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Brittle Fracture of Fractal Cubic Aggregates

Dep. of Agronomy, Univ. of Kentucky, Lexington, KY 40546

B. D. Kay

Dep. of Land Resource Science, Univ. of Guelph, Guelph, ON, Canada N1G 2W1

*Corresponding author (eperfl{at}ukcc.uky.edu).

ABSTRACT

The conventional Weibull model for brittle fracture assumes soil aggregates are Euclidean cubes. Recent developments in fractal theory suggest that fractal cubes may provide a more realistic representation of soil aggregates. We modified the Weibull model for fractal cubes, and compared the performance of the modified model with the conventional model using previously published brittle fracture data for air-dry aggregates, ranging in equivalent cubic length from 1.19 to 25.275 mm, collected from different soils under the same crop, and similar soils under different crops. Goodness-of-fit statistics showed that the modified model fit the data much better than the conventional model. The modified model also produced a more accurate estimate of the spread in aggregate strength values. The modified model has an extra parameter. This parameter is the mass fractal dimension (D) of the solid phase. The theoretical range for D is zero to three. All of the estimates of D were less than three. However, 5% of the estimates were significantly less than zero. We attributed these negative estimates to the absence of any relationship between strength and size (within the range of length scales investigated) in the case of the weakest aggregates. The D increased with increasing clay content. We showed that the D for the solid phase is theoretically identical to the D for the pore-size distribution. Thus, it may be possible to predict the pore-size distribution of soil aggregates from brittle fracture data.

Received for publication March 16, 1994.

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