Mass fractal dimension of soil macropores using computed tomography: from the box‐counting to the cube‐counting algorithm

Summary Transport phenomena in porous media depend strongly on three-dimensional pore structures. Macropore networks enable water and solute to move preferentially through the vadose zone. A complete representation of their geometry is important for understanding soil behaviour such as preferential flow. Once we know the geometrical, topological and scaling attributes of preferential flow paths, we can begin computer simulations of water movement in the soil. The box-counting method is used in three dimensions (i.e. cube-counting algorithm) to characterize the mass fractal dimension of macropore networks using X-ray computed tomography (CT) matrices. We developed an algorithm to investigate the mass fractal dimension in three dimensions and to see how it compares with the co-dimensions obtained using the box-counting technique in two dimensions. For that purpose, macropore networks in four large undisturbed soil columns (850 mm × 77 mm diameter) were quantified and visualized, in both two and three dimensions, using X-ray CT. We observed an increasing trend between the fractal dimension and macroporosity for the four columns. Moreover, similar natural logarithm functions were obtained for the four cores by a least squares fit through plots of mass fractal dimension against macroporosity.

[1]  E. Perfect,et al.  Fractal Theory Applied to Soil Aggregation , 1991 .

[2]  W. J. Rawls,et al.  Fractal Description of Macroporosity , 1992 .

[3]  B. Griffiths,et al.  An investigation into sources of soil crack heterogeneity using fractal geometry , 1997 .

[4]  John W. Crawford,et al.  The relation between the moisture-release curve and the structure of soil , 1995 .

[5]  R. R. Allmaras,et al.  Fractal dimensions for volume and surface of interaggregate pores — scale effects , 1997 .

[6]  N. Bird,et al.  Water retention models for fractal soil structures , 1996 .

[7]  John W. Crawford,et al.  The fractal structure of soil aggregates: its measurement and interpretation , 1991 .

[8]  Philippe Baveye,et al.  Influence of image resolution and thresholding on the apparent mass fractal characteristics of preferential flow patterns in field soils , 1998 .

[9]  Gabriel B. Mindlin,et al.  An efficient algorithm for fast O(N*ln(N)) box counting , 1990 .

[10]  S. O. Prasher,et al.  Three‐Dimensional Quantification of Macropore Networks in Undisturbed Soil Cores , 1999 .

[11]  R. A. Shcherbakov,et al.  SCALING OF SOIL WATER RETENTION USING A FRACTAL MODEL , 1995 .

[12]  E. Perfect,et al.  Fractal Dimensions of Soil Aggregate‐size Distributions Calculated by Number and Mass , 1992 .

[13]  Horgan.  Mathematical morphology for analysing soil structure from images , 1998 .

[14]  Scott W. Tyler,et al.  Fractal processes in soil water retention , 1990 .

[15]  G. Sposito,et al.  MODELS OF THE WATER RETENTION CURVE FOR SOILS WITH A FRACTAL PORE SIZE DISTRIBUTION , 1996 .

[16]  Peter Pfeifer,et al.  Fractal dimension to describe soil macropore structure using X ray computed tomography , 1994 .

[17]  C. J. Gantzer,et al.  Fractal Dimension and Lacunarity of Bulk Density Determined with X-ray Computed Tomography , 1996 .

[18]  H.W.G. Booltink,et al.  Using fractal dimensions of stained flow patterns in a clay soil to predict bypass flow. , 1992 .

[19]  H. Stanley,et al.  I Fractals and multifractals: the interplay of Physics and Geometry , 1991 .

[20]  Shiv O. Prasher,et al.  CHARACTERIZATION OF MACROPORE MORPHOLOGY IN A SANDY LOAM SOIL USING X-RAY COMPUTER ASSISTED TOMOGRAPHY AND GEOSTATISTICAL ANALYSIS , 1998 .

[21]  Richard Webster,et al.  The topology of pore structure in cracking clay soil I. The estimation of numerical density , 1988 .

[22]  R. Allmaras,et al.  Fractal Characterization of Aggregate-Size Distribution: The Question of Scale Invariance , 1996 .

[23]  Alex B. McBratney,et al.  Soil Mass, Surface, and Spectral Fractal Dimensions Estimated from Thin Section Photographs , 1996 .

[24]  John W. Crawford,et al.  On the relation between number-size distributions and the fractal dimension of aggregates , 1993 .

[25]  L. Liebovitch,et al.  A fast algorithm to determine fractal dimensions by box counting , 1989 .

[26]  J. Crawford,et al.  Heterogeneity of the pore and solid volume of soil: Distinguishing a fractal space from its non-fractal complement , 1996 .

[27]  I. Young,et al.  The analysis of fracture profiles of soil using fractal geometry , 1992 .

[28]  J. Scott Shepard,et al.  Using a Fractal Model to Compute the Hydraulic Conductivity Function , 1993 .

[29]  Garrison Sposito,et al.  Fractal Fragmentation, Soil Porosity, and Soil Water Properties: I. Theory , 1991 .

[30]  W. Rawls,et al.  Predicting Saturated Hydraulic Conductivity Utilizing Fractal Principles , 1993 .