定侧压下混凝土三轴疲劳性能试验与理论研究
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摘要
混凝土结构的疲劳是一个广为关注的问题，本文针对这一问题结合国家自然科学基金项目——混凝土多轴变幅疲劳破坏准则(50078010)的研究，利用自制的试验加载装置完成了两向定侧压约束下混凝土三轴受压、三轴拉-压等幅和变幅疲劳试验，对试验结果进行了分析。并在此基础上确定了疲劳变形定量化规律和疲劳强度计算方法；比较全面深入地描述了混凝土多轴疲劳损伤机理和劣化规律，建立了疲劳剩余寿命预测方法和疲劳本构模型，为混凝土结构的疲劳设计和分析提供了基础。本文共分如下七章：
第一章是绪论，阐述了本课题的选题背景和意义；系统地综述了混凝土疲劳试验和理论研究的当前国内外发展现状，在此基础上提出了本文的工作和内容。
第二章简要地介绍了本文三轴疲劳试验装置，进行了两向等侧压约束下混凝土立方体试件三轴受压等幅和变幅疲劳试验，分析了三轴受压疲劳破坏机理，给出了相应的疲劳破坏试验判断标准；得到了混凝土在两向侧压约束下单级和多级受压疲劳的变形发展规律，包括最大(最小)纵向应变、残余应变、最大纵向应变率和疲劳变形模量等随循环次数的发展规律以及疲劳损伤的演变规律，并给出了相应的经验公式。
第三章根据本文定侧压下三轴受压疲劳试验数据，并结合已有的单轴受压和双轴受压疲劳试验结果，建立了综合考虑侧压应力水平和疲劳应力比的统一S-N曲线方程，得到了混凝土多轴受压疲劳强度；分析了从混凝土初始极限强度概率分布出发和疲劳寿命概率分布出发来计算混凝土条件疲劳极限强度的一致性原理，从而为应用小样本常规疲劳试验结果计算条件疲劳极限强度提供了理论和方法。
第四章进行了两向等侧压约束下变截面混凝土棱柱体试件的三轴拉-压等幅和变幅疲劳试验，分析了三轴拉．压疲劳破坏机理和破坏形态；建立了综合考虑侧压应力水平和疲劳荷载的统一S-N曲线方程；得到了混凝土在两向定侧压约束下三轴拉．压疲劳变形发展规律，包括循环应力．应变特性、纵向应变、第二阶段应变率、疲劳变形模量和损伤等演变规律，并给出了相应的经验公式。
第五章综合评价了已有的各类混凝土非线性累积损伤模型的特点和适用性，并应用非线性动力学观点论证了经典Miner线性累积损伤准则在预测疲劳剩余寿命方面的固有缺陷；在考虑加载历史对疲劳寿命的影响下，建立了描述混凝土累积损伤的非线性模型；并根据损伤等效原理给出了混凝土疲劳剩余寿命的预测方法和步骤。
第六章讨论了混凝土材料静力加载和疲劳加载下的特性；在综合考虑塑性和脆性相结合的复杂性质基础上，运用损伤理论和塑性理论在应变空间分别建立了一个能描述混凝土应变和刚度变化的损伤面和塑性面，应用有效应力和弹塑性耦合的概念来描述混凝土的多轴疲劳本构特征。
第七章为结论和展望，总结了本文完成的主要成果和相应结论，指出了在本文研究基础上需要进一步开展的几个问题。
It is widely concerned in fatigue of concrete structures. In this paper, concrete triaxial compression fatigue experiments and tension-compression fatigue experiments with constant confinements in two lateral directions have been carried out using a self-modified loading apparatus. Based on the analysis of the test data, the quantitative principles of concrete fatigue deformation and the calculation method of fatigue strength are determined. Moreover, the multi-axial fatigue damage mechanics and process are discussed more extensively, and a nonlinear cumulative damage model to predict the remaining fatigue life and a constitutive model to describe concrete fatigue characteristics are established. The thesis is an important part of the project of National Natural Science Foundation-Fatigue failure criterion of concrete under multi-axial variable-amplitude fatigue loading (No. 50078010), the contents of which include seven chapters as follows.
The first chapter is preface. It expounds the significance of this study and the relevant literatures. Meanwhile the historical and present background of the research on experiment and theory of plain concrete is introduced systematically. Based on the information, the objectives of this paper are put forward.
The second chapter introduces the test system simply at first. Then an experiment is carried out on concrete cube specimens to investigate the deformation characteristics of plain concrete under triaxial constant-amplitude and variable-amplitude compression fatigue loading with constant confinement in two lateral directions. The damage mechanics under multi-axial compressive fatigue loading is analyzed and the damage criterion is determined. The deformation characteristics including the development of the maximum/minimum longitudinal strains, the residual strain, the maximum longitudinal strain creep rate, the deformation modulus and the damage cumulation of concrete in terms of cyclic number are gained. In addition, some experience formulas for them are regressed.
The third chapter establishes a unified S-N curve equation to calculate multi-axial fatigue ultimate strength of concrete considering both the effect of confinement and minimum/maximum stress ratio, based on the triaxial fatigue test data in this paper and the test results under uniaxial and biaxial fatigue loading in previous literatures. Moreover, the consistency of calculating condition fatigue ultimate strength with fatigue life distribution and initial ultimate strength distribution is analyzed. Thus the calculation of condition fatigue ultimate strength using common fatigue experiment with small samples is available.
The fourth chapter carries out the triaxial tension-compression fatigue experiments on tapered prism specimens subjected to constant-amplitude and variable-amplitude fatigue loading with constant confinement in two lateral directions. The damage mechanics and failure mode are analyzed. A unified S-N curve equation to calculate tension-compression fatigue ultimate strength of concrete is established. In addition, the deformation characteristics including the development of the cyclic stress-strain curve, the longitudinal strains, the secondary stage strain rate, the deformation modulus and the damage cumulation of concrete in terms of cyclic number are obtained.
The fifth chapter reviews the applicability and characteristics of previous nonlinear cumulative damage models synthetically, and the inherent limitation of Miner's rule on
predicting remaining fatigue life is also proofed from the point of view of the nonlinear dynamic. Taking into account of the effect of loading history, a new nonlinear cumulative damage model is established and the steps to predict remaining fatigue life with the model is given.
The sixth chapter discusses the characteristics of concrete under static and fatigue loading in detail. Considering the complicated characteristics of plasticity and brittleness, a two-surface model is established. The so-called two surfaces are a damage surface established by the co
第一章是绪论，阐述了本课题的选题背景和意义；系统地综述了混凝土疲劳试验和理论研究的当前国内外发展现状，在此基础上提出了本文的工作和内容。
第二章简要地介绍了本文三轴疲劳试验装置，进行了两向等侧压约束下混凝土立方体试件三轴受压等幅和变幅疲劳试验，分析了三轴受压疲劳破坏机理，给出了相应的疲劳破坏试验判断标准；得到了混凝土在两向侧压约束下单级和多级受压疲劳的变形发展规律，包括最大(最小)纵向应变、残余应变、最大纵向应变率和疲劳变形模量等随循环次数的发展规律以及疲劳损伤的演变规律，并给出了相应的经验公式。
第三章根据本文定侧压下三轴受压疲劳试验数据，并结合已有的单轴受压和双轴受压疲劳试验结果，建立了综合考虑侧压应力水平和疲劳应力比的统一S-N曲线方程，得到了混凝土多轴受压疲劳强度；分析了从混凝土初始极限强度概率分布出发和疲劳寿命概率分布出发来计算混凝土条件疲劳极限强度的一致性原理，从而为应用小样本常规疲劳试验结果计算条件疲劳极限强度提供了理论和方法。
第四章进行了两向等侧压约束下变截面混凝土棱柱体试件的三轴拉-压等幅和变幅疲劳试验，分析了三轴拉．压疲劳破坏机理和破坏形态；建立了综合考虑侧压应力水平和疲劳荷载的统一S-N曲线方程；得到了混凝土在两向定侧压约束下三轴拉．压疲劳变形发展规律，包括循环应力．应变特性、纵向应变、第二阶段应变率、疲劳变形模量和损伤等演变规律，并给出了相应的经验公式。
第五章综合评价了已有的各类混凝土非线性累积损伤模型的特点和适用性，并应用非线性动力学观点论证了经典Miner线性累积损伤准则在预测疲劳剩余寿命方面的固有缺陷；在考虑加载历史对疲劳寿命的影响下，建立了描述混凝土累积损伤的非线性模型；并根据损伤等效原理给出了混凝土疲劳剩余寿命的预测方法和步骤。
第六章讨论了混凝土材料静力加载和疲劳加载下的特性；在综合考虑塑性和脆性相结合的复杂性质基础上，运用损伤理论和塑性理论在应变空间分别建立了一个能描述混凝土应变和刚度变化的损伤面和塑性面，应用有效应力和弹塑性耦合的概念来描述混凝土的多轴疲劳本构特征。
第七章为结论和展望，总结了本文完成的主要成果和相应结论，指出了在本文研究基础上需要进一步开展的几个问题。
It is widely concerned in fatigue of concrete structures. In this paper, concrete triaxial compression fatigue experiments and tension-compression fatigue experiments with constant confinements in two lateral directions have been carried out using a self-modified loading apparatus. Based on the analysis of the test data, the quantitative principles of concrete fatigue deformation and the calculation method of fatigue strength are determined. Moreover, the multi-axial fatigue damage mechanics and process are discussed more extensively, and a nonlinear cumulative damage model to predict the remaining fatigue life and a constitutive model to describe concrete fatigue characteristics are established. The thesis is an important part of the project of National Natural Science Foundation-Fatigue failure criterion of concrete under multi-axial variable-amplitude fatigue loading (No. 50078010), the contents of which include seven chapters as follows.
