chaos theory, fractal geometry, artificial neural networks, grey system theory, motion stability theory, catastrophe theory, and so on. The main contents are as follows.
(1) The method of the phase space reconstruction and determination of its parameters of crack dynamic system are investigated. Calculation is made about the characteristic invariants such as correlation dimension, maximal Lyapunov exponent and Kolmogorov entropy of the crack dynamic system. The results indicate that the time series of cracks are chaotic ones.
(2) Owing to the low prediction precision of the conventional statistic model for crack opening displacements, three statistic model and chaos theory - based hybrid prediction models with higher precision are presented. Aiming at the deficiencies in the CTOD criterion applied to analysis of critical crack propagation, a new fracture criterion is established.
(3) The methods of detecting sub-critical propagation of cracks in concrete dams are explored by use of grey system theory, motion stability theory and catastrophe theory, and three criteria for sub-critical crack propagation are given.
(4) Because calculation of stress intensity factors using the finite element method of the linear elastic fracture mechanics cannot satisfy the need for the real-time monitoring and the real-time analysis of cracks in concrete dams, a four-layer neural network optimized by genetic algorithm and chaos optimization algorithm is proposed. The example shows that the optimized neural network can yield good results.
(5) Aiming at irregularity of a real fracture surface or a real crack profile, applying Griffith's criterion and fractal geometry, the real asymptotic expression at the crack tip is developed, and it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.
(1)研究了裂缝动力系统的相空间重构方法以及裂缝相空间重构参数的确定方法，计算了裂缝动力系统混沌特征量—关联维数D_2、最大Lyapunov指数和Kolmogorov熵，计算结果表明裂缝时间序列具有混沌特性。
(2)传统的裂缝开度统计模型的预测精度较低，提出了三种预测精度更高的统计与混沌混合预测模型。针对CTOD准则在混凝土坝裂缝失稳扩展分析中的不足，提出了一种裂缝失稳扩展新判据。
(3)采用灰色系统理论、运动稳定性理论和突变理论，研究了混凝土坝裂缝亚临界扩展识别方法，给出了三个裂缝亚临界扩展判据。
(4)用断裂力学有限元计算应力强度因子不能满足对混凝土坝裂缝实时监测、实时分析中的要求，提出了利用遗传算法和混沌优化算法改进的四层神经网络的解决方法，实例分析表明，本文提出的四层优化神经网络计算的应力强度因子接近于用断裂力学有限元计算的应力强度因子。
(5)针对实际断裂面或裂缝的不规则性，利用Griffith能量平衡原理及分形几何，推导了裂缝尖端实际应力场和位移场的表达式，研究发现，裂缝的分形性减小了裂缝尖端应力的奇异性。
Some problems related to crack stability of concrete dams in the field of dam monitoring are studied in this dissertation using theories and mathematics such as chaos theory, fractal geometry, artificial neural networks, grey system theory, motion stability theory, catastrophe theory, and so on. The main contents are as follows.
(1) The method of the phase space reconstruction and determination of its parameters of crack dynamic system are investigated. Calculation is made about the characteristic invariants such as correlation dimension, maximal Lyapunov exponent and Kolmogorov entropy of the crack dynamic system. The results indicate that the time series of cracks are chaotic ones.
(2) Owing to the low prediction precision of the conventional statistic model for crack opening displacements, three statistic model and chaos theory - based hybrid prediction models with higher precision are presented. Aiming at the deficiencies in the CTOD criterion applied to analysis of critical crack propagation, a new fracture criterion is established.
(3) The methods of detecting sub-critical propagation of cracks in concrete dams are explored by use of grey system theory, motion stability theory and catastrophe theory, and three criteria for sub-critical crack propagation are given.
(4) Because calculation of stress intensity factors using the finite element method of the linear elastic fracture mechanics cannot satisfy the need for the real-time monitoring and the real-time analysis of cracks in concrete dams, a four-layer neural network optimized by genetic algorithm and chaos optimization algorithm is proposed. The example shows that the optimized neural network can yield good results.
(5) Aiming at irregularity of a real fracture surface or a real crack profile, applying Griffith's criterion and fractal geometry, the real asymptotic expression at the crack tip is developed, and it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.
引文
[1]吴中如，沈长松，阮焕祥．水工建筑物安全监控理论及其应用．南京：河海大学出版社，1990
[2]王仁钟、李君纯、刘嘉忻等，中国水利大坝安全与管理，99大坝安全及监测国际研讨会议文集，中国书籍出版社，1999年10月
[3]吴中如，大坝病变和机理探讨，中国水利，2000年9月
[4]乔生祥，水工混凝土缺陷检测和处理，北京：中国水利水电出版社，1997
[5]吴中如、顾冲时、李雪红、等，佛子岭、梅山两座连拱坝的工作性态分析，大坝与安全，1999，4：35～40
[6]河海大学，梅山水电站大坝观测资料分析及结构正反分析，1999，5
[7]顾冲时、李雪红等，梅山连拱坝1962年事故部位性态的跟踪分析，水电能源科学，1999，17(3)：5～8
[8]顾冲时、李雪红、吴中如、等，梅山连拱坝的变形性态研究，河海大学学报(自然科学版)，2000，28(2)：59～63
[9]陈村水电厂，陈村大坝裂缝初步分析与主要缺陷报告，1988年11月
[10]陈村重力拱坝裂缝加固方案及其效应初探，河海大学学报，1994，22(5)：15～22
[11]西北勘测设计研究院，龙羊峡水电厂坝体裂缝检测报告，1999年10月
[12]邢林生，我国水电站大坝事故分析与安全对策，水利水电科技进展，2001，21(2)
[13]宋恩来、孙向红，混凝土重力拱坝出现裂缝的初步分析，东北电力技术，1998，10：5～8
[14]顾冲时、马福恒、吴中如，青铜峡大坝变形“疑点”的物理成因分析，水力发电，1999，6：18～20
[15]朱伯芳，重力坝的劈头裂缝，水力发电学报，1997，4：85～91
[16]吴中如，典型拱坝的严重事故及解析，工程力学，2001(增刊)
[17]Tonini, D. Observed behavior of several leakier arch dams. Proc .ASCE, Journal of the Power Division,Vol.82,Dec 1956
[18]Xerez, A., Lamas, J.F. Methods of analysis of arch dam behavior. V1 Congress on Large Dams,R.39, Q.21, New York, 1958
[19]Rocha, M. et al. A Quantitative method for the interpretation of the results of the observation of dams.VI Congress on Large Dams, Report on Question 21 New York,1958
[20]Silveria, A., E Pedro, Jose. Quantitative interpretation of results obtained in the observation of concrete dams.8th ICOLD Congress, Q.29, R.43, 1964, Edinburgh
[21]中村庆一、饭田隆一，实测资料举动解析，土木技术资料，Vol．5，No12，1963
[22]Widmann, R. Evaluation of deformation measurements performed at concrete dam. Commission Internationals of Grands Banrages, 1967
[23]Willm, G., Beaujoint, N. 9th Congress ICOLD, R.30, Q.34, Istanbul.
[24]Bonaldi, P., Fanelli, M. Giusepptti, G. Automatic observation and instantaneous control of dam safety. ISMES, 1980
[25]Marazio, P., et al. Behavior of Enel's 4large dams. Enel's report, Roma, 1980
[26]Pedro, J., O. et al. Stress evaluation in concrete dams, the example of verosa dam. International conference on safety of dams, Coimbra, 1984
[27]Gueds, Q., M., Coelho, P., S., M. Statistical behaviour model of dams.15th ICOLD congress, Q.56,R. 16, Lausanne
[28]Gomezlaa, G., Rodriguez Gonzalez, J.A. In search of a deterministic hydraulic monitoring model
of concrete dam foundation. XVth ICOLD, Q.58, R.49, 1985
[29] Purer, E., Steiner, N. Application of statistical methods in monitoring dam behaviour. International Water Power & Dam Construction,December, 1986
[30] Kalkani, E., C. Polynomial regression to forecast earth dam piezometer levels. Journal of Irrigation &Drainage Engineering, ASCE. Vol. 115, Aug. 1989, 45～55
[31] Luc E. Chouinard et al. Statistical analysis in real time of monitoring data for idukki arch dam. 2nd international conference on dam safety evaluation, Trivandrum, India. 1996,381～385
[32] Maria. Experimental study of concrete arch dams 40 years of LNEC experience. Lisboa, July 1986
[33] Fanelli, M. Automatic observation for dam safety. International Water Power &Dam Construction, Nov, Dec 1979
[34] Yoshida, M. Mechanical behaviour of Kurobe dam and its foundation and safety of the dam.R.2, Q52, XIVth Congress ICOLD, 1982
[35] Serafim, J.L. Safety aspects in the design and inspection of dams. International Water Power &Dam Construction, 1982,5
[36] Rocha, M., Serafim J. L. da Silveiva, A.E and Guerreivo M. Q. Observation of concrete dams: results obtained in cabril dam.Ⅵ Congress on Large Dams, Report on Question 21,New York,1958
[37] Ram ESharma. Deterministic forecasting model and retrofit instrumentation for safety monitoring of boundary dam. 18th Congress ICOLD, Q.68, R.62, 1982
[38] Oliver Crepon. An analytical approach to monitoring. International Water Power & Dam Construction, June, 1999.52～54
[39] Silva Gomes, A., F., Silva Matos, D. Quantitative analysis of dam monitoring result, State of The Art,Applications and prospects. 15th Congress ICOLD, Q.56 R.39, Lausannne
[40] 陈久宇，应用实测位移资料研究刘家峡重力坝横缝的结构作用，水利学报，1982，12：12～20
[41] 吴中如，混凝土坝观测物理量的数学模型及其应用，华东水利学院学报，1984，3：20～25
[42] 吴中如、沈长松、阮焕祥，论混凝土坝变形统计模型的因子选择，河海大学学报，1988，6
[43] 吴中如，论混凝土坝安全监控的确定性模型和混合模型，水利学报，1989(5)：64～70
[44] 李旦江、张思俊，大坝观测量的混合模型及其应用，水电部南京自动化研究所印，1987
[45] Kaplan M E Crack propagation and the fracture of concrete. J Am Concr Inst, 1961,58(11):591～610.
