Improvements can be made to importance sampling by recognising some of the essential features of the time-independent structural reliability problem. Thus non-interesting regions in the integration domain can be deleted from consideration using a priori information and updating techniques. These can also be used to obtain the point(s) of maximum likelihood, a central parameter for importance sampling in cartesian co-ordinates.
Data for the mass loss of a variety of magnesium alloys as a function of an exposure period show that corrosion loss follows bimodal trending with time for different exposure environments, with both laboratory and field supporting these findings. For datasets sufficient to discriminate bimodal behavior, the instantaneous rate of corrosion at the commencement of the second mode is (close to) four times the instantaneous rate of corrosion at the end of the first mode (i.e., through the transition period). This observation is consistent with the theoretical relative diffusivities of oxygen and hydrogen through the corrosion product layer as it exists during the transition period. These findings support the notion that the bimodal model has corrosion in mode 1 rate-controlled by the cathodic oxygen reduction reaction and the inward diffusion of oxygen while in mode 2 corrosion is rate-controlled by the cathodic hydrogen evolution reaction and the outward diffusion of hydrogen. Similar findings have been made previously for various ferrous and other alloys and thus throws new light on the development of corrosion of magnesium alloys. It also provides reasons for measurements of hydrogen evolution and electrochemical techniques underestimating magnesium corrosion rates. A new procedure for combining these is proposed.
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The ‘ensemble’ up-crossing rate technique consists of averaging the rate at which a random load process up-crosses a deterministic barrier level over the resistance distribution at successive time points. Averaging over the resistance makes the assumption of independent up-crossings less appropriate. As a result, first passage failure probabilities may become excessively conservative in problems with other than extremely low failure probabilities. The ensemble up-crossing rate technique has a significant potential in simplifying the solution of time variant reliability problems under resistance degradation. However, little is known about the quality of this approximation or its limits of application. In the paper, a Monte Carlo simulation-based methodology is developed to predict the error in the approximation. An error parameter is identified and error functions are constructed. The methodology is applied to a range of time-invariant and time-variant random barriers, and it is shown that the error in the original ensemble up-crossing rate approximation is largely reduced. The study provides unprecedented insight into characteristics of the ensemble up-crossing rate approximation.
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Improvements on the approximate solutions for the standard multinormal or multivariate normal distribution function based on the first order structural reliability concepts are proposed. The numerical accuracy and efficiency of three methods of obtaining the solutions are compared. For parallel systems problems, it is shown that the suggested first order multinormal (FOMN) approach produces results significantly closer to the exact answer than either those of the crude or the improved FOMN solutions. The performance of the improved and general FOMN approaches when applied to high reliability series systems appears to be as good as or even better than those obtained by the well-known second order bounds. (Author/TRRL)
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Optimization of structures for design has a long history, including optimization using numerical methods and optimality criteria. Much of this work has considered a subset of the complete design optimization problem—that of the technical issues alone. The more general problem must consider also non-technical issues and, importantly, the interplay between them and the parameters which influence them. Optimization involves optimal setting of design or acceptance criteria and, separately, optimal design within the criteria. In the modern context of probability based design codes this requires probabilistic acceptance criteria. The determination of such criteria involves more than the nominal code failure probability approach used for design code formulation. A more general view must be taken and a clear distinction must be made between those matters covered by technical reliability and non-technical reliability. The present paper considers this issue and outlines a framework for rational optimization of structural and other systems given the socio-economic and political systems within which optimization must be performed.
Measures of Structural Reliability. Structural Reliability Assessment. Integration and Simulation Methods. Second-Moment and Transformation Methods. Reliability of Structural Systems. Time Dependent Reliability. Load and Load Effect Modelling. Resistance Modelling. Codes and Structural Reliability. Probabilistic Evaluation of Existing Structures. Appendices. References. Index.
For reinforced concrete structures the conventional wisdom is that after some years of exposure to marine conditions reinforcement corrosion is inevitable. Much attention is paid in the literature to the rate of ingress of chlorides through the concrete cover to the reinforcing bars and to ensuring highly impermeable cover and/or deeper cover, to try top prevent chloride-induced or carbonation-induced corrosion initiation. Actual field experience shows that there are many reinforced concrete structures that have survived remarkably well for many decades despite having very high chloride concentrations next to the reinforcing bars. Even with very modest concrete cover by modern standards, exhumation often finds bars free from corrosion. Detailed investigations of a number of such cases showed no corrosion if the concrete pH levels are above about 9. On the other hand, very severe reinforcement corrosion was observed in the few cases where the concrete had cracked right through the cover to the bars. Often there was no external evidence or signs of interior corrosion, including longitudinal cracking. The implications of these findings for practice are discussed.
