SERVICE-LIFE PREDICTION OF CONCRETE BRIDGE DECKS USING CASE-BASED REASONING

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混凝土氯离子和硫酸盐侵蚀破坏机理研究进展

引言混凝土结构的耐久性是指其暴露于预期使用环境时，能抵抗风化作用、化学侵蚀、磨损或任何退化过程，以保持其原始形状、质量和可用性的能力。

当材料劣化时，混凝土结构的耐久性开始降低，尽管材料劣化不会立即产生安全问题，但它们会导致结构逐渐损坏，造成安全风险。

由于实际使用环境中存在侵蚀离子，混凝土结构的实际使用寿命通常比设计的使用寿命缩短很多。

而由氯离子引起的钢筋腐蚀和硫酸根离子对混凝土体积稳定性产生的影响，被认为是影响混凝土结构耐久性的两个主要因素。

方万里[1]采用电量综合法研究了混凝土1年内龄期抗氯离子渗透性能，并通过5年龄期自然扩散法和电量综合法试验对比研究了混凝土抗氯离子渗透性能的时变规律，结果表明，采用低水胶比和优质矿物掺混凝土氯离子和硫酸盐侵蚀破坏机理研究进展于连平1　郭保林2　夏　雨1　刘　帅21. 青岛交发高速建设投资有限公司山东青岛 2661002. 山东省交通科学研究院山东济南 250000摘要：在侵蚀性环境的长期作用下，会引起钢筋腐蚀和混凝土劣化，使建筑结构的承载力严重下降。

其中，混凝土材料在侵蚀性环境中的耐久性，如抗氯离子渗透性和抗硫酸盐侵蚀性，一直是各国学者的研究重点。

本文综述了在侵蚀环境下混凝土氯离子渗透机理、氯离子侵蚀机制和无损检测方法，归纳总结了硫酸盐侵蚀的破坏机理、主流检测方法及应对措施，阐述了在海洋环境中硫酸盐与氯盐对混凝土的耦合侵蚀机理；最后简要回顾了海洋环境中氯离子及其他侵蚀离子对混凝土结构的影响机理，评述了Cl--SO42-对混凝土结构的耦合侵蚀机理，提出了相关寿命数学预测模型，为综合提升混凝土耐久性提供思路。

关键词：氯离子渗透；硫酸盐侵蚀；破坏机理；检测方法Research Progress on the Failure Modes and Degradation Mechanisms of Chloride and Sulfate Corrosion in ConcreteAbstract: Under the long-term action of corrosive environments, it can cause corrosion of steel bars and deterioration of concrete, resulting in a serious decrease in the bearing capacity of building structures. Among them, the durability of concrete materials in corrosive environments, such as resistance to chloride ion penetration and resistance to sulfate attack, has always been a research focus of scholars from various countries. This paper provides an overview of the chloride ion penetration mechanism, chloride ion erosion mechanism, and non-destructive testing methods in concrete under corrosive environments. It summarizes the damage mechanism, mainstream testing methods, and response measures of sulfate erosion, and elaborates on the coupling erosion mechanism of sulfate and chloride salts on concrete in marine environments; finally, it conducts a brief review on the impact mechanism of chloride ions and other corrosive ions on concrete structures in the marine environment, evaluates the coupled corrosion mechanism of Cl--SO42- on concrete structures, and proposes a related mathematical prediction model for service life，providing ideas for comprehensively improving the durability of concrete.Key words: Chloride ion permeation; sulfate erosion; destruction mechanism; detecting methods收稿日期：2023-9-15第一作者：于连平，1983年生，高级工程师，主要从事道路工程相关研究工作，E-mail：*****************通信作者：郭宝林，1986年生，高级工程师，E-mail：*****************合料等技术措施配制的抗氯盐高性能混凝土，具有优良的抗氯离子渗透性能，采用这种技术可为解决氯盐环境中混凝土结构耐久性问题的主要措施；掺入大量矿物掺合料可有效降低混凝土的绝热温升值，矿物掺合料掺量、种类及比例对混凝土导热、导温系数和比热容影响较小；混凝土抗氯离子渗透性能随着龄期的延长而显著提高，氯离子扩散系数符合指数衰减规律，其龄期系数与混凝土水胶比和矿物掺合料掺量等因素有关。

碳化环境下混凝土结构耐久性模型的更新方法

文章编号：1000-4750(2021)05-0113-09碳化环境下混凝土结构耐久性模型的更新方法谷慧，李全旺，侯冠杰(清华大学土木工程系，北京 100084)摘要：碳化环境下的混凝土结构耐久性模型，是基于扩散理论、快速试验、自然暴露试验以及工程经验建立的。

由于结构固有的不确定性和服役环境的复杂性，理论模型的预测结果与实际结构检测的耐久状况存在较大偏差。

该文利用工程耐久性检测获得的碳化深度、检测钢筋锈蚀比例、检测混凝土开裂比例，综合先验知识，基于贝叶斯理论，提出碳化环境下的耐久性模型更新方法。

结合结构实际的检测结果，经过更新的耐久性预测模型与待评估结构实际耐久状况更相符。

依此模型进行相应剩余耐久寿命的概率预测和耐久性评级，为既有结构耐久性评估提供参考。

关键词：耐久性评估；碳化环境；检测信息；模型更新；寿命预测中图分类号：TU375 文献标志码：A doi: 10.6052/j.issn.1000-4750.2020.06.0361UPDATING METHOD FOR DURABILITY MODELS OF CONCRETESTRUCTURES IN CARBONATION ENVIRONMENTGU Hui , LI Quan-wang , HOU Guan-jie(Department of Civil Engineering, Tsinghua University, Beijing 100084, China)Abstract: The durability models for concrete structures in a carbonation environment have been proposed based on diffusion theory, on accelerated tests and on engineering experience. Due to the inherent- uncertainty of structures and to the complexity of actual service environment, the calculation results of these models often have a big deviation from the actual test results. In the light of the point, a durability model updating method in a carbonation environment is proposed based on Bayesian theory by utilizing the durability inspection data with carbonation depth, with corrosion ratio of steel reinforcement and with cracking ratio of concrete. With the actual test results, the updated durability prediction model which consistent with the actual durability condition of the structure, is more consistent with the actual durability state of the evaluation structure. According to the model,the probability prediction of the residual durability life and durability rating are carried out, so as to provide a reference for the durability evaluation of existing structures.Key words: durability assessment; carbonation environment; inspection information; model updating; lifeprediction钢筋混凝土结构是现存最广泛的建筑结构形式，碳化环境下混凝土结构的耐久性问题，是目前我国既有混凝土结构普遍存在的问题。

在役混凝土桥梁剩余寿命预测方法研究

在役混凝土桥梁剩余寿命预测方法研究秦吉丽;王毅娟【摘要】合理预测现有混凝土桥梁剩余寿命,对于公路和城市交通运输具有重要的安全、技术与经济意义.为了更好地研究在役混凝土桥梁的工作状态和为预测桥梁使用寿命提供技术方法参考,追踪介绍了目前桥梁寿命预测方法的发展现状,并总结归纳出这些方法的主要类型,进而对其中比较常用的回归分析法、基于可靠度理论方法、灰色预测法、马尔可夫法、灰色马尔科夫法、神经网络法等预测方法做了特点与适用性方面的比较研究.%Reasonable prediction of the existing concrete bridge residual life has important significance in safety,technology and economics for highway and city transportation.To better study the service state of the existing concrete bridge and provide technical reference for the bridge service life prediction,the current status of bridge service life prediction method are introduced in the paper;the main type of these methods is summarized;and the characteristics and applicability are compared for the commonly used methods such as regression analysis method,method based on the reliability theory,the gray theory method,Markov method,gray Markov method and neural network prediction method.【期刊名称】《北京建筑工程学院学报》【年(卷),期】2012(028)003【总页数】5页(P14-18)【关键词】桥梁;寿命预测;回归分析;可靠度;灰色理论;马尔可夫链;神经网络【作者】秦吉丽;王毅娟【作者单位】北京建筑工程学院土木与交通工程学院,北京100044;北京建筑工程学院土木与交通工程学院,北京100044【正文语种】中文【中图分类】U448.33桥梁是公路交通与城市道路的咽喉，由于车辆的超限运输、结构的老化和病害、设计标准的演变、意外碰撞、钢筋的锈蚀、混凝土的碳化、荷载的变化等因素的影响，桥梁结构的性能会随着时间逐渐退化，进而桥梁使用寿命缩短，甚至发生恶性倒塌事故.那么，为了保证桥梁运营的安全，就必须对在役桥梁结构性能与状况进行合理评估.在役桥梁的评估是桥梁维修、加固的前期工作，桥梁的评估结果将决定结构是否需要进行维修改建；而桥梁剩余使用寿命的预测则是桥梁评估中非常重要的一个方面，因此现役桥梁结构的评估以及现役桥梁结构剩余寿命的预测是我国桥梁工程界亟待解决的问题.合理评估与预测现有混凝土桥梁的承载能力与剩余寿命，对于避免桥梁因带险运营而出现事故；避免因其进行不合时机的修理替换而带来高额费用，为现有桥梁结构的维修、加固与替换决策提供合理依据，具有重要的安全、技术与经济意义.截止目前，虽然有不少学者提出了一些相关桥梁寿命的预测理论，但大都停留在理论设想阶段，尚缺少系统化的研究，更没有应用于实际工程建设,桥梁寿命还是一个有待于规范化的设计指标.基于上述原因，本文将介绍并分析几种桥梁结构剩余寿命预测模型,以求为探究桥梁剩余寿命预测问题提供参考思路.1 寿命预测方法的主要类型在英国的建筑物耐久性标准中，提出了要求使用寿命、预期使用寿命、设计寿命的不同概念.英国的Somerville从使用寿命终结的角度出发，将使用寿命分为：技术性使用寿命、功能性使用寿命、经济性使用寿命三类[1].西南交通大学的屈文俊提出桥梁的寿命分为技术使用寿命和经济使用寿命，前者为随机变量，后者为经济优化的结果.从期望效益与期望经济风险的优化分析入手，建立桥梁结构的修、废判别标准，并提出了桥梁经济使用寿命的优化方法[2].大连理工大学的赵尚传，首先把结构的失效状态分为真性失效和假性失效，然后从结构剩余寿命与维护费用之间的关系角度入手，对在役混凝土结构的使用寿命进行了优化[3].目前，人们所说的桥梁使用寿命基本上是指其技术使用寿命和经济使用寿命，桥梁改造的时机，一般取决于桥梁的技术使用寿命和经济使用寿命.本文中探讨的是技术使用寿命.而桥梁剩余使用寿命则是指桥梁使用寿命与已使用年限的差值.总体来看，国内外采用的寿命预测方法主要有以下五种类型：1.1 比较预测法这种方法采用甚少，它的假定条件是：混凝土如果在某一期限内是耐久的，则相似环境下的相似混凝土也将有同样的寿命.显然，由于材料、形状、施工质量、荷载和环境的变异性，每一种桥梁结构往往是独一无二的，不同的小气候条件也会影响混凝土的使用寿命.所以即便有相似的使用条件，将过去的经验直接用来比较则不太合理.1.2 经验预测法这种方法是根据实验室和现场的大量实验结果及以往经验的积累，对使用寿命做半定量化的预测，比如回归分析法.但如若结构的设计寿命比较长，使用环境条件恶劣，或者因对结构进行加固而使结构状态发生较大改变，这种预测方法就不太可靠了.1.3 随机预测法上述的寿命预测方法都属于确定性方法，即：将影响结构使用寿命的各因素均作为确定的量值，由此得到的寿命预测结果只能是均值意义上的使用寿命.在耐久性评估中无论采用哪一种寿命准则，由于影响结构使用寿命的各因素都是随机变量，甚至是随时间变化的随机过程，结构的荷载与抗力都是随机过程.因此应用概率方法进行结构的剩余使用寿命的预测是比较合理的，但这种方法用起来却非常复杂.1.4 数学模型预测法利用数学模型预测使用寿命是目前较多使用的方法，其预测的可靠程度与模型的合理性以及材料与环境参数选取的准确性有关.现在发展较为完善的有灰色模型、马尔可夫模型等.1.5 智能预测法目前，基于智能的方法已经开始广泛用于对工程中某些特性参数的预测，如基于模糊数学理论的模糊预测法、基于遗传算法的预测法、基于神经网络的预测法，其中应用较多的是神经网络法.智能预测系统具有很强的学习能力、组织综合能力、自适应能力和优化能力，能很好的适应桥梁衰退过程的非线性、时变性和不确定性的特点.2 寿命预测方法的特点比较2.1 预测方法的主要特点2.1.1 回归预测法回归预测法就是利用桥梁在t0时刻前各个检测时刻的实际检测资料与分析结果，通过回归分析，建立桥梁技术状态与使用时间的关系，以此得出桥梁的剩余使用寿命.回归分析的模型多采用指数型、多项式，计算值以损伤度系数或养护规范中提出的评分值为基础.文献[4]中引入总损伤度系数Dt，采用指数型中值预报方程，将Dt表为:Dt=kt+ε(t)，建立了损伤度系数与时间的关系，求得桥梁的使用年限为其中Df 为寿命终止时的损伤系数，由专家根据工程经验给出)，剩余寿命为:ts=tE-tc，tE 为可使用年限，tc为已使用年限.2.1.2 基于可靠度的寿命预测可靠度方法建立在可靠度-时间关系的基础上，认为结构可靠度衰减到可接受的最小值或者失效概率增大到可接受的最大值的时间为使用寿命.结构的时变可靠度定义为:结构在设计基准期内，在正常的设计、使用和维护条件下，考虑环境等因素的影响，在任意时刻完成预定功能的概率Pf(t),t∈[0,T].结构的功能函数：Z(t)=R(t)-S(t)结构的失效概率：Pf(t)=P[R(t)-S(t)<0]结构的时变可靠指标：β(t)=Φ-1(1-Pf)式中：Φ-1(*)为标准正态分布函数的反函数.可靠指标是结构服役时间t的函数. 图1所示为在役桥梁结构剩余寿命预测步骤，即通过分析桥梁结构影响衰退的主要因素，建立其抗力和荷载效应模型，计算时变可靠度，从而建立结构可靠度与时间之间的函数关系，即可反推出桥梁的剩余使用寿命.文献[5]中对抗力模型和荷载模型作了具体研究，并给出了抗力和荷载效应模型的统计参数.图1 可靠度理论法求算剩余寿命的步骤可靠度指标β(t)计算方法：结构可靠度的计算方法分精确法和近似法两种.精确法是指按照积分公式求解结构的失效概率的方法，称全概率法，大多为一多重积分问题，因一些基本变量由于各种原因，很难确定其实际的概率分布，所以，一般很难求得解析解，工程实践中难以采用.常用的近似法有中心点法、验算点法(JC法)和蒙特卡罗模拟法.中心点法基本原理是将极限状态功能函数Z=g(X1，X2，…，Xn)在平均值处(即中心点)用级数展开，使之线性化，然后近似计算极限功能函数的平均值和标准差，可靠指标直接用功能函数的平均值和标准差之比,即β==验算点法(JC法)是把非正态变量转换成正态变量的近似方法，适用于随机变量为任意分布下结构可靠指标的求解，不仅通俗易懂，而且计算精度能满足工程实际需要目标可靠度的确定.JC法依据下列假设进行当量正态化：1)在设计点处，正态变量的分布函数值FX与非正态变量X的分布函数值FY相等，即FX=FY；2)在设计点处，正态变量的概率密度函数值fX与非正态变量X的概率密度函数值fX相等，即fX=fX；根据上述两个条件求得当量正态分布的平均值μx和标准差σx，最后计算结构的可靠指标.蒙特卡洛模拟法：蒙特卡洛方法是一种采用统计抽样理论近似地求解数学问题或物理问题的方法，是随电子计算机地发展而逐步发展起来的一种独特的数值方法.常用到的有三种分布：正态分布、对数正态分布、极值Ⅰ型分布.失效标准[β]：根据我国《公路工程结构可靠度设计统一标准》(GB/T50283—1999)中桥梁结构构件可靠度校准结果，参考国内外各种结构构件目标可靠度指标的建议值，建议在设计基准期年内的目标可靠度指标β0值如表1所示.表1 公路桥梁结构构件目标可靠指标的建议值构件破坏类型安全等级一级二级三级延性破坏4 74 23 7脆性破坏5 24 74 2根据文献 [6][7],将[β]=0.85β0作为既有桥梁结构寿命终止的标志，认为此时结构达到极限状态、到达寿命的终点或者已经到达维修加固的时间.2.1.3 灰色理论预测法灰色预测是根据过去的及现在己知的或非确定的信息建立的一个从过去引申到未来的灰色模型，从而确定系统未来发展的趋势，灰色预测的核心是灰色模型的建立.灰色系统理论[8]是邓聚龙教授于1982年提出，随后被用于各个领域的预测，包括桥梁寿命和技术状态预测.灰色理论预测法首先评估桥梁的整体损伤度或养护规范中提出的评分值，再以桥梁总体损伤度或评分值为原始序列，采用一次累加后生成新的序列，在此基础上，建立技术状态的灰色预测模型，根据预测模型外推出桥梁剩余技术使用寿命.2.1.4 马尔可夫预测马尔可夫过程的定义：在时刻t0系统处于状态i的条件下，在时刻t(t≥t0)系统所处的状态和时刻以前所处的状态无关，只与时刻所处的状态有关.马尔可夫链可用于预测桥梁的使用年限,是以根据桥梁状态等级确定状态和求得桥梁状况从一个状态转变到另一个状态的概率为基础的.这些概率以矩阵形式表示出来, 此矩阵叫做状态转移概率矩阵，其求解是马尔可夫预测模型求解的最关键问题.常用的方法有经验判断、统计分析和回归分析、逆阵法[9]等.根据马尔可夫链，系统在任何时刻的状态概率是由初始状态概率分布向量和转移概率矩阵确定的，对应任意时刻t时的状态矢量Q(t)可以由初始状态矢量Q(0)和转换概率矩阵P的t次幂的乘积求得，即Q(t)=Q(0)*pt.文献[10]中引入了模糊综合法对桥梁技术状态进行判别得到了初始状态概率分布，并用逆阵法求得状态转移矩阵，求得了预测年限的状态概率分布，根据寿命期结束时的等级要求可推算出桥梁的剩余寿命.2.1.5 灰色马尔科夫预测法灰色马尔可夫预测法是将灰色理论和马尔可夫法相结合，灰色理论能有效预测数据的变化趋势，而马尔可夫理论采用了状态转移矩阵，能较好地适应数据的波动性，灰色马尔可夫理论作为两者的结合吸取了两者的优点，需用的数据相对来说较少，而且很好体现桥梁状态发展的总体趋势和波动性，精度较高.具体方法：建立GM(1,1)模型，划分状态，计算状态转移概率矩阵，确定预测值的变动区间和预测值.2.1.6 神经网络法该方法从全桥的角度综合考虑各种因素影响，利用因果分析图及数学模糊规则，事先归纳出影响混凝土桥梁整体寿命的几种主要因素，利用自编程序构建一种由预测时的衰减到容许值时所需年限的网络模型，一般由输入层、隐层和输出层构成，通过几种主要因素大量的样本数据训练，使网络自身学习得到一组稳定的权向量，来反映输入与输出之间的映射关系，从而使每给出一组输入就能得出一组输出结果，而达到寿命预测功能.训练结果表明，只要网络结构选择合理，配合正常的检测制度与专门的数据采集系统，其对全桥剩余寿命进行模糊预测的结果是具有实用价值的.2.2 预测方法的综合比较1)回归分析法：桥梁结构剩余使用寿命回归预测模型的主要特点是计算简单，使用方便，对检测时刻的选取没有特别要求；主要缺点是它要求所选择的样本容量要足够大，否则将不能保证中值预报公式的有效性和精度.因此，该模型可适用于使用过程中检测频繁的结构.2)可靠性评估：可利用可靠度指标或失效概率Pf来统一描述结构的安全水平，使评估结果更确切与稳定.但在结构体系可靠性研究方面还需进一步的深入，特别是大型、特大型桥梁结构体系可靠性的研究还很少.关于容许的最小目标可靠指标β的取值问题.用到的桥梁结构失效指标0.85β0，这个取值还有待进一步研究.3)人工神经网络法：网络模型的显著特点是容错性好，特别适合于处理某些残缺不全与模糊不清的信息，也适用于对桥梁剩余寿命的预测，但目前仅应用于桥梁的局部构件.该方法还处于初步探索阶段，有待进一步研究与完善.4)灰色模型：很容易接受新的信息并调整模型去适应新的情况，具有较强的自适应能力，同时该模型不直接采用原始序列而采用一次累加生成后的序列去推测系统的发展变化规律，在一定程度上消除了原始序列的随机性，使模型在信息量较少，数据质量不高的情况下也有较高的预测精度.其主要缺点是离散化的模型要求参加分析的序列为一段时间序列，因此，该模型可适应于定期检测的桥梁.5)马尔可夫模型:其研究对象是一个随机变化的动态系统，它是根据状态之间的转移概率来预测系统发展的趋势，转移概率反映了各种随机因素的影响程度，反映了各状态之间转移的内在规律性，因此马尔可夫法适合预测随机波动性较大数据列的预测问题，如桥梁结构条件突然恶化或者加固维修造成的状态突变.6)灰色马尔可夫模型：吸收了灰色模型和马尔科夫模型的优点，需用的数据相对来说较少，而且很好体现桥梁状态发展的总体趋势和波动性，精度较高.3 结语在役桥梁达到剩余使用寿命的终点也并不意味着桥梁结构的完全失效,而是不宜再继续承载,需要对主要承重构件进行加固.对于桥梁结构寿命预测的主要目的是为了进行工程规划实施上的决策, 至于更精确的关于桥梁结构的破坏时间并没有太大的实际意义.从这种意义上讲,决策者可根据自己的知识水平、所掌握的信息种类和数量等主客观条件来选用不同的模型进行预测分析和决策制定.同时上面几个模型中对有些参数的取值和对一些问题的处理所存在的不妥之处, 将随着实践经验的积累不断地得到改进和完善, 使所建模型能更好地适合桥梁结构的实际情况.参考文献：[1]G Somerville.The Design Life of Structures [M].Glasgow and London: Blackie and Son Ltd, 1992[2]屈文俊，车惠民.混凝土桥梁的优化等耐久性设计[J].土木工程学报,1998,31(4):23-30[3]赵尚传，赵国藩，贡金鑫.在役混凝土结构最优剩余使用寿命预测[J].大连理工大学报,2002,42(1):83-88[4]林兵,郑丹,周建庭, 等.西南地区桥梁寿命预测分析[J].重庆交通大学学报：自然科学版,2008, 27(3):374-378[5]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[6]赵尚传.钢筋混凝土结构基于可靠度的耐久性评估与实验研究[D].大连理工大学,2001[7]赵国藩.工程结构可靠性理论与应用[M].大连：大连理工大学出版社,1996[8]邓聚龙.灰色系统理论教程[M].2版.武汉：华中理工大学出版社, 1990[9]张晓华,邱延峻.基于逆阵的路面综合性能马尔可夫预测[J].东北公路,2003,26(3):7-10[10]吕颖钊,贺栓海,在役桥梁承载力模糊可靠性的马尔科夫预测[J].长安大学学报(自然科学版), 2005, 25(4):39-43。

