ON THE RELATION BETWEEN NUMBER SIZE DISTRIBUTIONS AND THE FRACTAL DIMENSION OF AGGREGATES

Number-size distributions (i.e. particle- and aggregate-size distribut ions) have historically been used as indicators of soil structure, and recent work has aimed to quantify this link using fractals to model t he soil fabric. This interpretation of number-size distributions is ev aluated, and it is shown that a number-size relation described by a po wer law does not in itself imply fractal structure as suggested, and a counter example is presented. Where fractal structure is assumed, it is shown that the power-law exponent, phi, describing the number-size distribution cannot be interpreted as the mass-fractal dimension, D(M) , of the aggregate. If the probability of fragmentation is independent of fragment diameter, then the exponent may be identified with the bo undary dimension, D(B), of the original matrix. If, however, as is lik ely, this probability is scale-dependent, then phi may over- or under- estimate the boundary dimension depending on whether the fragmentation probability increases or decreases with fragment size. The significan ce of these conclusions is discussed in terms of the interpretation of number-size distributions, and alternative methods for quantifying an d interpreting soil structure are evaluated.