Aspects of fractal geometry have been used to give quantitative measurements of soil structure. Fractal dimensions measured were the mass fractal dimension (Dm), surface fractal dimension (Ds), and the spectral dimension (d). We investigated the fractal component of a computer program, STRUCTURA, which measures the fractal dimension of soil from images of soil thin sections. Six thin sections, each showing different structural characteristics, were analyzed in order to obtain a range of fractal dimensions. The dimensions, in particular Dm and d, were shown to discriminate the different structures. The values of Dm and d ranged from 1.682 to 1.852 and 1.236 to 1.668, respectively. A further objective was to use these results, together with fractal theory, to show the potential fractal geometry has in predicting physical processes such as diffusion within the soil. To assist with the interpretation of fractal dimensions, the dimensions of different soil samples with the same porosity were compared.

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Fractal models of soil structure can be used to predict the scaling properties of associated transport coefficients. For gas diffusion, the structure of the soil pore space is relevant, while the structure of the solid matrix is most implicated in heat conduction. In fractal soil structures, the magnitude of the relevant diffusivities can be written in the generic form , where D(r) is a length‐dependent diffusion coefficient, A is the normalization coefficient, r is the Pythagorean length, and ϕ is a structure‐dependent constant. The dependence of ϕ on structure has been described elsewhere; however, the influence of structure on the magnitude of A has not been previously elaborated. Here, we determine the functional dependence of A on the structural parameters of the soil. The heterogeneity and connectivity, as quantified by the mass fractal dimension (Dm) and spectral dimension (d), respectively, and porosity are estimated from sections of undisturbed soil cores. For these soil structures, we demonstrate that the magnitude of the thermal and gas diffusivities is more sensitive to the porosity than to the scale dependency inherent in fractal structures. A methodology is developed and applied to rank the predicted thermal and gas diffusivities for the soil structures studied.

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