Fractal dimension of soil fragment mass-size distribution: A critical analysis

• Arithmetic averaging concept is not supported in the mass-based fractal model.
• Beside fractal dimension, lower and upper cutoffs of scale must be reported.
• Accurate fractal scaling parameters estimate needs precise measurement and analysis.

In this rapid communication, we address two important issues regarding the calculation of fragment mass-size distribution fractal dimension. We particularly focus on particle-size distribution, as a special case of fragment mass-size distribution, and demonstrate that the arithmetic mean concept frequently used in the literature is not supported. We also show that ignoring lower and upper cutoffs of fractal scaling may significantly alter the mass fractal dimension value. For these purposes, two examples using experiments available in the literature are given, and critical analyses are discussed in detail. We also reanalyze three databases reported in the literature, recalculate the mass fractal dimension, and show that applying the arithmetic mean concept and/or ignoring the lower and upper cutoffs may result in substantially different fractal dimension values. We note that the lower and upper cutoffs have to be reported in addition to the mass fractal dimension value. We also emphasize that accurate determination of the fractal scaling parameters, such as fractal dimension and lower and upper cutoffs requires precise characterization of the mass-size distribution.