Variability of Gardner's α for coarse‐textured sediments

Abstract

Vadose zone soils in arid regions often contain a high gravel fraction (>2 mm size). This paper examines, for coarse‐textured soils, variability of the slope α of Gardner's [1958] unsaturated hydraulic conductivity K versus matric potential ψ relation, K = Kseαψ. The steady state head control method was used to obtain unsaturated K for tensions as high as 386 cm. A total of 79 samples were analyzed in the laboratory; the gravel fraction for the 41 gravelly samples ranged from 20 to 71% (by weight); the remaining 38 samples were sandy with no gravel fraction. The measured K values for the gravelly samples fall within a narrow range and are well within the range of measured K values for the sandy samples. The bulk of both gravelly and sandy samples can be described using a single‐slope exponential model; Gardner's α and the intercept K0 are based on a least squares fit to the late time measurements at lower ψ. The mean and variance of α for the gravelly samples are lower compared with the sandy type. The α values for the gravelly soils follow a normal distribution, whereas the K0 estimates and the laboratory‐measured Ks follow lognormal distributions. For the sandy type, α, K0, and Ks follow lognormal distributions. The α values appear to be related to the median particle diameter d50 and the slope of the particle size distribution. A clear reduction in variability of α is apparent with an increase in d50, suggesting that the unsaturated K and α variability for the gravelly soils can be estimated within narrow ranges. The flow‐weighted characteristic pore size λm is clearly dependent on the soil type; λm values for the gravelly soils are characterized by a smaller mean and variance than for the sandy type. This helps explain the finding that the range in unsaturated K for the gravelly soils is less than for the sandy type. At higher tensions the mean and variance of α and lnK0 as well as the cross correlation between α and lnK0 are important inputs to stochastic models of unsaturated flow. The implications of their variability on flow in heterogeneous media are discussed.