Two-dimensional Capillarity-Driven Seepage From a Lined Buried Ditch: the Kornev Subsurface Irrigation "Absorptional" Method Revisited

Abstract

Kornev's (1935, see e.g. p.74, Fig.34 - right panel) "open system" of capillarity-driven wetting of a fine-textured soil from a buried ditch filled by a coarse porous material is modeled analytically, using the methods of hodograph, and numerically, with the help of HYDRUS2D. Gravity, Darcian resistance of the soil at full saturation but negative pressure, and capillarity are three physical competing factors involved through the Vedernikov-Bouwer analytical model, which assumes 2-D, tension-saturated flow in a homogeneous soil sandwiched between the free surfaces (capillary fringe boundaries) and Kornev's impermeable liner of the ditch. Water seeps up from a line source, viz. a zero-pressure segment such that everywhere in the flow domain pressure remains negative. Lining minimizes deep percolation and facilitates upward and lateral spread of pore water by soil's capillarity. The free surfaces are streamlines, along which the pressure head is a negative constant (the air entrance pressure head, soil's property). For a small-depth ditch the hodograph domain is either a circular trigone, tetragon or sextagon, that determines three different flow topologies (with J.R.Philip's "dry shadow", "dry bulb" and no dry zone at all on the leeward side of the liner and "wet lobes" hanging on the edge of the liner). The flow domain makes a capillary "fountain". The complex potential domain is a half-strip such that the inversion method and conformal mappings are used. Transient, 2-D seepage in subsurface irrigation of a soil composite ("constructozem"), which consists of an ambient fine-textured soil and a buried Kornev's ditch (backfilled by a sand or peat), is numerically modeled by HYDRUS2D. Evapotranspiration is the fourth moisture-driving factor, which uplifts vadose zone moisture, combatting Pluto's gravity. The seepage flow rates, isobars, isohumes, isotachs, flow nets, vector-fields of Darcian velocity and other kinematic-dynamic seepage descriptors are found for various combinations of the physical properties of two contrasting porous materials and geometrical sizes (the width and depth of Kornev's ditch, depth of its burial, distance between neighbouring emitting ditches in a periodic irrigation system).