A Bayesian network framework for statistical characterisation of model parameters from accelerated tests: application to chloride ingress into concrete

This paper addresses the topic of long-term characterisation and probabilistic modelling of chloride ingress into reinforced concrete (RC) structures. Since the corrosion initiation stage may cover various decades, normal tests which simulate chloride penetration into concrete in laboratory conditions as the same as natural conditions, will require significant experimental times. Hence, long-term lifetime assessment of RC structures under chloride attack remains still a challenge. In practice, this problem is solved through the use of accelerated tests which speed up the chloride ingress rate and provide valuable mid- and long-term information on the chloride penetration process. Nevertheless, this information cannot be directly used for parameter statistical characterisation if the equivalent times required in natural conditions to reach the same chloride concentrations in the accelerated tests are unknown. Consequently, this study proposes a novel iterative approach based on Bayesian network updating to estimate chloride ingress model parameters from the data obtained under accelerated laboratory conditions. The Bayesian network structure and iterative approach are first tested with numerical evidences. Thereafter, the complete proposed methodology is verified with results from real experimental measurements. The results indicate that combining data from normal and accelerated tests significantly reduces the statistical characterisation error of model parameters.     

硅烷憎水处理混凝土的氯离子电场迁移模型研究

电场下的氯离子迁移试验常被用来评价混凝土中的氯离子扩散系数及抵抗氯离子侵蚀的能力。研究了硅烷憎水处理混凝土的氯离子电场迁移模型。以往的试验发现忽略普通混凝土中孔隙结构分布对离子迁移过程的影响将导致预测值和试验值不吻合。Stanish等人因此提出了考虑氯离子扩散迁移速度离散性的氯离子电场迁移模型,并较好地预测了试验结果。在Stanish模型的基础上,假设氯离子扩散系数而不是氯离子迁移速度符合对数正态分布,从而简化了氯离子电场迁移模型的理论表达式,并更清晰地反映了混凝土微观结构的随机性,计算结果表明两种假设等价。基于上述理论模型,对于饱水的硅烷憎水处理混凝土试件的电通量试验结果进行分析,证明上述理论模型适用于硅烷憎水处理混凝土试件。分析结果亦表明:硅烷憎水处理过的混凝土的电通量试验结果,只反映硅烷憎水性涂层对混凝土表面氯离子浓度的影响,并不反映憎水处理对内部混凝土的扩散系数的影响,硝酸银显色法并不适用于硅烷憎水处理混凝土的电通量试验。     

海洋环境下预应力混凝土桥梁耐久性分析与设计

为了研究海洋环境下氯离子侵蚀引起的混凝土结构耐久性行为,在重点考虑材料、环境、混凝土应力水平以及表层对流区影响的基础上,建立了预应力混凝土氯离子侵入扩散模型;随后,基于预应力混凝土桥梁结构耐久性失效的特点,提出了以预应力筋临界锈蚀作为耐久性极限状态的标志;并在各随机变量统计分析的基础上,采用Monte-Carlo方法研究了不同水胶比、不同保护层厚度时的可靠指标变化情况,得出了给定目标可靠指标下预应力筋的最小保护层厚度。相关研究成果可以为工程设计提供一定参考。     

Modelling of chloride ingress into concrete from a saline environment

A mathematical model previously developed for the simulation of electrochemical chloride removal (ECR) process is utilised to predict the ionic mass transport associated with chloride ingress into concrete or hydrated cement paste from a saline environment by incorporating the convection of pore solution. Compared to the existing models, the present model has advantages in the aspect of numerical calculations as it avoids the difficulty of solving the Poisson equation about electrostatic potential. The significant effects of ionic interaction and the convection of pore solution on the chloride ingress are examined. Simulation results are compared with those obtained from the models using Fick's second law. The comparison shows that the present model is more detailed and accurate. It can be applied to various different cases with unified ionic diffusivities.     

力学荷载对混凝土中氯离子渗透扩散行为影响述评

近海及海洋工程结构的混凝土在服役过程中不仅会经受环境作用(如氯盐侵蚀),还会承受包括风、车辆、波浪荷载甚至地震作用等。荷载作用不仅会改变混凝土中微/细观结构形式,甚至产生新的裂纹,改变氯离子的渗透扩散途径,从而影响混凝土的渗透扩散特性。从低荷载水平和高荷载水平两个方面,分别综述了荷载对混凝土中氯离子渗透及扩散性能影响的试验研究、理论分析及数值分析角度的研究进展,发现已有研究工作特点为：试验研究多,理论研究少;饱和混凝土研究多,非饱和混凝土研究少;宏观模型研究多,微/细观非均质模型研究少。建议今后进行复杂环境、复杂应力状态下的试验研究,建立高/低水平荷载对氯离子扩散行为影响的统一理论及数值模型,实现荷载-环境耦合作用下的多场多尺度分析。     

