摘要
由于材料老化、不利环境以及管理和使用不当等,使得既有钢筋混凝土(RC)桥梁在服役过程中结构性能不断退化,可靠性降低,结构的正常使用受到影响。既有RC桥梁服役期的可靠性属于时变可靠性范畴,在对其当前可靠性评价或未来可靠性预测过程中,受实验手段以及时间和空间等的限制,使得人们对以往和未来一些结构抗力和可靠性的影响因素认识存在局限性,从而产生不确定性。这些不确定性包括模糊性、随机性及知识不完善性或未知性。知识不完善性是一种弱的不确定性,当其与前两者并存时可并于前两者中来考虑。
为了真实合理地评估既有RC桥梁整个服役期间的可靠性,本文结合国家自然科学基金项目“既有钢筋混凝土桥梁时变可靠度研究(50478032)”和国家西部交通建设科技项目“混凝土桥梁剩余寿命评估方法研究(200631800019)”,主要针对既有RC梁桥,对考虑模糊性与随机性的时变可靠性等相关问题进行了深入研究,主要工作包括以下几个方面:
(1)建立了同时考虑模糊性和随机性的材料耐久性退化概率模型。针对RC桥梁中氯离子导致的钢筋锈蚀,同时考虑模糊性与随机性,研究了锈蚀初始时间的模糊概率特征;引入Monte Carlo区间抽样数值模拟技术,分别建立了均匀锈蚀和局部锈蚀状态下的主筋截面积退化概率模型,并对比了其异同;鉴于局部锈蚀对小直径钢筋影响显著,建立了箍筋截面积退化概率模型;基于不同构件中锈后钢筋力学性能试验研究,得到了质量损失率——屈服强度以及截面损失率——屈服强度之间的关系,建立了钢筋强度退化概率模型。在已有的混凝土强度时变模型基础上,进一步考虑模糊性,建立了混凝土强度退化概率模型。
(2)建立了同时考虑模糊性与随机性的受弯构件抗力退化概率模型。基于建立的材料耐久性退化模型,考虑锈后粘结力退化对构件抗力的影响,以模糊随机过程和误差传递理论为基础,推导了不修复情况下的构件抗力退化均值和标准差模糊随机时变函数,以RC梁桥为例,建立了受弯构件抗力模糊随机概率模型,同时,提出了模糊性随服役时间变化的抗力均值和标准差分析方法。
(3)基于服役多年的两座RC桥梁构件室内的试验研究,提出了一种抗力估算方法。分析了构件抗力退化的影响因素,并分别建立了这些影响因素无损检测结果的模糊隶属函数,将定性描述定量化,利用模糊数学和层次分析(AHP)法把这些既相互关联又相互影响的不确定因素系统化,从而计算出在这些影响因素下的承载能力综合折减系数,再与不考虑损伤的有限元计算结果相结合,实现对件抗力的估算。估算结果与静载试验结果吻合,可为既有RC桥梁构件抗力评估提供参考。
(4)基于平衡更新过程建立了既有公路桥梁车辆荷载效应模型。依据我国现有车辆荷载统计数据,通过截尾概率分布限制不同连续到达间距和车重最值,采用卷积公式计算连续n个车辆到达间距及总重的概率密度函数,应用平衡更新过程推求车队长度概率函数,进一步结合桥梁影响线函数,建立我国既有公路桥梁车辆荷载效应模型。该模型以截尾概率分布和平衡更新过程为理论基础,可以考虑混合交通,适用于既有桥梁可靠性评估。
(5)针对现有统计资料中桥梁构件设计容重采用定值,以及既有桥梁自重分布统计参数受很多因素的影响难以用确定性的量值加以准确描述的特点,将恒载均值和标准差作为有界闭模糊数来考虑,将其概率模型用模糊概率分布来描述,利用选取的模糊隶属函数中阈值а的取值变化,来解决既有桥梁恒载分布统计参数可能发生变异的问题。
(6)提出了同时考虑模糊性与随机性的既有RC桥梁时变可靠性分析方法。考虑抗力和车辆荷载效应的模糊随机时变性、恒载的模糊随机性以及失效准则的模糊性,建立了承载能力模糊极限状态方程,改进JC法并采用Matlab语言编制相应程序来求解模糊时变可靠指标。分析了一座RC梁桥可靠指标随时间和阈值а变化情况,以及模糊性随时间变化时可靠指标变化规律。将常规既有RC桥梁时变可靠性分析过程中只考虑随机性,扩展到同时考虑模糊性与随机性。
The structural performance of existing reinforced concrete (RC) bridges gradually deteriorates during active time due to material aging, adverse environment, inappropriate management and service. The structural reliability decreases and regular service is affected. The reliability of existing RC bridge is time-variant. The research on influencing factors of future or former structural resistance and reliability is largely restricted by experimental means and space time. So the limitation of some conclusions can not be avoided, and the uncertainty including fuzziness, randomness, and faultiness of knowledge can appear. The faultiness of knowledge is a weak uncertainty, and can be considered into fuzziness and randomness when it coexists with them.
In order to rationally evaluate reliability of existing RC bridge during the whole active life, the problems on the time-variant reliability under fuzziness and randomness for mainly existing RC beam bridge are deeply investigated. This research project is supported by National Natural Science Fund of China under the Project No. 50478032“Research on Time-variant Reliability of Existing RC Bridge”and National West Communication Construction Fund of China under the Project No. 200631800019“Research on Residual Life of Concrete Bridge”. The main research works include as follows:
(1) The material durability degradation models under fuzziness and randomness are established. The reinforcement corrosion in RC bridge is considered to be induced by chloride ion. The fuzziness and randomness are simultaneously considered. The fuzzy probabilistic characteristic of the corrosion initiation time is studied. The Monte Carlo interval numerical simulation is introduced, and the degradation probabilistic models of time-variant main reinforcement area under two corrosion states are established. Meantime, the degradation probabilistic models under general and pitting corrosion are compared. The effect of pitting corrosion on small-diameter reinforcement is obvious, and the degradation probabilistic model of time-variant stirrup area is established. Based on the experimental investigation on mechanical property of corroded reinforcement in different members, the relationships between the quality corrosion rate and yield strength, the area corrosion rate and yield strength are obtained, and the degradation probabilistic model of reinforcement strength is established. Based on some existing time-variant models of concrete strength, the fuzziness is introduced, and the degradation probabilistic model of concrete strength is established.
