• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.2
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• pp.129-140
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• 1999

추계론적 해석은 구조계 내의 해석인수에 존재하는 공간적 또는 시간적 임의성이 구조계 반응에 미치는 영향에 대한 고찰을 목적으로 한다. 확률장은 구족계 내에서 특정한 확률분포를 가지는 것으로 가정된다. 구조계 반응에 대한 이들 확률장의 영향 평가를 위하여 통계학적 추계론적 해석과 비통계학적 추계론적 해석이 사용되고 있다. 본 연구에서는 비통계학적 추계론적 해석방법 중의 하나인 가중적분법을 제안하였다. 특히 구조계의 공간적 임의성이 큰 특성을 가지고 있는 반무한영역에 대한 적용 예를 제시하고자 한다. 반무한영역의 모델링에는 무한요소를 사용하였다. 제안된 방법에 의한 해석 결과는 통계학적 방법인 몬테카를로 방법에 의한 결과와 비교되었다. 제안된 가중적분법은 자기상관함수를 사용하여 확률장을 고려하므로 무한영역의 고려에 따른 해석의 모호성을 제거할 수 있다. 제안방법과 몬테카를로 방법에 의한 결과는 상호 잘 일치하였으며 공분산 및 표준편차는 무한요소의 적용에 의하여 매우 개선된 결과를 나타내었다.

• The Journal of Engineering Geology
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• v.5 no.3
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• pp.301-308
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• 1995

In this study, a stochastic finite element method is proposed with a view to consider rock property variations in the analysis of structural behavior on underground caverns. Here, the Monte carlo simulation technique, which has been widely used in probabilistic applications in many engineering fields, is applied for the analysis of the effect rock property distribution. Using the newly developed computer program based on the above - mentioned method, the underground opening in biaxial stress field is analyzed considering the effect of material property variation.

• Journal of the Korean Geotechnical Society
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• v.27 no.10
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• pp.93-104
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• 2011

In this paper, a numerical procedure of probabilistic steady seepage analysis that considers the spatial variability of soil permeability is presented. The procedure extends the deterministic analysis based on the finite element method to a probabilistic approach that accounts for the uncertainties and spatial variation of the soil permeability. Two-dimensional random fields are generated based on a Karhunen-Lo$\grave{e}$ve expansion in a fashion consistent with a specified marginal distribution function and an autocorrelation function. A Monte Carlo simulation is then used to determine the statistical response based on the random fields. A series of analyses were performed to verify the application potential of the proposed method and to study the effects of uncertainty due to the spatial heterogeneity on the seepage behavior of soil foundation beneath water retaining structure with a single sheet pile wall. The results showed that the probabilistic framework can be used to efficiently consider the various flow patterns caused by the spatial variability of the soil permeability in seepage assessment for a soil foundation beneath water retaining structures.

• Magazine of the Korean Society of Agricultural Engineers
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• v.36 no.1
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• pp.54-62
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• 1994

The expanding technique of the Stochastic Finite Element Method(SFEM) is proposed in this paper for adapting direct integration methods in stochastical dynamic analysis of structures. Grafting the direct integration methods and the SFEM together, one can deal with nonlinear structures and nonstationary process problems without any restriction. The stochastical central diffrence and stochastic Houbolt methods are introduced to show the expanding technique, and their adaptabilities are discussed. Results computed by the proposed method (the Stochastic Finite Element Method in Dynamics: SFEMD) for two degree-of-free- dom system are compared with those obtained by Monte Carlo Simulation.

• 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.

• Computational Structural Engineering
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• v.2 no.4
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• pp.89-98
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• 1989

In order to take account of the statistical properties of random variables used in the structural analysis, the conventional approach usually adopts the safety factor based on past experiences for the qualitative assessment of structural safety problem. Recently, new approach based on the probabilistic concept has been applied to the assessment of structural safety in order to circumvent the difficulties of the conventional approach in choosing the appropriate safety factor. Thus, computer program called "Probabilistic finite element method" is developed by incorporating the probabilistic concept into the conventional matrix method in order to investigate the effects of the random variables on the final output of the structural analysis. From the comparison of some examples, it can be concluded that the PFEM developed in this study deals consistently with the uncertainty of random variables and provides the rational tool for the assessment of structural safety of plane frame.