The first chapter is preface. It expounds the significance of this study and the relevant literatures. Meanwhile the historical and present background of the research on experiment and theory of plain concrete is introduced systematically. Based on the information, the objectives of this paper are put forward.
The second chapter introduces the test system simply at first. Then an experiment is carried out on concrete cube specimens to investigate the deformation characteristics of plain concrete under triaxial constant-amplitude and variable-amplitude compression fatigue loading with constant confinement in two lateral directions. The damage mechanics under multi-axial compressive fatigue loading is analyzed and the damage criterion is determined. The deformation characteristics including the development of the maximum/minimum longitudinal strains, the residual strain, the maximum longitudinal strain creep rate, the deformation modulus and the damage cumulation of concrete in terms of cyclic number are gained. In addition, some experience formulas for them are regressed.
The third chapter establishes a unified S-N curve equation to calculate multi-axial fatigue ultimate strength of concrete considering both the effect of confinement and minimum/maximum stress ratio, based on the triaxial fatigue test data in this paper and the test results under uniaxial and biaxial fatigue loading in previous literatures. Moreover, the consistency of calculating condition fatigue ultimate strength with fatigue life distribution and initial ultimate strength distribution is analyzed. Thus the calculation of condition fatigue ultimate strength using common fatigue experiment with small samples is available.
The fourth chapter carries out the triaxial tension-compression fatigue experiments on tapered prism specimens subjected to constant-amplitude and variable-amplitude fatigue loading with constant confinement in two lateral directions. The damage mechanics and failure mode are analyzed. A unified S-N curve equation to calculate tension-compression fatigue ultimate strength of concrete is established. In addition, the deformation characteristics including the development of the cyclic stress-strain curve, the longitudinal strains, the secondary stage strain rate, the deformation modulus and the damage cumulation of concrete in terms of cyclic number are obtained.
The fifth chapter reviews the applicability and characteristics of previous nonlinear cumulative damage models synthetically, and the inherent limitation of Miner's rule on
predicting remaining fatigue life is also proofed from the point of view of the nonlinear dynamic. Taking into account of the effect of loading history, a new nonlinear cumulative damage model is established and the steps to predict remaining fatigue life with the model is given.
The sixth chapter discusses the characteristics of concrete under static and fatigue loading in detail. Considering the complicated characteristics of plasticity and brittleness, a two-surface model is established. The so-called two surfaces are a damage surface established by the co
引文
[1] ACI Committee 215. Considerations for design of concrete structures subjected to fatigue loading[J]. ACI Journal, 1974,71 (3):97-121
[2] CEB欧洲国际混凝土委员会．1990年CEB-FIP模式混凝土结构规范[S]．北京，中国建设科学研究院建筑结构研究所，1989．12
[3] Det Norske Veritas. Rules for classification of fixed offshore installation structures[S]. Part 3, Chapter 1, Structural Design, July 1989
[4] GB50216-94．铁路工程结构可靠度设计统一标准[S]．北京，中国计划出版社，1994
[5] GB50010-2002．混凝土结构设计规范[S]．北京，中国建筑工业出版社，2002
[6] 混凝土疲劳专题组．混凝土受弯构件疲劳可靠性验算方法的研究[M]．北京，中国建设工业出版社，1994
[7] 中华人民共和国国家标准TBJ-85．铁路桥涵设计规范[S]．北京，中国铁道出版社，1985
[8] British Standards Institution. Steel, concrete and composite bridges[S]. BS5400: Pt. 5-10, 1978-83
[9] 36-RDL report. Long term random dynamic loading of concrete structures[J]. Matedaux et Constructions, 1984,17(97): 1-13
[10] Considere.M. Influence des armatures metalligues sur les proprietes des mortiers et betons[J]. Compte Rendu de l'academie Des Sciences, 1898, 127:992-995
[11] De Joly. La resistance et l'elastic des ciments porland[J]. Annales Des Ponts et Chausses, Memoires, 1898,16(7): 198-244
[12] Van Ornum J.L. Fatigue of cement products[J]. Transactions, ASCE, 1903,51,443
[13] Clemmer H.E. Fatigue of concrete[J]. Proceeding, ASTM, 1922,22(Part Ⅱ): 408-419
[14] Graf O. and Brenner E.. Experiments for investigating the resistance of concrete under often repeated compression loads. 1[J]. Bulletin, Deutscher Ausschuss fur Stahlbeton, Berlin, 1934,1 (76): 17-25
[15] Graf O. and Brenner E.. Experiments for investigating the resistance of concrete under often repeated compression loads.2[J]. Bulletin, Deutscher Ausschuss fur Stahlbeton, Berlin, 1936,2(83):45-53
[16] Gray.W., Mclaughlin.J.F and Antrim.J.C. Fatigue propertities of lightweight aggregate concrete[J]. ACI Journal, 1961:149-161
[17] Murdock J.W.. A critical review of research on fatigue of plain concrete[P]. Engineering Experiment Station Bulletin, 1965, No.475:25
[18] Bennett E. W. and Muir S.E.J.. Some fatigue tests on high-strength concrete in axial compression[J]. Magazine of Concrete Research, 1967,19(59):113-117
[19] N. K. Raju. Comparative study of the fatigue behavior of concrete, motar and paste in uniaxial compression[J]. ACI Journal, 1970,67:461-463
[20] Aas-Jakobsen K.. Fatigue of concrete beams and columns[J]. Bulletin No.70-1. NTH Institute for Betonkonstruksjoner, 1970.9
[21] Ralejs Tepfers and Thomas Kutti. Fatigue strength of plain, ordinary, and lightweight concrete[J]. ACI Journal, 1979(5): 635-653
[22] Matsushita H. and Tokumitsu Y.. A study on compressive fatigue strength of concrete considered survival probability[J]. Proceeding of J SCE, 1972, 198:127-138
[23] Thomas T.C.Hsu. Fatigue of plain concrete[J]. ACI Journal, 1981(2):292-305
[24] Petkovic G, Lenschow R, Stemland H. and Rosseland S.. Fatigue of high-strength concrete[J]. ACI, Special Publication, SP-121-25, 1991:505-525
[25] 姚明初．混凝土在等幅和变幅重复应力下疲劳性能的研究，铁道部科学研究院报告，1990
[26] Jin-Keun Kim and Yun-Yong Kim. Experimental study of the fatigue behavior of high strength concrete[J]. Cement and Concrete Research, 1996,26(10): 1513-1523
[27] C.P.Whaley and A.M.Neville. Non-elastic deformation of concrete under cyclic compression[J]. Magazine of Concrete Research, 1973,25(84): 145-154
[28] P.R.Sparks and J.B.Menzies. The effect of rate of loading upon the static and fatigue strengths of plain concrete in compression[J]. Magazine of Concrete Research, 1973,25(83):73-80
[29] P.R.Sparks. The influence of rate of loading and material variability on the fatigue characteristics of concrete[J]. ACI Publication SP-75, 1982:331-343
[30] Jan Ove Holmen. Fatigue of concrete by constant and variable amplitude loading[J]. Fatigue Strength of Concrete Structures, SP-75 ACI, 1982:71-110
[31] 欧进萍，林燕清．混凝土疲劳损伤的强度和刚度衰减试验研究[J]．哈尔滨建筑大学学报，1998，31(4)：1-7
[32] 欧进萍，林燕清．混凝土高周疲劳损伤的性能劣化试验研究[J]．土木工程学报，1999,32(5)：15-21
[33] 吴佩刚，赵光仪，白利明．高强混凝土抗压疲劳性能研究[J]．土木工程学报，1994，27(3)：33-40
[34] 王瑞敏，赵国藩，宋玉普．混凝土的受压疲劳性能研究[J]．土木工程学报，1991，24(4)：38-47
[35] 李朝阳，宋玉普，赵国藩．混凝土疲劳残余应变性能研究[J]．大连理工大学学报，2001，41(3)：355-358
[36] 王时越，张立翔，徐人平．弹性模量对混凝土疲劳性能的影响[J]．昆明理工大学学报，2001，26(5)：18-20，25
[37] Raithby K.D. and Galloway J.W.. Effects of moisture condition, age and rate of loading on fatigue of plain concrete[J]. Fatigue of Concrete, SP-41, American Concrete Institute, Detroit, 1974,15-34
[38] 邓宗才．轻质高强混凝土抗压疲劳特性的研究[J]．建筑技术开发，1996，5：27-29
