Estimating scale dependence of saturated hydraulic conductivity in soils

Abstract

Understanding the effect of sample volume on hydraulic and physical properties of soils has broad applications to problems in hydrogeology, soil physics, and environmental engineering. The scale dependence of flow and transport is attributed to spatial heterogeneities, such as pore-size distribution and pore connectivity at small scales (e.g., core), fracture orientation and long-range correlations at large scales (e.g., field). In this study, we apply concepts from percolation theory to estimate the scale dependence of saturated hydraulic conductivity, Ksat. For this purpose, we use a database of undisturbed soil samples from four Danish sites (Jyndevad, Tylstrup, Estrup, and Silstrup) where the value of Ksat was measured on small (100 cm3) and large (6280 cm3) sample volumes, while porosity and soil water retention data were only available on small sample volumes. First, we apply a classification approach, widely used in petroleum engineering, to group soils based on their similarities in hydraulic properties using porosity and Ksat measurements at the small sample volume. We detect nine different soil classes with the average flow zone indicator (FZI) from 0.05 μm in class 1 to 9 μm in class 9. Next, using percolation theory, we characterize the scale dependence of critical pore-throat radius. We use the critical path analysis to link the critical pore-throat radius to the Ksat and, consequently, determine its scale dependency. Theoretical estimates compare reasonably well with the experimental measurements at the large sample volume based on the soil water retention curve and Ksat measured at the small sample volume. We find the root mean square log-transformed error (RMSLE) values 0.45, 0.77, 1.9, and 2.05 for sites Jyndevad, Tylstrup, Silstrup, and Estrup, respectively. Results show that the theory tends to provide more accurate estimations in coarser textures and unstructured soils as well as soil classes with FZI values greater than 0.7 μm (soil classes 6 to 9).