Probabilistic evaluation of initiation time of chloride-induced corrosion

The paper presents a model for chloride ingress into concrete. The model accounts for two mechanisms which control the chloride ingress—diffusion and convection. Using one-dimensional (1-D) formulation of the model, the influence of chloride binding and ambient humidity on chloride ingress into concrete has been investigated. Based on results of this investigation parameters for probabilistic analysis have been selected. Probabilistic evaluation of the time to corrosion initiation has then been carried out for a reinforced concrete (RC) wall (1-D problem) and a RC column (2-D problem) in a marine environment. Results of the analysis show that for the same thickness of the concrete cover the probability of corrosion initiation in the corner reinforcing bars of the RC column is much higher than in reinforcing bars in the middle part of the RC wall. The results demonstrate the importance of 2-D modelling for correct prediction of corrosion initiation in such RC elements as columns and beams.     

Probabilistic approach to corrosion risk due to carbonation via an adaptive response surface method

A study about a probabilistic approach to corrosion risk of reinforcements embedded in concrete due to carbonation is presented. The carbonation model is based on a single non-linear diffusion equation of the carbon dioxide. A global balance relationship between the carbon dioxide partial pressure and the solid calcium content in the hydrates of concrete is used in order to express the sink term of the equation and to render the solving easily tractable in a classical finite element analysis. The performance function invoked in the probabilistic approach is the deviation between the carbonation depth, i.e. the output of the carbonation model, and the concrete cover. The Hasofer–Lind reliability index is determined by the Rackwitz–Fiessler algorithm in which the performance function is replaced by a quadratic response surface in order to reduce computational cost and gain accuracy. An adaptive building of the numerical experimental design is proposed: points efficiently positioned with respect to the design point are re-used in the new iteration of the experimental design. In the case of explicit performance functions frequently reported in the literature comparisons with surface response techniques previously developed reveal the interest of the proposed technique. A practical application to a concrete girder shows that the reliability index decreases significantly with time.     

Behavior of corrosion-damaged RC columns wrapped with FRP under combined flexural and axial loading

This paper presents the results of a research program aimed at investigating the effectiveness of carbon fiber-reinforced polymers (CFRP) to upgrade corrosion-damaged eccentrically loaded reinforced concrete (RC) columns. A total of 16 square RC columns with end corbels were constructed. Test specimen had an overall length of 1200 mm whereas each end corbel had a cross section of and a length of 350 mm. The specimen in the test region was having longitudinal steel ratio of 1.9%. The damaged specimens were exposed to 30 days of accelerated corrosion that corresponded to a steel mass loss of about 4.25%. The main test parameters were the CFRP repair scheme (no wrapping, full-wrapping, and partial-wrapping) and the eccentricity-to-section height (e/h) ratio (0.3, 0.43, 0.57, and 0.86). The strength of the damaged columns fully wrapped with CFRP was up to 40% higher than that of the control undamaged columns. The strength gain was inversely proportional to the eccentricity ratio. Partial CFRP-wrapping was 8% less effective than full CFRP-wrapping at nominal e/h of 0.3. At higher e/h values, the confinement level had a negligible effect on the columns’ strength. An analytical model was then proposed to predict the columns’ strength under eccentric loading. A comparative analysis between predicted and experimental results demonstrated the model’s accuracy and reliability.     

Optimization of clamped columns under distributed axial load and subject to stress constraints

The optimum designs are given for clamped-clamped columns under concentrated and distributed axial loads. The design objective is the maximization of the buckling load subject to volume and maximum stress constraints. The results for a minimum area constraint are also obtained for comparison. In the case of a stress constraint, the minimum thickness of an optimal column is not known a priori, since it depends on the maximum buckling load, which in turn depends on the minimum thickness necessitating an iterative solution. An iterative solution method is developed based on finite elements, and the results are obtained for n=1, 2, 3 defined as I=α _n A ⁿ , with I being the moment of inertia, and A the cross-sectional area. The iterations start using the unimodal optimality condition and continue with the bimodal optimality condition if the second buckling load becomes less than or equal to the first one. Numerical results show that the optimal columns become larger in the direction of the distributed load due to the increase in the stress in this direction. Even though the optimal columns are symmetrical with respect to their mid-points when the compressive load is concentrated at the end-points, in the case of the columns subject to distributed axial loads the optimal shapes are unsymmetrical.     