Life-365 Service Life Prediction Model for Reinforced Concrete Exposed to

Factors inﬂuencing chloride transport in concrete structuresexposed to marine environmentsHa-Won Song *,Chang-Hong Lee,Ki Yong AnnSchool of Civil and Environmental Engineering,Yonsei University,Seoul 120-749,Republic of Korea Received 4May 2006;received in revised form 30August 2007;accepted 18September 2007Available online 25September 2007AbstractThe present study concerns a literature review regarding chloride transport in terms of the diﬀusion coeﬃcient (D )and surface chlo-ride content (C S )in concrete structures exposed to a marine environment.In addition,a reﬁned model is proposed for D and C S for time-dependent chloride transport.It is found that both D and C S are time-dependent:D decreases and C S increases with time,due to further cement hydration development.D and C S are signiﬁcantly inﬂuenced by concrete mix proportion,air void content in concrete,curing methods,degree of exposure to seawater and climate.Blended cement concretes are beneﬁcial in decreasing D ,but increase C S ,presum-ably due to a reﬁnement of the concrete pore structures and chloride binding.An increase in the air void content in concrete increases D ,but decreases C S .The C S depends on curing methods such as water,membrane and aeration.The degree of exposure to seawater does not have a clear relationship with C S :higher exposure levels did not result in a higher level of C S .Exposure in tropical areas results in higher C S in concrete jetty structures with a similar level of D ,mainly due to an increased temperature and concentration of salinity.Based on these ﬁndings,a reﬁned model for C S was proposed to provide more realistic prediction of the build-up of chlorides by chloride transport in concrete structures exposed to marine environments.Ó2007Elsevier Ltd.All rights reserved.Keywords:Chloride transport;Diﬀusion coeﬃcient;Surface chloride;Concrete structures;Marine environment1.IntroductionReinforced concrete is usually durable and cost eﬀective,which has resulted in its widespread use for the construc-tion of semi-permanent structures.However,it has become increasingly apparent that attack by aggressive agents such as chloride ions,leading to corrosion of embedded steel,may cause a structure to deteriorate.Thus,the corrosion of reinforcing steel in concrete due to chloride transport in concrete structures in a marine environment has received increasing attention in recent years because of its wide-spread occurrence and the high cost of repair [1,2].The steel in concrete is protected by an oxide passive ﬁlm generated in a highly alkaline environment [3],although the corrosion cell is fully composed:cathodic molecules such as moisture and oxygen,anode,electrolyte and electric circuit.However,a build-up of chloride at the depth of the steel accompanied by a local fall in the pH of the pore solution depassivates the protective ﬁlm prior to steel corrosion [4].To prevent the chloride permeation into concrete,the use of ﬁnely grained materials [5–7]and resin-based treatment on the cover concrete [8]have been investigated and achieved some success.Simultaneously,investigation on predicting the chloride proﬁle in concrete exposed to a marine environment has been performed using the Fick’s second law.Many authors have used this model to predict the time to chloride-induced corrosion with a given diﬀusion coeﬃcient (D )and surface chloride content (C S ),assuming that cement0958-9465/$-see front matter Ó2007Elsevier Ltd.All rights reserved.doi:10.1016/j.cemconcomp.2007.09.005*Corresponding author.Tel.:+82(0)221232806;fax:+82(0)23645300.E-mail address:song@yonsei.ac.kr (H.-W.Song)/locate/cemconcompAvailable online at Cement &Concrete Composites 30(2008)113–121matrix in concrete is chemically inert and evenly porous[9–12].However,this hypothesis and models have been challenged,since Bamforth and Price[13]addressed the time-dependent characteristic of chloride transport in terms of D and C S,and Bentz et al.[14]showed a change of D with time.The present study surveys published data on chloride transport of concrete specimens or structures exposed to a marine environment(i.e.aerated,splash and tidal zones) for the duration from1to64years.Time-dependent char-acteristics of D were extensively investigated altogether with other factors inﬂuencing chloride transport such as concrete mix proportion,curing method,degree of expo-sure to seawater and climate,while a change in C S has been rarely dealt with.The present study suggests a reﬁned model for chloride transport considering time-dependency of the C S along with extensive investigation on C S.2.Chloride transport model2.1.Diﬀusion modelThere are a number of mechanisms by which chloride transport can take place in concrete.These include diﬀusion under the inﬂuence of a concentration gradient,absorption due to a capillary action,migration in an electricalﬁeld,a pressure-inducedﬂow and wick action when water absorp-tion and water vapor diﬀusion are combined[15].Diﬀusion is the process by which ions or molecules move from an area of higher concentrations to lower concentra-tions.Diﬀusion is the primary mechanism of chloride transport in concrete where there is no applied electricﬁeld and the moisture condition of the concrete pore structure is stable.For one dimensional into a semi-inﬁnite medium,an error function solution to the Fick’s second law[16]is usually used as follows:Cðx;tÞ¼C S1Àerfx 2ﬃﬃﬃﬃﬃDt p;ð1Þwhere D=diﬀusion coeﬃcient(m2/s);t=time of exposure (s);C(x,t)=chloride concentration at depth x after time t (%/m3);C s=surface chloride concentration(%/m3);and erf is the error function.A true D can be achieved using Eq.(1),if concrete is homogeneous as being an ideal media, D and C S are constant with time,and the chlorides either do not react with cement matrix or if the ratio of chloride binding is constant.This model is commonly used in deter-mining chloride transport in concrete[17].2.2.MeasurementMeasurements of a chloride proﬁle to calculate D and C S usually follow the following procedures.The chloride proﬁle is obtained from samples collected by grinding the concrete in a certain increment of depth from concrete surface to the steel.The chloride content of each sample can be usually determined in total chloride content for the convenience by acid soluble extraction in a nitric acid solution followed by potentiometric titration against silver nitrite.The chloride concentration of each solution sample is often given in ppm,which is then converted to the per-centage by weight of concrete andﬁnally the percentage of chloride by weight of cement,assuming a uniform distri-bution of cement through the cover concrete.This gives the chloride proﬁle at the time when the specimens are removed from concrete structures in seawater or saline environment.The D can be determined byﬁtting the error function solution to Fick’s second law,for non-steady state diﬀusion in a semi-inﬁnite medium,given by Eq.(1).In the analysis of the chloride proﬁle,the sum of the squared diﬀerences between theﬁtted(theoretical)and the actual data for the chloride content of each sample must be minimised by adjusting the regressor variable.Once a bestﬁt is achieved,the D can be calculated.The initial chloride content(i.e.from the mix ingredients)is usually very low and thus is neglected in analyzing the chloride proﬁles.D can be calculated from a measurement of the chloride concentrations at each depth of concrete,whereas a direct measurement of the C S is unreliable,because the C S is the chloride content at the exposed surface of concrete.The approach to obtain the C S is toﬁt a curve to the chloride proﬁle with the C S and the D as independent variables.The diﬃculty in determining the C S usually arises from the reduction of chloride content at the concrete surface of cover concrete as shown in Fig.1.The chloride content within millimeters inside the outer surface of cover concrete is decreased,because the concrete skin has a diﬀerent com-position,compared to the internal concrete,due to phe-nomena such as a contact with the moulds,segregation of aggregates or dielectric reaction between the concrete surface and chloride environment[18].Moreover,chlorides at the surface of cover concrete can often be washed out in preparation of sampling and thus lowers the C S.114H.-W.Song et al./Cement&Concrete Composites30(2008)113–1213.Reported values of D and C SA summary of D and C S reported from published data is given in Table1,which includes information on the type of sample and its exposure condition from which the data was obtained.The information includes reinforced structures, laboratory concrete specimens exposed to an outdoor envi-ronment and concrete specimens exposed in a controlled laboratory environment.In this study,total chloride content is expressed as a percentage by weight of cement/ binder.For the cases that the chloride content is only reported as a percentage by weight of concrete specimen/ structure but its mix design is not reported,a cement con-tent of350kg/m3and a concrete density of2300kg/m3have been assumed.If D and C S were not provided,D in all the works have been estimated using the Fick’s second law and C S was obtained byﬁtting the curve to the chloride proﬁle.The degree of contact with chlorides in an environment is a key factor for each diﬀerent level of the surface chloride content.The C S for a concrete exposed to seawater may not be changed with time due to the chemical equilibrium, but at the tidal zone the chloride content on concrete sur-face can be increased by a number of wet and dry cycles. Also it is seen that degree of contact to seawater much inﬂuences C S.For example,C S obtained from submerged condition in seawater was higher than that for tidal/splash, and specimens/structures exposed to airborne chlorides produces the lowest level of C S.However,D or C S from published data does not provide clear relationship with the time of exposure,due to other various factors to chlo-ride transport including binder type,free water/binder ratio(W/B),curing condition,location of sampling in structure and weathering.4.Inﬂuencing factors to chloride transportFor chloride transport,aggregates usually have very low permeability and therefore have little impact on the perme-ation of chloride.Although the interface between coarse aggregate and cement paste often provides an easier path for chloride ions to move through concrete so that the size of aggregate aﬀects D[27],the rate of transport in a con-crete is largely dependant on the characteristics of cement paste.In this study,concrete mix proportion,curing condi-tion,exposure to seawater and other physical properties of concrete are mainly taken as inﬂuencing factors to chloride transport.4.1.Concrete mixIt is well known that binder type and W/B signiﬁcantly aﬀects chloride transport because formation of pore struc-ture is diﬀerent,depending on concrete mix proportion. For example,pulverized fuel ash(PFA)or ground granu-lated blast-furnace slag(GGBS)in concrete produces a dense cement matrix with fewer capillary pores due to theTable1Reported values of the diﬀusion coeﬃcients D and surface chloride contents C S of concrete structures and specimens exposed to marine environments C S(%,cem.)D(·10À12m2/s)Time(years)Exposure Concrete mix ReferencesBinder W/B4.08Unknown2Laboratory(submerged)OPC0.4Gjørv and Vennesland[19]2.550.51.330.63.74–5.54 3.52–4.6616Structure(tidal/splash)OPC Unknown Funahashi[10]0.43–2.22Unknown23–58Structure(aerated)OPC Unknown Uji et al.[20]0.83–5.23Structure(splash)2.39–6.41Structure(tidal)1.50–3.102.13–3.3924Structure(splash/tidal)OPC0.5Liam et al.[21]1.97 3.5020Structure(splash/tidal)OPC Unknown Kudoh et al.[22]0.20–2.43Unknown30Structure(aerated)OPC Unknown Morinaga[23]0.016–0.143 4.41–4.911Specimen(aerated)OPC0.5Mustafa and Yusof[24]2.93,4.7212,201,4Specimen(submerged)OPC0.4Bentz et al.[14]2.10,4.80 1.3,5.030%PFA0.48,3.05 6.53,7.853,8Specimen(tidal)OPC0.66Bamforth and Price[13,31]0.63,4.540.89,0.7830%PFA0.540.64,3.250.76,0.5670%GGBS0.480.69,3.66 3.98,3.258%SF0.723.53 2.14215Specimen(submerged)OPC0.45Mohammed et al.[25]4.120.486GGBS5.800.552PFA10.510.04233Structure(splash/tidal)OPC0.44–0.6Troconis de Rinco´n et al.[26] 10.510.648389.260.0276011.960.13664H.-W.Song et al./Cement&Concrete Composites30(2008)113–121115pozzolanic reaction[28].Moreover,the particle size distri-bution in theﬁnest range,which accounts for100–1000A˚, along withﬁller eﬀect is more likely to reduce a chloride transport[29].This study collected published data on D and C S of con-crete containing OPC,PFA,GGBS and silica fume(SF) exposed to a marine environment.Fig.2shows the rela-tionship between D and W/B,and C S and W/B.A curve wasﬁtted to the values of D for OPC concretes,in the form of D=a e b(W/B),indicating an increase in D,by an increase in W/B by neglecting exposure durations.In contrast,the curves by recent data from JSCE[30]wereﬁtted in the form of D=a(W/B)b to the values for OPC and SF con-cretes.It is seen that an increase in W/B results in an increase in D for both OPC and SF concretes,and D for SF concrete was lower than that for OPC concrete.PFA, GGBS or SF in concrete was,as expected,eﬀective in enhancing the resistance to chloride transport.Decrease in D for PFA,GGBS or SF concretes occurs due to mainly a reﬁnement of pore structure[29],and the increased bind-ing capacity of GGBS[31,32].The comparison of the results by Bentz et al.[14]and Bamforth[33]shows that the D for the concrete with W/B=0.4was about one order greater than the D with W/B=0.66,even with similar exposure duration and external environment,which may be explained by the eﬀect of binder content.Buenfeld and Okundi[34]also showed, from chloride solution-exposure testing,that the higher binder content,at a given W/B,could increase chloride ion ingress in concrete.A reduction of C S with higher W/B was reported as shown in Fig.2b.In Fig.2b,a single study with same con-ditions from Gjørv and Vennesland[19]showed that theC S at a given cement content was reduced by an increase in W/B for a two-year submerge in chloride solution.This can be explained by the skin eﬀect that reduces C S by a for-mation of cement paste layer on the outer surface of cover concrete of the specimen.Higher W/B is more likely to form a thicker cement paste layer on the concrete surface (i.e.concrete skin),so that the layer would enhance the dielectric activity between hydroxyl ions in the concrete skin and chloride ions in solution,and thus the increased repulsive force removes chloride ions from the surface of concrete.The C S was also much inﬂuenced by binder type as shown in Fig.2b.Irrespective of exposure condition and duration,C S for blended cement concretes was greater than that for OPC concrete,presumably due to the higher level of chloride binding and sorptivity.With increased chloride binding capacity,total chloride contents increase nearer the surface of the concrete,but decrease deeper in the concrete [35].The increase in the C S can be induced by the binding eﬀect which allows the progressive build-up of higher total chloride content on the surface of cover concrete.4.2.CuringCuring methods and duration can control the concrete quality including mainly strength and durability of con-crete.Bamforth[33],and Bamforth and Price[13] addressed the inﬂuence of curing methods on chloride transport reporting that D for OPC,30%PFA,70%GGBS and8%SF concretes was not signiﬁcantly aﬀected by the curing method,while the C S was varied with curing. Fig.3shows the various levels of C S for diﬀerent curing methods(water,membrane and aeration),when the con-crete specimens were submerged in seawater for3and8 years,respectively.It is seen again that the C S was increased with time,ranging from0.44%to0.69%by weight of cement for the3year exposure,while the C S increased up to 1.66–6.45%after the8year exposure. The C S shows a marginal change for theﬁrst3years with curing methods,whereas the C S for the8years exposure was varied much with each curing method.For OPC and 8%SF concretes,aerated curing is beneﬁcial in reducing C S,compared to water curing.For30%PFA concretes,116H.-W.Song et al./Cement&Concrete Composites30(2008)113–121C S is much less with either water curing or membrane,compared with aerated curing.Hence,curing method should be carefully chosen,depending on binder type,in order to minimise C S and thus the chloride transport in concrete.4.3.Exposure conditionThe value of D and C S may vary to a large degree by the location of the structure in a marine environment,i.e.,the degree of exposure to chloride environment and weathering condition with regard to prevailing winds and rainfall.For marine concrete structures,the vicinity to seawater could mainly govern the chloride transport behaviour.However,there has been little study concerning the eﬀect of location from sea level,except several limited data [21,36],which are shown in Fig.4for D and C S for jetty structures exposed to tidal/splash zones for 24years.The height from sea level was limited within 2m higher or about 1m lower from sea level.It seems that splash zone near sea level is the eas-iest for chlorides to accumulate on the surface of concrete,while a build-up of C S took place the least at the sea level.This may be due to the wet/dry cycles,resulting in a succes-sive supply of chlorides by wetting with seawater,and evaporation and salt crystallization by drying.Water absorption may lead to very rapid penetration of chloride ions dissolved in seawater.It is,for example,well known that concrete in the tidal zone of an oﬀshore structure or bridge decks subjected to regular applications of deicing salts,may suﬀer from rapid chloride ion ingress due to the water absorption.However,Uji et al.[20]showed from a long term monitoring from 23to 58years that the order of C S with regard to the level from seawater is tidal >splash >atmospheric zone.The diﬀerence of C S build-up between these data is not clearly known,but presumably diﬀerent weathering and concrete mix may have aﬀected to the process of chloride transport.Fig.5shows two sets of the C S build-up measured from specimens and structures exposed to a chloride aerated environment (i.e.coastal area)for 1and 30years,H.-W.Song et al./Cement &Concrete Composites 30(2008)113–121117respectively[23,24],along with a Japanese Standard Spec-iﬁcation for airborne chloride build-up[37].The C S from Mustafa and Yusof[24]was marginally changed with the distance from sea,because of a relatively short-term expo-sure to the chloride atmospheric condition.Moreover,the values of C S were too small to set a high level of chloride concentration gradient in concrete for corroding the embedded steel.For a30-year exposure period,it is clearly seen that the distance from the sea strongly inﬂuences a build-up of C S,ranging from0.20%to2.43%by weight of cement,for the distance50–1000m away from sea.It is notable that the values of C S speciﬁed by the JapaneseStandard[37]nearly equate to the C S after a30years expo-sure to airborne conditions.It suggests that aerated chlo-rides also may impose a risk of corrosion of steel,when structures are located in the coast close to sea and the expo-sure duration is long enough for C S to accumulate.How-ever,structures about1km away from coast may be free from a chloride-induced corrosion deterioration,because it would take extremely long for chloride ions,with a lower level of C S,to reach the chloride threshold level[39]for steel corrosion at the depth of the steel.Miera et al.[44] provide additional information on chloride accumulation in concrete due to natural exposure to marine aerosols. 4.4.Other factorsThe importance of air void content in concrete has been emphasized due to its inﬂuence on concrete strength as well as corrosion initiation[38].However,to date,the inﬂuence of air void on chloride transport has rarely been addressed. Ann and Song[39]indicated an increase in D and a decrease in C S,resulting from an increase in air void con-tent.Fig.6shows D and C S with the air void content for OPC,30%PFA and65%GGBS concretes.As expected, 65%GGBS and30%PFA concrete indicated lower levels of D,compared to D for OPC concrete.For each mix,D slightly increased as the air voids increased,except for the30%PFA concrete where D was relatively constant. It seems likely that larger air void content,which may be induced by various sources(e.g.,poor compaction in the casting of the concrete)results in the formation of pore structures that favor the transport of chloride ions.It is, however,notable that an increase in the air void content resulted in a decrease in C S,irrespective of binder as shown in Fig.6b.Fig.7shows an inﬂuence of climate on chloride trans-port in terms of C S.Three diﬀerent series of C S were mea-sured in the UK,Japan and Venezuela,where the latitudes of sampling places are diﬀerent.The exposed duration was 8,7–58and7–64years from the UK,Japan and Venezuela, respectively.The specimens from the UK were only sub-merged in seawater and the others were exposed in the tidal/splash zones.The C S from the UK(i.e.the highest in the latitude)were the lowest,probably because of the short duration of exposure as well as the submerged condi-tion,compared to the C S from Japan and Venezuela,which were measured after the even longer durations of exposure. However,the C S from Venezuela was much higher than that from Japan,despite a similar exposure condition and duration.This diﬀerence may be due to diﬀerent climates, since the tropical climate fosters chloride ion movement118H.-W.Song et al./Cement&Concrete Composites30(2008)113–121into concrete due to the high levels of relative humidity, temperature and chloride concentration.High temperature and high humidity will help chloride ions to transport in concrete via absorption altogether with diﬀusion.More-over,higher concentration of chloride ions in seawater will increase the chloride ingress,which is responsible for the high C S.5.Reﬁnement of basic modelTheﬁxed value of D and C S have been extensively used in predicting the chloride ingress using the Fick’s second law,when structures are exposed to a marine environment [17].However,the D decreases with time,because develop-ment of cement hydration reduces the pore distribution in theﬁne size,and hydration products react with chloride ions to form Friedel’s salt and/or to adsorb the chlorides physically,which delays chloride transport in concrete. Also,the C S has been intuitively hypothesized to be inde-pendent of time,when concrete structures are exposed to a tidal/splash environment,whereas in salt aerated condi-tion,chlorides have been considered to be accumulated on the surface of concrete with time[40,44].A literature review showed that both D and C S are time-dependent and moreover the values are inﬂuenced by binder type, W/B,exposure condition and even weathering.To predict the service life of concrete structures subjected to chloride-induced corrosion,the complexity of chemical,physical reactions between the cement hydration species and chloride ions must be taken into account for the analysis of chloride transport.However,it would be very diﬃcult to consider all these factors in the analysis of chloride transport.Thus,the present study suggests a reﬁned model, considering the time-dependent characteristics of D and C S.A number of works used for the model for time-depen-dent D in predicting the chloride proﬁle[30,36].Time-dependency of D and C S may be mainly associated with hydration of the cement matrix.Capillary pore volume and its connectivity are important in assessing chloride transport,and the capillary pores reduce and are partially blocked as the cement matrix hydrates[41,42],which implies a loss of paths for chloride ions.Thus,D can be decreased by time(i.e.degree of hydration)and C S can be increased by the increase in chloride binding and the build-up of chlorides.The so-called time-dependent model of D in the most cases was empirically obtained as follows:DðtÞ¼D0t0tm;ð2Þwhere D(t)=diﬀusion coeﬃcient at time t(m2/s);D0=dif-fusion coeﬃcient at t0(m2/s);t0=standard time(1year or 28days)(s);t=time(s);and m=constant value.For C S,a reﬁned model was previously suggested[17,40]and is being used commercially(eg.LIFE365).For a linear build-up of C S over time,the chloride ingress with regard to the con-crete cover depth and time can be obtained from Eq.(3), and for a square root build-up of C S over time,Eq.(4) can be used to determine the chloride ingress,C SðtÞ¼k1t;ð3ÞC SðtÞ¼k2ﬃtp;ð4Þwhere C S(t)=surface chloride concentration at time t(%/m3);and k1,k2are constant values.However,these models do not consider an initial build-up of chlorides on the surface of cover concrete,at an early age concrete ex-posed to a salt environment.For example,the C S would be negligibly small for a1-year exposure,accounting for 0.10%and0.77%by weight of cement from Eqs.(3)and (4),respectively,whereas a measured C S accounts for 2.1–2.5%for only a28-day exposure.For60years of expo-sure,Eqs.(3)and(4)overestimate C S build-up as7.6–8.2%, compared to6%obtained from exposure test data[14]. Moreover,these models for C S do not consider the chloride build-up for the diﬀerent conditions of tidal/splash,sub-merged zone and aerated zone.Hence,the models may not apply for predicting chloride transport of concrete structures exposed to a marine environment both for diﬀer-ent very short-term and long-term exposure and chloride content at an early stage of exposure in a chloride environ-ment is nulliﬁed.Hence,it is required to reﬁne a model for the time-dependent C S,considering the initial build-up of chlorides on the surface of concrete.The following model empirically derived from published data on C S is proposed to consider the initial build-up of chlorides:C SðtÞ¼C0þa lnðtÞ;ð5Þwhere C0=surface chloride at the standard time(1year or 28days)(%/m3)and a=a constant value.Fig.8shows an increase of C S with time,based on Eqs.(3)–(5).For the bestﬁt,k1,k2,and a were determined as 0.137%/yr,1.001%/yr0.5and0.977%/exp(yr),respectively. For Eq.(5),C0was taken as the C S for a28days exposure from Bentz et al.[14].It is seen that the C S values from models of linear and square root build-up(Eqs.(3)and (4),respectively)are unrealistically low at an early age, while the reﬁned model in this study indicated the C S aboveH.-W.Song et al./Cement&Concrete Composites30(2008)113–1211192.0%.After60years,the rate of C S increase for the pro-posed model is the lowest and reaching a plateau,whereas the C S for linear and square root build-up models are increasing more rapidly.6.ConclusionThis paper studied the change of the apparent diﬀusion coeﬃcient D and surface chloride content C S with time from structures/specimens exposed to marine environ-ments,as reported from published data.It was found that D for a concrete structure decreases with time due to a subsequent hydration of cement matrix,which makes the concrete pore structure denser,or removes chloride ions by binding.C S is also time-dependent,when exposed to tidal and splash zones or even submerged in seawater. Altogether with the time-dependent characteristics,there are a number of inﬂuencing factors in chloride transport in terms of D and C S:concrete mix proportion(i.e.free water/binder ratio(W/B)and binder type),curing methods,the proximity to seawater,air void content in concrete and external environments.This study provides the following conclusions.(1)It was found that,from a single series of data,anincrease in W/B resulted in an increase in D,due to formation of increased pore structure,and C S was decreased by an increase in W/B,which seems due to the concrete skin eﬀect.Blended cement concrete containing PFA,GGBS or SF decreases D and increases C S,due to a reﬁnement of the concrete pore structure and an increased chloride binding capacity, respectively.(2)It was seen that chloride transport depends on curingmethods:water,membrane and aeration.For OPC and SF concretes,aerated curing is beneﬁcial in reducing the C S,whereas water curing is beneﬁcial for PFA and GGBS concretes.However,D does not seem to be much aﬀected by curing duration.(3)For the exposure to tidal and splash zones,D and C Swere aﬀected by the height from sea level(i.e.degree of contact to seawater).As the height increases from sea level,both D and C S increase.For airborne chlo-ride environments,the exposed time and the distance from sea are key factors to C S,but the level of C S at a given D was negligibly low to impose a corrosion risk, compared to tidal/splash or submerged region. (4)Environmental conditions like climate signiﬁcantlyaﬀect chloride transport.Concrete structures exposed to a marine environment near the Equator produceda remarkably high C S,compared to the C S from thehigh latitudes.The higher C S in the tropical area is due to an enhanced ionic transport and high concen-tration of chlorides.(5)Air void content in concretes inﬂuences D and C S.Anincrease in air voids resulted in increased D and decreased C S.A large air void content(due to poor compaction,for example)increases pore structure formation,which provides more open pathways for chloride transport.(6)A reﬁned model for C S which considers time-depen-dent characteristics of chloride build-up and binding capacity is proposed in this study.This model pro-vides a more realistic build-up of C S,compared to a few basic models for C S accumulation in an aerated condition.However,further reﬁnement of the model and veriﬁcation with long-term exposure data is nec-essary for practical prediction of chloride proﬁles in concrete structures exposed to marine environments. AcknowledgementsThe authors would like to acknowledgeﬁnancial sup-ports from a project on Standardization of Performance based Construction Speciﬁcations and Design and a Centre for Concrete Corea,Korea.References[1]Federal Highway Administration.Building more durable bridges.Washington DC:FOCUS Federal Highway Administration;Sep-tember,2001.p.6.[2]BRE Centre for Concrete Construction.Guide to the maintenance,repair and monitoring of reinforced concrete structures.DME report No.4.Watford,UK;2001.[3]Page CL.Mechanism of corrosion protection in reinforced concretemarine structure.Nature1975;256:514–5.[4]Page CL,Treadaway KWJ.Aspects of the electrochemistry of steel inconcrete.Nature1982;297:109–15.[5]Gjørv OE,VenneslandØ.Evaluation and control of steel corrosionin oﬀshore structures.In:Scanlon JM,editor.Concrete durability.ACI SP100;1987.p.1575–1602.[6]Berke NS,Sundberg KM.The eﬀect of admixtures and concrete mixdesigns on long-term concrete durability in chloride environments.In: Corrosion-89,NACE conference.Texas,US;1989.p.386.[7]Kropp J.Chlorides in concrete.In:Kropp J,Hilsdorf HK,editors.Performance criteria for concrete durability,E&FN SPON;1995.p.138–64.120H.-W.Song et al./Cement&Concrete Composites30(2008)113–121。

