Spatial variability of damage and expected maintenance costsfor deteriorating RC structures

The paper develops a technique to predict life-cycle costs, using probabilistic information about the likelihood and extent of corrosion-induced cracking to reinforced concrete (RC) structures. The present paper focuses on the likelihood and extent of severe cracking as the criterion for the timing and cost of maintenance. The life-cycle cost and expected maintenance cost considers multiple repairs and various inspection intervals over the service life of the structural element. A repair cost function is also developed. Two common maintenance strategies are considered: repair and rehabilitation. It was found that for a 2% discount rate the benefits of delaying the timing of repairs outweigh the cost of increased extent of damage, for maintenance of a RC bridge deck.     

基于寿命函数的斜拉索系统维修更换策略研究

展开寿命周期内拉索劣化规律和维修更换策略的研究,获得桥梁结构的最优成本-效益比,是缆索桥梁养护维修的重要研究内容之一。根据拉索寿命函数和拉索系统的串并联模型,研究斜拉桥拉索系统失效概率变化即结构劣化的规律,分析全寿命周期内不同维修更换措施对结构失效概率的影响。运用周期成本理论,进一步分析不同维修更换时间和更换策略的经济性。结合一斜拉桥模型,验证了模型的适用性,并且以延长使用寿命和累积维修费用最低为目标,获得该桥的最优维修策略。研究表明,寿命函数和周期成本理结合是确定斜拉桥拉索更换优化策略的有效途径,为工程拉索更换策略提供有益的参考。     

Bridge life-cycle performance and cost: analysis,prediction, optimisation and decision-making

The development of a generalised framework for assessing bridge life-cycle performance and cost, with emphasis on analysis, prediction, optimisation and decision-making under uncertainty, is briefly addressed. The central issue underlying the importance of the life-cycle approach to bridge engineering is the need for a rational basis for making informed decisions regarding design, construction, inspection, monitoring, maintenance, repair, rehabilitation, replacement and management of bridges under uncertainty which is carried out by using multi-objective optimisation procedures that balance conflicting criteria such as performance and cost. A number of significant developments are summarised, including time-variant reliability, risk, resilience, and sustainability of bridges, bridge transportation networks and interdependent infrastructure systems. Furthermore, the effects of climate change on the probabilistic life-cycle performance assessment of highway bridges are addressed. Moreover, integration of SHM and updating in bridge management and probabilistic life-cycle optimisation considering multi-attribute utility and risk attitudes are presented.     

Stochastic life-cycle analysis: renewal-theory life-cycle analysis with state-dependent deterioration stochastic models

For the life-cycle analysis (LCA) of deteriorating engineering systems, it is critical to model and incorporate the various deterioration processes and associated uncertainties. This paper proposes a renewal-theory life-cycle analysis (RTLCA) with state-dependent stochastic models (SDSMs) that describe the deterioration processes. The SDSMs capture the multiple deterioration processes and their interactions through modelling the changes in the system state variables due to different deterioration processes. Then proper capacity and demand models that take the time-variant state variables as input are adopted to fully capture the impact of deterioration processes on the capacity, demand, and other time-variant performance indicators of the engineering system. The SDSMs are then integrated into RTLCA to efficiently evaluate various life-cycle performance quantities such as availability, operation cost and benefits of the engineering system. To implement the proposed formulation, a sampling-based approach is adopted to simulate samples from the relevant probability density functions (PDFs) to estimate the life-cycle performance quantities, while stochastic simulation-based approach is adopted to estimate the time-variant performance indicators needed to inform intervention activities. As an illustration, the proposed formulation is used to analyse the life-cycle performances of an example reinforced concrete bridge subject to deterioration due to corrosion and seismic loading.     

