Abstract
The Boussinesq equation has been proved reliable for modeling water table fluctuations in response to external excitations imposed on the aquifer system. This study presents an analytical solution for two-dimensional linearized Boussinesq equation in anisotropic, rectangular-shaped aquifers with sloping impermeable base. Two different configurations of hydrogeological boundary conditions (constant-head and no-flow) are examined. The analytical model is capable of describing the groundwater head distribution due to downward transient recharge from an overlying basin. First, a transformation technique is adopted in order to simplify the mathematical treatment of the problem. Closed form expression for point-recharge is then obtained by applying the method of Green’s function and eigenfunction expansion. This allows treating any arbitrary-shaped recharge basin subject to spatiotemporal varying recharge. It is shown that a number of existing analytical groundwater models may be regarded as special cases of the solution presented herein. Finally, hypothetical examples describing the nature of transient recharge in sloping aquifers are presented. Qualitative examination of the resulting water table maps confirms the validity of the solution, particularly in the vicinity of aquifer borders. Sensitivity analysis is performed to demonstrate how groundwater mounding is affected by variation in various hydrogeological parameters.
Similar content being viewed by others
References
Bansal RK, Das SK (2010) Analytical study of water table fluctuation in unconfined aquifers due to varying bed slopes and spatial location of the recharge basin. J Hydrol Eng 15:909–917
Brutsaert W (1994) The unit response of groundwater outflow from a hillslope. Water Resour Res 30(10):2759–2763
Chan YK, Mullineux N, Reed JR, Wells GG (1978) Analytic solutions for drawdowns in wedge-shaped artesian aquifers. J Hydrol 36:233–246
Chang YC, Yeh HD (2007) Analytical solution for groundwater flow in an anisotropic sloping aquifer with arbitrarily located multiwells. J Hydrol 347:143–152
Chipongo K, Khiadani M (2015) Comparison of simulation methods for recharge mounds under rectangular basins. Water Resour Manag. doi:10.1007/s11269-015-0974-2
Ferris JG, Knowles DB, Brown RH, Stallman RW (1962) Theory of aquifer tests. Ground-Water Hydraulics, Geological Survey, Water-Supply Paper 1536-E
Healy RW (2010) Estimating groundwater recharge. Cambridge University Press, UK
Liang X, Zhang YK (2012) Analytical solution for drainage and recession from an unconfined aquifer. Ground Water 50(5):793–798
Mahdavi A, Seyyedian H (2013) Transient-state analytical solution for groundwater recharge in triangular-shaped aquifers using the concept of expanded domain. Water Resour Manag 27:2785–2806
Mahdavi A, Seyyedian H (2014) Steady-state groundwater recharge in trapezoidal-shaped aquifers: a semi-analytical approach based on variational calculus. J Hydrol 512:457–462
Manglik A, Rai SN (1998) Two-dimensional modelling of water table fluctuations due to time-varying recharge from rectangular basin. Water Resour Manag 12:467–475
Manglik A, Rai SN (2000) Modeling of water table fluctuations in response to time-varying recharge and withdrawal. Water Resour Manag 14:339–347
Manglik A, Rai SN, Singh VS (2004) Modelling of aquifer response to time varying recharge and pumping from multiple basins and wells. J Hydrol 292:23–29
Manglik A, Rai SN, Singh VS (2013) A generalized predictive model of water table fluctuations in anisotropic aquifer due to intermittently applied time-varying recharge from multiple basins. Water Resour Manag 27:25–36
Marino MA (1974) Growth and decay of groundwater mounds induced by percolation. J Hydrol 22:295–301
Polubarinova-Kochina PY (1962) Theory of ground water movement. Princeton University Press, Princeton
Rai SN, Manglik A (2012) An analytical solution of Boussinesq equation to predict water table fluctuations due to time varying recharge and withdrawal from multiple basins, wells and leakage sites. Water Resour Manag 26:243–252
Rai SN, Manglik A, Singh VS (2006) Water table fluctuation owing to time-varying recharge pumping and leakage. J Hydrol 324:350–358
Ram S, Chauhan HS (1987) Analytical and experimental solutions for drainage of sloping lands with time-varying recharge. Water Resour Res 23(6):1090–1096
Ramana DV, Rai SN, Singh RN (1995) Water table fluctuation due to transient recharge in a 2-D aquifer system with inclined base. Water Resour Manag 9:127–138
Rao NH, Sarma PBS (1981) Groundwater recharge from rectangular areas. Ground Water 19(3):271–274
Samani N, Zarei-Doudeji S (2012) Capture zone of a multi-well system in confined and unconfined wedge-shaped aquifers. Adv Water Resour 39:71–84
Serrano SE (1995) Analytical solutions of the nonlinear groundwater-flow equation in unconfined aquifers and the effect of heterogeneity. Water Resour Res 31(11):2733–2742
Szymkiewicz R (2010) Numerical modeling in open channel hydraulics. Springer, New York
Verhoest NE, Troch PA (2000) Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer. Water Resour Res 36(3):793–800
Yeh H-D, Chang Y-C (2006) New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions. Adv Water Resour 29:471–480
Zomorodi K (1991) Evaluation of the response of a water table to a variable recharge. Hydrol Sci J 36:67–78
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mahdavi, A. Transient-State Analytical Solution for Groundwater Recharge in Anisotropic Sloping Aquifer. Water Resour Manage 29, 3735–3748 (2015). https://doi.org/10.1007/s11269-015-1026-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-015-1026-7