An improved steady-state semianalytical solution for assessing the two-dimensional hydraulic head distribution induced by an underground dam in a sloping unconfined aquifer

A steady-state semianalytical solution for evaluating the hydraulic head distribution created by a rectangular underground dam that fully penetrates a sloping aquifer is proposed. The length of the dam concerns only a limited part of the aquifer width. This solution uses the second method of linearization of the nonlinear partial differential equation, a closer approximation of the exact solution, which allows for the consideration that the saturated thickness varies in space. This solution improves upon a previous solution, which was developed with the use of the first method of linearization (assuming a negligible variation in saturated thickness). Results show that the maximum differences in aquifer hydraulic head upgradient and downgradient across the centre of the dam are almost identical (deviation < 2%), even when the degree of saturation or desaturation near the dam (beta) is similar to 50%. However, the previous solution overestimates the hydraulic head upgradient of the dam and underestimates it downgradient with deviations increasing as beta increases. This study shows that if beta <= 20% the solution with the first linearization method gives satisfactory results, which is similar to previous studies. Otherwise, it is preferable to use the new solution developed. Analysis of the solution included sensitivity tests and type curves to evaluate the maximum hydraulic differences induced by the underground dam. The proposed solution can be implemented as an operational tool for engineers designing underground dams and is meant to supplement existing hydrogeological models for improving the design of such structures.