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.     

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.     

On the accuracy of diffusion models for life-cycle assessment of concrete structures

In durability analysis and life-cycle assessment of concrete structures transport of chlorides and other aggressive agents is generally described by using Fick’s laws of diffusion. This model is frequently applied in a simplified one-dimensional (1D) form. However, in practical applications the diffusion process is more properly described by two- or three-dimensional patterns of concentration gradients. In this paper, the accuracy of the 1D modelling of diffusion and its impact on the life-cycle assessment of concrete structures under corrosion is evaluated in deterministic and probabilistic terms with respect to more accurate two-dimensional (2D) formulations. The influence of the diffusion modelling on the time-variant corrosion damage of concrete cross-sections is studied with reference to the local damage of the reinforcing steel bars and the global deterioration of bending moment–curvature capacity curves. The results show that 2D diffusion models may be necessary for a realistic life-cycle assessment of concrete structures under corrosion, since 1D models can lead to significant inaccuracies depending on the geometrical aspect ratio of the cross-section, location of reinforcing steel bars and exposure conditions.     

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.     

A model for earthquake risk management based on the life-cycle performance of structures

Over 50 years of design life, buildings are exposed to different magnitudes and frequencies of earthquakes that require consideration of life-cycle cost (LCC). The LCC entails quantifying the building performance under seismic hazard and investments throughout the life of the structures. Traditional LCC utilises probabilities of being in different damage states. However, for buildings with inherent irregularities (e.g. vertical irregularity and plan irregularity), these probabilities are not readily available. In this paper, a system-based approach, utilising fuzzy set theory, is used to quantify the possibility of being in different damage states. The analysis is limited to study the effect of seismic exposure on the building LCC. The proposed method is illustrated with two case studies, a six-storey reinforced concrete (RC) building located in Vancouver, Canada, and vulnerability of an urban centre with 1000 RC buildings. Furthermore, sensitivity analysis is carried out to highlight the impact of different building performance modifiers on the LCC.     

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.     

Life-cycle cost-oriented multiobjective optimization of composite frames considering the slab effect

The life-cycle cost-oriented design philosophy is a promising tool for building resilient cities as it helps in gaining insights into the impact of hazard-induced damage and repair of civil and infrastructure systems. In this study, a socioeconomic parameter-independent practical formulation was introduced for life-cycle cost analysis by combining the economic loss rate associated with different damage limit states and cloud analysis-based probabilistic seismic demand model. A framework for life-cycle cost analysis-based seismic design optimization was proposed using an emerging nature-inspired algorithm, namely, the multiobjective cuckoo search. By considering an eight-story prototype composite frame, the framework was used to determine the trade-off design alternatives between competing optimization objectives. Conventional and improved fiber models were developed to comparatively evaluate the influence of the slab spatial composite effect on Pareto optimal designs. The key drivers of change in three cost indicators were identified using generalized linear models. The result indicates that the overstrength factor is the critical design parameter affecting the initial construction, seismic damage, and life-cycle costs, with statistical significance at the 0.001 level.     

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.     

Extent of spatially variable corrosion damage as an indicator of strength and time-dependent reliability of RC beams

A spatial time-dependent reliability model is developed for a RC beam subject to corrosion-induced pitting corrosion. The analysis considers the spatial and time-dependent variability of pitting corrosion and its effect on cover cracking and shear and flexural resistance. The model uses extreme value theory to predict maximum pit depth as a function of bar diameter and reinforcing bar length. The effect of corrosion on the mechanical behaviour of reinforcement and associated loss of ductility is also considered. A 1D spatial model is included where concrete properties, concrete cover and the surface chloride concentration are treated as random fields. The model is then used to predict the likelihood and extent of corrosion-induced cracking (corrosion damage). The spatial time-dependent reliability model allows the loss of structural capacity and reliability to be calculated conditional to the observed extent of corrosion damage. This allows the interaction between corrosion damage and loss of structural safety to be inferred for a deteriorating RC beam. It was found that the crack width at time of structural collapse is often well in excess of 1 mm. It was also found that the extent and location of severe cover cracking is an important indicator of structural reliability.     

Seismic life-cycle cost analysis of ageing highway bridges under chloride exposure conditions: modelling and recommendations

Chloride-induced corrosion of highway bridges constitutes a critical form of environmental deterioration and may result in significant escalation of seismic life-cycle costs due to increased fragility during earthquake events. Most of existing literature tends to adopt simplistic uniform area loss assumptions in lieu of potentially complex, yet realistic and more detrimental, pitting corrosion models for seismic vulnerability analysis. Since the degree of deterioration depends on the severity and duration of exposure, there exists a need to investigate the influence of uniform vs. pitting corrosion assumption on seismic life-cycle costs for varied chloride exposure conditions. A case-study example of a highway bridge in Central and Southeastern US reveals consideration of pitting corrosion as critical for extreme exposures compared to relatively minor settings. Subsequently this study provides recommendations to aid bridge engineers and stakeholders to balance between computational cost and accuracy of results to aid prompt decisions on rehabilitation of ageing bridges in different exposure conditions. A framework is also included to compute seismic life-cycle costs from generic measures of corrosion, independent of assumed exposure scenario. This framework is particularly helpful for seismic loss assessment of highway bridges in chloride exposure zones with periodic field measurements to estimate the extent of structural deterioration.     

