Macroscopic capillary length, sorptivity, and shape factor in modeling the infiltration rate

Infiltration tests in the field involve measurements of sorptivity and macroscopic capillary length. These two parameters are strongly related through the shape factor, which is a measure of the nonlinearity of the soil hydraulic diffusivity. In this study, relationships were developed between the macroscopic capillary length, the sorptivity, and the shape factor and the parameters of the Brooks and Corey and van Genuchten expressions of hydraulic conductivity and diffusivity. These relationships are important for users of numerical models who need to estimate the parameters of these expressions to predict water dow and contaminant transport in soils. Numerical simulations with a dimensionless form of Richards' equation show that the predicted infiltration rate will not be very sensitive to small variations in the shape factor, provided the macroscopic capillary length is the same. This result is encouraging because the shape factor Is difficult to determine accurately in the field. The similarity of the dimensional infiltration solutions implies that the macroscopic capillary length is a scale factor, because (i) it renders predictions of infiltration rates fairly insensitive to the expressions of hydraulic conductivity and diffusivity used, and (ii) it reduces the number of parameters needed to characterize infiltration. Therefore, the infiltration curve into a particular soil can be deduced by choosing units of length and time (i.e., scaling) of a generalized infiltration solution.