(2) The resistance degradation probabilistic model under fuzziness and randomness for flexural member is established. The effect of the bond strength degradation on resistance is incorporated. To consider material durability degradation, the fuzzy time-variant functions of the mean value and standard deviation for the unrepaired member resistance are derived based on the fuzzy stochastic process and error transfer theory. The fuzzy random time-variant probabilistic model of flexure member is established by an example RC beam bridge, and the analytical method for the mean value and standard deviation of resistance under the fuzziness changing with time is presented.
(3) Based on the laboratory experimental investigation on members from two RC bridges, an estimation method on resistance is presented. Some influencing factors reducing member resistance are analyzed. The fuzzy membership functions on the nondestructive examination results of these factors are established, and the qualitative description is quantified. The fuzzing mathematics and analytic hierarchy process (AHP) are used to systematize these interrelated and interactional uncertain influencing factors. The synthetical reduction coefficient reflecting these influencing factors is computed accordingly. After that the finite element result without damage is combined with synthetical reduction coefficient to estimate the carrying capacity. The theoretical results are agreed with experimental values. This method can provide scientific basis for evaluation of existing RC bridge resistance.
(4) The traffic load effect model for the existing highway bridge is established based on the equilibrium renewal process. The existing vehicle statistic data in China are used. The extreme values of the spacing intervals for different continuous arrivals and the vehicle weight are controlled by the truncated probabilistic distribution. The probability density functions of total weight and spacing intervals for n continuous arrivals are computed by the convolution formula. The probability density function of the length of convoy is derived based on the equilibrium renewal process. After that the bridge influence line transitive function is further combined to establish the traffic load effect model for existing highway bridge. This model can consider the varying traffic condition, and apply to reliability evaluation of existing bridges.
(5) The design specific density of bridge member is considered as the constant value in exiting statistical data. The statistical parameters of the dead load of existing bridge are difficult to describe truly by the certain value due to some uncertain influencing factors. To consider these problems, the mean value and standard deviation of existing bridge dead load are described as the bounded closed fuzzy numbers, and the probabilistic model for dead load is expressed as the fuzzy probabilistic distribution. The variability of existing bridge dead load distribution parameters can be reflected by variety of threshold valueαin the selected fuzzy membership function.
(6) The analytical method on the time-variant reliability under fuzziness and randomness for existing RC bridge is presented. To consider the fuzzy random time-variant characteristic of resistance and live load, fuzziness and randomness of dead load, fuzziness of failure criterion, the fuzzy limit state equation of load carrying capacity is established. The JC method is improved to solve the fuzzy time-variant reliability index, and the computing procedure is developed by Matlab language. The variety in reliability index of an example existing RC beam bridge with time and threshold valueаis analyzed. The variety law of reliability index under the fuzziness changing with service time is discussed. The conventional existing RC bridge time-variant reliability analysis considering randomness is developed to include simultaneously fuzziness and randomness.
引文
[1] Enright MP, Frangopol DM. Survey and evaluation of damaged concrete bridges[J]. Journal of Bridge Engineering, ASCE. 2000, 5(1):31-38.
[2] Hong HP. Assessment of reliability of aging reinforced concrete structures[J]. Journal of Structural Engineering, ASCE. 2000, 126(12):1458-1465.
[3] 赵国藩, 贡金鑫, 赵尚传. 我国土木工程结构可靠性研究的一些进展[J]. 大连理工大学学报. 2000, 43(3):253-258.
[4] 赵国藩. 工程结构可靠度理论与应用[M]. 大连: 大连理工大学出版社, 1996.
[5] 张跃, 王光远. 模糊随机动力系统理论[M]. 北京: 科学出版社, 1995.
[6] Park C-H. Time dependent reliability models for steel girder bridges [D]: [The Philosophy Doctor Thesis of University of Michigan]. Detroit: University of Michigan, 1999.
[7] Wang H. Steel-free hybrid reinforcement system for reinforced concrete flexural members [D]: [The Philosophy Doctor Thesis of University of MIssouri-rolla]. Missouri: University of MIssouri-rolla, 2005.
[8] Nowak AS, Tharmabala T. Bridge reliability evaluation using load tests [J]. Journal of Structural Engineering, ASCE. 1988, 114(10):2268-2279.
[9] Stewart MG, Val DV. Role of load history in reliability-based decision analysis of aging bridge [J]. Journal of Structural Engineering, ASCE. 1999, 125(7):776-783.
[10] 交通部. 公路桥涵通用设计规范(JGT D60-2004)[S]. 北京: 人民交通出版社, 2004.
[11] 金伟良, 赵羽习. 混凝土结构耐久性[M]. 北京: 科学出版社, 2002.
[12] 牛荻涛. 混凝土结构耐久性与寿命预测[M]. 北京: 科学出版社, 2003.
[13] 张誉, 蒋利学, 张伟平等. 混凝土结构耐久性概论[M]. 上海: 上海科学技术出版社, 2003.
[14] 金伟良, 赵羽习. 混凝土结构耐久性研究的回顾与展望[J]. 浙江大学学报(工学版). 2002, 36(4):371-380.
[15] Ho DWS, Lewis RL. The carbonation of concrete and Its prediction[J]. Cement and Concrete Research. 1987, 17:489-504.
[16] Dhir RK, Hewlett PC, Chan YN. Near surface characteristics of concrete: prediction carbonation resistance [J]. Magazine of Concrete Research. 1989, 42:137-143.
[17] Papadakis VG. Physical and chemical characteristics affecting the durability of concrete[J]. ACI Materials Journal. 1991, 88:186-196.
[18] Papadakis VG. Fundamental modeling and experimental investigation of concrete carbonation[J]. ACI Materials Journal. 1991, 88:363-373.
[19] Papadakis VG. Experimental investigation and mathematical modeling of the concrete carbonation problem[J]. Chemical Engineering Science. 1991, 46:1333-1338.
[20] 蒋利学, 张誉. 基于碳化机理的混凝土碳化深度实用数学模型[J]. 工业建筑. 1999, 29(1):16-19.
