Optimal economic strategies with considerations of reliability of fatigue-sensitive structural systems

The integrity of structural systems relative to fatigue and fracture can be ensured by a rational program which coordinates a design, inspection, and repair process to minimize life-cycle costs in the context of a reliability analysis which treats uncertainties in fatigue design factors and inspection performance. The features of the process are summarized, and a simple illustration is provided. Research needs relative to this problem, delineated herein, are principally those of developing reliability models of material behavior, obtaining the data to compute parameter values, and developing efficient computational methods for fatigue reliability and maintainability analysis of “large”-scale series and redundant structures.     

Risk based inspection planning for structural systems

Risk based inspection (RBI) planning for engineering systems is considered. Due to difficulties in formulating computationally tractable approaches for RBI for systems, most procedures hitherto have focused exclusively on individual components or have considered system effects in a very simplified manner only. Several studies have pointed to the importance of taking systems effect into account in inspection planning. Especially for large engineering systems it is not possible to identify cost optimal solutions if the various types of functional and statistical dependencies in the systems are not explicitly addressed. Based on new developments in RBI for individual components, the present paper presents an integral approach for the consideration of entire systems in inspection planning. The various aspects of dependencies in the systems are presented and discussed, followed by an introduction to the decision problems encountered in inspection and maintenance planning of structural systems. It is then shown how these decision problems can be consistently represented by decision theoretical models. The presentation of a practical procedure for the inspection planning for steel structures subject to fatigue concludes the paper.     

Role of non-destructive evaluation in time-dependent reliability analysis

Uncertainties exist in the ability of nondestructive evaluation (NDE) methods to detect and measure flaws. Probabilistic methods can be used for characterizing these uncertainties and for updating flaw sizes predicted from stochastic fatigue crack growth analysis. The impact of NDE on condition assessment and reliability of structures, in which fatigue crack growth is occurring as a result of cyclic random service loads, is examined. Examples of probability-based condition assessment using magnetic particle or ultrasonic inspection and its potential impact on time-dependent fatigue reliability analysis are illustrated for a steel miter gate at a lock operated by the US Army Corps of Engineers.     

Evaluation of crack growth in miter gate weldments using stochastic fracture mechanics

Many of the welded-steel miter gates found in the lock and dam system in the inland waterway system in the United States have been in service for decades and are experiencing varying degrees of degradation, primarily from fatigue and corrosion. This paper presents a finite element-based probabilistic method for assessing fatigue damage in existing miter gate structures, synthesizing several recent research developments in structural reliability for the analysis of a practical engineering problem. Analyses of miter gate structural performance revealed that the fatigue limit state often is more significant than is traditionally assumed by designers. The results of a comprehensive stochastic fatigue analysis of two gates emphasized the importance of fabrication and inspection quality control in minimizing fatigue damage in service. To support planning of inspection intervals, order statistics were used to predict the time to early fatigue failures in a structure with a number of similar weld details. This study demonstrates that stochastic fatigue analysis can be used as a practical tool for assessing the fatigue performance observed in some miter gates and for inspection and maintenance planning. It also was found that poor fatigue performance can be mitigated by modest improvements in detailing practices and inspection methods, rather than by costly changes in design practices.     

Dauerhaftigkeit der Verschlüsse von Schleusen und Wehranlagen

Durability of the gates of locks and weir plants. Hydraulic steel constructions are special steel structures. They have a high relevance for the operability and bearing capacity of a water‐structural plant and are subject to special requirements and operating conditions. Therefore high demands are made on their durability. Due to the immersion medium “Water” the steel structures of the gates of shiplocks and movable weirs are exposed to corrosion hazards exceedingly. Gates of ship locks are stresses by fatigue additionally. Concerning the steel structures of weirs corrosive, abrasive and/or hydrodynamic effects dominate. An overview will be given which methods and possibilities are used to achieve an appropriate durability during the intended service life under these circumstances. In this context the importance of a regular structure‐maintenance will be shown too. Furthermore new innovative gate structures may offer advantages with regard to fatigue strength, simplified maintenance and inspection possibilities and favorable corrosion protection characteristics.     

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.     

Reliability assurance for fatigue crack growth by repeated in-service inspections

The effect of repeated in-service inspections on the reliability degradation due to fatigue crack growth is investigated based upon a stochastic fracture mechanics. The random loading stress and the random growth resistance are simultaneously taken into account in the stochastic crack growth model. A method is first presented for evaluating the failure probability under inspection plans with prespecified intervals, on the assumption that the component is exchanged when cracks are detected. The results are then numerically applied to investigate how the reliability of structures behaves under repeated ultrasonic inspections. It is clarified that inspection policy and the diffusive effect in the crack growth process significantly affect the behaviors of the reliability degradation.     

