Reliability-based condition assessment of deteriorating concrete bridges considering load redistribution

A wide variety of models have been proposed for estimating the reliability of highway bridges. For reinforced concrete bridges subjected to environmental attack, time-variant reliability methods have to be used. In this study, the condition of reinforced concrete girder bridges is assessed using a time-variant system reliability approach in which both load and resistance are time-variant quantities. Several system models are considered, including failure of any girder (series system) and failure of a specified number of adjacent girders (series-parallel system). Adaptive importance sampling is used to determine the cumulative-time system failure probability. An existing reinforced concrete T-beam bridge located near Pueblo, Colorado, is investigated. The influence of resistance degradation and post-failure load redistribution is included. A comparison of reliability estimates for several system models is given, including the influence of correlation among initial girder strengths. The results can be used as a guide for the selection of system models for bridge reliability analysis, identification of critical girders in a bridge system, and for the development of optimal reliability-based maintenance strategies for reinforced concrete highway bridges.     

既有RC桥梁时变可靠性分析

为了研究构件抗力劣化和车辆荷载对既有RC桥梁服役期间的可靠度影响,首先分析讨论了抗力的衰减模型,并将车辆荷载率视为随机变量。在此基础上,分析了不同的抗力衰减模型和车辆荷载对结构可靠性的敏感性。结果表明,行车道板抗弯失效模式的失效概率最大,车辆荷载对结构可靠性影响较大,抗力按不同的规律衰减导致结构的可靠指标降低趋势表现出不同的规律。     

Fatigue reliability model for steel railway bridges

Railway bridges are exposed to repetitive high stress due to the live load which may lead to failure even when the stress level is lower than the allowable stress. Therefore, components and connections need to be analysed for possible damage caused by fatigue. The basic approach for estimating the remaining fatigue life of a structure element is to use S–N curves. However, those laboratory specimens tested with a constant-amplitude stress range show a wide range variability in the results. This means that fatigue resistance has to be considered as a random variable. If load and resistance parameters are random variables, structural performance should be measured in terms of reliability. The objective of this study is to present a reliability model for the fatigue limit states demonstrated on a typical steel railway bridge. The results from the reliability analysis for the fatigue limit state are presented for various time periods from 10 to 100 years and three cases of operating conditions. In each considered case of load, the lowest reliability indices were obtained for the riveted angle in the stringer-to-floor-beam connection which means that this member has the highest probability of fatigue crack development in the entire bridge.     

基于二阶泰勒级数展开和风驱动优化算法的结构有限元模型修正

为得到结构响应与修正参数之间的函数关系、简化参数迭代过程，通过推导结构响应关于修正参数的一阶与二阶泰勒级数展开，并选用具有寻优效率高、全局搜索能力强的风驱动优化算法，建立了基于二阶泰勒级数展开和风驱动优化算法的结构有限元模型修正方法。同时，为求解响应关于修正参数的二阶泰勒级数展开，采用差分法近似求得响应关于修正参数的一阶和二阶偏导数。利用该方法对算例模型进行了修正，并对比了一阶和二阶泰勒级数展开的修正效果。结果表明：二阶泰勒级数展开的修正效果明显优于一阶泰勒级数展开，增加二阶偏导数项可以更好地反映响应与修正参数之间的函数关系。基于该方法，采用实桥的静动力测试数据对青林湾大桥的有限元模型进行了修正，修正后的有限元模型能够较好地反映大桥的实际状况。     

Prediction of the combination of failure modes for an arch bridge system

An innovative prediction method for the combination of failure modes of an arch bridge is proposed for its probabilistic risk assessment and is compared with the conventional system reliability analysis method. The suggested method reveals various combinations of failure modes in significantly reduced time and efforts in comparison to the previous permutation method or the conventional system reliability analysis method. Additionally, the suggested method can be used for the verification of the system reliability with more specific predictions of the failure modes.Component reliabilities of girders have been evaluated by using response surfaces of the design variables at the selected critical sections, i.e. the maximum shear and negative moment locations. Response Surface Method (RSM) is successfully applied for the reliability analyses of complex structure with relatively small probability of failure. Previous methods such as Monte Carlo Simulations or First Order Second Moment method cannot easily calculate the derivative terms of implicit limit state functions. Hence, the target bridge system is modeled as a series-connection system for the analysis of its system reliability. The upper and lower bound of the probabilities of failure for the structural system have been evaluated and are compared with the suggested prediction method for all possible combination of failure modes.     