[39] 周新刚，吴江龙．高温后混凝土轴压疲劳性能初探[J]．工业建筑，1996，26(5)：33-35
[40] Miroslaw Grzybowski and Christian Meyer. Damage accumulation in concrete with and without fiber reinforcement[J]. ACI Materials Journal, 1993, 90(6):594-604
[41] Handong Yan, Wei Sun and Huisu Chen. The effect of silica fume and steel fiber on the dynamic mechanical performance of high-strength concrete[J]. Cement & Concrete Research, 1999, 29:423-426
[42] 鞠杨，樊承谋．循环载荷作用在钢纤维混凝土的损伤及演化行为的定量描述[J]．工程力学，1998，15(1)：94-104
[43] 鞠杨，樊承谋，潘景龙．变幅疲劳荷载下钢纤维混凝土的损伤演化行为研究[J]．实验力学，1997，12(1)：99-118
[44] 鞠杨，樊承谋，潘景龙．钢纤维混凝土疲劳损伤行为研究[J]．工业建筑，1997,27(3)：38-42，62
[45] Rafeeq A.S., Ashok G. and Krishnamoorthy S.. Influence of steel fibers in fatigue resistance of concrete in direct compression[J]. Journal of Materials in Civil Engineering, 2000, 12(2): 172-179
[46] Paulo B.Cachin, Joaquim A.Figueiras and Paulo A.A. Pereira. Fatigue behavior of fiber-reinforced concrete in compression[J]. Cement & Concrete Composites, 2002, 24:211-217
[47] Jeragh A.A.. Deformation behavior of plain concrete subjected to biaxial-cyclic loading[D]. PhD
dissertation, New Mexico State University, University Park, 1978
[48] Traina L.A., and Jeragh A.A.. Fatigue of plain concrete subjected to biaxial cyclical loading[J]. ACI Publications, SP-75, 1982:217-234
[49] Oral Buyukozturk and Tsi-ming Tseng. Concrete in biaxial cyclic compression[J]. Journal of Structural Engineering, 1984, 110(3):461-476
[50] 吕培印．混凝土单轴、双轴动态强度和变形试验研究[D]．大连理工大学博士论文，2001，11
[51] 朱劲松．混凝土双轴疲劳试验与破坏预测理论研究[D]．大连理工大学博士论文，2003，9
[52] Eric C.M.Su and Thomas T.C.Hsu. Biaxial Compression fatigue and discontinuity of concrete[J]. ACI Materials Journal, 1988, 85(3): 178-188
[53] Weisu Yin and Thomas T.C.Hsu. Fatigue behavior of steel reinforced concrete in uniaxial and biaxial compression[J]. ACI Materials Journal, 1995,92(1):71-81
[54] Erik L. Nelson, Ramon 1. Carrasquillo. Behavior and failure of high-strength concrete subjected to biaxial-cyclic compression loading[J]. ACI Materials Journal, 1988, 85(3):248-253
[55] Shengrui Lan and Zhenhai Guo. Biaxial compression behavior of concrete under repeated Ioading[J],. Journal of materials in Civil Engineering, 1999, 11(2): 105-114
[56] 俞茂宏，赵均海，郑树俊等．复杂应力下混凝土疲劳强度的试验研究[J]．西安交通大学学报，1998，32(3)：89-92
[57] Kolluru V. Subtamaniam, John S.Popovics and Surendra P.Shah. Fatigue response of concrete subjected to biaxial stresses in the compression-tension region[J]. ACI Materials Journal, 1999, 96(6):663-669
[58] 揽生瑞，过镇海．定侧压下混凝土二轴受压变形特性的试验研究[J]．土木工程学报，1996，29(2)：28-35
[59] 过镇海，王传志．多轴应力下混凝土的强度和破坏准则研究[J]．土木工程学报，1991，24(3)：1-14
[60] 过镇海．混凝土的强度和变形试验基础和本构关系[M]．北京，清华大学出版社，1997
[61] P.Desayi, K.T.Sundara Raja lyengar and T.Sanjeeva Reddy. Stress-strain characteristics of concrete confined in steel spirals under repeated loading[J]. Materials and Structures, 1969, 12(71):375-383
[62] Surendra P. Shah, Apostolos Fafitis and Richard Arnold. Cyclic loading of spirally reinforced concrete[J]. Journal of Structural Engineering, 1983, 109(7): 1695-1710
[63] Tan Teng Hooi. Effects of passive confinement on fatigue properties of concrete[J]. Magazine of Concrete Research, 2000, 52(1):7-15
[64] Cheong and Hong Zeng. Stress-strain relationship for concrete confined by lateral steel reinforcement[J]. ACI Materials Journal, 2002, 99(3):250-255
[65] A.L.F.Taliercio and Gobbi. Experimental investigation on the triaxial fatigue behavior of plain concrete[J]. Magazine of Concrete Research, 1996, 48(176): 157-172
[66] A.L.F.Taliercio and Gobbi. Fatigue life and change in mechanical properties of plain concrete under triaxial deviatoric cyclic stresses[J]. Magazine of Concrete Research, 1998, 50(3):247-255
[67] A.L.F.Taliercio, M.Berra and A.Pandolfi. Effect of high-intensity sustained triaxial stresses on the mechanical properties of plain concrete[J]. Magazine of Concrete Research, 1999, 51(6):437-447
[68] Linger D.A. and Gillespie H.A.. A study of the mechnism of concrete fatigue and fracture[J]. HRB research news, 1966,No.22
[69] Tepfers Ralejs. Tensile fatigue strength of plain concrete[J]. ACI Journal, 1979, 76(8):919-933
[70] A.J.Zielinski, H.W.Reinhard and H.A.Kormeling. Experiments on concrete under repeated uniaxial impact tensile loading[J]. Material Construction and Material Structures, 1981, 14(8): 163-169
[71] Volker Slowik, Giovanni Angelo Plizzari and Victor E. Saouma. Fracture of concrete under variable amplitude fatigue loading[J]. ACI Materials Journal, 1996, 93(3):272-283
[72] D.J.Cook and P.Chindaprasirt. Influence of loading history upon the tensile properties of concrete[J]. Magazine of Concrete Research, 1981, 33(116): 154-160
[73] Saito. M and Imai.S. Direct tensile fatigue of concrete by the Ues of friction grips[J]. ACI Journal, Proceeding, 1983, 80(5):431-438
[74] Saito.M. Tensile fatigue of strength of lightweight concrete[J]. International Journal of Cement Composites and Lightweight Concrete, 1984, 6(3):143-149
[75] H.A.W.Cornelissen and H.W.Reinhardt. Fatigue of plain concrete in uniaxial tension and in alternating tension compression loading[J]. Fatigue of steel and Concrete Structures, IABSE Colloguium, 1982,273-282
[76] H.A.W.Cornelissen and H.W.Reinhardt. Uniaxial tensile fatigue failure of concrete under constant-amplitude and programme loading[J]. Magazine of Concrete Research, 1984, 36(129):216-226
[77] H.W.Reinhardt and H.A.W.Cornelissen. Post-peak cyclic behavior of concrete in uniaxial tensile and alternative tensile and compressive loading[J]. Cement and Concrete Research, 1984, 14:263-270
[78] 赵光仪，吴佩刚，詹巍巍．高强混凝土的抗拉疲劳性能[J]．土木工程学报，1993，26(6)：13-19
[79] 赵东拂．混凝土多轴疲劳破坏准则研究[D]．大连理工大学博士论文，2002，12
[80] 杨健辉．侧压下混凝土静态受拉和受拉疲劳性能研究[D]．大连理工大学博士论文，2003，4
[81] Hatt W.K. Report on experiments on extensibility of concrete[J]. Proc. 5th annual meeting, Highway Research Board, 1925, Dec. 112-118
[82] Crepps R. B. Fatigue of mortal[J]. Proc. ASTM. 1923, 23, Part Ⅱ, 329-340
[83] Tepfers R. Fatigue of plain concrete subjected to stress reversals[J]. ACI J., Special Publication, 1982,75(9): 195-215
[84] 宋玉普，吕培印．混凝土轴心拉-压疲劳性能研究[J]．建筑结构学报，2002，23(4)：36-41
[85] Williams H.A. Fatigue tests of lightweight aggregate concrete beams[J]. ACI Journal Proceedings, 1943,39(5):108-112
[86] Hilsdorf H.K. and Kesler C.E.. Fatigue strength of concrete under varying flexural stress[J]. ACI Journal, 1966,63(10): 1059-1076
[87] Hubert K.Hilsdorf and Clyde E.Kesler. Fatigue strength of concrete under varying flexural stresses[J]. Journal of the American Concrete Institute, 1966, 1060-1076
[88] Byung Hwan Oh. Cumulative damage theory of concrete under variable-amplitude fatigue loading[J]. ACI Materials Journal, 1991, 88(1):41-48
[89] A.Mor, B.C.Gerwick and W.T.Hester. Fatigue of high-strength reinforced concrete[J]. ACI Materials Journal, 1992, 89(2): 197-207
[90] X. P. Shi, T. F. Fwa and S. A. Tan. Flexual fatigue strength of plain concrete[J]. ACI Materials Journal, 1993, 90(5):435-440
[91] Bingsheng Zhang and KeruWu. Residual fatigue strength and stiffness of ordinary concrete under bending[J]. Cement and Concrete Research, 1997, 27(1): 115-126
[92] B.Zhang, D.V.Phillips and K.Wu. Further research on fatigue properties of plain concrete[J]. Magazine of Concrete Research, 1997, 49(180): 241-252
[93] B.Zhang. Relationship between pore structure and mechanical properties of ordinary concrete under bending fatigue[J]. Cement and Concrete Research, 1998, 28(5):699-711
[94] A.E.Naaman and H.Hammoud. Fatigue characteristics of high performance fiber-reinforced concrete[J].
