Silty topsoil structure and its dynamics: the fractal approach

Abstract This paper describes the application of fractal geometry to the structure and dynamics of tilled silty topsoil. The soil structure of each topsoil sample has been experimentally quantified directly by image analysis and indirectly by both water retention and mercury porosimetry. Any fractal scaling laws were mostly determined within a relevant common pore radius yardstick scale. Their scale invariants were fractal dimensions of either the matrix ( D m ) or the solid:pore interfaces ( D s ). We showed that the D m or D s values computed from water retention data were higher than their D m or D s value counted from mercury porosimetry data, which were themselves much higher than their microscopic fractal dimension value counterparts (only D m ). This was attributed to (i) partial pore-volume filling by either water or mercury and (ii) hysteresis between water drainage and mercury intrusion. A positive relationship between the fractal dimensions of the solid:pore interfaces and their solid mass fractal dimension counterparts have also been found, with the value of D m being higher than the corresponding value of D s , characterizing complex fractal structures with interconnected pores. We also showed that clay content has a positive effect on both D m and D s values from either water retention or mercury porosimetry data as well on the positive relationship occurring between the D s values and their D m value counterparts. The physical process underlying this behaviour is proposed to be partial volume-pore filling by clays and, concomitantly, an increase in the rugosity of the microscopic solid: pore interfaces. In contrast, the temporal variability of either D m or D s values was moderate and can be attributed to both increase of pore connectivity and water hysteresis which occurred during the drying and wetting cycles of the studied cultivation period.