[46] Evans R H, Marathe M S. Stress distribution around holes in concrete. Mater Struct, 1968,1(1):57～60.
[47] Swartz S E, Hu K K, Jones G L. Compliance Monitoring of crack growth in concrete. J Eng Mech Div, ASCE, 1978, 104(EM4):789～800.
[48] Evans A G, Clifton J R, Anderson E. The fracture mechanics of mortars. Cem Concr Res,1980,10(4): 509～519.
[49] Brown J H. The failure of glass-fiber-reinforced notched beams in flexure. Mag Concr Res, 1973,25(82):31～38.
[50] Brown J H, Pomeroy C D. Fracture toughness of cement paste and mortars. Cem Concr Res, 1973,3(4):475～480.
[51] Gjorv O E, Sorensen S I, Arnesen A. Notch sensitivity and fracture toughness of concrete. Cem Concr Res, 1977, 7(3):333～344.
[52] Harris B, Varlow J, Ellis C D. The fracture Behavior of fiber reinforced concrete. Cem Concr Res,1972, 2(4):447～461.
[53] Mai Y W. Strength and fracture properties of asbestos-cement mortar composites. J Mater Sci,
1979, 14(9):2091～2102.
[54] Hillemeier B, Hilsdorf H K. Fracture mechanics studies on concrete compounds. Cem Concr Res,1977, 7(5):523～536.
[55] Romualdi J P, Batson G B. Mechanics of crack arrest in concrete. J Eng Mech Div, ASCE, 1963,87(EM6):775～790.
[56] Brown J H. Measuring the fracture toughness of cement paste and mortars. Mag Concr Res, 1972,24(81):189～193.
[57] Desayi P. Fracture of concrete in compression. Mater Struct, 1977, 10(57): 139～144.
[58] Waston K L. The estimation of fracture surface energy as a measure of the toughness of hardened cement paste. Cem Concr Res, 1978, 8(5):651～4556.
[59] Higgins D D, Bailey J E. Fracture measurements on cement paste. J Mater Sci, 1976,11(11): 1995～2003.
[60] Strange P C, Bryant A G. Experimental tests on concrete fracture. J Eng Mech Div, ASCE, 1979,105(EM2):337～343.
[61] Strange P C, Bryant A G. The role of aggregate in the fracture of concrete. J Mater Sci, 1979,14:1863～1868.
[62] Ziegeldorf S, Muller H S, Hilsdoff H K. A model law for the notch sensitivity of brittle materials. Cem Concr Res, 1980, 10(5):589～599.
[63] Shah S P, McGarry F J. Griffith fracture criterion and concrete. J Eng Mech Div, ASCE, 1971,97(EM6):1663～1676.
[64] Naus D J, Lott J L. Fracture toughness of Portland cement concrete. J Am Concr hast, 1969,66(6):481～489.
[65] Mindess S, Lawrence F V, Kesler C E. The J-integral as a fracture criterion for fiber reinforced concrete.. Cem Concr Res, 1977, 7(6):731～742.
[66] Walsh P E Crack initiation in plain concrete. Mag Concr Res, 1976, 28(94):37～41.
[67] Carpinteri A. Static and energetic fracture parameters for rock and concretes. Mater Struct, 1981,14(81):151～162
[68] Nadeau J S, Mindess S, Hay J M. Slow crack growth in cement paste. J Am Ceram Soc, 1974,57(2):51～54.
[69] Mindess S, Nadeau J S, Hay J M. Effect of different curing conditions on slow crack growth in cement paste. Cem Concr Res, 1974, 4(6):953～965.
[70] Wecharatana M, Shah S P. Slow growth in cement composites. J Struct Div, ASCE, 1982, 108(ST6):1400～1413.
[71] Gluckilch J. Fracture of plain concrete. J Eng Mech Div, ASCE, 1963, 89(EM6):127-138.
[72] Shah S P, Chandra J. Critical stress, volume change, and microcracking of concrete. J Am Concr Inst, 1968(6), 65:770～781.
[73] Hsu T T C. Mathematical analysis of shrinkage stresses in a model of hardened concrete. J Am Coner Inst, 1963, 60(3):371～390.
[74] Hsu T T C, Slate F O. Tensile bond strength between aggregate and cement paste or mortar. J Am Concr Inst, 1963, 60(4):465～486.
[75] Hsu T T C, Slate F O, Sturman G M, et al. Microcracking of plain concrete and the shape of the stress-strain curve. J Am Concr Inst, 1963, 60(2):209～224.
[76] Slate F O, Olsefski S. X-ray for study of intemai structure and microcracking of concrete. J Am Concr Inst, 1963, 60(5):575～588.
[77] Bazant Z P. Size effect in blunt fracture: concrete, rock, metal. J Eng Mech, ASCE, 1984,
110(4):518～535.
[78] Havlvorsen G T. J-integral study of steel fiber reinforced concrete. Int J Cem Composites, 1980, 2(1)13～22.
[79] Velazco F, Visalvanich K, Shah S P. Fracture behavior and analysis of fiber reinforced concrete beams. Cem Concr Res, 1980, 10(1):41～51.
[80] Visalvanich K, Naaman A E. Fracture methods in cement composites. J Eng Mech, ASCE, 1981,107(6):1155～1171.
[81] 徐世熄、赵国藩，大试件断裂韧度和高混凝土坝裂缝评定的断裂准则，大连理工大学学报，1988
[82] 徐世娘、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
[83] 吴智敏、赵国藩、徐世烺，大尺寸混凝土试件的断裂韧度，水利学报，1997，6：67～70
[84] Rashid Y R. Analysis of prestressed concrete pressure vessel. 1968, 7(4):334～344.
[85] Hillerborg A, Modeer M, Petersson P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res, 1976, 6(6):773～782
[86] Petersson P E. Fracture energy of concrete: method of determination. Cem Concr Res, 1980, 10(1):78～89
[87] Petersson P E. Fracture energy of concrete: practical performance and experiment. Cem Concr Res, 1980, 10(1):91～101
[88] Bazant Z P, Cedolin L. Blunt crack band propagation in finite element analysis. J Eng Mech Div, ASCE, 1979, 105(EM6):297～315
[89] Wecharatana M, Shah S P. Prediction of nonlinear fracture process zone in concrete. J Eng Mech Div, ASCE, 1983, 109(5):1231～1246
[90] Jenq Y S, Shah S P. A fracture toughness criterion for concrete. Eng Fract Mech, 1985, 21(5):1055～1069
[91] Jenq Y S, Shah S P. Two parameter fracture model for concrete. J Eng Mech, ASCE, 1985, 111(10):1227～1241
[92] 徐道远、符晓陵、朱为玄、等，坝体混凝土损伤—断裂模型，大连理工大学学报，1997，37(增刊)：1～6
[93] 冯伯林、徐道远、周先贵、等，温度荷载作用下拱坝裂缝的断裂力学分析方法，合肥工业大学学报(自然科学版)，2000，23(6)：1003～1008
[94] 张镜剑、涂金良、翟奇愚、等，龙滩碾压混凝土重力坝水平层面稳定安全的断裂分析，华北水利水电学院学报，1996，17(4)：2～7
[95] 杨延毅，混凝土损伤断裂过程研究，浙江大学学报，1993，5：654～661
[96] 孙静、李守义、杨菊生，高拱坝三维非线弹性损伤破坏分析，岩石力学与工程学报，2001(增2)：1358～1361
[97] 吴胜兴，混凝土裂缝开展宽度计算的有限元法，计算力学学报，1997，14(1)：69～77
[98] 巫昌海、汪基伟、夏颂佑，混凝土三维非正交弥散裂缝模型，河海大学学报，1999，27(5)：17～20
[99] 岑章志、秦飞，损伤分析的边界元法，第四届全国工程中的边界元法会议论文集，南京：河海大学出版社，1994
[100] Zhang G X, Sugiura Y, Hasegawa H. Fracture simulation using manifold and singular boundary element method. J Geotech Eng, JSCE, 1999, 624/Ⅲ—47:1～10
[101] 栾茂田、黎勇、林皋，非连续变形计算力学模型及其在有缝重力坝静力分析中的应用，水利学报，2001，4：40～45
[102] 寇晓东、周维垣，应用无单元法近似计算拱坝开裂，水利学报，2000，10：28～35
[103] 陈予恕、唐云、等，非线性动力学中的现代分析方法，北京：科学出版，1992
[104] Lorenz E. Deterministic nonperiodic flow. J Atmos Sci, 1963, 20:130～141
[105] Ruelle D, Takens F. On the nature of turbulence. Commum Math Phys 1971, 20(1)
[106] Li T Y, Torke J A. Period three implies chaos. Am Math Monthly, 1975,82
[107] May R. Simple mathematical models with very complicated dynamics. Nature, 1976, 261
[108] Feigenbaum M J. Quantitative universality for a class of nonlinear transformation. J Stat Phys. 1978, 19(1)
[109] Packard N H, Grutchfield J P, Farmer J D, et al. Geometry from a time series. Plays Rev Lett, 1980,45:712～716
[110] Takens F. Detecting strange attractors in turbulence. In: Dynamical systems and turbulence. Lecture Notes in Mathematics, 1981,898:245～262
[111] Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physica D, 1983, 9:189～208