[21] 朱安民. 混凝土碳化与钢筋混凝土耐久性[J]. 混凝土. 1992, (6):18-22.
[22] 牛荻涛, 陈亦奇. 混凝土结构的碳化模式与碳化寿命分析[J]. 西安建筑科技大学学报. 1995, 27(4):365-369.
[23] Saettaa AV, Vitaliani RV. Experimental investigation and numerical modeling of carbonation process in reinforced concrete structures Part I: Theoretical formulation[J]. Cement and Concrete Research. 2004, 34(4):571-579.
[24] 涂永明, 吕志涛. 应力状态下混凝土的碳化试验研究[J]. 东南大学学报(自然科学版). 2003, 33(5):573-576.
[25] 金祖权, 伟 孙, 张云升等. 荷载作用下混凝土的碳化深度[J]. 建筑材料学报. 2005, 8(2):179-183.
[26] 张海燕, 把多铎, 王正中. 混凝土碳化深度的预测模型[J]. 武汉大学学报(工学版). 2006, 39(5):42-45.
[27] 梁咏宁, 袁迎曙. 硫酸盐腐蚀后混凝土单轴受压应力应变全曲线[J]. 混凝土. 2005, (7):59-61.
[28] 陈元素. 受腐蚀混凝土力学性能试验研究[D]: [大连理工大学硕士学位论文]. 大连: 大连理工大学, 2006.
[29] 翟运琼. 腐蚀混凝土单轴受压本构模型及其在混凝土构件力学分析中的应用[D]: [重庆大学硕士学位论文]. 重庆: 重庆大学, 2005.
[30] 牛荻涛, 王庆霖. 一般大气环境下混凝土强度经时变化模型[J]. 工业建筑. 1995, 25(6):36-38.
[31] 张建仁, 刘扬. 混凝土桥梁构件服役期的抗力概率模型[J]. 长沙理工大学学报(自科版). 2004, 1(1):27-33.
[32] Stewart MG, Rosowsky DV. Time-dependent reliability of deteriorating reinforced concrete bridge decks[J]. Structural Safety. 1998, 20:91-109.
[33] Kim J-K, Han SH, Song YC. Effect of temperature and aging on the mechanical properties of concrete Part I. Experimental results[J]. Cement and Concrete Research. 2002, 32(7):1087-1094.
[34] Kim J-K, Han SH, Park SK. Effect of temperature and aging on the mechanical properties of concrete Part II. Prediction model[J]. Cement and Concrete Research. 2002, 32(7):1095-1100.
[35] 曹双寅, 朱伯龙. 受腐蚀混凝土和钢筋混凝土的性能[J]. 同济大学学报(自然科学版). 1990, 18(2):239-242.
[36] 张喜德, 韦树英, 彭修宁. 钢筋锈蚀对混凝土抗压强度影响的试验研究[J]. 工业建筑. 2003, 33(3):5-7.
[37] Alexander S, Kefei L, Olivier C. Aging approach to water effect on alkali–silicadegradation of structures[J]. Journal of Engineering Mechanics, ASCE. 2003, 129(1):50-59.
[38] Basheer L, Kropp J, Clelandc DJ. Assessment of the durability of concrete from its permeation properties: a review[J]. Construction and Building Materials. 2001, 15:93-103.
[39] Hansson CM. Comments on electrochemical measurements of the rate of corrosion of steel in concrete[J]. Cement Concrete Research. 1984, 14:574-584.
[40] Gjorv OE, Venndsland O, El-Busaidy AHS. Diffusion of dissolved oxygen through concrete[J]. Mataerials Performance. 1986:39-44.
[41] Page CL, Lambert P. Kinetics of Oxygen diffusion in hardened cement pastes[J]. Journal of Materials Science. 1987, 22:942-946.
[42] Gonzalez JA, Molina A, Otero E. On the mechanism of steel corrosion in concrete: the role of Oxygen diffusion[J]. Mataerials of Concrete Research. 1990, 42(150):23-27.
[43] Kobayashi K, Suttoh K. Oxygen diffusivity of various cementitious materials[J]. Cement Concrete Research. 1991, 21:273-284.
[44] Mohammed TU, Otsuki N, Hamada H. Oxygen Permeability in cracked concrete reinforced with plian and deformed bars[J]. Cement and Concrete Research. 2001, 31:829-834.
[45] Bazant ZP. Physical model for steel corrosion in concrete sea structures-theory[J]. Journal of Structural Division, ASCE. 1979, 105(6):1137-1153.
[46] Tuutti K. Corrosion of steel in concrete: Research Report. CBI. Stockholm, Sweden, 1982.
[47] Mozer J. Corrosion of reinforcing bars in concrete[J]. Journal of the American Concrete Institute. 1965:909-931.
[48] Uhlig H. Corrosion and corrosion control[M]. New York: John Wiley and Sons, 1983.
[49] Berkely K, Pathmanaban S. Cathodic protection of reinforcement steel in concrete[M]. London: Butterworths & Co. Ltd., 1990.
[50] Ho D, Lewis R. Carbonation of concrete and its prediction[J]. Cement Concrete Research. 1987, 17:489-504.
[51] Cao HT, Sirivivatnanon V. Corrosion of steel in concrete with and without silica fume[J]. Cement and Concrete Research. 1990, 20:316-324.
[52] Arya C, Buenfeld N, Newman J. Assessment of simple methods of determining the free chloride ion content of cement pastes[J]. Cement Concrete Research. 1987, 17:907-918.
[53] Hope B, Alan IK. Chloride corrosion threshold in concrete[J]. Materials Journal, ACI. 1987, 84:306-314.
[54] Pullar-Strecker P. Corrosion damaged concrete: assessment and repair[M]. London: Butterworths, 1987.
[55] Batis G, Rakanta E. Corrosion of steel reinforcement due to atmospheric pollution[J]. Cement & Concrete Composites. 2005, 27:269-275.
[56] Alonso C, Andrade C, Castellote M, Castro P. Chloride threshold values to depassivatereinforcing bars embedded in a standardized OPC mortar[J]. Cement and Concrete Research. 2000, 30(7):1047-1055.
