Fractal Fragmentation, Soil Porosity, and Soil Water Properties: I. Theory

Abstract Recent efforts to characterize soil water properties in terms of porosity and particle‐size distribution have turned to the possibility that a fractal representation of soil structure may be especially apt. In this paper, we develop a fully self‐consistent fractal model of aggregate and pore‐space properties for structured soils. The concept underlying the model is the representation of a soil as a fragmented fractal porous medium. This concept involves four essential components: the mathematical partitioning of a bulk soil volume into self‐similar pore‐ and aggregate‐size classes, each of which is identified with a successive fragmentation step; the definition of a uniform probability for incomplete fragmentation in each size class; the definition of fractal dimensions for both completely and incompletely fragmented porous media; and the definition of a domain of length scales across which fractal behavior occurs. Model results include a number of equations that can be tested experimentally: (i) a fractal dimension ≤3; (ii) a decrease in aggregate bulk density (or an increase in porosity) with increasing aggregate size; (iii) a power‐law aggregate‐size‐distribution function; (iv) a water potential that scales as an integer power of a similarity ratio; (v) a power‐law expression for the water‐retention curve; and (vi) an expression for hydraulic conductivity in terms of the conductivities of single‐size arrangements of fractures embedded in a regular fractal network. Future research should provide experimental data with which to evaluate these predictions in detail.