Steady state moisture flows in unsaturated soil containing a plane, isolated, impermeable barrier

A three-dimensional, axially symmetrical, steady state flow of moisture in an unsaturated soil has been analysed. The steady state infiltration is maintained by a constant flux across a circular disc on the horizontal soil surface. The flow encounters an obstacle in the form of a plane circular impermeable barrier of arbitrary radius. Except for this isolated barrier, at a given arbitrary depth, the rest of the soil is homogeneous and isotropic. The governing differential equation is linearized by assuming the hydraulic conductivity to be an exponential function of the pressure head. Techniques associated with dual integral equations constitute the basic tools that are employed in solving this problem. Explicit formulae and expressions are obtained for computing the solution for arbitrary values of the radius of the source, of the radius of the obstacle, and of the distance between them. Keeping the radius of the source as unity, the barrier radius and depth were varied in illustrative examples. Results are plotted in a series of figures. The concluding section briefly mentions relevance of such analysis to interpretation of field data on moisture contents or calculations of hydraulic conductivity. The problem of flow around an isolated disc in infinite space, with a uniform gravitational flow at large distances from this disc, can also be solved by the methods developed here. This has been done, and the results are plotted in a figure.