Water absorption by a swelling porous medium

Although the mathematical theory for water movement through a swelling porous medium has been developing for a number of years, experimental testing and verification of that theory has been limited, especially for unsaturated media. The intent of the present research was to test, and modify if necessary, this existing theory. Experimentally, water was applied to the top end of an initially air-dry column of swelling soil (50% bentonite clay and 50% quartz silt), with the top end allowed to rise upward as swelling occurred. A narrowly collimated beam of dual-energy gamma rays was employed to measure the soil bulk density and water content nondestructively, within the column, over a time period of 1 to 2 wk. It was found necessary to extend the existing theory, by considering the soil void ratio to be a function of both fractional water saturation (volume of water per unit pore volume) and time. This also introduced an auxiliary time dependence into the water diffusivity function. Furthermore, to allow for an experimentally feasible boundary condition, the governing differential flow equation was recast in terms of the fractional water saturation. A mathematical solution of the flow problem was sought and found in terms of product-form separation of variables. Some early-time departure from square-root-of-time dependence was found. Also, measurements within the soil column were employed in the mathematical solution to predict the cumulative water absorption and the upward rise of the top end of the swelling soil column. These predicted values were in reasonable agreement with experimental values obtained outside the soil column by direct observation