横向弯曲裂缝对混凝土内氯离子侵蚀作用的影响

分析了横向开裂混凝土内氯离子的侵入机理及其主要影响因素,建立了基于双重孔隙介质模型的修正Fick定律氯离子扩散模型,并对持续加载下的开裂钢筋混凝土梁构件进行了氯盐干湿循环侵蚀试验。试验采用浓度为5%的NaCl溶液,在进行15个干湿循环后,借助快速氯离子含量检测RCT（Rapid Chloride Testing）法,对各裂缝处不同深度的氯离子含量进行了测定。试验结果表明：1）干湿循环侵蚀作用下,开裂混凝土表层0~20 mm范围内氯离子含量出现峰值,故可取表层对流区深度为15~20 mm左右;2）当表面裂缝宽度小于0.3 mm时,等效氯离子扩散系数平稳增大,模型的预测精度较高;当裂缝宽度大于0.3 mm后,等效氯离子扩散系数快速增大,氯离子侵入受对流作用的影响加大;3）受弯开裂混凝土等效氯离子扩散系数的劣化因子与裂缝宽度有直接关系,建议采用二次幂函数或分段函数来进行描述。     

Obtaining progressive chloride profiles in cementitious materials

The ingress of chloride into concrete is controlled by its absorption and diffusion characteristics. The authors have carried out an investigation to monitor the rate of ingress of chlorides during a 48-week cyclic wetting and drying regime using a variety of cement blends, viz. pulverised fuel ash, ground granulated blast furnace slag, metakaolin and microsilica. Chloride profiles were obtained by analysing concrete dust samples extracted from different depths from the surface that was exposed to the chloride exposure regime. The resistivity of the concrete was determined by measuring conductance between pairs of electrodes, in order to assess if this could be used to determine the presence of chlorides. The water absorption (sorptivity) of the concrete was also measured in order to determine if any correlation existed with the chloride ingress. The chloride profiles depended on both the duration of exposure and the type of cementitious material. A linear relationship was established between the depths to a constant chloride concentration of 0.2% by weight of cementitious material and the square root of time, yielding a rate of chloride ingress coefficient. This coefficient was found to depend on the type of cementitious material. The lowest value was obtained for slag concrete and the highest value was found for the OPC concrete. This corresponded well with the results from the resistivity profiles which indicated slag cement was best at resisting chloride penetration and the OPC concrete the worst. The sorptivity decreased significantly after the testing regime, due to pore refinement caused by continued hydration and the binding of chloride ions, leading to a reduction in continuous porosity. No correlation was found between the sorptivity and the rate of chloride ingress, which indicates that the dominant mechanism responsible for the transport of the chloride ions was not absorption.     

氯盐环境条件下预应力混凝土氯离子侵蚀模型研究

文章总结了国内外有关混凝土中氯离子侵蚀模型的研究现状,并对国内外几种典型的扩散方程进行了分析评价;针对氯盐侵蚀的预应力混凝土结构,讨论了氯离子扩散系数的计算。氯离子扩散系数对于预应力混凝土来说是一个重要的因素,因此合理确定氯离子扩散系数,对预测氯离子环境条件下预应力结构的耐久性具有重要意义。对于预应力混凝土,计算氯离子扩散系数除了要考虑混凝土与氯离子之间的结合能力、环境温度、湿度影响外,还要考虑混凝土的应力水平,氯离子有效扩散系数是变化的,且氯离子扩散系数对PC结构耐久性的影响很大。本文对预应力混凝土氯离子侵蚀模型进行了改进,并根据试验结果对改进后模型进行了评价。     

基于FEMLAB的结构混凝土中氯离子侵蚀量预测分析

分析了氯离子侵入混凝土的特性,采用FEMLAB有限元数值分析软件对结构混凝土内氯离子扩散规律进行了数值模拟,通过与试验结果的比较,验证了数值模拟的可行性与合理性;随后,在考虑表面氯离子浓度以及扩散速度随时间变化特性的情况下,研究了结构混凝土中氯离子的扩散行为,并与不考虑两者时变因素情况下的结果进行了比较.结果表明,差异十分明显.     

