A MODIFIED NUMBER-BASED METHOD FOR ESTIMATING FRAGMENTATION FRACTAL DIMENSIONS OF SOILS

Fractal theory has been applied to the characterization of particle- a nd aggregate-size distributions in soils. We used a number-based metho d for estimating fragmentation fractal dimensions from these distribut ions. This method has several inconsistencies. The objectives of our s tudy were to: (i) propose a modified number-based method, (ii) evaluat e the modified method using published data on particle- and aggregate- size distributions, and (iii) apply the modified method to a large par ticle-size distribution data base to analyze the validity of fractal s caling. Assuming scale-invariant fragmentation to be a valid model of particle-size distribution within size ranges of fractions, we derived a formula expressing the characteristic grain size as a function of t he fractal dimension and limits of the grain size range. Parameters of Turcotte's fractal fragmentation model were found by minimizing the s um of squares of differences between measured and calculated masses of grain fractions. Comparison berween original and modified number-base d methods showed that the modified method generally resulted in lower fragmentation fractal dimensions than the original method. The modifie d method was applied to a data set of particle-size distributions of 2 600 soil samples. In 80% of samples, the fractal scaling was not appli cable across the whole range of particle size between 0.002 and 1 mm, since errors of the fractal fragmentation model were statistically sig nificantly larger than measurement errors, and estimates of the fracta l dimension were larger than 3. It appears that models more sophistica ted than scale-invariant fragmentation are required to simulate soil p article-size distributions.