The Analysis of the Seepage Quantity of Reservoir Embankment using Stochastic Response Surface Method

확률론적 응답면 기법을 이용한 저수지 제체의 침투수량 해석

  • 봉태호 (서울대학교 생태조경.지역시스템공학부 대학원) ;
  • 손영환 (서울대학교 조경.지역시스템공학과) ;
  • 노수각 (서울대학교 생태조경.지역시스템공학부 대학원) ;
  • 최우석 (서울대학교 생태조경.지역시스템공학부 대학원)
  • Received : 2013.04.03
  • Accepted : 2013.05.03
  • Published : 2013.05.31


The seepage quantity analysis of reservoir embankment is very important for assessment of embankment safety. However, the conventional analysis does not consider uncertainty of soil properties. Permeability is known that the coefficient of variation is larger than other soil properties and seepage quantity is highly dependent on the permeability of embankment. Therefore, probabilistic analysis should be carried out for seepage analysis. To designers, however, the probabilistic analysis is not an easy task. In this paper, the method that can be performed probabilistic analysis easily and efficiently through the numerical analysis based commercial program is proposed. Stochastic response surface method is used for approximate the limit state function and when estimating the coefficients, the moving least squares method is applied in order to reduce local error. The probabilistic analysis is performed by LHC-MCS through the response surface. This method was applied to two type (homogeneous, core zone) earth dams and permeability of embankment body and core are considered as random variables. As a result, seepage quantity was predicted effectively by response surface and probabilistic analysis could be successfully implemented.


  1. Ahmed, A. A., 2009. Stochastic analysis of free surface flow through earth dams. Computers and Geotechnics 36(7): 1186-1190.
  2. Baecher, G. B., and J. T. Christian, 2003. Reliability and Statistics in Geotechnical Engineering. John Wiley & Sons.
  3. Berveiller, M., B. Sudret, and M. Lemaire, 2004. Comparison of methods for computing the response coefficients in stochastic finite element analysis. Proc. Second International ASRANet Colloquium, Barcelona, Spain.
  4. Box G. E. P., and K. B. Wilson, 1951. On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society B 13(1): 1-45.
  5. Bucher, C. G., and U. Bourgund, 1990. A fast and efficient response surface approach for structural reliability problems. Structural Safety 7(1): 57-66.
  6. Cho, S. E., 2006. Stochastic Seepage Analysis of Dam. Journal of the Korean Geotechnical Society 22(4): 73-83 (in korea).
  7. Cho, S. E., 2011. Probabilistic Seepage Analysis by the Finite Element Method Considering Spatial Variability of Soil Permeability. Journal of the Korean Geotechnical Society 27(10): 93-104 (in korea).
  8. Christian, J. T., C. C. Ladd, and G. B. Baecher, 1994. Rliability applied to slope stability analysis. Journal of Geotechnical Engineering 120(12): 2180-2207.
  9. Duncan, J. M., 2000. Factors of safety and reliability in geotechnical engineering. Journal of Geotechnical and Geoenvironmental Engineering 126(4): 307-316.
  10. El-Ramly, H., N. R. Morgenstern and D. M. Cruden, 2002. Probabilistic Slope Stability Analysis for Practice. Canadian Geotechnical Journal 39(3): 665-683.
  11. Isukapalli, S. S., A. Roy, and P. G. Georgopoulos, 1998. Stochastic response surface methods (SRSMs) for uncertainty propagation: application to environmental and biological systems. Risk Analysis 18(3): 351-363.
  12. Kim, S. H., and S. W. Na, 1995. Structural Reliability Analysis Using Improved Response Surface Method. Journal of the Korean Society of Civil Engineers 15(1): 63-72 (in korea).
  13. Lancaster, P., and K. Salkauskas, 1986. Curve and Surface Fitting: An introduction. Academic Press, San Diego.
  14. Lumb, P., 1974. Application of Statistics in Soil Mechanics, Ch. 3. In Soil Mechanics: New Horizons, ed. I. K. Lee, Elsevier, New York.
  15. Rajaschekhar, M. R., and B. R. Ellingwood, 1993. A new look at the response surface approach for reliability analysis. Structural Safety 12(3): 205-220
  16. Shepard, D. D., 1968. A Two Dimensional Interpolation Function for Irregularly Spaced Data. Proceeding of the 23rd ACM National Conference, 517-524.
  17. Sudret, B., 2008. Global sensitivity analysis using polynomial chaos expansions. Journal of Reliability Engineering & System Safety 93(7): 964-979.
  18. Tatang, M. A., 1995. Direct Incorporation of Uncertainty in Chemical and Environmental Engineering Systems. PhD thesis, Massachusetts Institute of Technology.
  19. Xiong, F., W. Chen, Y. Xiong, and S. Yang, 2011. Weighted stochastic response surface method considering sample weights. Journal of Structural and Multidisciplinary Optimization 43(6): 837-849.
  20. Yang, Y. S., J. O. Lee, and P. Y. Kim, 1996. Structural Reliability Analysis via Response Surface Method. The Society of Naval Architects of Korea 33(1): 98-108 (in Korea).