Structural reliability of concrete bridges including improved chloride-induced corrosion models

A structural deterioration reliability (probabilistic) model has been used herein to calculate probabilities of structural failure. New reinforced concrete corrosion initiation, corrosion rate and time-variant load models are proposed. Three durability design specifications are considered in a lifetime reliability analysis of a RC slab bridge. Time-variant increases in loads are considered also. It was found that the application of de-icing salts causes significant long-term deterioration and reduction in structural safety for poor durability design specifications. A reduced cover or increased water-cement ratio increases failure probabilities. When compared to the case of “no deterioration”, it was observed also that the probability of failure only marginally increased for good durability design specifications. The approaches described herein are relevant to other physical infrastructure also.     

氯盐侵蚀下修正混凝土桥梁的结构可靠性退化模型

结构退化可靠性(概率论)模型已经被用于计算结构的失效性。考虑钢筋混凝土腐蚀初始点、腐蚀速度以及时变荷载提出相应的修正模型。耐久性设计规范中已考虑混凝土桥梁的全寿命周期的可靠性分析以及时变荷载,但对于耐久性设计考虑不周,没有考虑到除冰盐的运用将引起长期退化和结构安全度的降低。另外,保护层厚度不足或水灰比过高也会增加结构失效的可能性。     

Lifetime seismic performance assessment for chloride-corroded reinforced concrete buildings

The main aim of this paper was to build an estimating procedure based on the static nonlinear analysis (pushover analysis) such that structural engineers can evaluate the seismic performance of a deteriorating reinforced concrete (RC) building. For engineers' convenience, this paper suggests the probabilistic deterioration prediction model and the visual estimation of deterioration degree to evaluate corrosion-induced weight loss of reinforcing steel bars. In addition, flexural and shear capacity models for a corroded column or beam are proposed and verified by full-scale corroded beam specimens, allowing engineers to simulate its nonlinear mechanical behaviour. This paper incorporates these mechanical models of corroded members into the static nonlinear analysis to construct a procedure for assessing the seismic performance of a deteriorating RC building. An elementary school at Lanyu Island, Taitung, Taiwan, is used as an example and its lifetime seismic performance is identified utilising the proposed approach.     

Seismic fragility estimates for corroding reinforced concrete bridges

Seismic fragility of reinforced concrete (RC) bridges is defined as the conditional probability that the seismic demand exceeds the corresponding capacity, specified for a certain performance level, for given seismic intensity measures. However, the structural properties of RC bridges change over time due to the onset of corrosion in the reinforcing steel. Therefore, seismic fragility of RC bridges changes during a bridge lifetime. This paper proposes a method to estimate the seismic fragility of corroding RC bridges. Structural capacities are defined using probabilistic models for deformation and shear capacities of RC columns. Probabilistic models are also used to estimate the corresponding demands for given seismic intensity measures. The capacity and demand models are then combined with probabilistic models for chloride-induced corrosion and time-dependent corrosion rate to model the dependency on time of the seismic fragility of RC bridges. In particular, the loss of reinforcing steel is modelled as a function of the thickness of the cover concrete for each reinforcing bar in the RC columns. The stiffness degradation in the cover concrete over time due to corrosion-induced cracking is also considered in the fragility estimates. Seismic fragility estimates are then formulated at the column, bent, and bridge levels. The fragility formulations properly incorporate the uncertainties in the capacity and demand models, and the inexactness (or model error) in modelling the material deterioration. The proposed method accounts for the variation of structural capacity and seismic demand over time due to the effects of corrosion in the reinforcing steel. As an application, seismic fragility estimates are developed for a corroding RC bridge with 11 two-column bents over a 100-year period.     

