Unsaturated‐saturated flow near a quasi‐linear line source

Soil water flow from a horizontal cylindrical cavity into a surrounding unsaturated soil is analyzed. The steady state saturated bulb is described following the assumption that the conductivity function is K s exp ( αh ), where K s is the saturated hydraulic conductivity (meters per second), α is a constant (meters −1 ), and h is the pressure head (meters). The approach is similar to that recently presented by Philip (1992) for a point source. When the dimensionless matric flux potential 2π K s /( αq ) is larger than 2.5, the corresponding saturated bulb is nearly a cylinder of radius R 0 = 4α −l exp [−(2π K s /α q ) − 0.5772], where q is the source strength (square meters per second). The center of the saturated cylinder is at a distance π R 0 2 K s / q below the line source singularity.