桥梁的时变可靠度及剩余寿命预测

桥梁的时变可靠度及剩余寿命预测摘要：本文基于桥梁时变可靠度理论及抗力退化主要影响因素分析等方面研究成果，提出了连续刚构桥使用寿命预测流程，并根据国内外相关抗力衰减模型规律，对某实桥进行了寿命预测，为桥梁工程的寿命预测提供方法借鉴。

关键词：桥梁工程；时变可靠度；寿命预测；可靠指标0引言桥梁结构在服役期间，其抗力是随时间不断衰减的。

而且，车辆荷载和人群荷载等活荷载是依赖于时间参数的随机变量。

因此，桥梁结构的可靠性也随服役时间而变化。

影响结构可靠性的很多因素都是与时间有关的，荷载效应就是一个随机变量，通常用随机过程来描述，因而引入了设计基准期的概念，设计基准期就是将随机过程转化为随机变量所取的一个时间域[1]。

1桥梁时变可靠度1.1桥梁抗力退化主要影响因素桥梁由混凝土和钢筋（包括预应力钢筋）两种材料组成，因此材料性能应考虑混凝土和钢筋两个方面。

随着时间的推移，这些影响因素的性能都会按不同规律变化，导致结构抗力产生相应的变化[2]。

1.2抗力衰减模型一般来说，抗力随时间的变化是非平稳随机过程，要确定抗力的衰减规律是一个非常复杂的问题，为了计算上的简化和实用化，可将非平稳随机过程平稳化，即将抗力表示为：（1）式中：——初始时刻的抗力随机变量；——抗力退化和修理导致抗力恢复的随机过程。

（1）国外抗力衰减模型文献[3]和文献[4]建议了由于钢筋锈蚀导致的混凝土梁抗弯承载力衰减函数：（2）表1抗力衰减模型抗力时变规律如图1所示。

图1抗力变化规律曲线（2）国内抗力衰减模型国内学者根据实际检测数据，对钢筋锈蚀和混凝土强度时变模型进行了修正后，给出了如图2所示的抗力时变规律。

图2抗力变化规律曲线1.3荷载概率模型对于既有桥梁，一般都有10年以上的服役史，因此后续服役期的长度小于100年，后续服役基准期内汽车荷载效应最大值分布依然服从极值I型分布，其基本统计参数要根据后续服役期的长度重新计算，参考文献[5]荷载随机变量的统计参数见表2。

Life-365 Service Life Prediction Model

Life-365 Service Life Prediction Modeland Computer Program for Predicting the Service Life and Life-Cycle Costs of Reinforced ConcreteExposed to ChloridesJanuary8,2008Life-365TM CreditsThe previous Life-365 v1.0 program and manual were written by E. C. Bentz and M. D.A. Thomas under contract to the Life-365 Consortium I, which consisted of W. R. Grace Construction Products, Master Builders, and the Silica Fume Association. The Life-365 v2.0 program and manual are adaptations of these, and were written by M. A. Ehlen under contract to the Life-365 Consortium II, which consists of the Concrete Corrosion Inhibitors Association, the National Ready Mix Concrete Association, the Slag Cement Association, and the Silica Fume Association.“Life-365 Service Life Prediction Model” and “Life-365” are trademarks of the Silica Fume Association. These trademarks are used with permission in the program and in this manual.Table of Contents1 Introduction 62 Life-365 Model Description 82.1 Predicting the Initiation Period 82.1.1 Predicting Chloride Ingress due to Diffusion 82.1.2 Input Parameters for Predicting the Initiation Period 92.1.3 Solution Procedure 142.2 Predicting the Propagation Period 152.3 Repair Schedule 152.4 Probabilistic Predictions of Initiation Period 152.5 Estimating Life-Cycle Costs 162.6 Calculating Life-Cycle Costs 163 Life-365 Users Manual 173.1 Installing Life-365 v2.0 173.2 Starting Life-365 173.3 Project Tab 193.4 Exposure Tab 203.5 Concrete Mixes 223.6 Individual Costs 263.7 Life-Cycle Costs 273.8 Service Life and Life-Cycle Cost Reports 313.9 Supporting Features 323.9.1 Default Settings and Parameters 323.9.2 Online Help 333.10 Advanced Analysis: Service Life Uncertainty 343.11 Special Applications 393.11.1 Epoxy-Coated Rebars for the Top Reinforcing Only 394 Life-365 Background Information 414.1 Service-Life Estimate 414.1.1 Initiation Period 424.2 Input Parameters for Calculating the Service Life (Time to First Repair) 434.2.1 Surface Concentration 454.2.2 Diffusion Coefficient 474.2.3 Diffusion Decay Index (m) 504.2.4 Chloride Threshold 534.2.5 Propagation Period 544.2.6 Temperature 554.3 Input Parameters for Calculating Life-cycle costs 554.4 Summary 55 References 57 Appendix A. Test Protocols for Life-365 Input Parameters 61List of FiguresFigure 1. Examples of Concrete Surface History and Environmental Temperatures (10)Figure 2. Relationship Between D28 and w/c (11)Figure 3. Effect of Silica Fume on D SF (11)Figure 4. Effects of Fly Ash and Slag on D t (12)Figure 5. Effects of Membranes and Sealers (14)Figure 6. Startup Screen (18)Figure 7. Project Tab (19)Figure 8. Exposure Tab (21)Figure 9. Concrete Mixes Tab (22)Figure 10. Service Lives Tab (24)Figure 11. Cross-section Tab (24)Figure 12. Concrete Initiation Graphs (25)Figure 13. Concrete Characteristics Tab (25)Figure 14. Individual Costs Tab (26)Figure 15. Default Concrete and Repair Costs (26)Figure 16. Life-Cycle Costs Tab (28)Figure 17. Life-Cycle Costs: Timelines Tab (29)Figure 18. Life-Cycle Costs: Sensitivity Analysis Tab (30)Figure 19. Service Life (SL) Report (31)Figure 20. LCC Report (32)Figure 21. Default Settings and Parameters Tab (33)Figure 22. Online Help (34)Figure 23. Concrete Mixes Tab: Initiation Time Uncertainty Tab (35)Figure 24. Uncertainty Prompt (36)Figure 25. Probability of Service Life Years, by Year (36)Figure 26. Cumulative Probability of Service Life, by Year (37)Figure 27. Life-cycle Costs Tab with Modify Uncertainty Panel (38)Figure 28. Modify Uncertainty Panel (39)Figure 29. Default and Modified Steel Costs for Hybrid Epoxy/Black Steel Slab (40)Figure 30. Components of Concrete Service Life (41)Figure 31. Chloride Levels, by Region of North America (46)Figure 32. Effects of w/cm on Diffusion Coefficient (48)Figure 33. Effects of Silica Fume on Diffusion Coefficient (49)Figure 34. Effects of Age on Diffusivity (52)List of TablesTable 1. Effects of Slag and Fly Ash on Diffusion Coefficients (12)Table 2. Effects of CNI on Threshold (13)Table 3. Build-up Rates and Maximum %, Various Chloride Zones (45)Table 4. Build-up Rates and Maximum %, by Structure Type (47)Table 5. Values of m, Various Concrete Mixes (50)Table 6. Doses and Thresholds, Various Inhibitors (54)Table 7. Model Inputs and Test Conditions (67)Life-365 DisclaimerThis Computer Program and accompanying Manual are intended for guidance in planning and designing concrete construction exposed to chlorides in service. These items are intended for the use of individuals who are competent to evaluate the significance and limitations of their content and recommendations and who will accept responsibility for the application of the material it contains. The members of the consortium responsible for the development of these materials shall not be liable for any loss or damage arising there from.Performance data included in the Computer Program and the Manual are derived from publications in the concrete literature and from manufacturers’ product literature. Specific products are referenced for informational purposes only.Users are urged to thoroughly read this Manual to understand the capabilities and limitations of the Computer Program.1IntroductionThe corrosion of embedded steel reinforcement in concrete due to the penetration of chlorides from deicing salts, groundwater or seawater is the most prevalent form of premature concrete deterioration worldwide and costs billions of dollars a year in terms of infrastructure repair and replacement. There are currently numerous strategies available for increasing the service life of reinforced structures exposed to chloride salts; these include the use of:•low-permeability (high-performance) concrete,•chemical corrosion inhibitors,•protective coatings on steel reinforcement (e.g. epoxy-coated or galvanized steel), •corrosion-resistant steel (e.g. stainless steel),•non-ferrous reinforcement (e.g. fiber-reinforced plastics),•waterproofing membranes or sealants applied to the exposed surface of the concrete,•cathodic protection (applied at the time of construction), and•combinations of the above.Each of these strategies has different technical merits and costs associated with their use. Selecting the optimum strategy requires the means to weigh all associated costs against the potential extension to the life of the structure. Life-cycle cost analysis (LCCA) is being used more and more frequently for this purpose. LCCA uses estimated initial construction costs, protection costs, and future repair costs to compute the costs over the design life of the structure. Many concrete protection strategies may reduce future repair costs by reducing the extent of future repairs or by extending the time between repairs. Thus, even though the implementation of a protection strategy may increase initial costs, it may still reduce life-cycle costs.A number of models for predicting the service life of concrete structures exposed to chloride environments or for estimating life-cycle costs of different corrosion protection strategies have been developed recently and some of these are available on a commercial basis. The approaches adopted by the different models vary considerably and consequently there can be significant variances between the solutions produced by individual models. This has caused some concern among the engineering community and in response to this, in May 1998 the Strategic Development Council (SDC) of the American Concrete Institute (ACI) identified the need to develop a “standard model” and recommended that a workshop be held to investigate potential solutions. In November 1998, such a workshop, entitled “Models for Predicting Service Life and Life-Cycle Cost of Steel-Reinforced Concrete”, was sponsored by the National Institute of Standards and Technology (NIST), ACI, and the American Society for Testing and Materials (ASTM). A detailed report of the workshop is available from NIST (Frohnsdorff, 1999). At this workshop a decision was made to attempt to develop a “standard model” under thejurisdiction of the existing ACI Committee 365 “Service Life Prediction.” Such a model would be developed and maintained following the normal ACI protocol and consensus procedure for producing committee documents.In order to expedite the process, a consortium was established under ACI’s SDC to fund the development of an initial life-cycle cost model based on the existing service life model developed at the University of Toronto (see Boddy et al., 1999). The funding members of this consortium, known as the Life-365 Consortium, were Master Builders Technologies, Grace Construction Products and the Silica Fume Association. Life-365 Version 1.0 was released in October 2000, and later revised as Version 1.1 in December 2001 to incorporate minor changes.The current version has many limitations in that a number of assumptions or simplifications have been made to deal with some of the more complex phenomena or areas where there is insufficient knowledge to permit a more rigorous analysis. Users are encouraged to run various “user-defined scenarios” in tandem with the Life-365 prediction with minor adjustments to the values (e.g. D28, m, C t, C s, t p)selected by Life-365. This will aid in the development of an understanding of the roles of these parameters and the sensitivity of the solution to their values.It is intended that Life-365 will eventually be handed over to ACI Committee 365 for review and possible adoption as an initial “standard” model, and that continued refinement and validation be carried out under the auspices of that committee.This manual is divided into four parts:Life-365 Model™ Description.This section provides a detailedexplanation of how the model, Life-365, estimates the service life (time tocracking and first repair) and the life-cycle costs associated with differentcorrosion protection strategies. The mathematical equations and empiricalrelationships incorporated in the model are presented in this section.Life-365 Users Manual. This section is an operator’s manual that givesinstructions on how to use Life365 v2.0, the input parameters required,and the various options available to the user.Background Information.This section presents published and otherinformation to support the relationships and assumptions used in themodel to calculate the service life and life-cycle costs. A discussion of thelimitations of the current model is also presented.Appendix A.This section provides recommended protocols fordetermining some of the input parameters used in Life-365.2 Life-365 Model DescriptionThe analyses carried out within Life-365 can be split into four separate steps:• Predicting the time to the onset of corrosion, commonly called the initiation period, t i ;• Predicting the time for corrosion to reach an unacceptable level, commonly called the propagation period, t p ; (Note that the time to first repair, t r , is the sum of these two periods: i.e. t r = t i + t p )• Determining the repair schedule after first repair; and• Estimating life-cycle costs based on the initial concrete (and other protection) costs and future repair costs.2.1 Predicting the Initiation PeriodThe initiation period, t i , defines the time it takes for sufficient chlorides to penetrate the concrete cover and accumulate in sufficient quantity at the depth of the embedded steel to initiate corrosion of the steel. Specifically, it represents the time taken for the critical threshold concentration of chlorides, C t , to reach the depth of cover, x d . Life-365 uses a simplified approach based on Fickean diffusion that requires only simple inputs from the user. It is intended that future versions of Life-365 will be capable of accounting for the combined effects of diffusion and convection, and also of chloride binding by the products of hydration. These capabilities have been implemented in more complex service life models (e.g., Boddy et al., 1999).2.1.1 Predicting Chloride Ingress due to DiffusionThe model predicts the initiation period assuming diffusion to be the dominant mechanism. Fick’s second law is the governing differential equation:22dxC dD dt dC !=, Eqn. 1 whereC = chloride content,D = apparent diffusion coefficient,x = depth (from the exposed surface), and t = time.The chloride diffusion coefficient is a function of both time and temperature, and Life-365 uses the following relationship to account for time-dependent changes in diffusion:()m ref ref t t D t D !!"#$$%&'=, Eqn. 2where D(t)= diffusion coefficient at time t , D ref= diffusion coefficient at time t ref (= 28 days in Life-365), and m = constant (depending on mix proportions).Life-365 selects values of D ref and m based on the mix design details (i.e., water-cementitious material ratio, w/cm , and the type and proportion of cementitious materials) input by the user. In order to prevent the diffusion coefficient decreasing with time indefinitely, the relationship shown in Eqn. 2 is only valid up to 25 years. Beyond this time, the value at 25 years (D 25) calculated from Eqn. 2 is assumed to be constant throughout the rest of the analysis period.Life-365 uses the following relationship to account for temperature-dependent changes in diffusion:()!!"#$$%&''()**+,-..=T T R U D T D ref ref 11exp , Eqn. 3where D(T) = diffusion coefficient at time t and temperature T ,D ref = diffusion coefficient at time t ref and temp. T ref ,U = activation energy of the diffusion process (35000 J/mol), R = gas constant, andT = absolute temperature.In the model, t ref = 28 days and T ref = 293K (20°C). The temperature T of the concrete varies with time according to the geographic location selected by the user. If the required location cannot be found in model database, the user can input the necessary temperature data.The chloride exposure conditions (e.g., rate of chloride build up at the surface and maximum chloride content) are selected by the model based on the type of structure (e.g., bridge deck, parking structure), the type of exposure (e.g., to marine or deicing salts) and the geographic location. Alternatively, the user can input data for these parameters.The solution is carried out using a finite difference implementation of Fick’s second law (Eqn. 1) where the value of D is modified at every time step using Eqns. 2 and 3.2.1.2 Input Parameters for Predicting the Initiation PeriodThe following general user inputs are required for each project:• Geographic location;• Type of structure and nature of exposure;• Depth of clear concrete cover to the reinforcing steel (x d ), and•Details of each protection strategy scenario such as water-cement ratio, type and quantity of mineral admixtures or corrosion inhibitors, type of steel and coatings, presence of membranes or sealers.From these input parameters the model selects the necessary coefficients for calculating the time to corrosion, as detailed above.Surface Chloride Build UpThe model determines a maximum surface chloride concentration, C s, and the time taken to reach that maximum, t max, based on the type of structure, its geographic location, and exposure as selected by the user. For example, if the user selected a bridge deck in an urban area of Moline, Illinois, the model would use the surface concentration profile shown in Figure 1. Alternatively, the user can input the maximum.Figure 1. Examples of Concrete Surface History and Environmental TemperaturesTemperature ProfileThe model determines yearly temperature profiles based on the user’s input for geographical location using a database compiled from meteorological data. For example, if the user selected Moline, Illinois, the model would use the temperature profile and make the necessary adjustments to the diffusion coefficient using Eqn. 3. Alternatively the temperature profile can be defined by the user.Base Case Concrete MixThe base case concrete mix assumed by the model is plain Portland cement concrete with no special corrosion protection applied. For the base case, the following values are assumed:D 28 = 1 x 10(-12.06 + 2.40w/c ) m 2/s, m = 0.20, andC t = 0.05% (by mass of concrete).The relationship between D 28 and the water-cementitious materials ratio (w/c ) is based on a large database of bulk diffusion tests. The nature of the relationship is shown opposite (corrected to 20°C). The value of m is based on data from the University of Toronto and other published data, and the value of C t is commonly used for service-life prediction purposes (and is close to a value of 0.40% chloride based on the mass of cementitious materials for a typical structural concrete mix).It should be noted that these relationships pertain to concrete produced with aggregates of normal density and may not be appropriate for lightweight concrete.Effect of Silica FumeThe addition of silica fume is known to produce significant reductions in thepermeability and diffusivity of concrete.Life-365 applies a reduction factor to thevalue calculated for Portland cement,D PC , based on the level of silica fume (%SF ) in the concrete. The following relationship, which is again based on bulk diffusion data, is used:D SF = D PC ·e -0.165·SF .The relationship is only valid up toreplacement levels of 15% silica fume.The model will not compute diffusionvalues (or make service life predictions)for higher levels of silica fume.Figure 2. Relationship Between D 28 andw/c Figure 3. Effect of Silica Fume on D SFLife-365 assumes that silica fume has no effect on either C t or m .Effect of Fly Ash and SlagNeither fly ash nor slag are assumed to effect the early-age diffusion coefficient, D 28, or the chloride threshold, C t . However, both materials impact the rate of reduction in diffusivity and hence the value of m . The following equation is used to modify m based on the level of fly ash (%FA ) or slag (%SG ) in the mix:m = 0.2 + 0.4(%FA /50 + %SG /70).The relationship is only valid up to replacement levels of 50% fly ash or 70% slag, and thus m ≤ 0.60. The modelwill not compute diffusion values (ormake service life predictions) for higherlevels of these materials.Figure 4 shows the effect of m for threemixes with w/cm = 0.40 and with (i) plain Portland cement (PC), (ii) 30% slag, and (iii) 40% fly ash. These mix proportions yield the coefficients listed in Table 1.Table 1. Effects of Slag and Fly Ash on Diffusion Coefficientsm(<=0.60) D 28(x 10-13m 2/s) D 10y(x 10-13m 2/s) D 25y(x 10-13m 2/s) PC 0.20 79 30 25 30% SG 0.37 79 13 9.3 40% FA0.52796.33.9Effect of Corrosion InhibitorsThe model accounts for two chemical corrosion inhibitors with documented performance: calcium nitrite inhibitor (CNI) and Rheocrete 222+ (a proprietary product from Master Builders; in the Life-365 software, it is referred to as “A&E,” for “amines and esters”). It is intended that more inhibitors be included when appropriate documentation of their performance becomes available.Figure 4. Effects of Fly Ash and Slag on D tFive dosage levels of 30% solution calcium nitrite are permitted in Life-365. The inclusion of CNI is assumed to have no effect on the diffusion coefficient, D28, or the diffusion decay coefficient, m. The effect of CNI on the chloride threshold, C t, varies with dose as shown in the following table.Table 2. Effects of CNI on ThresholdCNI Dose litres/m3gal/cy Threshold, C t (% wt. conc.)0 0 0.0510 2 0.1515 3 0.2420 4 0.3225 5 0.3730 6 0.40A single dose of Rheocrete 222+ (or amines and esters, as it is referred to in the software) is permitted in the model; the dose is 5 litres/m3 concrete. This dose of the admixture is assumed to modify the corrosion threshold to C t= 0.12% (by mass of concrete). Furthermore, it is also assumed that the initial diffusion coefficient is reduced to 90% of the value predicted for the concrete without the admixture and that the rate of chloride build up at the surface is decreased by half (in other words it takes twice as long for C s to reach its maximum value). These modifications are made to take account of the pore modifications induced by Rheocrete 222+ (or amines and esters), which tend to reduce capillary effects (i.e. sorptivity) and diffusivity.Effect of Membranes and SealersMembranes and sealers are dealt with in a simplified manner: it is assumed that both membranes and sealers only impact the rate of chloride build-up. Membranes start with an efficiency of 100%, which deteriorates over the lifetime of the membrane; the default lifetime is 20 years. This means that the rate of build-up starts at zero and increases linearly to the same rate as that for an unprotected concrete at 20 years. In the example shown in Figure 5, the surface chloride for unprotected concrete increases at a rate of 0.04% per annum and reaches a maximum concentration of 0.60% at 15 years. Both the initial efficiency and the lifetime of the membrane can be changed by the user. Also the membrane can be reapplied at regular intervals in the same manner as sealers (described below).Figure 5. Effects of Membranes and SealersSealers are dealt with in the same way, except that the default lifetime is only 5 years. The example in Figure 5 shows the effect of reapplying the sealer every 5 years. Each time the sealer is applied, the build-up rate is reset to zero and then allowed to build up back to the unprotected rate (0.04% per annum in the example) at the selected lifetime of the sealer (5 years in the example). Membranes and sealers can only be reapplied up to the time of the first repair.Effect of Epoxy-Coated SteelThe presence of epoxy-coated steel does not affect the rate of chloride ingress in concrete, nor would it be expected to impact the chloride threshold of the steel at areas where the steel is unprotected. Consequently, the use of epoxy-coated steel does not influence the initiation period, t i. However, it is assumed in the model that the rate of damage build up is lower when epoxy-coated steel is present and these effects are dealt with by modifying the propagation period, t p (see below).Effect of Stainless SteelIn the current version of Life-365 it is assumed that grade 316 stainless steel has a corrosion threshold of C t= 0.50% (i.e., ten times black steel).2.1.3Solution ProcedureThe Life-365 Computer Program uses a finite difference implementation of Fick's Second Law, the general advection-dispersion equation. Implicit in the model are the following assumptions:•The material under consideration is homogeneous (e.g. no surface effects);•The surface concentration is constant around the concrete member at any given time;•The properties of the elements are constant during each time step, calculated at the start of each time step; and•The diffusion constant is uniform over the depth of the element.2.2Predicting the Propagation PeriodThe propagation period, t p, is fixed at 6 years. In other words, the time to repair, t r, is simply given by t r = t i + 6 years. The only protection strategy that influences the duration of the propagation period is the use of epoxy-coated steel, which increases the period to t p = 20 years. The propagation period can be changed by the user.2.3Repair ScheduleThe time to the first repair, t r, is predicted by Life-365 from a consideration of the properties of the concrete, the nature of any corrosion protection strategy and details of the environmental exposure. The cost and extent of this first repair (i.e., the percentage of area to be repaired) and the cost, extent, and schedule of future repairs are estimated by the user.2.4Probabilistic Predictions of Initiation PeriodLife-365 includes probabilistic calculations using the method explained in a recent paper (Bentz 2003); see the paper for details. This method applies the following steps:a)Estimate time to first corrosion for average values of all input.b)For each of the five input variables of relevance (D ref, C s, m, C t, x d), perform fiveadditional deterministic calculations with each of the variable sequentiallyadjusted by 10%.c)From the results of step b) compared to the result from step a), estimate thederivative of corrosion initiation time with respect to each of the five variables.This determines the sensitivity of the results to variations in each of the inputvariables.d)Use the results from step c) to estimate the single parameter of variability, similarto a standard deviation, for the log-normal assumed variation of time to corrosion initiation. Thus the distribution of time to first corrosion is assumed to follow alog-normal distribution, shown by Bentz to work well. The average value of thisdistribution is taken from the deterministic analysis in step a). The variability ofthis assumed distribution is determined from the results of steps b) and c).2.5Estimating Life-Cycle CostsPrice InformationThe user is responsible for providing the following cost information to be used in the life cycle cost analysis:•Cost of concrete mixes (including corrosion inhibitors) for the various strategies under consideration,•Cost of repairs,•Inflation rate, i, and•Real discount rate, r.Life-365 provides the following default costs for various rebar protection strategies: •Black steel = $1.00/kg ($0.45/lb)•Epoxy-coated rebar = $1.33/kg ($0.60/lb)•Stainless steel = $6.60/kg ($2.99/lb)The costs of these materials can be changed by the user.2.6Calculating Life-Cycle CostsPresent Worth CalculationsThe total life-cycle costs are calculated as the sum of the initial construction costs and the discounted future repair costs over the life of the structure.The initial construction costs are simply the cost of the concrete + the cost of the steel (or other reinforcement) plus the cost of any surface protection (membrane or sealer). These costs are expressed on the basis of a unit area of the structure (e.g. $/m2).Future repair costs are calculated on a “present worth” basis using the inflation rate, i, and the real discount rate, r, both provided by the user. The present worth, PW, of a future cost c ($/m2) at time t (years) is given by the formula:!PW=c1+i1+r"#$%&'tEqn. 4All the predicted future repair costs over the entire design life of the structure are calculated in this manner and added to the initial construction costs to give the total life-cycle costs.3Life-365 Users ManualThe concrete service life and life-cycle costing methodologies described in Chapter 2 are implemented in the Life-365 computer program in a way that allows for easy input of the environmental, concrete, and economic parameters, and for rapid sensitivity analysis of the parameters that most influence concrete service life and life-cycle cost. This chapter first describes the basic characteristics of approach and the software, and then describes optional additional features designed for experienced practitioners.3.1Installing Life-365 v2.0Life-365 runs on personal computers, including those running Microsoft Windows, Apple OS X, and Linux. It requires Java 1.5 (or higher), which comes preinstalled with current versions of Windows and Mac OS X, or can be installed from the Java website.1To install Life-365 itself:•From the Life-365 CD: In Windows, select “InstallWindows.bat”; on other operating systems, select “InstallNonWindows.jar.”•From the Life-365 installation zip file: download and then unzip the file on your desktop, enter the folder of contents, and then make the Windows or non-Windows selection you would above.3.2Starting Life-365Installing Life-365 puts a start menu item, “Life-365,” in your Windows Programs folder (accessible from the Start button in the lower left-hand corner of your screen); it will typically also put an icon on your desktop. (Other platforms such as Apple OS X may not, depending on your Java settings). To start Life-365, simply select this menu item or the desktop icon.When Life-365 starts, your screen should look like Figure 6. This screen has two components. On the left-hand side there is a navigation menu that, under the Navigator section, lets you open new or existing Life-365 project files; under the Settings section, lets you change the default settings and get help with particular screens; and under the Tips section, displays text that gives you information and tips on using the software.1 Java 1.5 is produced by Sun Microsystems, Inc., and can be installed by downloading from/javase/downloads/index.jsp (accessed September 18, 2007).。

