Multifractal properties of porosity as calculated from computed tomography (CT) images of a sandy soil, in relation to soil gas diffusion and linked soil physical properties

Abstract

Relationships between soil porosity and diffusive gas flux are poorly understood, partly because of a difference in measurement scales between the two. The complexity of soil pore systems can be described by multifractal analysis at the microscopic scale, whereas relative soil gas diffusion coefficients ( D s / D o ) are usually evaluated at the core scale. The objectives of this study were to (i) define a quantitative ‘pseudo‐macroporosity gas ’ from high‐resolution X‐ray computed tomography (CT) scanning images and characterize it for 10 intact soil cores, (ii) analyse the frequency distribution of pseudo‐macropores gas in the columns with a multifractal approach and (iii) assess relationships between D s / D o measured at the core scale and multifractal parameters describing the pore system heterogeneity within a core. The shape and symmetry of the singularity spectra and the degree of curvilinearity of the Rényi spectra show that the multifractal behaviour of the pseudo‐macroporosity gas distribution for a given CT image thresholding varied among soil columns. Correlations found between D s / D o and some parameter estimates of the singularity spectrum suggest that the distribution of pseudo‐macropores gas , depending on the CT image thresholding, influenced D s / D o . In particular, a strong correlation between D s / D o and the entropy dimension (D q = 1 ) indicates that D s / D o was influenced by the degree of spatial heterogeneity of the pseudo‐macroporosity gas distribution. The correlation dimension (D q = 2 ) was also linked to D s / D o , suggesting that a second‐order power law might describe the scaling relationship between pseudo‐macroporosity gas distribution and D s / D o . In conclusion, the multifractal description of soil porosity as calculated from CT images may be regarded as a way to improve our understanding of gas movement in soils at the core scale.