[논문]통계오차를 고려한 사면안정 신뢰성 해석

김진만

doi:10.7843/kgs.2007.23.3.51

[국내논문] 통계오차를 고려한 사면안정 신뢰성 해석
Reliability Analysis of Slope Stability with Sampling Related Uncertainty 원문보기

韓國地盤工學會論文集 = Journal of the Korean geotechnical society, v.23 no.3, 2007년, pp.51 - 59

김진만 (Dept. of Civil Engrg., Pusan National Univ.)

초록
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다양한 불확실성을 체계적으로 반영하는 신뢰성 기반 해석기법을 사면안정 해석의 한 형식으로 제시한다. 통계오차, 공간 변동성, 그리고 공간 평균의 효과를 고려할 수 있는 지반특성 표현식이 사용되었다. 여러 가지 형식의 지반특성 표현식을 이용하여 사면안정 신뢰성 해석을 수행한 결과 통계오차, 공간적 상관성, 그리고 조건부 해석기법을 사용할 경우가 기존의 단순 확률변수 기법에 비해 상당히 작은 파괴확률을 제시한다는 사실이 밝혀졌다. 이 결과는 사면안정 해석에서 공간적 변동성과 통계오차가 합리적으로 고려되어야 한다는 점을 제시한다.

Abstract ▼ AI-Helper

A reliability-based approach that can systematically model various sources of uncertainty is presented in the context of slope stability. Expressions for characterization of soil properties are developed in order to incorporate sampling errors, spatial variability and its effect of spatial averaging. Reliability analyses of slope stability with different statistical representations of soil properties show that the incorporation of sampling error, spatial correlation, and conditional simulation leads to significantly lower probability of failure than that obtained by using simple random variable approach. The results strongly suggest that the spatial variability and sampling error have to be properly incorporated in slope stability analysis.

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문제 정의

This paper reports a follow-up analytical study that investigated the influence of inherent variability and sampling errors in the analysis of static slope stability. Kim (2003) briefly described some of the findings from that study and this paper reports all the remaining findings in details.

제안 방법

Although the above formulation provides a simple and yet systematic tool to quantify the absolute and relative uncertainty in the determination of soil properties, in some situations as described in the following section, more general approach may be necessary to consider the correlation between the measurements.
For limit equilibrium analyses, the author is interested in simulating the random soil properties that represent the spatial averages of the vertical soil slices and thus we need to compute the statistics of averaged soil properties for each slice. Figures 2a and 2b show sauries of simulated shear strengths over the 40 slices of the slip surface for both unconditional and conditional cases, assuming a Gaussian distribution.
Kim (2003) briefly described some of the findings from that study and this paper reports all the remaining findings in details. In this work, the author is particularly interested in the development of the statistics of the local average of the material property of a certain portion of the space, since soils generally exhibit plastic behavior and the stability of a soil slope tends to be controlled by the averaged soil properties rather than the properties at a particular location along the potential slip surface (i.e., Li and White 1987a, Tang et al. 1976, Vanmarcke 1977b). In this regard the author extends the previous applications of the spatial averaging method presented by Vanmarcke (1977a, 1977b) and Li and White (1987a, 1987b) by accounting for the sampling errors and the locations of measurements.
The results suggest that if the size of the averaging domain is sufficiently large, relative to the sc시e of fluctuation, the variance associated with inherent uncertainty may be practically neglected, thus allowing us to focus on the san甲ling-related uncertainty such as the statistical uncertainty.

이론/모형

Previous experience with local geology indicates that the soil can be modeled as a homogeneous random field, and scales of fluctuation are taken as 6x=5m and Sy= Im respectively. A separable 2-D exponential autocorrelation function is employed to model the correlation (i.e., Vanmarcke 1983; Li and White 1987a). It is known that the computed statistics of the local average is generally not sensitive to the type of autocorrelation fimction (i.
The potential sliding mass was divided into 40 vertical soil slices of equal width for stability analyses using the Simplified Bishop method. Deterministic analyses of the static slope stability, with the mean soil properties, yielded a factor of safety 1.
than one. The reliability computations were carried out with the aid of CALREL, a general-p나rpose structural reliability analysis program developed by Liu et al. (1989), linked to user-defined subroutine programs for static slope stability analyses including STAGLEM and GLEM developed by Kim (2001). The undrained strength of soil was modeled with both normal and lognormal distributions in order to examine the influence of uncertainty of distribution forms on the risk level of the problem.

성능/효과

The results of analyses confirm that the variability of the local average is always less than that of the point value and that it decreases with increase of the size of the averaging domain. Another important outcome of the stochastic treatment is that the variability of the local average always decreases as the dimension of a domain increases.