几种老化系数计算方法的比较

几种老化系数计算方法的比较饶瑞1，刘爱荣1，王荣辉2【摘要】摘要:以计算结果与Bastgen试验结果的吻合程度作为判别计算精度的标准，比较继效法、老化法、B-K法、王勋文法和中值法5种老化系数计算方法对于长期老化系数和短期老化系数的计算精度，讨论了TROSTH、周建民老化系数建议值的合理性.研究发现:王勋文法无论在长期老化系数还是短期老化系数的计算上均有较高精度.在采用按龄期调整的有效模量法分析具有多次加载过程的结构徐变分析时，宜用该方法计算老化系数.【期刊名称】广州大学学报（自然科学版）【年(卷),期】2011(010)004【总页数】5【关键词】关键词:徐变;按龄期调整的有效模量法;老化系数按龄期调整的有效模量法(AEMM)是分析结构徐变效应的一种有效方法［1－2］.它具有概念明确，便于电算的优点，故最为研究者所乐用.在运用该方法的过程中，除了混凝土的徐变系数外，还涉及到另一个系数——老化系数.老化系数是在计算随时间变化的力所产生的徐变变形时，用于对徐变系数进行修正的系数，也可理解为反映徐变量随着混凝土老化而逐渐衰减的一种系数，是运用按龄期调整的有效模量法进行结构徐变分析必不可少的系数之一.其取值问题，是用按龄期调整有效模量法求解的关键问题.其取值的合适与否，决定着徐变分析质量的高低.TROST H［3］认为老化系数的平均值在0.82左右，并建议一般情况下取0.8.周建民［4］则认为老化系数应该取为0.67.除此之外，学者们还提出了一系列老化系数的计算方法，如基于老化理论和继效理论的计算方法［5］、基于松弛系数经验公式的计算方法［6］、基于考虑龄期影响的徐变本构理论与继效流动理论相结合的计算方法［7］以及基于积分中值定理的计算方法［8－9］.上述方法均有各自的理论依据，孰优孰劣，尚无定论.因此，在运用按龄期调整的有效模量法进行结构徐变分析的过程中，在老化系数计算方法的选取上，一般都是出于经验或习惯.各种方法都不乏应用案例.本文将从结构徐变效应分析的按龄期调整的有效模量法入手，寻找比较的着眼点，进而对上述几种老化系数计算方法进行比较.以期获得有益的结论，为老化系数计算方法的选择提供参考.1 老化系数计算方法为了文章的完整性起见，先扼要介绍几种老化系数计算方法.为了描述方便，记t0为加载龄期，t为计算龄期，x(t，t0)为老化系数，φ(t，t0)为徐变系数，J(t，t0)为徐变柔量，R(t，t0)为松弛系数，E(28)为混凝土28 d弹性模量.其中，龄期以天为单位，老化系数徐变系数和徐变柔量为无量纲量，弹性模量以MPa为单位.在老化系数计算方法中，最为常用的方法是基于继效理论和老化理论的计算方法(分别简称为继效法和老化法)［5］，这两种方法具有相同的计算式，其区别在于式中常数α和β的取值.这两种表达式可分别写为BAZANT等［6］提出了松弛系数的经验公式，并由此推出老化系数的计算公式(B-K法):王勋文［7］运用考虑龄期影响的徐变本构理论与继效流动理论相结合的方法(王勋文法)，推导得出老化系数计算公式为而在徐变电算中较为常用的老化系数计算公式则是由积分中值定理推导得出的［8－9］，文中称为中值法，其表达式可写成2 按龄期调整的有效模量法设t0时刻在混凝土结构上作用恒应力σ(t0)，假定弹性模量不随时间变化，在t 时刻，由Trost-Bazant理论［10］，混凝土的徐变应变(应变增量)和应力存在如下关系:式中，φ(t，t0)为加载龄期t0至t时刻混凝土的徐变系数;Δεcr(t)和Δσcr(t)分别为t时刻的徐变应变和应力增量;Eφ(t，t0)为按龄期调整的有效模量;χ (t，t0)为老化系数.式(6)为按龄期调整的有效模量法(AEMM)［10］的徐变应变—应力基本方程.对于具有多次加载的过程结构，其应力和时间的关系可用图1近似表示.图1中，σ(ti)为ti时刻的瞬时弹性应力增量，σcr(i)为ti－1至ti时段(i时段)的徐变应力.根据式(6)，tn时刻的徐变应变和tn－1时刻的徐变应变可用式(7)和式(8)表示.根据式(7)和式(8)可得n时段的徐变应变增量如式(9).3 比较结果分析从式(9)可知，在用AEMM法计算结构徐变时，必须先求出和Eφ(tn，tn－1)3种按龄期调整的有效模量，也即必须获得和3 种老化系数.这些老化系数的时间区间(以χ(tn，ti－1)为例，时间区间即为tn－ti－1)可能包括一个阶段或者多个阶段，即从时间跨度上看，这些老化系数有长期和短期之分.因此，有效的计算方法必须兼顾到长期老化系数和短期老化系数的计算精度.为此，本文将分别从长期老化系数计算精度和短期老化系数计算精度两个角度对上述几种老化系数计算公式进行对比分析.Bastgen试验［11］是一个研究混凝土老化的试验.该试验以加载龄期28 d，徐变系数终值1.5的混凝土块为试验试件，获得了持载龄期和老化系数的关系曲线.由于相关试验较少，Bastgen试验结果一直以来都用于验证老化系数计算公式计算结果的有效性.本文也将其用于验证各种方法的计算结果，将各种老化系数计算公式的计算结果与Bastgen试验值比较，以计算结果与试验结果的吻合程度作为判别计算精度的标准.从式(1)至(5)可以发现，老化系数与徐变系数有很大关系.不同的徐变系数推算表达式和不同的徐变计算理论都将得到不同的老化系数值.为了使各公式的计算结果具有可比性，统一采用现行公路桥梁规范中的徐变计算模式——CEBFIP1990模式计算得出的徐变系数进行老化系数的计算.此外，为了便于与Bastgen试验值比较，计算过程中，加载龄期取28 d，徐变系数的终值取1.5.计算结果如图2所示.为了表示得更加清晰，图2仅给出按继效法和B-K法计算所得曲线的一部分.从图2中可见:各种老化系数的计算效果显然是不同的，以按王勋文法计算的结果与试验值最为接近.继效法和B-K法的计算结果前期(100 d以前)与试验值相差较大，它们与试验值的偏差随持载时间的增加而减小，到100 d以后，与试验值基本吻合.继效法、B-K法和王勋文法的计算结果与试验结果随持载时间的增加趋向0.81，与TROST H的建议值基本相同.可见，TROST H建议值实际上是老化系数随时间增长的收敛值.该建议值应用于徐变效应计算中可起到简化计算的作用，但也将造成一定的精度损失.由于该建议值是老化系数的下限，因此，用此建议值得出的结果将低估徐变效应.中值法的计算结果一开始与TROST H的建议值比较接近，而且与试验值的偏差也不大，但是随着持载时间的增加，偏差越来越大，无收敛的趋势.至于其他两种方法，老化法计算值和周建民建议值，由始至终均与试验值偏差较大.上述分析表明，继效法和B-K法适合用于计算时间区间较长的老化系数;中值法较适合用于计算时间区间较短的老化系数;老化法不适合用于老化系数的计算;而王勋文法适用面较广，无论时间区间长短，均能得到比较满意的老化系数计算结果.至于TROST H建议值，则适用于计算区间较长的场合.在不同加载龄期的情况下，进一步研究继效法、王勋文法和中值法对计算短期老化系数的适用性.本文以持载两周为例，分别用3种公式计算7种不同的加载龄期的混凝土的短期老化系数，结果列于表1.表1中可见，王勋文法的计算结果大于其它两种方法的计算结果.虽然有部分计算结果与继效法的计算结果比较接近，但从总体上，王勋文法和中值法的计算结果更加接近.究竟哪一组计算结果更合理，下面将结合文献［11］的研究成果进行判断.研究发现，老化系数与混凝土加载龄期成正比［11］.因此，在相同的持载时间下，加载龄期越大的混凝土，其老化系数越大.从不同加载龄期的老化系数随持载龄期变化曲线(图3)可以看出，王勋文法和中值法的计算结果与这个规律是吻合的，而继效法的计算结果则违背了这个规律.另外，加载龄期越大，其老化系数该越接近1［11］，这与王勋文法和中值法计算结果也是吻合的.可见，王勋文法和中值法的计算结果较继效法的合理，更适合用于短期老化系数的计算.4 结论本文从长期和短期两种角度，比较继效法、老化法、B-K法、王勋文法和中值法5种老化系数计算方法的计算精度，同时讨论了TROST H、周建民建议值的合理性.分析发现:(1)在上述5种计算方法中，老化法的计算误差最大;继效法和B-K法适合于计算长期老化系数;中值法适合于计算短期老化系数;而王勋文法的适用范围较广，无论用于计算长期老化系数还是短期老化系数，均能得到比较满意的结果. (2)TROST H建议值实际上是老化系数随时间增长的收敛值，该建议值应用于徐变效应计算中可起简化计算的作用，但将造成一定的精度损失.该建议值是老化系数的下限，因此，用此建议值得出的结果将低估徐变效应.与TROST H建议值相比，周建民建议值更是低估了老化系数.综上，推荐用王勋文法计算老化系数，该公式较好地反映混凝土老化的基本规律，对于长期和短期老化系数的计算结果均有较高精度.References:［1］HU Di，WENG Yun-xin，YU Zhi-wu.Analysis of creep effecton reinforced concrete thin plate［J］.Engineering Mechanics，2011，28(3):185 －190.(in Chinese)［2］WANGWen-wei，HEChu-sheng，FENG Zhu-lin，et al.Incrementl differentialmodeling of creep and shrinkage of steel-concrete composite beams［J］.Journal of Southeast University:Natural Science Edition，2010，40(6):1252-1256.(in Chinese)［3］ TROST H.Auswirkungen des superpositionsprinzips auf kriech-und relaxations probleme bei beton and spannbeton［J］.Beton-und Stahlbetonbau，1967，61:203-238，261-269.［4］ZHOU Jian-min.Analysismethod of RC structures under the consideration of time factor［D］.Shanghai:Tongji University，2006.(inChinese)［5］ XIAO Ru-cheng.Analysis of bridge structure and program system ［M］.Beijing:China Communications Press，2002.(in Chinese)［6］BAZANT Z P，KIM SS.Approximate relaxation function for concrete［J］.Journal of the Structural Divison，1983，105:2695-2705.［7］WANG Xun-wen，PAN Jia-ying.Evaluating aging coefficient in age-adjusted effective modulus method ［J］.China Railway Science，1996，17(3):12-23.(in Chinese)［8］YAN Dong-huang，TIAN Zhong-chu，LIXue-wen.Finite elementmethod and application for the shrinkage and creep of concrete bridges［J］.China Journal of Highway and Transport，2004，17(2):55-58.(in Chinese)［9］WANG Yin-hui，CHEN Shan-lin.Application of compulsive strain method to creep analysis of concrete bridges［J］.Bridge Construction，2007(1):74-77.(in Chinese)［10］BAZANT Z P.Prediction of concrete creep effects using age-adjusted effective modulus method［J］.ACIJournal，1972，69:212-217［11］NEVILLE A M，DILGERW H，BROOK JJ.Creep of plain and structural concrete［M］.London and New York:Construction Press，1983.参考文献:［1］胡狄，翁运新，余志武.钢筋混凝土矩形薄板徐变效应分析［J］.工程力学，2011，28(3):185-190.［2］王文炜，何初生，冯竹林，等.钢－混凝土组合梁混凝土收缩徐变的增量微分方法［J］.东南大学学报:自然科学版，2010，40(6):1252-1256.［4］周建民.考虑时间因素的混凝土结构分析方法［D］.上海:同济大学，2006.［5］肖汝诚.桥梁结构分析及程序系统［M］.北京:人民交通出版社，2002.［7］王勋文，潘家英.按龄期调整有效模量法中老化系数γ的取值问题［J］.中国铁道科学，1996，17(3):12-23.［8］颜东煌，田仲初，李学文，等.混凝土桥梁收缩徐变计算的有限元方法与应用［J］.中国公路学报，2004，17(2):55-58.［9］王银辉，陈山林.强迫应变法在混凝土桥梁徐变分析中的应用［J］.桥梁建设，2007(1):74-77.【责任编辑:刘少华】基金项目:国家自然科学基金项目(50978062);广东省自然科学基金项目(9151065004000002);广东省科技计划项目(2010A030200014);广州市建委专项科技项目(2004047)资助。

基于连续介质损伤力学的坑蚀高强钢丝疲劳寿命预测

安徽建筑中图分类号：U444文献标识码：A文章编号：1007-7359（2024）1-0062-03DOI:10.16330/ki.1007-7359.2024.1.0230引言大量悬索桥和斜拉桥其拉索吊杆服役期间，在腐蚀环境和疲劳荷载的共同作用下内部钢丝出现严重的锈蚀损伤，其疲劳损伤直接影响整个桥梁结构体系安全[1]。

国内外的实地工程调研表明，大跨度桥梁事故大多是由拉索内部高强钢丝的腐蚀产生的蚀坑导致疲劳寿命急剧衰减造成的[2]。

可见，高强钢丝的腐蚀与疲劳特性评估对于桥梁的安全运营具有重要意义。

构件疲劳性能研究存在多种方法，传统基于试验的S-N 曲线法依赖大量试验数据进行公式拟合，只关注材料疲劳寿命而忽略了疲劳损伤的非线性发展[3]。

断裂力学方法则聚焦单一宏观裂纹的扩展规律，无法考虑钢丝疲劳损伤过程中的应力应变演化进程[4]。

连续介质损伤力学的方法将构件看作连续的整体，通过定义损伤变量来研究循环荷载下构件的损伤以及力学性能退化规律[5]。

基于CDM 方法研究材料损伤演化以及疲劳寿命分析已有大量文献，如W.P.Hu 等[6]基于连续介质损伤力学建立了与腐蚀疲劳的损伤演化方程，预测了2024-T62铝合金在盐雾中的腐蚀疲劳寿命，预测结果与试验数据较符合。

Zhang T 等[7]采用三维有限元法将CDM多轴损伤应用于钛合金中，验证了微动疲劳研究中的有效性。

张昉等[8]进行了疲劳试验，对CDM 模型进行参数标定，并通过ABAQUS 的二次开发平台UMAT 实现了坑蚀钢筋的疲劳寿命预测，发现疲劳寿命预测与试验结果吻合良好。

上述研究表明CDM 法对于循环荷载下含有损伤的材料疲劳寿命预测具有良好的适用性，但鲜有文献将CDM 模型应用于坑蚀高强钢丝的疲劳寿命预测。

本文通过6根无锈蚀钢丝疲劳试验标定了CDM 模型参数，利用ABAQUS 的二次开发平台UMAT 编写钢丝材料本构程序，通过电化学加速锈蚀获取了25根具有不同坑蚀尺寸的钢丝，并进行单向拉伸疲劳试验，用于验证模型的疲劳寿命预测。

基于GA-BP神经网络长服役期内结构混凝土的强度演变预测

第 55 卷第 2 期2024 年 2 月中南大学学报(自然科学版)Journal of Central South University (Science and Technology)V ol.55 No.2Feb. 2024基于GA-BP 神经网络长服役期内结构混凝土的强度演变预测张学鹏1，张戎令1, 2，陈心亮3，杨海花3，于大海3，宋毅1(1. 兰州交通大学土木工程学院，甘肃兰州，730070；2. 兰州交通大学道桥工程灾害防治技术国家地方联合工程实验室，甘肃兰州，730070；3. 中国铁路呼和浩特局集团有限公司，内蒙古呼和浩特，010000)摘要：为研究长服役期内既有混凝土结构的强度演变规律及其预测模型，以唐包铁路、西户铁路等实际工程为研究背景，以服役时间为2、16、25、30、40、52、66、88、95和100 a 的在役桥涵为研究对象，基于混凝土回弹法，开展役桥涵混凝土强度试验，分析长服役期内既有桥涵混凝土强度动态发展过程。

同时，基于试验实测混凝土强度数据与收集的230组同类条件下在役桥涵(服役时间2~88 a)混凝土强度数据，构建GA-BP 神经网络混凝土强度预测模型。

此外，为提高模型可应用性，基于高精度GA-BP 神经网络强度预测模型，建立一般矩阵公式和简化公式。

基于本文构建的混凝土强度预测模型，分析该类地区(试验中已调研区域)长服役期内混凝土结构的强度演变规律。

研究结果表明：相较于既有混凝土强度预测模型，本文构建的GA-BP 神经网络混凝土强度预测模型可有效预测不同服役时间下的混凝土强度，预测数据的平均绝对百分比误差为8.76%，决定系数为0.83。

本文简化公式(C25)精度较高，平均绝对百分比误差为6.6%，为便于简化计算，推荐简化公式(C25)作为长服役期内混凝土强度预测公式。

百年服役期内混凝土强度经历2个时间阶段，即混凝土强度缓慢上升期(1~49 a)、混凝土强度快速下降期(49~100 a)。

混凝土碳化深度测量方法

混凝土碳化深度测量方法文章标题：混凝土碳化深度测量方法及其应用引言：混凝土作为一种普遍应用于建筑领域的材料，其性能和耐久性是保证结构稳定和使用寿命的重要因素之一。