Analysis of lifetime losses of low-rise reinforced concrete buildings attacked by corrosion and earthquakes using a novel method

In the estimation of the losses caused by an earthquake for a reinforced concrete (RC) building, the effect of corrosion of the reinforcing steel incurred by environmental conditions, e.g. carbonation and chloride ions, is seldom mentioned because of the corrosion with uncertainty and time dependence. However, because the structural capacity of a corroded RC building declines over time, one must apply an appropriate method that estimates the structural capacity of an RC building in a corrosive environment. Therefore, this work integrated degradation factors into the structural properties of a corroded RC building. Additionally, by considering life-cycle earthquake events, lifetime losses resulting from earthquakes and corrosion can be derived. This work can help both owners and investors to identify lifetime losses of RC buildings due to seismic structural damage, including the corrosion effect, within a specified service life. Although the case study only addresses a selection of the most appropriate concrete cover depth for an RC building corroded by chloride ions, the proposed procedure can be utilised when making decisions about whether to prevent building deterioration based on economic considerations.     

Lifetime reliability-based optimization of reinforced concrete cross-sections under corrosion

This paper presents a lifetime reliability-based approach to the optimization of reinforced concrete (RC) cross-sections in an aggressive environment. The lifetime structural performance is evaluated by using a general methodology for time-variant analysis of RC structures subjected to diffusive attacks from aggressive agents with corrosion of the reinforcement. The lifetime probabilistic optimization is formulated at the cross-sectional level and is aimed to minimize the material cost under a time-dependent constraint on the structural reliability. The optimization problem is solved by combining a discrete gradient-based optimization method with a Monte Carlo simulation. The obtained results demonstrate that in a lifetime-oriented design the amount and location of the steel reinforcement and the value of the concrete cover play a crucial role for the optimal achievement of the desired lifetime structural performance.     

基于锈胀开裂路径的混凝土构件耐久性能概率预测模型及应用

基于混凝土锈胀开裂过程的随机性,提出了一种预测钢筋锈蚀程度、锈胀裂缝开展状况及承载力退化程度时变特性的路径概率模型,并编制了计算程序,能有效评估和预测氯离子侵蚀、混凝土碳化及两者耦合作用环境下钢筋锈蚀状况、锈胀裂缝宽度开展及构件承载力退化程度在不同时段的概率分布,实现了混凝土构件从有害物质侵蚀、钢筋锈蚀、混凝土开裂、钢筋锈蚀加剧、混凝土裂缝宽度增大到构件承载力下降的性能劣化全过程的数值模拟。可预测的性能特征参数包括钢筋样本锈蚀百分比,锈蚀率,混凝土开裂面积百分比,裂缝宽度及构件承载力退化百分比。预测结果与现场检测获得的统计结果吻合良好,验证了该模型的可靠性和有效性。图18表5参18     

Deteriorating beam finite element for nonlinear analysis of concrete structures under corrosion

A three-dimensional reinforced concrete (RC) deteriorating beam finite element for nonlinear analysis of concrete structures under corrosion is presented in this study. The finite element formulation accounts for both material and geometrical nonlinearity. Damage modelling considers uniform and pitting corrosion and includes the reduction of cross-sectional area of corroded bars, the reduction of ductility of reinforcing steel and the deterioration of concrete strength due to splitting cracks, delamination and spalling of the concrete cover. The beam finite element is validated with reference to the results of experimental tests carried out on RC beams with corroded reinforcement. The application potentialities of the proposed formulation are shown through the finite element analysis of a statically indeterminate RC beam and a three-dimensional RC arch bridge under different damage scenarios and corrosion penetration levels. The results indicate that the design for durability of concrete structures exposed to corrosion needs to rely on structural analysis methods capable to account for the global effects of local damage phenomena on the overall system performance.     