Seismic system reliability analysis of bridges using the multiplicative dimensional reduction method

Abstract

A combined method of finite element reliability analysis and multiplicative dimensional reduction method (M-DRM) is proposed for systems reliability analysis of practical bridge structures. The probability distribution function of a structural response is derived based on the maximum entropy principle. To illustrate the accuracy and efficiency of the proposed approach, a simply supported bridge structure is adopted and the failure probability obtained are compared with the Monte Carlo simulation method. The validated method is then applied for the system reliability analysis for a practical high-pier rigid frame railway bridge located at the seismic-prone region. The finite element model of the bridge is developed using OpenSees and the M-DRM method is used to analyse the structural system reliability under earthquake loading.     

Probabilistic Evaluation of Structural Fire Resistance

The work described herein seeks to investigate a probabilistic framework to evaluate the fire resistance of structures given uncertainty in the fire load and structural resistance parameters. The methodology involves (i) the identification and characterization of uncertain parameters in the system, (ii) a stochastic analysis of the thermo-mechanical response of the structure, and (iii) the evaluation of structural reliability based on a suitable limit state function. The methodology is demonstrated through the analysis of a protected steel beam using Monte Carlo simulation with embedded finite element simulations. Model dimensionality is reduced using a response sensitivity analysis, and limit state functions are defined based on limiting deflection criteria used in fire resistance tests. Results demonstrate that the 1-h rated beam resists a natural fire exposure with a failure probability of less than ten percent, although additional discussion is warranted regarding what might be considered an acceptable level of risk in structural fire design. The study also demonstrates that probabilistic analysis of structural fire resistance provides an enhanced understanding of the factors affecting the resistance of structures to fire and offers a means for rationally improving structural designs to meet target performance objectives.     

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.     

预应力混凝土斜拉桥合龙段置换加固施工过程分析

预应力混凝土斜拉桥合龙段置换加固技术是为解决合龙段与相邻主梁节段之间的湿接缝失效问题而提出的.为分析这种加固技术的受力特点,介绍了这种加固技术的实现途径和施工要点,建立了典型的预应力混凝土斜拉桥的结构计算模型,系统地给出了施工阶段分析的方法,包括合龙段置换的结构基准计算模型的建立和合龙段置换施工过程的模拟,依据计算结果...     

Time-dependent reliability assessment of aging series systems subjected to non-stationary loads

Civil infrastructure systems provide physical supports to a community’s functionalities and are expected to achieve acceptable safety levels subjected to extreme load effects. However, these systems may deteriorate with time as a result of aggressive environmental or operating conditions in service, implying that the system reliability may decline beyond the baseline as assumed for design. Moreover, the increasing trend of the external loads may also contribute to the reduction of the system reliability. In this paper, a semi-analytical method is proposed for assessing the reliability of aging systems subjected to non-stationary loads. The series system is considered, where the system failure is defined as the failure of any single component (structure) among the system. The application of the proposed method is illustrated using a representative series bridge network with several individual bridges. The role of parameters such as the variations in the load intensity, resistance correlation and number of components under attack in the system reliability are investigated.     