钢筋阻锈剂对临界氯离子浓度的影响

采用半电池电位和线性极化法监测钢筋在掺有两种常用阻锈剂的模拟孔溶液和硬化砂浆中的锈蚀时间,研究钢筋阻锈剂对临界氯离子浓度的影响。试验结果表明:掺入阻锈剂后,提高了钢筋在砂浆中的临界氯离子浓度,延长了钢筋发生锈蚀的时间。通过阻锈剂在混凝土中的抗氯离子渗透性研究,探讨了阻锈剂的作用机理。     

Influence of fly ash fineness on the chloride penetration of concrete

In this paper, the resistance to chloride penetration of concrete containing fly ash of various finenesses was examined. Three different fly ash finenesses viz., original fly ash, 45% fine portion and 10% fine portion fly ashes were used for the study. Chloride resistance of concretes was evaluated using the measurement of the Coulomb charge as per ASTM C1202 and by determination of chloride ingress after different periods of exposure to 3% NaCl solution in full immersion and partial immersion modes. From the tests, it is found that the resistance to chloride penetration of concrete depends on the fineness of fly ash. The rapid chloride permeability test (ASTM C1202) clearly indicates that the Coulomb charge of concrete at the age of 28 days is significantly reduced with the incorporation of fly ash. The decrease is promoted with an increase in fly ash fineness. The immersion of cut cylinders in the 3% NaCl solution for 3 and 6 months confirm that the resistance of the chloride penetration of concrete increases with an incorporation with fly ash and with an increase in the fly ash fineness.     

Reliability-based design method of suppressing chloride ingress for reinforced concrete buildings located in coastal regions of Taiwan

The main purpose of this work is to propose an estimating procedure that building designers can use to choose methods of suppressing chloride ingress, i.e. concrete-cover thickness, concrete-surface coating and concrete mix (water–cement ratio), for reinforced concrete (RC) buildings with a specified durability performance. At first, the authors build equations for estimating airborne chloride concentrations in coastal regions in Taiwan by regressing measurement data. Then, an analytical model incorporates these data into a deterioration model for chloride-induced corrosion and to estimate corrosion of reinforcing steel bars. This work also presents a novel computational procedure to calculate the risk of corrosion for reinforcing steel bars embedded in concrete, while considering uncertainties in environmental conditions, material properties and model error. Using risk curves of corrosion, building designers can set an allowable durable reliability to determine the minimal required concrete-cover thickness for RC members. Finally, this work adopts coastal regions in Taiwan as an example to determine the minimum required concrete-cover thicknesses. Furthermore, reliability-based methods of suppressing chloride ingress for RC buildings are also suggested for each division zone of Taiwan.     

钢筋混凝土结构的工作寿命设计-针对氯盐污染环境

混凝土耐久性现在正在向定量化发展,同时正在融入钢筋混凝土结构可靠度和工作寿命设计体系。通过将氯盐污染、氯离子渗透和导致钢筋锈蚀,转换为与时间相关的环境荷载与结构劣化进程,目前已形成具有实用价值、可操作的结构工作寿命设计体系。本文介绍了这方面最新进展,包括氯盐污染对结构的破坏作用,氯离子渗透数学模型与主要参数,以结构混凝主耐久性为基础的工作寿命、可靠度概念和理论计算方法,以及设计高耐久性钢筋混凝土结构的技术路线。     

Chloride penetration in concrete under marine atmospheric environment – analysis of the influencing factors

Marine atmospheric exposure conditions provide a severe environment for reinforced concrete structures, mainly due to the occurrence of chloride-induced reinforcement corrosion. This procedure was influenced by many parameters related to the concrete properties and to the environmental condition. In this paper, cubic concrete specimens with 150-mm edge, different types of cementitious material and different strengths, were arranged on a structure, which exposed them to a natural marine atmospheric environment. The purpose was to evaluate quantitatively the influence of different exposure conditions on the durability of concrete, measured in terms of chloride penetration into concrete. Both relative humidity (RH) and temperature were monitored in the experiment. The results indicated that the surface RH and temperature of the concrete were much different from that of the air. The diffusion coefficient and surface chloride concentration were time- and location-dependent, and were influenced by the RH, temperature, and the concrete strength. The results also indicate that error results would be made when using constant diffusion coefficient and surface chloride concentration with the air RH and temperature to predict long-term chloride penetration.     

Application of machine learning technique for predicting and evaluating chloride ingress in concrete

The degradation of concrete structure in the marine environment is often related to chloride-induced corrosion of reinforcement steel. Therefore, the chloride concentration in concrete is a vital parameter for estimating the corrosion level of reinforcement steel. This research aims at predicting the chloride content in concrete using three hybrid models of gradient boosting (GB), artificial neural network (ANN), and random forest (RF) in combination with particle swarm optimization (PSO). The input variables for modeling include exposure condition, water/binder ratio (W/B), cement content, silica fume, time exposure, and depth of measurement. The results indicate that three models performed well with high accuracy of prediction (R²≥ 0.90). Among three hybrid models, the model using GB_PSO achieved the highest prediction accuracy (R² = 0.9551, RMSE = 0.0327, and MAE = 0.0181). Based on the results of sensitivity analysis using SHapley Additive exPlanation (SHAP) and partial dependence plots 1D (PDP-1D), it was found that the exposure condition and depth of measurement were the two most vital variables affecting the prediction of chloride content. When the number of different exposure conditions is larger than two, the exposure significantly impacted the chloride content of concrete because the chloride ion ingress is affected by both chemical and physical processes. This study provides an insight into the evaluation and prediction of the chloride content of concrete in the marine environment.     

