Abstract
In this article, we are concerned with the statistics of steady unsaturated flow in soils with a fractal hydraulic conductivity distribution. It is assumed that the spatial distribution of log hydraulic conductivity can be described as an isotropic stochastic fractal process. The impact of the fractal dimension of this process, the soil pore-size distribution parameter, and the characteristic length scale on the variances of tension head and the effective conductivity is investigated. Results are obtained for one-dimensional and three-dimensional flows. Our results indicate that the tension head variance is scale-dependent for fractal distribution of hydraulic conductivity. Both tension head variance and effective hydraulic conductivity depend strongly on the fractal dimension. The soil pore-size distribution parameter is important in reducing the variability of the unsaturated hydraulic conductivity and of the fluxes.
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References
Ababou, R.; Gelhar L.W. 1990: Self-similar randomness and spectral conditioning: Analysis of scale effects in subsurface hydrology. In: Cushman, J.H. (ed.) Dynamics of fluids in hierarchical porous formations. Academic Press Ltd., London
Bakr, A.A.; Gelhar L.W.; Gutjahr A.L.; MacMillan, J.R. 1978: Stochastic analysis of spatial variability in subsurface flows, 1. Comparison of one- and three-dimensional flows. Water Resour. Res. 14(2), 263–271
Burrough, P.A. 1983a: Multiscale sources of spatial variation in soil. I: The application of fractal concepts to nested levels of soil variation. J. Soil Sci. 34, 577–597
Burrough, P.A. 1983b: Multiscale sources of spatial variation in soil. II: A non-brownian fractal model and its application in soil survey. J. Soil Sci. 34, 599–620
Burrough, P.A. 1981: Fractal dimension of landscapes and other environmental data. Nature, 294, 240–242
Freyberg, D.L. 1986: A natural gradient experiment on solute transport in a sand aquifer: 2. Spatial moments and the advection and dispersion of nonreactive tracers. Water Resour. Res. 22(13), 2031–2046
Hewett, T.A. 1986: Fractal distributions of reservoir heterogeneity and their influence on fluid transport, paper SPE15386 presented at the 61 st Annual Technical Conference, Soc. of Pet. Eng., New Orleans, La., Oct. 5–8
Kemblowski, M.W.; Chang, C-M. 1993: Infiltration in soils with fractal permeability distribution. Ground Water. March–April
Mandelbrot, B.B. 1983: The Fractal geometry of nature, 468, W.H. Freeman, New York
Sudicky, E.A. 1986: A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process. Water Resour. Res. 22(13), 2069–2082
Yeh, T-C.; Gelhar, L.W.; Gutjahr, A.L. 1985a: Stochastic analysis of unsaturated flow in heterogeneous soils, 1. Statistically isotropic media. Water Resour. Res. 21 (4), 447–456
Yeh, T-C.; Gelhar, L.W.; Gutjahr, A.L. 1985b: Stochastic analysis of unsaturated flow in heterogeneous soils, 2. Statistically anisotropic media with variable α. Water Resour. Res. 21(4), 457–464
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Chang, C.M., Kemblowski, M.W. Unsaturated flows in soils with self-similar hydraulic conductivity distribution. Stochastic Hydrol Hydraul 8, 281–300 (1994). https://doi.org/10.1007/BF01588758
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DOI: https://doi.org/10.1007/BF01588758