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Fractal Dimension and Lacunarity of Bulk Density Determined with X-ray Computed Tomography

Dep. of Civil Engineering

C. J. Gantzer and S. H. Anderson

Dep. of Soil and Atmospheric Sciences, Univ. of Missouri, Columbia, MO 65211

*Corresponding author (c587478{at}showme.missouri.edu).

ABSTRACT

Quantification of soil structure is important for understanding soil behavior. The objectives of this study were to: (i) introduce the use of the point-distribution method (PDM) for calculating fractal parameters of soil density (_b), and (ii) introduce the use of fractal lacunarity in conjunction with the fractal dimension for quantifying small-scale soil structure data collected with x-ray computed tomography. Undisturbed silt loam soil cores were taken from forest and grassland sites. Additional silt loam soil collected from a nearby cultivated field was sieved and repacked in 76-mm-diam. cores. Four cores were packed with soil passing through a 2-mm sieve but retained on a 1-mm sieve (1–2 mm). Four additional cores were packed with the soil passing through a 1-mm sieve (<1 mm). Computed tomography (CT) was used to measure small-scale _b of each 0.1 by 0.1 by 2 mm volume element (voxel) of a slice through a soil core. Calculation of fractal dimension and lacunarity was accomplished using the PDM on CT _b data. Results show that CT _b data are fractal when analyzed using the PDM. Mean fractal dimension (±SD) of the forest, grassland, <1 mm, and 1- to 2-mm groups were 2.42 ± 0.13, 2.35 ± 0.14, 2.50 ± 0.025, and 2.47 ± 0.013, respectively. Corresponding mean fractal lacunarity of these four groups at a voxel size of 3.1 mm were 0.24 ± 0.025, 0.24 ± 0.019, 0.16 ± 0.005, and 0.20 ± 0.012. Fractal lacunarity, which reflects the second-order statistics of _b, or the uniformity of pores and aggregates within a soil core, is essential for discriminating soils of similar but slightly different structure.

This paper was supported in part by Agric. Exp. Stn. Project no. 260, and USDA-CSRS Competitive Grant no. 91-34214-6012.

Received for publication July 24, 1995.

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