[57] 龚洛书, 柳春圃. 混凝土的耐久性及其防护修补[M]. 北京: 中国建筑工业出版社, 1990.
[58] 洪乃丰. 混凝土中钢筋腐蚀与结构物的耐久性[J]. 公路. 2001, (2):66-69.
[59] Verbeck G. Field and laboratory studies of the sulphate resistance of concrete. In: Performance of concrete. Toronto: University of Toronto Press, 1968.
[60] Rasheeduzzafar, Al-Gahtani A, Al-Saadoun S. Influence of construction practices on concrete durability[J]. ACI Materials Journal. 1989, 86(6):566-575.
[61] Ahmad S. Reinforcement corrosion in concrete structures, its monitoring and service life prediction-a review[J]. Cement & Concrete Composites. 2003, 25:459-471.
[62] Williamson S, Clark L. The influence of the permeability of concrete cover on Reinforcement corrosion[J]. Magazine of Concrete Research. 2001, 53(3):183-195.
[63] 张平生. 混凝土状况对钢筋锈蚀的影响[J]. 西安建筑科技大学学报. 1998, 30(1):5-8.
[64] 董振平, 牛荻涛, 刘西芳等. 一般大气环境下钢筋开始锈蚀时间的计算方法[J]. 西安建筑科技大学学报(自然科学版). 2006, 38(2):204-209.
[65] 李果, 袁迎曙, 耿欧. 气候条件对碳化混凝土内钢筋腐蚀速度的影响[J]. 混凝土. 2005, (8):40-43.
[66] 洪定海. 混凝土中钢筋腐蚀与防护[M]. 北京: 中国铁道出版社, 1998.
[67] Thoft-Christensen P, Jensen FM, Middleton CR. Assessment of the reliability of concrete slab bridges. In: Frangopol DM, editor. Reliability and Optimization of Structral Systems. Pergamon: Elsevier, New York, 1997, 321-328.
[68] Thoft-Christensen P. Lifetime reliability assessment of concrete slab bridges. In: Frangopol DM, editor. Optimal Performance of Civil Infrastructure Systems. Reston: ASCE, 1998, 181-193.
[69] Enright MP. Time-variant reliability of reinforced concrete bridges under environmental attack[D]: [The Philosophy Doctor Thesis of University of Colorado]. Denver: University of Colorado, 1998.
[70] Rafiq M. Health monitoring in proactive reliability management of deteriorating concrete bridges[D]: [The Philosophy Doctor Thesis of University of Surrey]. Surrey, UK: University of Surrey, 2005.
[71] Liu T. Modeling the dynamic corrosion process in chloride contaminated structure[J]. Cement & Concrete Reseach. 1984, 28:365-379.
[72] 孙启明, 弓国军, 杨娟娟等. 氯盐环境下混凝土钢筋腐蚀速度实用公式[J]. 低温建筑技术. 2006, (3):1-2.
[73] 王东方. 钢筋混凝土构件氯离子侵蚀条件下钢筋初始锈蚀时间的计算方法[D]: [北京工业大学硕士学位论文]. 北京: 北京工业大学, 2003.
[74] Vu KAT, Stewart MG. Structural reliability of concrete bridges including improved chloride-induced corrosion models[J]. Structural Safety. 2000, 22:313-333.
[75] Elsener B. Corrosion rate of steel in concrete—Measurements beyond the Tafel law[J]. Corrosion Science. 2005, 47:3019-3033.
[76] Liu Y, Weyers R. Modeling the time-to-corrosion cracking in chloride contaminated reinforced concrete structures[J]. ACI Materials Journal. 1998, 95(6):675-681.
[77] Bazant ZP. Physical model for steel corrosion in concrete sea structures-application[J]. Journal of Structural Division , ASCE. 1979, 105(6):1155-1166.
[78] Maaddawy TE, Soudki K. A model for prediction of time from corrosion initiation to corrosion cracking[J]. Cement & Concrete Composites. 2007, 29:168-175.
[79] Liang M-T, Lin L-H, Liang C-H. Service life prediction of existing reinforced concrete bridges exposed to chloride environment[J]. Journal of Infrastructure Systems, ASCE. 2002, 8(3):76-85.
[80] Zivica V. Utilization of electrical resistance method for the evaluation of the state of steel reinforcement in concrete and the state of its corrosion[J]. Construction and Building Materials. 2000, 14:351-358.
[81] 牛荻涛, 李峰, 王庆霖. 一般室内环境混凝土锈蚀开裂前钢筋锈蚀量的估计[J]. 西安建筑科技大学学报. 1996, 28(2):124-128.
[82] 牛获涛, 王庆霖, 王林科. 锈蚀开裂前混凝土中钢筋锈蚀量的预测模型[J]. 工业建筑. 1996, 26(4):8-10.
[83] 牛荻涛, 王庆霖, 王林科. 一般大气环境混凝土中钢筋锈蚀量的估计[J]. 工程力学. 1997, 14(2):92-98.
[84] 徐善华, 牛荻涛, 王庆霖. 大气环境条件下混凝土中钢筋的锈蚀[J]. 建筑技术. 2003, 34(4):267-269.
[85] 金伟良, 鄢飞, 张亮. 考虑混凝土碳化规律的钢筋锈蚀率预测模型[J]. 浙江大学学报. 2000, 34(2):158-163.
[86] Liang M-T, Jin W-L, Yang R-J. Predeterminate model of corrosion rate of steel in concrete[J]. Cement and Concrete Research. 2005, 35:1827-1833.
[87] 陈莹, 王天稳. 碳化引起混凝土锈胀开裂前钢筋锈蚀量的研究[J]. 混凝土. 2005, (12):63-66.
[88] Stewart MG. Spatial variability of pitting corrosion and its influence on structural fragility and reliability of RC beams in flexure[J]. Structural Safety. 2004, 26:453-470.
[89] 惠云玲. 混凝土结构中钢筋锈蚀深度评估和预测试验研究[J]. 工业建筑. 1997, 27(6):6-9.
[90] 张伟平. 混凝土结构的钢筋锈蚀损伤预测及其耐久性评估[D]: [同济大学博士学位论文]. 上海: 同济大学, 1999.
