A multiscale study of silty soil structure

Abstract

SummaryDependency of soil properties on scale is a crucial issue in soil physics. In this paper, fractal approaches are used in two case studies in France and Australia, respectively, to study how measured physical soil properties change with the sample spacing and the scale of observation. At a scale of 10–1000 m (104 to 106 mm), fractals were applied to sample data from a linear transect, while at the 10−6 to 102 mm scale, fractals were applied in two dimensions to analyse both soil micro‐ and macrostructure, based on thin section samples. Porosity was characterized by short‐range spatial variations using sample spacings of 0.5 and 5 m (from the transect data), and a sample spacing of 1 cm (from the thin section analysis). The size of the representative elementary volume (REV) or representative elementary area (REA), required to represent statistically the elementary soil structure, was identified in three ways: (i) by the correlation length of a representative interconnected pore network, (ii) by the upper limit of the non‐linear increase with observation scale of mean porosity (upper limit of the solid mass fractal domain), and (iii) by the non‐linear decrease with observation scale of the coefficient of variation, CV, of mean porosity. Two embedded REAs were identified: the first (0.1–0.4 mm) related to the soil microstructure whereas a second (11–44 mm) related to the soil macrostructure. The solid mass fractal dimensions of the two embedded structural domains showed that hierarchical heterogeneity of soil structure was more pronounced for microstructures than for macrostructures. The mean area ratio of microstructural matrix/total surface and the CV of mean microporosity both scale similarly at observation scales smaller than the REA size. Their scaling exponents were both related to the fractal dimension of microstructural matrix. This preliminary study shows that the theory of fractals applied to soil structures at a specific scale range cannot be directly applied to predict soil physical properties at another scale range. This is because there are different interdependent structuring processes operating at different scales resulting in fractal dimensions being consistent only over particular domain limits.