Cement and Concrete Research, 1998, 20:353-363
[95] Seok-Goo Youn and Sung-Pil Chang. Behavior of composite brigde decks subjected to static and fatigue loading[J]. ACI Structural Journal, 1998, 95(3):249-258
[96] 李永强，车惠民．混凝土弯曲疲劳累积损伤性能研究[J]，中国铁道科学，1998，19(2)：52-58
[97] Kamal Tawfiq, Jamshid Armaghani and Rodolfo Ruiz. Fatigue cracking of polypropylene fiber reinforced concrete[J]. ACI Materials Journal, 1999, 96(2):226-233
[98] Giovanni, A.Piizzari, Stefano Cangiano and Nicola Cere. Postpeak behavior of fiber-reinforced concrete under cyclic tensile loads[J]. ACI Materials Journal, 2000, 97(2): 182-192
[99] W.Ahn and D.V.Reddy. Galvanostatic testing for the durability of marine concrete under fatigue loading[J]. Cement and Concrete Research, 2001, 31:343-349
[100] Chen Ying-bo, Lu Zhe-an and huang Da. Fatigue defect of layer steel fiber reinforced concrete[J]. Journal of Wuhan University of Technology-Mater. Sci. Ed., 2003, 18(1):65-68
[101] Mazars. J. Evolution of microcracks in Concrete: the formation of cracks[P]. Annales de PITBTP, Serie Beton-202, October 1981
[102] Saito M.. Characteristics of microcracking in concrete under static and repeated tensile loading[J]. Cement and Concrete Research, 1987, 17:211-218
[103] 鞠杨，樊承谋．高-低两级变幅荷载下钢纤维混凝土轴向压缩疲劳效应[J]．哈尔滨建筑大学学报，1995，28(3)：78-82
[104] 鞠杨，潘景龙，樊承谋．钢纤维混凝土疲劳损伤机理初探[J]．哈尔滨建筑大学学报，1997，30(3)：34-40
[105] 谢和平，鞠杨．分数空间中的损伤力学研究初探[J]．力学学报，1999，31(3)：300-310
[106] Slate, F.O. and Olsefski.S. X-ays for study of internal structure and microcracking of concrete[J]. ACI, 1974, 65:575-578
[107] W.Suaris, V.Femando. Ultrasonic pulse attenuation as a measure of damage growth during cyclic loading of concrete[J]. ACI materials journal, 1987, 84(3):185-193
[108] 严碧歌，袁益民，李泉臻．混凝土材料超声检测[J]．西北大学学报，2002，32(1)：20-22
[109] 刘学文，林吉中，袁祖贻．应用声发射技术评价材料疲劳损伤的研究[J]．中国铁道科学，1997，18(4)：74-81
[110] 杜云，张春明，尾崎韧．混凝土疲劳试验的AE特性研究[J]．辽宁工程技术大学学报(自然科学版)，2001，29(1)：46-49
[111] 林燕清．混凝土疲劳累积损伤与力学性能劣化研究[D]．哈尔滨建筑大学博士论文，1998，5
[112] B.P.Sinha, Hurt H.Gerstle and Leonard G.Tulin. Stress-strain relations for concrete under cyclic loading[J]. Journal of the American Concrete Institute, 1964, 195-211
[113] 程光旭，楼志文，匡震邦．一种基于材料延性耗散模型的疲劳损伤研究方法[J]．力学学报，1993，25(4)：496-499
[114] L.Yang and A.Fatemi. Cumulative fatigue damage mechanics and quantifying parameters: a literature review[J]. Journal of Testing and Evaluation, 1998,26(2):89-100
[115] 姜菊生，张伟根，郭乙木等．金属材料疲劳损伤的定量研究[J]．材料科学与工程，2000，18(1)：43-46
[116] 余寿文，冯西桥．损伤力学[M]．北京，清华大学出版社，1997：286-292
[117] 张滨生，吴科如．水泥混凝土疲劳破坏的损伤力学分析[J]．同济大学学报，1989，17(1)：59-69
[118] Ju Yang and Xie Heping. Application of damage defination based on hypothesis of strain equivalence[J]. Journal of Coal Science & Engineering, 2000, 6(2):9-14
[119] Wei Jun, Wu Xing-hao, Zhao Xiao-long. A damage model of concrete under freeze-thaw cycles[J].
Journal of Wuhan University of Technology-Mater. Sci. Ed. 2003, 18(3):40-42
[120] Ravindra Gettu, Antonio Aguado and Marcel O.F.Oliveira. Damage in high-strength concrete due to monotonic and cyclic compression-a study based on splitting tensile strength[J]. ACI Materials Journal, 1996, 93(6):519-523
[121] 逯静洲．三轴受压混凝土损伤特性理论与试验研究[D]．大连理工大学博士论文，2001，10
[122] 赵永利，孙伟．混凝土材料疲劳损伤方程的建立[J]．重庆交通学院学报，1999，18(1)：17-22
[123] 王瑞敏，宋玉普，赵国藩．混凝土疲劳累积损伤准则[J]．水利学报，1992，(5)：72-76
[124] 李朝阳，宋玉普，车轶．混凝土的单轴抗压疲劳损伤累积性能研究[J]．土木工程学报，2002，35(2)：38-40
[125] K.K.Phoon et al. Development of statistical quality assurance criterion for concrete using ultrasonic pulse velocity method[J]. ACI Materials Journal, 1999, 96(5):568-573
[126] S.Yuyama, Z.-W.Li, M.Yoshizawa, T.Tomokiyo and T.Uomoto. Evaluation of fatigue damage in reinforced concrete slab by acoustic emission[J]. NDT & International, 2001, 381-387
[127] M.A.Miner. Cumulative fatigue damage[J]. Journal of the applied mechanics, 1945, 67(12): 159-164
[128] 李朝阳，宋玉普。混凝土海洋平台疲劳损伤累积Miner准则适用性研究[J]．中国海洋平台，2001，16(3)：1-4
[129] 赵造东，张立翔．基于P-D-ε曲线的混凝土疲劳累积损伤分析[J]．云南水力发电，2001，18(2)：86-91
[130] Corten, H.T. and Dolan, T.L.. Cumulative fatigue damage[J]. Proceed. of the Inter. Confer on Fatigue of Materials, IME and ASME, 1956
[131] Manson, S.S. Application of a double linear damage rule to cumulative fatigue[J]. ASTM STP 415, 1967
[132] S.P.Shah. Predictions of cumulative damage for concrete and reinforced concrete[J]. Materials and Constructions, 1984, 17(97):65-68
[133] 林燕清，欧进萍，黄文虎．混凝土疲劳损伤累积和剩余寿命预测研究[C]．疲劳与断裂2000，气象出版社，2000：464-468
[134] 刘长虹，沈梦月等．多级加载下疲劳寿命的分岔现象探讨[J]．机械科学与技术，2001，20(6)：894-896
[135] 曹伟，宋玉普．多级加载下混凝土疲劳剩余寿命预测新方法[J]．大连理工大学学报，2003，43(5)：659-662
[136] John T. McCall. Probability of fatigue failure of plain concrete[J]. Journal of the American Concrete Institution, 1958, 30(2):233-244
[137] Byung Hwan Oh. Fatigue-life distributions of concrete for various stress levels[J]. ACI Materials Journal, 1991, 88(2): 122-128
[138] Xiaozhi Yu, Yiu-wing Mai and Brain Cotterell. A statistical theory of time-dependent fracture for cementitious materials subjected to cyclic loading[J]. Journal of Materials Science, 1989, 24:3118-3122
[139] Enrique Castillo and Alfonso Fernandez-Canteli. A general regression model for lifetime evaluation and prediction[J]. International Journal of Fracture, 2001, 107:117-137
[140] D.Yang. A distribution function for the fatigue life of concrete[J]. Magazine of Concrete Research, 1994, 46(168): 215-221
[141] 李靖华，李果，刘刚．混凝土疲劳寿命规律预测新方法[J]．大连理工大学学报，1997，37(1增刊) 115-121
[142] 董聪．疲劳寿命分布模型的统一描述[J]．强度与环境，1996，3：1-7
[143] 伍石生，武建民．水泥混凝土疲劳试验数据中含非破坏数据的处理方法[J]．重庆交通学院学报，2002，21(1)：34-36
[144] 宋玉普，赵东拂．混凝土强度与疲劳寿命试验样本容量分析[J]．大连理工大学学报，2002，42(4)：464-466
[145] 谢里阳，林文强．疲劳剩余寿命分布的当量关系及可靠性计算方法[J]．东北大学学报(自然科学版)，1995，16(6)：598-602
[146] 杨伟军，赵传智，郭在林．钢筋混凝土吊车梁的混凝土疲劳概率分析[J]．工程力学，1999，16(3)：140-144
[147] 贡金鑫，赵国藩．腐蚀环境下钢筋混凝土结构疲劳可靠性的分析方法[J]．土木工程学报，2000，33(6)：50-56
[148] 姜海波，车惠民．既有铁路混凝土梁疲劳与承载力可靠性评估[J]．土木工程学报，2000，33(1)：27-31
[149] 赵尚传．钢筋混凝土结构基于可靠度的耐久性评估与试验研究[D]．大连理工大学博士论文，2001
[150] Y.S.Petryna, D.Pfanner, F.Stangenberg, W.B.Kratzig. Reliability of reinforced concrete structures under fatigue[J]. Reliability Engineering and System Safety, 2002, 77:253-261