在役钢吊车梁基于疲劳动态可靠度的维修加固决策

对在役钢结构吊车梁进行定期、不定期的检查是避免发生疲劳失效的最有效方法。从经济的观点要求维护方法的费用最小 ,同时还应满足最小的安全指标。基于疲劳动态可靠度 ,对在役钢结构吊车梁的维修加固策略进行了探讨 ,考虑维修加固效益和维修加固后的经济影响 ,提出了以疲劳动态可靠度为约束 ,以维修加固总效益为目标函数的维修加固优化决策模式 ,并通过某钢厂圆弧端吊车梁的维修加固实例进行验证。可为工业建筑吊车梁的设计、管理和维护提供依据。     

Reliability analysis and inspection updating by stochastic response surface of fatigue cracks in mixed mode

The analysis of engineering structures under fatigue crack growth aims at ensuring an appropriate reliability level over the entire operational lifetime. This paper deals with a new approach, namely the Stochastic Response Surface, to couple finite element analysis and reliability methods. The stochastic collocation method provides an explicit expression of the limit state function related to fatigue failure. This expression is used in first and second order reliability methods in order to compute the failure probability at a given structural age. When inspection is carried out, the structural reliability can be easily updated in terms of the observed crack length. Two numerical applications dealing with fatigue crack growth are presented to illustrate the proposed method, showing its performance in terms of numerical efficiency and accuracy.     

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.     

LRFD for assessment of deteriorating existing structures

The deterioration of infrastructures is a widespread problem in many countries. In order to assess such structures for continued future service, simple and practical tools need to be developed for evaluating the time-dependent reliability and performance of the structures. This paper describes the concept of a resistance reduction factor due to degradation of a component to approximate a time-dependent reliability problem as a time-independent one. With the factor the time-varying resistance can be equivalently replaced with a time-invariant resistance, and load and resistance factors can be determined for the assessment applying simple AFOSM. An approximation method to determine the factor is proposed, and a numerical example shows that the target reliability level can be achieved fairly accurately using an approximate reduction factor. It is also demonstrated that the approximation method can be applied to estimate a resistance reduction factor including the cases when the strength of a component is restored to some extent by means of inspection and repair, and, accordingly, to evaluate the effect of inspection and repair on the reliability of the component.     

Fatigue analysis of offshore platforms with uncertainty in foundation conditions

Foundation flexibility is an important consideration, in designing offshore structures against fatigue, since it has a significant effect on the system's dynamic response. However, a considerable amount of uncertainty is expected in the estimation of foundation flexibility due to the natural nonhomogeneity of the soil as well as laboratory and in-situ testing errors. The proposed method explicitly uses of the statistical nature of uncertainty in the soil stiffness to estimate the variability in the instanteneous and fatigue response using the First-Order Second Moment technique, with emphasis on uncertainties in the dynamic shear modulus along with random wave loading. Uncertainties in the response are estimated considering the randomness in the eigen values, eigen vectors, and the mechanical transfer function. Fatigue life is estimated at different levels of uncertainty for the dynamic shear modulus. It is observed that the uncertainty in the dynamic shear modulus of the soil has more significant effect on the fatigue life of the joints close to the base. The variability in the fatigue response increases with a reduction in the mean dynamic shear modulus. The response is more sensitive to changes in the dynamic shear modulus at its lower values.     

Improved Bayesian network configurations for probabilistic identification of degradation mechanisms: application to chloride ingress

Probabilistic modelling of deterioration processes is an important task to plan and quantify maintenance operations of structures. Relevant material and environmental model parameters could be determined from inspection data; but in practice, the number of measures required for uncertainty quantification is conditioned by time-consuming and expensive tests. The main objective of this study was to propose a method based on Bayesian networks for improving the identification of uncertainties related to material and environmental parameters of deterioration models when there is limited available information. The outputs of the study are inspection configurations (in space and time) that could provide an optimal balance between accuracy and cost. The proposed methodology was applied to the identification of random variables for a chloride ingress model. It was found that there is an optimal discretisation for identifying each model parameter and that the combination of these configurations minimises identification errors. An illustration to the assessment of the probability of corrosion initiation showed that the approach is useful even if inspection data are limited.     

Wind and structural modelling for an accurate fatigue life assessment of tubular structures

Based on the joint probability with regard to wind speed and its main direction, the current paper presents a practical and efficient approach for calculating wind induced fatigue of tubular structures, the effects of the wind direction, across wind and wind grid size on the high cycle fatigue of the structure are addressed. In each time step of the dynamic response calculation, the large deformation effects and the wind induced drag forces due to the updated structural deformations are taken into account. It is found that, the directional wind effects on the fatigue damage mainly depend on the orientation of the structure, the location and the support condition of the selected joints, and the relative probability of occurrence for the high winds speed in each direction, etc. Furthermore, the across wind components are proved to be a significant contributor on the fatigue damage and cannot be ignored. The fatigue damage is also found to be rather sensitive to the wind grid size for generating the wind fields. It is also concluded that vibration of each individual member interacts with the global dynamic response and the wind loading, and a fatigue check should therefore be against both individual member and global response. The wind fatigue calculation procedure presented in the current paper has the merit of reducing uncertainties without degrading a required safety level, this may lead to a positive economic impact with regard to construction and maintenance costs. It has been applied on quite a few industry and research projects and can be widely applied on the similar study of structures.     

