Stochastic analysis of fatigue of concrete bridges

A novel method is proposed in this work for the assessment of the remaining fatigue life and fatigue reliability of concrete bridges subjected to random loads. The fatigue reliability of a bridge is a function of the fatigue damage accumulation; a stochastic fatigue damage model (SFDM) with physical mechanism is introduced for deriving the fatigue damage process. In order to implement the probabilistic analysis, based on the probability density evolution method (PDEM), the generalised density evolution equation (GDEE) for the remaining fatigue life is developed. Finally, a prestressed concrete continuous beam bridge located in China is illustrated. The random fatigue load acting on the bridge is modelled as the compound Poisson process, and the simulation of the random load uses the stochastic harmonic function (SHF) method. To simplify the reliability analysis, an equivalent constant-amplitude (ECA) load process is introduced based on energy equivalence. By employing SFDM, the finite element analysis of the bridge under the fatigue loading is performed. Then, the fatigue damage accumulation process of the bridge under the fatigue loading is obtained. Through solving the probability density evolution equation for the remaining fatigue life, the probability density functions (PDFs) of the remaining fatigue life evolving with time is obtained. The fatigue reliability is then calculated by integrating the PDF of the corresponding remaining life.     

Fatigue reliability analysis of steel bridge details based on field-monitored data and linear elastic fracture mechanics

This article presents the fatigue reliability analysis of welded details of a 40-year old steel box-girder bridge, based on the linear elastic fracture mechanics (LEFM) and the long-term stress monitoring. The fatigue crack growth is described by using the LEFM, based on which the ultimate limit state is established as a function of the crack size. Effective stress ranges are obtained from daily stress range histograms, and lognormal probability density functions (PDFs) are used to model the uncertainties in stress data. Details at discontinuous backing bar splices, which have not been explicitly listed in the American Association of State Highway and Transportation Officials (AASHTO) specification, and the welded details at the base of bridge bents are evaluated on their fatigue reliabilities. It is found that the backing bar splice detail may have high fatigue reliability, considering that low stress ranges and small number of cycles occurred in the monitoring period. For the weld detail at the base of bent, stress ranges higher than the constant amplitude fatigue limit (CAFL) existed, and currently the reliability indexes are all below the target value, showing that maintenance or retrofit actions may be required. For the details at the upper base of bridge bents, sufficient reliabilities are expected throughout the service life.     

Reliability-based fatigue design of wind-turbine rotor blades

A probabilistic model for analysis of the safety of a wind-turbine rotor blade against fatigue failure in flapwise bending is presented. The model is based on a Miner's rule approach to cumulative damage and capitalizes on a conventional S–N curve formulation for fatigue resistance in conjunction with a new ‘distorted Weibull' distribution for representation of wind-induced bending moment ranges. The model accounts for inherent variability and statistical uncertainty in load and resistance, and model uncertainties are also included. The model is applied to an analysis of the reliability of a site-specific wind turbine of a prescribed make. A 20-year design lifetime is considered. The probability of fatigue failure in flapwise bending of the rotor blade is calculated by means of a first-order reliability method. It is demonstrated how the reliability analysis results can be used to calibrate partial safety factors for load and resistance for use in conventional deterministic fatigue design.     

Fatigue reliability analysis for the crack propagation compared with LRFD specification

In this study, a fatigue reliability is assessed taking into account the uncertainties in load and resistance of a steel specimen, in which fatigue crack propagates. The results of the deterministic fatigue crack propagation has been compared with AASHTO LRFD specification. A response surface method (RSM) combined with an advanced first order second moment method has been applied in order to assess the probability of the remaining life of the specimen under cyclic load as a function of crack length. For composing limit state functions, the stress ranges, stress intensity factor and the remaining life was selected as input random variables for the developed fatigue-reliability analysis program. The choice of Bayesian Belief Nets (BBNs) as a tool for assessing uncertainties in resistant component of a limit state function allows an extended probabilistic assessment for the resultant fatigue life of a target specimen, in terms of resistant components of stress range, stress intensity factor, and material property. Additionally, fragility curve models are proposed to compare the probabilistic fatigue life as describing the probability of a structure to suffer a given damage level when it is subject to a given fatigue life. The proposed integrated stochastic models can significantly contribute to the design and maintenance of infra-structures, demonstrated in the numerical example in terms of damage index with the probability of exceedance the considered damage levels.     

既有铁路混凝土梁疲劳与承载力可靠性评估

将列车荷载视为随机过程,考虑既有铁路混凝土梁的抗力劣化,采用时变的可靠性计算方法对川黔线一座铁路混凝土梁剩余使用期内承载力失效概率进行了计算.顾及到铁路混凝土梁的钢筋疲劳,对该梁随时间变化的疲劳可靠性指标进行了计算.综合这两种失效模式对桥梁安全性的影响,对该梁的体系可靠性进行了评估,预测了该梁的剩余使用寿命,进而提出了整改措施.     

