Economic and Environmental Geology (자원환경지질)

The Korean Society of Economic and Environmental Geology (대한자원환경지질학회)
권호 표지

Evaluation of the Probability of Failure in Rock Slope Using Fuzzy Reliability Analysis

퍼지신뢰도(fuzzy reliability) 해석기법을 이용한 암반사면의 파괴확률 산정

  • Park, Hyuck-Jin (Department of Geoinformation Engineering, Sejong University)
  • 박혁진 (세종대학교 지구정보공학과)
  • Published : 2008.12.28
Download PDF
⟨ Previous Next ⟩

Abstract

Uncertainties are pervasive in engineering geological problems. Therefore, the presence of uncertainties and their significance in analysis and design of slopes have been recognized. Since the uncertainties cannot be taken into account by the conventional deterministic approaches in slope stability analysis, the probabilistic analysis has been considered as the primary tool for representing uncertainties in mathematical models. However, some uncertainties are caused by incomplete information due to lack of information, and those uncertainties cannot be handled appropriately by the probabilistic approach. For those uncertainties, the theory of fuzzy sets is more appropriate. Therefore, in this study, fuzzy reliability analysis has been proposed in order to deal with the uncertainties which cannot be quantified in the probabilistic analysis due to the limited information. For the practical example, a slope is selected in this study and both the probabilistic analysis and the fuzzy reliability analysis have been carried out for planar failure. In the fuzzy reliability analysis, the dip angle and internal friction angle of discontinuity are considered as triangular fuzzy numbers since the random properties of the variables cannot be obtained completely under the conditions of limited information. In the study, the fuzzy reliability index and the probabilities of failure are evaluated from fuzzy arithmetic and compared to those from the probabilistic approach using Monte Carlo simulation and point estimate method. The analysis results show that the fuzzy reliability analysis is more appropriate for the condition that the uncertainties arise due to incomplete information.

불확실성은 사면의 안정성을 해석하는 과정에서 특성자료의 부족이나 지질공학적 특성의 공간적 변동성 등의 원인으로 포함되며 따라서 불확실성으로 인해 변수들의 정확한 값을 획득하기 힘들게 된다 이러한 문제점을 해결하기 위하여 확률론적 해석기법이 활용되어 왔으며 최근에는 퍼지집합이론(fuzzy set theory)을 이용한 해석기법이 활용되고 있다. 특히 확률변수들의 자료 양이 제한적인 경우 변수의 확률특성을 정확하게 파악하기 힘들어 확률론적 해석기법의 활용이 제한적일 수 있으며 이러한 경우 퍼지집합이론은 확률변수의 특성을 효과적으로 표현할 수 있다. 본 연구에서는 암반사면의 안정성 해석과정에서 포함되는 불확실성을 정량화하기 위해 퍼지신뢰도척도(fuzzy reliability measure)를 활용하여 분석을 수행하였으며 특히 암반사면의 안정성에 영향을 미치는 여러 지질공학적 특성중 불연속면의 경사와 내부마찰각을 삼각형 퍼지숫자(fuzzy number)로 해석하였다 이를 위하여 연구대상사면을 선정하여 암반사면에서 발생하는 평면파괴를 대상으로 분석을 수행하였다. 퍼지신뢰도(fuzzy reliability) 해석에서는 퍼지숫자에 대한 퍼지 연산을 통해 퍼지신뢰도 지수(fuzzy reliability index)를 획득하였으며 이러한 결과를 확률론적 해석 결과와 비교하기 위하여 몬테카를로모사기법(Monte Carlo simulation)과 점추정법(point estimate method)을 이용한 확률론적 해석을 수행하였다. 해석결과 불충분한 자료 등으로 인해 불확실성의 정량화가 어려운 경우 퍼지신뢰도 해석을 통해 적절한 퍼지신뢰도 지수와 파괴확률을 획득할 수 있을 것으로 판단된다.

Keywords

References

  1. Dodagoudar, G.R. and Venkatachalam, G. (2000) Reliability analysis of slope using fuzzy sets theory. Computers and Geotechnics, v. 27, p. 101-115 https://doi.org/10.1016/S0266-352X(00)00009-4
  2. Harr, M.E. (1987) Reliability Based on Design in Civil Engineering. McGraw-Hill, New York
  3. Hoek, E.T. (1998) Factor of safety and probability of failure. Course notes. Internet edition, http:www.rockeng. utoronto.ca/hoekcorner.htm
  4. Giasi, C.I., Masi, P., and Cherubini, C. (2003) Probabilistic and fuzzy reliability analysis of a sample slope near Aliano. Engineering Geology, v.67, p.391-402 https://doi.org/10.1016/S0013-7952(02)00222-3
  5. Juang, C.H., Jhi, Y.Y., and Lee, D.H. (1998) Stability analysis of existing slopes considering uncertainty. Engineering Geology, v.49, p.111-122 https://doi.org/10.1016/S0013-7952(97)00078-1
  6. Mostyn, G.R. and Li, K.S. (1993) Probabilistic slope analysis - state of paly. Proceeding of Conference on Probabilistic Method in Geotechnical Engineering, p.89-109
  7. Nilsen, B. (2000) New trend in rock slope stability analysis. Bull. Eng. Geol. Environ., v.58, p.173-178 https://doi.org/10.1007/s100640050072
  8. Park, H.J. (2002) Evaluation of failure probability for planar failure using point estimate method. Tunnel and Underground. v. 12, p. 189-197
  9. Park, H.J., West, T.R. and Woo, I. (2005) Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40. Engineering Geology, v. 79, p. 230-250 https://doi.org/10.1016/j.enggeo.2005.02.001
  10. Pathak, D. and Nilsen, B. (2004) Probabilistic rock slope stability analysis for Himalayan condition. Bull. Eng. Geol. Environ., v. 63, p. 25-32 https://doi.org/10.1007/s10064-003-0226-1
  11. Schultze, E. (1975) The general significance of statistics for the civil engineer. Proc. of 2nd Int. Conf. on Application of Statistics and Probability in Soil and Structural Engineering. Aachen
  12. Zadeh, L.A. (1975) Fuzzy sets. Information and Control, v.8, p.338-353 https://doi.org/10.1016/S0019-9958(65)90241-X
  13. Zimmermann, H.J. (1991) Fuzzy Set Theory and its Application. Kluwer Academics, p. 456