Transient dynamics of groundwater levels in sloping aquifers: Effects of recharge variability, semi-permeable bottoms, and subsurface drainage

This research addresses the linearized Boussinesq equation based on the Dupuit-Forchheimer assumption to analytically explore groundwater level changes resulting from initial water levels under three conditions after installing subsurface drainage pipes along two boundaries. The analytical solutions are derived using the integral transform method associated with an efficient time-stepping linearized technique. To validate the present solution, the trial and error method was employed to calibrate the physical parameters to fit the previous research results, which was satisfactory. Further analyses were conducted to assess the impact of different parameters on the efficacy of subsurface drainage. Simulations indicate that time-varying surface recharge affects the rise in groundwater levels during the initial drainage phase. The recharge factor from semi-permeable layers influences the groundwater levels in the later phase, while the slope factor affects the overall distribution of groundwater levels. The slope increases the flow velocity and thus increases the drainage speed. The hydraulic resistance retards the upward recharge via the semi-permeable layer and becomes the dominant factor affecting groundwater levels at later stages. The present analytical model employs the time-stepping technique to linearize the nonlinear term in the Boussinesq equation. It can address any pattern of temporally varying surface recharge using unit step functions and evaluate upward subsurface recharge through a semi-permeable layer under distinct initial groundwater levels in a sloping aquifer. The study underscores the importance of considering multiple recharge sources and geomorphological factors in designing effective drainage systems. It enhances understanding of the effectiveness of underground drainage systems under various geological parameters via applied mathematics.