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http://dx.doi.org/10.5389/KSAE.2006.48.4.041

Estimation of Permeability Coefficient Using Fractal Dimension of Particle Size Distribution Curve in Granular Soils  

Park Jae-Seong (극동엔지니어링(주) 기술연구소)
Chang Pyoung-Wuck (서울대학교 지역시스템공학전공)
Son Young-Hwan (서울대학교 대학원)
Kim Seong-Pil (서울대학교 대학원)
Publication Information
Journal of The Korean Society of Agricultural Engineers / v.48, no.4, 2006 , pp. 41-49 More about this Journal
Abstract
Since particle size distribution curves are useful to estimate permeability of soil, many formulae for permeability coefficient (k) have been published using the parameter from the curves and factors, such as grain size, particle shape and void ratio of soils. However, the parameters such as $C_c,\;C_u$ and $D_n$ derived from only some discrete points on the curve are insufficient to represent the whole gradation. In this paper fractal dimension which is quite new concept and known to be able to represent the entire curve of particle size distribution is employed for the parameters. An empirical formula of permeability coefficient has been developed with fractal dimension and percent of finer than 0.075 mm. The formula developed from this study has confirmed its effectiveness by a series of laboratory tests and comparison to other published formulae. It is found that permeability coefficient is proportional to fractal dimension and inversely proportional to percent of fines.
Keywords
Permeability coefficient; Fractal dimension; Fragmentation fractal; Particle size distribution curve;
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1 Hazen, A. 1892, Some physical properties of sands and gravels, with special reference to their use in filtration, 24th Annual Rep., Massa-chusetts State Board of Health, Pub. Doc. No. 34, 539 - 556
2 Tyler, S. W. and S.W. Wheatcraft. 1992, Fractal Scaling of Soil Particle Size Distributions: Analysis and Limitations, Soil Sci. Soc. Am. J. Vol. 56, pp. 362-369   DOI
3 Yu, C. Ahn, S. Y., Lee, C. N. and Baveye, P. C., 2002, 'The Soil Particles Distributions and Fractal Dimension'. Journal of Korean Geotechnical Society. Vol. 18. No.6. pp. 25-32
4 Amer, A. M. and Awad, A. A. 1974, Permeability of Cohesionless Soils, J. Geotech. Eng. Div. Am. Soc. Civ. Eng., 100(12), pp. 1309-1316
5 Moore, C. A. and Donaldson, C. F. 1995, Quantifying soil micro-structure using fractals, Geotechnique, 45(1), pp. 105-116   DOI   ScienceOn
6 Adolfo, N. D. Posadas, Daniel Gimenez, Marco Bittelli, Carlos M. P. Vaz, and Markus Flury. (2001), 'Multifractal characterization of soil particle-size distributions', Soil Sci. Soc. AM. J., Vol. 65, pp. 1361-1367   DOI   ScienceOn
7 Alyamani, M. S. and Sen, Z. 1993, Determination of Hydraulic Conductivity from Complete Grain-Size Distribution Curves, Ground Water, 31 (4), pp. 551-555   DOI   ScienceOn
8 Krumbien, W. C. and Monk, G. D. 1942, Permeability as a Function of the Size Parameters of Unconsolidated Sand, Am. Inst. Mining Eng., Littleton, Co, Tech. Pub
9 Bittelli, M., Camlbell, G. S. and Flury, M. 1999, Characterization of particle-size distribution in soils with a fragmentation model, Soil Sci. Soc. AM. J., Vol. 63, pp. 782-788   DOI
10 Turcotte, D. L. 1986, Fractals and Fragmentation, J. Geophys. Res. Vol. 91, pp. 1921-1926   DOI
11 Min, T. K. and Lee, W. J., 2003, 'Fragmentation Fractal Analysis on Particle-size Distribution', Journal of Korean Geotechnical Society, Vol. 19, No.2, pp. 199-206
12 Mandelbrot, B. B. 1982, The Fractal Geometry of Nature. Freeman and Co., San Francisco
13 Carman, P. G. 1956, Flow of gases through porous media, Butterworths Scientific Publications, London
14 Berg, R. R. 1970, Method for determining permeability from reservoir rock properties, Trans. Gulf Coast Assn. Geol. Soc. Vol. 20, pp. 303-317
15 Vallejo, L. E. 1995, Fractal analysis of granular materials, Geotechnique, 45 (1), pp. 159-163   DOI   ScienceOn
16 Hazen, A. 1911, Discussion of 'Dams on Sand Foundations' by A. C. Koenig, Trans. Am. Soc. Civ. Eng., Vol. 73, pp. 199
17 Matsushita, M. 1985, Fractal Viewpoint of Fracture and Accretion, J. Phys. Soc. Jpn, Vol. 54, pp. 857-860   DOI   ScienceOn
18 Hyslip, James P. and Vallejo, L.E. 1997, Fractal analysis of the roughness and size distribution of granular materials, Elsevier, Eng. Geology, Vol. 48, pp. 231-244   DOI   ScienceOn
19 Song, Y. W. and Lee, I, K, 2002, 'Prediction of hydraulic Conductivity from Grainsize Distribution Parameters', Journal of Korean Geotechnical Society, Vol. 18, No.3, pp. 5-12