在役钢筋混凝土桥梁承载能力退化数值模拟和维修需求预测
|
摘要
钢筋锈蚀是影响钢筋混凝土桥梁耐久性的重要因素，随着锈蚀过程的持续，结构可靠度降低、失效概率增大。在桥梁的设计基准期(生命周期)内，如何合理地选择维修方案，就有着相当重要的现实意义。本文的研究包括了腐蚀介质在混凝土中的传播、钢筋锈蚀速度、时变可靠度分析、维修需求预测模型等，通过吴淞江桥的工程实际，对设计基准期内的不同维修方案进行了比较，预测了结构在设计基准期内的维修需求。
混凝土碳化、氯离子渗透、钢筋锈蚀是结构生命周期内可靠度评估的重要基础，本文在已有研究成果的基础上，对混凝土碳化和氯离子渗透进行有限元分析，用数值分析的方法预测钢筋锈蚀开始时间。通过现有模型的比较分析，提出一般大气条件下钢筋锈蚀速度的建议模型和新的桥梁维修需求预测模型。在通过试验对计算假定进行验证的基础上，分析了结构响应的敏感度，计算了其在设计基准期内的时变可靠度和失效概率。最后，对进一步工作的方向进行了简要的讨论。本文的主要研究工作和创新成果有：
(1)在已有研究成果和数学模型的基础上，提出了混凝土碳化有限元数值模拟方法，并通过文献中的试验资料进行了验证。探讨了碳化区内物质含量的分布规律，并利用分析成果对结构长期碳化过程中的影响因素和计算参数的合理取值进行了研究；
(2)通过氯离子渗透模型的有限元分析，对开裂混凝土裂缝深度对氯离子渗透速度的影响进行了研究。得出了在裂缝深度较大时，氯离子渗透的研究必须建立2维模型的结论；
(3)通过现有钢筋锈蚀模型的比较，提出了一般大气环境下钢筋脱钝后锈蚀速度的建议计算公式；
(4)提出考虑关键截面约束条件的有限元计算方法，并通过文献中的试验资料进行验证。以钢筋锈蚀时间为研究变量，对结构的时变可靠度和失效概率进行计算。
(5)在已有模型的基础上，通过比较分析，提出综合考虑目标可靠度和维修成本效益分析的维修需求预测模型；
(6)以吴淞江桥为工程实例，进行了模型的综合应用和维修方案比较，证明了本文提出方法的适用性和有效性。
The rebar corrosion is the important factor that has an effect on the durability of reinforced concrete bridge. With the development of corrosion, the reliability of bridge structures will be reduced and the fail probability will be increased. How to choose repair plan reasonably in the lifetime of bridges will be critical. The thesis includes the transportation process of corrosive substances in the concrete, rebar corrosion model, structural time-varied reliability analysis and repair demand forecast model. At last, all above mentioned models are used in the Wusongjiang Bridge, and as a result, the different repair plans are analyzed and compared.
Concrete carbonation, chloride ion permeation and rebar corrosion are the bases of the structural reliability assessment in the lifetime of bridges. Based on existing research achievements, the finite element method is used in the numerical simulation of carbonation process and chloride ion permeation in the concrete, and then the initial time of rebar corrosion in the concrete can be predicted by numerical method. By the comparison of existing models, the rebar corrosion model under normal atmosphere and new repair demand forecast model are proposed. The computational assumptions are verified by test results of Buckhouse beam, and then the sensitivity of structural response, time-varied structure reliability and failure probability are computed. In the finality, the problems in further studies are briefly discussed. The major contributions of the work presented in this thesis are listed as follows:
(1) Based on existing rsearch works and mathematical models, the finite element numerical simulation method of concrete carbonation is first proposed, and the predictions of this method are shown to be in close agreement with available test results. Next, the variation principles of substances contents in carbonated zone of concrete are discussed and the results are used in the study of parameters in the long term carbonation process of existing structure.
(2) The influence of crack depth on the velocity of chloride ion permeation in concrete is studied by finite element analysis, and the conclusion that the chloride
permeation model in cracked concrete should be two-dimensional is given.