[112] Grassberger P, Procaccia I. Characterization of strange attractors. Phys Rev Lett, 1983, 50:346～349
[113] Wolf A, Swift J B, Swinney H L, et al. Determining Lyapunov exponents from a time series. Physica D, 1985, 16:285～317
[114] Farmer J D, Sidorowich J J. Predicting chaotic time series. Phys Rev Lett, 1987, 59(8):845～848
[115] 丁晶、邓育仁、傅军，洪水相空间预报，成都科技大学学报，1995，85(4)：7～11
[116] 叶中行、龙如军，混沌时间序列的区间预测，上海交通大学学报，1997，31(2)：7～12
[117] 梁志珊、王丽敏、付大鹏，基于Lyapunov指数的电力系统短期负荷预测，中国电机工程学报，1998，18(5)：368～371
[118] 温权、张勇传、张周胜，基于混沌动力学的日径流时间序列预测，华中理工大学学报，1998，26(12)：62～64
[119] 汪树玉、刘国华、杜王盖、等，大坝观测数据序列中的混沌现象，水利学报，1999，7：22～26
[120] 康玲、王乘，混凝土坝裂缝混沌特性的初步研究，水电能源科学，2000，18(1)：19～21
[121] 徐洪钟、单泰松、吴中如，大坝观测数据的模糊神经网络分析，大坝观测与土工测试，2001，25(3)：17～22
[122] 张乾飞、徐洪钟、吴中如、等，基于模糊聚类的神经网络模型及其在渗流分析中的应用，水力发电学报，2002，2：37～43
[123] 苏怀智、吴中如、温志萍、等，基于模糊联想记忆神经网络的大坝安全监控系统建模研究，武汉大学学报(工学版)，2001，34(4)：21～24
[124] 郭海庆、吴中如、张乾飞，渗透系数反演的CHNN模型方法，长江科学院院报，2001，18(3)：25～28
[125] 赵斌、吴中如、张爱玲，BP模型在大坝安全监测预报中的应用，大坝观测与土工测试，1999，23(6)：1～4
[126] 李雪红、徐洪钟、顾冲时、等，主成分神经网络模型在大坝观测资料分析中的应用，大坝观测与土工测试，2001，25(5)：14～16
[127] 陈继光等，土坝观测数据的模糊人工神经网络分析，水利学报，2000，1：19～21
[128] 李守巨、刘迎曦、王登刚、等，基于神经网络的岩体渗透系数反演方法及其工程应用，岩石力学与工程学报，2002，21(4)：479～483
[129] Mandelbrot B B. The fractal geometry of nature. San Francisco, CA: W.H. Freeman and Company, 1983
[130] Mandelbrot B B, Passoja D E, Paullay A J. Fractal character of fracture surfaces of metals. Nature,
1984, 308:721～722
[131] Lopez J M, Schmittbuhl J. Anomalous scaling of fracture surfaces. Phys Rev. E, 1998, 57(6): 6405～6408
[132] Issa M A, Hamnad A M. Assessment and evaluation of fractal dimension of concrete fracture surface digitized images. Cem Concr Res, 1994, 24 (2): 325～334
[133] Xie H P, Wang J A, Stein E. Direct fractal measurement and multifractal properties of fracture surfaces. Phys Lett A, 1998, 242:41～50
[134] 吴科如、张东，混凝土断裂面三维重构，建筑材料学报，1999，2(3)
[135] Chen Z, Mecholsky J J, Joseph T, et al. The fractal geometry of Si_3N_4 wear and fracture surfaces.J Mater Sci, 1997, 32:6317～6323
[136] Hill T J, Mecholsky J J, Anusavice K J. Fractal analysis of toughening behavior in 3BaO. 5SiO_2 glass-ceramics. J Am Ceram Soc, 2000, 83 (3): 545～552
[137] Saouma V E, Barton C C, Gamaleldins N A. Fractal characterization of fracture surfaces in concrete. Eng Fract Mech, 1990, 35 (1): 47～53
[138] Issa M A, Hammad A M. Fractal characterization of fracture surfaces in mortar. Cem Coner Res, 1993, 23:7～12
[139] Saouma V E, Barton C C. Fractals, fractures and size effects in concrete. J Eng Mech, ASCE, 1994,120(4):835～853
[140] Dougan L T, Addison P S. Fractal analysis of fracture: a comparison of dimension estimate. Mech Res Comum, 2000, 27 (4): 383～392
[141] Issa M A, Hammad A M, Islam M S, et al. Fractal dimension-a measure of fracture roughness and toughness of concrete. Eng Fract Mech 2003, 70:125～137
[142] Pande C S, Richards L R, Smith S. Fractal characteristics of fractured surfaces. J Mater Sci Lett 1987, 6:295～297
[143] Dougan L T, Addison P S. Estimating the cut-off in the fractal scaling of fractured concrete. Cem Concr Res, 2001, 31:1043～1048
[144] Dubuc B, Quiniou J F, Roques C, et al. Evaluating the fractal dimension of profiles. Phy Rev A, 1989, 39(3):1500～1512
[145] Morel S, Bouchard E, Schmittbuhl J. R-cuve behavior and roughness development of fracture surfaces. Int J Fract, 2002, 114:307～325
[146] Su H, Zhang Y, Yan Z. Fractal analysis of microstructures and properties in ferrite-martensite steels. Scripta Metall Mater 1991, 25:651～554
[147] Wang Z G, Chen D L, Jiang X X, et al. Relationship between fractal dimension and fatigue threshold value in dual-phase steels. Scripta Met 1988, 22:827～832
[148] Mecholsky J J, Passoja D E, Feinberg-Ringel K S. Quantitative analysis of brittle fracture surfaces using fractalgeometry. J Am Ceram Soc 1989, 72(1):60～65
[149] Balankin A S, Bravo-Ortega A, Galicia-Cortes M A, et at. Size effect of self-affine roughness on crack mechanics in solids. Int J Fract, 1996, 79:R63～R68
[150] Bouchard E. Fractal dimension of fractured surfaces: a universal value? Europhys Lett 1990, 13(1):73～79
[151] Mu ZQ, Lung CW, Kang Y, Long QY. Perimeter-maximum method for measuring the fractal dimension of a fractured surface. Phys Rev B, 1993, 48(10):7679～7681
[152] 董连科，分形理论及其应用，沈阳：辽宁科学技术出版社，1991
[153] 谢和平，分形—岩石力学导论，北京：科学出版社，1997
[154] 潘家铮，世界上没有无裂缝的水坝，中国三峡建设，2002，4：6～7
[155] 朱伯芳，大体积混凝土温度应力与温度控制，北京：中国电力出版社，1999
[156] 何涛，混凝土常见裂缝的探讨，建材研究与应用，2002，4：56～57
[157] 赵杰，混凝土结构裂缝及其防治，电力建设，2000，2：40～42
[158] 卓文仁，混凝土结构裂缝探讨分析，水利科技，2002，2：43～44
[159] 王象文、邱文恒、吕刚，混凝土开裂原因与防治措施，科技情报开发与经济，1997，6：40～41
[160] 徐世烺，混凝土断裂韧度的概率统计分析，水利学报，1984，10：51～58
[161] Browand F K. The structure of the turbulent mixing layer. Physica D, 1986(18):135～148
[162] 苏怀智，大坝安全监控感知融合理论和方法及应用研究，河海大学博士学位论文，2001
[163] 徐洪钟，大坝动力系统的安全监控非线性分析模型研究，河海大学博士学位论文，2001
[164] 帕利斯、梅罗，动力系统几何理论引论，陈藻平译，北京：科学出版社，1988
[165] Devaney R L. An introduction to chaotic dynamic systems. California: Addison-Wesley, 1989
[166] 卢侃、孙建华、欧阳容白、等，混沌动力学，上海：上海翻译出版公司，1990
[167] 陈予恕、唐云、等，非线性动力学中的现代分析方法，北京：科学出版，1992
[168] 黄润生，混沌分形及其应用，武汉：武汉大学出版社，2000
[169] 王东生、曹磊，混沌分形及其应用，合肥：中国科学技术大学出版社，1995
[170] Tsonis AA. Chaos From theory to application. New York: Plenum Press, 1992
[171] 黄胜伟，工程结构混沌振动、混沌最优化算法及其应用，河海大学博士论文，2002
[172] Sauer T, Yorke J A, Casdagli M. Embedology. J Stat Phys, 1991, 65:579～616
[173] Sauer T, Yorke J A. How many delay coordinates do you need. Int J Bifurcation and Chaos, 1993, 3:737～741
[174] Broomhead D S, King G P. Extracting qualitative dynamics from experimental data. Physica D,1986, 20:217～236
[175] Casdagli M, Eubank S, Farmer J D, et al. State space reconstruction in the presence of noise.Physica D, 1991, 51:52～98
[176] 赵永龙、丁晶、邓育仁，混沌分析在水文预测中的应用和展望，水科学进展，1998，9(2)：181～186
[177] Fraser A M, Swinney H L. Independent coordinates for strange attractors from mutual information. Phys Rev A, 1986, 33(2):1134～1140
[178] Liebert W, Schuster H G. Proper choice of the time delays for the analysis of chaotic time series. Phys Lett A, 1989, 142:107～111
[179] Kugiumtzis D. State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length. Physica D, 1996, 95:13～28
[180] Kim H S, Eykholt R, Salas J D. Nonlinear dynamic, delay times, and embedding windows. Physica D, 1999, 127:48～60
[181] 吕金虎、陈君安、陈士华，混沌时间序列分析及其应用，武汉：武汉大学出版，2002
[182] Grebogi C, Ott E, Yorke J A. Crises, sudden changes in chaotic attractors and transient chaos. Physica D, 1983, 7
[183] Provenzale A, Smith L A, Vio R, et al. Distinguishing between low-dimensional dynamics and randomness in measured time series. Physica D, 1992, 58:31～49
[184] Greenside H S, Wolf A., Swift J B, et al. The impracticability of a box-counting algorithm for calculating the dimensionality of strange attractors. Phys Rev A, 1982, 25:3453～3456
[185] Theiler J. Spurious dimension from correlation algorithms applied to limited time series data.