Probabilistic seismic demand model and fragility estimates for critical failure modes of un-anchored steel storage tanks in petroleum complexes

Estimation of seismic vulnerability of existing equipment in petroleum complexes, traditionally has been done by using general fragility curves which have been developed for a group of equipment without considering their physical specifications. Although these kinds of fragility are suitable for preparing emergency plans and governmental decision making, for the sake of seismic upgrading of existing facilities, specific equipment fragilities are needed. In this paper un-anchored steel storage tanks, which is among the most vulnerable equipment in petroleum facilities, are selected for a case study. Probabilistic demand models for Elephant Foot Buckling (EFB) and welding failure at the connection between the bottom plate and shell are developed based on FEM analytical data, and a Bayesian updating rule is used to assess the unknown demand model parameters. The approach properly accounts for both aleatory and epistemic uncertainties. Developed probabilistic demand models are used to estimate the fragility of critical failure modes of selected tanks and real world data. The approach can be applied for other failure modes and other equipment, as well.     

An integrated approach to inventory and flexible capacity management subject to fixed costs and non-stationary stochastic demand

In a manufacturing system with flexible capacity, inventory management can be coupled with capacity management in order to handle fluctuations in demand more effectively. Typical examples include the effective use of temporary workforce and overtime production. In this paper, we discuss an integrated model for inventory and flexible capacity management under non-stationary stochastic demand with the possibility of positive fixed costs, both for initiating production and for using contingent capacity. We analyze the characteristics of the optimal policies for the integrated problem. We also evaluate the value of utilizing flexible capacity under different settings, which enable us to develop managerial insights.     

Probabilistic prediction models for crack initiation and progression of spray sealed pavements

Cracking is one of the primary distress modes in spray (chip)-sealed pavement surface performance and its prediction is a major concern for pavement engineers. In order to identify, manage and asses effectively and efficiently cracked pavement at a network level, a probabilistic modelling approach is utilised to develop cracking initiation and progression models. This study aims to predict the probability of pavement cracks occurring using a binary logistic model and cracks progression over time using an ordinal logistic regression model. These models have been developed to take into account the effect of variations among observations, among sections and among highways. Readily available historical time series data (from 2004 to 2011) from 40 highway segments have been collected and prepared for modelling. These time series include surface cracking as a performance parameter and traffic loading, expansion potential of subgrade soil, climate condition, condition of drainage system and pavement strength as predictor parameters. Cracking data include all types of cracking: transverse, longitudinal and crocodile cracking and is reported as a percent of the affected area. The study estimates the probability of crack initiation at a certain time and predicts the probability of a pavement maintaining its current level of cracking. It is found that with the 50% estimated probability, about 82% of the observations are correctly predicted by the crack initiation model and 65% of the observations are correctly predicted by the crack progression model. The study has concluded that the effect of time is stronger than the other variables on crack initiation and progression. Also, the effect of traffic loading is stronger than the effect of initial pavement strength in crack initiation phase. However, the effect of pavement strength at any time is stronger than the effect of traffic loading in crack progression phase. The predicted probabilities have been successfully validated using another data-set from the same network and the results indicate that the developed probability models are well estimating the crack conditions and have the ability to predict future conditions accurately.     

Inspection and monitoring planning for RC structures based on minimization of expected damage detection delay

The deterioration mechanism of reinforced concrete (RC) structures under corrosion is highly dependent on environment and material properties. Uncertainties in structural damage occurrence and propagation due to corrosion should be considered in a rational way using a probabilistic approach. In this study, such an approach is proposed to establish a life-cycle optimum inspection plan under uncertainty. This plan leads to cost-effective maintenance interventions, considering uncertainties associated with damage occurrence/propagation and inspection methods. Uncertainties associated with prediction of damage occurrence time are considered by using the Monte Carlo simulation. A damage detectability function is used to assess the quality of inspection method according to damage intensity. The inspection planning is formulated as an optimization problem with the objective of minimizing the expected damage detection delay. This formulation is further used for optimum monitoring planning. Effects of number of inspections and/or monitoring actions, quality of inspection, monitoring duration, and uncertainties associated with damage occurrence/propagation are investigated. The proposed approach is applied to an existing highway bridge. This approach can be used to develop cost-effective management strategies by considering effects of damage detection delay on life-cycle cost and performance of deteriorating structures.     

Drift time detection and adjustment procedures for processes subject to linear trend

This paper considers production processes when the mean of a quality characteristic is drifted linearly with time. First, it introduces a procedure to detect the drift time of the process mean as early as possible. Then, based on the estimate of the drift time, a new adjustment procedure based on the maximum likelihood estimate of the drift time is developed to keep the process mean on target. The paper analyses and compares the performance of the proposed estimator with cumulative sum (CUSUM) and exponentially moving average (EWMA) change point estimation procedures. It is observed that the proposed procedure indeed estimates the drift time effectively for moderate and large trend rates. However, there is a noticeable decrease in its ability to detect drift time at small trend rates. Furthermore, the performance of the new adjustment procedure is compared with EWMA controllers. It is shown that the new procedure is more stable through a wide range of trend rates and its performance does not depend on any parameters of the process.     