(3) By the comparison of existing rebar corrosion models, the rebar corrosion model under normal atmosphere is suggested.
(4) The finite element method based on constraint in critical section is proposed, and the computation results are shown to be in good agreement with test results. In addition, regarding rebar corrosion as studying parameter, the time-varied structure reliability and failure probability are discussed.
(5) Based on existing models, the new repair demand forecast model including target reliability index and cost-benefit analysis is proposed.
(6) At last, all above mentioned models are used in the Wusongjiang Bridge, and as a result, the different repair plans are analyzed and compared, which proves the effectiveness and validation of methods proposed in this thesis.
混凝土碳化、氯离子渗透、钢筋锈蚀是结构生命周期内可靠度评估的重要基础，本文在已有研究成果的基础上，对混凝土碳化和氯离子渗透进行有限元分析，用数值分析的方法预测钢筋锈蚀开始时间。通过现有模型的比较分析，提出一般大气条件下钢筋锈蚀速度的建议模型和新的桥梁维修需求预测模型。在通过试验对计算假定进行验证的基础上，分析了结构响应的敏感度，计算了其在设计基准期内的时变可靠度和失效概率。最后，对进一步工作的方向进行了简要的讨论。本文的主要研究工作和创新成果有：
(1)在已有研究成果和数学模型的基础上，提出了混凝土碳化有限元数值模拟方法，并通过文献中的试验资料进行了验证。探讨了碳化区内物质含量的分布规律，并利用分析成果对结构长期碳化过程中的影响因素和计算参数的合理取值进行了研究；
(2)通过氯离子渗透模型的有限元分析，对开裂混凝土裂缝深度对氯离子渗透速度的影响进行了研究。得出了在裂缝深度较大时，氯离子渗透的研究必须建立2维模型的结论；
(3)通过现有钢筋锈蚀模型的比较，提出了一般大气环境下钢筋脱钝后锈蚀速度的建议计算公式；
(4)提出考虑关键截面约束条件的有限元计算方法，并通过文献中的试验资料进行验证。以钢筋锈蚀时间为研究变量，对结构的时变可靠度和失效概率进行计算。
(5)在已有模型的基础上，通过比较分析，提出综合考虑目标可靠度和维修成本效益分析的维修需求预测模型；
(6)以吴淞江桥为工程实例，进行了模型的综合应用和维修方案比较，证明了本文提出方法的适用性和有效性。
The rebar corrosion is the important factor that has an effect on the durability of reinforced concrete bridge. With the development of corrosion, the reliability of bridge structures will be reduced and the fail probability will be increased. How to choose repair plan reasonably in the lifetime of bridges will be critical. The thesis includes the transportation process of corrosive substances in the concrete, rebar corrosion model, structural time-varied reliability analysis and repair demand forecast model. At last, all above mentioned models are used in the Wusongjiang Bridge, and as a result, the different repair plans are analyzed and compared.
Concrete carbonation, chloride ion permeation and rebar corrosion are the bases of the structural reliability assessment in the lifetime of bridges. Based on existing research achievements, the finite element method is used in the numerical simulation of carbonation process and chloride ion permeation in the concrete, and then the initial time of rebar corrosion in the concrete can be predicted by numerical method. By the comparison of existing models, the rebar corrosion model under normal atmosphere and new repair demand forecast model are proposed. The computational assumptions are verified by test results of Buckhouse beam, and then the sensitivity of structural response, time-varied structure reliability and failure probability are computed. In the finality, the problems in further studies are briefly discussed. The major contributions of the work presented in this thesis are listed as follows:
(1) Based on existing rsearch works and mathematical models, the finite element numerical simulation method of concrete carbonation is first proposed, and the predictions of this method are shown to be in close agreement with available test results. Next, the variation principles of substances contents in carbonated zone of concrete are discussed and the results are used in the study of parameters in the long term carbonation process of existing structure.
(2) The influence of crack depth on the velocity of chloride ion permeation in concrete is studied by finite element analysis, and the conclusion that the chloride
permeation model in cracked concrete should be two-dimensional is given.
