A variable sorptivity infiltration equation

Horizontal and vertical one-dimensional infiltration are compared when they both occur in a homogeneous isotropic porous body initially at a uniform low water content _n under constant concentration (₀) or constant pressure head (H ₀) conditions. From a consideration of the physics governing infiltration under such conditions, the conclusion is reached that the magnitude of the pressure head gradient atx=0, wherex=0 denotes the infiltration surface in the horizontal case, must be larger than the magnitude of the pressure head gradient atz=0, wherez=0 denotes the infiltration surface in the vertical case, for all finitet>0, so that for the hydraulic head gradient atz=0 to be greater than (1/2K ₀)S _x t ^–1/2 but smaller than (1/2K ₀)S _x t ^–1/2+1],K ₀ being the hydraulic conductivity at ₀ andS _x the sorptivity during horizontal infiltration. On these grounds, it is further argued that if the sorptivityS _z is introduced for the case of vertical infiltration, then it must be equal toS _x fort=0 only and that it must decrease with time. Results obtained by solving soil-water flow equations for the infiltration conditions defined above, and from experiment, support the above conclusions. An equation for the relationship between cumulative infiltration and time during vertical infiltration is developed after assuming thatS _z decreases with time in an exponential manner. Cumulative infiltration versus time relationships given by this equation are compared with those obtained from the numerical solution of the soil-water flow equation and from experiment.