Journal of the Korean Geotechnical Society (한국지반공학회논문집)

Korean Geotechnical Society (한국지반공학회)
권호 표지

The Soil Particles Distributions and Fractal Dimension

흙의 입도분포와 플랙탈 차원

  • Yu, Chan (Dept. of Agricultural Engrg., Gyeongsang Nat'l Univ.) ;
  • Ahn, Sung-Yul (Dept. of Agricultural Engrg., Chonbuk Nat'l Univ.) ;
  • Lee, Chang-No (Dept. of Civil Engrg., Univ. of Seoul) ;
  • Baveye, Philippe C. (Dept. of Crop & Soil Science, Cornell Univ)
  • 유찬 (경상대학교 농공학과) ;
  • 안성율 (전북대학교 대학원 농공학과) ;
  • 이창노 (서울시립대학교 대학원 토목공학과) ;
  • Published : 2002.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

The fractal dimension that was evaluated with soil components from the traditional particle-size distribution(PSD) curve was analyzed using the results of Wu et al.(1993) and Bittelli et al.(1999). In order to find the change of the variation of fractal dimension with the upper and lower limit, three limit values(200$\mu{m}$, 63$\mu{m}$, and 125$\mu{m}$) were chosen, and these results of fractal dimension analysis were compared to the result that was evaluated in the whole range of the soils. The results showed that it is possible to evaluate fractal dimension from the traditional PSD curve with the soil contents, and it showed that Bittelli et at.(1999)'s upper and lower limit value was more reasonable than Wu et al.(1993). Equations that were presented by Bittelli et at.(1999) also showed a good agreement with the analytical results in the silt domain.

전통적인 흙의 입도분포 곡선상에서 흙의 구성 성분에 따른 프랙탈 차원의 변화에 대해서 Wu등(1993)과Bittelli 등(1999)의 연구결과를 중심으로 Buchan 등(1993)의 실험결과를 이용하여 고찰하였다. 자료분석시에는 실트와 모래의 경계값의 변화에 따른 프랙탈 차원의 변화를 알아보기 위하여 20$\mu{m}$, 63$\mu{m}$ 그리고 125$\mu{m}$에 대한 프랙탈 차원을 산정하여 전체 범위에서 구한 프랙탈 차원과 비교하였다. 분석결과에서는 전통적인 입도분포곡선상에서 프랙탈 차원의 산정은 가능한 것으로 나타났으며, 실트와 모래성분의 경계값은 Wu 등(1993)이 제시한 것 보다 Bittelli 등(1999)이 제시한 경계값이 더 적절함을 알 수 있었다. 또한 Bittelli 등(1999)이 제시한 실험식을 이용해서 실트영역의 프랙탈 차원을 비교적 정확하게 산정할 수 있었다.

Keywords

References

  1. Soil Sci. Soc. Am. J. v.62 Concepts of Fractals in Soil Science: Demixing Apples and Oranges Baveye, P. C.;Boast, C.W. https://doi.org/10.2136/sssaj1998.03615995006200050046x
  2. Fractals in Soil Science Baveye, P. C.;Parlange, J.-Y.;Stewart, B. A.(ed.)
  3. Soil Sci. Soc. Am. J. v.63 Characterization of Particle-Size distribution in Soils with a Fragmentation Model Bittelli, M.;Campbell G. S.;Flury M. https://doi.org/10.2136/sssaj1999.634782x
  4. Colloids Surf. Physicochem. Eng. Aspects v.73 Surface Area and Size Distributions of Soil Particles Borkovec, M.;Wu, Q.; Degovics, G.;Laggner, P.;Sticher, H. https://doi.org/10.1016/0927-7757(93)80007-2
  5. J. Geotech. Geoenvir. engrg. v.125 no.10 Fractal Representation of Soil Cohesion Bonala M. V. S.;Reddi L. N. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:10(901)
  6. Aust. J. Soil Res. v.31 no.4 A Comparison of Sedigraph and Pippette Methods for Soil Particle-size Analysis Buchan, G. D.;Grewal, K. S.;Claydon, J. J.;McPherson, R.J. https://doi.org/10.1071/SR9930407
  7. Fractals Feder, J.
  8. Fractal Geometry: Mathematical Foundations and Applications Falconer, K.
  9. Methods of Soil Amalysis. Part 1. (2nd Ed.) Agron. Manag. 9. Particle-size Analysis Gee, G. W.;Bauder, J. W.;A. Klute(ed.)
  10. Fractals v.1 no.4 Examples of Fractals in Soil Mechanics Herrmann, H. J.;Sahimi, M.;Tzschhichholz, F. https://doi.org/10.1142/S0218348X93000824
  11. Soil Sci. Soc. Am. J. v.60 A modified Number-based Method for Estimating Fragmentation Fractal Dimension of Soils Kozak, E.;Pachepsky, Y. A.;Sokolowski, S.;Sokolowska, Z.;Stepniewski, W. https://doi.org/10.2136/sssaj1996.03615995006000050002x
  12. The Fractal Geometry of Nature Mandelbrot, B. B.
  13. Fractals: From, Chance and Dimension Mandelbrot, B.B.
  14. J. Phys. Soc. Japan v.54 no.3 Fractal Viewpoint of Fracture and Accretion Matsushita, M. https://doi.org/10.1143/JPSJ.54.857
  15. Soil Sci. Soc. Am. J. v.61 On Interpretation and Misinterpretation of Fractal Models: A Reply to comment on number-size distributions, soil structure, and fractals Pachepsky, Ya.;Gimenez, D.;Logsdon;S. Allmaras, R. R.;Kozak. E. https://doi.org/10.2136/sssaj1997.03615995006100060037x
  16. Chaos and Fractals: New Frontiers of Science Peitgen H.-O.;Jurgens, H.;Saupe, D.
  17. Soil Sci. Soc. Am. J. v.55 Fractal Fragmentation, Soil Porosity, and Soil Water Properties: I. Theory Rieu, M.;Sposito, G. https://doi.org/10.2136/sssaj1991.03615995005500050006x
  18. Fractal Programming in C Stevens, R. T.
  19. J. Geotech. Geoenvir. engrg. v.124 no.1 Fractal Model for Flow through Saturated Soils Thevanayagam, S.;Nesarajah, S. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:1(53)
  20. J. Geophy. Res. v.91 no.B2 Fractals and Fragmentation Turcotte, D.L. https://doi.org/10.1029/JB091iB02p01921
  21. Soil Sci. Soc. Am. J. v.56 Fractal Scaling of Soil Particle-Size Distributions: Analysis and Limitations Tyler, S. W.;Wheatcraft, S. W. https://doi.org/10.2136/sssaj1992.03615995005600020005x
  22. Soil Sci. Soc. Am. J. v.53 Application of Fractal Mathematics to Soil Water Retention Estimation Tyler, S. W.;Wheatcraft, S. W. https://doi.org/10.2136/sssaj1989.03615995005300040001x
  23. Geotechnique v.45 no.1 Fractal analysis of Granular materials Vallejo, L. E. https://doi.org/10.1680/geot.1995.45.1.159
  24. Soil Sci. Soc. Am. J. v.57 On Particle-size distribution in soils Wu, Q.;Borkovec, M.;Sticher, H. https://doi.org/10.2136/sssaj1993.03615995005700040001x
  25. Soil Sci. Soc. Am. J. v.61 Comment on Number-size Distributions, Soil Structure, and Fractals Young, I. M.;Crawford, J. W.;Anderson, A.;McBratney, A. https://doi.org/10.2136/sssaj1997.03615995006100060036x