(3) By the comparison of existing rebar corrosion models, the rebar corrosion model under normal atmosphere is suggested.
(4) The finite element method based on constraint in critical section is proposed, and the computation results are shown to be in good agreement with test results. In addition, regarding rebar corrosion as studying parameter, the time-varied structure reliability and failure probability are discussed.
(5) Based on existing models, the new repair demand forecast model including target reliability index and cost-benefit analysis is proposed.
(6) At last, all above mentioned models are used in the Wusongjiang Bridge, and as a result, the different repair plans are analyzed and compared, which proves the effectiveness and validation of methods proposed in this thesis.
引文
[1] 王路．丑陋的混凝土?．世界建筑，2001(2)：18-23
[2] 周定友．混凝土饰面的建筑表现和技术．世界建筑，2001(2)：24-30
[3] 赵冬兵．基于动态有限元分析的桥梁快速评估．中国市政工程，2002,(3)：61-64
[4] Dunker KR, Rabbat BG. Why America's bridges are crumbling. Sci Am 1993:66-72
[5] 上海市市政工程管理局科技情报站．上海地区桥梁技术．1996
[6] Metha P K. Concrete durability-fifty year's progress. Proc. of the 2nd Inter. Conf. on concrete Durability. ACI SP 126-1, 1991: 1-31
[7] 牛荻涛．混凝土结构耐久性与寿命预测．北京：科学出版社，2003
[8] Ivanov, etc. Durability of reinforced concrete in aggressive media. 1993
[9] 张誉等．混凝土结构耐久性概论．上海：上海科学技术出版社，2003
[10] 白广忱等．系统可靠度的模糊优化分配．哈尔滨建筑大学学报，1994，(6)：1-6
[11] 李清富等．结构概率寿命估计．工业建筑．1995，Vol．25(8)：8-10+60
[12] 段忠东等．基于概率疲劳累积损伤理论的构件抗力衰减分析．哈尔滨建筑大学学报，1996，(1)：1-8
[13] 陶峰等．服役钢筋混凝土构件承载力的试验研究．工业建筑．1996，Vol．26(4)：17-20+27
[14] 李田等．混凝土结构耐久性分析与设计．北京：科学出版社，1999
[15] Oskar Klinghoffer, etc. ACI Fall Convention 2000, Toronto, Canada, Committee 365 "Practical Application of Service Life Models"
[16] 张德峰等．裂缝对预应力混凝土结构耐久性的影响．工业建筑．2000，Vol．30(11)：12-14
[17] Scherer, W. T. and D. M. Glagola. Markovian models for bridge maintenance management. Journal of Transportation Engineering, 1994, Vol. 120 (1): 37-51
[18] Cambridge Systematics, Inc.. Pontis 3.2 Users Manual, American Association of State Highway and Transportation Officials, Washington, DC, USA, 1997
[19] Detlef Kuhl, Falko Bangert and Guenther Meschke. European Congress on Computational Methods in Applied Sciences and Engineering. ECCOMAS 2000. Barcelona, 2000:11-14
[20] F. Bangert, D. Kuhl, and G. Meschke. Finite element simulation of chemo-mechanical damageunder cyclic loading conditions. Fracture Mechanics of Concrete Structures, 2001, Vol. 1:145-152
[21] Petryna, Y.S. Schadigung, Versagen und Zuverlassigkeit von Tragwerken des Konstruktiven Ingenieurbaus, Habilitationsschrift. Schriftenreihe des Instituts für Konstruktiven Ingenieurbau, Ruhr-Universitat Bochum, Heft 2004-2, Shaker Verlag, Aachen, 2004
[22] 范立础．桥梁工程安全性与耐久性—展望设计理念进展．上海公路，2004，(1)：1-7
[23] Matthies, G., etc. Uncertainties in probabilistic numerical analysis of structures and solids-stochastic finite elements. Struct. Safety, 1997, Vol. 19(3): 283-336
[24] U.S. Department of transportation, Federal Highway Administration. Bridge Inspector's Reference Manual. Publication No. FHWA NHI 03-001. 2002