Proof load testing for bridge assessment and upgrading

Bridge deterioration with time and ever increasing traffic loads raise concerns about reliability of aging bridges. One of the ways to check reliability of aging bridges is proof load testing. A successful proof load test demonstrates immediately that the resistance of a bridge is greater than the proof load. This reduces uncertainty in the bridge resistance and so increases the bridge reliability. The paper considers a reliability-based calibration of intensities of proof loads for aging bridges to verify either an existing or increased load rating taking into account possible bridge deterioration. Intensities of proof loads are calibrated based on a consistent target reliability index. The influence of test risk, dead to live load ratio, and uncertainties associated with dead and live loads and bridge resistance is considered. The results presented in the paper relate to short and medium span bridges.     

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.     

随机风荷载作用下的桥梁颤振可靠性分析

基于现有的结构可靠性理论,通过极限状态方程建立起桥梁颤振的可靠性分析模型,并提出了用以确定桥梁颤振稳定失效概率的计算方法。其中颤振可靠性分析模型中的极限状态方程以桥梁颤振临界风速为结构抗力变量,以桥址处随机风速为荷载变量。本文采用一次二阶矩理论的几种失效概率计算方法对主跨602m的上海杨浦大桥进行了颤振失效概率计算。     

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.     

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.     

Reliability-based strength limit state for steel railway bridges

Railway bridges require special attention to provide safe and economical service. To assess the reliability of a structure, all critical parameters need to be specified. Load and resistance are random in nature; hence, the probabilistic approach is the best method for accurate evaluation of the performance of a bridge. In this study, identification of critical parameters was conducted on a typical through-plate girder, riveted, open deck railway bridge. This type of structure is a weakest link system. In such a system, the failure of one component can lead to failure of the entire structural system. This research involved identification of the basic load and resistance parameters and the development of analytical procedures for modelling the structural behaviour. The finite element method (FEM) was used to investigate the structural performance characteristics of the evaluated bridge. A three-dimensional structural model was developed to determine stress distribution in the members and connections. Based on the results of FEM analysis, the reliability indices were calculated for critical components.     

Research on reasonable value of target reliability index for steel main girder of cable-stayed bridge considering durability

Abstract

This article studies the relationship between the target reliability index and the design life of the main girder of a long-span cable-stayed bridge to provide a theoretical basis for the design of steel girders for such an application. The changes of the bending section modulus under atmospheric corrosion and the residual ultimate stress of the section of a steel box girder under alternating loads are discussed. A resistance attenuation function for a steel girder of a cable-stayed bridge to predict the resistance change of a steel box girder over the service period is proposed, and the change characteristics of the time-varying reliability index of a steel box girder of a cable-stayed bridge are studied. By analysing the relationship between the time-varying reliability index and the evaluating benchmark value of the reliability index, the time point of maintenance and reinforcement is predicted. Based on the change over time of the difference between the time-varying reliability index and the evaluating benchmark value of the reliability index, the relation function between the target reliability index and the service lifetime of a bridge considering resistance attenuation are provided.     

既有铁路钢筋混凝土梁桥动态可靠性评估

介绍了既有桥梁结构的动态可靠性分析方法,提出了桥梁的恒载概率模型、活载概率模型及抗力概率模型,并对可靠度计算方法中的验算点法进行了介绍。以一座既有铁路钢筋混凝土梁桥为工程背景,计算了该桥的活载效应统计参数、恒载效应统计参数及抗力统计参数等,利用验算点法计算了桥梁结构构件的可靠度指标,又采用PNET方法分析了整个桥梁体系的可靠性,最后给出了桥梁的可靠性评估结果。结果显示动态可靠性评估应用于铁路钢筋混凝土梁桥可以得到较好的评估结果。     

格构式桅杆顺风向风振疲劳可靠性分析

本文首先研究了桅杆风振疲劳分析的风荷载、风振响应和疲劳损伤计算 ,并根据风洞试验结果得到了带宽修正系数 ,采用等效窄带法计算桅杆的疲劳寿命。通过引入三个对数正态分布随机变量来考虑桅杆疲劳分析过程中的不确定性 ,用Wirsching模型计算了一个格构式桅杆的疲劳可靠性 ,算例表明用可靠度指标对应桅杆疲劳寿命的表达形式更有参考意义     