Probabilistic physics-of-failure models for component reliabilities using Monte Carlo simulation and Weibull analysis: a parametric study

In reliability engineering, component failures are generally classified in one of three ways: (1) early life failures; (2) failures having random onset times; and (3) late life or ‘wear out’ failures. When the time-distribution of failures of a population of components is analysed in terms of a Weibull distribution, these failure types may be associated with shape parameters β having values <1, 1, and >1 respectively. Early life failures are frequently attributed to poor design (e.g. poor materials selection) or problems associated with manufacturing or assembly processes.

We describe a methodology for the implementation of physics-of-failure models of component lifetimes in the presence of parameter and model uncertainties. This treats uncertain parameters as random variables described by some appropriate statistical distribution, which may be sampled using Monte Carlo methods. The number of simulations required depends upon the desired accuracy of the predicted lifetime. Provided that the number of sampled variables is relatively small, an accuracy of 1–2% can be obtained using typically 1000 simulations.

The resulting collection of times-to-failure are then sorted into ascending order and fitted to a Weibull distribution to obtain a shape factor β and a characteristic life-time η.

Examples are given of the results obtained using three different models: (1) the Eyring–Peck (EP) model for corrosion of printed circuit boards; (2) a power-law corrosion growth (PCG) model which represents the progressive deterioration of oil and gas pipelines; and (3) a random shock-loading model of mechanical failure. It is shown that for any specific model the values of the Weibull shape parameters obtained may be strongly dependent on the degree of uncertainty of the underlying input parameters. Both the EP and PCG models can yield a wide range of values of β, from β>1, characteristic of wear-out behaviour, to β<1, characteristic of early-life failure, depending on the degree of dispersion of the uncertain parameters. If there is no uncertainty, a single, sharp value of the component lifetime is predicted, corresponding to the limit β=∞. In contrast, the shock-loading model is inherently random, and its predictions correspond closely to those of a constant hazard rate model, characterized by a value of β close to 1 for all finite degrees of parameter uncertainty.

The results are discussed in the context of traditional methods for reliability analysis and conventional views on the nature of early-life failures.     

Performance evaluation and capacity planning in a metallurgical job-shop system using open queueing network models

In this paper, we apply performance evaluation and capacity allocation models to support decisions in the design (or redesign) and planning of a job-shop queueing network of a metallurgical plant. Approximate parametric decomposition methods are used to evaluate system performance measures, such as the expected work-in-process (WIP) and production leadtimes. Based on these methods, optimisation models are then applied for the allocation (or reallocation) of capacity to the stations of the job-shop network. These models are also used to generate approximate trade-off curves between capacity investment and WIP or leadtime, which are valuable for a production manager to estimate how much capacity should be allocated to the stations to reach some targeted performance measures. These curves are also useful for the sensitivity analysis of the solutions to changes in the input parameters, such as the variability of the product demands, the mix of the production and the throughput rate of the network.     

A probabilistic physics-of-failure model for prognostic health management of structures subject to pitting and corrosion-fatigue

A combined probabilistic physics-of-failure-based model for pitting and corrosion-fatigue degradation mechanisms is proposed to estimate the reliability of structures and to perform prognosis and health management. A mechanistic superposition model for corrosion-fatigue mechanism was used as a benchmark model to propose the simple model. The proposed model describes the degradation of the structures as a function of physical and critical environmental stresses, such as amplitude and frequency of mechanical loads (for example caused by the internal piping pressure) and the concentration of corrosive chemical agents. The parameters of the proposed model are represented by the probability density functions and estimated through a Bayesian approach based on the data taken from the experiments performed as part of this research. For demonstrating applications, the proposed model provides prognostic information about the reliability of aging of structures and is helpful in developing inspection and replacement strategies.     

Evaluation of accelerated degradation test methods for cementitious composites subject to sulfuric acid attack; application to conventional and alkali-activated concretes

The degradation of cementitious composite materials under chemical sulfuric acid attack has been widely investigated. The agglomeration of a global database of test results is complicated by the differing test methodologies employed in each study. As a result it is difficult to isolate the influence of individual test parameters and hence directly compare the relative performance of different cementitious material. In this study the existing accelerated test methodologies including: brushing, wetting and drying cycling, and increased concentration of sulfuric acid are investigated such that the influence of test methodology on degradation rate and microstructural performance can be identified. This approach is taken with the view of developing a common methodology for indicating the susceptibility of a given cementitious material in an aggressive environment. Rather than comparing the performance of individual materials this work aims to compare the influence of test methodology when applied to different materials.     