Closed-form seismic fragility estimates,sensitivity analysis and importance measures for reinforced concrete columns in two-column bents

Closed-form seismic fragility estimates are developed for reinforced concrete (RC) columns in bridges with two-column bents. Deformation and shear modes of failure are considered. The closed-form solutions incorporate the important uncertainties associated with both structural properties and ground motion characteristics. Probabilistic capacity and demand models for RC columns in two-column bents are used for the fragility formulation. Sensitivity and importance measures are computed for the parameters and random variables, respectively, included in the limit state function expressed in terms of probabilistic capacity and demand models. The sensitivity measures suggest that the vulnerability of RC columns in two-column bents can be effectively improved by using high strength reinforcement for the column confinement, reducing the spacing between confining reinforcement, and limiting the use of high strength concrete. The importance measures suggest that the random errors in the probabilistic capacity and demand models represent the principal sources of uncertainty. Thus, an approximate closed-form solution for a fragility estimation of a RC column can be developed by considering only the uncertainty in the random errors of the capacity and demand models. Only a marginal difference exists between the closed-form fragility estimates and the corresponding predictive fragility estimates that include all uncertainties.     

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。     

Probabilistic service life of reinforced concrete structures with randomly distributed corrosion-induced cracks

This paper proposed a probabilistic service life prediction method for reinforced concrete (RC) structures with randomly distributed chloride corrosion-induced cracking. In the proposed method, spatial randomness of environmental, geometric and physical factors was considered that influence corrosion process and crack propagation of RC structures at the material level. Karhunen–Loéve (KL) expansion method was utilised for modelling the spatial random fields. Four limit state functions were proposed based on four deterioration events (corrosion initiation, surface crack initiation, modulus degradation and exceedance of repair limit). Then, time-dependent reliability analyses of an RC bridge slab were conducted using the proposed method. Finally, sensitivity analysis of the statistical parameters including mean, variance, correlation length as well as the truncation number for KL expansion method were conducted to determine the effects of those parameters to the service life.     

Risk-based decision support for seismic rehabilitation of structures

This study presents a risk-based decision support framework for seismic retrofit of building structures where the decision criterion is to minimize the sum of the cost required for the rehabilitation and the expected seismic loss over a specified time period. Probabilistic seismic hazard model (PSHM) and probabilistic seismic demand model (PSDM) are utilized for manipulation of the uncertainty propagation from the seismic hazard to the structural damage. A mathematical formula is then developed for probabilistic estimation of the seismic damage and losses over a specified time period. The analysis procedure is developed such that the effect of the different configurations of the decision inputs can be promptly observed. The proposed procedure is demonstrated by performing a decision analysis for a hypothetical RC building structure for determination of the optimal level of seismic rehabilitation using steel bracings.     

水平双向加载下钢筋混凝土柱抗震性能试验研究

针对双向水平地震作用下钢筋混凝土框架柱的抗震性能,开展了9个钢筋混凝土框架柱的水平双向拟静力试验研究,考察轴压比、体积配箍率、纵筋配筋率以及加载路径对柱抗震性能的影响,对双向加载下柱的受力特点、承载力变化、位移延性和极限侧移角等指标进行分析。结果表明：相对于水平单向加载,双向加载对柱的抗震性能存在显著不利影响：柱的抗弯承载力及极限位移均明显减小,损伤程度明显加重;随加载方式由单向-十字-菱形-方圈变化,相同位移下柱的强度退化与抗弯承载力下降幅度均有所增加。考虑双向受力后,典型技术标准给出的RC框架结构极限层间侧移角限值的安全冗余度显著降低。基于试验结果初步提出结构设计及分析建议：考虑双向水平地震动影响时,框架柱的抗震设计宜适当降低轴压比、增加约束箍筋、适当折减柱的抗弯承载力;采用层间侧移角进行结构倒塌判别时,可取双向地震动作用下结构最大层间侧移矢量的大小作为判别位移,并根据分析性质（结构设计或既有结构分析）选取恰当的极限层间侧移角判断标准。     

Seismic performance analysis and evaluation of tall structures using grille-type steel plate composite shear walls

Grille-type steel plate composite (GSPC) shear wall is an innovative wall system consisting of concrete cores, steel faceplates, steel tie plates, and steel channels with more advantages than conventional reinforced concrete (RC) walls, including better ductility, higher bearing capacity, and easy-modular characteristics. This paper mainly discusses the seismic performance and damage resistance of GSPC walls to the entire structure from the aspect of the structural level. Three nonlinear numerical models of high-rise structures with different structural heights and types were established by PERFORM-3D software to study the influence of GSPC walls on the change in structural internal forces and deformations compared with RC walls. One of these structures was selected to conduct the seismic fragility analysis based on the incremental dynamic analysis and to assess the structure's seismic performance with GSPC walls. Finally, the seismic damage prediction method was used to evaluate the damage levels of the GSPC wall structure. Results indicate that the structures with GSPC walls suffer more significant seismic forces than those with RC walls, although they experience lesser structural deformations. Moreover, GSPC walls can effectively improve the structure's collapse and seismic damage resistance.     