Phys Rev A, 1986, 34(3):2427～2431
[186] Eckman J P, Kamphorst S O, Ruelle D, et al. Lyapunov exponent from time series. Phys Rev A,1986, 34(4):4971～4980
[187] Abarbanel H D I, Brown R, Kadtke J B. Prediction in chaotic systems: methods for time series with broadband Fourier spectra. Phys Rev A, 1990, 41 (2):1782～1807
[188] Benettin G, Galgani L, Strelcyn J M. Kolmogorov entropy and numerical experiments. Phys Rev A, 1976, 14(6):2338～2345
[189] Nicolis J S, Meyer-Kress G, Hallbs G. Non-uniform information processing by strange attractors of chaotic maps and flows. In: Stochastic phenomena and chaotic behavior of complex systems, Berlin: Springer-Verlag, 1984:124～139
[190] Kantz H. A robust method to estimate the maximal Lyapunov exponent of a time series. Phys Lett A, 1994, 185:77～87
[191] Kantz H, Schreiber T, Nonlinear time Series analysis. Cambridge: Cambridge University Press, 1997
[192] Rosenstein M T, Collins J J, De Luca C J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D, 1993, 65:117～134
[193] Grassberger P, Procaccia I. Estimation of the Kolmogorov entropy from a chaotic signal. Phys Rev A, 1983, 28(4):2591～2593
[194] 邓昌铁，意大利水电站大坝安全监控概况，河海大学科技情报，1989，9(2)：32～42
[195] 章书寿、吴中如、华锡生，葡萄牙大坝安全监测与模型试验技术综述，河海大学科技情报，1989，9(2)：8～15
[196] 彭虹，法国大坝安全监测的新进展，河海大学科技情报，1989，9(2)：16～31
[197] 张进平，大坝监测数学模型因子集的扩充，大坝观测与土工测试，1999，23(2)：1～4
[198] Tremmel E. Analysis of pendulum measurements. 6th ICOLD, Q.21, R. 15, 1958, New York
[199] 包腾飞、吴中如、顾冲时、等，基于统计模型与混沌理论的大坝安全监测混合预测模型，河海大学学报(自然科学版)，2003，31(5)：534～538
[200] Wells A A. Application of fracture mechanics and at beyond general yielding. British Welding Journal, 1963, 10(10):563～570
[201] GB／T2358-94，金属材料裂纹尖端张开位移试验方法
[202] JB／T4291-1999，焊接接头裂纹张开位移(CTOD)试验方法
[203] BS7448-1 1991, Method for Determination of K_(Ic), Critical CTOD and Critical J Values of Metallic Materials
[204] BS7448-2 1997, Method for Determination of K_(Ic), Critical CTOD and Critical J Values of Welds in Metallic Materials.
[205] ASTME 1290-99, Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement.
[206] Visalvanich K, Naaman A E. Fracture methods in cement composites. J Eng Mech, ASCE, 1981,107(6):1155～1171.
[207] 徐世烺、赵国藩，混凝土裂缝稳定扩展过程与临界裂缝尖端张开位移，水利学报，1989，4：33～44
[208] 徐世烺、赵国藩，混凝土断裂力学研究，大连：大连理工大学出版社，1991
[209] 吴智敏、赵国藩，混凝土裂缝扩展的CTOO_c准则，大连理工大学学报，1995，35(5)：699～702
[210] 吴智敏、王金来、徐世烺、刘毅，基于虚拟裂缝模型的混凝土等效断裂韧度，工程力学，2000，17(1)：99～104
[211] 于骁中、张玉美、郭桂兰，混凝土断裂能G_F，水利学报，1987，7：30～37
[212] Farmer J D, Sidorowich J J. Predicting chaotic time series. Phys Rev Lett, 1987, 59(8):845～848
[213] Casdagli M. Nonlinear prediction of chaotic time series. Physica D, 1989, 35:335～356
[214] 吴宗敏，函数的径向基表示，数学进展，1998，27(3)：202～208
[215] Floater M S, Iske A. Multistep scattered data interpolation using compactly supported radial basis functions. J Comput Appl Math, 1996, 73:65～78
[216] Wendland H. Piecewise polynomial, positive definite and compactly supported redial basis functions of minimal degree. Adv Comput Math, 1995, 4:389～396
[217] Wu Z M. Multivariate compactly supported positive definite radial functions. Adv Comput Math, 1995, 4:283～292
[218] 吴宗敏，径向基函数、散乱数据拟合与无网格偏微分方程数值解，工程数学学报，2002，19(2)：1～12
[219] 林振山，长期预报的相空间理论和模式，北京：气象出版社，1993
[220] 蒋传文，电力负荷预报理论及新方法的研究，华中理工大学博士学位论文，1999
[221] 吴中如、顾冲时，大坝安全综合评价专家系统，北京：北京科学技术出版社，1997
[222] 吴中如、顾冲时，大坝原型反分析及其应用，南京：江苏科学技术出版，2001
[223] 包腾飞、郑东健、郭海庆，新安江大坝典型坝(?)坝顶水平位移监控指标的拟定，水利水电技术，2003，34(3)：46～49
[224] 孙芳垂、陈星焘、胡世平，工程规划中的概率(?)念，北京：冶金工业出版社，1985
[225] 吴世伟，结构可靠度分析，北京：人民交通出版社，1990
[226] 方开泰，统计分布，北京：科学出版社，198
[227] Eckmann J P, Rulle D. Ergodic theory of cha and strange attractors. Rev Mod Phys, 1985, 57:617～653
[228] Evans R.H, Marathe M S. Microcracking and stess-strain curve for concrete in tension. Mateiauxet constructions, 1968, 1 (1):61～464
[229] Crepon O, Michel. An analytical approach to monitoring. International Water Power & Dam Construction, 1999, 51 (6):52～54
[230] 舒仲周、张继业、曹登庆，运动稳定性，北京：中国铁道出版，2001
[231] 刘思峰、郭天榜、党耀国、等，灰色系统理论及其应用，北京：科学出版社，1999
[232] 邓聚龙，灰色控制系统，武汉：华中工学院出版，1987
[233] 黄建平、衣育红，利用观测资料反演非线性动力模型，中国科学B辑，1991，3：331～336
[234] 杨文采，非线性地震道的混沌反演——Ⅰ、Ⅱ，地球物理学报，1993，36(2)：222～232，36(3)：376～386
[235] 吴中如、潘卫平，应用李雅普诺夫函数分析岩土边坡的稳定性，水利学报，1997，8：29～33
[236] 秦元勋、王慕秋、王联，运动稳定性理论与应用，北京：科学出版，1981
[237] 王照林，运动稳定性及其应用，北京：高等教育出版，1992
[238] Thom R，结构稳定性与形态发生学，成都：四川教育出版社，1992
[239] Saunders P T. An introduction to catastrophe theory. Cambridge University Press, 1980
[240] 程学军、蔡美峰、李长洪，灰色突变模型及其在声发射监测预报中的应用，中国矿业，1997，6(2)：37～39
[241] 凌复华，突变理论及其应用，上海：上海交通大学出版社，1987
[242] Wecharatana M, Shah S P. Double torsion tests for studying slow crack growth of Portland cement
mortar. Cem Concr Res, 1980, 10(6):833～844
[243] 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
[244] 于骁中、居襄、曹建国，单支墩大头坝劈头裂缝稳定性分析，水利学报，1981，1：30～37
[245] 赵中极，重力坝坝面和坝踵水平裂缝的断裂力学分析，水利学报，1982，6：11～19
[246] 河海大学，佛子岭连拱坝资料分析报告，南京：河海大学，1986
[247] 河海大学，陈村水电站原型观测资料及结构正反分析报告，南京：河海大学，2002
[248] 河海大学，龙羊峡重力拱坝监测资料分析及裂缝成因与稳定分析，南京：河海大学，2002
[249] Hornik K, Stinchcombe M, White H. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks, 1990, 3:551～560
[250] 沈清、胡德文、时春，神经网络应用技术，长沙：国防科技大学出版社，1998
[251] 从爽，面向Matlab工具箱得的神经网络理论与应用，合肥：中国科技大学出版社，1998
[252] 徐道远、符晓陵，断裂力学，南京：河海大学研究生教材，1981
[253] 朱伯芳，有限单元法原理与应用，北京：中国水利水电出版社，2000
[254] 王旭、王宏、王义辉，人工神经元网络原理与应用，沈阳：东北大学出版社，2000
[255] 李学桥、马莉，神经网络工程应用，重庆：重庆大学出版社，1996
[256] 王小平、曹立明，遗传算法—理论、应用与软件实现，西安：西安交通大学出版社，2002
[257] 李兵、蒋慰孙，混沌优化方法及应用，控制理论及应用，1997，14(4)：613～615
[258] 雷德明，利用混沌搜索全局最优解的一种混合遗传算法，系统工程与电子技术，1999，21(12)：81～82
[259] Panagiotopoulos P D. Fractal geometry in solids and structures. Int J Sol Struct 1991, 29:2151～2175
[260] Panagiotopoulos P D, Mistakidis E S, Panagouli O K. Fractal interfaces with unilateral contact and friction conditions. Comput Meth Appl Mech Eng, 1992, 99: 395～412.
[261] Barnsley M. Fractals everywhere. Boston: Academic press, 1988
[262] Wallin H. The trace to the boundary of Sobolev spaces on a snowflake [R] .Rep Dep Math Univ Umea, 1989
[263] Adams R A，索伯列夫空间，叶其孝、王耀东、应隆安、等译，北京：人民教育出版社，1981
[264] Theocaris P S, Panagiotopoulos P D. Cracks of fractal geometry with unilateral contact and friction interface conditions. Int J Fract 1993, 60:293～310.
