New linearized two-parameter infiltration equation for direct determination of conductivity and sorptivity

Abstract

A new two-parameter (the sorptivity, S [ L / T 0.5 ], and saturated soil hydraulic conductivity, K s [ L / T ]) vertical infiltration equation is proposed. A three-parameter accurate approximate equation is derived. The proposed two-parameter equation is a specific solution that is approximately located at the middle of the domain of real soils defined by two “limiting” behavior soils. According to the proposed equation, plotting the square of cumulative infiltration, i [ L ], divided by time, t [T], as a function of i , a linear line is obtained and it is easy to determine S squared as the intercept and K s as the slope of the line and to test the adequacy of the proposed equation. The equation approaches Philip semi-analytical infinite-series solution at small and moderate times, whereas the infiltration rate approaches the constant K s at large times. It is expressed in a form explicit in i as function of t and vice versa. The equation is validated through comparison with other common nonlinear models (with two- and three-parameters) on a number of reference soils from the literature (both real and analytical) The parameter estimates of the equation are practically insensitive to the number of data points used in fitting, as well as to random measurement errors. Two illustrative infiltration tests for more realistic conditions (non-uniform soil and initial moisture profiles) were also performed. The tests demonstrate the advantage of the linearized equation over other common nonlinear models to be able visually detect and eventually eliminate abnormalities of infiltration process.