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

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 (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.

Macrostructural changes in compacted earthen construction materials under loading

“…The lacunarity, L, represents the interconnectivity (or 148 heterogeneity or gappiness) of the pattern, and can be considered to be the P (λ) intercept of 149 the linear fit to the plot of λ against P (λ). A larger value of L therefore indicates that there 150 are more gaps between the objects so that a greater number of boxes is required to cover the 151 pattern (Zeng et al, 1996). Both the lacunarity and the fractal dimension are therefore required …”

Applications of X-Ray Computed Tomography for Examining Soil Structure: A Review

“…Various studies have used X-ray CT to quantify properties of macropore network morphology, including pore diameter Zeng et al, 1996), crack formation , pore network structure (Baveye et al, 2002;Aravena et al, 2011) and pore circularity (Gantzer and Anderson, 2002).…”

“…In 1974, Fourie used for the first time the CT in his researches of paleontology, and after that Conroy and Vannier (1984) and Houbitz et al (1988) also used it with great success. In sedimentology, it was used by researchers for the analysis of sedimentary structures (Kenter, 1989;Peyton et al, 1992;Zeng et al, 1996). It was also used for the study of rock porosity, material density and fractures (Jacobs et al, 1995 The aim of this study is to present a review of the application of X-ray CT in soil science, as a modern technique for structural analysis.…”

Influence of thresholding in mass and entropy dimension of 3-D soil images

“…Peyton et al (1994) evaluated the fractal dimension of macropore-scale density. Zeng et al (1996) calculated fractal lacunarity in a silt loam soil. Several authors have dedicated their attention to the appropriate pore-solid CT threshold, before calculating mass fractal and surface fractal dimensions (Rogasik et al, 1999;Gantzer and Anderson, 2002;Perret et al, 2003;Rachmant et al, 2005).…”