참고문헌 (25)

Ang, A. H. S., and Tang, W. H. (1984), Probability Concepts in Engineering Planning and Design, Volume II-Decision, Risk, and Reliability, John Wiley & Sons, New York
Ang, A. H. S., and Tang, W. H. (1975), Probability Concepts in Engineering Planning and Design, Volume I-Basic Principles, John Wiley & Sons, New York
Christian, J. T., Ladd, C. C., and Baecher, G. B. (1994), 'Reliability Applied to Slope Stability Analysis', Journal of Geotechnical Engineering, ASCE, Vol.120, No.12, pp.2180-2207

상세보기
Christian, J. T., and Urzua, A. (1998), 'Probabilistic Evaluation of Earthquake-Induced Slope Failure', Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol.124, No.11, pp.1140-1143

상세보기
Cornell, C. A. (1969), 'Structural Safety Specification Based on Second-Moment Reliability', Symposium, International Association of Bridge and Structural Engineers, London
Duncan, J. M. (2000), 'Factors of Safety and Reliability in Geotechnical Engineering', Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol.126, No.4, pp.307-316

상세보기
Faravelli, L. (1989), 'Response Surface Approach for Reliability Analysis', Journal of Engineering Mechanics, ASCE, Vol.115, No.12, pp.2763-2781

상세보기
Journel, A G. (1989), Fundamentals of Geostatistics in Five Lessons, American Geophysical Union
Kim, J. (2001), Probabilistic Approach to Evaluation of EarthquakeInduced Permanent Deformation of Slopes, Ph.D. Dissertation, Dept. of Civil and Env. Engineering, University of California at Berkeley
Kim, J. (2003), 'The Importance of Geotechnical Variability in the Analysis of Earthquake-Induced Slope Deformations', Journal of Korean Geotechnical Society, Vol.19, No.2, pp.123-133
Krige, D. G. (1966), 'Two-Dimensional Weighted Moving Averaging Trend Surfaces for Ore Evaluation', Proceedings of Symposium on Mathematical Statistics and Computer Applications for Ore Evaluation, Johannesburg, S. A, pp.13-38
Li, K. S., and Lumb, P. (1987), 'Probabilistic Design of Slopes', Canadian Geotechnical Journal, Vol.24, pp.520-535

상세보기
Li, K. S., and White, W. (1987a), Probabilistic Characterization of Soil Profiles, Research Report No.19, Department of Civil Engineering, University College, The University of New South Wales, Canberra, Australia
Li, K. S., and White, W. (1987b), Probabilistic Approaches to Slope Design, Research Report No. 20, Department of Civil Engineering, University College, The University of New South Wales, Canberra, Australia
Lin, P. L., and Der Kiureghian, A (1986), 'Multivariate Distribution Models with Prescribed Marginals and Covariances', Probabilistic Engineering Mechanics, Vol.1, No.2, pp.105-112

상세보기
Liu, P. L., Lin, H. Z., and Der Kiureghian, A (1989), CALREL User Manual, Report No. UCB/SEMM-89/18, Department of Civil Engineering, University of California at Berkeley, USA
Madsen, H. 0., Krenk, S., and Lind, N. C. (1986), Methods of Structural Safety, Prentice-Hall, Englewood Cliffs, NJ
Matheron, G. (1967), 'Kriging or Polynomial Interpolation Procedures', Canadian Institute of Mining Bulletin, Vol.60, pp.1041
Rubinstein, R. Y. (1981), Simulation and the Monte Carlo method, John Wiley & Sons, New York
Shinozuka, M. (1983), 'Basic Analysis of Structural Safety', Journal of Structural Engineering, ASCE, Vol.109, No.3, pp.721-740

상세보기
Tang, W. H. (1984), 'Principles of Probabilistic Characterization of Soil Properties', Proceedings of the Symposium on Probabilistic Characterization of Soil Properties, Atlanta, Georgia, pp.74-89
Tang, W. H., Yucemen, M. S., and Ang, A H. S. (1976), 'Probability Based Short Term Design of Soil Slope', Canadian Geotechnical Journal, Vol.13, pp.201-215

상세보기
Vanmarcke, E. (1983), Random Fields: Analysis and Synthesis, The MIT Press, Cambridge, Massachusetts
Vanmarcke, E. H. (1977a), 'Probabilistic Modeling of Soil Profiles', Journal of Geotechnical Engineering Division, ASCE, Vol.103 (GT11), pp.1227-124
Vanmarcke, E. H. (1977b), 'Reliability of Earth Slopes', Journal of Geotechnical Engineering Division, ASCE, Vol.103 (GT11), pp.1247-1265

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[국내논문] 통계오차를 고려한 사면안정 신뢰성 해석
Reliability Analysis of Slope Stability with Sampling Related Uncertainty 원문보기

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[국내논문] 통계오차를 고려한 사면안정 신뢰성 해석 Reliability Analysis of Slope Stability with Sampling Related Uncertainty 원문보기

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[국내논문] 통계오차를 고려한 사면안정 신뢰성 해석
Reliability Analysis of Slope Stability with Sampling Related Uncertainty 원문보기

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