Cyclic hysteretic flow in porous medium column: model, experiment, and simulations

A periodic vertical movement of the groundwater table results in a subseque nt cyclic response of the water content and pressure profiles in the vadose zone. The sequence of periodic wetting and drying processes can be affecte d by hysteresis effects in this zone. A one-dimensional saturated/unsaturat ed flow model based on Richards' equation and the Mualem (Soil Sci. 137 (19 84) 283) hysteresis model is formulated which can take into account multi-c ycle hysteresis effects in the relation between capillary pressure and wate r content. The numerical integration of the unsaturated flow equation is ba sed on a Galerkin-type finite element method. The flow domain is discretise d by finite elements with linear shape functions. Simulations start with st atic water content and pressure profiles, which correspond to either a boun dary drying or wetting retention curve. To facilitate the numerical solutio n of the hysteretic case an implicit non-iterative procedure was chosen for the solution of the nonlinear differential equation. Laboratory experiment s were performed with a vertical sand column by imposing a high frequency p eriodic pressure head at the lower end of the column. The total water volum e in the column, and the periodic water content profile averaged over time were measured. The boundary drying and wetting curves of the relation betwe en water content and capillary pressure were determined by independent expe riments. The simulations of the experimental conditions show a clear effect of the hysteresis phenomenon on the water content profile. The simulations with hysteresis agree well with the measurements. Computed dimensionless w ater content profiles are presented for different oscillation frequencies w ith and without consideration of hysteresis. (C) 2001 Elsevier Science B.V. All rights reserved.