[25] 交通部行业标准．公路养护技术规范(JTJ073-96)．北京：人民交通出版社，1996
[26] 涂辉招等．桥梁决策支持系统中的评价模型研究．中国市政工程，2002，(s1)：68-71
[27] 张永清等．用层次分析法评价桥梁的安全性．西安公路交通大学学报，2001，Vol．21(3)：52-56
[28] 城市桥梁技术状况鉴定准则(试行)．上海市市政工程管理局．2002
[29] 公路旧桥承载能力鉴定方法(试行)，交通部，1988
[30] 项贻强等．桥梁运营、养护和管理所面l临的问题、现状及对策研究．中国科技论文在线．
[31] Bridge management in Europe. European Commission DG Ⅶ 4th Framework Program. 1999
[32] 蒋利学等．混凝土碳化区物质含量变化规律的数值分析．工业建筑．1999，Vol．29(1)：8-11
[33] Anna, etc. 1993. Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part Ⅰ: Theoretical formulation. Cement and Concrete Research, 2004, Vol. 34(4): 571-579
[34] Houst&Wittmann. Influence of porosity and water content on the diffusivity of CO_2 and O_2 through hydrated cement paste. Cement and Concrete Research, 1994, Vol. 24(6): 1165-1176
[35] Papadakis, etc. A Reaction Engineering Approach to the Problem of Concrete Carbonation. AIChE Journal, 1989, Vol. 35(10): 1639-1650
[36] Papadakis V G etc. Physical and Chemical Characteristics Affecting the Durability of Concrete. ACI Materials Journal, 1991 Vol. 88(2): 186-196
[37] 张誉等．基于碳化机理的碳化深度实用数学模型．工业建筑．1998，Vol．28(1)：16-19
[38] Thomee, Vidar. Galerkin finite element methods for parabolic problems. Berlin: Springer, 1997
[39] 金达应等．混凝土配合比设计计算手册．沈阳：辽宁科学技术出版社，1997
[40] Cláudio A. Rigo da Silva, etc. Carbonation-Related Microstructural Changes in Long-Term Durability Concrete. Materials Research. 2002, Vol. 5(3): 287-293
[41] Anna V. Saetta, etc. Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part II. Practical applications. Cement and Concrete Research. 2005, Vol. 35(5): 958-967
[42] CEB-FIP Model Code, Section 2.1.9, Transport of Liquids and Gases in Hardened Concrete, Thomas Telford London, United Kingdom, 1990
[43] Byung Hwan Oh. SMiRT 16, Washington DC. 2001
[44] Thoft-Christensen. IFIP Working Conference, Osaka, Japan, 2002
[45] Rodriguez, O. G. Influence of Cracks on Chloride Ingress into Concrete. ACI MATERIALS JOURNAL, 2003,Vol. 100(2): 120-126
[46] Maheswaran, etc.A semi-closed-form solution for chloride diffusion in concrete with time-varying parameters. MAGAZINE OF CONCRETE RESEARCH, 2004, Vol. 56(6): 359-366
[47] Mehta, P. K. Concrete Structure, Properties and Materials, Prentice-Hall, Inc.. 1993
[48] Petre-Lazar, Evaluation du comportement en service des ouvrages en beton arme sounis a la corrosion des aciers, PhD thesis, Quebec, Laval University, 2000
[49] Dimitri V Val. Robert E Melchers. Reliability of deteriorating RC slab bridges, Structural Engineering, ASCE, 1997, Vol. 123(12): 1638-1644
[50] THESE N°. MODELS FOR IDENTIFICATION OF COST EFFECTIVE INTERVENTIONS ON EXISTING STRUCTURES. Ingénieur civil diplomé de l'Université de Belgrade et de nationalité yougoslave. 2002
[51] Yalsyn H, etc. The prediction of corrosion rates of reinforcing steel in concrete. Cement and Concrete Research, 1996, Vol. 26(10): 1593-1599
[52] 常大民等．桥梁结构可靠性分析与设计．北京：中国铁道出版社，1995
[53] Gumbel,E.J. Statistics of extremes. Col umbia University Press, 1958
