Search

In the second-order reliability method (SORM), the failure probability is generally estimated using a parabolic approximation of a performance function. In the present paper, the moment properties of a second-order approximation of performance functions are investigated, and a moment approximation for a second-order reliability method and a simple second-order third-moment reliability index are proposed for the estimation of failure probability corresponding to both the simple and general parabolic approximations. Based on the property that the parabolic approximation approaches a unit normal random variable, the ranges of three parameters are investigated: the number of variables, the principal curvature, and the first-order reliability index. A simple analytical judgment formula is derived, which can help us judge when the first-order reliability method is sufficiently accurate and when the SORM is required. A simple second-order second-moment reliability index is also proposed for problems with relatively small principal curvatures. Through some numerical examples, the simplicity and accuracy of the second-order second- and third-moment reliability indices are demonstrated. DOI: 10.1061/(ASCE)0733-9445(2002)128:8(1087) CE Database keywords: Reliability; Failure; Curvature; Performance.

First- and second-order reliability methods are generally considered to be among the most useful for computing structural reliability. In these methods, the uncertainties included in resistances and loads are generally expressed as continuous random variables that have a known cumulative distribution function. The Rosenblatt transformation is a fundamental requirement for structural reliability analysis. However, in practical applications, the cumulative distribution functions of some random variables are unknown, and the probabilistic characteristics of these variables may be expressed using only statistical moments. In the present study, a structural reliability analysis method with inclusion of random variables with unknown cumulative distribution functions is suggested. Normal transformation methods that make use of high-order moments are investigated, and an accurate third-moment standardization function is proposed. Using the proposed method, the normal transformation for random variables with unknown cumulative distribution functions can be realized without using the Rosenblatt transformation. Through the numerical examples presented, the proposed method is found to be sufficiently accurate to include the random variables with unknown cumulative distribution functions in the first- and second-order reliability analyses with little extra computational effort.

In the earthquake resistance design of flame structures, the yielding of all the beams in flexure prior to possible yielding of columns is generally considered to be a preferable mode; this is defined as a beam-hinging pattern in this paper. Structures are therefore generally weak-beam, strong-column designed with a column overdesign factor (COF). In reality however, the designed weak-beam, strong-column structures may not collapse according to the preferable failure mode because of large uncertainties in external loads and member strengths. These uncertainties may change the COF and the structure may collapse according to some unpreferable failure modes such as the weak story mechanisms. The object of this paper is probabilistic evaluation of the target values of COFs for which the occurrence probability of unpreferable failure modes can be limited to within a specific tolerance. A stochastic limit analysis procedure using the linear programming method and the first-order reliability method is developed, and the likely failure modes of weak-beam, strong-column designed structures are investigated using this procedure. The target value of COF is discussed in probabilistic terms. It is found that a much higher value of COF is required in the case of uncertain loads and member strengths than is expected in deterministic cases.

In the second-order reliability method, the Hessian matrix is used to construct a paraboloid approximation of the limit state surface and compute a second-order estimate of the failure probability. In this paper, a practical point-fitting second-order reliability approximation is proposed, by which the explicit second-order approximation of the performance function is obtained directly in standard normal space with neither the computation of Hessian matrix nor the computation of gradients of the function. Once the point-fitted performance function is obtained, the failure probability is estimated by the empirical second-order reliability index, which is generally simple and works well compared to other second-order reliability method formulas. For accurate computation of the failure probability, an IFFT method is proposed, from which the failure probability is obtained conveniently using the Inverse Fast Fourier Transformation. The proposed methods are investigated and their accuracy and efficiency are demonstrated using numerical examples.

The system reliability evaluation of ductile frame structures presents two difficulties. One is the identification of significant failure modes; the other is the computation of overall failure probabilities contributed from these significant modes. In this paper, a practical procedure is developed, in which a failure mode independent performance function is defined using load factor obtained by limit analysis, and a response surface approach is used to approximate the performance function. With the performance function of explicit second-degree polynomial, the failure probability can be readily obtained using First and Second Order Reliability Method (FORM/SORM). Several examples are investigated, and it is found that the obtained response surface is a good approximation of the inner connotative surface of the limit state surfaces of the structural system. The proposed procedure has good efficiency and enough accuracy for system reliability evaluation of ductile frame structures. The difficulty in both failure mode identification and failure probability computation can be avoided by using the proposed procedure.