[91] 潘振华, 牛荻涛, 王庆霖. 钢筋锈蚀开裂条件的实验研究[J]. 工业建筑. 1999, 29(5):46-49.
[92] 徐善华. 混凝土结构退化模型与耐久性评估[D]: [西安建筑科技大学博士学位论文]. 西安: 西安建筑科技大学, 2003.
[93] 牛荻涛, 王庆霖, 王林科. 锈蚀开裂后混凝土中钢筋锈蚀量的预测模型[J]. 工业建筑. 1996, 26(4):11-13.
[94] Maslehuddin M, Allam IM, Al-Sulaimani GJ. Effect of rusting of reinforcing steel on its mechanical properties and bond with concrete[J]. ACI Materials Journal. 1990, 87(5):496-502.
[95] Maslehuddin M, Ibrahim I, Saricimen H. Influence of atmospheric corrosion on the mechanical properties of reinforcing steel[J]. Construction and Building Materials. 1993, 8(1):35-41.
[96] Almusallam AA. Effect of degree of corrosion on the properties of reinforcing steel bars[J]. Construction and Building Materials. 2001, 15:361-368.
[97] Apostolopoulos CA, Papadopoulos MP, Pantelakis SG. Tensile behavior of corroded reinforcing steel bars BSt 500s[J]. Construction and Building Materials. 2006, 20:782-789.
[98] 惠云玲, 林志伸, 李荣. 锈蚀钢筋性能试验研究分析[J]. 工业建筑. 1997, 27(6):10-13.
[99] 马良哲, 白常举. 钢筋锈蚀后力学性能的试验研究. 第五届全国混凝土耐久性学术交流会. 杭州, 2000.
[100] 袁迎曙, 贾福萍, 蔡跃. 锈蚀钢筋的力学性能退化研究[J]. 工业建筑. 2000, 30(1):43-46.
[101] 杨淑慧. 腐蚀对钢筋力学性能影响的研究[D]: [郑州大学硕士学位论文]. 郑州: 郑州大学, 2002.
[102] 王军强. 大气环境下锈蚀钢筋力学性能试验研究分析[J]. 徐州建筑职业技术学院学报. 2003, 3(3):25-27.
[103] Alexopoulos ND, Apostolopoulos CA, Papadopoulos MP. Mechanical performance of BStIV grade steel bars with regard to the long-term material degradation due to corrosion damage[J]. Construction and Building Materials. 2007, 21:1362-1369.
[104] Lee HS, Noguchi T, Tomosoma F. FEM analysis for structural performance of deteriorated RC structures due to rebar corrosion[C]. The Second International Conference on Concrete Under Severe Conditions. Tromso, 1998:1010-1019.
[105] 张伟平, 商登峰, 顾祥林. 锈蚀钢筋应力-应变关系研究[J]. 同济大学学报(自然科学版). 2006, 34(5):586-592.
[106] Apostolopoulos CA. Mechanical behavior of corroded reinforcing steel bars S500s tempcore under low cycle fatigue[J]. Construction and Building Materials. 2007, 21:1447-1456.
[107] Al-Sulaimani GJ, Kaleemullan N, Basunbul IA. Influence of corrosion and cracking onbond behavior and strength of reinforced concrete members[J]. ACI StructuralJournal. 1990, 87(2):220-231.
[108] L.Amleh, S.Mirza. Corrosion influence on bond between steel and concrete[J]. ACI Structural Journal. 1999, 96(3):415-423.
[109] Mangat PS, Elgarf MS. Bond characteristics of corroding reinforcement in concrete beams[J]. Materials and Structures. 1999, 32(3):89-97.
[110] Auyeung YB. Bond behavior of corroded reinforcement bars[J]. ACI Materials Journal. 2000, 97(2):214-220.
[111] Auyeung Y, Balaguru P, Chung L. Bond behavior of corroded reinforced bars[J]. ACI Materials Journal. 2000, 97(2):214-221.
[112] Lee H-S, Noguchi T, Tomosawa F. Evaluation of the bond properties between concrete and reinforcement as a function of the degree of reinforcement corrosion[J]. Cement and Concrete Research. 2002, 32:1313-1318.
[113] 赵羽习, 金伟良. 锈蚀钢筋与混凝土粘结性能的试验研究[J]. 浙江大学学报(工学版). 2002, 36(4):352-356.
[114] Fanga C, Lundgrenb K, Chen L. Corrosion influence on bond in reinforced concrete[J]. Cement and Concrete Research. 2004, 34:2159-2167.
[115] 潘振华, 牛荻涛, 王庆霖. 锈蚀力与极限粘结强度关系的试验研究[J]. 工业建筑. 2000, 30(5):10-12.
[116] 张伟平, 张誉. 锈蚀开裂后钢筋混凝土粘结滑移本构关系研究[J]. 土木工程学报. 2001, 34(5):40-44.
[117] Bhargava K, Ghosh AK, Yasuhiro Mori. A proposed model for corrosion-induced bond degradation in reinforced concrete. In: Charney FA, Grierson DE, Hoit M, editors. 17th Analysis and Computation Specialty Conference. St. Louis, Missouri, USA: ASCE, 2006.
[118] Fang C, Lundgren K, Plos M. Bond behaviour of corroded reinforcing steel bars in concrete[J]. Cement and Concrete Research 2006, 36(10):1931-1938.
[119] Wang X, Liu X. Bond strength modeling for corroded reinforcements[J]. Construction and Building Materials. 2006, 20(3):177-186.
[120] Bhargava K, Ghoshb AK, Mori Y. Corrosion-induced bond strength degradation in reinforced concrete-analytical and empirical models[J]. Nuclear Engineering and Design. 2007, 237(11):1140-1157.
[121] Fang C, Gylltoft K, Lundgren K. Effect of corrosion on bond in reinforced concrete under cyclic loading[J]. Cement and Concrete Research. 2006, 36:548-555.
[122] Mangat P, Elgarf M. Flexural Strength of Concrete Beams with Corroding Reinforcement[J]. ACI Structural Journal. 1999, 96(1):149-158.
[123] 袁迎曙, 章鑫森, 姬永生. 人工气候与恒电流通电法加速锈蚀钢筋混凝土梁的结构性能比较研究[J]. 土木工程学报. 2006, 39(3):42-46.
