Fractal Theory Applied to Soil Aggregation

Abstract

AbstractRecent advances in fractal theory may be applicable to the characterization of soil structure. This study explored two such applications. Aggregates were assumed to be approximated by cubes of constant dry density. Under this condition, the fractal dimension, D, provides a measure of fragmentation. The value of D increases with increasing fragmentation. The influence of energy input (wet sieving) on the D of aggregates from a Conestogo silt loam soil (finesilty, mixed, mesic Aquic Eutrocrept) was investigated. Aggregates were obtained from five cropping treatments, ranging from 15 yr of continuous corn (Zea mays L.) to 15 yr of continuous bromegrass (Bromus inermis Leyss.). The value of D was estimated from cumulative size‐frequency distribution data plotted on a log‐log scale. Computed values of D ranged from 2.51 to 3.52. Energy input, cropping history, and their interaction all had a significant effect on D. Fragmentation increased with energy input and time under corn production. Relations between D and the breakdown of individual aggregates were investigated. A scale‐invariant breakdown model was developed and tested. The model permits calculation of apparent probabilities of failure, P, as a function of aggregate size, x. Stepwise multiple regression analysis selected the rate of change in P with x as the best predictor of D following energy input. Fractal theory offers potential for modeling aggregate breakdown, as well as characterizing the degree of fragmentation.