Reliability analysis for highway bridge deck assessment

An assessment procedure based on structural system reliability principles, has been developed for highway bridges with concrete or composite decks. It concentrates on the ultimate flexural limit state of slabs and takes account of the fact that the failure of the structure is dependent on the combination of the applied loads, their variability, both spatial and in amplitude, and on the variability of geometric and material properties. Recognising that each of a number of topologically distinct collapse mechanisms may contribute to the overall probability of system failure, an optimisation technique is used in conjunction with structural reliability analysis in order to establish for each mechanism the critical geometry and the associated probability of occurrence.The procedure can be implemented in the assessment of existing bridge structures, where the use of plastic analysis may reveal strength reserves not utilised in design and, hence, alleviate the need for strengthening. By modelling the bridge as a virtual series system and analysing a finite number of collapse mechanisms, bounds on system failure probability in flexure can be estimated. An example of its intended use is presented for a solid slab concrete bridge deck.     

正交异性钢桥面板结构体系的疲劳破坏模式和抗力评估

正交异性钢桥面板的疲劳问题属于包含多疲劳破坏模式的结构体系疲劳问题。基于这一本质特性,以典型的正交异性钢桥面板结构体系为研究对象,由结构体系的主导疲劳破坏模式出发,提出正交异性钢桥面板结构体系疲劳抗力评估的新方法。以纵肋与顶板焊接细节和纵肋与横隔板交叉构造细节为主要研究对象,设计8个足尺节段模型,主要包括传统纵肋与顶板焊接细节、新型镦边纵肋与顶板焊接细节和纵肋与横隔板交叉构造细节,通过模型试验研究了两类重要构造细节的主导疲劳破坏模式和实际疲劳抗力,在此基础上结合切口应力评估方法探讨正交异性钢桥面板构造细节切口应力S-N曲线方程、结构体系的主导疲劳破坏模式等关键问题。研究结果表明：传统纵肋与顶板焊接细节和新型镦边纵肋与顶板焊接细节的主导疲劳破坏模式均为疲劳裂纹萌生于焊根并沿顶板厚度方向扩展,二者的实际疲劳抗力基本相同;纵肋与横隔板交叉构造细节的疲劳破坏模式为焊趾开裂沿纵肋腹板方向扩展;对于研究对象而言,萌生于纵肋与顶板焊接细节焊根并沿顶板厚度方向扩展的疲劳破坏模式为控制结构体系疲劳抗力的主导疲劳破坏模式。     

System reliability models for bridges

There is a need for efficient bridge evaluation procedures. A considerable number of existing bridges in the United States require repair and/or replacement. Accurate estimate of the current strength and the remaining life time is essential for optimum distribution of the available limited resources. The major parameters which determine the structural performance are random variables. Statistical models of load and resistance can be derived from the test data, observations and analysis. For bridge members the reliability can be calculated using this available data, observations and analysis. considerable discrepancy between the reliability level of individual members and the overall bridge reliability. Due to load sharing and redundancies, the actual load-carrying capacity often exceeds the theoretical value. System reliability methods allow us to reveal an actual safety reserve in the structure. This paper summarizes the practical bridge reliability models. Using a special sampling technique, the reliability is evaluated for typical girder bridges.     

Performance of steel bridge deck pavement structure with ultra high performance concrete based on resin bonding

This research investigated a pavement system on steel bridge decks that use epoxy resin (EP) bonded ultra-high performance concrete (UHPC). Through FEM analysis and static and dynamic bending fatigue tests of the composite structure, the influences of the interface of the pavement layer, reinforcement, and different paving materials on the structural performance were compared and analyzed. The results show that the resin bonded UHPC pavement structure can reduce the weld strain in the steel plate by about 32% and the relative deflection between ribs by about 52% under standard axial load conditions compared to traditional pavements. The EP bonding layer can nearly double the drawing strength of the pavement interface from 1.3 MPa, and improve the bending resistance of the UHPC structure on steel bridge decks by about 50%; the bending resistance of reinforced UHPC structures is twice that of unreinforced UHPC structure, and the dynamic deflection of the UHPC pavement structure increases exponentially with increasing fatigue load. The fatigue life is about 1.2 × 10⁷ cycles under a fixed force of 9 kN and a dynamic deflection of 0.35 mm, which meets the requirements for fatigue performance of pavements on steel bridge decks under traffic conditions of large flow and heavy load.     

