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Analysis of Aggregate Fractal Dimensions and Aggregate Densities Back-Calculated from Hydraulic Conductivity

USDA-ARS, National Soil Tilth Lab., 2150 Pammel Drive, Ames, IA 50011

*Corresponding author (logsdon{at}nstl.gov).

ABSTRACT

Recently, aggregate size distributions (ASDs) have been characterized by fractal dimension (D, i.e., slope of the log of cumulative aggregate number as a function of the log of aggregate size). To simplify the laboratory work, aggregates are often considered to have scale-invariant density (). The D describes the completely fragmented ASD after sampling and sieving the aggregates, but a bulk D_r describes an incompletely fragmented ASD in situ. The D_r requires an estimate of scale-variant _i for each class. Then the ASD may be used to determine pore distributions and hydraulic conductivity (K) of the soil. The objectives of this study were to start with K determinations to back-calculate _i, D, D_r, and scale-invariant , and compare these with measured and D from measured ASDs taken near the locations of the K measurements. Back-calculated _i was not significantly different between class sizes for aggregates >2.8 to 5 mm, and the _i differences between aggregate sizes 1.26 to 25.2 mm would be difficult to determine with the precision (0.03–0.1 g cm^–3) of current methods for determining _i. The calculated _i and scale-invariant were all significantly less than measured . The D from back-calculated ASD were all greater than three, but they should have been less than the D_r from back-calculated ASD, which were all less than three. The D and D_r from back-calculated ASD were significantly different from D for measured ASD. Further study is needed to determine the relationship between ASD and K.

Received for publication June 20, 1994.