Influence of capillarity on a simple harmonic oscillating water table: Sand column experiments and modeling

Abstract

Comprehensive measurements of the water table response to simple harmonic forcing at the base of a sand column are presented and discussed. In similar experiments, Nielsen and Perrochet (2000) observed that fluctuations in the total moisture were both damped and lagged relative to the water table fluctuations. As a result, the concept of a complex effective porosity was proposed as a convenient means to account for the damping and phase lag through its magnitude and argument, respectively. The complex effective porosity then enables simple analytical solutions for the water table (and total moisture) dynamics including hysteresis. In this paper, these previous experiments are extended to cover a wider range of oscillation frequencies and are conducted for three well-sorted materials with median grain diameters of 0.082, 0.2, and 0.78 mm, respectively. In agreement with existing theory, the influence of the capillary fringe is shown to increase with the oscillation frequency. However, the complex effective porosity model corresponding to the classical Green and Ampt (1911) capillary tube approximations is shown to be inadequate when compared to the data. These limitations are overcome by the provision of an empirical, frequency-dependent complex effective porosity model fit to the data. Using measured moisture retention parameters, numerical simulation of the data solving a nonhysteretic van Genuchten-Richards' equation type model is unable to replicate the observations. Existing results of a hysteretic numerical model are shown to be in good agreement with the extended database.