Simulation studies of methods to delay corrosion and increase service life for cracked concrete exposed to chlorides

The ingress of chlorides in reinforced concrete leads to the onset of steel reinforcement corrosion and eventually compromises a structure’s integrity. To extend its service life and improve safety, it is crucial to develop sound repair strategies for our nation’s infrastructure. In this paper, results are presented for numerical simulations to study the effectiveness of fillers for repair of cracks in concrete, so as to delay the onset of corrosion in reinforcing steel. Concretes without cracks and with either a 50 μm or 500 μm wide crack located directly above the steel reinforcement are simulated, with the addition of silica fume, a corrosion inhibitor, or epoxy-coated reinforcement being considered as additional scenarios. The effectiveness of the crack filler depends not only on its inherent diffusivity with respect to chloride ions, but also on its ability to penetrate and fill the damaged zone or interface between the open crack region and the bulk concrete. Additional simulations indicate that using continuum models instead of models that include details of the rebar placement can lead to underestimating the chloride concentration and overestimating the service life. Experiments are needed to study the ingress of chlorides in damaged (interfacial) regions adjacent to the crack or at the reinforcement surface, as the local transport properties of these regions can significantly influence service life predictions.     

HPFL加固受火RC梁二次受力正截面承载力研究

 高性能复合砂浆钢筋网(high performance ferrocement laminate, HPFL)作为一种新型的加固方式,具有防火、耐高温、施工简易等优点．为研究其加固受火钢筋混凝土（reinforced concrete, RC）梁的性能,结合已有的对高性能复合砂浆钢筋网的试验研究和对受火后混凝土梁强度、弹性模量等性能的研究成果,采用ANSYS中的PLANE55单元对高温后RC梁截面的温度场进行模拟,并利用计算二台阶模型简化成等效T形截面,考虑未卸载完全下高性能复合砂浆钢筋网同原材料间的应力—应变滞后现象,计算初始荷载下待加固构件的滞后应变,在此基础上结合构件受力情况推导出高性能复合砂浆钢筋网加固受火RC梁二次受力下的正截面承载力计算公式,将计算结果同试验数据进行比较,并给出了工程实际算例．结果表明,理论值与试验值吻合较好,采用高性能复合砂浆钢筋网加固后能提高受火RC梁的承载力,可供有关混凝土结构加固设计参考．     

钢管混凝土柱-双面组合作用梁框架节点抗震性能试验研究

梁柱节点受剪承载力计算是混凝土框架结构节点抗震设计的关键点之一,由于节点剪力传递机理与构造的复杂性,目前尚未形成完善的节点受剪承载力计算理论。该文阐述了预应力混凝土梁-型钢混凝土柱新型框架节点的受力机理,并基于桁架模型和斜压杆模型,提出了一种同时考虑预应力筋与型钢贡献的节点受剪承载力计算方法。开展了新型节点受力性能拟静力试验,分别选取了梁端破坏与节点剪切破坏两种破坏形式的节点试验数据,对所建立的新型节点受剪承载力计算方法进行了验证评估,结果表明,该文提出的预应力混凝土梁-型钢混凝土柱框架节点承载力计算方法具有较好的精度。

     

潮汐区GFRP筋珊瑚海洋混凝土柱轴压性能试验及承载力计算

为解决海洋工程中钢筋耐久性不足以及海上建筑材料短缺问题,提出了一种新型玻璃纤维增强树脂复合材料(GFRP)筋珊瑚海洋混凝土柱.对28个海洋潮汐区混凝土柱试件进行轴压静力加载试验,观察了受力破坏过程,获取了荷载-位移全过程曲线和特征点应力应变数据,分析了试件的受压破损机制及各参数对轴压力学性能的影响规律,并探讨了潮汐区该...     

An unconditionally convergent algorithm for the evaluation of the ultimate limit state of RC sections subject to axial force and biaxial bending

We present a numerical procedure, based upon a tangent approach, for evaluating the ultimate limit state (ULS) of reinforced concrete (RC) sections subject to axial force and biaxial bending. The RC sections are assumed to be of arbitrary polygonal shape and degree of connection; furthermore, it is possible to keep fixed a given amount of the total load and to find the ULS associated only with the remaining part which can be increased by means of a load multiplier. The solution procedure adopts two nested iterative schemes which, in turn, update the current value of the tentative ultimate load and the associated strain parameters. In this second scheme an effective integration procedure is used for evaluating in closed form, as explicit functions of the position vectors of the vertices of the section, the domain integrals appearing in the definition of the tangent matrix and of the stress resultants. Under mild hypotheses, which are practically satisfied for all cases of engineering interest, the existence and uniqueness of the ULS load multiplier is ensured and the global convergence of the proposed solution algorithm to such value is proved. An extensive set of numerical tests, carried out for rectangular, L‐shaped and multicell sections shows the effectiveness of the proposed solution procedure. Copyright © 2007 John Wiley & Sons, Ltd.