Fractal dimensions for volume and surface of interaggregate pores - scale effects

D. Giménez, R. R. Allmaras, E. A. Nater, D. R. Huggins

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


Geometrical attributes of pore systems in soil have shown fractal scaling. Scaling in natural materials is inherently statistical, i.e., fractal dimensions may change with scale. While fractal dimensions characterizing pore surface roughness. D(s), or scaling of pore sizes. D(v), have been reported, seldom are both measurements made at more than one scale. We examine a scale effect on D(v) and D(s) values, and relationships between fractal dimensions of both properties. Natural and artificial types of soil structure were studied in a Normania soil. Natural soil structure was sampled from experiments involving: (1) three primary tillage tools sampled immediately after tillage; and (2) three tillage systems, sampled alter consolidation. Artificial soil structure was formed in columns packed with aggregate assemblies that included two single aggregate-size fractions, and two mixtures of six aggregate-size fractions (each covering two ranges) made to obtain fractal aggregate-size distributions. Block-like samples from all sources were resin-impregnated in situ and a face was cut and polished. Images of UV-illuminated faces were obtained at three magnifications and then pooled into two groups. A box-counting technique was applied to area and outline of pores to obtain D(v-box), and D(s-box), respectively; D(s) was also calculated from area-perimeter relations (D(s-AP). Box-count data showed two segments: D(v-box) and D(s-box) were evaluated in relation to each segment and to D(s-AP). Coefficients of determination in the relation D(s-AP) vs D(s-box), were relatively low, indicating discrepancies between the two methods. Fractal dimensions were not scale-invariant. Values of D(s-box) for aggregate assemblies decreased with resolution, especially for single aggregate size fractions. Values of D(v-box) were more influenced by aggregate than resolution. Both D(s-box) and D(v-box) varied with resolution for freshly tilled soil. For somewhat consolidated soil, variations in values of both fractal dimensions were related to tillage systems. Values if D(s-box) and D(v-box) were highly correlated, with linear relations depending on magnification and type of soil structure.

Original languageEnglish (US)
Pages (from-to)19-38
Number of pages20
Issue number1
StatePublished - May 1997


  • area perimeter
  • box-counting
  • pore geometry
  • soil aggregates
  • tillage


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