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Transient-State Analytical Solution for Groundwater Recharge in Anisotropic Sloping Aquifer

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  • Ali Mahdavi

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. Copyright Springer Science+Business Media Dordrecht 2015

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  • Ali Mahdavi, 2015. "Transient-State Analytical Solution for Groundwater Recharge in Anisotropic Sloping Aquifer," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(10), pages 3735-3748, August.
    • Handle: RePEc:spr:waterr:v:29:y:2015:i:10:p:3735-3748
    DOI: 10.1007/s11269-015-1026-7
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    References listed on IDEAS

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    1. Ali Mahdavi & Hamid Seyyedian, 2013. "Transient-State Analytical Solution for Groundwater Recharge in Triangular-Shaped Aquifers Using the Concept of Expanded Domain," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(8), pages 2785-2806, June.
    2. Kudzai Chipongo & Mehdi Khiadani, 2015. "Comparison of Simulation Methods for Recharge Mounds Under Rectangular Basins," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(8), pages 2855-2874, June.
    3. A. Manglik & S. Rai, 1998. "Two-Dimensional Modelling of Water Table Fluctuations due to Time-Varying Recharge from Rectangular Basin," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 12(6), pages 467-475, December.
    4. A. Manglik & S. Rai & V. Singh, 2013. "A Generalized Predictive Model of Water Table Fluctuations in Anisotropic Aquifer Due to Intermittently Applied Time-Varying Recharge from Multiple Basins," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(1), pages 25-36, January.
    5. A. Manglik & S. Rai, 2000. "Modeling of Water Table Fluctuations in Response to Time-varying Recharge and Withdrawal," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 14(5), pages 339-347, October.
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    1. Iraj Saeedpanah & Ramin Golmohamadi Azar, 2017. "New Analytical Expressions for Two-Dimensional Aquifer Adjoining with Streams of Varying Water Level," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(1), pages 403-424, January.
    2. Ali Mahdavi, 2019. "Response of Triangular-Shaped Leaky Aquifers to Rainfall-Induced Groundwater Recharge: an Analytical Study," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(6), pages 2153-2173, April.
    3. Mahdi Asadi-Aghbolaghi & Gholam Reza Rakhshandehroo, 2016. "Delineating Capture Zone of a Pumping Well in a Slanting Regional Groundwater Flow to a Stream with a Leaky Layer," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(12), pages 4273-4291, September.

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