Effective hydraulic conductivity of stony soils: General effective medium theory

Abstract

Despite a longstanding interest in understanding the effects of rock fragments on soil hydraulic properties, physically-based models to describe the effective hydraulic conductivity of stony soils are still rare. The conductivity of stony soils is mostly described by simple scaling approaches, assuming impermeable rock fragments. We present a model based on the general effective medium (GEM) theory to calculate the effective hydraulic conductivity of stony soils. The model accounts for the volumetric content, shape, and orientation of rock fragments in the main direction of water flow. Rock fragments can either be permeable or impermeable in the model which allows to calculate the effective unsaturated hydraulic conductivity curve of stony soils over the full range of soil matric potentials. Existing models assume rock fragments to be isolated and their application is therefore limited to low to moderately stony soils. In GEM model interaction between rock fragments is allowed, which makes it applicable in stony soils with high contents of rock fragments. The mathematical simplicity of the model makes it suitable for practical applications and provides a strong theoretical basis for improving predictions of flow and transport in hydrological models applied in forested and agricultural watersheds and mountainous areas.