Statistical and Stochastic Analyses of Hydraulic Conductivity and Particle‐Size in a Fluvial Sand

Abstract An untilled medium‐grained fluvial sand near Socorro, N. Mex., was sampled in horizontal and vertical transects to study the statistical and stochastic properties of particle‐size parameters and saturated hydraulic conductivity. Hydraulic conductivity is log‐normally distributed, whereas the 10% finer, median, and geometric mean particle sizes are normally distributed. The strongest correlation between hydraulic conductivity and particle‐size distribution parameters is that of the log of hydraulic conductivity with the 10% finer particle size. Stochastic analyses using the autocorrelation function and spectrum indicate that the log of hydraulic conductivity and particle size are characterized by dissimilar spatial correlation structures in the vertical directions. In general, particle size is more structured, regular, and predictable and shows a close similarity with the stratigraphy as observed in the field. On the other hand, hydraulic conductivity in the vertical direction may best be modeled as a simple random variable. Variogram and kriging analyses indicate that both hydraulic conductivity and particle size are relatively isotropic in the horizontal plane and that marked similarities in spatial structure exist in this plane. The spatial distribution of saturated hydraulic conductivity in the horizontal plane is estimated reasonably well using the empirical relationship between particle size and conductivity along with the kriged estimates of the 10% finer particle size.