• KSCE Journal of Civil and Environmental Engineering Research
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• v.40 no.6
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• pp.555-561
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• 2020

In this study, the applicability of Hunt's analytical solution for a two-layered leaky aquifer system, which was developed to estimate stream depletion due to the groundwater pumping of the upper shallow aquifer, was evaluated. The 5-year averaged stream depletions were estimated using Hunt's analytical solution for various combinations of hydraulic characteristic values such as transmissivity, storage coefficient of the two aquifers, interlayer leakage coefficient, stream-well distance, hydraulic conductivity of the streambed, and stream width. Through comparison with the numerical solution accurately simulated with a MODFLOW groundwater flow model, the analytical solution derived by regarding the stream width as a point was evaluated. It was found that the error in the stream depletion calculated by the analytical solution can be reduced to less than 0.05 when the stream-well distance is greater than the stream width or when the stream depletion factor (SDF) is more than about 3,000 days. In addition, when the streambed hydraulic conductivity is less than 1 m/d, the hydraulic diffusion coefficient of the lower aquifer layer is less than 100 ㎡/d, the hydraulic diffusion coefficient ratio of the upper and lower aquifer layers is 5 or more, and the leakage coefficient between the layers is less than 0.0004 m/d, the overall analytical solutions were overestimated compared with the numerical solutions.

• Journal of Korea Water Resources Association
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• v.49 no.11
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• pp.923-930
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• 2016

This study was to evaluate the stream depletion from groundwater pumping in shallow aquifer using the Hunt's analytical solution (2009) which considers a two-layer leaky aquifer-stream system. From the total 2,187 cases of simulations with combinations of various aquifer and stream properties, the streamflow depletion rates divided by the groundwater pumping rate showed the low values when the stream depletion factor (SDF) is higher than 1,000-10,000, and was more sensitive to the aquitard hydraulic conductivity than the streambed hydraulic conductivity. The comparison of the Hunt's solution (2009) with the Hunt's solution (1999) of a single layer aquifer indicated that the maximum difference between the dimensionless stream depletions calculated by using both solutions is above 0.3, and the stream depletion is significantly affected by the hydraulic properties of the $2^{nd}$ layer as the SDF of the first layer increases. The Hunt's solution (2009) was applied to the real shallow groundwater well that is located in Chunju-Si, and the results revealed that the groundwater pumping has significant effects on streamflow in a short period of time, showing that the dimensionless stream depletion exceeds 0.8 within a few days. It was also found that the shallow groundwater pumping effects on stream depletion are highly dependent on the stream-well distance for the locations with high hydraulic diffusivity of $1^{st}$ layer and low vertical leakance between $1^{st}$ and $2^{nd}$ layers.

• Journal of Korea Water Resources Association
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• v.51 no.2
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• pp.99-107
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• 2018

This study was to evaluate the stream depletion due to groundwater pumping from 17 wells near the Anseongcheon upper stream using the Baalousha's analytical solution (2012) which directly considers stream width and streambed hydraulic conductivity. The input hydraulic values of aquifer and streambed were obtained from the pumping tests and seepage experiments. The estimated streamflow depletion rates divided by pumping rate (dimensionless stream depletion) showed a range from 0.23 to 0.89 for 5 year pumping. In particular, the results revealed that the groundwater pumping has insignificant effects on streamflow when the stream depletion factor (SDF) is higher than 1,000 with values of dimensionless stream depletion lower than 0.4. A more simple Hunt's solution (1999) also applied to the same wells, and the results showed that the difference between the dimensionless stream depletions calculated by using both solutions could be negligible. From the comparison of the Baalousha's solution (2012) with the Hunt's solution (1999) with total 3,000 cases of simulations with combinations of various aquifer and stream properties, the stream-well distance should be more longer than stream width for reducing the discrepancy between both solutions.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.37 no.6
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• pp.1001-1008
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• 2017

This study was to evaluate the stream depletion rate from groundwater pumping with varying stream-well distance, aquifer transmissivity, storage coefficient, leakage coefficient, streambed hydraulic conductance using the Zlotnik and Tartakovsky analytical solution which considers a two-layer leaky aquifer-stream-well system. For the hydraulic conditions applied in this study, the streambed hydraulic conductance and the aquitard leakage coefficient were assessed to have a dominant influence on the stream depletion rate. In order to evaluate the applicability of Zlotnik and Tartakovsky analytical solution ignoring the change in the drawdown in the lower aquifer and applying the fixed head boundary condition, the solution was compared with Hunt analytical solution derived from the more practical conditions simultaneously taking into account the drawdown changes in the upper and lower aquifers. As a result, the Zlotnik and Tartakovsky analytical solution is suitable for predicting short-term effects of less than one year in the pumping period, and when the stream depletion factor (SDF) is greater than 2,500 days, or when the product of the leakage coefficient and the stream-well distance is less than 10 cm/s.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.1B
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• pp.111-114
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• 2008

Explicit solutions of the wave dispersion equation are developed using the recursive relation in terms of the relative water depth. We use the solutions of Eckart (1951), Hunt (1979), and the deep-water and shallow-water solutions for initial values of the solution. All the recursive solutions converge to the exact one except that with the initial value of deep-water solution. The solution with the initial value by Hunt converged much faster than the others. The recursive solutions may be obtained quickly and simply by a hand calculator. For the transformation of linear water waves in whole water depth, the use of the recursive solutions will yield more accurate analytical solutions than use of previously developed explicit solutions.

