Estimating the Maximum Safe Pumping Rate in Sloping Unconfined Coastal Aquifers

Unconfined coastal aquifers with a sloping aquifer bed are ubiquitous. However, most analytical solutions previously developed to estimate pumping‐induced seawater intrusion considered a horizontal aquifer bed. In this study, we first developed a steady‐state analytical solution to quantify the maximum safe pumping rate in sloping unconfined coastal aquifers with a fixed‐flux inland boundary condition, using the single potential approach. The analytical solution corrected by an empirical factor is validated against the numerical simulation, which reproduces the corresponding numerical results well. It is found that coastal aquifers with a higher aquifer bed toward inland (i.e., a positive sloping angle) yield a higher maximum safe pumping rate than that of coastal aquifers with a horizontal aquifer base, since the elevated freshwater head prevents seawater intrusion and enhances groundwater pumping. Specifically, for the aquifer bases with the sloping angle of 0.01 and −0.01, the maximum safe pumping rate is increased by 42.6% and decreased by 48.4%, respectively, in comparison to the case of a horizontal aquifer base, suggesting that neglecting the aquifer base slop can result in a significant error in estimating the maximum safe pumping rate. Moreover, the sensitivity analysis reveals that the maximum safe pumping rate increases with a lower hydraulic conductivity and a larger dispersivity. Our results provide valuable insights into the effect of the aquifer base slope on the maximum safe pumping in coastal aquifers, and analytical solutions developed can serve as a powerful tool for quick assessment of pumping‐induced seawater intrusion in sloping unconfined coastal aquifers. Analytical solutions for pumping‐induced seawater intrusion in a sloping unconfined coastal aquifer are developed Analytical solutions of the maximum safe pumping rate are validated through numerical simulation Neglecting the aquifer bed slope would result in a significant error in estimating the maximum safe pumping rate, as expected