Analysis of Aggregate Fractal Dimensions and Aggregate Densities Back-Calculated from Hydraulic Conductivity
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 (ρ). The D describes the completely fragmented ASD after sampling and sieving the aggregates, but a bulk Dr describes an incompletely fragmented ASD in situ. The Dr requires an estimate of scale-variant ρi 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 ρi, D, Dr, and scale-invariant ρ, and compare these with measured ρ and D from measured ASDs taken near the locations of the K measurements. Back-calculated ρi was not significantly different between class sizes for aggregates >2.8 to 5 mm, and the ρi 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 ρi. The calculated ρi and scale-invariant ρ were all significantly less than measured ρ. The D from back-calculated ASD were all greater than three, but they should have been less than the Dr from back-calculated ASD, which were all less than three. The D and Dr from back-calculated ASD were significantly different from D for measured ASD. Further study is needed to determine the relationship between ASD and K.Please view the pdf by using the Full Text (PDF) link under 'View' to the left.
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