[151] 周详．同时考虑结构抗力模糊性与随机性的结构可靠性计算模型[J]．武汉工业大学学报．1995，17(1)：60-64
[152] 李云贵，赵国藩．基于模糊随机概率理论的可靠度分析模型[J]．大连理工大学学报，1995，35(4)：528-531
[153] 王烜．疲劳破坏随机预测模型的研究及应用[J]．土木工程学报，1999，32(2)：71-74
[154] 陈惠发．土木工程材料的本构方程(上下册)[M]．华中科技大学出版社，2001
[155] David Z.Yankelevsky and Hans W.Reinhardt. Model for cyclic compressive behavior of concrete[J]. Journal of Structural Engineering, 1987, 113(2):228-240
[156] David Z.Yankelevsky and Hans W.Reinhardt. Uniaxial behavior of concrete in cyclic tension[J]. Journal of Structural Engineering, 1989, 115(1): 166-182
[157] Young J.Park. Fatigue of concrete under random loading[J]. Journal of Structural Engineering, 1990, 116(11): 3228-3235
[158] J.Enrique Martinez-Ruela and A.S.Elnashai. Confined concrete model under cyclic load[J]. Materials and Structures, 1997, 30:139-147
[159] Byong Youl Bahn and Cheng-Tzu Thomas Hsu. Stress-strain behavior of concrete under cyclic loading[J]. ACI Materials Journal, 1998,95(2): 178-193
[160] K.Gylltoft. A fracture mechanics model for fatigue in concrete[J]. Materials and Constructions, 1984, 17, 97:55-58
[161] E.Papa. A damage model for concrete subjected to fatigue loading[J]. European Journal of Mechanics, 1993, 12(3):429-440
[162] J.Mazars,Y.Berthaud,S.Ramtani. The unilateral behavior of damage concrete[J]. Engineering Fracture Mechanics, 1990, 35(4/5):629-635
[163] Enrico Papa,Alberto Taliercio. Anisotropic damage model for the multiaxial static and fatigue behaviour of plain concrete[J]. Engineering Fracture Mechanics, 1996, 55(2): 163-179
[164] Josko Ozbolt and Zdenek P.Bazant. Microplane model for cyclic triaxial behavior of concrete[J]. Journal of Engineering Mechanics, 1992, 118(7): 1365-1386
[165] En-Sheng Chen and Oral Buyukozturk. Constitutive model for concrete in cyclic compression[J].
Journal of Engineering Mechanics, 1985, 111(6):797-814
[166] Wimal Suaris,Chengsheng Ouyang, Viraj M.Fernando. Damage model for cyclic loading of concrete[J]. Journal of Engineering Mechanics, 1990, 116(5): 1020-1034
[167] Michael N Fardis, Bunu Alibe and John L. Tassoulas. Monotonic and cyclic constitutive law for concrete[J]. Journal of Engineering Mechanics, 1983, 109(2):516-536
[168] Bing-lin Yang,F.Dafalias,Leonard R.Herrmann. A bounding surface plasticity model for concrete[J]. Journal of Engineering Mechanics, 1985, 111(3):359-380
[169] M.N.Fardis,E.S.Chen. A cyclic multiaxial model for concrete[J]. Computatial Mechanics, 1986(1):301-315
[170] Anna Pandolfi, Alberto Taliercio. Bounding surface models applied to fatigue of plain concrete[J]. Journal of Engineering Mechanics, 1998, 124(5):556-564
[171] Taher M.Abu-Lebdeh,George Z.Voyiadjis. Plasticity-damage model for concrete under cyclic multiaxial loading[J]. Journal of Engineering Mechanics, 1993, 119(7): 1465-1484
[172] E.Hansen,K.Willam. A two-surface anisotropic damage/plasticity model for plain concrete[J]. Fracture Mechanics of Concrete Materials, 2001:540-556
[173] 宋玉普，赵国藩．应变空间混凝土的破坏准则[J]．大连理工大学学报，1991，31(4)：455-461
[174] David J.Stevens and Dajin Liu. Strain-based constitutive model with mixed evolution rules for concrete[J]. Journal of Engineering Mechanics, 1992, 118 (6): 1184-1200
[175] 张承柱，刘信声．应变空间表述的混凝土弹塑性耦合本构模型[J]．清华大学学报(自然科学版)，1995，36(3)：59-64
[2] CEB欧洲国际混凝土委员会．1990年CEB-FIP模式混凝土结构规范[S]．北京，中国建设科学研究院建筑结构研究所，1989．12
[3] Det Norske Veritas. Rules for classification of fixed offshore installation structures[S]. Part 3, Chapter 1, Structural Design, July 1989
[4] GB50216-94．铁路工程结构可靠度设计统一标准[S]．北京，中国计划出版社，1994
[5] GB50010-2002．混凝土结构设计规范[S]．北京，中国建筑工业出版社，2002
[6] 混凝土疲劳专题组．混凝土受弯构件疲劳可靠性验算方法的研究[M]．北京，中国建设工业出版社，1994
[7] 中华人民共和国国家标准TBJ-85．铁路桥涵设计规范[S]．北京，中国铁道出版社，1985
[8] British Standards Institution. Steel, concrete and composite bridges[S]. BS5400: Pt. 5-10, 1978-83
[9] 36-RDL report. Long term random dynamic loading of concrete structures[J]. Matedaux et Constructions, 1984,17(97): 1-13
[10] Considere.M. Influence des armatures metalligues sur les proprietes des mortiers et betons[J]. Compte Rendu de l'academie Des Sciences, 1898, 127:992-995
[11] De Joly. La resistance et l'elastic des ciments porland[J]. Annales Des Ponts et Chausses, Memoires, 1898,16(7): 198-244
[12] Van Ornum J.L. Fatigue of cement products[J]. Transactions, ASCE, 1903,51,443
[13] Clemmer H.E. Fatigue of concrete[J]. Proceeding, ASTM, 1922,22(Part Ⅱ): 408-419
[14] Graf O. and Brenner E.. Experiments for investigating the resistance of concrete under often repeated compression loads. 1[J]. Bulletin, Deutscher Ausschuss fur Stahlbeton, Berlin, 1934,1 (76): 17-25
[15] Graf O. and Brenner E.. Experiments for investigating the resistance of concrete under often repeated compression loads.2[J]. Bulletin, Deutscher Ausschuss fur Stahlbeton, Berlin, 1936,2(83):45-53
[16] Gray.W., Mclaughlin.J.F and Antrim.J.C. Fatigue propertities of lightweight aggregate concrete[J]. ACI Journal, 1961:149-161
[17] Murdock J.W.. A critical review of research on fatigue of plain concrete[P]. Engineering Experiment Station Bulletin, 1965, No.475:25
[18] Bennett E. W. and Muir S.E.J.. Some fatigue tests on high-strength concrete in axial compression[J]. Magazine of Concrete Research, 1967,19(59):113-117
[19] N. K. Raju. Comparative study of the fatigue behavior of concrete, motar and paste in uniaxial compression[J]. ACI Journal, 1970,67:461-463
[20] Aas-Jakobsen K.. Fatigue of concrete beams and columns[J]. Bulletin No.70-1. NTH Institute for Betonkonstruksjoner, 1970.9
[21] Ralejs Tepfers and Thomas Kutti. Fatigue strength of plain, ordinary, and lightweight concrete[J]. ACI Journal, 1979(5): 635-653
[22] Matsushita H. and Tokumitsu Y.. A study on compressive fatigue strength of concrete considered survival probability[J]. Proceeding of J SCE, 1972, 198:127-138
[23] Thomas T.C.Hsu. Fatigue of plain concrete[J]. ACI Journal, 1981(2):292-305
