UNSATURATED QUASI-LINEAR FLOW ANALYSIS IN V-SHAPED DOMAINS

Abstract

An explicit, essentially 2D solution for steady unsaturated seepage flow from infinity to a corner, with boundaries kept at constant suction, is obtained for the Kirchhoff potential by the method of separation of variables. A system of coordinates coinciding with the corner boundaries is selected. Distributions of the pressure, stream lines and velocities are derived. Non-existence of steady flows at certain corner orientations, deflection of the incident flow by slanted boundaries and inflection points on the stream lines close to the vertex are discussed. One-dimensional limit for zones far from the trough is examined. Refraction and further collimation of the upper 2D flow in the second underlying porous medium with implications to geotechnical capillary barriers is studied. A vadose zone originated accretion is matched with a saturated ‘wing’, which appears on a slanted bedrock. Mathematically, this matching is done by linking the Dupuit–Forchheimer and quasi-linear models. A tilted water table is shown to entrain the recharging moisture with curvilinear stream lines in the unsaturated zone.