其中混凝土内部的碳化现象对其力学性能和耐久性有着重要的影响。

因此，准确测量混凝土碳化深度是评估混凝土结构损伤程度的关键一步。

本文将介绍一些常用的混凝土碳化深度测量方法，并探讨其应用和局限性。

一、表观碳化深度的测量方法表观碳化深度是指混凝土表面颜色发生变化的厚度，通常用于初步评估结构中碳化的情况。

常用的测量方法包括观察法、刚度法和石蜡浸渍法。

1. 观察法：观察法是通过肉眼观察混凝土表面的颜色变化来估计表观碳化深度。

这种方法简单易行，但仅适用于颜色变化较明显的碳化情况，不能给出精确的测量结果。

2. 刚度法：刚度法是利用刚度仪来测量混凝土表面的硬度和弹性模量变化来估计表观碳化深度。

该方法在一定程度上提高了测量的定量性，但仍存在受到表面涂层的影响以及无法测量混凝土内部的限制。

3. 石蜡浸渍法：石蜡浸渍法是将熔化的石蜡浸渍混凝土表面，然后切割薄片进行显微观察和测量碳化深度。

这种方法能够提供较为精确的测量结果，但操作繁琐，且测量结果受到浸渍时间和温度的影响。

二、电化学方法测量混凝土碳化深度电化学方法是通过测量混凝土中的电阻或电导率变化来估计碳化深度。

常用的电化学方法包括极化曲线法、电导率法和表面激活电阻法。

1. 极化曲线法：极化曲线法是通过测量混凝土表面的电流密度-电位（I-V）曲线，来得到混凝土的电极反应动力学参数，从而推断碳化深度。

该方法操作简便，测量结果较为准确，但需要对混凝土表面进行处理以保证电极的稳定性。

2. 电导率法：电导率法是利用浸泡在混凝土中的电极来测量混凝土中的电导率变化。

该方法不需要对混凝土表面进行处理，结果可靠性较高，但无法提供具体的碳化深度数值。

3. 表面激活电阻法：表面激活电阻法是通过测量混凝土表面的电阻来评估碳化深度，该方法简单易行且成本较低，但对于混凝土表面涂层存在一定限制，不适用于涂层较厚或粗糙的情况。