• Journal of the Earthquake Engineering Society of Korea
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• v.12 no.2
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• pp.33-44
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• 2008

Most of the civil structure - bridges, offshore structures, plant, etc. - have been designed by the classical approaches which deal with all the design parameters as deterministic variables. However, some more advanced techniques are required to evaluate the inherent randomness and uncertainty of each design variable. In this research, a seismic safety assessment algorithm based on the structural reliability analysis has been formulated and computerized for more reasonable seismic design of turbine-generator foundations. The formulation takes the design parameters of the system and loading properties as random variables. Using the proposed method, various kinds of parametric studies have been performed and probabilistic characteristics of the resulted structural responses have been evaluated. Afterwards, the probabilistic safety of the system has been quantitatively evaluated and finally presented as the reliability indexes and failure probabilities. The proposed procedure is expected to be used as a fundamental tool to improve the existing design techniques of turbine-generator foundations.

• Tunnel and Underground Space
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• v.13 no.5
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• pp.397-402
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• 2003

Generally it is likely that rock mass properties are expressed not by a mean value but by values with variation due to its characteristic uncertainty. This characteristic is one of the most important parts for the design of undergound structures, but yet to be fully examined. Stochastic finite element method (SFEM) is contrary to deterministic finite element method in its concept as the former has been developed in order to take the randomness of structural systems into account. Using SFEM, the response variability of structural system can be obtained and it leads probabilistic stability of structure to be analyzed. In this study, displacement response variability of circular opening with hydrostatic stress field are analyzed in terms of rock mass properties having a certain mean and a standard deviation using the SFEM. The analyzed response variability shows that the necessity of probabilistic stability analysis of underground structures using reliable mean value and standard deviation of deformation modulus.

• Journal of the Korean Geotechnical Society
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• v.25 no.12
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• pp.13-25
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• 2009

In this paper, a numerical procedure of probabilistic slope stability analysis that considers the spatial variability of soil properties is presented. The procedure extends the deterministic analysis based on the limit equilibrium method of slices to a probabilistic approach that accounts for the uncertainties and spatial variation of the soil parameters. Making no a priori assumptions about the critical failure surface like the Random Finite Element Method (RFEM), the approach saves the amount of solution time required to perform the analysis. Two-dimensional random fields are generated based on a Karhunen-Lo$\grave{e}$ve expansion in a fashion consistent with a specified marginal distribution function and an autocorrelation function. A Monte Carlo simulation is then used to determine the statistical response based on the random fields. A series of analyses were performed to verify the application potential of the proposed method and to study the effects of uncertainty caused by the spatial heterogeneity on the stability of slope. The results show that the proposed method can efficiently consider the various failure mechanisms caused by the spatial variability of soil property in the probabilistic slope stability assessment.

• Geotechnical Engineering
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• v.5 no.2
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• pp.33-44
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• 1989

In this paper, uncertainties in dynamic soil structure interaction (SSI) of nuclear poi.or plants subjected to seismic loading are studied considering the random characteristics of soils surround- ing the structure. Firstly sensitivity analysis is performed to study the effect of uncertain dynamic soil properties on the response of the structure. Secondly, to take into account the non-neterministic characteristics in analysis caused by random characteristics of the soil properties, Perturbation method and Rosenblueth's Two point estimates were used for this studu. The procedure is based on the comptex response method which is constituted by a combined usage of conventional finite elements for the near field and infinite elements for the far field. Results of the sensitivity analysis show that dynamic soil properties greatly affect the response of the sol.uc- lure. Results of the probabilistic analysis show that the Two-point estimate method produces good agreements with the Perturbation method.