Effects of the hydraulic conductivity of the matrix/macropore interface on cumulative infiltrations into dual-permeability media

Modeling of water infiltration into the vadose zone is important for better understanding of movement of water-transported contaminants. There is a great need to take into account the soil heterogeneity and, in particular, the presence of macropores or cracks that could generate preferential flow. Several mathematical models have been proposed to describe unsaturated flow through heterogeneous soils. The dual-permeability model (referred to as the 2K model) assumes that flow is governed by Richards equation in both porous regions (matrix and macropores). Water can be exchanged between the two regions following a first-order rate law. Although several studies have dealt with such modeling, no study has evaluated the influence of the hydraulic conductivity of the matrix/macropore interface on water cumulative infiltration. And this is the focus of this study. An analytical scaling method reveals the role of the following main parameters for given boundary and initial conditions: the saturated hydraulic conductivity ratio (R_Ks), the water pressure scale parameter ratio (R_hg), the saturated volumetric water content ratio (R_θs), and the shape parameters of the water retention and hydraulic conductivity functions. The last essential parameter is related to the interfacial hydraulic conductivity (Ka) between the macropore and matrix regions. The scaled 2K flow equations were solved using HYDRUS-1D 4.09 for the specific case of water infiltrating into an initially uniform soil profile and a zero pressure head at the soil surface. A sensitivity of water infiltration was studied for different sets of scale parameters (R_Ks, R_hg, R_θs, and shape parameters) and the scaled interfacial conductivity (Ka). Numerical results illustrate two extreme behaviors. When the interfacial conductivity is zero (i.e., no water exchange), water infiltrates separately into matrix and macropore regions, producing a much deeper moisture front in the macropore domain. In the opposite case when the interfacial conductivity is high, water exchange between the macropore and matrix domains is fast, resulting in a similar penetration of moisture fronts into both matrix and macropore domains. In all cases, differences between cumulative infiltrations do not exceed 10-15 % and depend only slightly upon values of R_Ks, R_hg, and R_θs. This result is of great importance since, whatever the value of the interfacial conductivity, the cumulative infiltration can be quite accurately approximated assuming no mass transfer between the two domains (i.e., zero interfacial conductivity). Consequently, the cumulative infiltration into a 2K media can be calculated as a linear combination of cumulative infiltrations into the macropore and matrix domains, each evaluated using a much simpler single-porosity model.