Robert E. Melchers

Importance sampling in structural systems

Abstract Importance sampling as a technique to improve the Monte Carlo method for probability integration can be shown to be extremely efficient and versatile. This paper addresses the accuracy and efficiency of the method, and its application to series and parallel systems in structures.

Effect of response surface parameter variation on structural reliability estimates

In the reliability estimation of complex structures, response surface methodology has been suggested as a way to estimate the actual but implicit limit state function. Typically the response surface is constructed from a polynomial function and fitted to the implicit function at a number of points. The location of these points has been noted as being an issue but the effect of varying their location has had little attention in the literature. In the present paper some simple examples are used to indicate possible effects. It is noted that the probability can be both under- and over-estimated, depending on the choice of points, but that no clear guidance for point selection can be given in any one case. A particularly disturbing feature is that for some types of problems there can be instability in the probability estimate as the location of the points is changed. This is demonstrated through a previously well-discussed example.

On the ALARP approach to risk management

Abstract There is an increasing trend by regulatory authorities for the introduction of the as low as reasonably practicable (ALARP) approach in dealing with risk management of proposed or existing complex hazardous systems. For these, decisions about acceptability or tolerability of risks and consequences can have very significant financial, economic and other consequences for the proponents. Conversely, there may be very significant social and socio-economic implications. ALARP as a guide to achieving a satisfactory outcome has a certain intuitive appeal for the practical management of industrial and other risks. However, as suggested herein, there are a number of areas of concern about the validity of this approach. These include representativeness, morality, philosophy, political reality and practicality. An important, and in some respects fundamental, difficulty is that the risk acceptance criteria are not fully open to public scrutiny and can appear to be settled by negotiation.

Analytical Model for Corrosion-Induced Crack Width in Reinforced Concrete Structures

Crack width is a parameter of the most practical significance for the design and assessment of reinforced concrete structures. Practical experience and observations suggest that corrosion-affected reinforced concrete structures are more prone to cracking than other forms of structural deterioration. Moreover, concrete cracking incurs considerable costs of repairs and inconvenience to the public due to interruptions. This gives rise to the need for a thorough investigation to achieve cost-effectiveness in maintaining the serviceability of concrete structures. This study attempts to derive an analytical model for corrosion-induced crack width based on the concept of smeared cracks. A merit of the derived model is that it is directly related to critical factors that affect the corrosion-induced concrete cracking. After verifying the derived model, a parametric study was undertaken to quantify the effect of these factors on cracking development. It was found that corrosion rate, as represented by corrosion current density icorr, is the most important single factor that affects both the time to surface cracking and the growth of crack width. It is concluded that the model derived in this paper can predict corrosion-induced crack width with reasonable accuracy.

Search-based importance sampling

Abstract Importance sampling as a special technique in Monte Carlo probability integration has been shown to be a highly efficient and rather unrestricted method. Non-Gaussian and dependent random variables and nonlinear limit functions can be treated relatively easily and with reasonable rates of convergence. A major draw-back, however, is the need to identify so-called “interesting” or “important” regions for integration. Reference to first-order second-moment (FOSM) methods may help, as well as numerical maximization routines applied. Each involves certain difficulties. An alternative procedure, based on directing and correcting the importance sampling function as sampling is carried out, is presented herein. In particular it is possible to have a multi-modal sampling function.

Mathematical modelling of the diffusion controlled phase in marine immersion corrosion of mild steel

Abstract In the mathematical modelling of the ‘general’ corrosion of mild and low alloy steels and of some other metals oxygen diffusion through the corrosion products to the corroding surface controls the rate of corrosion at least during some period in the corrosion–time behaviour relationship. Under slightly different theoretical assumptions various early authors derived expressions for this phase. It was usually assumed the derived relationship applied from initial immersion. Only very limited laboratory support for the derived relationships exists. They have been applied to field data for atmospheric corrosion but with constants and exponents modified empirically. In the present paper the theory is reviewed and extended. It is argued that diffusion control cannot apply from first immersion and that this provides considerably greater freedom to mathematical modelling. Allowance is made for non-uniform corrosion product density and permeability and for loss of corrosion product. Recent detailed ‘at-sea’ experimental observations obtained on the Eastern Australian seaboard are applied to test the theory for mild steel. It is shown that the most likely competing mathematical relationships produce relatively similar results. The derived relationship is fitted to literature data to deduce its temperature dependence.

Effect of reinforcement corrosion on reliability of highway bridges

This paper presents several aspects of a method for reliability assessment of reinforced concrete (RC) slab bridges with corroded reinforcement. It is assumed that corrosion will lead to a reduction in cross-sectional area of the reinforcing steel and/or a reduction in bond strength. Two types of corrosion are considered: general and localized corrosion. The method includes a non-linear finite element structural model and probabilistic models for traffic loads, corrosion propagation, bond characteristics, material properties, element dimensions and reinforcement placement. Reliability is estimated in terms of the reliability index using the first-order reliability method (FORM). For illustrative purposes, bridge reliabilities are calculated for a deteriorating, simple-span RC slab bridge, for ultimate strength and serviceability limit states.

Corrosion uncertainty modelling for steel structures

Abstract Marine environments are well-known to be very corrosive for mild and low alloy steels. For reasons of economy, such steels are still the preferred materials for off-shore structures, ship hulls, sheet piling and harbour-side facilities. Despite some quite extensive, long-term experimental test programs, the prediction of the likely corrosion loss of material is still rather simplistic, even though the various factors that can influence marine corrosion are known. However, precise understanding of the mechanics of marine corrosion has been slow to develop and mathematical formulation has been largely neglected. This paper reviews the various factors of importance in marine corrosion, outlines previous models and describes on-going work aimed at developing a probabilistic phenomenological model for time-dependent material loss of mild and low alloy steels in immersion conditions.

Probabilistic analysis of underground pipelines subject to combined stresses and corrosion

This paper presents a nonlinear limit state model for the analysis of underground pipelines, stressed both in the circumferential and the longitudinal directions. The effects of internal fluid pressure, external soil and traffic loads, temperature and longitudinal pipe bending etc., are considered. A nonlinear corrosion model is used to represent the loss of pipe wall thickness with time. To allow for the uncertainties of the design variables, a reliability analysis technique has been adopted; this also allows calculation of the relative contribution of the random variables and the sensitivity of the reliability index or failure probability. Results obtained for typical pipelines are presented.

General multi-dimensional probability integration by directional simulation

Abstract n-Dimensional integration by Monte Carlo directional importance sampling using analytical or numerical integration for each simulated direction is discussed. A suitable general class of sampling distributions is considered. The class is denoted as the class of mixed ūgm-centred standard Gaussian and D -truncated ūgm-centred standard Gaussian distributions, where ūgm is a position vector and is a pragmatically chosen subset of R n. The relative efficiency of different choices of the sampling distribution from the class is studied by way of examples for probability integration in particular. In addition, the same integrals are formulated in different variable representations by the substitution method before the directional Monte Carlo integration is carried out. Moreover, it is demonstrated how sensitivities of the integrals with respect to parameter variations or integration boundary variations can be obtained during the same Monte Carlo simulation primarily set up for obtaining the integral. The novelty compared with previous reports on the topic of integration in the standard Gaussian space is the demonstration that the combination of simulation and numerical integration can be applied for general integrals without any significant change of efficiency.