Heterogeneity of the pore and solid volume of soil: Distinguishing a fractal space from its non-fractal complement

Crawford, J. W. and Matsui, N. (1996) Heterogeneity of the pore and solid volume of soil: Distinguishing a fractal space from its non-fractal complement. Geoderma, 73(3-4), pp. 183-195. (doi: 10.1016/0016-7061(96)00045-6)

Abstract

The scaling properties of fractals are formally defined only in the limit of infinite or infinitessimal length scales, while measurements are necessarily restricted to finite scales. The implications of this limitation are studied from the perspective of characterising the heterogeneity of a fractal and its complement. An examination of the scaling properties of the solid and pore space of soil aggregates is presented as a case study. A relationship is derived between the heterogeneity of the solid volume and that of the pore space, under the assumption that either the solid or pore can be approximated by a fractal. If the solid is fractal, then the pore volume (its space complement) is asymptotically homogeneous as the sample volume increases to infinity i.e. the porosity is effectively scale-independent for large sample sizes. For smaller sample volumes, however, the porosity is scale-dependent, and this dependency is a function of the fractal dimension of the solid. Where the solid has a fractal dimension close to the Euclidean value, the pore volume behaves like a fractal, and this presents a problem from a methodological point of view, in distinguishing between a fractal and its complement. It is shown how misinterpretation can lead to errors in the prediction of moisture distribution and transport processes. A method for making the distinction is presented here, and is tested using image analysis of soil thin sections.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Crawford, Professor John
• Authors: Crawford, J. W., and Matsui, N.
• College/School: College of Social Sciences > Adam Smith Business School > Management
• Journal Name: Geoderma
• Publisher: Elsevier
• ISSN: 0016-7061
• ISSN (Online): 1872-6259