Ar. Kacimov, ESTIMATION AND OPTIMIZATION OF TRANSIENT SEEPAGE WITH FREE-SURFACE, Journal of irrigation and drainage engineering, 119(6), 1993, pp. 1014-1025
Single sink depths providing maximum ground-water table decrease durin
g a fixed time interval within a selected area are found for the 2-D a
nd 3-D cases. The curve of the maximal phreatic surface position (unde
rflooding curve) in the aquifer from flood induced variation in water
level of the ground-water reservoir is calculated. Well-known analytic
al solutions based on nonlinear and linear potential theories and the
Dupuit-Forchheimer approximation are applied to calculate the objectiv
e function, decision variables, and boundary of the fully saturated zo
ne. In the linear case, an explicit analytic solution gives the unique
maximum of the water table decrease at the compliance point for a giv
en pumping duration. For small values of sink depth, the linear approa
ch is invalid. In the nonlinear case, complex analysis and series expa
nsions are used. For small values of drain depth, the series technique
becomes untenable. For the reservoir-aquifer problem the spreading ph
reatic surface is a rotating straight line and the underflooding curve
is a parabola.