• Journal of Korea Water Resources Association
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• v.52 no.7
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• pp.483-492
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• 2019

An analytical model was developed to estimate the stream depletion due to cyclic groundwater pumping by extending the Hunt's analytical solution which was derived from considering the hydraulic characteristics of the aquifer and the streambed. The model was applied to analyze the long-term effects of groundwater pumping on stream depletion during irrigation season. For the case of a total of 1,500 conditions according to various aquifer and streambed hydraulic characteristics and stream-well distance, the stream depletion due to cyclic groundwater pumping for 10 years was calculated and the results were graphically represented. Especially, the maximum and average stream depletion rates were calculated and compared with the results for continuous groundwater pumping. Furthermore, considering both stream depletion and return flow rates, the limit hydraulic condition that minimizes the influence of groundwater pumping for irrigation water supply on stream depletion was suggested.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.40 no.4
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• pp.383-391
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• 2020

In this study, Hunt's analytical solution and Ward & Lough's analytical solution for two-layered leaky aquifer system were used to estimate stream depletions due to shallow and deep groundwater pumping, and their differences were compared. Depending on the combination of the separation distance between the stream and the well, the transmissivity and the storage coefficient of the aquifer, and the leakage coefficient between the upper and lower layers, the stream depletion, which is the amount of stream water reduction compared to the amount of groundwater pumping, for each of 45,000 cases was calculated for both shallow and deep groundwater pumping, and the differences were analyzed quantitatively. When the leakage coefficient was very small, with a value of 10^-61/d, the difference in the average five-year stream depletion due to the pumping of shallow and deep groundwater showed a large deviation of up to 0.9 depending on the given hydraulic characteristics; this value exponentially decreased as the stream depletion factor (SDF) increased. This exponential relationship gradually weakened as the leakage coefficient increased due to interaction effects between layers, resulting in a small difference of up to 0.2 when the leakage coefficient reached 10^-31/d. Under the condition of greater interlayer hydraulic connectivity, there was little influence of the depth of groundwater pumping on the stream water reduction.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.327-327
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• 2016

하천 인근에서 지하수를 채수할 경우 지하수위 저하로 인해 하천으로의 지하수 유출이 감소하거나 하천수가 역으로 지하수계로 유입되어 하천수 감소(stream depletion) 현상이 발생한다. 이러한 지하수 양수로 인한 하천수 감소량을 산정하기 위한 방법으로 현지 계측, 수치해석 모델링, 해석해 적용 등이 있으며, 이 중에서 해석해를 이용하는 방법은 실제 하천수-지하수 연계시스템을 단순화한 조건에서 유도되었다는 단점이 있지만 비용이나 시간적 측면에서는 가장 유리하다. 본 연구에서는 Hunt(1999)가 개발한 해석해를 전산프로그램화하고 이를 하천변에 위치한 실제 지하수 관정 109개에 적용하여 양수로 인한 지하수위 강하 및 하천수 감소량을 산정하여 대수층 및 하천의 수리특성, 하천과 관정간의 이격거리에 따른 변동 특성을 분석하였다. Hunt 해석해로 양수 시간에 따른 하천수 감소량을 계산한 결과, 양수후 5년 뒤에는 지하수 양수량 대비 하천수 감소량의 비율이 80%를 초과하는 관정이 대부분인 것으로 나타났으며, 특히 수리확산계수가 $1,000m^2/d$를 넘고 하천고갈인자(Stream Depletion Factor, SDF)값이 100 보다 작은 범위에서는 양수의 영향이 크게 발생하는 것으로 분석되었다.

• Proceedings of the Korea Contents Association Conference
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• 2010.05a
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• pp.633-634
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• 2010

축대칭 함몰지형 위를 진행하는 확장형 완경사 방정식의 해석해를 유도하였다. 변수분리법을 이용하여 지배방정식을 상미분방정식으로 만들었으며, 파속과 군속도로 표현되는 계수들은 Hunt(1979)의 근사식을 이용하여 양함수의 형태로 표현하였다. 마지막으로 Frobenius기법을 이용하여 확장형 완경사방정식의 해를 유도하였다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.36 no.5
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• pp.769-777
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• 2016

The objective of this study was to evaluate the stream depletion from groundwater pumping in deep aquifer using the Ward and Lough's analytical solution (2011) which considers a two-layer leaky aquifer system. The calculated results for each pumping from the 110 wells beside streams showed a wide range of non-dimensional stream depletion, that is the streamflow depletion rate divided by the groundwater pumping rate, from lower than 0.1 to more than 0.9 on average for 5 years depending on the specific properties of well location. From the comparison with Hunt's solution (1999) of a single layer aquifer, the Ward and Lough's solution showed about 50% lower than the Hunt's solution due to the difference of hydraulic properties between the first and second layers as well as the lagged effect of vertical leakance. It was also found that the groundwater pumping has a minor effect on the stream depletion if the stream depletion factor (SDF) of the 1st layer is higher than about 1,000 or the SDF of the 2nd layer is higher than about 100, or the vertical leakance is smaller than $10^{-5}s^{-1}$. Furthermore, in the present study, the variations of the stream depletion were assessed according to the magnitude of unmeasured hydraulic properties such as transmissivity and storage coefficient of the 1st layer, vertical hydraulic conductivity of the 2nd layer, the streambed hydraulic conductance.