Estimating scale dependence of saturated hydraulic conductivity in soils

Abstract

Understanding the effect of scale on hydraulic and physical properties of soils has broad applications to scaling 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, K_sat. For this purpose, we use a database including undisturbed soil samples from four Danish sites (Jyndevad, Tylstrup, Estrup, and Silstrup). The value of K_sat was measured at small (100 cm³) and large (6280 cm³) scales. First, we apply a classification approach, widely used in petroleum engineering, to group soils based on their similarities in hydraulic properties using porosity and K_sat measurements at the small scale. We detect nine different soil classes with the average flow zone indicator (FZI) from 0.05 [mu]m in class 1 to 9 [mu]m 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 K_sat and, consequently, determine the scale dependence of K_sat. Comparing the theoretical estimations with the experimental measurements show that the percolation theoretic model reasonably well estimates the K_sat at the large scale from the soil water retention curve and K_sat measured at the small scale. We find the root mean square log-transformed error (RMSLE) values 0.45, 0.77, 1.9, and 2.05 (cm/day) 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 [mu]m.