An analytical solution to the steady one-dimensional Gardner-based infiltration equation for an inclined heterogeneous soil with any arbitrary root-water uptake function

An accurate polynomial solution is worked out for the general Gardner-based infiltration equation for a heterogeneous soil column with the sink term of the equation being treated as any valid root-water uptake function along the length of an infiltrating space. The solution can predict infiltration behavior through any arbitrarily inclined soil column and can also accommodate any valid spatial variations of the root-water extraction function and the soil hydraulic parameters of the infiltration equation, along the length of an infiltrating column. The validity of the proposed solution is checked by comparing with the analytical works of others for a few simplified infiltration situations; also, a few numerical checks on it are also carried out. Further, an experimental check on the proposed solution for a relatively simple infiltration situation is also performed. The developed solution is new since there is currently no analytical solution to the Gardner-based infiltration equation even for a homogeneous soil for all possible variations of soil parameters of this equation when a root-water extraction term exists in an infiltrating space. As field soils are mostly heterogeneous, the developed model is expected to provide a better picture of infiltration in a field soil as compared to relatively simple available models on infiltration. The study shows that infiltration hydraulics in a soil in many instances may be affected in a major way by the heterogeneities of the soil and an infiltration model based on the homogeneity soil assumption may lead to appreciable error if the same is being used to study infiltration in a heterogeneous soil. This is true both when a root-water function is present in an infiltrating space and when it is absent. The study also shows that infiltration on a heterogeneous soil with a spatially varying root-water sink term is a complex process involving many variables and that the final infiltration dynamics associated with such a system is generally not governed by one or two variables alone but by the intricate interplay of all the variables of the system. In the derivation of the model, it is assumed that flow is Darcian, steady and one-dimensional. These are thus a few limitations of the proposed model which, for more generality of the model, may be addressed in a future study of the Gardner-based infiltration equation.