Variability of Gardner's α for coarse-textured sediments

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 alpha of Gardner's [1958] unsaturated hydraulic conductivity K versus matric potential psi relation, K = K(s)e(alpha psi). 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 alpha and the intercept K-0 are based on a least squares fit to the late time measurements at lower Jr. The mean and variance of alpha for the gravelly samples are lower compared with the sandy type. The alpha values for the gravelly soils follow a normal distribution, whereas the K-0 estimates and the laboratory-measured K-s follow lognormal distributions. For the sandy type, alpha, K-0, and K-s follow lognormal distributions. The alpha values appear to be related to the median particle diameter d(50) and the slope of the particle size distribution. A clear reduction in variability of alpha is apparent with an increase in d(50), suggesting that the unsaturated K and alpha variability for the gravelly soils can be estimated within narrow ranges. The flow-weighted characteristic pore size lambda (m) is clearly dependent on the soil type; lambda (m) 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 alpha and lnK(0) as well as the cross correlation between alpha and lnK(0) are important inputs to stochastic models of unsaturated flow. The implications of their variability on flow in heterogeneous media are discussed.