[265] Panagouli O K, Mistakidis E S, Panagiotopoulos P D. On the fractal fracture in brittle structures: Numerical approach. Comput Meth Appl Mech Eng, 1997,147:1～15
[266] Mistakidis E S. Fractal geometry in structural analysis problems: a variational formulation for fractured bodies with non-monotone interface conditions. Chaos, Solitons and Fractals 1997, 8(2):269～285
[267] Underwood E, Banerji K. Fractals in fractography. Mater Sci Eng, 1986, 80(1):1～14
[268] Falconer K. Fractal geometry: Mathematical foundations and applications. Chichester: John Wiley and Sons, 1990
[269] Balankin A S. Physics of fracture and mechanics of self-affine cracks. Eng Fract Mech, 1997, 57(2-3):135～203
[270] Mandelbrot B B, Passoja D E, Paullay A J. Fractal character of fracture surfaces of metals. Nature, 1984, 308:721～722
[271] Schmittbuhl J, Roux S, Berthand Y. Development of roughness in crack propagation. Europhys Lett, 1994, 28:585～590
[272] Mecholsky J J, Mackin T J. Fractal analysis of fracture in Ocala chert. J Mater Sci Lett, 1988, 7:1145～1147
[273] Bouchard E, Lapasset G, Planes J, et al. Stastics of brauched fracture surface. Phys Rev B, 1993, 48:2917～2928
[274] Daguier P, Henanx S, Bouchard E, et al. Quantitative analysis of a fractal surface by atomic force microscopy. Phys Rev E, 1996, 53:5673～5642
[275] Daguier P, Nghiem B, Bouchaud E, et al. Pinning and depinning of crack fronts in heterogeneous materials. Phys Rev Lett, 1997, 78:1062～1065
[276] Morel S, Schmittbuhl J, Lopez J M. Anomalous roughening of wood fracture surface. Phys Rev E, 1998, 58 (6): 6999～7005
[277] 刘小艳，混凝土轴拉试件的应力—应变全曲线研究及其断裂面分析，南京：河海大学硕士论文，2002
[278] Borodich F M. Some fractal models of fracture. J Mech Phys Solids, 1997, 45 (2) :239～259
[279] Borodich F M. Fractals and fractal sealing in fracture mechanics. Int J Fract, 1999, 95:239～259
[280] Borodich F M. Self-similar models and size effect of multiple fracture. Fractals, 2001, 9 (1) :17～30
[281] Mosolov A B. Fractal Griffiths cracks. Zh Tekh Fiz SSSR, 1991, 61:57～60
[282] Gol'dshtein R V, Mosolov A B. Cracks with a fractal surface. Dokl Akad Nauk SSSR, 1991, 319:840～844
[283] Gol'dshtein R V, Mosolov A B. Fractal cracks. Prikl Mat Mekh SSSR, 1992, 56(4):663～671
[284] Mosolov A B, Borodich F M. Fractal fracture of brittle bodies during compression. Dokl Akad Nauk SSSR, 1992, 324:546～549
[285] Xie H, Sanderson D J. Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities. Int J Fract, 1995, 74:29～42
[286] Yavari A, Sarkani S, Moyer E T. The mechanics of self-similar and self-affine fractal cracks. Int J Fract, 2002, 114:1～27
[287] Yavari A, Sarkani S, Moyer E T On fractal cracks in micropotar elastic solids. J Appl Mech, ASCE 2002, 69 (1):45～54
[288] Voss R F. Random fractals: characterization and measurement. In: Scaling phenomena in disordered systems. Ed. Punn R and Skjeltorp A, New York: Plenum, 1985, pp1～11
[2]王仁钟、李君纯、刘嘉忻等，中国水利大坝安全与管理，99大坝安全及监测国际研讨会议文集，中国书籍出版社，1999年10月
[3]吴中如，大坝病变和机理探讨，中国水利，2000年9月
[4]乔生祥，水工混凝土缺陷检测和处理，北京：中国水利水电出版社，1997
[5]吴中如、顾冲时、李雪红、等，佛子岭、梅山两座连拱坝的工作性态分析，大坝与安全，1999，4：35～40
[6]河海大学，梅山水电站大坝观测资料分析及结构正反分析，1999，5
[7]顾冲时、李雪红等，梅山连拱坝1962年事故部位性态的跟踪分析，水电能源科学，1999，17(3)：5～8
[8]顾冲时、李雪红、吴中如、等，梅山连拱坝的变形性态研究，河海大学学报(自然科学版)，2000，28(2)：59～63
[9]陈村水电厂，陈村大坝裂缝初步分析与主要缺陷报告，1988年11月
[10]陈村重力拱坝裂缝加固方案及其效应初探，河海大学学报，1994，22(5)：15～22
[11]西北勘测设计研究院，龙羊峡水电厂坝体裂缝检测报告，1999年10月
[12]邢林生，我国水电站大坝事故分析与安全对策，水利水电科技进展，2001，21(2)
[13]宋恩来、孙向红，混凝土重力拱坝出现裂缝的初步分析，东北电力技术，1998，10：5～8
[14]顾冲时、马福恒、吴中如，青铜峡大坝变形“疑点”的物理成因分析，水力发电，1999，6：18～20
[15]朱伯芳，重力坝的劈头裂缝，水力发电学报，1997，4：85～91
[16]吴中如，典型拱坝的严重事故及解析，工程力学，2001(增刊)
[17]Tonini, D. Observed behavior of several leakier arch dams. Proc .ASCE, Journal of the Power Division,Vol.82,Dec 1956
[18]Xerez, A., Lamas, J.F. Methods of analysis of arch dam behavior. V1 Congress on Large Dams,R.39, Q.21, New York, 1958
[19]Rocha, M. et al. A Quantitative method for the interpretation of the results of the observation of dams.VI Congress on Large Dams, Report on Question 21 New York,1958
[20]Silveria, A., E Pedro, Jose. Quantitative interpretation of results obtained in the observation of concrete dams.8th ICOLD Congress, Q.29, R.43, 1964, Edinburgh
[21]中村庆一、饭田隆一，实测资料举动解析，土木技术资料，Vol．5，No12，1963
[22]Widmann, R. Evaluation of deformation measurements performed at concrete dam. Commission Internationals of Grands Banrages, 1967
[23]Willm, G., Beaujoint, N. 9th Congress ICOLD, R.30, Q.34, Istanbul.
[24]Bonaldi, P., Fanelli, M. Giusepptti, G. Automatic observation and instantaneous control of dam safety. ISMES, 1980
[25]Marazio, P., et al. Behavior of Enel's 4large dams. Enel's report, Roma, 1980
[26]Pedro, J., O. et al. Stress evaluation in concrete dams, the example of verosa dam. International conference on safety of dams, Coimbra, 1984
[27]Gueds, Q., M., Coelho, P., S., M. Statistical behaviour model of dams.15th ICOLD congress, Q.56,R. 16, Lausanne
[28]Gomezlaa, G., Rodriguez Gonzalez, J.A. In search of a deterministic hydraulic monitoring model
of concrete dam foundation. XVth ICOLD, Q.58, R.49, 1985
[29] Purer, E., Steiner, N. Application of statistical methods in monitoring dam behaviour. International Water Power & Dam Construction,December, 1986
[30] Kalkani, E., C. Polynomial regression to forecast earth dam piezometer levels. Journal of Irrigation &Drainage Engineering, ASCE. Vol. 115, Aug. 1989, 45～55
[31] Luc E. Chouinard et al. Statistical analysis in real time of monitoring data for idukki arch dam. 2nd international conference on dam safety evaluation, Trivandrum, India. 1996,381～385
[32] Maria. Experimental study of concrete arch dams 40 years of LNEC experience. Lisboa, July 1986
[33] Fanelli, M. Automatic observation for dam safety. International Water Power &Dam Construction, Nov, Dec 1979
[34] Yoshida, M. Mechanical behaviour of Kurobe dam and its foundation and safety of the dam.R.2, Q52, XIVth Congress ICOLD, 1982
[35] Serafim, J.L. Safety aspects in the design and inspection of dams. International Water Power &Dam Construction, 1982,5
[36] Rocha, M., Serafim J. L. da Silveiva, A.E and Guerreivo M. Q. Observation of concrete dams: results obtained in cabril dam.Ⅵ Congress on Large Dams, Report on Question 21,New York,1958
[37] Ram ESharma. Deterministic forecasting model and retrofit instrumentation for safety monitoring of boundary dam. 18th Congress ICOLD, Q.68, R.62, 1982
[38] Oliver Crepon. An analytical approach to monitoring. International Water Power & Dam Construction, June, 1999.52～54
[39] Silva Gomes, A., F., Silva Matos, D. Quantitative analysis of dam monitoring result, State of The Art,Applications and prospects. 15th Congress ICOLD, Q.56 R.39, Lausannne
[40] 陈久宇，应用实测位移资料研究刘家峡重力坝横缝的结构作用，水利学报，1982，12：12～20
[41] 吴中如，混凝土坝观测物理量的数学模型及其应用，华东水利学院学报，1984，3：20～25
[42] 吴中如、沈长松、阮焕祥，论混凝土坝变形统计模型的因子选择，河海大学学报，1988，6
[43] 吴中如，论混凝土坝安全监控的确定性模型和混合模型，水利学报，1989(5)：64～70
[44] 李旦江、张思俊，大坝观测量的混合模型及其应用，水电部南京自动化研究所印，1987
[45] Kaplan M E Crack propagation and the fracture of concrete. J Am Concr Inst, 1961,58(11):591～610.
[46] Evans R H, Marathe M S. Stress distribution around holes in concrete. Mater Struct, 1968,1(1):57～60.
[47] Swartz S E, Hu K K, Jones G L. Compliance Monitoring of crack growth in concrete. J Eng Mech Div, ASCE, 1978, 104(EM4):789～800.
[48] Evans A G, Clifton J R, Anderson E. The fracture mechanics of mortars. Cem Concr Res,1980,10(4): 509～519.
[49] Brown J H. The failure of glass-fiber-reinforced notched beams in flexure. Mag Concr Res, 1973,25(82):31～38.
[50] Brown J H, Pomeroy C D. Fracture toughness of cement paste and mortars. Cem Concr Res, 1973,3(4):475～480.
[51] Gjorv O E, Sorensen S I, Arnesen A. Notch sensitivity and fracture toughness of concrete. Cem Concr Res, 1977, 7(3):333～344.
[52] Harris B, Varlow J, Ellis C D. The fracture Behavior of fiber reinforced concrete. Cem Concr Res,1972, 2(4):447～461.
[53] Mai Y W. Strength and fracture properties of asbestos-cement mortar composites. J Mater Sci,
1979, 14(9):2091～2102.
[54] Hillemeier B, Hilsdorf H K. Fracture mechanics studies on concrete compounds. Cem Concr Res,1977, 7(5):523～536.
[55] Romualdi J P, Batson G B. Mechanics of crack arrest in concrete. J Eng Mech Div, ASCE, 1963,87(EM6):775～790.
[56] Brown J H. Measuring the fracture toughness of cement paste and mortars. Mag Concr Res, 1972,24(81):189～193.
[57] Desayi P. Fracture of concrete in compression. Mater Struct, 1977, 10(57): 139～144.
[58] Waston K L. The estimation of fracture surface energy as a measure of the toughness of hardened cement paste. Cem Concr Res, 1978, 8(5):651～4556.
[59] Higgins D D, Bailey J E. Fracture measurements on cement paste. J Mater Sci, 1976,11(11): 1995～2003.