[24] Petkovic G, Lenschow R, Stemland H. and Rosseland S.. Fatigue of high-strength concrete[J]. ACI, Special Publication, SP-121-25, 1991:505-525
[25] 姚明初．混凝土在等幅和变幅重复应力下疲劳性能的研究，铁道部科学研究院报告，1990
[26] Jin-Keun Kim and Yun-Yong Kim. Experimental study of the fatigue behavior of high strength concrete[J]. Cement and Concrete Research, 1996,26(10): 1513-1523
[27] C.P.Whaley and A.M.Neville. Non-elastic deformation of concrete under cyclic compression[J]. Magazine of Concrete Research, 1973,25(84): 145-154
[28] P.R.Sparks and J.B.Menzies. The effect of rate of loading upon the static and fatigue strengths of plain concrete in compression[J]. Magazine of Concrete Research, 1973,25(83):73-80
[29] P.R.Sparks. The influence of rate of loading and material variability on the fatigue characteristics of concrete[J]. ACI Publication SP-75, 1982:331-343
[30] Jan Ove Holmen. Fatigue of concrete by constant and variable amplitude loading[J]. Fatigue Strength of Concrete Structures, SP-75 ACI, 1982:71-110
[31] 欧进萍，林燕清．混凝土疲劳损伤的强度和刚度衰减试验研究[J]．哈尔滨建筑大学学报，1998，31(4)：1-7
[32] 欧进萍，林燕清．混凝土高周疲劳损伤的性能劣化试验研究[J]．土木工程学报，1999,32(5)：15-21
[33] 吴佩刚，赵光仪，白利明．高强混凝土抗压疲劳性能研究[J]．土木工程学报，1994，27(3)：33-40
[34] 王瑞敏，赵国藩，宋玉普．混凝土的受压疲劳性能研究[J]．土木工程学报，1991，24(4)：38-47
[35] 李朝阳，宋玉普，赵国藩．混凝土疲劳残余应变性能研究[J]．大连理工大学学报，2001，41(3)：355-358
[36] 王时越，张立翔，徐人平．弹性模量对混凝土疲劳性能的影响[J]．昆明理工大学学报，2001，26(5)：18-20，25
[37] Raithby K.D. and Galloway J.W.. Effects of moisture condition, age and rate of loading on fatigue of plain concrete[J]. Fatigue of Concrete, SP-41, American Concrete Institute, Detroit, 1974,15-34
[38] 邓宗才．轻质高强混凝土抗压疲劳特性的研究[J]．建筑技术开发，1996，5：27-29
[39] 周新刚，吴江龙．高温后混凝土轴压疲劳性能初探[J]．工业建筑，1996，26(5)：33-35
[40] Miroslaw Grzybowski and Christian Meyer. Damage accumulation in concrete with and without fiber reinforcement[J]. ACI Materials Journal, 1993, 90(6):594-604
[41] Handong Yan, Wei Sun and Huisu Chen. The effect of silica fume and steel fiber on the dynamic mechanical performance of high-strength concrete[J]. Cement & Concrete Research, 1999, 29:423-426
[42] 鞠杨，樊承谋．循环载荷作用在钢纤维混凝土的损伤及演化行为的定量描述[J]．工程力学，1998，15(1)：94-104
[43] 鞠杨，樊承谋，潘景龙．变幅疲劳荷载下钢纤维混凝土的损伤演化行为研究[J]．实验力学，1997，12(1)：99-118
[44] 鞠杨，樊承谋，潘景龙．钢纤维混凝土疲劳损伤行为研究[J]．工业建筑，1997,27(3)：38-42，62
[45] Rafeeq A.S., Ashok G. and Krishnamoorthy S.. Influence of steel fibers in fatigue resistance of concrete in direct compression[J]. Journal of Materials in Civil Engineering, 2000, 12(2): 172-179
[46] Paulo B.Cachin, Joaquim A.Figueiras and Paulo A.A. Pereira. Fatigue behavior of fiber-reinforced concrete in compression[J]. Cement & Concrete Composites, 2002, 24:211-217
[47] Jeragh A.A.. Deformation behavior of plain concrete subjected to biaxial-cyclic loading[D]. PhD
dissertation, New Mexico State University, University Park, 1978
[48] Traina L.A., and Jeragh A.A.. Fatigue of plain concrete subjected to biaxial cyclical loading[J]. ACI Publications, SP-75, 1982:217-234
[49] Oral Buyukozturk and Tsi-ming Tseng. Concrete in biaxial cyclic compression[J]. Journal of Structural Engineering, 1984, 110(3):461-476
[50] 吕培印．混凝土单轴、双轴动态强度和变形试验研究[D]．大连理工大学博士论文，2001，11
[51] 朱劲松．混凝土双轴疲劳试验与破坏预测理论研究[D]．大连理工大学博士论文，2003，9
[52] Eric C.M.Su and Thomas T.C.Hsu. Biaxial Compression fatigue and discontinuity of concrete[J]. ACI Materials Journal, 1988, 85(3): 178-188
[53] Weisu Yin and Thomas T.C.Hsu. Fatigue behavior of steel reinforced concrete in uniaxial and biaxial compression[J]. ACI Materials Journal, 1995,92(1):71-81
[54] Erik L. Nelson, Ramon 1. Carrasquillo. Behavior and failure of high-strength concrete subjected to biaxial-cyclic compression loading[J]. ACI Materials Journal, 1988, 85(3):248-253
[55] Shengrui Lan and Zhenhai Guo. Biaxial compression behavior of concrete under repeated Ioading[J],. Journal of materials in Civil Engineering, 1999, 11(2): 105-114
[56] 俞茂宏，赵均海，郑树俊等．复杂应力下混凝土疲劳强度的试验研究[J]．西安交通大学学报，1998，32(3)：89-92
[57] Kolluru V. Subtamaniam, John S.Popovics and Surendra P.Shah. Fatigue response of concrete subjected to biaxial stresses in the compression-tension region[J]. ACI Materials Journal, 1999, 96(6):663-669
[58] 揽生瑞，过镇海．定侧压下混凝土二轴受压变形特性的试验研究[J]．土木工程学报，1996，29(2)：28-35
[59] 过镇海，王传志．多轴应力下混凝土的强度和破坏准则研究[J]．土木工程学报，1991，24(3)：1-14
[60] 过镇海．混凝土的强度和变形试验基础和本构关系[M]．北京，清华大学出版社，1997
[61] P.Desayi, K.T.Sundara Raja lyengar and T.Sanjeeva Reddy. Stress-strain characteristics of concrete confined in steel spirals under repeated loading[J]. Materials and Structures, 1969, 12(71):375-383
[62] Surendra P. Shah, Apostolos Fafitis and Richard Arnold. Cyclic loading of spirally reinforced concrete[J]. Journal of Structural Engineering, 1983, 109(7): 1695-1710
[63] Tan Teng Hooi. Effects of passive confinement on fatigue properties of concrete[J]. Magazine of Concrete Research, 2000, 52(1):7-15
[64] Cheong and Hong Zeng. Stress-strain relationship for concrete confined by lateral steel reinforcement[J]. ACI Materials Journal, 2002, 99(3):250-255
[65] A.L.F.Taliercio and Gobbi. Experimental investigation on the triaxial fatigue behavior of plain concrete[J]. Magazine of Concrete Research, 1996, 48(176): 157-172
[66] A.L.F.Taliercio and Gobbi. Fatigue life and change in mechanical properties of plain concrete under triaxial deviatoric cyclic stresses[J]. Magazine of Concrete Research, 1998, 50(3):247-255
[67] A.L.F.Taliercio, M.Berra and A.Pandolfi. Effect of high-intensity sustained triaxial stresses on the mechanical properties of plain concrete[J]. Magazine of Concrete Research, 1999, 51(6):437-447
[68] Linger D.A. and Gillespie H.A.. A study of the mechnism of concrete fatigue and fracture[J]. HRB research news, 1966,No.22
[69] Tepfers Ralejs. Tensile fatigue strength of plain concrete[J]. ACI Journal, 1979, 76(8):919-933
[70] A.J.Zielinski, H.W.Reinhard and H.A.Kormeling. Experiments on concrete under repeated uniaxial impact tensile loading[J]. Material Construction and Material Structures, 1981, 14(8): 163-169