基于Weibull分布的灌区混凝土建筑物寿命预测

第３９卷第５期２０２０年５月硅㊀酸㊀盐㊀通㊀报ＢＵＬＬＥＴＩＮＯＦＴＨＥＣＨＩＮＥＳＥＣＥＲＡＭＩＣＳＯＣＩＥＴＹＶｏｌ.３９㊀Ｎｏ.５Ｍａｙꎬ２０２０基于Ｗｅｉｂｕｌｌ分布的灌区混凝土建筑物寿命预测徐存东１ꎬ２ꎬ３ꎬ张㊀鹏１ꎬ连海东１ꎬ２ꎬ３ꎬ王㊀燕１ꎬ３ꎬ李㊀振１ꎬ谷丰佑１(１.华北水利水电大学ꎬ水利学院ꎬ郑州㊀４５００００ꎻ２.水资源高效利用与保障工程河南省协同创新中心ꎬ郑州㊀４５００００ꎻ３.河南省水工结构安全工程技术研究中心ꎬ郑州㊀４５００００)摘要:为了探究混凝土建筑物的服役状态和强度衰退在冻融作用下的性能劣化规律ꎬ选取了地处寒旱地区的甘肃省景电灌区输水渡槽建筑物为研究对象ꎬ采用回弹法和超声波检测法检测分析不同服役年限混凝土结构的表面强度和内部损伤程度ꎬ选用时间和相对动弹模量为指标ꎬ建立Ｗｅｉｂｕｌｌ寿命预测模型ꎬ利用现场数据进行了验证分析ꎮ结果表明ꎬ灌区渡槽的寿命预测结果符合Ｗｅｉｂｕｌｌ分布ꎬ其中渡槽槽壳损伤严重ꎬ其寿命直接决定渡槽整体的服役寿命ꎬ根据威布尔预测目标渡槽建筑物寿命约为６０~７０年ꎮ相关研究可为寒旱灌区更新改造提供理论依据ꎮ关键词:混凝土ꎻ渡槽ꎻ超声波平测法ꎻ回弹法ꎻＷｅｉｂｕｌｌ分布ꎻ寿命预测中图分类号:ＴＶ４３１㊀㊀文献标识码:Ａ㊀㊀文章编号:１００１￣１６２５(２０２０)０５￣１４８３￣０８ＬｉｆｅＰｒｅｄｉｃｔｉｏｎｏｆＣｏｎｃｒｅｔｅＢｕｉｌｄｉｎｇｓｉｎＩｒｒｉｇａｔｅｄＡｒｅａｓＢａｓｅｄｏｎＷｅｉｂｕｌｌＤｉｓｔｒｉｂｕｔｉｏｎＸＵＣｕｎｄｏｎｇ１ꎬ２ꎬ３ꎬＺＨＡＮＧＰｅｎｇ１ꎬＬＩＡＮＨａｉｄｏｎｇ１ꎬ２ꎬ３ꎬＷＡＮＧＹａｎ１ꎬ３ꎬＬＩＺｈｅｎ１ꎬＧＵＦｅｎｇｙｏｕ１(１.ＳｃｈｏｏｌｏｆＷａｔｅｒＣｏｎｓｅｒｖａｎｃｙꎬＮｏｒｔｈＣｈｉｎａＵｎｉｖｅｒｓｉｔｙｏｆＷａｔｅｒＲｅｓｏｕｒｃｅｓａｎｄＥｌｅｃｔｒｉｃＰｏｗｅｒꎬＺｈｅｎｇｚｈｏｕ４５００００ꎬＣｈｉｎａꎻ２.ＣｏｌｌａｂｏｒａｔｉｖｅＩｎｎｏｖａｔｉｏｎＣｅｎｔｅｒｏｆＷａｔｅｒＲｅｓｏｕｒｃｅｓＥｆｆｉｃｉｅｎｃｙａｎｄＰｒｏｔｅｃｔｉｏｎＥｎｇｉｎｅｅｒｉｎｇꎬＺｈｅｎｇｚｈｏｕ４５００００ꎬＣｈｉｎａꎻ３.ＨｅｎａｎＰｒｏｖｉｎｃｉａｌＨｙｄｒａｕｌｉｃＳｔｒｕｃｔｕｒｅＳａｆｅｔｙＥｎｇｉｎｅｅｒｉｎｇＲｅｓｅａｒｃｈＣｅｎｔｅｒꎬＺｈｅｎｇｚｈｏｕ４５００００ꎬＣｈｉｎａ)Ａｂｓｔｒａｃｔ:Ｉｎｏｒｄｅｒｔｏｅｘｐｌｏｒｅｔｈｅｄｅｔｅｒｉｏｒａｔｉｏｎｒｕｌｅｏｆｔｈｅｐｅｒｆｏｒｍａｎｃｅｏｆｃｏｎｃｒｅｔｅｂｕｉｌｄｉｎｇｓｕｎｄｅｒｔｈｅａｃｔｉｏｎｏｆｆｒｅｅｚｅ￣ｔｈａｗｏｎｔｈｅｓｅｒｖｉｃｅｓｔａｔｅａｎｄｓｔｒｅｎｇｔｈｄｅｃｌｉｎｅꎬｔｈｅｃｏｎｖｅｙａｎｃｅａｑｕｅｄｕｃｔｂｕｉｌｄｉｎｇｓｉｎＪｉｎｇｄｉａｎｉｒｒｉｇａｔｉｏｎａｒｅａｏｆＧａｎｓｕｐｒｏｖｉｎｃｅꎬｗｈｉｃｈａｒｅｌｏｃａｔｅｄｉｎｔｈｅｃｏｌｄａｎｄｄｒｙａｒｅａꎬｗｅｒｅｓｅｌｅｃｔｅｄａｓｔｈｅｒｅｓｅａｒｃｈｏｂｊｅｃｔ.Ｔｈｅｓｕｒｆａｃｅｓｔｒｅｎｇｔｈａｎｄｔｈｅｄａｍａｇｅｌｅｖｅｌｓｏｆｃｏｎｃｒｅｔｅｓｔｒｕｃｔｕｒｅｓｗｉｔｈｄｉｆｆｅｒｅｎｔｓｅｒｖｉｃｅｙｅａｒｓｗｅｒｅｍｅａｓｕｒｅｄａｎｄａｎａｌｙｚｅｄｂｙｒｅｂｏｕｎｄｍｅｔｈｏｄａｎｄｕｌｔｒａｓｏｎｉｃｍｅｔｈｏｄ.ＡｌｉｆｅｐｒｅｄｉｃｔｉｏｎｍｏｄｅｌｂａｓｅｄｏｎＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎｗａｓｅｓｔａｂｌｉｓｈｅｄ.Ｔｈｅｆｉｅｌｄｄａｔａｗｅｒｅｖｅｒｉｆｉｅｄａｎｄａｎａｌｙｚｅｄ.ＴｈｅｒｅｓｕｌｔｓｓｈｏｗｔｈａｔｔｈｅｌｉｆｅｐｒｅｄｉｃｔｉｏｎｒｅｓｕｌｔｓｏｆａｑｕｅｄｕｃｔｉｎｉｒｒｉｇａｔｉｏｎａｒｅａａｃｃｏｒｄｗｉｔｈＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎ.Ｔｈｅａｑｕｅｄｕｃｔｓｈｅｌｌｉｓｓｅｒｉｏｕｓｌｙｄａｍａｇｅｄꎬａｎｄｉｔｓｌｉｆｅｄｉｒｅｃｔｌｙｄｅｔｅｒｍｉｎｅｓｔｈｅｏｖｅｒａｌｌｓｅｒｖｉｃｅｌｉｆｅｏｆａｑｕｅｄｕｃｔ.ＡｃｃｏｒｄｉｎｇｔｏＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎꎬｔｈｅｌｉｆｅｏｆｔｈｅｔａｒｇｅｔａｑｕｅｄｕｃｔｂｕｉｌｄｉｎｇｉｓａｂｏｕｔ６０￣７０ｙｅａｒｓ.Ｔｈｅｒｅｌｅｖａｎｔｒｅｓｅａｒｃｈｃａｎｐｒｏｖｉｄｅｔｈｅｏｒｅｔｉｃａｌｂａｓｉｓｆｏｒｔｈｅｒｅｎｅｗａｌａｎｄｒｅｃｏｎｓｔｒｕｃｔｉｏｎｏｆｃｏｌｄａｎｄｄｒｙｉｒｒｉｇａｔｉｏｎａｒｅａ.Ｋｅｙｗｏｒｄｓ:ｃｏｎｃｒｅｔｅꎻａｑｕｅｄｕｃｔꎻｕｌｔｒａｓｏｎｉｃｈｏｒｉｚｏｎｔａｌｍｅａｓｕｒｅｍｅｎｔꎻｒｅｂｏｕｎｄｍｅｔｈｏｄꎻＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎꎻｌｉｆｅｐｒｅｄｉｃｔｉｏｎ基金项目:国家自然科学基金(５１５７９１０２ꎬ３１３６０２０４)ꎻ河南省高校科技创新团队支持计划(１９ＩＲＴＳＴＨＮ０３０)ꎻ河南省高等学校重点科研项目计划(２０Ａ５７０００６)作者简介:徐存东(１９７２￣)ꎬ男ꎬ博士ꎬ教授ꎮ主要从事水工结构优化设计和耐久性研究ꎮＥ￣ｍａｉｌ:ｘｃｕｎｄｏｎｇ＠１２６.ｃｏｍ通讯作者:张㊀鹏ꎬ硕士研究生ꎮＥ￣ｍａｉｌ:９０３７５８６７１＠ｑｑ.ｃｏｍ０㊀引㊀言在我国西北的寒旱区ꎬ渡槽㊁泵站等作为灌区常用的水工建筑物ꎬ随着服役年限的增长ꎬ在使用过程中ꎬ受到冻融㊁干湿循环㊁碳化等长期交替作用ꎬ造成灌区内的渡槽㊁泵站管道支墩等水工混凝土建筑物受损严重[１]ꎮ目前在西部灌区更新改造之际ꎬ需对现有建筑物进行评估ꎬ指导更新改造的进行ꎬ因此对于现有建筑物进行寿命预测十分必要ꎮ近年来ꎬ国内外学者对混凝土寿命预测[２￣４]进行了大量的研究ꎬ１９９７年Ｍｅｔｈａ[５]指出钢筋锈蚀㊁寒冷冻害㊁侵蚀作用是混凝土建筑物破坏的三大主要原因ꎮＦｒｏｈｎｓｄｏｒｆ等[６]采用加速试验法１４８４㊀水泥混凝土硅酸盐通报㊀㊀㊀㊀㊀㊀第３９卷对混凝土构件模型进行多方面分析ꎬ从室内试验角度得出寿命预测模型ꎮ自８０年代起ꎬ国内也对混凝土耐久性展开系统研究ꎮ在此基础上ꎬ关宇刚等[７]采用单一冻融和硫酸盐冻融实验ꎬ确立了基于Ｗｅｉｂｕｌｌ模型的耦合作用下的混凝土寿命预测方法ꎮ余红发等[８]研究了暴露条件对混凝土结构使用寿命的影响规律ꎬ建立了结构寿命的预测模型ꎮ牛荻涛等[９￣１０]根据现场获得的数据应用材料劣化模型对运煤栈桥的寿命进行了预测ꎬ从现场收集的数据较从室内得到的数据得出的预测结果更可靠ꎮ乔宏霞等[１１]根据混凝土在冻融循环作用下的特性ꎬ建立了对不同损坏程度的三参数威布尔寿命预测模型ꎬ该实验对本研究具有重要的指导意义ꎮ基于众学者的研究成果可知ꎬ进行的实验多为室内实验或模拟室外实验ꎬ不能全面反映实际运行情况ꎬ得到的结果与实际情况存在差别ꎮ因此ꎬ为更好评估灌区建筑物运行状态ꎬ采用不同运行年限建筑物实际数据进行预测ꎮ本文采用与实际情况较吻合的威布尔寿命预测模型ꎬ根据数据得出混凝土建筑物威布尔寿命预测模型ꎬ相关结果可为西北寒旱灌区混凝土结构更新改造提供参考ꎮ１㊀灌区建筑物室外试验１.１㊀工程概况本文选取甘肃省景泰川电力提灌灌区(后称景电灌区 )内２０１５年建造的二期总干的双排新２４＃渡槽中的渡槽为目标建筑物ꎬ利用灌区内具备相似服役环境且运行年限不同的建筑物作为对照组ꎮ对这些建筑物在现场采取无损检测方法ꎬ对具有不同服役年限的各对照建筑物的耐久性指标进行试验分析ꎬ探测混凝土表面强度和内部损伤ꎬ利用威布尔分布理论为基础对其进行相应的寿命预测ꎬ以探究在实际环境下混凝土各耐久性指标的衰减规律ꎮ其中景电灌区内二期总干２４＃渡槽和其他建筑物的结构形式与服役状态如图１(ａ)和(ｂ)所示ꎬ目标建筑物与对照建筑物的基本信息如表１所示ꎮ图１㊀灌区建筑物结构形式及服役状态图Ｆｉｇ.１㊀Ｄｉａｇｒａｍｏｆｓｔｒｕｃｔｕｒｅｆｏｒｍａｎｄｓｅｒｖｉｃｅｓｔａｔｅｏｆｂｕｉｌｄｉｎｇｓｉｎｉｒｒｉｇａｔｉｏｎａｒｅａ表１㊀目标建筑物与对照建筑物的基本信息Ｔａｂｌｅ１㊀ＢａｓｉｃｉｎｆｏｒｍａｔｉｏｎａｂｏｕｔｔｈｅｔａｒｇｅｔａｎｄｃｏｎｔｒｏｌｂｕｉｌｄｉｎｇｓＢｕｉｌｄｉｎｇＹｅａｒｓｏｆｃｏｍｐｌｅｔｉｏｎＣｏｎｃｒｅｔｅｇｒａｄｅＷａｔｅｒｃｅｍｅｎｔｒａｔｉｏＰｈａｓｅⅡｍａｉｎｃａｎａｌ２４＃ａｑｕｅｄｕｃｔ(ｎｅｗ)２０１５Ｃ３００.４０ＰｈａｓｅⅠｍａｉｎｃａｎａｌ４＃ａｑｕｅｄｕｃｔ１９７１Ｃ３００.４０ＰｈａｓｅⅡｍａｉｎｃａｎａｌ２４＃ａｑｕｅｄｕｃｔ(ｏｌｄ)１９８５Ｃ３００.４０ＰｈａｓｅⅡｍａｉｎｃａｎａｌ１８＃ａｑｕｅｄｕｃｔ(ｏｌｄ)１９８９Ｃ３００.４０Ｗａｔｅｒｄｉｖｅｒｓｉｏｎｐｒｏｊｅｃｔ１＃ａｑｕｅｄｕｃｔ２０００Ｃ３００.４０１.２㊀试验方法及参数选取混凝土强度大小是评价结构耐久性的重要因素ꎬ因此对于建筑物强度的检测十分必要ꎮ但对于实际建筑物不能采用室内的有损实验ꎬ所以本试验采用无损测量ꎮ分别利用回弹仪㊁超声波无损检测仪等仪器对槽身㊁排架部位的超声波波速和抗压强度等进行检测ꎬ探寻不同服役年限建筑物的耐久性参数变化规律ꎬ揭示结构的耐久性参数随服役年限的演化规律ꎮ第５期徐存东等:基于Ｗｅｉｂｕｌｌ分布的灌区混凝土建筑物寿命预测１４８５㊀混凝土强度与超声波声速之间有着密切关系ꎬ混凝土越密实ꎬ其强度就越高ꎬ声波在混凝土中的传输时间就越短ꎬ声速越大ꎮ相反ꎬ混凝土越松散ꎬ其强度就越低ꎬ声波在混凝土中的传输时间就越长ꎬ声速越小ꎮ本文采用的是ＺＢＬ￣Ｕ５２０非金属超声波检测仪对各对照建筑物进行测量ꎬ每个建筑物选取三个测区ꎬ其中测区１为水位线上ꎬ测区２为水位线下ꎬ测区３为槽底ꎬ排架测区１~３分别为排架下㊁中(连系梁)㊁上区域ꎮ对测区进行试验测量ꎬ得出相关数据ꎮ基于«超声波检测混凝土缺陷技术规程»ꎬ超声波检测仪实测的超声波波速如图２中的波形图所示ꎬ其可作为测点超声波波速的另一种直观体现ꎮ图２㊀非金属超声波检测仪测试数据Ｆｉｇ.２㊀Ｎｏｎ￣ｍｅｔａｌｕｌｔｒａｓｏｎｉｃｄｅｔｅｃｔｏｒｔｅｓｔｄａｔａ图３㊀回弹法测表面强度Ｆｉｇ.３㊀Ｓｕｒｆａｃｅｓｔｒｅｎｇｔｈｉｓｍｅａｓｕｒｅｄｂｙｒｅｂｏｕｎｄｍｅｔｈｏｄ基于«回弹法检测混凝土抗压强度技术规程»ＪＧＪ/Ｔ２３２０１１中规定的步骤与方法ꎬ对５个参照建筑物的槽身与排架部分进行现场回弹值的测量ꎬ如图３所示ꎬ每个构件拥有１２个测试区域ꎬ一组含有４个测试区域ꎬ选取２００ｍｍˑ２００ｍｍ作为每个测区面积ꎬ按照回弹法要求对测试构件进行实验准备ꎬ用回弹仪对混凝土的表面进行水平弹击ꎬ其中每个测试分两个相对测试面各８次ꎬ采集并整理数据ꎬ除去最大值和最小值保留１０个数据并取其平均值计算混凝土的实际强度ꎮ１.３㊀参数转换根据«普通混凝土长期性能和耐久性试验方法»ＧＢ５００８２２００９ꎬ当试件的相对动弹模损失至６０％即判定该试件损坏ꎮ根据«混凝土结构设计规范»ＧＢＪ１０８９中给出的转换公式ꎬ即式(１)或式(２)将测出的抗压强度值或超声波波速近似转变为动弹性模量ꎬ进而基于试验得出的初始动弹性模量计算得到相对动弹性模量ꎬ开展下一步计算ꎮＥｄ＝１０５２.２＋３４.７ｆｃ(１)Ｅｄ＝２(１＋λ)３(０.８７＋１.１２λ)２ρｖ２(２)其中ꎬｆｃ为混凝土抗压强度(ＭＰａ)ꎻＥｄ为混凝土动弹模量(ＭＰａ)ꎻλ为混凝土泊松比ꎬ取０.２ꎻρ为混凝土密度(ｋｇ/ｍ３)ꎬ取２４００ꎻｖ为超声波波速(ｍ/ｓ)ꎮ２㊀试验结果分析２.１㊀抗压强度采用回弹法测试混凝土强度ꎬ将建筑物分区ꎬ每个测试区域测试１６次ꎬ采集并整理数据ꎬ去除最大值和最小值保留１０个数据取其平均值推算混凝土的实际强度ꎬ具体转化结果如表２所示ꎮ１４８６㊀水泥混凝土硅酸盐通报㊀㊀㊀㊀㊀㊀第３９卷表２㊀回弹法测得各运行年限建筑物强度值Ｔａｂｌｅ２㊀ＢｕｉｌｄｉｎｇｓｔｒｅｎｇｔｈｍｅａｓｕｒｅｄｂｙｓｐｒｉｎｇｂａｃｋｍｅｔｈｏｄＢｕｉｌｄｉｎｇＰｏｓｉｔｉｏｎＣｏｎｖｅｒｔｅｄｓｔｒｅｎｇｔｈｖａｌｕｅ/ＭＰａＳｕｒｖｅｙａｒｅａ１Ｓｕｒｖｅｙａｒｅａ２Ｓｕｒｖｅｙａｒｅａ３Ａｖｅｒａｇｅｖａｌｕｅ/ＭＰａＰｈａｓｅⅠｍａｉｎｃａｎａｌ４＃Ａｑｕｅｄｕｃｔ(１９７１)Ｇｒｏｏｖｅｄｅｐｔｈ２４.８２４.５２５.７２５.７Ｂｅｎｔｆｒａｍｅ２８.９２５.７２２.４２５.０ＰｈａｓｅⅡｍａｉｎｃａｎａｌ２４＃Ａｑｕｅｄｕｃｔ(１９８５)Ｇｒｏｏｖｅｄｅｐｔｈ２９.０２６.３２４.１２６.８Ｂｅｎｔｆｒａｍｅ２４.９２５.０３０.５２６.６ＰｈａｓｅⅡｍａｉｎｃａｎａｌ１８＃Ａｑｕｅｄｕｃｔ(１９８９)Ｇｒｏｏｖｅｄｅｐｔｈ２９.５２９.３２５.５２８.０Ｂｅｎｔｆｒａｍｅ２５.２２８.９３０.０２８.１ＷａｔｅｒＤｉｖｅｒｓｉｏｎＰｒｏｊｅｃｔ１＃Ａｑｕｅｄｕｃｔ(２０００)Ｇｒｏｏｖｅｄｅｐｔｈ３１.２３１.６３２.０３１.９Ｂｅｎｔｆｒａｍｅ３０.９２８.８３６.０３１.６ＰｈａｓｅⅡｍａｉｎｃａｎａｌ１８＃Ａｑｕｅｄｕｃｔ(２０１５)Ｇｒｏｏｖｅｄｅｐｔｈ３７.９３７.６３６.９３６.９Ｂｅｎｔｆｒａｍｅ３３.６３７.８３９.４３７.２㊀㊀利用公式(１)将得到的强度值转化为动弹模量ꎬ具体结果如表３所示ꎮ表３㊀各运行年限建筑物动弹模量Ｔａｂｌｅ３㊀Ｄｙｎａｍｉｃｍｏｄｕｌｕｓｏｆｂｕｉｌｄｉｎｇｓｆｏｒｅａｃｈｏｐｅｒａｔｉｎｇｌｉｆｅ㊀㊀ＳｅｒｖｉｃｅｌｅｎｇｔｈＥｄ/ＭＰａ㊀㊀４７３３２９１８３Ｇｒｏｏｖｅｄｅｐｔｈ２８.１７２８.６１２９.０８３０.４２３１.８４Ｂｅｎｔｆｒａｍｅ２７.８７２８.５３２９.１１３０.３２３１.９２㊀㊀通过回弹法对渡槽的槽身和排架表面强度进行测量ꎬ发现其受渡槽和排架的运行方式及所处位置影响ꎮ渡槽槽身的下部较上部强度小ꎬ排架越接近地面位置强度越小ꎮ其中ꎬ部分年份数据表现不一致ꎬ猜想是由于混凝土搅拌不均匀等施工原因造成ꎬ导致部分部位的强度呈无规律化ꎬ总体符合实际情况ꎮ而且随着运行年限增加ꎬ槽身和排架强度逐渐减小ꎬ且槽身强度明显小于排架ꎮ说明在相同环境条件下的运行过程中ꎬ渡槽槽身危险系数更高ꎮ２.２㊀超声波波速将渡槽槽身和排架进行分区ꎬ将三个区的波速值平均后得出槽身和排架的波速值ꎬ最终结果如表４所示ꎮ表４㊀非金属超声波探测仪测得各运行年限建筑物波速值Ｔａｂｌｅ４㊀ＷａｖｅｖｅｌｏｃｉｔｙｖａｌｕｅｓｏｆｂｕｉｌｄｉｎｇｓｏｆｖａｒｉｏｕｓｏｐｅｒａｔｉｎｇｙｅａｒｓｗｅｒｅｍｅａｓｕｒｅｄｂｙｎｏｎｍｅｔａｌｕｌｔｒａｓｏｎｉｃｄｅｔｅｃｔｏｒＢｕｉｌｄｉｎｇＰｏｓｉｔｉｏｎＵｌｔｒａｓｏｎｉｃｗａｖｅｖｅｌｏｃｉｔｙ/(ｍ/ｓ)Ｓｕｒｖｅｙａｒｅａ１Ｓｕｒｖｅｙａｒｅａ２Ｓｕｒｖｅｙａｒｅａ３Ａｖｅｒａｇｅｖａｌｕｅ/(ｍ/ｓ)ＰｈａｓｅⅠｍａｉｎｃａｎａｌ４＃Ａｑｕｅｄｕｃｔ(１９７１)Ｇｒｏｏｖｅｄｅｐｔｈ１.１３１.１４１.１３１.１３７Ｂｅｎｔｆｒａｍｅ１.１２１.０８１.０８１.０８２ＰｈａｓｅⅡｍａｉｎｃａｎａｌ２４＃Ａｑｕｅｄｕｃｔ(１９８５)Ｇｒｏｏｖｅｄｅｐｔｈ１.４５１.６５１.３３１.４７４Ｂｅｎｔｆｒａｍｅ１.２８１.２５１.３１１.２８２ＰｈａｓｅⅡｍａｉｎｃａｎａｌ１８＃Ａｑｕｅｄｕｃｔ(１９８９)Ｇｒｏｏｖｅｄｅｐｔｈ１.５６１.５２１.５３１.５３８Ｂｅｎｔｆｒａｍｅ１.３１１.２５１.５１１.５１０ＷａｔｅｒＤｉｖｅｒｓｉｏｎＰｒｏｊｅｃｔ１＃Ａｑｕｅｄｕｃｔ(２０００)Ｇｒｏｏｖｅｄｅｐｔｈ１.７９１.８０１.８９１.８２３Ｂｅｎｔｆｒａｍｅ１.８２１.８６１.８５１.８４４ＰｈａｓｅⅡｍａｉｎｃａｎａｌ１８＃Ａｑｕｅｄｕｃｔ(２０１５)Ｇｒｏｏｖｅｄｅｐｔｈ２.３２２.２３２.２１２.３１２Ｂｅｎｔｆｒａｍｅ２.３３２.３４２.３５２.３４７㊀㊀利用公式(２)将得到的强度值转化为动弹模量ꎬ具体结果如表５所示ꎮ利用超声波法对渡槽进行测量ꎬ发现渡槽槽身和排架的波速随高度下降而减小ꎬ这和渡槽和排架的运行方式和所处位置有关ꎬ可能是由于混凝土搅拌不均匀等施工原因ꎬ导致部分部位的强度呈无规律化ꎬ总体符合实际情况ꎮ槽身和排架超声波波速随着运行年限增加而逐渐减小ꎬ且槽身波速较排架小ꎬ表明在同样运行环境中ꎬ渡槽槽身存在危险ꎮ第５期徐存东等:基于Ｗｅｉｂｕｌｌ分布的灌区混凝土建筑物寿命预测１４８７㊀表５㊀各运行年限建筑物动弹模量Ｔａｂｌｅ５㊀Ｄｙｎａｍｉｃｍｏｄｕｌｕｓｏｆｂｕｉｌｄｉｎｇｓｆｏｒｅａｃｈｏｐｅｒａｔｉｎｇｌｉｆｅ㊀㊀ＳｅｒｉｖｃｅｌｅｎｇｔｈＥｄ/ＭＰａ㊀㊀４７３３２９１８３Ｇｒｏｏｖｅｄｅｐｔｈ２７.９５２８.５３２８.８３３０.３３３１.８６Ｂｅｎｔｆｒａｍｅ２７.６６２８.３９２８.６０２９.６５３０.３３３㊀Ｗｅｉｂｕｌｌ寿命预测模型的建立及验证分析３.１㊀模型的建立根据损伤力学原理ꎬ混凝土材料在受力过程中内部逐渐发生破坏ꎬ可通过损伤度[１１]研究材料破坏的过程ꎮ混凝土材料强度的测量手段可以分为无损检测和有损检测ꎬ因考虑到混凝土建筑物的正常运行ꎬ此处采用无损检测中的超声波回弹法进行试验ꎮ根据室内外实验得到的结果和参照相关规范规定ꎬ本文以动弹性模量作为指标来描述损伤程度ꎮ其中损伤度Ｄ的定义为:Ｄｎ＝Ｅ０－ＥｎＥ０(３)其中ꎬＤｎ为ｎ次冻融的损伤度ꎻＥｎ为ｎ次冻融的动弹模量ꎻＥ０为同配合比室内试验混凝土初始动弹模量ꎬ此处选３９.３ＭＰａꎮ本文采用与混凝土较吻合的两个参数的模型用来预测混凝土结构的寿命ꎮ其中假定混凝土结构的使用寿命为ｎꎬ则其运行寿命ｎ的威布尔概率密度函数为:ｆ(ｎ)＝ｂａｎａ()ｂ－１ｅｘｐ－ｎａ()ｂ[](４)其中ꎬａ为尺度标准ꎬｂ为形状标准ꎬ则混凝土结构的运行寿命概率分布函数为:Ｆ(ｎ)＝１－ｅｘｐ－ｎａ()ｂ[](５)当经历ｎ１次冻融侵蚀后ꎬ混凝土的失效概率为:Ｐｆ(ｎ１)＝１－ｅｘｐ－ｎ１ａæèçöø÷ｂ[](６)随着冻融破坏的进行ꎬ混凝土结构达到使用寿命时则认定为失效ꎬ此时Ｐｆ(ｎ１)＝１ꎮ当经历ｎｎ次冻融循环后ꎬ混凝土结构的运行寿命至ｎｎ时ꎬ此时就有Ｄ(ｎｎ)＝１ꎬ因此有等式:Ｐｆ(ｎ１)＝Ｄ(ｎｎ)(７)由威布尔的分布函数可得其可靠性函数为:Ｒ(ｎ)＝１－Ｆ(ｎ)＝ｅｘｐ－ｎａ()ｂ[]＝１－Ｄ(ｎ)(８)对式(８)进行威布尔变换ꎬ两边同时取两次对数可得:ｌｎｌｎ１Ｒｎ()()＝ｂ(ｌｎ(ｎ)－ｌｎ(ａ))(９)令Ｙ＝ｌｎ(ｌｎ(１/Ｒ(ｎ))ꎬＸ＝ｌｎ(ｎ)ꎬＣ＝－ｂｌｎ(ａ)ꎬ则上式可变化为Ｙ＝Ｙ(Ｘ)＝ｂｘ＋Ｃ如果实际混凝土结构的运行寿命符合威布尔分布ꎬ则Ｙ＝{ｌｎ[－ｌｎ(１－Ｆ(ｎ)]}与Ｘ＝ｌｎ(ｎ)应该成一定的线性关系ꎮ通过最小二乘法进行相关分析ꎬ得出相关参数ｂ㊁Ｃ和相关程度Ｒ２ꎮ若相关系数Ｒ２超过０.９ꎬ则Ｙ与Ｘ线性相关性强ꎬ即渡槽建筑物寿命符合威布尔分布ꎮ根据水科院和南京水科院关于冻融循环所做的全国不同地区室内外对比实验可知ꎬ混凝土实际的运行寿命可用式(１０)表示ꎮｔ＝ｅＮ/Ｍ(１０)其中ꎬｔ为构件的使用寿命(年)ꎻｅ为冻融比例系数(一般为１２)ꎬ即室内与室外的比值ꎻＮ为室内试验的冻融循环次数ꎻＭ为实际经历的冻融次数ꎮ１４８８㊀水泥混凝土硅酸盐通报㊀㊀㊀㊀㊀㊀第３９卷３.２㊀模型验证分析通过威布尔相关性检验方程ꎬ对实际渡槽建筑物易破坏部位寿命进行相关性分析ꎬ判定是否符合威布尔分布ꎮ此处采用回弹法和超声波法进行分析ꎬ分别得到表面强度和超声波波速ꎬ进而转化为动弹模量ꎮ将运行年限转化为实际冻融次数作为自变量进行分析ꎬ利用Ｏｒｉｇｉｎ分析软件进行拟合ꎬ得到渡槽结构寿命的威布尔分布值ꎮ３.２.１㊀回弹法分析通过回弹法测得的混凝土强度值ꎬ转化为动弹模量ꎬ计算得到相对动弹模量ꎬ分别计算威布尔相关参数Ｒ(ｎ)㊁Ｘ㊁Ｙꎬ其中Ｒ(ｎ)为相对动弹性模量ꎮ表６㊀回弹法测量槽身的威布尔分布值Ｔａｂｌｅ６㊀ＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎｖａｌｕｅｏｆｔｈｅａｑｕｅｄｕｃｔｂｏｄｙｗａｓｍｅａｓｕｒｅｄｂｙｒｅｂｏｕｎｄｍｅｔｈｏｄＴｉｍｅｎ１/Ｒ(ｎ)Ｘ＝ｌｎ(ｎ)Ｙ＝ｌｎ(ｌｎ(１/Ｒ(ｎ)))３２９.５１.２１２１８６３.３８４３９－１.６４８０４５１１１８１７７１.２６９０８１５.１７６１５－１.４３４２５４６０５２９２８５.１６６７１.３２７５６４５.６５３０７４－１.２６１０８６８６９３３３２４.５１.３４８９８４５.７８２２８６－１.２０６１３７１２２４７４６２.１６６７１.３７０３７５６.１３５９２６－１.１５４９１４４３５表７㊀回弹法测量排架位置的威布尔分布值Ｔａｂｌｅ７㊀ＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎｖａｌｕｅｏｆｔｈｅｓｈｅｌｆｏｆｔｈｅａｑｕｅｄｕｃｔｗａｓｍｅａｓｕｒｅｄｂｙｒｅｂｏｎｄｍｅｔｈｏｄＴｉｍｅｎ１/Ｒ(ｎ)Ｘ＝ｌｎ(ｎ)Ｙ＝ｌｎ(ｌｎ(１/Ｒ(ｎ)))３２９.５１.１６５４１.２１２１８６－１.８７６９１８１７７１.２２６８９４１.２６９０８１－１.５８７２６２９２８５.１６６７１.２７７７７４１.３２７５６４－１.４０６０１３３３２４.５１.３０３６７８１.３４８９８４－１.３２７３１４７４６２.１６６７１.３３４７３６１.３７０３７５－１.２４２２５㊀㊀对表６和表７的威布尔值进行线性拟合ꎬ得到相应的威布尔参数值ｂ和Ｃꎬ如图４和表８所示ꎮ图４㊀回弹法测渡槽的威布尔分布寿命线性回归直线图Ｆｉｇ.４㊀ＬｉｎｅａｒｒｅｇｒｅｓｓｉｏｎｏｆＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎｌｉｆｅｌｉｎｅｏｆａｑｕｅｄｕｃｔｍｅａｓｕｒｅｄｂｙｒｅｂｏｕｎｄｍｅｔｈｏｄ表８㊀回弹法测量渡槽的威布尔分布线性回归结果Ｔａｂｌｅ８㊀ＬｉｎｅａｒｒｅｇｒｅｓｓｉｏｎｒｅｓｕｌｔｓｏｆＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎｏｆａｑｕｅｄｕｃｔｗｅｒｅｍｅａｓｕｒｅｄｂｙｒｅｂｏｕｎｄｍｅｔｈｏｄＣｌａｓｓｉｆｉｃａｔｉｏｎＬｉｆｅｂＣＲ２ＧｒｏｏｖｅｄｅｐｔｈＮ１０.１８－２.２８１７０.９４２ＢｅｎｔｆｒａｍｅＮ２０.２２６８－２.６７３４０.９５４６㊀㊀通过回弹法进行威布尔分析ꎬ得到渡槽的威布尔寿命线性回归直线图ꎬ由图可知两者的相关系数Ｒ２较大ꎬ说明Ｙ和Ｘ的线性相关性较好ꎬ即测得数据满足威布尔分布ꎮ则对应的参数代入混凝土建筑物实际冻㊀第５期徐存东等:基于Ｗｅｉｂｕｌｌ分布的灌区混凝土建筑物寿命预测１４８９融循环下的混凝土威布尔分布寿命预测模型:Ｙ＝ｌｎ(ｌｎ(１/Ｒ(ｎ)))＝０.１８ｌｎ(ｎ)－２.２８１７(１１)Ｙ＝ｌｎ(ｌｎ(１/Ｒ(ｎ)))＝０.２２６８ｌｎ(ｎ)－２.６７３４(１２)根据前面所述规范可知ꎬ当Ｒ(ｎ)＝０.６时混凝土构件可以判定为失效ꎬ即相对动弹模量为６０％ꎬ将其分别代入上面得到的模型中ꎬ可得出Ｎ１＝７８６３ꎬＮ２＝７０８０ꎬ又知西北地区年平均冻融次数约为８.８[１３]ꎬ所以在冻融循环的条件下的安全运行年限分别为６６[１４]年和６０年ꎮ３.２.２㊀超声波法分析通过非金属超声波探测仪测得的混凝土波速ꎬ转化为动弹模量ꎬ计算得到相对动弹模量ꎬ分别计算威布尔相关参数Ｒ(ｎ)㊁Ｘ㊁Ｙꎬ其中Ｒ(ｎ)为相对动弹性模量ꎮ表９㊀超声波测量槽身的威布尔分布值Ｔａｂｌｅ９㊀ＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎｖａｌｕｅｏｆｔｈｅａｑｕｅｄｕｃｔｂｏｄｙｗａｓｍｅａｓｕｒｅｄｂｙｕｌｔｒａｓｏｎｉｃｄｅｔｅｃｔｉｏｎｍｅｔｈｏｄＴｉｍｅｎ１/Ｒ(ｎ)Ｘ＝ｌｎ(ｎ)Ｙ＝ｌｎ(ｌｎ(１/Ｒ(ｎ)))３２９.５１.２１２１８６３.３８４３９－１.８６５０２８９４８１８１７７１.２６９０８１５.１７６１５－１.５８８２７８６０２２９２８５.１６６７１.３２７５６４５.６５３０７４－１.３６６８３４６６６３３３２４.５１.３４８９８４５.７８２２８６－１.３２７２８８４９４４７４６２.１６６７１.３７０３７５６.１３５９２６－１.２５２０３９９３９表１０㊀超声波测量排架的威布尔分布值Ｔａｂｌｅ１０㊀ＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎｖａｌｕｅｏｆｔｈｅｓｈｅｌｆｏｆｔｈｅａｑｕｅｄｕｃｔｗａｓｍｅａｓｕｒｅｄｂｙｕｌｔｒａｓｏｎｉｃｄｅｔｅｃｔｉｏｎｍｅｔｈｏｄＴｉｍｅｎ１/Ｒ(ｎ)Ｘ＝ｌｎ(ｎ)Ｙ＝ｌｎ(ｌｎ(１/Ｒ(ｎ)))３２９.５１.２１２１８６３.３８４３９－１.８６５０３１８１７７１.２６９０８１５.１７６１５－１.５８８２８２９２８５.１６６７１.３２７５６４５.６５３０７４－１.３６６８３３３３２４.５１.３４８９８４５.７８２２８６－１.３０８０１４７４６２.１６６７１.３７０３７５６.１３５９２６－１.２１６１６㊀㊀对表９和表１０的威布尔值进行线性拟合ꎬ得到相应的威布尔参数值ｂ和Ｃꎬ如图５和表１１所示ꎮ图５㊀超声波测渡槽的威布尔分布寿命线性回归直线图Ｆｉｇ.５㊀ＬｉｎｅａｒｒｅｇｒｅｓｓｉｏｎｏｆＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎｌｉｆｅｌｉｎｅｏｆａｑｕｅｄｕｃｔｍｅａｓｕｒｅｄｂｙｕｌｔｒａｓｏｎｉｃｄｅｔｅｃｔｉｏｎｍｅｔｈｏｄ表１１㊀超声波测量渡槽的威布尔分布线性回归结果Ｔａｂｌｅ１１㊀ＬｉｎｅａｒｒｅｇｒｅｓｓｉｏｎｒｅｓｕｌｔｓｏｆＷｅｉｂｕｌｌｄｉｓｔｒｉｂｕｔｉｏｎｏｆａｑｕｅｄｕｃｔｗｅｒｅｍｅａｓｕｒｅｄｂｙｕｌｔｒａｓｏｎｉｃｄｅｔｅｃｔｉｏｎｍｅｔｈｏｄＣｌａｓｓｉｆｉｃａｔｉｏｎＬｉｆｅｂＣＲ２ＧｒｏｏｖｅｄｅｐｔｈＮ３０.２１８－２.６４９８０.９５２２ＢｅｎｔｆｒａｍｅＮ４０.２３３－２.６８６８０.９４３５１４９０㊀水泥混凝土硅酸盐通报㊀㊀㊀㊀㊀㊀第３９卷㊀㊀通过超声波法进行威布尔分析ꎬ得到渡槽的威布尔寿命线性回归直线图ꎬ由图可知两者的相关系数Ｒ２较大ꎬ说明Ｙ和Ｘ的线性相关性较好ꎬ即测得数据满足威布尔分布ꎮ则对应的参数代入混凝土建筑物实际冻融循环下的混凝土威布尔分布寿命预测模型:Ｙ＝ｌｎ(ｌｎ(１/Ｒ(ｎ)))＝０.２１８ｌｎ(ｎ)－２.６４９８(１３)Ｙ＝ｌｎ(ｌｎ(１/Ｒ(ｎ)))＝０.２３３ｌｎ(ｎ)－２.６８６８(１４)根据前面所述规范可知ꎬ当Ｒ(ｎ)＝０.６时混凝土构件可以判定为失效ꎬ即相对动弹模量为６０％ꎬ将其分别代入上面得到的模型中ꎬ可得出Ｎ３＝８４９６ꎬＮ４＝７８６４ꎬ又知西北地区年平均冻融次数约为８.８ꎬ所以在冻融循环的条件下的安全运行年限分别为７２年和６６年ꎮ４㊀结㊀论(１)选取了相对动弹模量作为评判指标ꎬ进行参数拟合并进行渡槽建筑物的寿命预测ꎬ验证所选模型的合理性与可靠性ꎬ对灌区混凝土的寿命预测具有一定的实用价值ꎮ(２)应用构建的预测模型得出景电二期２４＃渡槽的运行寿命为６０~７０年ꎮ渡槽槽身处损伤破坏较排架构件处破坏严重ꎬ渡槽槽壳损伤严重ꎬ寿命明显低于其内部ꎮ(３)将景电灌区各渡槽数据代入本文模型ꎬ得到灌区各相似输水渡槽结构各构件的寿命ꎬ与实际情况相符ꎬ可推广到灌区其他水工建筑物ꎬ为西部灌区更新改造的评估提供参考ꎮ参考文献[１]㊀付传清ꎬ屠一军ꎬ金贤玉ꎬ等.荷载和环境共同作用下混凝土中氯离子传输的试验研究[Ｊ].水利学报ꎬ２０１６ꎬ４７(５):６７４￣６８４. [２]㊀高㊀升.基于耐久性的混凝土寿命预测方法研究进展[Ｊ].混凝土ꎬ２０１８(６):２５￣３０.[３]㊀秦吉丽ꎬ王毅娟.在役混凝土桥梁剩余寿命预测方法研究[Ｊ].北京建筑工程学院学报ꎬ２０１２ꎬ２８(３):１４￣１８.[４]㊀徐存东ꎬ高懿伟ꎬ程㊀昱ꎬ等.超声波平测法在混凝土盐冻损伤检测中的应用研究[Ｊ].混凝土ꎬ２０１９(１１):２９￣３３＋３８.[５]㊀ＭｅｔｈａＰＫ.Ｄｕｒａｂｉｌｉｔｙ￣ｃｒｉｔｉｃａｌｉｓｓｕｅｓｆｏｒｔｈｅｆｕｔｕｒｅ[Ｊ].ＣｏｎｃｒｅｔｅＩｎｔｅｒｎａｔｉｏｎａｌꎬ１９９７ꎬ２０(７):２７￣３３.[６]㊀Ｆｒｏｈｎｓｄｏｒｆｆ.Ｄｕｒａｂｉｌｉｔｙｏｆｂｕｉｌｄｉｎｇｍａｔｅｒｉａｌｓ:ｄｕｒａｂｉｌｉｔｙｒｅｓｅａｒｃｈｉｎｔｈｅＵｎｉｔｅｄＳｔａｔｅｓａｎｄｔｈｅｉｎｆｌｕｅｎｃｅｏｆＲＩＬＥＭｏｎｄｕｒａｂｉｌｉｔｙｒｅｓｅａｒｃｈ[Ｊ].Ｍａｔｅｒｉａｌｓ＆Ｓｔｒｕｃｔｕｒｅｓꎬ１９８５ꎬ１８(３):２０５￣２１４.[７]㊀关宇刚ꎬ孙㊀伟ꎬ缪昌文.基于可靠度与损伤理论的混凝土寿命预测模型Ⅱ:模型验证与应用[Ｊ].硅酸盐学报ꎬ２００１(６):５３５￣５４０. [８]㊀黄泓萍ꎬ余红发ꎬ张㊀娜ꎬ等.碱式硫酸镁水泥的配料规律与基本物理力学性能研究[Ｊ].硅酸盐通报ꎬ２０１６ꎬ３５(８):２５６１￣２５６７＋２５７４. [９]㊀关㊀虓ꎬ牛荻涛ꎬ王家滨ꎬ等.基于耐久性检测的运煤栈桥碳化寿命预测[Ｊ].西安建筑科技大学学报(自然科学版)ꎬ２０１５ꎬ４７(１):７１￣７６. [１０]㊀苑立冬ꎬ牛荻涛ꎬ姜㊀磊ꎬ等.硫酸盐侵蚀与冻融循环共同作用下混凝土损伤研究[Ｊ].硅酸盐通报ꎬ２０１３ꎬ３２(６):１１７１￣１１７６.[１１]㊀乔宏霞ꎬ郭向柯ꎬ朱彬荣.三参数Ｗｅｉｂｕｌｌ分布的多因素作用下混凝土加速寿命试验[Ｊ].材料导报ꎬ２０１９ꎬ３３(４):７４￣７８.[１２]㊀李金玉.冻融环境下混凝土结构耐久性设计与施工指南[Ａ].中国硅酸盐学会２００３年学术年会水泥基材料论文集(下册)[Ｃ]ꎬ２００３. [１３]㊀殷英政ꎬ李志国.我国代表城市混凝土冻融循环次数探讨[Ｊ].低温建筑技术ꎬ２０１５ꎬ３７(１１):１２￣１５.[１４]㊀谢佳琳.基于模糊可拓层次分析法的盐冻作用下混凝土材料耐久性评价[Ｄ].郑州:华北水利水电大学ꎬ２０１８.。