[60] Strange P C, Bryant A G. Experimental tests on concrete fracture. J Eng Mech Div, ASCE, 1979,105(EM2):337～343.
[61] Strange P C, Bryant A G. The role of aggregate in the fracture of concrete. J Mater Sci, 1979,14:1863～1868.
[62] Ziegeldorf S, Muller H S, Hilsdoff H K. A model law for the notch sensitivity of brittle materials. Cem Concr Res, 1980, 10(5):589～599.
[63] Shah S P, McGarry F J. Griffith fracture criterion and concrete. J Eng Mech Div, ASCE, 1971,97(EM6):1663～1676.
[64] Naus D J, Lott J L. Fracture toughness of Portland cement concrete. J Am Concr hast, 1969,66(6):481～489.
[65] Mindess S, Lawrence F V, Kesler C E. The J-integral as a fracture criterion for fiber reinforced concrete.. Cem Concr Res, 1977, 7(6):731～742.
[66] Walsh P E Crack initiation in plain concrete. Mag Concr Res, 1976, 28(94):37～41.
[67] Carpinteri A. Static and energetic fracture parameters for rock and concretes. Mater Struct, 1981,14(81):151～162
[68] Nadeau J S, Mindess S, Hay J M. Slow crack growth in cement paste. J Am Ceram Soc, 1974,57(2):51～54.
[69] Mindess S, Nadeau J S, Hay J M. Effect of different curing conditions on slow crack growth in cement paste. Cem Concr Res, 1974, 4(6):953～965.
[70] Wecharatana M, Shah S P. Slow growth in cement composites. J Struct Div, ASCE, 1982, 108(ST6):1400～1413.
[71] Gluckilch J. Fracture of plain concrete. J Eng Mech Div, ASCE, 1963, 89(EM6):127-138.
[72] Shah S P, Chandra J. Critical stress, volume change, and microcracking of concrete. J Am Concr Inst, 1968(6), 65:770～781.
[73] Hsu T T C. Mathematical analysis of shrinkage stresses in a model of hardened concrete. J Am Coner Inst, 1963, 60(3):371～390.
[74] Hsu T T C, Slate F O. Tensile bond strength between aggregate and cement paste or mortar. J Am Concr Inst, 1963, 60(4):465～486.
[75] Hsu T T C, Slate F O, Sturman G M, et al. Microcracking of plain concrete and the shape of the stress-strain curve. J Am Concr Inst, 1963, 60(2):209～224.
[76] Slate F O, Olsefski S. X-ray for study of intemai structure and microcracking of concrete. J Am Concr Inst, 1963, 60(5):575～588.
[77] Bazant Z P. Size effect in blunt fracture: concrete, rock, metal. J Eng Mech, ASCE, 1984,
110(4):518～535.
[78] Havlvorsen G T. J-integral study of steel fiber reinforced concrete. Int J Cem Composites, 1980, 2(1)13～22.
[79] Velazco F, Visalvanich K, Shah S P. Fracture behavior and analysis of fiber reinforced concrete beams. Cem Concr Res, 1980, 10(1):41～51.
[80] Visalvanich K, Naaman A E. Fracture methods in cement composites. J Eng Mech, ASCE, 1981,107(6):1155～1171.
[81] 徐世熄、赵国藩，大试件断裂韧度和高混凝土坝裂缝评定的断裂准则，大连理工大学学报，1988
[82] 徐世娘、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
[83] 吴智敏、赵国藩、徐世烺，大尺寸混凝土试件的断裂韧度，水利学报，1997，6：67～70
[84] Rashid Y R. Analysis of prestressed concrete pressure vessel. 1968, 7(4):334～344.
[85] Hillerborg A, Modeer M, Petersson P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res, 1976, 6(6):773～782
[86] Petersson P E. Fracture energy of concrete: method of determination. Cem Concr Res, 1980, 10(1):78～89
[87] Petersson P E. Fracture energy of concrete: practical performance and experiment. Cem Concr Res, 1980, 10(1):91～101
[88] Bazant Z P, Cedolin L. Blunt crack band propagation in finite element analysis. J Eng Mech Div, ASCE, 1979, 105(EM6):297～315
[89] Wecharatana M, Shah S P. Prediction of nonlinear fracture process zone in concrete. J Eng Mech Div, ASCE, 1983, 109(5):1231～1246
[90] Jenq Y S, Shah S P. A fracture toughness criterion for concrete. Eng Fract Mech, 1985, 21(5):1055～1069
[91] Jenq Y S, Shah S P. Two parameter fracture model for concrete. J Eng Mech, ASCE, 1985, 111(10):1227～1241
[92] 徐道远、符晓陵、朱为玄、等，坝体混凝土损伤—断裂模型，大连理工大学学报，1997，37(增刊)：1～6
[93] 冯伯林、徐道远、周先贵、等，温度荷载作用下拱坝裂缝的断裂力学分析方法，合肥工业大学学报(自然科学版)，2000，23(6)：1003～1008
[94] 张镜剑、涂金良、翟奇愚、等，龙滩碾压混凝土重力坝水平层面稳定安全的断裂分析，华北水利水电学院学报，1996，17(4)：2～7
[95] 杨延毅，混凝土损伤断裂过程研究，浙江大学学报，1993，5：654～661
[96] 孙静、李守义、杨菊生，高拱坝三维非线弹性损伤破坏分析，岩石力学与工程学报，2001(增2)：1358～1361
[97] 吴胜兴，混凝土裂缝开展宽度计算的有限元法，计算力学学报，1997，14(1)：69～77
[98] 巫昌海、汪基伟、夏颂佑，混凝土三维非正交弥散裂缝模型，河海大学学报，1999，27(5)：17～20
[99] 岑章志、秦飞，损伤分析的边界元法，第四届全国工程中的边界元法会议论文集，南京：河海大学出版社，1994
[100] Zhang G X, Sugiura Y, Hasegawa H. Fracture simulation using manifold and singular boundary element method. J Geotech Eng, JSCE, 1999, 624/Ⅲ—47:1～10
[101] 栾茂田、黎勇、林皋，非连续变形计算力学模型及其在有缝重力坝静力分析中的应用，水利学报，2001，4：40～45
[102] 寇晓东、周维垣，应用无单元法近似计算拱坝开裂，水利学报，2000，10：28～35
[103] 陈予恕、唐云、等，非线性动力学中的现代分析方法，北京：科学出版，1992
[104] Lorenz E. Deterministic nonperiodic flow. J Atmos Sci, 1963, 20:130～141
[105] Ruelle D, Takens F. On the nature of turbulence. Commum Math Phys 1971, 20(1)
[106] Li T Y, Torke J A. Period three implies chaos. Am Math Monthly, 1975,82
[107] May R. Simple mathematical models with very complicated dynamics. Nature, 1976, 261
[108] Feigenbaum M J. Quantitative universality for a class of nonlinear transformation. J Stat Phys. 1978, 19(1)
[109] Packard N H, Grutchfield J P, Farmer J D, et al. Geometry from a time series. Plays Rev Lett, 1980,45:712～716
[110] Takens F. Detecting strange attractors in turbulence. In: Dynamical systems and turbulence. Lecture Notes in Mathematics, 1981,898:245～262
[111] Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physica D, 1983, 9:189～208
[112] Grassberger P, Procaccia I. Characterization of strange attractors. Phys Rev Lett, 1983, 50:346～349
[113] Wolf A, Swift J B, Swinney H L, et al. Determining Lyapunov exponents from a time series. Physica D, 1985, 16:285～317
[114] Farmer J D, Sidorowich J J. Predicting chaotic time series. Phys Rev Lett, 1987, 59(8):845～848
[115] 丁晶、邓育仁、傅军，洪水相空间预报，成都科技大学学报，1995，85(4)：7～11
[116] 叶中行、龙如军，混沌时间序列的区间预测，上海交通大学学报，1997，31(2)：7～12
[117] 梁志珊、王丽敏、付大鹏，基于Lyapunov指数的电力系统短期负荷预测，中国电机工程学报，1998，18(5)：368～371
[118] 温权、张勇传、张周胜，基于混沌动力学的日径流时间序列预测，华中理工大学学报，1998，26(12)：62～64
[119] 汪树玉、刘国华、杜王盖、等，大坝观测数据序列中的混沌现象，水利学报，1999，7：22～26
[120] 康玲、王乘，混凝土坝裂缝混沌特性的初步研究，水电能源科学，2000，18(1)：19～21
[121] 徐洪钟、单泰松、吴中如，大坝观测数据的模糊神经网络分析，大坝观测与土工测试，2001，25(3)：17～22
[122] 张乾飞、徐洪钟、吴中如、等，基于模糊聚类的神经网络模型及其在渗流分析中的应用，水力发电学报，2002，2：37～43
[123] 苏怀智、吴中如、温志萍、等，基于模糊联想记忆神经网络的大坝安全监控系统建模研究，武汉大学学报(工学版)，2001，34(4)：21～24
[124] 郭海庆、吴中如、张乾飞，渗透系数反演的CHNN模型方法，长江科学院院报，2001，18(3)：25～28
[125] 赵斌、吴中如、张爱玲，BP模型在大坝安全监测预报中的应用，大坝观测与土工测试，1999，23(6)：1～4
[126] 李雪红、徐洪钟、顾冲时、等，主成分神经网络模型在大坝观测资料分析中的应用，大坝观测与土工测试，2001，25(5)：14～16
[127] 陈继光等，土坝观测数据的模糊人工神经网络分析，水利学报，2000，1：19～21
[128] 李守巨、刘迎曦、王登刚、等，基于神经网络的岩体渗透系数反演方法及其工程应用，岩石力学与工程学报，2002，21(4)：479～483
[129] Mandelbrot B B. The fractal geometry of nature. San Francisco, CA: W.H. Freeman and Company, 1983
[130] Mandelbrot B B, Passoja D E, Paullay A J. Fractal character of fracture surfaces of metals. Nature,
1984, 308:721～722
[131] Lopez J M, Schmittbuhl J. Anomalous scaling of fracture surfaces. Phys Rev. E, 1998, 57(6): 6405～6408
[132] Issa M A, Hamnad A M. Assessment and evaluation of fractal dimension of concrete fracture surface digitized images. Cem Concr Res, 1994, 24 (2): 325～334
[133] Xie H P, Wang J A, Stein E. Direct fractal measurement and multifractal properties of fracture surfaces. Phys Lett A, 1998, 242:41～50
[134] 吴科如、张东，混凝土断裂面三维重构，建筑材料学报，1999，2(3)