建安预应力混凝土斜拉桥系统可靠度分析

应用结构可靠性理论,分析计算了桂林建安预应力混凝土斜拉桥各基本构件的失效概率,在此基础上探索性地采用传力树法分析各构件失效与桥梁系统失效之间的关系,推导出预应力混凝土斜拉桥系统可靠度的实用计算方法,可供类似的桥梁结构设计参考。     

Effect of secondary elements on bridge structural system reliability considering moment capacity

Secondary elements such as barriers, sidewalks, and diaphragms may increase the load carrying capacity of girder bridges. This in turn affects reliability. The objective of this study is to evaluate the potential benefit of secondary elements on the system reliability of girder bridges, if these elements are designed with the structural system to participate resisting vehicular live loads. Simple span, two lane structures are considered, with composite steel girders supporting a reinforced concrete deck. For structural analysis, a finite element procedure is developed that combines a grillage model of the bridge deck with solid elements for edge-stiffening effects. Random variables considered are composite girder, barrier, and sidewalk flexural strengths (each in turn composed of many random variables), load magnitude (dead load and truck traffic live load), and live load position. System resistance parameters are estimated with a point integration method. System resistance is evaluated in terms of maximum load carried at ultimate capacity. It was found that the interaction of typical secondary element combinations has a varying effect on system reliability, depending on element stiffness, bridge span, and girder spacing.     

高效求解结构体系可靠度的新方法

传统的结构体系可靠度分析方法主要依赖于结构失效路径的分枝和约界技术,难以识别主要失效模式且结构体系失效概率计算工作量巨大。为了提高结构体系可靠度计算效率,以β-约界法和联合失效概率分枝约界法为基础,提出了一种快速求解结构体系可靠度分析方法。首先利用结构分析原理,推导出结构单元的安全余量函数并求出其对应的失效概率,拆除失效概率最大值对应的杆件并施以虚拟力形成新的结构,然后再对新的结构重新分析。循环上述步骤,直至结构形成机构为止,并利用构件的失效概率计算结构体系可靠度。算例对比研究表明,该方法计算过程简单、计算精度较高,可以获得结构的失效路径,适合于大型结构的体系可靠度计算。     

基于可靠度的评估法在桥梁管理系统中的应用

论述了桥梁管理系统的基本结构及其主要功能关系,介绍了基于结构可靠度理论的桥梁评估方法在桥梁管理系统中的应用,对可靠度评估模型的层次结构进行了分析研究,为该评估法在桥梁管理系统中的实现提供了保证。     

基于改进一次二阶矩法的桥梁颤振可靠性评价

随着以悬索桥和斜拉桥为代表的大跨度柔性桥梁的发展,由风与桥梁的相互作用而引起桥梁颤振稳定问题倍受关注,而在各种随机因素作用下的桥梁颤振可靠性评价也受到了人们的重视.在对传统的一次二阶矩可靠度计算方法改进的基础上,对国内14座大跨度桥梁进行了颤振可靠性评价.通过与Monte Carlo数值模拟结果的对比表明,所提出的改进一次二阶矩方法能够有效提高小失效概率条件下的可靠度计算精度.     

服役砌体结构建筑抗震可靠性向量及加固分析

根据具有中介状态结构可靠性向量理论,认为砌体结构具有"安全-中介-失效"三级工作模式,这里的"中介"即为砌体结构带"故障"工作状态,砌体结构处于3种工作模式的概率组成可靠性向量。基于工程结构全寿命期抗力退化模型,提出了一种适合评价现役砌体结构抗震性能的时变可靠性向量分析方法。以砌体抗剪强度为指标,分别建立了砌体结构的三层次时变可靠性向量计算模型,同时给出了加固砌体结构时变可靠性向量计算的一般方法。文中运用时变可靠性向量分析方法,分析了一栋4层砌体结构,得到了原结构与加固结构墙体、楼层、结构体系三层次可靠性向量,并进行了对比分析。可为砌体结构的抗震性能评价和加固设计提供理论依据。