Optimization of bridge maintenance strategies based on structural health monitoring information

Highway bridges are subjected to strength degradation processes. Under budget constraints, it is important to determine the best maintenance strategies. Optimized strategies, based on prediction models, are already considered for the maintenance and operation of highway bridges. Prediction models are updated both in space and time by using non-destructive testing methods. Nevertheless, there is an urgent need for the efficient inclusion of structural health monitoring (SHM) data in structural assessment and prediction models. Indeed, SHM allows keeping strength degradation processes under control and should be included in life-cycle cost models. The lifetime reliability of structures is characterized by survivor functions. The SHM data enable to update the probability density function of time to failure through a Bayesian process. The aim of this paper is threefold: (a) to include SHM data in a bridge life-cycle cost analysis, (b) to determine optimal maintenance strategies based on monitoring information, and (c) to show the benefits of SHM. Optimal strategies are determined considering the cases without and with including monitoring results; the benefit of monitoring is then highlighted. The proposed concepts are applied to the I-39 Northbound Bridge over the Wisconsin River in Wisconsin, USA. A monitoring program of that bridge was performed by the ATLSS Engineering Research Center at Lehigh University.     

基于模糊综合评判的结构寿命周期总费用评估

结构寿命周期总费用评估是实施基于性能的抗震设计的关键问题,其中失效损失期望评估中结构失效概率的计算往往需要多次结构重分析,计算量很大,成为结构寿命周期总费用评估中的一个主要问题。本文利用模糊综合评判理论进行结构寿命周期损失期望的评估,以失效概率方法评估结果为参照,研究了隶属度函数的不同形式、结构不同重要性对模糊评判方法结果的影响,并计算了钢筋混凝土框架算例。结果表明,利用模糊综合评判进行结构损失期望评估,可以在保证一定精度的前提下,大大简化了失效损失期望评估的计算量。     

Risk-based life-cycle maintenance strategies for corroded reinforced concrete buildings located in the region with high seismic hazard

In this study, several developed models have been adopted to investigate deterioration induced by chloride ingress by considering uncertainty in order to estimate the initiation and rate of corrosion. Besides, the structural capacity and serviceability of RC buildings, i.e. the shear capacity, bending strength and width of cracking or spalling of columns and beams with corroded reinforcing bars, were also calculated using simple formulas developed from previous experiments. Based on the information of annual spalling/cracking and failure probabilities, the deterioration risk of an RC building attacked by chloride can be evaluated using the concept of reliability of a series system. In order to find the optimal maintenance plan, probabilistic effect assessment models for repair/retrofit strategies (five repair/retrofit strategies were selected) that consider the recurrence of deterioration in repaired areas and the deterioration proceeding in unrepaired areas were developed in this research. These models reflect the effects of the maintenance strategies on the failure and spalling probability directly and can be used to estimate the life-cycle performance and cost of RC buildings. Finally, on the basis of the minimal life-cycle cost, the optimal life-cycle maintenance strategy can also be identified by using the genetic algorithm; case studies were used to discuss the applicability of this system.     

基于时变可靠度的锈蚀混凝土结构全寿命成本模型

为了分析混凝土结构在氯盐环境下的全寿命周期成本,基于现有氯离子扩散模型和裂缝宽度预测模型,采用MATLAB软件进行Monte-Carlo抽样模拟,建立结构失效概率与可靠度指标的拟合公式。通过研究维护-加固措施对可靠度指标的影响,建立全寿命周期内维护-加固费用计算评估方法,并以混凝土桥梁结构为例计算了全寿命周期维护-加固成本。结果表明:失效概率与可靠度指标可用以失效概率等于0.1为界的分段函数进行描述;维护-加固效果持续时间对结构构件服役年限延长的影响最显著;当保护层厚度取60 mm时,维护-加固阶段费用有明显下降,较保护层厚度取40 mm时减少25%~50%。     