南京站主站房地震模拟振动台试验研究

南京站主站房下部为混凝土结构,屋盖为斜拉钢结构。由于建筑造型的需要,结构复杂。对这种混合结构进行地震模拟振动台试验时,如何保证原结构与模型间的相似性是一个很重要的问题。本文较详细地介绍了此次地震模拟振动台试验的过程,包括模型材料的选择、模型的制作、地震波的选择、振动试验、结果分析等方面的内容,可为类似结构进行振动台试验提供参考。模型试验结果表明,在振动台模型中分别用砂浆和铜材模拟混凝土和钢材是完全可行的;对于屋盖为钢结构,下部为钢筋混凝土结构的混合结构,在地震作用下,下部钢筋混凝土更为不利;对于类似单向受力特性明显的结构,加强纵向联系是十分必要的。     

A probability model for investigating the trend of structural deterioration of wastewater pipelines

Canada’s infrastructure is aging and deteriorating. New legislation requires the municipalities to estimate operating and capital expenditures for running the systems into the future and to develop financial sustainability plans. Wastewater pipelines deterioration is currently not well understood and realistic deterioration models need to be developed.This paper demonstrates how the condition assessment data from trenchless visual inspections of wastewater pipelines can be used to understand the performance of wastewater pipelines. A new ordinal regression model for the deterioration of wastewater pipelines based on cumulative logits is elaborated. The model is presented using the Generalized Linear model formulation and takes into account the interaction effect between the explanatory variables. The new model is demonstrated and validated using the City of Niagara Falls high quality wastewater collection network condition assessment data for reinforced concrete (RC) and vitrified clay (VC) pipes.This new model is found to represent the City of Niagara Falls RC and VC pipes’ deterioration behavior for pipes in service for up to 110 years. RC pipes deterioration is found to be age dependent while VC pipes deterioration is not age dependent. This finding is contrary to other deterioration model studies that indicate that VC deterioration is age dependent. The service life for RC pipes is estimated to be approximately 75 years while VC pipes are found to have an indefinite service life if installed without structural damage.The cumulative logit model can be used to determine wastewater pipelines’ service life, predict future condition states, and estimate networks’ maintenance and rehabilitation expenditures. The latter is critical if realistic wastewater networks’ future maintenance and operation budgets are to be developed for the life of assets and to meet new regulatory reporting requirements. Further research is required to validate this new methodology for other networks and the deterioration modeling of pipe materials other than RC and VC.     

Spatial time-dependent reliability analysis of reinforced concrete slab bridges subject to realistic traffic loading

Resistance and loads are often correlated in time and space. The paper assesses the influence of these correlations on structural reliability/probability of failure for a typical two-lane reinforced concrete (RC) slab bridge under realistic traffic loading. Spatial variables for structural resistance are cover and concrete compressive strength, which in turn affect the strength and chloride-induced corrosion of RC elements. Random variables include pit depth and model error. Correlation of weights between trucks in adjacent lanes and inter-vehicle gaps are also included and are calibrated against weigh-in-motion data. Reliability analysis of deteriorating bridges needs to incorporate uncertainties associated with parameters governing the deterioration process and loading. One of the major unanswered questions in the work carried out to date is the influence of spatial variability of load and resistance on failure probability. Spatial variability research carried out to date has been mainly focused on predicting the remaining lifetime of a corroding structure and spatial variability of material, dimensional and environmental properties. A major shortcoming in the work carried out to date is the lack of an allowance for the spatial variability of applied traffic loads. In this article, a two-dimensional (2D) random field is developed where load effects and time-dependent structural resistance are calculated for each segment in the field. The 2D spatial time-dependent reliability analysis of an RC slab bridge found that a spatially correlated resistance results in only a small increase in probability of failure. Despite the fact that load effect at points along the length of a bridge is strongly correlated, the combined influence of correlation in load and resistance on probability of failure is small.     

Reliability-based service life assessment for deteriorating reinforced concrete buildings considering the effect of cumulative damage

Most engineering systems used in maintenance strategies must consider deterioration and seismic structural damage. To identify the effects of deterioration and earthquakes simultaneously on structural performance, this study applies an integral simulation method. Compared with that of previous studies, the feature of the proposed method is its analysis of the time-dependent structural capacity of a deteriorating reinforced concrete (RC) building and the simulation of life-cycle earthquake events within a specified service period, while considering cumulative damage induced by deterioration and earthquakes. In addition, the proposed assessment method is applied to derive the reliability-based service life of a deteriorating RC building located in a region with high seismic hazard. Briefly, for deteriorating RC buildings, the proposed reliability-based service life assessment method provides useful information related to maintenance based on both serviceability and safety.     