The main purpose of this work is to develop a reliability analysis of concrete cover against the ingress of airborne chloride ions, and then to use it to determine the appropriate thicknesses of concrete cover or the water–cement or water–binder ratios of concrete (W/C or W/B) for meeting a reliability requirement. At first, for determining the corrosion occurrence time of reinforcing bars embedded in concrete, in addition to the one-dimensional diffusion model of chloride ions in concrete, a two-dimensional diffusion model for circular RC piers is developed. In order to be applicable in engineering practice, an amplification factor of chloride concentrations of the concrete surfaces is proposed to modify the one-dimensional diffusion model of chloride ions in concrete for considering the two-dimensional diffusion effect. In addition to Monte Carlo simulation (MCS), the first-order reliability method (FORM) and the moment method are used to calculate the reliability of concrete cover against the ingress of airborne chloride ions. Based on the comparison results of various reliability analysis methods, the third-moment reliability design procedure is selected to determine the appropriate thickness of concrete cover or, W/C or W/B of concrete for meeting a reliability requirement. [ABSTRACT FROM AUTHOR]

In both seismic design and probabilistic seismic-hazard analyses, site effects are typically characterized as the ratio of the response spectral ordinate on the ground surface to that on the bedrock based on the scaling law borrowed from the Fourier spectral ordinate. Recent studies have shown that different from the Fourier spectral ratio (FSR), the response spectral ratio (RSR) does not purely reflect the site effects but also depends on the earthquake scenario even for linear analysis. However, previous studies are limited to theoretical analysis. This study statistically compares the two spectral ratios by analyzing many actual seismic ground motions recorded at nearby soil and rock sites. It is observed that the average RSR and FSR have similar overall shapes, and their maximum values occur at approximately the same period; however, the values around the peak are clearly different with FSRs consistently exceeding the RSRs. The RSR–FSR relationship depends on the earthquake scenario and the oscillator damping; their difference at periods longer than the site's fundamental period decreases as the magnitude and epicentral distance increase, and the RSRs generally approach the FSRs as the oscillator damping decreases. [ABSTRACT FROM AUTHOR]

In recent decades, the outcrossing rate method has gained popularity for structural time-dependent reliability assessments (TRA). Despite numerous efforts, developing a general analytical outcrossing rate method for a nonstationary non-Gaussian performance function to estimate the failure probability within the forecast time interval remains a significant challenge. This paper introduces an analytical outcrossing rate method for non-Gaussian cases, named the three-moments-based outcrossing rate (TMO) method. The outcrossing rate is formulated based on the third-moment outcrossing rate with no assumption of the correlation between the performance function and its derivative process, allowing for a comprehensive understanding of the performance characteristics of a structure. Following the development of the proposed outcrossing rate, a TRA methodology is established to evaluate the failure probability of the nonstationary non-Gaussian performance function. Notably, the TMO method only requires statistical moments of the nonstationary non-Gaussian performance function, which are easy to calculate, facilitating efficient implementation. Three numerical examples are presented to demonstrate the applicability, efficiency, and accuracy of the proposed TMO method. It can be concluded that the proposed TMO method provides an accurate and useful approach for TRA in engineering applications. [ABSTRACT FROM AUTHOR]

In practice, structural limit state function (LSF) is often combined with finite element (FE) models, and the corresponding time‐dependent reliability assessment (TRA) inevitably involves dealing with computational inefficiency. In this paper, a general moment‐based outcrossing rate (GMO) method is proposed to conduct TRA efficiently, with no limitation in the form of LSF. There are two innovations of GMO method: firstly, an explicit moment‐based outcrossing rate is developed; secondly, a separate algorithm is proposed that facilitates the separation of FE analysis from TRA cycle. The proposed method minimizes the computational cost associated with FE analysis and enables TRA cycle to be conducted more efficiently with the assistance of an explicit moment‐based outcrossing rate and explicit moment‐based outcrossing rate. Three numerical examples are investigated to examine the accuracy and efficiency of GMO method for TRA cycle. GMO method is found from the results that it can efficient and accurate to conduct TRA. Such improvements in computational efficiency are particularly valuable for complex structures where FE analysis is computationally expensive and time‐consuming. [ABSTRACT FROM AUTHOR]