Response of Triangular-Shaped Leaky Aquifers to Rainfall-Induced Groundwater Recharge: an Analytical Study

摘要

Different aspects of groundwater mound dynamics in triangular-shaped aquifers are investigated analytically under spatially uniform recharge of time-varying rate. The aquifer response is analyzed relying on 2-D linearized Boussinesq equation, subject to two different configurations of hydrogeological boundary conditions (constant-head streams and no-flow barrier). The aquifer is homogeneous, isotropic and rests over a horizontal, semipervious layer, through which vertical leakage can take place. Point-recharge formula (Green's function) is first derived for the intended aquifer domain and then properly converted to accommodate the effect of rainfall-induced areal recharge. Components of groundwater budget are evaluated in terms of volumetric rates, taking into account the jointed effects of leakage, mound storage and outflow to adjacent streams. The resulting expressions are then proven to obey the expected mass balance in a rigorous mathematical fashion. Hypothetical examples illustrating main features of flow field are presented, with attention paid on groundwater equpotentials and streamlines. The computed mound profiles appear to agree well with numerical results from finite element method. Further, the most influential parameters affecting each component of groundwater budget are identified with the help of sensitivity analysis. Finally, the combined effects of a pumping well and rainfall-induced mound are discussed. The present solution may serve as a test case for verifying numerical schemes that are being developed for more comprehensive mound analysis.