Analytical and HYDRUS2D Modeling for Buried Peat-filled Trapezoidal Ditches as Subsurface Capillarity-Driven Irrigating Units

Abstract

Intelligent design and construction of urban and agricultural soils ("constructozems"), as porous substrates on which strips of green vegetation are cultivated, aims at optimizing the plants' soil moisture consumption (high WUE). A lens (or double-periodic cluster of lenses) made of peat or other relatively coarse material is buried under the ground surface. This lens(es) is surrounded by a fine-textured indigenous soil. The pore water motion to/from the lens, acting intermittently as a draining entity (collecting pore water from the ambient soil) and a subsurface irrigator (emitting water to this soil), in such an engineered smartly-heterogenized vadose zone becomes essentially 2-D. Kornev (1935) experimented with backfilled ditches generating capillarity-maintained "wet bulbs". The emitter-emanated "bulbes" targeted the roots of row crops in arid/semiarid regions. In the context of Kornev's subirrigation we complete Vedernikov's (1940) analytical solution for steady 2-D seepage from a trapezoidal ditch having a zero-depth water level. The free boundaries of the capillary fringe are found as streamlines and special isobars (the Vedernikov-Bouwer model). The deep percolation flow rate is evaluated by considering an analytical element (Strack, 1989) with a line source (ditch bed) and sink at infinity, i.e. a generalized "dipole". For this purpose, the complex potential half-strip is conformally mapped onto a circular polygon in the hodograph plane. The isohumes, isotachs, isobars and other kinematic/dynamic descriptors of seepage are determined from the integral representation for characteristic holomorphic functions. With the help of HYDRUS2D, we also model a transient seepage in a homogeneous natural soil, as well as in "constructozems" made of such soil with a buried engineered coarse-texture lens. Free drainage (deep percolation) versus evaporation (ascending flux) from a dry soil surface are concatenated via a separatrix (with a stagnation point on the mid-segment between two neighbouring ditches) inside a polygonal HYDRUS flow domain where the Richards-Richardson equation is solved.