Modelling of 2-D seepage from aquifer towards stream via clogged bed: The toth-trefftz legacy conjugated

Baseflow-type interaction between a river and adjacent/subjacent aquifer across a thin clogging layer of fine sediments controls the dynamics of surface-pore water resources, quality of both waters, seepage induced erosion of the river bed and other hydrological phenomena. Transient 2D phreatic flow from an unconfined aquifer into a river with a thin low-permeable cake (hydraulic skin) is approximated by a sequence of steady states, each of which assumes the water table to be horizontal. The scalar and vector fields of piezometric head, stream function and Darcian velocity are found from analytical solution of the Dirichlet and Robin (linear combination of the velocity potential and its normal derivative) boundary value problems for the piezometric head (harmonic function). The time-shrinking Tothian “unit basins” are a half-strip, half-plane or rectangle. Stream banks are assumed to be horizontal or vertical segments. Cross-flow from the aquifer into the stream is controlled by the aquifer-skin conductivity ratio and the stages of the river and adjacent aquifer. The head and cross-flux on the interface (Robin's boundary) is shown to vary along this line and therefore even for vertical river banks the Dupuit–Forchheimer approximation is not strictly valid. Numerical simulations in HYDRUS2D are reasonably close to the analytical results. Early-stage drawdown of a rectangular cake due to a sudden drop of the water level on the river side and formation of a seepage face is analysed with potential applications to stability of earth dams.