工程结构目标可靠指标确定方法综述

工程结构目标可靠指标确定方法综述摘要：本文首先综合分析了国内外工程结构目标可靠指标的确定方法，然后指出了校准法、费用效益法、事故类比法、性能退化法的特点以及适用范围。

最后，结合随机过程相关内容，对确定目标可靠指标的研究方向进行了分析展望。

基于随机过程模拟结构性能退化，并结合校准法的相关内容，有望发展出精度高且普遍适用的目标可靠指标计算方法。

关键词：目标可靠指标；工程结构；随机变量；计算方法引言目标可靠指标是一个国家或地区在进行结构设计时，预期能够接受的结构最低可靠指标，是结构可靠性设计的重要依据。

目标可靠指标的确定与工程造价、构件维护与使用费用、社会可接受风险标准、人民的生命财产安全等因素有关。

因此，结构目标可靠指标的确定，是一项必须综合考虑国家科技、经济、社会政策的问题，决不能单纯地从安全性或经济效益等单个角度考虑。

目前，国内外已广泛研究了结构目标可靠指标的确定方法，主要有校准法、费用效益法、事故类比法及性能退化法。

本文后续对这三种方法进行详细的阐述。

1.校准法关于校准法，目前国内所有关于建筑物目标可靠指标的确定基本都可以利用校准法。

虽然此方法受制于目前的技术水平，但在使用中仍存在以下优势：1、保证了规范在安全水平上的连续性；2、明确了结构构件失效概率计算值与构件实际损坏概率的差异。

本方法主要通过对现有设计规范安全水平进行校正，利用反演方法，找出结构隐含的可靠度，以此确定结构的目标可靠指标。

现阶段，该方法受到学者的广泛运用，如：李铁夫[1]基于校准法，校准了不同长度下铁路钢桁梁的目标可靠指标，研究结果表明钢桁梁的目标可靠指标值建议取为5.0；钢板梁目标可靠指标值，抗弯情况下建议取5.0，抗剪情况下可取4.3。

冷福增[2]等对荷载效应进行基本组合，计算得到了不同设计基准期内汽车荷载的统计参数。

然后运用校准法对不同设计基准期下的桥梁结构进行可靠度分析，得到了不同构件在不同设计基准期内的目标可靠指标值。

发射药使用寿命预估技术

火工品INITIATORS&PYROTECHNICS文章编号：1003-1480（2021）01-0035-04发射药使用寿命预估技术闫光虎，赵煜华，肖霞，张玉成，严文荣，刘毅（西安近代化学研究所，陕西西安，710065）摘要：为更简单而准确地对发射药的使用寿命进行预估，以经典内弹道理论为基础，建立了基于发射药动静态燃速相关性的内弹道性能预估模型；对不同老化年限的发射药进行了弹道性能的预估，并进行了验证试验。

结果表明：在相同的装药量下，建立的预估模型可以对老化样品的内弹道性能做出准确的预估，压力误差小于2%，速度误差小于1%，可以为库存发射药的使用寿命检测提供一种新的手段。

关键词：发射药；动态燃速；内弹道；使用寿命中图分类号：TQ562文献标识码：A DOI：10.3969/j.issn.1003-1480.2021.01.010Prediction Technique of Gun Propellant Service LifeYAN Guang-hu，ZHAO Yu-hua，XIAO Xia，ZHANG Yu-cheng，YAN Wen-rong，LIU Yi(Xi’an Modern Chemistry Research Institute,Xi’an,710065)Abstract：In order to predict propellant service life simply and exactly,interior ballistic performance prediction model was built,based on the static and dynamic burning rate relativity of propellant,and the classic interior ballistic theoretic.Ballistic performance evaluation and validate experiments were also carried out for different aged gun propellant.The results show that the estimate model could make exactly estimate for interior ballistic performance of aged samples under the same charge mass.The pressure deviation is less than2%and the velocity deviation less than1%.The technique could provide a new measure method for service life of storaged propellant.Key words：Propellant；Dynamic burning rate；Interior ballistic；Service life发射药在贮存过程中，由于物理和化学因素的作用会导致老化，随着贮存时间不断延长，安定剂含量降低，发射药会加速分解，甚至出现自燃或自爆的可能，给弹药系统的贮存带来重大的安全隐患。

外文翻译混凝土中钢侵蚀的有关问题

外文原文II:Some questions on the corrosion of steel in concrete.PartⅡ: Corrosion mechanism and monitoring, servicelife prediction and protection methods. Gonzdlez , S. Felifd, P. Rodffguez , W. Lfpez , E. Ramlrez , C. Alonso , C.AndradeABSTRACTThis second part addresses some important issues that remain controversial despite the vast amounts of work devoted to investigating corrosion in concrete-embedded steel. Specifically,these refer to: 1) the relative significance of galvanic macrocouples and corrosion microcells in reinforced concrete structures; 2) the mechanism by which reinforcements corrode in an active state; 3) the best protective methods for preventing or stopping reinforcement corrosion; 4) the possibility of a reliable prediction of the service life of a reinforced concrete structure ; and 5) the best corrosion measurement and control methods. The responses provided are supported by experimental results, most of which were obtained by the authors themselves.1. INTRODUCTIONConcrete-embedded steel is known to remain in apassive state under normal conditions as a result of the highly alkaline pH of concrete.The passivity of reinforcements ensures unlimited durability of reinforced concrete (1KC) structures. However, there are some exceptional conditions that disrupt steel passivity and cause reinforcements to be corroded in an active state. This has raised controversial interpretations, some of which were discussed in Part I of this series [1]. This Part II analyses though far from exhaustively, other - to the authors minds at least - equally interesting issues on which no general consensus has been reached.2. MATERIALS AND METHODSThe reader is referred to Part I for a detailed description of the materials and methods used in this work. Most of the experimental results discussed herein were obtained with the same types of specimens and couples were determined on speciallydesigned specimens, such as those shown in Figs. 1 and conditions were simulated by using a beam that was 160cm long and 7 x 10 cm in cross-section. The beam was made from 350 kg cement/m 3, half of whichcontained no additives, while the other half included 3% CaC12 by cement weight [2], (Fig. 1). In order to study the effect of the Sanod/Scathoa ratio on galvanic macrocouples, they were modelled by surrounding a small carbon steel anode with a stainless steel (AISI 304) cathode and vice versa(Fig. 2). In this way, the ratio's consistensy was assured. In addition, thepotential and icorr of stainless steal and those of the passive structures were very similar.Fig. 1 - Beam used to measure icoTr and Ecorr in Fig. 2 - Scheme of galvanic macrocouples embeddedconcrete with and without chlorides and to in chloride- containing mortar used to study theillustrate the significance of passive steel/active effect of the Sanod/Scathod ratio and their relativesteel macrocouples.significance to corrosion microcells.3. RESULTS AND DISCUSSIONWhat is the relative significance of galvanic macrocouples and corrosionmicrocells in RC structuresAccording to several authors [3, 5], the polarization resistance method provides an effective means for estimating the corrosion rate of steel in P,C ; the method is quite rapid, convenient, non-destructive, quantitative and reasonably precise. However, it is uncertain whether it may give rise to serious errors with highly-polarized electrodes by the effect of passive/active area galvanicmacrocouples in the reinforcements [6].Based on the authors' own experience with the behaviour of galvanic macrocouples in PC, the contribution of these macrocouples to overall corrosion is very modest rehtive to that of the corrosion microcells formed in the active areas of reinforcements in the presence of sufficient oxygen and moisture [2, 7, 8]. Thus, it has been experimentally checked that:(a) Galvanic macrocouples have a slight polarizing effect on anodic areas in wet concrete, whose potential is thereby influenced in only a few millivolts.(b) On the other hand, macrocouples have a strong polarizing effect on passive areas despite the low galvanic currents involved relative to the overall corrosion current.(c) As a result, galvanic currents can result in grossly underestimated icorr values for the active areas since they are often smaller than 10% of the ico= values estimated from polarization resistance measurements. (d) The corrosive effect ofcoplanar macrocouples on RC structures only proves dangerous within a small distance from the boundary of active and passive areas.Fig. 3 compares the estimated icorr and ig values, in mortar containing 3 o~ A CaC12, per anode surface unit for a number of anode/cathode surface ratios for AISI 304 stainless steel/carbon steel macrocouples in support of the above conclusions [9].By what mechanism do reinforcements corrode in an active state When the passive state is lost, the rate of reinforcement corrosion in inversely proportional to the resistivity of concrete over a wide resistivity range [10]. BecauseFig. 3 - Relative significance of corrosion microcells Fig. 4 - Trends in ico. and Ecorr for(icorr) and galvanic macrocouples (i.) in corrosion specimens exposed to an oxygen-freeof steel embedded in mortar containing no chloride. environment.Both currents were calculated relative to Sanod(carbon steel in the macrocouples of Fig. 2).the environment's relative humidity and ionic additives of concrete determine concrete resistivity, these factors, together with oxygen availability at reinforcement surfaces,control the corrosion rate [11].The electric resistivity of water-saturated concrete structures is relatively very low, and the corrosion rate is believed to be essentially controlled by the diffusion of dissolved oxygen through the concrete cover up to reinforcements. This is consistent with the widespread beliefthat the sole possible cathodic reaction in neutral and alkaline solutions is oxygen reduction.The significance ascribed to the role of oxygen justifies the efforts to determine its diffusion coefficient in concrete[12, 13]. The variety of methods and experimental conditions used for this purpose have led to a wide range of diffusivity values (from 10 -12 to 10 -8 m2/s) for oxygen incement paste [14].Since the diffusion coefficient of oxygen in aqueous solutions (1)O2 = 10 -5 cm2/s-1), is saturation concentration (CO2 = x 10 -7 mol/cm 3) and the approximate thickness of diffusion layers in stagnant solutions (8 = 0.01 cm) are wellknown, the limiting diffusion current can be calculated as :ilo2 = - z FD02C02/r = 8 x 10 -4 A/cm 2 (80 pA/cm 2)where z is the number of equivalents per mole (4) and F the Faraday (96,500 A.s/eq).For 1-cm thick mortar covers of average porosity 15%(see Fig. 1 in Part I) [1] and a diffusioja layer thickness of the same order as the cover thickness, 11o2 = laA/cm 2, which is quite consistent with the icorr values estimated under pore saturation conditions at the end of the curingprocess, both for mortars containing no chloride ions and for thoseincluding 2, 4 or 6% C1- [16].On the other hand, icorr values of ca. 10 liA/cm 2 (see Fig. 9 in Part I) [4] have been obtained by several authors for mortars with chlorides or carbonated mortars which are incompatible with the rates allowed by the limiting diffusion current of oxygen. Therefore, in some circumstances, alternative cathodic processes allowing for faster kinetics must therefore be involved. In recent work, the concurrence of crevices, chloride ions and dissolved oxygen at the steel/concrete interface was claimed to provide the thermodynamic conditions required for protons to be reduced and the alternative mechanism to occur [11, 17].There are a number of facts that refute oxygen reduction as being the sole corrosion rate-determining step, namely:- Under some circumstances, once corrosion in an activestate has started, it develops at the same rate even though oxygen is being removed from the medium (Fig. 4) [11].- As saturation of concrete pores decrease, concrete resistivity controls ico~r over a wide resistivity range ; therefore, the corrosion rate seems to decrease in proportion to the ease with which oxygen penetrates into the structure(Fig. 5)[10].On the other hand, there are several arguments in favour of proton reduction in Ca(OH)2-saturated solutions or cement mortars [11] :- The pH decreases from to ca. 5 within crevices at the steel/electrolyteinterface upon exposure of the steel to a Ca(OH)2-saturated solution with C1- additions and wellaerated. If sufficient oxygen is available, the pH can drop as low as 1-2.- The emergence of acid exudates ofpH 1-5 from cracks and macropores in chloride-containing mortar specimens under wet atmospheres at high corrosion rates (5-10 pA/cm2).- The formation of gas bubbles over iron hydroxide membrane-coated pits when the steal is polarized anodically in a Ca(OH)2-saturated, chloride-contaminated solution at potentials below those required for oxygen release. Everything points to pits with a low enough pH for the anodic current applied to overlap with a corrosion process involving proton reduction as a cathodic half-reaction.When concrete-embedded steel is corroded in an active state, its corrosion kinetics rise exponentially with increasing pore saturation (Fig.6), similarly to atmospheric corrosion in bare steel as the environment's relative humidity increases [18]. At some points in the reinfor- cements, a catalytic cycle may take place, ., those put forward by Schikorr for atmospheric corrosion of steel [19], with chloride ion rather than SO2-as the catalyst (Fig. 6).Fig. 5 - Relationship between mortar resistivity Fig. 6 - Influence of the degree of pore saturationand the corrosion rate of reinforcements. on the corrosion rate of reinforcements.中文翻译II:混凝土中钢侵蚀的有关问题Ⅱ：侵蚀机理和监督、利用年限的预测和爱惜方式. Gonzdlez , S. Felifd, P. Rodffguez , W. Lfpez , E. Ramlrez , C. Alonso , C.Andrade摘要:第二部份论述几个仍然存在争议的重要问题，尽管已经在混凝土中钢侵蚀的调查研究投入了大量的工作。

收缩率垂直方向英文

收缩率垂直方向英文Shrinkage Rate in the Vertical DirectionShrinkage refers to the reduction in size or volume of a material or object. When it comes to the vertical direction, shrinkage can occur in various contexts, such as in construction, manufacturing, or even in biological processes. In this discussion, we will explore the concept of shrinkage rate in the vertical direction and its impact in different fields.In construction, shrinkage is a crucial consideration, especially in concrete structures. Concrete shrinkage can occur due to several factors, including the evaporation of water, chemical reactions, or load-induced stress. The shrinkage rate in the vertical direction is an important parameter that determines the dimensional stability of concrete structures. It is typically expressed as a percentage or a fraction of the original size.Understanding the shrinkage rate is crucial for several reasons. Firstly, it helps in estimating the potential shrinkage and planning for compensatory measures. For instance, in concrete construction, engineers may use reinforcement or control joints to accommodate the expected shrinkage and minimize cracking. Additionally, the shrinkage rate also impacts the durability and service life of the structure. Excessive shrinkage can lead to structural integrity issues and compromise the overall performance.In the manufacturing industry, shrinkage rate plays a significant role in the production of various products. For example, when molding plastic or metal parts, shrinkage in the vertical directionmust be accounted for in the design and fabrication process. Manufacturers use shrinkage rate data to adjust the dimensions of the mold or tooling to ensure the final product meets the desired specifications. Failure to consider shrinkage properly can result in products that do not fit together or have dimensional inaccuracies.The concept of shrinkage rate extends beyond construction and manufacturing and has implications in other fields as well. In biology, for instance, shrinkage rate is a crucial parameter in understanding biological processes such as cell shrinkage or tissue contraction. It is often studied in the context of medical research or pathology, where changes in cell volume and tissue shrinking are essential indicators of disease progression, dehydration, or injury.Accurate measurement and prediction of shrinkage rate in the vertical direction often require specialized techniques and instruments. These may include strain gauges, displacement transducers, or image analysis systems, depending on the application and level of precision required. Researchers and engineers utilize such tools to obtain precise data and develop models to better understand and predict shrinkage behavior.In conclusion, the shrinkage rate in the vertical direction is a crucial parameter that impacts various fields ranging from construction to manufacturing and biology. It influences the dimensional stability of concrete structures, the accuracy of manufactured products, or the understanding of biological processes. Accurate measurement and prediction of shrinkage rates are critical for designing and producing reliable and durablestructures or products and advancing our understanding in scientific research.。

马拉开波桥(Maracaibo bridge)

