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The probabilistic Analysis of Degree of Consolidation by Spatial Variability of Cv

압밀계수의 공간변동성에 따른 압밀도의 확률론적 해석

  • 봉태호 (서울대학교 생태조경.지역시스템공학부 대학원) ;
  • 손영환 (서울대학교 조경.지역시스템공학과, 서울대학교 농업생명과학연구원) ;
  • 노수각 (서울대학교 생태조경.지역시스템공학부 대학원) ;
  • 박재성 (서울대학교 생태조경.지역시스템공학부 대학원)
  • Received : 2012.02.13
  • Accepted : 2012.05.14
  • Published : 2012.05.31

Abstract

Soil properties are not random values which is represented by mean and standard deviation but show spatial correlation. Especially, soils are highly variable in their properties and rarely homogeneous. Thus, the accuracy and reliability of probabilistic analysis results is decreased when using only one random variable as design parameter. In this paper, to consider spatial variability of soil property, one-dimensional random fields of coefficient of consolidation ($C_v$) were generated based on a Karhunen-Loeve expansion. A Latin hypercube Monte Calro simulation coupled with finite difference method for Terzaghi's one dimensional consolidation theory was then used to probabilistic analysis. The results show that the failure probability is smaller when consider spatial variability of $C_v$ than not considered and the failure probability increased when the autocorrelation distance increased. Thus, the uncertainty of soil can be overestimated when spatial variability of soil property is not considered, and therefore, to perform a more accurate probabilistic analysis, spatial variability of soil property needed to be considered.

Keywords

References

  1. Agterberg, F. B., 1970. Autocorrelation function in geology, proceeding of a colloquium on geostatistics, University of Kansas, Lawrence: 113-141.
  2. Baecher, G. B., 1982. Simplified Geotechnical Data Analysis, Proc., NATO Advanced Study Inst. on Reliability Theory and Its Application in Struct. and Soil Mech., Martinus Nijhoff Publishers, Bornholm, Denmark: 257-277.
  3. Buckheit, J. B., 1996. Statistical applications of adaptive basis selection. Ph.D. diss., Stanford university.
  4. Cho, S. E., and H. C. Park, 2009. Probabilistic stability analysis of slopes by the limit equilibrium method considering spatial variability of soil property, Journal of Korean Geotechnical Society, 25(12): 13-25 (in Korean).
  5. Christian, J, T,. 2004. Geotechnical engineering reliability: How well do we know what we are doing?, Journal of Geotechnical and Geoenvironmental Engineering, 130(10): 985-1003. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:10(985)
  6. DeGroot, D. J., and G. B. Baecher, 1993. Estimating Autoconvariance of In-situ Soil Properties, Journal of Geotechnical and Geoenvironmental Engineering, 119(1): 147-166. https://doi.org/10.1061/(ASCE)0733-9410(1993)119:1(147)
  7. Diego, L. A., and I. C. Vincenzo, 2009. Discretization of 2D random fields: A genetic algorithm approach, Engineering Structures, 31(5): 1111-1119. https://doi.org/10.1016/j.engstruct.2009.01.008
  8. Elkateb, T., R. Chalaturnyk, and P. K. Robertson, 2002. An overview of soil heterogeneity: quantification and implications on geothchnical field problems, Canadian Geotechnical Journal, 40(1): 1-15.
  9. Ghanem, R. G., and P. D. Spanos, 2003. Stochastic Finite Elements: A Spectral Approach, Revised Edition, Dover Publications.
  10. Lacasse, S., and F. Nadim, 1996. Uncertainties in characteristic soil properties, Proceedings of Uncertainty 1996, Geotechnical Special Publication, 58(1): 49-75.
  11. Li, K. S., and P. Lumb, 1987. Probabilistic design of slopes, Canadian Geotechnical Journal, 24(4): 520-535. https://doi.org/10.1139/t87-068
  12. Lumb, P., 1966. Variability of Natural Soils, Canadian Geotechnical Journal, 3(2): 74-97. https://doi.org/10.1139/t66-009
  13. Lumb, P., 1968. Statistical aspects of soil measurements. Proc. 4th Australian Road Research Conference, 4: 1761-1770.
  14. Lumb P., 1975. Spatial variability of soil properties, Proc. 2nd Intl Conference on Application of Statistics and Probability to Soil and Structural Engineering. Aachen, 2: 397-421.
  15. Mckay, M. D., R. J. Bechman, and W. J. Conover, 1979. A comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer code, Technometrics, 21(2): 239-245.
  16. Olson, A., G. Sandberg, and O. Dahlblom, 2003. On Latin hypercube sampling for structural reliability analysis, Structural Safety, 25: 47-68. https://doi.org/10.1016/S0167-4730(02)00039-5
  17. Padilla, J. D., and E. H. Vanmarcke, 1974. settlement of structure on shallow foundation, Research report R74-9, Department of Civil Engineering, MIT, Cambridge.
  18. Rackwitz, R., 2000. Reviewing probabilistic soils modelling, Computer and Geotechnics, 26: 199-223. https://doi.org/10.1016/S0266-352X(99)00039-7
  19. Spanos, P. D., and R. G. Ghanem, 1989. Stochastic Finite Element Expansion for Random Media, Journal of Engineering Mechanics, 115(5): 1035-1053. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:5(1035)
  20. Stein, M., 1987. Large sample properties of simulations using Latin Hypercube Sampling, Technometrics, 29(2): 143-151. https://doi.org/10.1080/00401706.1987.10488205
  21. Sudret, B., and A. Der Kiureghian, 2000. Stochastic Finite Element Methods and Reliability: A State-of the-Art Report, Tech. Rep. Report No. UCB/SEMM-2000/8, Department of Civil Engineering & Environmental Engineering, University of California, Berkeley.
  22. Terzaghi, K., 1923. Die Berechnung der Durchlassigkeitsziffer des Tones aus dem Verlauf der Hydrodynamischen, Sber. Akad. Wiss. Wein, Ausria, 182: 125-138.
  23. Van Trees, H. L., 2001. Detection, estimation and modulation theory, Part I, Republished in paperback, John Wiley and Sons, Inc., New York.
  24. Vanmarcke, E. H., 1983. Random field: Analysis and Synthesis, The MIT Press, Cambridge, MA.