某煤矿钢筋混凝土结构厂房检测和可靠性鉴定

某煤矿钢筋混凝土结构厂房因主体结构的劣化以及选煤工艺重介技术的变更,需要对其进行可靠性鉴定,评定其安全性、正常使用性和可靠性等级。并对主厂房的结构作用、工作环境、基础承载力和变形、构件的表观质量和裂缝、构件的混凝土碳化和强度、钢筋锈蚀率、钢筋分布和保护层厚度、构件的动力性能分别进行检测,根据检测结果复核结构的安全性。在此基础上,对主厂房的可靠性鉴定评级,并提出维护、修复和加固的建议。     

Life-cycle cost analysis of reinforced concrete structures in marine environments

Chloride-induced corrosion of carbon steel reinforcement is the main cause of deterioration of reinforced concrete (RC) structures in marine environments. One of the ways to protect RC structures from corrosion is to use corrosion-resistant stainless steel reinforcing bars. However, stainless steel is between six and nine times more expensive than carbon steel. Thus, its use can only be justified on a life-cycle cost basis. In the paper a time-variant probabilistic model was presented to predict expected costs of repair and replacement which was then used to calculate life-cycle costs for RC structures in marine environments under different exposure conditions. Results of the life-cycle cost analysis can be applied to select optimal strategies improving durability of RC structures in marine environments, including the use of stainless steel reinforcement.     

Some considerations on the performance cycle analysis of concrete girders in France

A performance assessment of corroded reinforced concrete (RC) structures requires an acute understanding of both material deterioration and its impact on structural behaviour, in order to evaluate its durability, safety, serviceability and remaining service life. The corrosion phenomenon is usually due to carbon dioxide and chloride ions. More generally, the environmental conditions may determine what kind of deterioration mechanism can produce structural degradation depending on relative humidity, temperature, severity of the surrounding environment, materials properties, etc. Consequently, the performance cycle prediction of reinforced concrete structures involves many factors, which introduce uncertainties. A probabilistic approach as opposed to a deterministic one is therefore more appropriate to generate reliable cycle predictions. This paper focuses on the application of the principles of such a probabilistic approach to calculate for a typical set of RC bridges in France, the critical times corresponding to every performance cycle, considering both chloride-induced corrosion and carbonation, but also concrete cracking and spalling. For this purpose, the impact of the environment on the RC structures and the principal material properties are taken into account in this analysis. A methodology is also provided for roughly assessing serviceability cycles from visual inspections.     

氯离子侵蚀效应对RC桥墩抗震性能的影响

为研究混凝土桥梁结构在服役期内由于环境氯离子侵蚀效应引起钢筋、混凝土锈蚀退化等导致结构抗震性能退化的规律,以某多跨钢筋混凝土连续梁桥为例,采用OpenSees软件建立非线性动力分析模型,根据已有研究成果并基于概率方法研究了墩柱截面主筋和箍筋锈蚀的开始时间和锈蚀率大小,进而建立了钢筋的直径及屈服强度退化模型;针对考虑纵筋锈蚀、考虑箍筋锈蚀、同时考虑纵筋和箍筋锈蚀3种情况,分别分析了材料退化对桥墩抗震性能的影响。结果表明:同等条件下箍筋锈蚀比纵筋锈蚀更早;随着时间的推移,氯离子侵蚀效应会导致桥墩抗震能力下降,结构的抗震需求明显增加;与以往只考虑纵筋锈蚀的情况相比,同时考虑箍筋和纵筋锈蚀时桥墩抗震性能退化更严重。     

Half a century of reinforced concrete electric poles maintenance: inspection,field-testing,and performance assessment

