A critical evaluation of the Miller and Miller similar media theory for application to natural soils

Abstract

The Miller-Miller similar media theory is widely applied to characterize the spatial variability of soil hydraulic properties. For a group of soils, a distinct scaling factor is commonly assigned to each individual soil to coalesce the soil water characteristic and hydraulic conductivity functions to single curves. It is generally assumed that the Miller-Miller theory is valid as long as soils are “similar” either with regard to their microscopic pore space geometry or the closely related macroscopic soil hydraulic functions. In this paper, it is illustrated that similarity is not the sole required condition for validity of the Miller-Miller theory. In addition, the interrelation between the soil water characteristic and the hydraulic conductivity functions considered for scaling need to be comparable. The interrelation is dependent not only on the pore space geometry, but also on solid-liquid interactions. Hence similar interrelation cannot be concluded from similarity of microscopic pore space geometry. A dimensionless parameter termed the “joint scaling factor” was defined and applied to evaluate the soundness of the interrelation condition for 26 soils from the UNSODA database that were grouped into six classes of similar soils. Obtained results clearly reveal the crucial importance of the interrelation condition for the Miller-Miller scaling theory, which has been hidden behind the “similarity” requirement, and contradict the general belief that Miller-Miller scaling is valid as long as soils are “similar.”.