Interpretation of chloride profiles from concrete exposed to tropicalmarine environmentsP.Castro a,*,O.T.De Rincon b,E.J.Pazini ca Centro de InvestigacioÂn y de Estudios Avanzados del IPN,Unidad MeÂrida,Km.6Antiqua Carretera a Progreso,C.P.97320,MeÂrida,YucataÂn,Mexicob Centro de Estudios de la CorrosioÂn de la Universidad del Zulia,P.O.10482,Maracaibo,Venezuelac Universidade Federal de GoiaÂs,Escola de Engenharia Civil,PracÎa UniversitaÂria,s/n,Setor UniversitaÂrio,GoiaÃnia,GO,BrazilReceived19November1999;accepted20December2000AbstractThe chlorides from the sea and marine breeze are the main source for corrosion in marine environments,and their profiles in concrete are commonly modeled and used for prediction purposes.However,no reliable results may be obtained if the action of environmental agents, such as the relative humidity(RH),temperature,winds,rains and drying periods,on such profiles are not well known through several periods of time.Although these limitations are recognized in several works,there are very few field and isolated data in the literature to explain and support,according to different exposure conditions and periods of time,the shape and meaning of the chloride profiles.Any prediction model could acquire more reliability only after knowing and incorporating such information.This work presents concentration profiles,which were obtained from concretes exposed to different microclimates,and discusses their behavior and meaning according to the environmental parameters,concrete quality and several periods of time.D2001Elsevier Science Ltd.All rights reserved.Keywords:Chloride;Concentration profile;Concrete;Corrosion;Tropical marine environment1.IntroductionThe chlorides coming from the marine breeze are the main source of aggressivity for reinforced concrete and the main cause for its deterioration.They can penetrate the concrete in different forms that depend,fundamentally,on the concrete quality conditions,as well as on the surround-ing atmosphere.The chlorides can penetrate the concrete through capil-lary suction when it is dry,by convection when a fluid (water)transports them[1],or also by a concentration gradient(diffusion)when the material is dampened.A combination of all of these mechanisms is present in the most of the cases due to the environment influence.The environment,which surrounds the concrete in tro-pical marine climates,can have strong variations of humid-ity(Fig.1),temperature(Fig.2),winds direction(Fig.3) and chlorides that could be deposited on the structures.Therefore,a monitoring of these variables from the atmo-sphere allows understanding of the chloride penetration mechanisms,and can help to make decisions in order to protect the concrete from deterioration.In general,the chloride concentration profiles obtained under different climates are used in mathematical models for obtaining diffusion coefficients and/or predicting remaining service life and corrosion thresholds[2±4].However,any effort to model the behavior of the chloride profile must be accompanied by an analysis and inclusion of the environ-mental parameters that originated it.Otherwise,the model would have a limited validity.Several authors[5±8]have obtained chloride profiles and related them with the environment that surrounds the concrete.The form of the profile is attributed in some of them to the environmental conditions,but more data are needed,in some cases,to justify that.Other important works [9]start to show multimechanistic chloride transport when modeling,but they are still limited and a lack of a significant quantity of field data avoid their perfectioning.The aim of this work is to present concentration profiles, which were obtained from concretes exposed to different*Corresponding author.Tel.:+52-99-81-29-05;fax:+52-99-81-29-17.E-mail address:pcastro@mda.cinvestav.mx(P.Castro).Cement and Concrete Research31(2001)529±5370008-8846/01/$±see front matter D2001Elsevier Science Ltd.All rights reserved.PII:S0008-8846(01)00453-7microclimates,and discuss their behavior and meaning according to the environmental parameters,concrete quality and several periods of time.2.ExperimentalThe chloride profiles,which will be discussed in this work,come from ongoing investigations about cylindricalprobes exposed to the marine environment of YucataÂn in MeÂxico,a bridge above the Maracaibo Lake in Venezuela and buildings in front of the beach of Recife in Brazil.The concrete cylinders had 7.5 0.3cm diameter Â15cm length with times of curing (tc)of 1,3and 7days,as well as water±cement (W/C)ratios of 0.76,0.70,0.53,0.50and 0.46.They were prepared using Portland cement (ASTM Type I)and crushing aggregates [10,11].Each W/C ratio and tc combination was represented by two cylin-ders,and the average of their measurements is represented in all the following figures and tables.The concrete cylin-ders have been exposed for about 4years to the tropicalmarine climate of YucataÂn at distances of 50,100and 780m from the seaside.The data from the bridge above the Maracaibo Lake correspond to cores of the same dimensions (300±400kg/m 3,W/C =0.40)that were taken at different locations after 33years of construction.The bridge is supported by cables in the longest spans and is 8678m long.The data from the beach of Recife correspond to cores of the same dimensions that were taken at different locations in several buildings of the coast,which were 10years old by then.The average compressive strength of the buildings was between 15and 25MPa,the annual range of temperature is between 25°C and 40°C,and the annual RH is around 75%.The only rain period in Recife is from March to July.The chloride amount was determined with the ion selec-tive electrode for the specimens exposed in Mexico and the Mohr method for those of the Venezuelan bridge.TheFig.1.Yearly average RH variation in (a)the Port of Progreso,YucataÂn,Me Âxico and (b)the Maracaibo Lake.Maximum and minimum values correspond to the monthly averages of the maximum and minimum RH.P .Castro et al./Cement and Concrete Research 31(2001)529±537530chloride amount was determined through the method of ASTM C1152in the case of Recife's samples.3.Results and discussion 3.1.Two-zone profileIn general and depending on the concrete quality,it is accepted that a continuous dampened zone exists close to the concrete nucleus and a wet and dry one at the surface [12].However,the consulted literature does not demonstrate under which conditions such a hypothesis is valid.Experimental trials in tropical climates have also shown no existence of these two zones in the absence of chlorides,where the denser concrete wets and dries completely during the day [13,14].However,things are different in tropical marine climates.Fig.4corresponds to cylinders exposed at 100m from the seaside in Mexico,and shows chloride profiles with an intermediate maximum,which could be the interface between the two mentioned zones.The two-zone profile could be due,among others,to some of the following reasons:the skin effect of concrete [15],the interface between carbonated and noncarbonated layers,chloride washing by rain [16]or the interface between the zones of dampening and continuous wetting and drying (absorption±desorption)[12].The concrete skin has a different composi-tion than the bulk due to the wall effect during casting or the precipitation of brucite during contact with seawater [17].The skin effect has a limited depth,which coincides most of the times with the interface between mortar and concrete.There are some works [18]that show profiles,which could be attributed to this effect.The maxima observed in this paper are not related with this effect because of the depth at which they take place.On the other hand,carbonation of the specimens was checked [19,20],and the carbonation front did not coincide with the maximum of our profiles as can be observed in Table 1.It is necessary to recognizethatFig.2.Yearly average temperature variation in (a)the Port of Progreso,YucataÂn,Me Âxico and (b)the Maracaibo Lake.Maximum and minimum values correspond to the monthly averages of the maximum and minimum temperature.P .Castro et al./Cement and Concrete Research 31(2001)529±537531carbonation was checked with phenolpthalein instead oftimolpthalein.The two-zone profile of our study is affected by the atmospheric drying and wetting effect,as well as by the chloride washing when raining.The profiles of Fig.4show that the denser the concrete,the widest internal zone confirming that,while denser the concrete,the dry periods will affect less the internal layers in the presence of chlorides.This means that the internal and continuing dampened zone is thicker in the denser concretes [21].The data from Fig.4were taken after an exposure longer than 24months to the tropical marine environment and during the rain period (Fig.5a).This means that the obtained profiles are reflected in the surface concentration,the effect of the rain washing,as well as the changes of RH and temperature from the whole period (Figs.1a and 2a).There were RH ranges between 55%and 95%,as well as temperature ranges from 20°C to 33°C during this long period as illustrated in Figs.1a and 2a,where the average of the maximum and minimum monthly values are repre-sented.These RH and temperature changes promoted per-iods of wetting and drying,which favored the chloride penetration and the formation of the concentration gradientsas shown in Fig.4.This situation was equivalent to that observed in piles from docks exposed to total saturationinFig.3.Yearly winds variation in (a)the Port of Progreso,YucataÂn,Me Âxico and (b)the MaracaiboLake.Fig.4.Concentration profiles identifying the two zones inside concrete for different W/C ratios.Data from specimens exposed for 24months at 100mfrom the seaside and with 7days of curing in Progreso,YucataÂn,Me Âxico.P .Castro et al./Cement and Concrete Research 31(2001)529±537532the immersion zone and wetting and drying cycles in the tidal zone [22].The existence of two zones was evident not only through the change in the chloride concentration profile,but on the concrete ohmic drop (directly related to resistivity)that showed a higher value close to the surface than close to the rebar as observed in Table 2.The above discussion makes the observer believe that the concrete internal layers do remain humid in the pre-sence of chlorides due to their hygroscopic character and despite the strong dry periods.Therefore,under these circumstances,the interface between the two zones could be established by a change in the direction of the chloride concentration gradient.Table 1Carbonation depth,distance from the concrete surface to the highest value of the chloride profile and highest value of the profile of concrete cylindersexposed to the tropical marine environment of Progreso,YucataÂn,Me Âxico for 24months,7days of curing and at three distances from the seaside Distance to the W/C ratio sea (m)0.760.700.530.500.4650A 11.509.50 5.50 3.50 2.50B 22.5017.5017.5012.5012.50C 3.82 3.32 1.78 1.70 1.20100A 17.5014.0010.009.50 3.00B 22.5017.5012.507.50 3.50C 1.050.750.980.820.52780A 20.0013.00 6.00 6.50 3.00B 22.5017.507.5012.5017.50C0.660.610.610.600.42(A)Carbonation depth (mm),(B)distance from the concrete surface to the highest value of the chloride profile (mm),(C)highest value of the chloride profile (percent by weight ofcement).Fig.5.Pluvial precipitation during the tested period in (a)the Port of Progreso,YucataÂn,Me Âxico and (b)the area close to the Maracaibo Bridge.Table 2Ohmic drop of concrete cylinders exposed to the tropical marineenvironment of Progreso,YucataÂn,Me Âxico for 24months,7days of curing and at three distances from the seaside Distance to the W/C ratio sea (m)0.760.700.530.500.4650A 0.70 1.65 3.95 1.75 3.35B 0.60 1.45 2.42 1.60 3.00C 0.070.14 1.100.180.30100A 10.60 3.3049.5019.507.75B 9.90 2.8021.5019.007.60C 0.660.47N.A.0.340.38780A 78.5065.5074.0041.4648.45B 77.0064.5073.5041.0048.00C1.330.820.500.4658.00(A)Ohmic drop of concrete (0±35mm),k V ;(B)ohmic drop of croncrete (0±17mm),k V ;(C)ohmic drop of concrete (17±35mm),k V .N.A.=not available.P .Castro et al./Cement and Concrete Research 31(2001)529±537533On the other hand,when a concrete is of good quality and positioned in environments with high chloride contamina-tion,it is more probable that only one zone exists,which remains always dampened,even when exposed in the tidal zone and despite the temperature gradients.Fig.6shows a chloride profile of the bridge over the Maracaibo Lake that exemplifies this case and,therefore,exhibits an apparent pure diffusion behavior.This behavior is understood due to the fluctuations of RH,temperature and winds observed in Figs.1b,2b and 3b.These fluctuations are around an average that allows the continuous dampening and chloride avail-ability as to maintain the form of the concentration profile.In Fig.4,the W/C ratio of 0.46shows a similar situation,but it is not exposed in a tidal zone so it is susceptible to the rain washing as observed in the surface concentration.The case of Recife is similar to that of Maracaibo,and some buildings present a similar profile as deduced from Table 3.This was due mainly to the concrete quality.The above information confirms that the form of the chloride concentration profile depends on the environmental conditions,and that it can change a lot depending also upon the concrete quality.Therefore,when doing mathematical modeling,it is necessary not only to take into account a large universe of profiles during several years in order to validate the predictions but also knowing the environmental parameters that promoted their form.The chloride concen-tration profile did not show significant influence of carbo-nation or the skin effect under our experimental trials.3.2.Effect of the microclimates on the form of the concentration profileOn the other hand,a microclimate can take place inside the concrete when it is exposed to different aggressives [7]or when buildings of the same type are positioned in the same piece of land but under different environments.Fig.7shows a 24-month-old concrete,which was exposed to the marine environment of Progreso.The form of the concentration profiles is similar even at different distances from the seaside (50,100and 780m).The same situation took place for all the other kinds of concretes exposed to the same environ-ment,and it demonstrates that under the conditions of this work the mechanism of chloride penetration does not change with the distance to the sea.However,the data in Table 4show that for 24months of exposure the surface concentra-tion of specimens cured for 7days having different W/C ratios,in general,increased with the sea proximity for any kind of concrete.This means that,despite all the rain periods,the surface concentration shows a well-defined trend with the distance to the sea.It also shows that,at short distances from the sea,the differences in the environment reflect on the chloride contamination grade.The behavior of the surface concentration regarding the W/C ratio will not be discussed here.On the other hand,Table 5shows in general a higher chloride concentration in the nucleus with the sea proximity,higher W/C ratio at 24months of exposure and 7days of curing.The analysis of the data in different micro-climates,as described in this paper,could allow the designofFig.6.Chloride concentration profile of the north face of the brace beam ``A''in the Maracaibo Bridge.Table 3Chloride values at different depths of a concrete building in Recife,Brazil Sample Sample depth (mm)%total chloride A 10 1.27B 200.79C300.41Fig.7.Chloride concentration profiles of concretes with W/C ratio of 0.53and 3days of curing exposed during 24months at 50,100and 780m from the seaside.P .Castro et al./Cement and Concrete Research 31(2001)529±537534structural elements not only based on the concrete quality but on the distance to the sea.On the other hand,the chloride penetration also changes with the height,as observed in the Maracaibo Bridge.Fig.8 illustrates this showing four profiles taken at different depths but all at the same time.As in the case of Progreso, the microclimates in the Maracaibo Lake are playing animportant role in the chloride accumulation,so these data could allow the design of structural elements based on the height from the sea.Other recommendations regarding structural design in microclimates but in cold weather and applied to bridges have been done also by Sandberg[22], who found a change in the form of penetration with the height.In this case,the combination of the atmospheric parameters allowed a two-zone profile.3.3.Effect of the time and the climatic conditions in the form of the concentration profileDuring a structure service life,the chloride can penetrate the concrete in different manners and the profile changes its form continuously.Each case is different depending on the predominant climatic conditions.Fig.9shows the changes in the form of the chloride concentration profile with time.It exemplified the case of a concrete with W/C ratio of0.50 and1day of curing noting that a similar situation happened in the other concretes with low W/C ratios.The chloride profile was flat before the exposure to the environment as expected.The amount of chloride measured was due to some contamination in the materials of this region[11]. The profile showed a diffusional form after about7 months of exposure due to,among other reasons,the chloride ingress that was constant,the fluctuation of RH between67%and95%(Fig.1a)and the lack of rain as observed in Fig.5a.The same behavior was observed in the cores taken from the Maracaibo Bridge(Fig.8),where the element was not exposed to the rain and the environmental conditions fluctuated less than those in Progreso(Figs.1b, 2b and3b).The profile obtained at about13months of exposure in Progreso showed the influence of the rain period of that year as observed in Fig.5a.The surface concentration decreased regarding that of the interior as a consequence of therains,Fig.9.Effect of aging in the form of the concentration profile for a concrete with W/C ratio of0.50and7days of curing and exposed during0,7,13,24 and45months at50m from the seaside in Progreso,YucataÂn,MeÂxico.Table4Chloride concentration(percent by weight of cement)on the concrete surface from cylinders exposed to the tropical marine environment of Progreso,YucataÂn,MeÂxico for24months,7days of curing and at three distances from the seasideW/C Surface chloride concentration,percent by weight of cement(7days of curing)ratio50m100m780m 0.460.410.460.430.500.730.410.16 0.530.770.330.27 0.70 1.390.320.24 0.76 1.430.310.21Fig.8.Chloride concentration profiles at different heights and depths of ashaft from the Maracaibo Bridge.Table5Chloride concentration(percent by weight of cement)on the concretenucleus,where the reinforcement is usually placed,from cylinders exposedto the tropical marine environment for24months,7days of curing and atthree distances from the seasideW/C Chloride concentration in the concrete nucleus,percent by weight of cement(3.2cm depth,7days of curing)ratio50m100m780m0.460.350.230.320.50 1.370.400.220.53 1.680.440.330.70 3.070.570.460.76 4.130.450.71P.Castro et al./Cement and Concrete Research31(2001)529±537535the RH variations ranges between67%and95%,and the temperature is between20°C and31°C(Figs.1a and5a).In this period,the two-zone profile started to appear clearly. The same form of profile appeared at24months of exposure,but with an increase in the internal concentration. The interface between the two zones had a displacement, where the dampened zone was thinner than at13months of exposure.This may be due to the higher temperature and RH gradients observed in this period(Figs.1a and2a). After45months of exposure,several rain periods and a greater chloride supply from the atmosphere affected the concrete.The profile was then reversed,possibly due to the chloride saturation in the nucleus and the continuous rain periods that caused,in this stage,a gradient to the external part.Because of the above observations,the form of the chloride profiles at different times and types of exposure in the same place makes it necessary to take into account that the concentration profile of a structural element can depend strongly from the environment and not to be reproduced with time.This situation suggests the use of mathematical models to make predictions only after having several field profiles,as well as the environmental para-meters to explain the observed behavior[23,24].Otherwise, any assumption will be valid only for the time scale at which it was obtained.4.Conclusions(1)The environmental conditions of the tropical marine climate in cylindrical concrete specimens promoted the formation of two zones:one internal that is always dam-pened and one external that is always wetting and drying. The thickness of these zones is a function of the concrete quality(W/C ratio)and the media aggressiveness.The two-zone profile does not exist in the absence of chlorides (concrete wets and dries completely during the day),or when the chloride concentration is high with stable envir-onmental conditions and concrete is of very good quality (like in the Maracaibo Lake or Recife Beach).(2)Under the conditions of this study,the mechanism of chloride penetration does not change with the microcli-mates.However,the chloride concentration in the concrete nucleus(where the rebars use to be)decreases when the distance to the sea and the W/C ratio increases.Several recommendations to the designers can be deduced from this study in order to take into account not only the concrete quality but also the distance and the height regarding the seashore in the structural design.(3)The form of the concentration profile changes with time as a result of the environmental agents interaction so that the mathematical modeling must take into account quite a few profiles with time in order to obtain reliable results and predictions.Otherwise,the obtained results will be valid only for the scale of time at which were obtained.AcknowledgmentsThe authors recognize the partial support of CONACyT (2186PA),CINVESTA V-MeÂrida,CONICYT and CNpQ.A special acknowledgement to M.BalancaÂn for her assistance in obtaining the profiles and the atmospheric parameters.The opinions and findings expressed here are those of the authors and not necessarily those of the supporting organizations.References[1]L.O.Nillson,L.Tang,Transport mechanisms in porous materials,in:H.Jennings,J.Kropp,K.Scrivener(Eds.),The Modelling of Microstructure and Its Potential for Studying Transport Properties and Durability,Kluwer Academic Publishing,Netherlands,1996, pp.289±311.[2]O.Troconis de RincoÂn,M.FernaÂndez de Romero,D.Contreras,O.MoroÂn,J.Ludovic,J.Bravo,Electrochemical diagnosis and rehabilitation of pilings of a marine bridge,Mater.Perform.35(8)(1996)14±21.[3]O.Troconis de RincoÂn,R.FernaÂndez,M.FernaÂndez,D.Contreras,C.Vezga,O.MoroÂn,M.SaÂnchez,PGRU Bridge.Rehabilitationbased on an electrochemical diagnosis,in:W.F.Silva-Araya,O.T.de RincoÂn,L.Pumarada(Eds.),Repair and Rehabilitation of Rein-forced Concrete Structures.The State of the Art,American Society of Civil Engineers,USA,1998,pp.60±81.[4]M.Masi,D.Colella,G.Radailii,L.Bertolini,Simulation of chloridepenetration in cement-based materials,Cem.Concr.Res.27(10) (1997)1591±1602.[5]Ch.Jaegermann,Effect of water±cement ratio and curing on chloridepenetration into concrete exposed to Mediterranean sea climate,ACI Mater.J.87(4)(1990)333±339.[6]V.E.Murray,G.C.Frantz,Chloride testing of27-year-old prestressedconcrete bridge beams,PCI J.37(5)(1992)68±79.[7]L.Tang,P.Sandberg,Chloride penetration into concrete exposedunder different conditions,in:C.SjoÈstroÈm(Ed.),Durability of Build-ing Materials and Components7,vol.1,E&FN Spon,London,1996, pp.453±461.[8]S.K.Roy,K.B.Poh,D.O.Northwood,Studies on durability of con-crete in Singapore:chloride ingress and leaching,in:C.SjoÈstroÈm (Ed.),Durability of Building Materials and Components7,vol.2, E&FN Spon,London,1996,pp.1001±1009.[9]A.Boddy,E.Bentz,M.D.A.Thomas,R.D.Hooton,An overview andsensitivity study of a multimechanistic chloride transport model,Cem.Concr.Res.29(6)(1999)827±837.[10]P.Castro,L.Maldonado,Initial efforts to evaluate the corrosionproblems in the infrastructure of the Mexican southeast coastal zones, in:V.Chaker(Ed.),Innovative Ideas for Controlling the Decaying Infrastructure,NACE International Book Publications,Houston, 1995,pp.119±136.[11]P.Castro,L.VeÂleva,M.BalancaÂn,Corrosion of reinforced concrete ina tropical marine environment and in accelerated tests,Constr.Build.Mater.11(2)(1997)75±81.[12]A.Neville,Properties of Concrete,Longman Scientific and Technical,1986,pp.433±435,London:UK.[13]P.Castro,L.Veleva,J.GarcõÂa,Distribution of relative humidity andtemperature in concrete exposed to a rural±urban atmosphere,Pro-ceedings of the XII National Congress of the Mexican Society of Electrochemistry,(1997)pp.42±50(in Spanish).[14]P.Castro,L.Veleva,Time of wetness and temperature as tools toevaluate corrosion risk in concrete blocks exposed to a humid tropical environment,in:S.W.Dean,G.HernaÂndez-Duque Delgadillo,J.B.Bushman(Eds.),Marine Corrosion in Tropical Environments,ASTMP.Castro et al./Cement and Concrete Research31(2001)529±537 536STP vol.1399,American Society for Testing and Materials,2000, pp.159±169,West Conshohocken:PA(USA).[15]C.Andrade,J.M.Diez,C.Alonso,Mathematical modeling of a con-crete surface``skin effect''on diffusion in chloride contaminated media,Adv.Cem.Based Mater.6(2)(1997)39±44.[16]Y.Masuda,Durability of construction materials,Proceedings of theRilem Congress,Chapman and Hall,New York,1987,pp.935±942.[17]N.R.Buenfeld,J.B.Newman,C.L.Page,The resistivity of mortarsimmersed in seawater,Cem.Concr.Res.16(4)(1986)511±524. [18]P.Sandberg,L.Tang,A.Andersen,Recurrent studies of chlorideingress in uncracked marine concrete at various exposure times and elevations,Cem.Concr.Res.28(10)(1998)1479±1488.[19]P.Castro,E.I.Moreno,J.GenescaÂ,Carbonation-induced corrosion ofconcrete coastal buildings in the North of YucataÂn,MeÂxico,Paper #565,CORROSION/99,NACE-International Annual Conference, San Antonio,TX,USA,1999.[20]P.Castro,E.I.Moreno,J.GenescaÂ,Effect of microclimate on carbo-nation of concrete coastal buildings in the North of YucataÂn,MeÂxico, Cem.Concr.Res.30(10)(2000)1565±1571.[21]P.Castro,Diffusion and corrosion by chloride ions in reinforced con-crete(in Spanish),PhD thesis,National University Autonomous from MeÂxico(UNAM),1995,170pp.[22]P.Sandberg,Cost-effective service life design of concrete structures insaline environment,in:C.SjoÈstroÈm(Ed.),Durability of Building Ma-terials and Components7,vol.2,E&FN Spon,London,1996,pp.1195±1204.[23]H.CastanÄeda,P.Castro,C.GonzaÂlez,J.GenescaÂ,Chloride diffu-sion model in reinforced concrete structures exposed in the Pe-ninsula of YucataÂn,MeÂxico,Rev.Metall.33(6)(1997)387±392 (in Spanish).[24]R.de Coss,G.Murrieta,P.Castro,Effect of weather cycles on chlor-ide diffusion in porous concrete,in:P.Castro,O.Troconis,C.An-drade(Eds.),Rehabilitation of Corrosion Damaged Infrastructure, NACE International,1998,pp.285±293,Houston:TX(USA).P.Castro et al./Cement and Concrete Research31(2001)529±537537。

冻融环境下超高性能混凝土生命周期预测

冻融环境下超高性能混凝土生命周期预测薛欢;马新伟;祁锦明;刘光旺【摘要】生命周期预测是混凝土结构耐久性研究的一项重要内容,其中冻融损伤机制是混凝土生命周期预测的基本途径之一.本文分析了目前基于冻融机制对于混凝土寿命进行预测的理论和模型,结合具体的试验数据,对超高性能混凝土(UHPC)的生命周期进行了预测分析.结果表明,以冻融机制为主导进行生命周期预测时,即使是在冻融严重的东北地区,使用寿命均在50年以上.%Study on the service life prediction plays an important role in the field of durability of concrete structure,in which freeze-thaw damage mechanism is one of the basic ways to predict the life cycle of concrete.This paper analyzed the theories and the models of the prediction of concrete life based on freeze-thaw bining with the specific test data,the service life of ultra-high performance concrete was predicted and analyzed.Based on the freeze-thaw mechanism,the results show that even in northeast region of China,which is one of the coldest areas in China,the service life prediction is more than 50 years.【期刊名称】《低温建筑技术》【年(卷),期】2018(040)001【总页数】3页(P21-23)【关键词】超高性能混凝土;氯离子渗透;抗冻性【作者】薛欢;马新伟;祁锦明;刘光旺【作者单位】哈尔滨工业大学(威海),山东威海264209;哈尔滨工业大学(威海),山东威海264209;鞍山远达电网工程有限公司,辽宁鞍山114016;鞍山远达电网工程有限公司,辽宁鞍山114016【正文语种】中文【中图分类】TU5280 引言随着混凝土技术的不断进步，为了改善传统混凝土结构的耐久性问题，尤其是提高混凝土在高寒、高盐地区的使用寿命，以超高性能混凝土（UHPC）为代表的新型混凝土得到了普遍重视。

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www.nrc.ca/irc/ircpubs
SERVICE-LIFE PREDICTION OF CONCRETE BRIDGE DECKS USING CASE-BASED REASONING
G. Morcous McGill University, Montreal, Canada Z. Lounis National Research Council of Canada, Ottawa, Canada M. S. Mirza McGill University, Montreal, Canada
Service-life prediction of concrete bridge decks using case-based reasoning
Morcous, G.; Lounis, Z.; Mirza, M.S.
NRCC-45661
A version of this document is publishcument se trouve dans : th Proceedings of 6 International Conference on Short and Medium Span Bridges, Vancouver, July 31-Aug. 2, 2002, v. II, pp. 769-776
Abstract
Bridge management systems (BMSs) are developed to assist decision-makers in optimizing the allocation of their limited budget on maintenance needs of bridge networks. Reliable deterioration models are essential constituents of BMSs that are used to predict the remaining service life of bridge components. The deterioration models incorporated in the recent BMSs have limitations that can be accepted for the analysis at the network level but not at the component level. Moreover, the current mechanistic deterioration models developed for the component level analysis are neither versatile nor adequately extensible to predict the service life of a large number of bridge components, or to incorporate additional deterioration parameters. Therefore, an artificial intelligence approach “Case-Based Reasoning (CBR)” is proposed to develop extensible, reliable, and generic deterioration models for the analysis at the component level. The CBR approach is utilized to predict the time to corrosion initiation of the reinforcing steel in concrete bridge decks. Data obtained from the Dickson Bridge in Montreal are used to generate the cases that populate the case library of the CBR model by applying the Monte Carlo Simulation techniques. Parameters that significantly affect the deterioration rate of concrete decks, such as the concrete cover thickness, apparent diffusion coefficient, and surface chloride concentration, are considered.
1. Introduction
Highway bridges constitute critical and vital links in any roadway network, because even a partial failure of these bridges may lead to serious catastrophes. In North America, highway bridges are characterized by their growing deterioration rate as a result of
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aging, increased traffic volumes and loads, exposure to aggressive environments, and inadequate inspection and maintenance. Maintenance, rehabilitation, and replacement (MR&R) of highway bridges require a tremendous amount of funds that too often exceed the available budgets of the transportation agencies. For example, MR&R costs for bridges in Canada were estimated to be $10 billion1 . Bridge Management Systems (BMSs) have been developed since the mid-1980’s to assist decision-makers in optimizing the allocation of their limited budgets on MR&R needs of bridge networks. The success of a BMS to provide the most cost-effective maintenance strategy is highly dependent on the accuracy and efficiency of the technique used for modeling bridge deterioration2 . That is why the American Association of State Highway and Transportation Officials (AASHTO) has prescribed bridge deterioration models as a minimum requirement for any BMS3 . The main function of bridge deterioration models is to predict the remaining service life of different bridge components. By definition, the service life of a bridge component is the period of time during which the component can fulfil its performance requirements 4 . Service life predictions enable decision makers to evaluate different maintenance alternatives based on their long-term costs and to estimate future funding requirements. Current BMSs employ different techniques for modeling bridge deterioration such as regression models and Markovian models. A detailed evaluation of these models was carried out by Morcous et al.5 This evaluation has revealed that these models ignore some of the essential factors that affect bridge deterioration, assume independent deterioration mechanisms of interacting components, and neglect the effects of the condition history on the future condition. These limitations may be acceptable for the analysis at the network level, where bridges are only prioritized for eligibility for maintenance funds. However, these deterioration models cannot be used effectively for the analysis at the component level (i.e. project level), where detailed information regarding certain deterioration mechanisms in specific bridge components is required. The deterioration of concrete bridge decks is one of the most serious problems of the transportation infrastructure in North America. For the last few decades, the service life of concrete bridge decks was found to be much shorter than that for the other bridge components (i.e. bridge foundation, substructure, and superstructure). Many bridge decks require replacement every 15 to 20 years while other components last for 40 years or more 6 . Although several deterioration mechanisms can occur in concrete bridge decks, such as sulphate attack, alkali-aggregate reaction, freezing-thawing cycles, and creep and shrinkage, corrosion of steel reinforcement is considered to be the most important contributor to their progressive deterioration7 . A recent study carried by the Strategic Highway Research Program (SHRP) has shown that the cost of corrosion damage in the United States was estimated at over $20 billion, and it is increasing at the rate of $500 million per year8 . Therefore, the focus of this study is on predicting the progress of corrosion of reinforcing steel in concrete bridge decks. However, the same