American Society of Civil Engineers


Approximate Engineering Solution for Predicting Groundwater Table Variation During Reservoir Drawdown on the Basis of the Boussinesq Equation


by Jianping Sun, Ph.D., (Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China. E-mail: sunjp@ntu.edu.sg), Jiachun Li, (corresponding author), (Professor, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China. E-mail: jcli05@imech.ac.cn), Qingquan Liu, (Professor, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China. E-mail: qqliu@imech.ac.cn), and Huiqin Zhang, Ph.D., (Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China. E-mail: zhanghuiqin@imech.ac.cn)

Journal of Hydrologic Engineering, Vol. 16, No. 10, October 2011, pp. 791-797, (doi:  http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000372)

     Access full text
     Purchase Subscription
     Permissions for Reuse  

Document type: Journal Paper
Abstract: With reservoir drawdown, the groundwater table in the adjacent aquifer falls down correspondingly. It is useful to calculate the groundwater table variation as a function of time during reservoir drawdown for hydraulic and hydrological purposes. The Boussinesq equation with a moving boundary is applied to analyze the groundwater table variation in the unconfined aquifer during reservoir drawdown. This approach assumes a negligible seepage face. Because the moving boundary condition in the mathematical formulation precludes analytical solutions even for the linearized Boussinesq equation, we have transformed the Boussinesq equation into an advection–diffusion equation to address the negligible seepage face and the moving boundary condition. On the basis of the Laplace transformation, we yield an analytical solution of a fixed boundary problem, which is further simplified to upper and lower polynomial solutions for convenient practical use. The polynomial approximate solutions are satisfactorily compared with a number of numerical simulations of the nonlinear Boussinesq equation. The results indicate that the polynomial solutions match well with the numerical solution, but demonstrate that the replacement of the sloped reservoir–aquifer interface by a vertical interface may cause errors of up to 10% of the height of the reservoir drawdown in the prediction of the groundwater table location. On the basis of the polynomial solutions, a methodology is provided to determine the ratio of hydraulic conductivity to specific yield along with a chart for convenient practical use. The limitation of the present study is that the presented solution tends to underestimate the groundwater table with seepage face neglected for rapid drawdown, high specific yield, low hydraulic conductivity, or mildly sloped interface cases.


ASCE Subject Headings:
Hydrologic models
Groundwater management
Water table
Boussinesq equations
Aquifers
Verification
Reservoirs

Author Keywords:
Hydrologic models
Water table
Boussinesq equations
Aquifers
Verification