Soil aggregates as mass fractals

Abstract

Soil aggregates have a fractal mass. That is, they are porous and, as they are studied in greater detail, more pores may be observed. Mass fractals have scale-dependent bulk density. Larger objects, or soil aggregates, have a smaller bulk density. Bulk density in soil studies is sometimes assumed to be constant. If this was the case, soil aggregates would not be mass fractals, and their porosity would not change with scale. The fact that soil aggregates are mass fractals places restrictions on the estimation of the fragmentation fractal dimension (Df) of soil. The mass fractal dimension of soil (Dm) may be calculated from bulk density-aggregate size data. Linear and nonlinear methods of estimating Dm were compared and were shown to give similar results. The Dm is shown to influence porosity and the saturated water content. Fractal theory, in particular Dm, has implications for the calculation of the pore-size distribution and the moisture characteristic. By equating Campbell's (1985) Version of the Brooks-Corey water retention function, � Proportional �(-1 / b)and an equivalent form to the Brooks-Corey relation given by Crawford (1994), � Proportional �(Dm - d) it is suggested that D-m = d - 1/b, where d is the embedding dimension.