Journal of the Korean Geotechnical Society (한국지반공학회논문집)

Korean Geotechnical Society (한국지반공학회)
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Probabilistic Seepage Analysis by the Finite Element Method Considering Spatial Variability of Soil Permeability

투수계수의 공간적 변동성을 고려한 유한요소법에 의한 확률론적 침투해석

  • Cho, Sung-Eun (Department of Civil Engineering, Hankyong National Univ.)
  • 조성은 (국립한경대학교 토목공학과)
  • Received : 2011.08.10
  • Accepted : 2011.10.21
  • Published : 2011.10.31
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Abstract

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.

본 연구에서는 댐이나 보와 같은 수리구조물이 설치된 포화 기초지반에서의 구속흐름(confined flow)에 대하여 확률론적 침투해석을 수행하였다. 침투해석은 유한요소법을 이용하였으며 투수계수의 수평방향과 연직방향의 공간적 상관성이 상이한 비등방성을 고려하였다. 지정된 입력 확률분포함수와 자기상관함수(autocorrelation function)를 따르는 2차원의 랜덤필드를 생성하기 위하여 Karhunen-Lo$\grave{e}$ve 전개법을 사용하였으며 생성된 랜덤필드를 이용하여 확률론적 응답을 얻기 위해 Monte Carlo 시뮬레이션을 수행하였다. 이로부터 투수계수의 불확실성과 공간적 변동성이 수리구조물과 기초의 침투로 인한 안정성과 관련된 기초를 통한 유량, 구조물 하부에 작용하는 양압력, 하류 유출면에서의 유출동수경사에 미치는 영향을 연구하였다. 해석결과로부터 투수계수의 확률분포와 자기상관 구조를 만족하는 랜덤필드로 고려하여 공간적 변동을 고려하는 방법은 결정론적 해석이나 투수계수를 하나의 랜덤변수로 고려하는 경우에 나타나지 않는 다양한 지반의 침투거동을 효과적으로 고려할 수 있음을 보여준다.