Multiobjective optimisation algorithm for sewer network rehabilitation

Understanding of deterioration mechanisms in sewers helps asset managers in developing prediction models for estimating whether or not sewer collapse is likely. Effective utilisation of deterioration prediction models along with the development and use of life cycle maintenance cost analysis contribute to reducing operation and maintenance costs in sewer systems. This article presents a model for life-cycle maintenance planning of deteriorating sewer network as a multi-objective optimisation problem that treats the sewer network condition and service life as well as life-cycle maintenance cost (LCMC) as separate objective functions. The developed model utilises Markov chain model for the prediction of the deterioration of the network. A multi-objective genetic algorithm is used to automatically locate an appropriate maintenance scenario that exhibits an optimised tradeoff among conflicting objectives. Monte Carlo simulation is used to account for LCMC uncertainties. The optimisation algorithm provides an improved opportunity for asset managers to actively select near-optimum maintenance scenario that balances life-cycle maintenance cost, condition and service life of deteriorating sewer network. A case study is used to demonstrate the practical features of developed methodology.     

基于全寿命环境成本的工程结构维护方案优化

工程结构全寿命过程中存在有害气体、污水和固体废弃物排放等环境问题,但是由其造成的经济损失却很少在结构设计或工程决策过程中予以考虑。为此,将三类污染物排放的防治成本计入工程活动的环境成本中,得到了多种建筑材料、能源消耗、运输方式和建筑机械使用的环境成本。通过将环境成本与经典全寿命成本模型相结合,建立了包含环境成本的全寿命总成本模型。根据所提出的环境成本模型和全寿命总成本模型,以某一沿海高速公路桥梁结构为例,通过设置预防性维护措施和必要性维护措施,对其进行维护方案的多目标优化,分析环境成本对工程决策的影响。并对直接成本和环境成本的不确定性进行了分析,研究了环境成本折现率对环境成本影响。结果表明,在结构优化过程中考虑环境成本能够得到经济效益和环境综合性能更佳的工程方案。     

Capacity loss evaluation of reinforced concrete bridges located in extreme chloride-laden environments

This article provides a comprehensive procedure for the structural performance evaluation and life-cycle cost (LCC) analysis of reinforced concrete highway bridges located in extreme chloride-laden environments. An integrated computational methodology is developed to simulate the chloride intrusion and to estimate the corrosion initiation time. The effects of various influential parameters on the chloride diffusion process are examined and the changes in geometry and material properties of structural members are calculated over the entire life of the bridge. In order to evaluate the global structural degradation due to the corrosion mechanisms, an inventory of bridges with different structural attributes are investigated. The extent of capacity loss is calculated using the moment-curvature and nonlinear static (pushover) analysis. Results of this study are then utilised to find the LCC of bridges. Different inspection and maintenance strategies are considered to minimise the total LCC, which includes the initial construction cost, inspection and maintenance costs and service failure costs. The proposed approach indicates the inspection and maintenance intervals in a way that the inspection and maintenance costs are optimised while the safety of the bridge is ensured.     

Generalized bridge network performance analysis with correlation and time-variant reliability

A novel approach and framework for the analysis of bridge networks is presented. The goal of the analysis is to assess the life-cycle performance of the network and its time-variant reliability. The proposed approach combines three important features that determine its ability to estimate with accuracy and robustness the reliability of a network along its life-cycle.The first one is that the reliability of the individual bridges is modeled as time-variant, due to the deterioration of their structural components. The network performance analysis is repeated for several time instants, with the relative reliability of the bridges. Therefore, the network performance indicators are also time-variant. In this way, the proposed procedure can be used as a basic tool for maintenance planning at the network level.The second asset is that the proposed framework takes into account complex (i.e. “generalized”) network layouts, not necessarily describable using series, parallel or series-parallel models. In fact, when all the possible traffic flows in a network and all the possible trip origins and destinations are considered, it is not feasible, in general, to model the network with a simple scheme. In the present paper, techniques derived from transportation engineering for the traffic flow distribution and assignment are used.The third feature is that the proposed approach considers a correlation structure among the states (in/out of service) of the various bridges of the network. In fact, bridges associated with the same network are likely to share similar characteristics and external loads. Therefore, a correlation structure for the service state of individual bridges is estimated and implemented in the analysis.A case study involving a transportation network with fourteen bridges is presented as a numerical application.     

