Pore size distribution, suction and hysteresis in unsaturated groundwater flow

Abstract

Formalism for calculating soil moisture suction via average relative humidity in the soil is reviewed and then extended via the concept of pore size distribution. Using an assumed form for pore size distribution and a form of the Kelvin equation for the vapor pressure of a fluid in a capillary allows direct calculation of the capillary contribution to suction under certain idealized conditions. The change in suction with changes in the concentration of total dissolved solids is then examined via the difference between the pressure of vapor over a pure solvent and that over a solution and changes in surface tension that occur when impurities are dissolved in water. The pore size distribution and an assumed form of volume per pore/capillary are used to construct and calculate the degree of saturation θ s( r) where the assumption is made that all pores/capillaries in the sample under consideration up to radius r are filled and those having radii larger than r are dry. Later in the development it is shown how this initial assumption can be refined. Negative suction and the degree of saturation θ s are calculated as explicit functions of r and plotted as implicit functions of each other, thereby yielding one of the family of hysteresis loops appropriate to the current formalism. If r 0 is the value of r for which the pore size distribution curve has its peak, the value of r 0 for the wetting branch is larger than that for the drying branch, since the drying curve “sees” smaller pores/capillaries on the average than does the wetting curve. The area enclosed by the hysteresis loop is calculated and represents the energy per unit volume lost to the formation on adsorbing and then desorbing moisture.