近场地震动作用下复合自复位结构考虑残余位移的性能评估

作为实现震后可恢复的一种结构解决方案,提出了一种复合自复位结构,并基于联合概率密度函数对其进行性能评估。复合自复位结构将结构在体系层次上分为基本功能分区和损伤控制分区。基本功能分区实现结构的正常使用功能,承担大部分的地震作用和全部的重力荷载;损伤分区实现结构自复位和耗能,分担剩余的地震作用和控制结构的层间位移集中程度。基于刚度需求的设计该结构,并对其基于联合概率密度函数进行评估,将最大层间位移角和残余层间位移角作为变量,计算得到易损性曲线、联合易损性概率矩阵和联合需求位移角曲面。结果表明,该体系不仅可以有效降低结构的损伤概率,而且可以有效地控制结构的层间位移集中程度。耗能分区可以通过耗能和自复位降低基本功能分区的最大层间位移角和残余层间位移角,并且可以降低结构出现局部薄弱层的整体损伤模式。     

Life-cycle performance of structures subject to multiple deterioration mechanisms

This paper studies structural deterioration as a result of the combined action of progressive degradation (e.g., corrosion, fatigue) and sudden events (e.g., earthquakes). The structural condition at a given time is measured in terms of the system’s remaining life, which is defined in practice by an appropriate structural performance indicator (e.g., inter-story drift). Structural reliability is evaluated against prescribed design and operation thresholds that can be used to establish limit states or intervention policies. It is assumed that sudden events conform to a compound point process with shock sizes and interarrival times that are independent and identically distributed random variables. Progressive deterioration is initially modeled as a deterministic function. Randomness is later included also as a shock process with times between random deterioration jumps described by a suitable deterministic function. Structural performance with time is modeled as a regenerative process and an expression for the limiting average performance is obtained. The model is illustrated with some examples and compared with similar models showing the importance of including the damage history when studying the life-cycle performance of infrastructure systems.     

Life-cycle cost optimal design of passive dissipative devices

The cost-effective performance of structures under natural hazards such as earthquakes and hurricanes has long been recognized to be an important topic in the design of civil engineering systems. A realistic comprehensive treatment of such a design requires proper integration of (i) methodologies for treating the uncertainties related to natural hazards and to the structural behavior over the entire life-cycle of the building, (ii) tools for evaluating the performance using socioeconomic criteria, as well as (iii) algorithms appropriate for stochastic analysis and optimization. A systematic probabilistic framework is presented here for detailed estimation and optimization of the life-cycle cost of engineering systems. This framework is a general one but the application of interest here is the design of passive dissipative devices for seismic risk mitigation. A comprehensive methodology is initially presented for earthquake loss estimation; this methodology uses the nonlinear time-history response of the structure under a given excitation to estimate the damage in a detailed, component level. A realistic probabilistic model is then presented for describing the ground motion time history for future earthquake excitations. In this setting, the life-cycle cost is uncertain and can be quantified by its expected value over the space of the uncertain parameters for the structural and excitation models. Because of the complexity of these models, calculation of this expected value is performed using stochastic simulation techniques. This approach, though, involves an unavoidable estimation error and significant computational cost, features which make efficient design optimization challenging. A highly efficient framework, consisting of two stages, is discussed for this stochastic optimization. An illustrative example is presented that shows the efficiency of the proposed methodology; it considers the seismic retrofitting of a four-story non-ductile reinforced-concrete building with viscous dampers.     

锈蚀钢筋混凝土柱基于变形的性能指标研究

采用ABAQUS有限元软件,对按GB 50011-2010《建筑抗震设计规范》和GB 50010-2010《混凝土结构设计规范》设计的342个锈蚀钢筋混凝土柱进行有限元分析,研究钢筋的锈蚀率、轴压比、剪跨比、配箍率和纵向钢筋配筋率等参数对钢筋混凝土柱变形性能的影响。结果表明：当钢筋的锈蚀率较小时,构件的变形性能受锈蚀率影响不大;当钢筋的锈蚀率达到10%以后,构件的破坏形态发生改变,变形能力急剧退化;随着轴压比的增大,构件的变形能力降低;轴压比较小的构件变形性能受剪跨比影响比轴压比较大的构件明显;随着配箍率和纵向钢筋配筋率的增大,构件的变形能力有所提高;提出了锈蚀钢筋混凝土柱抗震性能等级和性能界限状态的划分方法,以塑性转角作为变形性能指标,对数值计算结果进行统计分析,得到了锈蚀钢筋混凝土柱各性能界限点的塑性转角统计特征值。研究成果可为钢筋混凝土结构全寿命的性能化抗震设计和抗震性能评估提供参考。