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SOIL PHYSICS

Using Complex Networks to Model Two- and Three-Dimensional Soil Porous Architecture

Sacha Jon Mooney^a,* and Dean Koroak^b,c

^a Environmental Sciences Section, School of Biosciences, Univ. of Nottingham, University Park, Nottingham NG7 2RD, UK
^b Center for Applied Mathematics and Theoretical Physics, Univ. of Maribor, Krekova 2, Maribor SI-2000, Slovenia
^c CUniv. of Maribor, Faculty of Civil Engineering, Chair for Applied Physics, Smetanova ulica 17, Maribor SI-2000, Slovenia

^* Corresponding author (sacha.mooney{at}nottingham.ac.uk).

The ability to quantify three dimensional (3-D) soil porous architecture is a key requirement in the advanced understanding of soil functioning. Recent developments in the visualization of soil structure using tools such as x-ray Computed Tomography (CT) provide new opportunities for pore-scale modeling. Here we apply a novel complex network approach to examine soil pore architecture in both two (2-D) and three dimensions (3-D). Using images of soil structure obtained by x-ray CT, we constructed and successfully validated a complex network derived from a simple measure for network links between two pores in 2-D. We were able to illustrate that the soil comprised a spatially embedded scale-free network characterized by a power-law degree distribution. Computation of the degree dependent clustering coefficient of the constructed networks showed the hierarchical organization of the soil pore architecture. Finally, we derived an algorithm to generate a soil structure model built on the underlying scale-free network which was in close agreement with an actual 3-D reconstructed soil structure. Considering the soil system as a complex network with scale-free properties is likely to have important consequences for the further understanding of function, in particular transport in soils.

Abbreviations: 2-D, two dimensional • 3-D, three dimensional • CT, computed tomography