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A model is proposed for general corrosion of mild and low-alloy steels under fully aerated at-sea immersion conditions as measured by weight loss. Because all factors influencing corrosion have inherent uncertainties, the proposed model is probabilistic, composed of a mean-value function and a zero-mean uncertainty function. The mean-value function is nonlinear in time, controlled by distinctly different phases—kinetic, diffusion, and anaerobic. Literature field data as well as new field observations indicate that seawater temperature has a strong influence on each phase. The model is used to interpret literature data together with additional inferred or collected environmental data. These are then used to calibrate the parameters for the mean-value function of the model. The calibrated parameters are used to predict a consolidated plot of expected corrosion loss—time-temperature. An example application is given.
For existing reinforced concrete structures exposed to saline or marine conditions, there is an increasing engineering interest in their remaining safety and serviceability. A significant factor is the corrosion of steel reinforcement. At present there is little field experience and other data available. This limits the possibility for developing purely empirical models for strength and performance deterioration for use in structural safety and serviceability assessment. An alternative approach using theoretical concepts and probabilistic modeling is proposed herein. It is based on the evidence that the rate of diffusion of chlorides is influenced by internal damage to the concrete surrounding the reinforcement. This may be due to localized stresses resulting from external loading or through concrete shrinkage. Usually, the net effect is that the time to initiation of active corrosion is shortened, leading to greater localized corrosion and earlier reduction of ultimate capacity and structural stiffness. The proposed procedure is applied to an example beam and compared to experimental observations, including estimates of uncertainty in the remaining ultimate moment capacity and beam stiffness. Reasonably good agreement between the results of the proposed procedure and the experiment was found.
The sustainability of Royal Australian Navy (RAN) ships is affected by structural deterioration, including corrosion, which results in material loss through the oxidation of exposed steel. Deterioration through corrosion is one of the determining factors in developing the operational planning and economic aspects of structural maintenance management. The extent of corrosion depends on many environmental parameters making it difficult to predict efficient repair strategies using periodical time based maintenance. With this consideration, and the fact that the RAN owns an increasingly ageing fleet, new and innovative ways are required to effectively manage a ship. Presently there is no simulation tool available to the RAN that allows ship corrosion to be predicted. Tools such as these have been developed empirically for some commercial ships, however the corrosion loss models exhibit a high variability. By taking into consideration the operational parameters of the vessel a greater accuracy in modelling corrosion can be achieved.
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Numerical modelling is used to trace the development of cracks starting from pits that from on the surface of corroded, brittle metal pipe. Under internal pressure applied to the pipe, two general cracking patterns are found to occur and these are related to pit shape. The numerical analysis used allows estimation of the area of the cracked region and of the pressure under which failure occurs. These results also facilitate Stress Corrosion Cracking (SCC) studies by estimating the critical area of the crack stemming from a pit. This may result in a more realistic approach to estimating the likelihood of occurrence of critical cracks in brittle pitting corroded pipes.
The external corrosion of old cast iron water mains is a major concern for water industries in many older cities. To better manage these assets, good quality mathematical models, based on real-world observations, are required for predicting future corrosion. Herein a recently proposed model for the long-term maximum corrosion depth of cast iron buried in soil is presented. The model is based on the bimodal model, recently shown to be applicable for cast iron corrosion in soil. The model was calibrated to field data from 37 sites. It was found that the main factors influencing soil corrosion are, in order, time of wetness and inorganic nitrate concentration (for microbiological attack). Other parameters including chloride, phosphate and carbonate content were also considered, but were found to be less important. The potential influence of poor quality backfill and physical damage to the pipe on corrosion depth is also discussed.
There are apparently conflicting observations about the influence of seawater temperature on the immersion corrosion of copper-nickel alloys, with both increases and decreases in temperature having been observed. During the 1980s, ASTM sponsored a worldwide corrosion study, which included 90:10 copper-nickel (UNS C070600). At first sight there is no order in the results regarding the effect of seawater temperature. However, when the results are examined in detail, allowing for water velocity and environmental conditions and carefully considering the implications of previous laboratory and field studies, some order can be obtained. This shows that a relationship between corrosion and temperature in the range of 10°C to 40°C can be proposed, which is consistent with previous observations.
