• Computational Structural Engineering
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• v.4 no.2
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• pp.111-117
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• 1991

The analysis method calculating the mean and standard deviation for the eigenvalue of complicated structures in which the limit state equation is implicitly expressed is formulated and applied to the buckling analysis by combining probabilistic finite element method with direct differential method which is a kind of sensitivity analysis technique. Also, the probability of buckling failure is calculated by combining classical reliability techniques such a MVFOSM and AFOSM. As random variables external load, elastic modulus, sectional moment of inertia and member length are chosen and Parkinson's iteration algorithm in AFOSM is used. The accuracy of the results by this study is verified by comparing the results with the crude Monte Carlo simulation and Importance Sampling Method. Through the case study of some structures the important aspects of buckling reliability analysis are discussed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.3
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• pp.273-279
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• 2007

Probabilistic Risk Assessment considering statistically random variables is performed for the preliminary design of an Arch Bridge. Component reliabilities of girders have been evaluated using the response surfaces of the design variables at the selected critical sections based on the maximum shear and negative moment locations. Response Surface Method (RSM) is successfully applied for reliability analyses lot this relatively small probability of failure of the complex structure, which is hard to be calculated by Monte-Carlo Simulations or by First Order Second Moment method that can not easily calculate the derivative terms in implicit limit state functions. For the analysis of system reliability, parallel resistance system composed of girders is modeled as a parallel series connection system. The upper and lower probabilities of failure for the structural system have been evaluated and compared with the suggested prediction method for the combination of failure modes. The suggested prediction method for the combination of failure modes reveals the unexpected combinations of element failures in significantly reduced time and efforts, compared with the previous permutation method or conventional system reliability analysis method.

• Composites Research
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• v.23 no.2
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• pp.40-47
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• 2010

In this paper, the hybrid response surface method(HRSM) is proposed and examined. Hybrid response surface method calculate a approximate model repeatedly based on MPP coordinates. To verify the performance, probability of failure, MPP(Most Probable failure Point) and reliability index are calculated for nonlinear function and composite laminated plate by using reliability analysis method and compared with results by using typical response surface method(RSM). Probability of failure is calculated under the assumption of the nonlinear limit state equation and given failure criterion. The results of proposed method shows performance improvement in estimating the probability of failure.

• Geotechnical Engineering
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• v.1 no.1
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• pp.47-58
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• 1985

A new approach is develped to analyze the reliability of the shallow foundation. The measure of the safety of the structhure is expressed In terms of the probability of failure, instead of the conventional factor of safety. Many uncertainties involved in the deterministic stability anaitsis can be reasouably treated by using the probabilistic approach. Both the soil properties and loads are assumed to be random variables. Accordingly, the capacity and demand are considered to be normal, log-normal, and beta variated. Use is made of Error Propagation Method to investigate the probability of failure. And the relationship is investigated between the probability of failure and the central factor of safety. The results are computer programed and several case studies are performed using developed program.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.4A
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• pp.647-657
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• 2006

Probabilistic Risk Assessment considering statistically random variables is performed for the preliminary design of a Cable Stayed Bridge, which is Prestressed Concrete Bridge consisted of cable and plate girders, based on the method of Working Stress Design and Strength Design. Component reliabilities of cables and girders have been evaluated using the response surface of the design variables at the selected critical sections based on the maximum shear, positive and negative moment locations. Response Surface Method (RSM) is successfully applied for reliability analyses for this relatively small probability of failure of the complex structure, which is hard to obtain through Monte-Carlo Simulations. or through First Order Second Moment Method that can not easily calculate the derivative terms of implicit limit state functions. For the analysis of system reliability, parallel resistance system consisting of cables and plate girder is changed into series connection system and the result of system reliability of total structure is presented. As a system reliability, the upper and lower probabilities of failure for the structural system have been evaluated and compared with the suggested prediction method for the combination of failure modes. The suggested prediction method for the combination of failure modes reveals the unexpected combinations of element failures in significantly reduced time and efforts compared with the previous permutation method or system reliability analysis method, which calculates upper and lower bound failure probabilities.