网壳结构寿命周期总费用的计算方法研究

现代结构系统在灾害中产生巨大经济损失的特点,使人们意识到在结构设计之初就对结构的寿命周期总费用进行有效评估、并反过来指导工程设计具有重要意义。对网壳结构寿命周期总费用的计算方法进行研究,分别提出初始造价、维护费用和失效损失的计算公式,并考虑寿命周期内网壳结构可能受到的荷载发生的概率,建立寿命周期总费用的计算方法,编制网壳结构寿命周期总费用的计算程序。通过一具体的网壳结构工程算例验证上述方法和程序的有效性。研究结果表明,网壳结构初始造价的追加投资会由于结构使用过程中失效损失费用的减小而得到补偿,而寿命周期总费用最小正是结构设计的最优状态,按照现行规范设计方法得到的结构配置方案不一定是寿命周期总费用最小的方案。     

Risk assessments of long-span bridges considering life-cycle cost concept and near-fault ground motion effect

The influence of the near-fault ground motion on the response of long-span bridges must be considered as a critical factor for seismic design because the response indicates different aspects from existing earthquake characteristics. Also, it is important to note that the safety index for the risk assessment of long-span bridges is determined based on the minimum expected life-cycle cost E(LCC). In this study, earthquake characteristics are analyzed by creating elastic and inelastic response spectrums with actual measurement records (Chi-Chi earthquake records) and then the numerical analysis of the long-span bridge in Namhae, Korea is performed according to the increase and reduction of the member stiffness based on the standard design., the reliability evaluation of the long-span bridge considering aleatory uncertainties is performed on the basis of the combined results of static analysis and seismic response analysis. Also, the minimum LCC is estimated based on failure probabilities by the different alternative design. Because of epistemic uncertainties, the results of reliability evaluation and the LCC of optimal design are selected as random variables; the safety index, failure probability and expected minimum LCC are re-evaluated with regard to critical percentage values for a risk-averse design of the long-span bridge, and are presented graphically using cumulative percentages. It is, therefore, expected that this study will provide the basic information for the risk assessment and optimal design method in performing seismic design of the long-span bridge considering earthquake characteristics.     

Maintenance plan optimization system for existing concrete bridge groups

In the present study a comprehensive decision support system is developed for the formation of maintenance strategies with/without annual budget limitations. This system is based on life-cycle cost analysis of an entire bridge inventory, which comprises part of a highway network. The formulation of an optimum bridge maintenance program for an entire stock of bridge structures has been impeded historically by insufficient information concerning the existing structural conditions. The capability of this optimization system was enhanced by employing Genetic Algorithms in the formation of semi-optimal solutions. This system was tested by employing to formulate a set of semi-optimal bridge management programs for a set of selected existing bridges representing a typical al bridge inventory.     

Comparative life-cycle analysis of steel-concrete composite bridges

Competitiveness of steel construction and, in particular, steel and composite bridges, requires a broader view that encompasses the concepts of sustainability and life-cycle assessment in parallel with the classical structural and geotechnical issues. Also, from the economical viewpoint, the progressive transfer of operational duties from the National Road Authorities to private companies in the context of design, build and operate contracts, reinforces the need for an integrated approach.It is the purpose of the present paper: (i) to present an integrated methodology for a life-cycle and sustainability analysis (LCA and LCCA); and (ii) to apply such an integrated approach to a case study of a composite bridge. The proposed approach, besides structural considerations, contemplates environmental aspects (energy consumption, raw materials, and environmental impacts), economical aspects and a brief discussion of degradation and maintenance aspects. The case study consists of a three-span continuous bridge with spans of 27.2 m + 35.0 m + 27.2 m, thus totalling 89.40 m. Finally, some comparisons are presented between alternative solutions.     