Evidence-based framework for real-time life-cycle management of fatigue-critical details of structures

Ship structures are subjected to repetitive wave loads that can lead to fatigue damage. Accumulation of fatigue damage may eventually result in structural failure. In order to mitigate fatigue hazard to ship structures, timely inspections and maintenance actions must be planned during their life-span. As delays in the process of decision-making could result in the increase of the risk of failure, decision-supportive frameworks working in a real-time fashion are extremely important. In this paper, a life-cycle management framework for fatigue-critical details is proposed on the basis of Dynamic Bayesian Network (DBN) and Influence Diagram (ID). The proposed framework, established based on a stochastic fatigue crack growth model, leverages exact inference and discretisation of continuous random variables to enable real-time Bayesian updating and utility-based decision-making. Compared with previous life-cycle management studies, the new framework is capable of making decisions regarding different inspection techniques and appropriate repair actions in a holistic manner. The relatively simple structure of DBN and ID also makes the proposed framework especially attractive to stakeholders and practitioners, who may have limited knowledge of statistics, Bayesian updating and utility theories.     

Probabilistic characterisation of metal-loss corrosion growth on underground pipelines based on geometric Brownian motion process

This article describes a geometric Brownian motion process-based model to characterise the growth rate of the depth of corrosion defects on underground steel pipelines based on inspection data subjected to measurement uncertainties. To account for the uncertainties from different sources, the hierarchical Bayesian method is used to formulate the growth model, and the Markov Chain Monte Carlo simulation techniques are used to numerically evaluate the probabilistic characteristics of the model parameters. The growth model considers the bias and random scattering error associated with the in-line inspection (ILI) tool as well as the correlations between the random scattering errors associated with different ILI tools. The application of the growth model is illustrated through an example involving real ILI data collected from an in-service pipeline in Canada. The results indicate that the model in general can predict the growth of corrosion defects reasonably well. The proposed model can be used to facilitate the development and application of reliability-based pipeline corrosion management.     

Coupled reliability model of biodeterioration, chloride ingress and cracking for reinforced concrete structures

Maintaining and operating civil infrastructure systems has been recognized as a critical issue worldwide. Among all possible causes of safety reduction during the structural lifetime, deterioration is particularly important. Structural deterioration is usually a slow time-dependent process controlled by safety and operation threshold specifications. This paper presents a model of RC deterioration by coupling biodeterioration (i.e., chemical, physical and mechanical action of live organisms), steel corrosion, and concrete cracking. The final purpose of the model is to compute the reduction of the concrete section and the area of steel reinforcement in order to assess the change of structural capacity with time. Given the uncertainties in both the parameters and the model, the probabilistic nature of loads, the material properties and the diffusion process are taken into account to evaluate structural reliability. The model is illustrated with an example where the inelastic behavior of a pile subject to random loading is considered. The results of the analysis have shown that the effect of biodeterioration on the structural performance is significant and can cause an important reduction of its lifetime. On the whole, the paper states that modeling the effects of biodeterioration in RC structures should be included as part of infrastructure planning and design, especially, when they are located in aggressive environments.     

Probabilistic properties of thin-walled elements

Thin-walled structures are relatively complicated structural systems governed by many parameters. These include the dimensions, the material properties and imperfection measures. In principle all of these are not known with certainty at the design stage, and even after construction some degree of uncertainty remains.

The present paper reviews briefly how such uncertainties are considered in modern structural reliability theory to estimate nominal probabilities of failure. An example application will be given to illustrate the process of estimating the probability density function for the failure stress of stiffened plates subject to axial forces.     

Reliability-based management of inspection,maintenance and repair of offshore structures

Development of reliability-based management of inspection, monitoring, maintenance and repair (IMMR) of various types of offshore structures is described, with a focus on management of hull damage due to crack growth and corrosion. Operational experiences with respect to degradation of various types of offshore structures are summarized. The interrelation between design criteria and IMMR is emphasized. Explicit design for robustness in terms of an accidental collapse limit state and monitoring by the use of the leak before break principle to identify damage are highlighted. It is shown how design for robustness, choice of inspection method and scheduling as well as repair strategy, need to be implemented to obtain an acceptable risk for various types of offshore structures. Finally, the particular features of reliability based structural reassessment for extension of the service life, are briefly outlined and exemplified.