Analytical and experimental solutions for drainage of sloping lands with time‐varying recharge

Abstract

M. J. Boussinesq's (1904) nonlinear partial differential equation for unsteady state flow of water through a phreatic aquifer resting on a sloping impervious barrier and receiving time‐varying recharge has been solved. Two patterns of recharge rates, i.e., linearly increasing and exponentially declining with time were considered. The initial conditions of the water table were taken at the drain level. Transformations were devised to transform the resulting approximate linearized Boussinesq equation to the form of a one‐dimensional heat flow equation for each case of recharge pattern, and analytical solutions for the height of the water table between parallel drains were obtained in the form of a convergent series. The analytical solutions were experimentally verified with a Hele‐Shaw model. A reasonably close agreement was found in the computed and observed phreatic surfaces. The results showed that the analytical solutions presented herein can be used with reasonable accuracy for designing subsurface drainage in sloping phreatic aquifers.