Keywords

References

  1. 댐설계기준 (2005), 건설교통부.
  2. 조성은, 박형춘 (2008), "지반의 공간적 변동성을 고려한 확률론적 해석기법에 관한 연구", 한국지반공학회논문집, 제24권 제8호, pp.111-123.
  3. Ahmed, A. A. (2009), "Stochastic analysis of free surface flow through earth dams", Computers and Geotechnics, Vol.36, No.7, pp.1186-1190. https://doi.org/10.1016/j.compgeo.2009.05.005
  4. Baecher, G. B., and Christian, J. T. (2003), Reliability and Statistics in Geotechnical Engineering, John Wiley & Sons.
  5. DeGroot, D. J., and Baecher, G. B. (1993), "Estimating autocovariance of in-situ soil properties", Journal of the Geotechnical Engineering, Vol.119, No.1, pp.147-166. https://doi.org/10.1061/(ASCE)0733-9410(1993)119:1(147)
  6. Duncan, J. M. (2000), "Factors of safety and reliability in geotechnical engineering", Journal of Geotechnical and Geoenvironmental Engineering, Vol.126, No.4, pp.307-316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307)
  7. Elkateb, T., Chalaturnyk, R., and Robertson, P. K. (2002), "An overview of soil heterogeneity: Quantification and implications on geotechnical field problems", Canadian Geotechnical Journal, Vol.40, No.1, pp.1-15.
  8. El-Ramly, H., Morgenstern, N. R., and Cruden, D. M. (2003), "Probabilistic stability analysis of a tailings dyke on presheared clay-shale", Canadian Geotechnical Journal, Vol.40, No.1, pp.192-208. https://doi.org/10.1139/t02-095
  9. Fenton, G. A., and Griffiths, D. V. (1997), "Extreme hydraulic gradient statistics in stochastic earth dam", Journal of Geotechnical and Geoenvironmental Engineering, Vol.123, No.11, pp.995-1000. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:11(995)
  10. Fenton, G. A., Griffiths, D. V. (1996), "Statistics of free surface flow through stochastic earth dam", Journal of Geotechnical and Geoenvironmental Engineering, Vol.122, No.6, pp.427-436. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:6(427)
  11. Ghanem, R. G., and Spanos, P. D. (1991), Stochastic Finite Element-A Spectral Approach, Springer Verlag, New York.
  12. Ghiocel, D. M., and Ghanem, R. G. (2002), "Stochastic Finite-element Analysis of Seismic Soil-structure Interaction", Journal of Engineering Mechanics, ASCE, Vol.128, No.1, pp.66-77. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:1(66)
  13. Griffiths, D. V., and Fenton, G. A. (1997), "Three-dimensional seepage through spatially random soil", Journal of Geotechnical and Geoenvironmental Engineering, Vol.123, No.2, pp.153-160. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:2(153)
  14. Griffiths, D. V., and Fenton, G. A. (1998), "Probabilistic analysis of exit gradients due to steady seepage", Journal of Geotechnical and Geoenvironmental Engineering, Vol.124, No.9, pp.789-797. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:9(789)
  15. Gui, S., Zhang, R., Turner J. P., and Xue, X. (2000), "Probabilistic slope stability analysis with stochastic hydraulic conductivity", Journal of Geotechnical and Geoenvironmental Engineering, Vol.126, No.1, pp.1-9. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:1(1)
  16. Hsu, S. C., and Nelson, P. P. (2006), "Material spatial variability and slope stability for weak rock masses", Journal of Geotechnical and Geoenvironmental Engineering, Vol.132, No.2, pp.183-193. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:2(183)
  17. Lacasse, S, and Nadim, F. (1996), "Uncertainties in characterizing soil properties", Uncertainty in the Geologic Environment: From theory to practice, (eds Shackleford, CD, Nelson, PP and Roth, MJS.), Geotechnical Special Publication, ASCE, No.58, pp.49-75.
  18. Li, K. S., and Lumb, P. (1987), "Probabilistic design of slopes", Canadian Geotechnical Journal, Vol.24, pp.520-535. https://doi.org/10.1139/t87-068
  19. Matthies, G., Brenner, C., Bucher, C., and Soares, C. (1997), "Uncertainties in probabilistic numerical analysis of structures and solids-stochastic finite elements", Structural Safety, Vol.19, No.3, pp.283-336. https://doi.org/10.1016/S0167-4730(97)00013-1
  20. Rackwitz, R. (2000), "Reviewing probabilistic soils modeling", Computers and Geotechnics, Vol.26, No.3, pp.199-223. https://doi.org/10.1016/S0266-352X(99)00039-7
  21. Spanos, P. D., and Ghanem, R. G. (1989), "Stochastic Finite Element Expansion for Random Media", Journal of Engineering Mechanics, ASCE, Vol.115, No.5, pp.1035-1053. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:5(1035)
  22. Srivastava, A., Sivakumar Babu, G. L., and Haldar, S. (2010), "Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis", Engineering Geology, Vol.110, No.(3-4), pp.93-101. https://doi.org/10.1016/j.enggeo.2009.11.006
  23. Stein, M. L. (1987), "Large Sample Properties of Simulations Using Latin Hypercube Sampling", Technometrics, Vol.29, No.2, pp.143-151. https://doi.org/10.1080/00401706.1987.10488205
  24. Sudret, B., and Der Kiureghian, A. (2000), Stochastic Finite Element Methods and Reliability: a State-of-the-art Report, Tech. Rep. Report No. UCB/SEMM-2000/08, Department of Civil & Environmental Engineering, University of California, Berkeley, Institute of Structural Engineering, Mechanics and Materials.
  25. Vanmarcke, E. H. (1983), Random Fields: Analysis and Synthesis, The MIT Press, Cambridge, MA.

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