• Journal of the Korea institute for structural maintenance and inspection
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• v.21 no.2
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• pp.46-52
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• 2017

Recently durability design based on deterministic or probabilistic method has been attempted since service life evaluation in RC(Reinforced Concrete) structure exposed to chloride attack is important. The deterministic durability design contains a reasonable method with time effect on surface chloride content and diffusion coefficient, however the probabilistic design procedure has no consideration of time effect on both. In the paper, a technique on PDF(Probability of Durability Failure) evaluation is proposed considering time effect on diffusion and surface chloride content through equivalent surface chloride content which has same induced chloride content within a given period and cover depth. With varying period to built-up from 10 to 30 years and maximum surface chloride content from $5.0kg/m^3$ to $10.0kg/m^3$, the changing PDF and the related service life are derived. The proposed method can be reasonably applied to actual durability design with preventing conservative design parameters and considering the same analysis conditions of the deterministic method.

• Geotechnical Engineering
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• v.5 no.1
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• pp.27-34
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• 1989

This study presents a probabilistic analysis of the stability of homogeneous soil slopes during earthquakes. The stability of the slope is measured through its probability of failure rather than the customary factor of safety. The maximum horizontal ground acceleration is deterimined with Donovan and McGuire equation. The earthquake magnitude (m) is a random variable the Probability density function f(m) has been obtained with a use of Richter law. The potential failure surfaces are taken to be of an exponential shape (log-spiral) , Uncertainties of the shear strength parameters along potential failure surface are expressed by one-dimensional random field model. From a first order analysis the mean and variance of safety margin is osculated. The dependence on significant seismic parameters of the probability of failure of the slope is examined and the results are presented in a number of graphs and tables. On the base of the results obtained in this study, it is concluled that (1) the present model is useful in assessing the reliability of soil slopes under both static and seismic conditions: and (2) the probability of failure of a soil slope is greatly affected by the values of the seismic parameters that are associated with it.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.667-670
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• 2001

For major structural components periodic inspections and integrity assessments are needed for the safety. However, many flaws are undetectable because sampling inspection is carried out during in-service inspection. Probabilistic integrity assessment is applied to take into consideration of uncertainty and variance of input parameters arise due to material properties and undetectable cracks. This paper describes a Probabilistic Fracture Mechanics(PEM) analysis based on the Monte Carlo(MC) algorithms. Taking a number of sampling data of probabilistic variables such as fracture toughness value, crack depth and aspect ratio of an initial surface crack, a MC simulation of failure judgement of samples is performed. For the verification of this analysis, a comparison study of th PFM analysis using a commercial code, mathematical method is carried out and a good agreement was observed between those results.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.3 no.3
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• pp.95-106
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• 1983

The probability of failure is used to analyze the reliability of three dimensional slope failure, instead of conventional factor of safety. The strength parameters are assumed to be normal variated and beta variated. These are interval estimated under the specified confidence level and maximum likelihood estimation. The pseudonormal and beta random variables are generated using the uniform probability transformation method according to central limit theorem and rejection method. By means of a Monte-Carlo Simulation, the probability of failure is defined as; $$P_f$$=M/N N: Total number of trials M: Total number of failures some of the conclusions derived from the case study include; 1. If the strength parameters are assumed to be normal variated, the relationship between safety factor and the probability of failure is fairly consistent, regardless of the procedures of analysis and dimensions of assumed rupture surfaces. 2. However if the strength parameters are beta variated, general relationship between $F_s$ and $P_f$ is hardly found.

• Journal of the Korean Geotechnical Society
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• v.29 no.9
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• pp.71-80
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• 2013

This work studies the reliability analysis of a slope that considers multiple failure modes. The analysis consists of two parts. First, significant failure modes that contribute most to system reliability are determined. The so-called barrier method proposed by Der Kiureghian and Dakessian to identify significant failure modes successively is employed. Second, the failure probability for the slope is estimated on the basis of the identified significant failure modes and corresponding design points. For reliability problems entailing multiple design points, failure probability can be estimated by the multi-point first-order reliability method (FORM), Ditlevsen's bounds method, and Monte Carlo simulation. In this paper, a comparative study between these methods has been made through example problems. Analysis results showed that while a soil slope may have a large number of potential slip surfaces, its system failure probability is usually governed by a few significant slip surfaces. Therefore, the most important step in the system reliability analysis for a soil slope is to identify all the significant failure modes in an efficient way.