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

Abstract

AbstractQuantification 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 (ρb), 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 ρb 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 ρb data. Results show that CT ρb 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 ρb, or the uniformity of pores and aggregates within a soil core, is essential for discriminating soils of similar but slightly different structure.