[124] Mangat P, Elgarf M. Strength and serviceability of repaired reinforced concrete beams undergoing reinforcement corrosion[J]. Magazine of Concrete Research,. 1999,51(2):97-112.
[125] Razak H, Choi F. The effect of corrosion on the natural frequency and modal damping of reinforced concrete beams[J]. Engineering Structures. 2001, 23(9):1126-1133.
[126] Ballim Y, Reid J, Kemp A. Deflection of RC beams under simultaneous load and steel corrosion[J]. Magazine of Concrete Research. 2001, 53(3):171-181.
[127] Ballim Y, Reid J. Reinforcement corrosion and the deflection of RC beams––an experimental critique of current test methods[J]. Cement and Concrete Composites. 2003, 25(6):625-632.
[128] Andrés A, Torres-Acosta, Sergio N-G. Residual flexure capacity of corroded reinforced concrete beams[J]. Engineering Structures. 2007, 29(6):1145-1152.
[129] Shannag M, Al-Ateek S. Flexural behavior of strengthened concrete beams with corroding reinforcement[J]. Construction and Building Materials. 2006, 20:834-840.
[130] Minh H, Mutsuyoshi H, Niitani K. Influence of grouting condition on crack and load-carrying capacity of post-tensioned concrete beam due to chloride-induced corrosion[J]. Construction and Building Materials. 2007, 21(7):1568-1575.
[131] 袁迎曙, 贾福萍, 蔡跃. 锈蚀钢筋混凝土梁的结构性能退化模型[J]. 土木工程学报. 2001, 34(3):47-52.
[132] 徐善华, 牛荻涛. 锈蚀钢筋混凝土简支梁斜截面抗剪性能研究[J]. 建筑结构学报. 2004, 25(5):98-104.
[133] 贡金鑫, 仲伟秋, 赵国藩. 受腐蚀钢筋混凝土偏心受压构件低周反复性能的试验研究[J]. 建筑结构学报. 2004, 25(5):92-98.
[134] 易伟建, 赵新. 持续荷载作用下钢筋锈蚀对混凝土梁工作性能的影响[J]. 土木工程学报. 2006, 39(1):7-12.
[135] Torres-Acosta AA, Navarro-Gutierrez S, Terán-Guillén J. Residual flexure capacity of corroded reinforced concrete beams[J]. Engineering Structures. 2007, 29:1145-1152.
[136] Castel A, Francois R, Arliguie G. Mechanical behaviour of corroded reinforced concrete beams. I. Experimental study of corroded beams[J]. Materials and Structures. 2000, 33(23):539-544.
[137] 惠云玲, 李容, 林志伸等. 混凝土基本构件钢筋锈蚀前后性能试验研究[J]. 工业建筑. 1997, 27(5):14-19.
[138] 任宝双, 钱稼茹. 在用钢筋混凝土简支桥面梁受弯承载力估算[J]. 工业建筑. 2000, 30(11):29-33.
[139] 范颖芳, 周晶, 黄振国. 受氯化物腐蚀钢筋混凝土构件承载力研究[J]. 工业建筑. 2001, 31(5):3-5.
[140] Fan Y-f, Jing Z, Xin F. Prediction of load carrying capacity of corroded reinforced concrete beam[J]. China Ocean Engineering. 2004, 18(1):107-118.
[141]潘毅, 陈朝晖. 钢筋混凝土基本构件腐蚀后性能的试验研究[J]. 四川建筑科学研究. 2004, 30(3):71-74.
[142] 吴瑾, 吴胜兴. 海洋环境下锈裂钢筋混凝土构件截面抗弯刚度识别[J]. 河海大学学报(自然科学版). 2004, 32(5).
[143] 邓冰, 丁乃庆. 天津港高桩码头锈蚀损面板残余承载力试验及估算方法的研究[J]. 港工技术. 1998, (1):25-31.
[144] 张建仁, 李传习, 王磊等. 既有钢筋混凝土拱肋承载能力测试和分析[J]. 工程力学. 2006, 23(12):136-142.
[145] Capozucca R, M.Nilde C. Influence of reinforcement corrosion-in the compressive zone-on the behaviour of RC beams[J]. Engineering Structures. 2003, 25(13):1575-1583.
[146] 金伟良, 赵羽习. 锈蚀钢筋混凝土梁抗弯强度的试验研究[J]. 工业建筑. 2001, 31(5):9-11.
[147] 吴瑾. 钢筋混凝土结构锈蚀损伤检测与评估[M]. 北京: 科学出版社, 2005.
[148] Azher S. A prediction model for the residual flexural strength of corroded reinforced concrete beams[D]: [The Philosophy Doctor Thesis of King Fand University of Petroleum and Minerals]. Dhahran: King Fand University of Petroleum and Minerals, 2005.
[149] Torres-Acosta A, Martinez-Madrid M. Residual life of corroding reinforced concrete structures in marine environment[J]. Journal of Materials in Civil Engineering. 2003, 15(4):344-353.
[150] 王小惠. 锈蚀钢筋混凝土梁正截面抗弯承载力的研究[J]. 混凝土与水泥制品. 2006, 3:39-42.
[151] 王小惠. 锈蚀钢筋混凝土梁的承载能力[D]: [上海交通大学博士学位论文]. 上海: 上海交通大学, 2004.
[152] 熊进刚, 祝建军, 霍艳华. 钢筋混凝土简支梁纵筋锈蚀对受剪承载力的影响[J]. 南昌大学学报. 2006, 28(2):194-196.
[153] Higgins C. Shear capacity assessment of corrosion-damaged reinforced concrete beams:final report SPR 326. Oregon Department of Transportation, Research Unit; Available from the National Technical Information Service, 2003.
[154] Mori Y, Ellingwood BR. Reliability-based service-life assessment of aging concrete structures[J]. Journal of Structural Engineering, ASCE. 1993, 119(5):1600-1621.
[155] Dey A, Mahadevan S. Reliability estimation with time-variant loads and resisitance[J]. Journal of Structural Engineering, ASCE. 2000, 126(5):612-620.