[71] Volker Slowik, Giovanni Angelo Plizzari and Victor E. Saouma. Fracture of concrete under variable amplitude fatigue loading[J]. ACI Materials Journal, 1996, 93(3):272-283
[72] D.J.Cook and P.Chindaprasirt. Influence of loading history upon the tensile properties of concrete[J]. Magazine of Concrete Research, 1981, 33(116): 154-160
[73] Saito. M and Imai.S. Direct tensile fatigue of concrete by the Ues of friction grips[J]. ACI Journal, Proceeding, 1983, 80(5):431-438
[74] Saito.M. Tensile fatigue of strength of lightweight concrete[J]. International Journal of Cement Composites and Lightweight Concrete, 1984, 6(3):143-149
[75] H.A.W.Cornelissen and H.W.Reinhardt. Fatigue of plain concrete in uniaxial tension and in alternating tension compression loading[J]. Fatigue of steel and Concrete Structures, IABSE Colloguium, 1982,273-282
[76] H.A.W.Cornelissen and H.W.Reinhardt. Uniaxial tensile fatigue failure of concrete under constant-amplitude and programme loading[J]. Magazine of Concrete Research, 1984, 36(129):216-226
[77] H.W.Reinhardt and H.A.W.Cornelissen. Post-peak cyclic behavior of concrete in uniaxial tensile and alternative tensile and compressive loading[J]. Cement and Concrete Research, 1984, 14:263-270
[78] 赵光仪，吴佩刚，詹巍巍．高强混凝土的抗拉疲劳性能[J]．土木工程学报，1993，26(6)：13-19
[79] 赵东拂．混凝土多轴疲劳破坏准则研究[D]．大连理工大学博士论文，2002，12
[80] 杨健辉．侧压下混凝土静态受拉和受拉疲劳性能研究[D]．大连理工大学博士论文，2003，4
[81] Hatt W.K. Report on experiments on extensibility of concrete[J]. Proc. 5th annual meeting, Highway Research Board, 1925, Dec. 112-118
[82] Crepps R. B. Fatigue of mortal[J]. Proc. ASTM. 1923, 23, Part Ⅱ, 329-340
[83] Tepfers R. Fatigue of plain concrete subjected to stress reversals[J]. ACI J., Special Publication, 1982,75(9): 195-215
[84] 宋玉普，吕培印．混凝土轴心拉-压疲劳性能研究[J]．建筑结构学报，2002，23(4)：36-41
[85] Williams H.A. Fatigue tests of lightweight aggregate concrete beams[J]. ACI Journal Proceedings, 1943,39(5):108-112
[86] Hilsdorf H.K. and Kesler C.E.. Fatigue strength of concrete under varying flexural stress[J]. ACI Journal, 1966,63(10): 1059-1076
[87] Hubert K.Hilsdorf and Clyde E.Kesler. Fatigue strength of concrete under varying flexural stresses[J]. Journal of the American Concrete Institute, 1966, 1060-1076
[88] Byung Hwan Oh. Cumulative damage theory of concrete under variable-amplitude fatigue loading[J]. ACI Materials Journal, 1991, 88(1):41-48
[89] A.Mor, B.C.Gerwick and W.T.Hester. Fatigue of high-strength reinforced concrete[J]. ACI Materials Journal, 1992, 89(2): 197-207
[90] X. P. Shi, T. F. Fwa and S. A. Tan. Flexual fatigue strength of plain concrete[J]. ACI Materials Journal, 1993, 90(5):435-440
[91] Bingsheng Zhang and KeruWu. Residual fatigue strength and stiffness of ordinary concrete under bending[J]. Cement and Concrete Research, 1997, 27(1): 115-126
[92] B.Zhang, D.V.Phillips and K.Wu. Further research on fatigue properties of plain concrete[J]. Magazine of Concrete Research, 1997, 49(180): 241-252
[93] B.Zhang. Relationship between pore structure and mechanical properties of ordinary concrete under bending fatigue[J]. Cement and Concrete Research, 1998, 28(5):699-711
[94] A.E.Naaman and H.Hammoud. Fatigue characteristics of high performance fiber-reinforced concrete[J].
Cement and Concrete Research, 1998, 20:353-363
[95] Seok-Goo Youn and Sung-Pil Chang. Behavior of composite brigde decks subjected to static and fatigue loading[J]. ACI Structural Journal, 1998, 95(3):249-258
[96] 李永强，车惠民．混凝土弯曲疲劳累积损伤性能研究[J]，中国铁道科学，1998，19(2)：52-58
[97] Kamal Tawfiq, Jamshid Armaghani and Rodolfo Ruiz. Fatigue cracking of polypropylene fiber reinforced concrete[J]. ACI Materials Journal, 1999, 96(2):226-233
[98] Giovanni, A.Piizzari, Stefano Cangiano and Nicola Cere. Postpeak behavior of fiber-reinforced concrete under cyclic tensile loads[J]. ACI Materials Journal, 2000, 97(2): 182-192
[99] W.Ahn and D.V.Reddy. Galvanostatic testing for the durability of marine concrete under fatigue loading[J]. Cement and Concrete Research, 2001, 31:343-349
[100] Chen Ying-bo, Lu Zhe-an and huang Da. Fatigue defect of layer steel fiber reinforced concrete[J]. Journal of Wuhan University of Technology-Mater. Sci. Ed., 2003, 18(1):65-68
[101] Mazars. J. Evolution of microcracks in Concrete: the formation of cracks[P]. Annales de PITBTP, Serie Beton-202, October 1981
[102] Saito M.. Characteristics of microcracking in concrete under static and repeated tensile loading[J]. Cement and Concrete Research, 1987, 17:211-218
[103] 鞠杨，樊承谋．高-低两级变幅荷载下钢纤维混凝土轴向压缩疲劳效应[J]．哈尔滨建筑大学学报，1995，28(3)：78-82
[104] 鞠杨，潘景龙，樊承谋．钢纤维混凝土疲劳损伤机理初探[J]．哈尔滨建筑大学学报，1997，30(3)：34-40
[105] 谢和平，鞠杨．分数空间中的损伤力学研究初探[J]．力学学报，1999，31(3)：300-310
[106] Slate, F.O. and Olsefski.S. X-ays for study of internal structure and microcracking of concrete[J]. ACI, 1974, 65:575-578
[107] W.Suaris, V.Femando. Ultrasonic pulse attenuation as a measure of damage growth during cyclic loading of concrete[J]. ACI materials journal, 1987, 84(3):185-193
[108] 严碧歌，袁益民，李泉臻．混凝土材料超声检测[J]．西北大学学报，2002，32(1)：20-22
[109] 刘学文，林吉中，袁祖贻．应用声发射技术评价材料疲劳损伤的研究[J]．中国铁道科学，1997，18(4)：74-81
[110] 杜云，张春明，尾崎韧．混凝土疲劳试验的AE特性研究[J]．辽宁工程技术大学学报(自然科学版)，2001，29(1)：46-49
[111] 林燕清．混凝土疲劳累积损伤与力学性能劣化研究[D]．哈尔滨建筑大学博士论文，1998，5
[112] B.P.Sinha, Hurt H.Gerstle and Leonard G.Tulin. Stress-strain relations for concrete under cyclic loading[J]. Journal of the American Concrete Institute, 1964, 195-211
[113] 程光旭，楼志文，匡震邦．一种基于材料延性耗散模型的疲劳损伤研究方法[J]．力学学报，1993，25(4)：496-499
[114] L.Yang and A.Fatemi. Cumulative fatigue damage mechanics and quantifying parameters: a literature review[J]. Journal of Testing and Evaluation, 1998,26(2):89-100
[115] 姜菊生，张伟根，郭乙木等．金属材料疲劳损伤的定量研究[J]．材料科学与工程，2000，18(1)：43-46
[116] 余寿文，冯西桥．损伤力学[M]．北京，清华大学出版社，1997：286-292
[117] 张滨生，吴科如．水泥混凝土疲劳破坏的损伤力学分析[J]．同济大学学报，1989，17(1)：59-69
[118] Ju Yang and Xie Heping. Application of damage defination based on hypothesis of strain equivalence[J]. Journal of Coal Science & Engineering, 2000, 6(2):9-14
[119] Wei Jun, Wu Xing-hao, Zhao Xiao-long. A damage model of concrete under freeze-thaw cycles[J].
