Analysis of subsurface drainage of sloping lands using the homotopy perturbation method

ABSTRACT

An analytical model is developed using the homotopy perturbation (HP) method for predicting explicitly the location of water table heights resulting from steady drainage of a homogeneous sloping aquifer overlying a uniformly sloping impervious barrier at a finite distance from the top of the soil. The model assumes the aquifer to receive a steady recharge at its surface, the drains to have equal water level heights in them and the head loss in the vertical direction as negligible. The necessary and a sufficient condition within which the proposed solution is expected to converge are been worked out and also its validity been checked by comparing with the works of others for a few tested situations. The proposed series solution is expected to converge for all hillslope drainage settings so long these drainage layouts respect the necessary and sufficiency conditions of the developed solution. As the existing analytical solutions to the hillslope drainage problem, unlike the present one, do not render a direct determination of the water table profile for such a system, it is hoped that the solution proposed here would relatively be simpler to use in designing subsurface drains in a hillslope aquifer.

KEYWORDS:

• Homotopy perturbation method
• drainage
• sloping aquifer

Disclosure statement

No potential conflict of interest was reported by the authors.