[156] Enright MP, Frangopol DM. Reliability-based condition assessment of deteriorating concrete bridges considering load redistribution[J]. Structural Safety. 1999, 21:159-195.
[157] Enright MP, Frangopol DM. Failure time prediction of deteriorating fail-safe structures[J]. Journal of Structural Engineering, ASCE. 1998, 124(12):1448-1457.
[158] Enright MP, Frangopol DM. Service-life prediction of deteriorating concrete bridges[J]. Journal of Structural Engineering, ASCE. 1998, 124(309-317).
[159] Nowak AS, Yamani AS, Tabsh SW. Probabilistic models for resistance of concrete bridge girders[J]. ACI Structural Journal. 1994, 91(3):269-276.
[160] Enright MP, Frangopol DM. Probabilistic analysis of resistance degradation of reinforced concrete bridge beams under corrosion[J]. Engineering Structures. 1998, 20(11):960-971.
[161] Noortwijk JMv, Pandey MD. A stochastic deterioration process for time-dependent reliability analysis. In: Maes MA, Huyse L, editors. the Eleventh IFIP WG 75 Working Conference on Reliability and Optimization of Structural Systems. Banff, Canada: M.A., 2003, 259-265.
[162] 牛荻涛, 王庆霖, 董振平. 服役结构抗力的概率模型及其统计参数[J]. 西安建筑科技大学学报. 1997, 29(4):355-359.
[163] 王剑, 刘西拉. 基于多层Bayes 先验抗力模型的结构信息更新[J]. 上海交通大学学报. 2004, 38(6):937-940.
[164] Nowak AS. Live load model for highway bridges[J]. Journal of structural safety. 1993, 13(1+2):53-66.
[165] Nowak AS, Nassif H, DeFrain L. Effect of truck loads on bridges[J]. Journal of Transportation Engineering, ASCE. 1993, 119(6):853-866.
[166] Gindy M. Development of a reliability-based deflection limit state for steel girder bridges[D]: [The Philosophy Doctor Thesis of State University of New Jersey]. New Jersey: State University of New Jersey, 2004.
[167] 公路桥梁车辆荷载研究课题组. 公路桥梁车辆荷载研究[J]. 公路. 1997, (3):8-12.
[168] 李扬海, 鲍卫刚, 郭修武等. 公路桥梁结构可靠度与概率极限状态设计[M]. 北京: 人民交通出版, 1997.
[169] Mao TJ. Bridge live load models with special reference to Hong Kong[D]: [The Philosophy Doctor Thesis of Hong Kong Polutechnic University]. Hong Kong: Hong Kong Polutechnic University, 2001.
[170] Mao TJ. Bridge live load models from WIM data[J]. Engineering Structures. 2002, 24(8):1071-1084.
[171] Crespo-Minguillón C, Casas JR. A comprehensive traffic load model for bridge safety checking[J]. Structural Safety. 1997, 19(4):339-359.
[172] Fu G, Hag-Elsafi O. Vehicular overloads: load model, bridge safety, and permit checking[J]. Journal of Bridge Engineering, ASCE. 2000, 5(1):49-57.
[173] Mei G, Qin Q, Lin DJ. Bimodal renewal processes models of highway vehicle loads[J]. Reliability Engineering & System Safety. 2004, 83(3):333-339.
[174] Cremona C. Optimal extrapolation of traffic load effects[J]. Structural Safety. 2001, 23(1):31-46.
[175] O'Connor A, O'Brien EJ. Traffic load modeling and factors influencing the accuracy of predicted extremes[J]. Canadian Journal of Civil Engineering. 2005, 32(1):270-278.
[176] Nowak AS, Ferrand DM. Truck load models for bridges. Proceedings of StructuresCongress. Nashville, Tennessee: The Structural Engineering Institute of the American Society of Civil Engineers, 2004:1-10.
[177] Ditlevsen O. Traffic loads on large bridges modeled as white-noise fields[J]. Journal of Engineering Mechanics, ASCE. 1994, 120(4):681-694.
[178] Ditlevsen O, Madsen HO. Stochastic vehicle-queue-load model for large bridges [J]. Journal of Engineering Mechanics, ASCE. 1994, 120(9):1829-1847.
[179] Kobza JE, Shen Y-c, Reasor RJ. A stochastic model of empty-vehicle travel time and load request service time in light-traffic material handling systems[J]. IIE Transaction. 1998, 30(2):133-142.
[180] 李广慧, 张存超, 王东炜等. 高速公路桥梁活荷载参数研究[J]. 郑州大学学报. 2005, 26(1):20-23.
[181] 杨伟军, 梁兴文, 张建仁. 服役桥梁评估荷载分析[J]. 中南公路工程. 2002, 27(3):31-33.
[182] 索清辉, 钱永久, 张方. 对公路桥梁剩余寿命时变荷载取值的研究[J]. 中国工程科学. 2004, 6(5):52-56.
[183] 张建仁, 王磊, 薛雷. 考虑抗力劣化的既有钢筋混凝土桥梁车辆荷载取值研究. 中国公路学会桥梁和结构分会 2005 年全国桥梁学术会议. 宁波: 人民交通出版社, 2005:859-864.
[184] Croce P, Salvatore W. Stochastic model for multilane traffic effects on bridges[J]. Journal of Bridge Engineering, ASCE. 2001, 6(2):136-143.
[185] 张建仁, 刘扬, 许福友等. 结构可靠度理论及其在桥梁工程中的应用[M]. 北京: 人民交通出版社, 2003.
[186] 杨伟军. 服役结构可靠度理论及其应用[M]. 长沙: 中南工业大学出版社, 2000.
[187] 王有志, 王广洋, 任锋等. 桥梁的可靠性评估与加固[M]. 北京: 中国水利电力出版社, 2002.
[188] 刘宁. 可靠度随机有限元法及其工程应用[M]. 北京: 中国水利水电出版社, 2001.
[189] 贡金鑫, 赵国藩. 国外结构可靠性理论的应用与发展[J]. 土木工程学报. 2005, 38(2):1-7.
[190] Val DV, Melchers RE. Reliability of deteriorating RC slab bridges[J]. Journal of Structural Engineering, ASCE. 1997, 123(12):1638-1644.