[135] Chen Z, Mecholsky J J, Joseph T, et al. The fractal geometry of Si_3N_4 wear and fracture surfaces.J Mater Sci, 1997, 32:6317～6323
[136] Hill T J, Mecholsky J J, Anusavice K J. Fractal analysis of toughening behavior in 3BaO. 5SiO_2 glass-ceramics. J Am Ceram Soc, 2000, 83 (3): 545～552
[137] Saouma V E, Barton C C, Gamaleldins N A. Fractal characterization of fracture surfaces in concrete. Eng Fract Mech, 1990, 35 (1): 47～53
[138] Issa M A, Hammad A M. Fractal characterization of fracture surfaces in mortar. Cem Coner Res, 1993, 23:7～12
[139] Saouma V E, Barton C C. Fractals, fractures and size effects in concrete. J Eng Mech, ASCE, 1994,120(4):835～853
[140] Dougan L T, Addison P S. Fractal analysis of fracture: a comparison of dimension estimate. Mech Res Comum, 2000, 27 (4): 383～392
[141] Issa M A, Hammad A M, Islam M S, et al. Fractal dimension-a measure of fracture roughness and toughness of concrete. Eng Fract Mech 2003, 70:125～137
[142] Pande C S, Richards L R, Smith S. Fractal characteristics of fractured surfaces. J Mater Sci Lett 1987, 6:295～297
[143] Dougan L T, Addison P S. Estimating the cut-off in the fractal scaling of fractured concrete. Cem Concr Res, 2001, 31:1043～1048
[144] Dubuc B, Quiniou J F, Roques C, et al. Evaluating the fractal dimension of profiles. Phy Rev A, 1989, 39(3):1500～1512
[145] Morel S, Bouchard E, Schmittbuhl J. R-cuve behavior and roughness development of fracture surfaces. Int J Fract, 2002, 114:307～325
[146] Su H, Zhang Y, Yan Z. Fractal analysis of microstructures and properties in ferrite-martensite steels. Scripta Metall Mater 1991, 25:651～554
[147] Wang Z G, Chen D L, Jiang X X, et al. Relationship between fractal dimension and fatigue threshold value in dual-phase steels. Scripta Met 1988, 22:827～832
[148] Mecholsky J J, Passoja D E, Feinberg-Ringel K S. Quantitative analysis of brittle fracture surfaces using fractalgeometry. J Am Ceram Soc 1989, 72(1):60～65
[149] Balankin A S, Bravo-Ortega A, Galicia-Cortes M A, et at. Size effect of self-affine roughness on crack mechanics in solids. Int J Fract, 1996, 79:R63～R68
[150] Bouchard E. Fractal dimension of fractured surfaces: a universal value? Europhys Lett 1990, 13(1):73～79
[151] Mu ZQ, Lung CW, Kang Y, Long QY. Perimeter-maximum method for measuring the fractal dimension of a fractured surface. Phys Rev B, 1993, 48(10):7679～7681
[152] 董连科，分形理论及其应用，沈阳：辽宁科学技术出版社，1991
[153] 谢和平，分形—岩石力学导论，北京：科学出版社，1997
[154] 潘家铮，世界上没有无裂缝的水坝，中国三峡建设，2002，4：6～7
[155] 朱伯芳，大体积混凝土温度应力与温度控制，北京：中国电力出版社，1999
[156] 何涛，混凝土常见裂缝的探讨，建材研究与应用，2002，4：56～57
[157] 赵杰，混凝土结构裂缝及其防治，电力建设，2000，2：40～42
[158] 卓文仁，混凝土结构裂缝探讨分析，水利科技，2002，2：43～44
[159] 王象文、邱文恒、吕刚，混凝土开裂原因与防治措施，科技情报开发与经济，1997，6：40～41
[160] 徐世烺，混凝土断裂韧度的概率统计分析，水利学报，1984，10：51～58
[161] Browand F K. The structure of the turbulent mixing layer. Physica D, 1986(18):135～148
[162] 苏怀智，大坝安全监控感知融合理论和方法及应用研究，河海大学博士学位论文，2001
[163] 徐洪钟，大坝动力系统的安全监控非线性分析模型研究，河海大学博士学位论文，2001
[164] 帕利斯、梅罗，动力系统几何理论引论，陈藻平译，北京：科学出版社，1988
[165] Devaney R L. An introduction to chaotic dynamic systems. California: Addison-Wesley, 1989
[166] 卢侃、孙建华、欧阳容白、等，混沌动力学，上海：上海翻译出版公司，1990
[167] 陈予恕、唐云、等，非线性动力学中的现代分析方法，北京：科学出版，1992
[168] 黄润生，混沌分形及其应用，武汉：武汉大学出版社，2000
[169] 王东生、曹磊，混沌分形及其应用，合肥：中国科学技术大学出版社，1995
[170] Tsonis AA. Chaos From theory to application. New York: Plenum Press, 1992
[171] 黄胜伟，工程结构混沌振动、混沌最优化算法及其应用，河海大学博士论文，2002
[172] Sauer T, Yorke J A, Casdagli M. Embedology. J Stat Phys, 1991, 65:579～616
[173] Sauer T, Yorke J A. How many delay coordinates do you need. Int J Bifurcation and Chaos, 1993, 3:737～741
[174] Broomhead D S, King G P. Extracting qualitative dynamics from experimental data. Physica D,1986, 20:217～236
[175] Casdagli M, Eubank S, Farmer J D, et al. State space reconstruction in the presence of noise.Physica D, 1991, 51:52～98
[176] 赵永龙、丁晶、邓育仁，混沌分析在水文预测中的应用和展望，水科学进展，1998，9(2)：181～186
[177] Fraser A M, Swinney H L. Independent coordinates for strange attractors from mutual information. Phys Rev A, 1986, 33(2):1134～1140
[178] Liebert W, Schuster H G. Proper choice of the time delays for the analysis of chaotic time series. Phys Lett A, 1989, 142:107～111
[179] Kugiumtzis D. State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length. Physica D, 1996, 95:13～28
[180] Kim H S, Eykholt R, Salas J D. Nonlinear dynamic, delay times, and embedding windows. Physica D, 1999, 127:48～60
[181] 吕金虎、陈君安、陈士华，混沌时间序列分析及其应用，武汉：武汉大学出版，2002
[182] Grebogi C, Ott E, Yorke J A. Crises, sudden changes in chaotic attractors and transient chaos. Physica D, 1983, 7
[183] Provenzale A, Smith L A, Vio R, et al. Distinguishing between low-dimensional dynamics and randomness in measured time series. Physica D, 1992, 58:31～49
[184] Greenside H S, Wolf A., Swift J B, et al. The impracticability of a box-counting algorithm for calculating the dimensionality of strange attractors. Phys Rev A, 1982, 25:3453～3456
[185] Theiler J. Spurious dimension from correlation algorithms applied to limited time series data.
Phys Rev A, 1986, 34(3):2427～2431
[186] Eckman J P, Kamphorst S O, Ruelle D, et al. Lyapunov exponent from time series. Phys Rev A,1986, 34(4):4971～4980
[187] Abarbanel H D I, Brown R, Kadtke J B. Prediction in chaotic systems: methods for time series with broadband Fourier spectra. Phys Rev A, 1990, 41 (2):1782～1807
[188] Benettin G, Galgani L, Strelcyn J M. Kolmogorov entropy and numerical experiments. Phys Rev A, 1976, 14(6):2338～2345
[189] Nicolis J S, Meyer-Kress G, Hallbs G. Non-uniform information processing by strange attractors of chaotic maps and flows. In: Stochastic phenomena and chaotic behavior of complex systems, Berlin: Springer-Verlag, 1984:124～139
[190] Kantz H. A robust method to estimate the maximal Lyapunov exponent of a time series. Phys Lett A, 1994, 185:77～87
[191] Kantz H, Schreiber T, Nonlinear time Series analysis. Cambridge: Cambridge University Press, 1997
[192] Rosenstein M T, Collins J J, De Luca C J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D, 1993, 65:117～134
[193] Grassberger P, Procaccia I. Estimation of the Kolmogorov entropy from a chaotic signal. Phys Rev A, 1983, 28(4):2591～2593
[194] 邓昌铁，意大利水电站大坝安全监控概况，河海大学科技情报，1989，9(2)：32～42
[195] 章书寿、吴中如、华锡生，葡萄牙大坝安全监测与模型试验技术综述，河海大学科技情报，1989，9(2)：8～15
[196] 彭虹，法国大坝安全监测的新进展，河海大学科技情报，1989，9(2)：16～31
[197] 张进平，大坝监测数学模型因子集的扩充，大坝观测与土工测试，1999，23(2)：1～4
[198] Tremmel E. Analysis of pendulum measurements. 6th ICOLD, Q.21, R. 15, 1958, New York
[199] 包腾飞、吴中如、顾冲时、等，基于统计模型与混沌理论的大坝安全监测混合预测模型，河海大学学报(自然科学版)，2003，31(5)：534～538
[200] Wells A A. Application of fracture mechanics and at beyond general yielding. British Welding Journal, 1963, 10(10):563～570
[201] GB／T2358-94，金属材料裂纹尖端张开位移试验方法
[202] JB／T4291-1999，焊接接头裂纹张开位移(CTOD)试验方法
[203] BS7448-1 1991, Method for Determination of K_(Ic), Critical CTOD and Critical J Values of Metallic Materials
[204] BS7448-2 1997, Method for Determination of K_(Ic), Critical CTOD and Critical J Values of Welds in Metallic Materials.
[205] ASTME 1290-99, Standard Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement.
[206] Visalvanich K, Naaman A E. Fracture methods in cement composites. J Eng Mech, ASCE, 1981,107(6):1155～1171.