Cost analysis for maintenance and seismic retrofit of existing bridges

The work describes an extensive cost analysis for maintenance and seismic retrofit of typical existing road bridges, based on integrated procedures for assessment of state and seismic vulnerability. In particular, visual inspections to evaluate total sufficiency ratings and a simplified seismic assessment were carried out for each structure, according to procedures proposed in earlier works. The results were then used as input data for statistical analysis, to calibrate new unit maintenance, seismic retrofit and total cost equations. The procedure was applied to a stock of bridges in the province of Vicenza, north-east Italy. The results will allow public authorities and private managing companies to estimate economic indicators regarding the extent of resources required for bridge maintenance and retrofit in areas subject to seismic events.     

Computational framework for risk-based planning of inspections,maintenance and condition monitoring using discrete Bayesian networks

This paper presents a computational framework for risk-based planning of inspections and repairs for deteriorating components. Two distinct types of decision rules are used to model decisions: simple decision rules that depend on constants or observed variables (e.g. inspection outcome), and advanced decision rules that depend on variables found using Bayesian updating (e.g. probability of failure). Two decision models are developed, both relying on dynamic Bayesian networks (dBNs) for deterioration modelling. For simple decision rules, dBNs are used directly for exact assessment of total expected life-cycle costs. For advanced decision rules, simulations are performed to estimate the expected costs, and dBNs are used within the simulations for decision-making. Information from inspections and condition monitoring are included if available. An example in the paper demonstrates the framework and the implemented strategies and decision rules, including various types of condition-based maintenance. The strategies using advanced decision rules lead to reduced costs compared to the simple decision rules when condition monitoring is applied, and the value of condition monitoring is estimated by comparing the lowest costs obtained with and without condition monitoring.     

Seismic fragility increment functions for deteriorating reinforced concrete bridges

Fragility increment functions are developed to estimate the seismic fragility of reinforced concrete (RC) bridges subject to deterioration due to the onset and progression of corrosion of the reinforcement. For each mode of failure considered, the fragility at time t of a deteriorating bridge is obtained by multiplying the initial fragility of the undeteriorated bridge by a corresponding increment function expressed in terms of the environmental conditions, the original material properties, time, a measure of the seismic demand, and a set of unknown model parameters. The developed increment functions account for the effects on the fragility estimates of the loss of the reinforcement and of the increasing uncertainty over time. As an application, the developed increment functions are used to estimate the seismic fragility of an example RC bridge. The proposed fragility increment functions are useful to estimate the fragility of deteriorating bridges without any extra reliability analysis once the fragility of the undeteriorated bridge is known. In particular, the proposed fragility increment functions can be used to assess the time-variant fragility of bridges for applications such as reliability-based design, life-cycle cost analysis, and risk analysis.     

Bridge Annual Maintenance Prioritization under Uncertainty by Multiobjective Combinatorial Optimization

Abstract:   Bridge managers are facing ever-increasing tasks of prioritizing limited budgets to cost-effectively maintain normal functionality of a huge inventory of deteriorating civil infrastructures such as highway bridges over the life cycle. A satisfactory maintenance planning scenario should meet managers' specified requirements for the optimum balance between whole-life costing and structural performance. This article presents a general computational procedure to prioritize on an annual basis maintenance efforts for deteriorating reinforced concrete bridge crossheads over a designated time horizon. Within each year, none or one of the available maintenance types with different performance improvement capabilities could be applied and the time of application for any maintenance intervention is considered to be uniformly distributed within a 1-year time interval. Effects of uncertainties associated with bridge crosshead deterioration processes with and without maintenance interventions are considered by means of Monte Carlo simulation to predict probabilistically structural performance and life-cycle maintenance cost. The resulting combinatorial optimization problem is automated by a multiobjective genetic algorithm. It produces a group of different sequences of annualized maintenance interventions that lead to optimized tradeoff among condition, safety, and life-cycle cost objectives. This enables bridge managers to determine a preferred annual maintenance prioritization solution by comparing different alternatives.