Application of reinforced concrete (RC) poles as overhead electrical transmission line supports has become of great interest during recent years worldwide. The higher strength, longer life, and the potential to span longer distances than steel poles are the key reasons behind this tendency. A great variety of architectural shapes, relatively low maintenance costs, and high electrical resistance make RC a prominent alternative to steel. The drawbacks related to the application of RC poles include the high self-weight and vulnerability to damage. Self-weight might be reduced by prestressing the reinforcement and/or forming a tubular structure for the poles. However, both of these options might increase the vulnerability of the supports. Moreover, long-term processes (deterioration of concrete and corrosion of steel reinforcement) complicate the prediction of structural properties. This paper presents results of the everlasting inspection of the overhead electric power distribution system in Lithuania: technical state of more than 500 RC supports was assessed; selected poles were tested until failure. A specific point of this research is that most of the inspected supports were under maintenance since the middle of last century. The inspection results were used for developing the technical condition of RC pole evaluation scale proposed in this paper.     

Life-cycle reliability assessment of reinforced concrete bridges under multiple hazards

This paper proposes a novel probabilistic methodology for estimating the life-cycle reliability of existing reinforced concrete (RC) bridges under multiple hazards. The life-cycle reliability of an RC bridge pier under seismic and airborne chloride hazards is compared to that of a bridge girder under traffic and airborne chloride hazards. When conducting a life-cycle reliability assessment of existing RC bridges, observational data from inspections can provide the corrosion level in reinforcement steel. Random variables related with the prediction of time-variant steel weight loss can be updated based on the inspection results using Sequential Monte Carlo Simulation (SMCS). This paper presents a novel procedure for identifying the hazards that most threaten the structural safety of existing RC bridges, as well as the structural components with the lowest reliability when these bridges are exposed to multiple hazards. The proposed approach, using inspection results associated with steel weight loss, provides a rational reliability assessment framework that allows comparison between the life-cycle reliabilities of bridge components under multiple hazards, helping the prioritisation of maintenance actions. The effect of the number of inspection locations on the updated reliability is considered by incorporating the spatial steel corrosion distribution. An illustrative example is provided of applying the proposed life-cyle reliability assessment to a hypothetical RC bridge under multiple hazards.     

基于小波变换的钢筋混凝土结构损伤识别

钢筋混凝土结构在其服役期内,由于受到荷载、地震以及其他因素的作用,会发生损伤,从而威胁整个结构的安全。为了保证结构的安全,需要尽早发现结构的损伤,并且采取防范和修复措施。基于小波变换的多分辨率的特点,提出一种分层小波搜索的方法对结构损伤进行在线检测,确定损伤位置和损伤发生的时刻。通过对某一框架进行数值模拟试验验证可行的基础上,将此法应用于地震作用下钢筋混凝土框架的损伤识别,并与结构模型的模拟地震振动试验观测结果相对比,表明分析结果与试验观测较好吻合。     

Prediction for lateral deformation capacity of corroded reinforced concrete columns

The deformation capacities of columns, which are the main lateral force‐resisting elements of reinforced concrete (RC) structures, have been the subject of great interest with the development of performance/displacement‐based seismic design. However, deterioration due to chloride‐induced corrosion causes a significant reduction in the seismic performance of RC columns. Although numerous investigations have focused on the deformation capacity of columns with corroded rebars and various strengthening measures have been proposed, little attention was paid to evaluating the contribution of each deformation component to the tip displacement under corrosion (i.e., bending, shear, and longitudinal bar slip at the column footing), which plays an important role in investigating and explaining the failure mechanisms of columns. This paper presents a computational prediction model to estimate the deformation capacity of RC columns with corroded rebars, and the contributions of bending and bar slip at the column footing are mainly considered in this model due to the negligible contribution of the shear deformation component for columns subjected to flexural failure mode. The calculation results obtained by the prediction model are compared with the quasistatic test results of both noncorroded and corroded RC columns. It turns out that the prediction model simulates the deformation capacity of RC columns with corroded rebars reasonably well considering its simplicity and computational efficiency, and it can be used for time‐variant capacity estimates for the lifetime seismic design and fragility assessment of RC columns exposed to corrosion.