[54] Hasofer, A.M. and Lind, N.C.. An Exact and Invariant First Order Reliability Format, Porc. ASCE, J. Eng. Mech. Div., 1974:111-121
[55] 袁国干．配筋混凝土结构设计原理．上海：同济大学出版社，1990
[56] BKR. Design Regulations of the Swedish Board of Housing, Building and Planning BKR. Swedish Board of Housing, Building and Planning, 2000
[57] Roelfstra, G. Modèle d'évolution de l'état de ponts-routes en béton. Thesis no. 2310, Ecole Polytechnique Fédérale de Lausanne, 2000
[58] Brance, F. A. and Brito, J. Decision criteria for concrete bridge repair. Structural Engineering International, Journal of the. International Association for Bridge and Structural Engineering, 1995 Vol. 5(2):92-95
[59] Frangopol, D. M., Lin, K.-Y. and Estes, A. C. Life-cycle cost design of deteriorating structures. Journal of Structural Engineering, A SCE, 1997, Vol. 123 (10): 1390-1401
[60] Decision on repair/replacement. The Brime project, Deliverable D7, 1999
[61] 吕西林等．钢筋混凝土非线性有限元理论与应用．上海：同济大学出版社．1997
[62] Guenter Hofstetter, etc. Computational Mechanics of Reinforced Concrete Structure. Vieweg, 1995
[63] Buckhouse, E.R. External Flexural Reinforcement of Existing Reinforced Concrete Beams Using Bolted Steel Channels. Master's Thesis, Marquette University, Milwaukee, Wisconsin. 1997
[64] 张银龙等．用响应面法分析装配式公路钢桥的结构响应．公路交通科技．2003，Vol．20(5)：45-49
[65] Chang-Soo Lee.In-Seok Yoon.Yong-Hyuk Kim. Probability Analysis on Carbonation Rate of Concrete Structures in Seoul Metropolitan Area. Seoul Studies, 2004, Vol. 5(1):No. 174
[66] Brite-Euram Project BE95-1347. DuraCrete-Probabilistic Performance Based Design of Concrete Structures.
[67] Anna V. Saetta, etc. Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part I: Theoretical formulation. Cement and Concrete Research, 2004,Vol. 34(4): 571-579
[68] Almusallam, A.A.,etc. Effect of Reinforcement Corrosion on Flexural Behavior of Concrete Slabs. Journal of Materials in Civil Engineering, 1996, Vol. 8(3): 123-127
[2] 周定友．混凝土饰面的建筑表现和技术．世界建筑，2001(2)：24-30
[3] 赵冬兵．基于动态有限元分析的桥梁快速评估．中国市政工程，2002,(3)：61-64
[4] Dunker KR, Rabbat BG. Why America's bridges are crumbling. Sci Am 1993:66-72
[5] 上海市市政工程管理局科技情报站．上海地区桥梁技术．1996
[6] Metha P K. Concrete durability-fifty year's progress. Proc. of the 2nd Inter. Conf. on concrete Durability. ACI SP 126-1, 1991: 1-31
[7] 牛荻涛．混凝土结构耐久性与寿命预测．北京：科学出版社，2003
[8] Ivanov, etc. Durability of reinforced concrete in aggressive media. 1993
[9] 张誉等．混凝土结构耐久性概论．上海：上海科学技术出版社，2003
[10] 白广忱等．系统可靠度的模糊优化分配．哈尔滨建筑大学学报，1994，(6)：1-6
[11] 李清富等．结构概率寿命估计．工业建筑．1995，Vol．25(8)：8-10+60
[12] 段忠东等．基于概率疲劳累积损伤理论的构件抗力衰减分析．哈尔滨建筑大学学报，1996，(1)：1-8
[13] 陶峰等．服役钢筋混凝土构件承载力的试验研究．工业建筑．1996，Vol．26(4)：17-20+27
[14] 李田等．混凝土结构耐久性分析与设计．北京：科学出版社，1999
[15] Oskar Klinghoffer, etc. ACI Fall Convention 2000, Toronto, Canada, Committee 365 "Practical Application of Service Life Models"
[16] 张德峰等．裂缝对预应力混凝土结构耐久性的影响．工业建筑．2000，Vol．30(11)：12-14
[17] Scherer, W. T. and D. M. Glagola. Markovian models for bridge maintenance management. Journal of Transportation Engineering, 1994, Vol. 120 (1): 37-51