[191] 贡金鑫, 赵国藩. 考虑抗力随时间变化的结构可靠度分析[J]. 建筑结构学报. 1998, 19(9):43-51.
[192]张宇贻, 秦权. 钢筋混凝土桥梁构件的时变可靠度分析[J]. 清华大学学报(自科版). 2001, 41(12):65-67.
[193] 刘扬, 张建仁. 钢筋混凝土桥梁服役期间的可靠性评价[J]. 中国公路学报. 2001, 14(2):61-65.
[194] 李运生, 张彦玲, 林玉森. 公路钢筋混凝土梁基于抗力劣化的可靠性分析[J]. 中国公路学报. 2003, 16(4):50-54.
[195] 吴方伯, 肖水华. 基于时变可靠度的 RC 梁正截面承载力可靠性评估[J]. 湖南大学学报(自科版). 2004, 31(1):52-55.
[196] 吴瑾, 吴胜兴. 锈蚀钢筋混凝土结构可靠度评估[J]. 工程力学. 2005, 22(1):118-122.
[197] 左志勇, 刘西拉. 结构动态可靠性的全随机过程模型[J]. 清华大学学报(自科版). 2004, 44(3):395-397.
[198] 秦权, 杨小刚. 退化结构时变可靠度分析[J]. 清华大学学报(自科版). 2005, 45(6):733-736.
[199] 张建仁, 秦权. 现有混凝土桥梁的时变可靠度分析[J]. 工程力学. 2005, 22(4):90-95.
[200] Li CQ, Lawanwisut W, Zheng JJ. Time-dependent reliability method to assess the serviceability of corrosion-affected concrete structures[J]. Journal of Structural Engineering, ASCE. 2005, 131(11):1647-1680.
[201] Akgül F, Frangopol DM. Time-dependent interaction between load rating and reliability of deteriorating bridges[J]. Engineering Structures. 2004, 24(12):1751-1765.
[202] Yang S-I, Frangopol DM, Neves LC. Service life prediction of structural systems using lifetime functions with emphasis on bridges[J]. Reliability Engineering and System Safety. 2004, 86(1):39-51.
[203] Liu M, Frangopol DM. Time-dependent bridge network reliability: novel approach[J]. Journal of Structural Engineering, ASCE. 2005, 131(2):329-337.
[204] Kaufmann A. Introduction to the fuzzy subsets[M]. New York: Academic Press, 1975.
[205] Liu Y, Qiao Z, Wang G. Fuzzy random reliability of structures based on fuzzy random variables[J]. Fuzzy sets and systems. 1997, 86:345-355.
[206] Jiang Q, Chen C-H. A numerical algorithm of fuzzy reliability[J]. Reliability Engineering and System Safety. 2003, 80:199-307.
[207] M?ller B, Graf W, Beer M. Safety assessment of structures in view of fuzzy randomness[J]. Computers & Structures. 2003, 81(15):1567-1582.
[208] Wu H-C. Fuzzy reliability estimation using bayesian approach[J]. Computers & Industrial Engineering. 2004, 46(3):1467-1493.
[209] Wu H-C. Bayesian system reliability assessment under fuzzy environments[J]. Reliability Engineering and System Safety. 2004, 83:277-286.
[210] Savoia M. Structural reliability analysis through fuzzy number approach, with application to stability[J]. Computers and Structures 2002, 80(12):1087-1102.
[211] M?ller B, Graf W, Beer M. Discussion on "Structural reliability analysis through fuzzy number approach, with application to stability"[J]. Computers and Structures. 2004, 82(2-3):325-327.
[212]Biondini F, Bontempi F, Malerba PG. Fuzzy reliability analysis of concrete structures[J]. Computers and Structures. 2004, 82(13-14):1033-1052.
[213] 张爱林, 赵国藩, 王光远. 现役结构模糊动态可靠度评估实用方法[J]. 应用基础与工程科学学报. 1998, 6(1):83-90.
[214]张俊芝, 李桂青. 在役结构的模糊动态可靠度分析[J]. 广西大学学报(自然科学版). 2002, 27(3):268-272.
[215] Sickert J-U, Graf W, Reuter U. Application of fuzzy randomness to time-dependent reliability. In: Augusti G, Sch?ller GL, Ciampoli M, editors. Proceedings ICOSSAR , Safty and Reliability of Engineering Systems and Structures. Rotterdam, Holand, 2005, 1709-1716.
[216] M?ller B, Beer M, Graf W. Time-dependent reliability of textile-strengthened RC structures under consideration of fuzzy randomness[J]. Computers & Structures. 2006, 83(8-9):585-603.
[217] Kirkpatrick TJ. Impact of specification changes on chloride induced corrosion service life of virginia bridge decks[D]: [The Philosophy Doctor Thesis of Virginia Polytechnic Institute and State University]. Blacksburg: Virginia Polytechnic Institute and State University, 2001.
[218] Tanaka Y, Watanabe H, Nakajo T. Study on required cover depth of concrete highway bridges in coastal environment. 17th US-Japan Bridge Engineering Workshop, 2001.
[219] Yanaka M. Reliability-based criteria for corrsion in prestressed concrete bridge gerders[D]: [The Philosophy Doctor Thesis of University of Michigan]. Detroit: University of Michigan, 2004.
[220] 马亚丽. 基于可靠性分析的钢筋混凝土结构耐久寿命预测[D]: [北京工业大学博士学位论文]. 北京: 北京工业大学, 2006.
[221] Marsh PS, Frangopol DM. Reinforced concrete bridge deck reliability model incorporating temporal and spatial variations of probabilistic corrosion rate sensor data[J]. Reliability Engineering and System Safety. 2008, 93(3):1-16.
[222] Val DV, Stewart MG, Melchers RE. Effect of reinforcement corrosion on reliability of highway bridges[J]. Engineering Structures. 1998, 20(11):1010-1019.
[223] 赵焕臣, 许树柏, 和金生. 层次分析法[M]. 北京: 科学出版社, 1986.
[224] 梁之舜, 邓永录. 随机点过程及其应用[M]. 北京: 科学出版社, 1998.
[225] 郭修武. 公路桥梁构件自重标准值的确定[J]. 中国公路学报. 1997, 10(1):33-38.