Why natural log of soil permeability is a linear function of void ratio for 0-400µm soils having a sandy-silty-clayey matrix?

Many authors working on soil permeability put forward the proportionality of its value with the term e³/(1+e), where e is the void ratio. Others working on soils having a sandy-silty-clayey matrix, consider that the natural logarithm of their permeability is proportional to e. These two relations are very different. The link between them will be presented. Then, the way to calculate the soil permeability through that of the 0-400µ fraction will be detailed.