[18] Cambridge Systematics, Inc.. Pontis 3.2 Users Manual, American Association of State Highway and Transportation Officials, Washington, DC, USA, 1997
[19] Detlef Kuhl, Falko Bangert and Guenther Meschke. European Congress on Computational Methods in Applied Sciences and Engineering. ECCOMAS 2000. Barcelona, 2000:11-14
[20] F. Bangert, D. Kuhl, and G. Meschke. Finite element simulation of chemo-mechanical damageunder cyclic loading conditions. Fracture Mechanics of Concrete Structures, 2001, Vol. 1:145-152
[21] Petryna, Y.S. Schadigung, Versagen und Zuverlassigkeit von Tragwerken des Konstruktiven Ingenieurbaus, Habilitationsschrift. Schriftenreihe des Instituts für Konstruktiven Ingenieurbau, Ruhr-Universitat Bochum, Heft 2004-2, Shaker Verlag, Aachen, 2004
[22] 范立础．桥梁工程安全性与耐久性—展望设计理念进展．上海公路，2004，(1)：1-7
[23] Matthies, G., etc. Uncertainties in probabilistic numerical analysis of structures and solids-stochastic finite elements. Struct. Safety, 1997, Vol. 19(3): 283-336
[24] U.S. Department of transportation, Federal Highway Administration. Bridge Inspector's Reference Manual. Publication No. FHWA NHI 03-001. 2002
[25] 交通部行业标准．公路养护技术规范(JTJ073-96)．北京：人民交通出版社，1996
[26] 涂辉招等．桥梁决策支持系统中的评价模型研究．中国市政工程，2002，(s1)：68-71
[27] 张永清等．用层次分析法评价桥梁的安全性．西安公路交通大学学报，2001，Vol．21(3)：52-56
[28] 城市桥梁技术状况鉴定准则(试行)．上海市市政工程管理局．2002
[29] 公路旧桥承载能力鉴定方法(试行)，交通部，1988
[30] 项贻强等．桥梁运营、养护和管理所面l临的问题、现状及对策研究．中国科技论文在线．
[31] Bridge management in Europe. European Commission DG Ⅶ 4th Framework Program. 1999
[32] 蒋利学等．混凝土碳化区物质含量变化规律的数值分析．工业建筑．1999，Vol．29(1)：8-11
[33] Anna, etc. 1993. Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part Ⅰ: Theoretical formulation. Cement and Concrete Research, 2004, Vol. 34(4): 571-579
[34] Houst&Wittmann. Influence of porosity and water content on the diffusivity of CO_2 and O_2 through hydrated cement paste. Cement and Concrete Research, 1994, Vol. 24(6): 1165-1176
[35] Papadakis, etc. A Reaction Engineering Approach to the Problem of Concrete Carbonation. AIChE Journal, 1989, Vol. 35(10): 1639-1650
[36] Papadakis V G etc. Physical and Chemical Characteristics Affecting the Durability of Concrete. ACI Materials Journal, 1991 Vol. 88(2): 186-196
[37] 张誉等．基于碳化机理的碳化深度实用数学模型．工业建筑．1998，Vol．28(1)：16-19
[38] Thomee, Vidar. Galerkin finite element methods for parabolic problems. Berlin: Springer, 1997
[39] 金达应等．混凝土配合比设计计算手册．沈阳：辽宁科学技术出版社，1997
[40] Cláudio A. Rigo da Silva, etc. Carbonation-Related Microstructural Changes in Long-Term Durability Concrete. Materials Research. 2002, Vol. 5(3): 287-293
[41] Anna V. Saetta, etc. Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part II. Practical applications. Cement and Concrete Research. 2005, Vol. 35(5): 958-967
[42] CEB-FIP Model Code, Section 2.1.9, Transport of Liquids and Gases in Hardened Concrete, Thomas Telford London, United Kingdom, 1990
[43] Byung Hwan Oh. SMiRT 16, Washington DC. 2001
[44] Thoft-Christensen. IFIP Working Conference, Osaka, Japan, 2002
[45] Rodriguez, O. G. Influence of Cracks on Chloride Ingress into Concrete. ACI MATERIALS JOURNAL, 2003,Vol. 100(2): 120-126
