Abstract
A new 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 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 considering that the saturated thickness varies in space. This solution improves the authors' previous solution (Dewandel et al. 2023), which was developed with the use of the first method of linearization (negligible variation in saturated thickness).Results show that the maximum differences in hydraulic head up- and downstream at the centre of the dam induced in the aquifer are almost identical (deviation <2%), even when the degree of saturation or desaturation near the dam () is about 50%. However, the previous solution overestimates the hydraulic head upstream of the dam and underestimates it downstream with deviations increasing as increases. This study shows that if ≤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 semi-analytical 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 operational tools for engineers designing underground dams and is meant to supplement existing hydrogeological models for improving the design of such structures.