| Title |
Reformulation of Baalousha’s Analytical Solution for Estimating Drawdown and Streamflow Depletion Induced by Groundwater Pumping |
| DOI |
https://doi.org/10.12652/Ksce.2026.46.5.0417 |
| Keywords |
지하수 양수; 수위 강하량; 하천수 감소량; Baalousha 해석해; 비대칭적 하천 누수 분포; 특성시간 Groundwater pumping; Drawdown; Streamflow depletion; Baalousha’s analytical solution; Distribution of asymmetric stream leakage; Characteristic time |
| Abstract |
The objective of this study is to evaluate the effects of the simplifying assumptions incorporated in Baalousha’s analytical solution and to assess its applicability for estimating groundwater drawdown and streamflow depletion from a finite-width stream induced by groundwater pumping. Baalousha’s analytical solution has the advantage of separately analyzing groundwater-level changes caused by groundwater pumping and stream leakage based on the principle of superposition, thereby allowing their respective effects to be evaluated. However, the solution involves several simplifying assumptions, including that the groundwater-level change induced by stream leakage is symmetrically distributed with respect to the stream center and that, under quasi-steady conditions, diffusion is considered only in the transverse direction. Therefore, in this study, Baalousha’s analytical approach was extended and reformulated as a boundary-value problem for two-dimensional transient groundwater flow without assuming symmetry in the groundwater-level change induced by stream leakage. An analytical model was developed by applying Fourier and Laplace transforms, followed by
numerical inverse transforms to determine groundwater drawdown and streamflow depletion in the time and spatial domains. The developed model was applied under various hydraulic and geometric conditions, including transmissivity, storativity, streambed hydraulic conductivity, stream width, and stream-well distance, and the results were compared with Baalousha’s analytical solution. The results showed that, under relatively low aquifer hydraulic diffusivity, the difference between the two solutions tended to increase with stream width. In particular, comparison of streamflow depletion ratios in terms of the dimensionless characteristic time, defined using time, the stream depletion factor, and relative distance, showed that when the dimensionless characteristic time exceeded 5, Baalousha’s solution yielded results similar to the present solution, which accounts for asymmetric groundwater-level changes induced
by stream leakage and two-dimensional transient groundwater flow. |