The origin and loss of fractal scaling in simulated soil aggregates

A growing body of evidence supports the use of fractals to approximate the heterogeneous structure of soil. Fractal models of transport processes in soil indicate that the fractal dimension and the upper limit to fractal scaling (denoted ξ) determine flow rates and scaling properties. A two-dimensional Monte Carlo simulation of soil aggregation is used to identify the key processes which may lead to fractal-like scaling in the soil matrix. A bonding law is developed which parameterizes the relative importance of chemical bonding to binding by microbial by-products and fungi. We investigate the sensitivity of the fractal dimension and ξ to the nature of the bonding law, and to aggregate fragmentation, initial particle size distribution and mechanical restructuring. Fractal-like structures result from the aggregation process. However, the measured fractal dimension is insensitive to the detailed form of the bonding law. The factor that most sensitively influences the fractal dimension is found to be mechanical restructuring such as would arise from the action of roots, soil fauna and natural weathering. By contrast, ξ is most sensitive to the bonding law. The results suggest that the fractal dimension and characteristic diameter of aggregates should be uncorrelated, and that increased binding by microbial by-products and fungi should produce larger, less dense, aggregates.