[46] Maheswaran, etc.A semi-closed-form solution for chloride diffusion in concrete with time-varying parameters. MAGAZINE OF CONCRETE RESEARCH, 2004, Vol. 56(6): 359-366
[47] Mehta, P. K. Concrete Structure, Properties and Materials, Prentice-Hall, Inc.. 1993
[48] Petre-Lazar, Evaluation du comportement en service des ouvrages en beton arme sounis a la corrosion des aciers, PhD thesis, Quebec, Laval University, 2000
[49] Dimitri V Val. Robert E Melchers. Reliability of deteriorating RC slab bridges, Structural Engineering, ASCE, 1997, Vol. 123(12): 1638-1644
[50] THESE N°. MODELS FOR IDENTIFICATION OF COST EFFECTIVE INTERVENTIONS ON EXISTING STRUCTURES. Ingénieur civil diplomé de l'Université de Belgrade et de nationalité yougoslave. 2002
[51] Yalsyn H, etc. The prediction of corrosion rates of reinforcing steel in concrete. Cement and Concrete Research, 1996, Vol. 26(10): 1593-1599
[52] 常大民等．桥梁结构可靠性分析与设计．北京：中国铁道出版社，1995
[53] Gumbel,E.J. Statistics of extremes. Col umbia University Press, 1958
[54] Hasofer, A.M. and Lind, N.C.. An Exact and Invariant First Order Reliability Format, Porc. ASCE, J. Eng. Mech. Div., 1974:111-121
[55] 袁国干．配筋混凝土结构设计原理．上海：同济大学出版社，1990
[56] BKR. Design Regulations of the Swedish Board of Housing, Building and Planning BKR. Swedish Board of Housing, Building and Planning, 2000
[57] Roelfstra, G. Modèle d'évolution de l'état de ponts-routes en béton. Thesis no. 2310, Ecole Polytechnique Fédérale de Lausanne, 2000
[58] Brance, F. A. and Brito, J. Decision criteria for concrete bridge repair. Structural Engineering International, Journal of the. International Association for Bridge and Structural Engineering, 1995 Vol. 5(2):92-95
[59] Frangopol, D. M., Lin, K.-Y. and Estes, A. C. Life-cycle cost design of deteriorating structures. Journal of Structural Engineering, A SCE, 1997, Vol. 123 (10): 1390-1401
[60] Decision on repair/replacement. The Brime project, Deliverable D7, 1999
[61] 吕西林等．钢筋混凝土非线性有限元理论与应用．上海：同济大学出版社．1997
[62] Guenter Hofstetter, etc. Computational Mechanics of Reinforced Concrete Structure. Vieweg, 1995
[63] Buckhouse, E.R. External Flexural Reinforcement of Existing Reinforced Concrete Beams Using Bolted Steel Channels. Master's Thesis, Marquette University, Milwaukee, Wisconsin. 1997
[64] 张银龙等．用响应面法分析装配式公路钢桥的结构响应．公路交通科技．2003，Vol．20(5)：45-49
[65] Chang-Soo Lee.In-Seok Yoon.Yong-Hyuk Kim. Probability Analysis on Carbonation Rate of Concrete Structures in Seoul Metropolitan Area. Seoul Studies, 2004, Vol. 5(1):No. 174
[66] Brite-Euram Project BE95-1347. DuraCrete-Probabilistic Performance Based Design of Concrete Structures.
[67] Anna V. Saetta, etc. Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part I: Theoretical formulation. Cement and Concrete Research, 2004,Vol. 34(4): 571-579
[68] Almusallam, A.A.,etc. Effect of Reinforcement Corrosion on Flexural Behavior of Concrete Slabs. Journal of Materials in Civil Engineering, 1996, Vol. 8(3): 123-127