[207] 徐世烺、赵国藩，混凝土裂缝稳定扩展过程与临界裂缝尖端张开位移，水利学报，1989，4：33～44
[208] 徐世烺、赵国藩，混凝土断裂力学研究，大连：大连理工大学出版社，1991
[209] 吴智敏、赵国藩，混凝土裂缝扩展的CTOO_c准则，大连理工大学学报，1995，35(5)：699～702
[210] 吴智敏、王金来、徐世烺、刘毅，基于虚拟裂缝模型的混凝土等效断裂韧度，工程力学，2000，17(1)：99～104
[211] 于骁中、张玉美、郭桂兰，混凝土断裂能G_F，水利学报，1987，7：30～37
[212] Farmer J D, Sidorowich J J. Predicting chaotic time series. Phys Rev Lett, 1987, 59(8):845～848
[213] Casdagli M. Nonlinear prediction of chaotic time series. Physica D, 1989, 35:335～356
[214] 吴宗敏，函数的径向基表示，数学进展，1998，27(3)：202～208
[215] Floater M S, Iske A. Multistep scattered data interpolation using compactly supported radial basis functions. J Comput Appl Math, 1996, 73:65～78
[216] Wendland H. Piecewise polynomial, positive definite and compactly supported redial basis functions of minimal degree. Adv Comput Math, 1995, 4:389～396
[217] Wu Z M. Multivariate compactly supported positive definite radial functions. Adv Comput Math, 1995, 4:283～292
[218] 吴宗敏，径向基函数、散乱数据拟合与无网格偏微分方程数值解，工程数学学报，2002，19(2)：1～12
[219] 林振山，长期预报的相空间理论和模式，北京：气象出版社，1993
[220] 蒋传文，电力负荷预报理论及新方法的研究，华中理工大学博士学位论文，1999
[221] 吴中如、顾冲时，大坝安全综合评价专家系统，北京：北京科学技术出版社，1997
[222] 吴中如、顾冲时，大坝原型反分析及其应用，南京：江苏科学技术出版，2001
[223] 包腾飞、郑东健、郭海庆，新安江大坝典型坝(?)坝顶水平位移监控指标的拟定，水利水电技术，2003，34(3)：46～49
[224] 孙芳垂、陈星焘、胡世平，工程规划中的概率(?)念，北京：冶金工业出版社，1985
[225] 吴世伟，结构可靠度分析，北京：人民交通出版社，1990
[226] 方开泰，统计分布，北京：科学出版社，198
[227] Eckmann J P, Rulle D. Ergodic theory of cha and strange attractors. Rev Mod Phys, 1985, 57:617～653
[228] Evans R.H, Marathe M S. Microcracking and stess-strain curve for concrete in tension. Mateiauxet constructions, 1968, 1 (1):61～464
[229] Crepon O, Michel. An analytical approach to monitoring. International Water Power & Dam Construction, 1999, 51 (6):52～54
[230] 舒仲周、张继业、曹登庆，运动稳定性，北京：中国铁道出版，2001
[231] 刘思峰、郭天榜、党耀国、等，灰色系统理论及其应用，北京：科学出版社，1999
[232] 邓聚龙，灰色控制系统，武汉：华中工学院出版，1987
[233] 黄建平、衣育红，利用观测资料反演非线性动力模型，中国科学B辑，1991，3：331～336
[234] 杨文采，非线性地震道的混沌反演——Ⅰ、Ⅱ，地球物理学报，1993，36(2)：222～232，36(3)：376～386
[235] 吴中如、潘卫平，应用李雅普诺夫函数分析岩土边坡的稳定性，水利学报，1997，8：29～33
[236] 秦元勋、王慕秋、王联，运动稳定性理论与应用，北京：科学出版，1981
[237] 王照林，运动稳定性及其应用，北京：高等教育出版，1992
[238] Thom R，结构稳定性与形态发生学，成都：四川教育出版社，1992
[239] Saunders P T. An introduction to catastrophe theory. Cambridge University Press, 1980
[240] 程学军、蔡美峰、李长洪，灰色突变模型及其在声发射监测预报中的应用，中国矿业，1997，6(2)：37～39
[241] 凌复华，突变理论及其应用，上海：上海交通大学出版社，1987
[242] Wecharatana M, Shah S P. Double torsion tests for studying slow crack growth of Portland cement
mortar. Cem Concr Res, 1980, 10(6):833～844
[243] 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
[244] 于骁中、居襄、曹建国，单支墩大头坝劈头裂缝稳定性分析，水利学报，1981，1：30～37
[245] 赵中极，重力坝坝面和坝踵水平裂缝的断裂力学分析，水利学报，1982，6：11～19
[246] 河海大学，佛子岭连拱坝资料分析报告，南京：河海大学，1986
[247] 河海大学，陈村水电站原型观测资料及结构正反分析报告，南京：河海大学，2002
[248] 河海大学，龙羊峡重力拱坝监测资料分析及裂缝成因与稳定分析，南京：河海大学，2002
[249] Hornik K, Stinchcombe M, White H. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks, 1990, 3:551～560
[250] 沈清、胡德文、时春，神经网络应用技术，长沙：国防科技大学出版社，1998
[251] 从爽，面向Matlab工具箱得的神经网络理论与应用，合肥：中国科技大学出版社，1998
[252] 徐道远、符晓陵，断裂力学，南京：河海大学研究生教材，1981
[253] 朱伯芳，有限单元法原理与应用，北京：中国水利水电出版社，2000
[254] 王旭、王宏、王义辉，人工神经元网络原理与应用，沈阳：东北大学出版社，2000
[255] 李学桥、马莉，神经网络工程应用，重庆：重庆大学出版社，1996
[256] 王小平、曹立明，遗传算法—理论、应用与软件实现，西安：西安交通大学出版社，2002
[257] 李兵、蒋慰孙，混沌优化方法及应用，控制理论及应用，1997，14(4)：613～615
[258] 雷德明，利用混沌搜索全局最优解的一种混合遗传算法，系统工程与电子技术，1999，21(12)：81～82
[259] Panagiotopoulos P D. Fractal geometry in solids and structures. Int J Sol Struct 1991, 29:2151～2175
[260] Panagiotopoulos P D, Mistakidis E S, Panagouli O K. Fractal interfaces with unilateral contact and friction conditions. Comput Meth Appl Mech Eng, 1992, 99: 395～412.
[261] Barnsley M. Fractals everywhere. Boston: Academic press, 1988
[262] Wallin H. The trace to the boundary of Sobolev spaces on a snowflake [R] .Rep Dep Math Univ Umea, 1989
[263] Adams R A，索伯列夫空间，叶其孝、王耀东、应隆安、等译，北京：人民教育出版社，1981
[264] Theocaris P S, Panagiotopoulos P D. Cracks of fractal geometry with unilateral contact and friction interface conditions. Int J Fract 1993, 60:293～310.
[265] Panagouli O K, Mistakidis E S, Panagiotopoulos P D. On the fractal fracture in brittle structures: Numerical approach. Comput Meth Appl Mech Eng, 1997,147:1～15
[266] Mistakidis E S. Fractal geometry in structural analysis problems: a variational formulation for fractured bodies with non-monotone interface conditions. Chaos, Solitons and Fractals 1997, 8(2):269～285
[267] Underwood E, Banerji K. Fractals in fractography. Mater Sci Eng, 1986, 80(1):1～14
[268] Falconer K. Fractal geometry: Mathematical foundations and applications. Chichester: John Wiley and Sons, 1990
[269] Balankin A S. Physics of fracture and mechanics of self-affine cracks. Eng Fract Mech, 1997, 57(2-3):135～203
[270] Mandelbrot B B, Passoja D E, Paullay A J. Fractal character of fracture surfaces of metals. Nature, 1984, 308:721～722
[271] Schmittbuhl J, Roux S, Berthand Y. Development of roughness in crack propagation. Europhys Lett, 1994, 28:585～590
[272] Mecholsky J J, Mackin T J. Fractal analysis of fracture in Ocala chert. J Mater Sci Lett, 1988, 7:1145～1147
[273] Bouchard E, Lapasset G, Planes J, et al. Stastics of brauched fracture surface. Phys Rev B, 1993, 48:2917～2928
[274] Daguier P, Henanx S, Bouchard E, et al. Quantitative analysis of a fractal surface by atomic force microscopy. Phys Rev E, 1996, 53:5673～5642
[275] Daguier P, Nghiem B, Bouchaud E, et al. Pinning and depinning of crack fronts in heterogeneous materials. Phys Rev Lett, 1997, 78:1062～1065
[276] Morel S, Schmittbuhl J, Lopez J M. Anomalous roughening of wood fracture surface. Phys Rev E, 1998, 58 (6): 6999～7005
[277] 刘小艳，混凝土轴拉试件的应力—应变全曲线研究及其断裂面分析，南京：河海大学硕士论文，2002
[278] Borodich F M. Some fractal models of fracture. J Mech Phys Solids, 1997, 45 (2) :239～259
[279] Borodich F M. Fractals and fractal sealing in fracture mechanics. Int J Fract, 1999, 95:239～259
[280] Borodich F M. Self-similar models and size effect of multiple fracture. Fractals, 2001, 9 (1) :17～30
[281] Mosolov A B. Fractal Griffiths cracks. Zh Tekh Fiz SSSR, 1991, 61:57～60
[282] Gol'dshtein R V, Mosolov A B. Cracks with a fractal surface. Dokl Akad Nauk SSSR, 1991, 319:840～844
[283] Gol'dshtein R V, Mosolov A B. Fractal cracks. Prikl Mat Mekh SSSR, 1992, 56(4):663～671
[284] Mosolov A B, Borodich F M. Fractal fracture of brittle bodies during compression. Dokl Akad Nauk SSSR, 1992, 324:546～549
[285] Xie H, Sanderson D J. Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities. Int J Fract, 1995, 74:29～42
[286] Yavari A, Sarkani S, Moyer E T. The mechanics of self-similar and self-affine fractal cracks. Int J Fract, 2002, 114:1～27
[287] Yavari A, Sarkani S, Moyer E T On fractal cracks in micropotar elastic solids. J Appl Mech, ASCE 2002, 69 (1):45～54
[288] Voss R F. Random fractals: characterization and measurement. In: Scaling phenomena in disordered systems. Ed. Punn R and Skjeltorp A, New York: Plenum, 1985, pp1～11