Reliability evaluation of reinforced concrete beams

The purpose of this paper is to evaluate the time-invariant reliability of reinforced concrete beams designed under the provisions of the ACI Building Code. A wide range of practical design situations is considered. The beams are subjected to bending, shear, and torsion. The interaction between shear and torsion is considered via an elliptical failure surface defined in the shear-torsion stress space. No interaction is assumed between flexural resistance and resistance in both shear and torsion. Representative statistics and appropriate probability distributions of the basic resistance and load variables are selected from previous related work. The reliability analysis is performed using modern reliability methods, in which the formulation of the limit-state functions is consistent with the underlying design criteria. Reliability indices for various failure modes are compared and a system reliability analysis is performed to include all failure modes. It is found that the reliability indices are most sensitive to live load, model uncertainties, and material strengths. For the failure modes considered, the reliability indices are found to be rather insensitive to design parameter values, indicating that the ACI Building Code achieves its desired objective of uniform reliability across a wide range of design situations.     

Time-variant reliability profiles for steel girder bridges

Evaluation of existing steel bridges becomes more important due to natural aging, increasing load spectra, deterioration caused by corrosion, and other problems. In the result, bridge structures exposed to aggressive environmental conditions are subjected to time-variant changes of resistance. Therefore, there is a need for evaluation procedures for an accurate prediction of the load carrying capacity and reliability of bridge structures, in order to make rational decisions about repair, rehabilitation, and expected life-cycle costs. The objective of this paper is to develop time-variant reliability models for steel girder bridges. Traditional methods based on deterministic analysis do not reveal the actual load carrying capacity of the structure. The proposed approach is based on reliability analysis of components and structural systems. The study involves the selection of representative structures, formulation of limit state functions, development of load models, development of resistance models for corroded steel girders, development of the reliability analysis method, reliability analysis of selected bridges, and development of the time-dependant reliability profiles including deterioration due to corrosion. The results of the study can be used for a better prediction of the service life of deteriorating steel girder bridges, and development of optimal reliability-based maintenance strategies.     

Fatigue reliability assessment of a historic railway bridge designed by Gustave Eiffel

The evolution of the railway traffic during the last century is studied as preliminary step towards the estimation of the remaining service life of a historical bridge. The selected case study concerns the El Ourit Bridge, designed in 1889 by Gustave Eiffel and located close to the town of Tlemcen, in Algeria. A finite element model of the structure is built and the response of the bridge to train-crossing loads is numerically evaluated with the purpose of identifying the element most affected by stress variations. The Palmgren–Miner accumulation model is used to quantify the fatigue damage in this element. A limit state function based on this criterion is formulated; then, a fully probabilistic approach is adopted by assuming that the stress amplitude, the fatigue strength and the damage threshold value play the role of random variables. The obtained results are discussed in order to evaluate the residual service life of the bridge.     

腐蚀环境下钢筋混凝土结构疲劳可靠度的分析方法

疲劳分析与验算是承受反复荷载作用结构设计的重要内容之一,相应的可靠度为疲劳可靠度.当结构处于腐蚀环境时,由于腐蚀介质的侵蚀,结构疲劳性能的降低要比静态性能的降低明显.本文研究了腐蚀环境下钢筋混凝土结构的疲劳可靠度问题,提出了相应的计算方法.计算表明,依赖于钢筋的锈蚀程度,钢筋混凝土结构的疲劳可靠度有不同程度的下降.     

大跨度斜拉桥智能可靠度评估方法研究

针对既有大跨度斜拉桥的评估管理系统中的可靠度评估问题,提出了基于RBF网络与Monte Carlo结合的可靠度评估方法。建立了招宝山大桥快速分析的RBF网络模型,网络训练样本按均匀设计方法,考虑几何非线性因素由ANSYS软件分析得到。对运营期的招宝山大桥进行了两类失效模式,三种极限状态下的可靠度评估,并分析了不同活载模式、不同功能函数及不同检测期对可靠度评估结果的影响。分析表明:基于RBF-MC的可靠度分析方法具有速度快、精度高的优点,并能同时计算多极限状态下的结构可靠指标,特别适合在基于可靠度的桥梁管理系统中采用;活载布置方式、选取的功能函数均影响可靠度评估的结果,招宝山大桥不同检测期可靠度水平变化不大,且均处于安全可靠状态。     

Reliability analysis of prestressed concrete bridge girders: comparison of Eurocode, Spanish Norma IAP and AASHTO LRFD

The objective of this paper is to compare the reliability level of prestressed concrete bridge girders designed using three codes: Spanish Norma IAP-98 (1998), ENV 1991-3 Eurocode 1 (1994), and AASHTO LRFD (1998). Typical precast girders used in Spain are considered. Load and resistance parameters are treated as random variables. The statistical parameters are based on the available literature, test data and load surveys. Reliability indices are calculated by iterations. The results indicate that Eurocode is more conservative than the other two codes, and AASHTO LRFD is the most permissive code.