Numerical simulation of the probability of corrosion initiation of RC elements made of reinforcing steel with improved corrosion performance

Abstract

Steel reinforcing bars in concrete are protected from corrosion by a thin oxide film that is created on the steel surface in the highly alkaline environment of the concrete. Corrosion process begins once this oxide film is destroyed, for example, by chloride ions penetrating from the element surface into the concrete and to the steel rebar. Critical chloride concentration is highly variable owing to numerous factors such as the type of reinforcing steel used. The TransChlor® software is used to simulate the time history of chloride ion ingress and corrosion initiation into a typical reinforced concrete structural element with four different types of reinforcing steel, namely, carbon steel, ferritic stainless steel (1.4003) with rolling skin, duplex stainless steel (1.4462) and ferritic stainless steel (1.4003) with pickled surface. A climate model is used to simulate two different exposure conditions of the structural element, namely direct and mist exposure, representatives for winter conditions in mountainous and lowland areas. A probabilistic method is applied to consider uncertainty of material properties in the model. The results show that reinforcing steel bars with enhanced corrosion performance significantly improve the durability of reinforced concrete.     

强感潮河口地区水工混凝土的氯离子侵蚀试验

在自然强感潮河口地区进行了水工混凝土氯离子的侵蚀试验,研究了暴露时间和水灰比等因素对混凝土中氯离子浓度分布的影响。结果表明:试验混凝土中的氯离子扩散都存在侵蚀对流区,其厚度为4~6 mm,受水灰比的影响较小;对流区的峰值浓度与暴露时间的相关性不明显,但受水灰比的影响较大。     

环境作用下混凝土结构性能演化与控制研究进展

以环境作用下混凝土结构的性能演化与控制为主线，对相关研究成果进行回顾与分析。结果表明，经过二十余年的研究，对环境介质的侵蚀机理、锈蚀混凝土构件的受力性能、结构的时变可靠度等基本理论问题有了清晰的认识；开发了钢筋锈蚀监测和检测、混凝土结构电化学和自修复技术；明确了结构全寿命设计与维护的基本概念。但要建立完善的结构全寿命设计与维护理论，未来尚应在研究方法上以不确定性的研究为主，在研究内容上聚焦时变性，充分关注环境作用的时空变异性和材料细观层面的非匀质性。     

Improved Bayesian network configurations for probabilistic identification of degradation mechanisms: application to chloride ingress

Probabilistic modelling of deterioration processes is an important task to plan and quantify maintenance operations of structures. Relevant material and environmental model parameters could be determined from inspection data; but in practice, the number of measures required for uncertainty quantification is conditioned by time-consuming and expensive tests. The main objective of this study was to propose a method based on Bayesian networks for improving the identification of uncertainties related to material and environmental parameters of deterioration models when there is limited available information. The outputs of the study are inspection configurations (in space and time) that could provide an optimal balance between accuracy and cost. The proposed methodology was applied to the identification of random variables for a chloride ingress model. It was found that there is an optimal discretisation for identifying each model parameter and that the combination of these configurations minimises identification errors. An illustration to the assessment of the probability of corrosion initiation showed that the approach is useful even if inspection data are limited.     

Finite element reliability analysis of chloride ingress into reinforced concrete structures

For many reinforced concrete structures corrosion of the reinforcement is an important problem since it can result in maintenance and repair actions. Further, a reduction of the load-bearing capacity can occur. In the present paper the Finite Element Reliability Method (FERM) is employed for obtaining the probability of exceeding a critical chloride concentration level at the reinforcement bars, both using Monte Carlo Simulation (MCS) and the First Order Reliability Method (FORM). The chloride ingress is modelled by the Finite Element Method (FEM) and the diffusion coefficient, surface chloride concentration and reinforcement cover depth are modelled by stochastic fields, which are discretized using the Expansion Optimum Linear Estimation (EOLE) approach. The response gradients needed for FORM analysis are derived analytically using the Direct Differentiation Method (DDM). As an example, a bridge pier in a marine environment is considered and the results are given in terms of distributions of time for initiation of corrosion.