Journal of Wuhan University of Technology-Mater. Sci. Ed. 2003, 18(3):40-42
[120] Ravindra Gettu, Antonio Aguado and Marcel O.F.Oliveira. Damage in high-strength concrete due to monotonic and cyclic compression-a study based on splitting tensile strength[J]. ACI Materials Journal, 1996, 93(6):519-523
[121] 逯静洲．三轴受压混凝土损伤特性理论与试验研究[D]．大连理工大学博士论文，2001，10
[122] 赵永利，孙伟．混凝土材料疲劳损伤方程的建立[J]．重庆交通学院学报，1999，18(1)：17-22
[123] 王瑞敏，宋玉普，赵国藩．混凝土疲劳累积损伤准则[J]．水利学报，1992，(5)：72-76
[124] 李朝阳，宋玉普，车轶．混凝土的单轴抗压疲劳损伤累积性能研究[J]．土木工程学报，2002，35(2)：38-40
[125] K.K.Phoon et al. Development of statistical quality assurance criterion for concrete using ultrasonic pulse velocity method[J]. ACI Materials Journal, 1999, 96(5):568-573
[126] S.Yuyama, Z.-W.Li, M.Yoshizawa, T.Tomokiyo and T.Uomoto. Evaluation of fatigue damage in reinforced concrete slab by acoustic emission[J]. NDT & International, 2001, 381-387
[127] M.A.Miner. Cumulative fatigue damage[J]. Journal of the applied mechanics, 1945, 67(12): 159-164
[128] 李朝阳，宋玉普。混凝土海洋平台疲劳损伤累积Miner准则适用性研究[J]．中国海洋平台，2001，16(3)：1-4
[129] 赵造东，张立翔．基于P-D-ε曲线的混凝土疲劳累积损伤分析[J]．云南水力发电，2001，18(2)：86-91
[130] Corten, H.T. and Dolan, T.L.. Cumulative fatigue damage[J]. Proceed. of the Inter. Confer on Fatigue of Materials, IME and ASME, 1956
[131] Manson, S.S. Application of a double linear damage rule to cumulative fatigue[J]. ASTM STP 415, 1967
[132] S.P.Shah. Predictions of cumulative damage for concrete and reinforced concrete[J]. Materials and Constructions, 1984, 17(97):65-68
[133] 林燕清，欧进萍，黄文虎．混凝土疲劳损伤累积和剩余寿命预测研究[C]．疲劳与断裂2000，气象出版社，2000：464-468
[134] 刘长虹，沈梦月等．多级加载下疲劳寿命的分岔现象探讨[J]．机械科学与技术，2001，20(6)：894-896
[135] 曹伟，宋玉普．多级加载下混凝土疲劳剩余寿命预测新方法[J]．大连理工大学学报，2003，43(5)：659-662
[136] John T. McCall. Probability of fatigue failure of plain concrete[J]. Journal of the American Concrete Institution, 1958, 30(2):233-244
[137] Byung Hwan Oh. Fatigue-life distributions of concrete for various stress levels[J]. ACI Materials Journal, 1991, 88(2): 122-128
[138] Xiaozhi Yu, Yiu-wing Mai and Brain Cotterell. A statistical theory of time-dependent fracture for cementitious materials subjected to cyclic loading[J]. Journal of Materials Science, 1989, 24:3118-3122
[139] Enrique Castillo and Alfonso Fernandez-Canteli. A general regression model for lifetime evaluation and prediction[J]. International Journal of Fracture, 2001, 107:117-137
[140] D.Yang. A distribution function for the fatigue life of concrete[J]. Magazine of Concrete Research, 1994, 46(168): 215-221
[141] 李靖华，李果，刘刚．混凝土疲劳寿命规律预测新方法[J]．大连理工大学学报，1997，37(1增刊) 115-121
[142] 董聪．疲劳寿命分布模型的统一描述[J]．强度与环境，1996，3：1-7
[143] 伍石生，武建民．水泥混凝土疲劳试验数据中含非破坏数据的处理方法[J]．重庆交通学院学报，2002，21(1)：34-36
[144] 宋玉普，赵东拂．混凝土强度与疲劳寿命试验样本容量分析[J]．大连理工大学学报，2002，42(4)：464-466
[145] 谢里阳，林文强．疲劳剩余寿命分布的当量关系及可靠性计算方法[J]．东北大学学报(自然科学版)，1995，16(6)：598-602
[146] 杨伟军，赵传智，郭在林．钢筋混凝土吊车梁的混凝土疲劳概率分析[J]．工程力学，1999，16(3)：140-144
[147] 贡金鑫，赵国藩．腐蚀环境下钢筋混凝土结构疲劳可靠性的分析方法[J]．土木工程学报，2000，33(6)：50-56
[148] 姜海波，车惠民．既有铁路混凝土梁疲劳与承载力可靠性评估[J]．土木工程学报，2000，33(1)：27-31
[149] 赵尚传．钢筋混凝土结构基于可靠度的耐久性评估与试验研究[D]．大连理工大学博士论文，2001
[150] Y.S.Petryna, D.Pfanner, F.Stangenberg, W.B.Kratzig. Reliability of reinforced concrete structures under fatigue[J]. Reliability Engineering and System Safety, 2002, 77:253-261
[151] 周详．同时考虑结构抗力模糊性与随机性的结构可靠性计算模型[J]．武汉工业大学学报．1995，17(1)：60-64
[152] 李云贵，赵国藩．基于模糊随机概率理论的可靠度分析模型[J]．大连理工大学学报，1995，35(4)：528-531
[153] 王烜．疲劳破坏随机预测模型的研究及应用[J]．土木工程学报，1999，32(2)：71-74
[154] 陈惠发．土木工程材料的本构方程(上下册)[M]．华中科技大学出版社，2001
[155] David Z.Yankelevsky and Hans W.Reinhardt. Model for cyclic compressive behavior of concrete[J]. Journal of Structural Engineering, 1987, 113(2):228-240
[156] David Z.Yankelevsky and Hans W.Reinhardt. Uniaxial behavior of concrete in cyclic tension[J]. Journal of Structural Engineering, 1989, 115(1): 166-182
[157] Young J.Park. Fatigue of concrete under random loading[J]. Journal of Structural Engineering, 1990, 116(11): 3228-3235
[158] J.Enrique Martinez-Ruela and A.S.Elnashai. Confined concrete model under cyclic load[J]. Materials and Structures, 1997, 30:139-147
[159] Byong Youl Bahn and Cheng-Tzu Thomas Hsu. Stress-strain behavior of concrete under cyclic loading[J]. ACI Materials Journal, 1998,95(2): 178-193
[160] K.Gylltoft. A fracture mechanics model for fatigue in concrete[J]. Materials and Constructions, 1984, 17, 97:55-58
[161] E.Papa. A damage model for concrete subjected to fatigue loading[J]. European Journal of Mechanics, 1993, 12(3):429-440
[162] J.Mazars,Y.Berthaud,S.Ramtani. The unilateral behavior of damage concrete[J]. Engineering Fracture Mechanics, 1990, 35(4/5):629-635
[163] Enrico Papa,Alberto Taliercio. Anisotropic damage model for the multiaxial static and fatigue behaviour of plain concrete[J]. Engineering Fracture Mechanics, 1996, 55(2): 163-179
[164] Josko Ozbolt and Zdenek P.Bazant. Microplane model for cyclic triaxial behavior of concrete[J]. Journal of Engineering Mechanics, 1992, 118(7): 1365-1386
[165] En-Sheng Chen and Oral Buyukozturk. Constitutive model for concrete in cyclic compression[J].
Journal of Engineering Mechanics, 1985, 111(6):797-814
[166] Wimal Suaris,Chengsheng Ouyang, Viraj M.Fernando. Damage model for cyclic loading of concrete[J]. Journal of Engineering Mechanics, 1990, 116(5): 1020-1034
[167] Michael N Fardis, Bunu Alibe and John L. Tassoulas. Monotonic and cyclic constitutive law for concrete[J]. Journal of Engineering Mechanics, 1983, 109(2):516-536
[168] Bing-lin Yang,F.Dafalias,Leonard R.Herrmann. A bounding surface plasticity model for concrete[J]. Journal of Engineering Mechanics, 1985, 111(3):359-380
[169] M.N.Fardis,E.S.Chen. A cyclic multiaxial model for concrete[J]. Computatial Mechanics, 1986(1):301-315
[170] Anna Pandolfi, Alberto Taliercio. Bounding surface models applied to fatigue of plain concrete[J]. Journal of Engineering Mechanics, 1998, 124(5):556-564
[171] Taher M.Abu-Lebdeh,George Z.Voyiadjis. Plasticity-damage model for concrete under cyclic multiaxial loading[J]. Journal of Engineering Mechanics, 1993, 119(7): 1465-1484
[172] E.Hansen,K.Willam. A two-surface anisotropic damage/plasticity model for plain concrete[J]. Fracture Mechanics of Concrete Materials, 2001:540-556
[173] 宋玉普，赵国藩．应变空间混凝土的破坏准则[J]．大连理工大学学报，1991，31(4)：455-461
[174] David J.Stevens and Dajin Liu. Strain-based constitutive model with mixed evolution rules for concrete[J]. Journal of Engineering Mechanics, 1992, 118 (6): 1184-1200
[175] 张承柱，刘信声．应变空间表述的混凝土弹塑性耦合本构模型[J]．清华大学学报(自然科学版)，1995，36(3)：59-64