Groundwater Flow in Sloping Aquifer under Localized Transient Recharge: Analytical Study
Publication: Journal of Hydraulic Engineering
Volume 139, Issue 11
Abstract
This paper analyzes the groundwater flow system in an unconfined downward-sloping aquifer of semi-infinite extent in response to localized transient recharge. The aquifer is in contact with a water body of constant water level at one end and receives localized transient recharge from a recharge basin of finite width. The mathematical model is based on the Boussinesq equation with Dupuit-Forchheimer assumption, in which the spatial coordinate of the recharge basin is treated as an additional parameter. Analytical solutions of the linearized Boussinesq equation are obtained using the Laplace transform technique by dividing the aquifer in a three-zone system containing both Dirichlet and Neumann boundary conditions at the hypothetical interfaces. Upward- and zero-sloping cases are deduced from the main results by appropriately adjusting the slope parameter. To assess the validity and efficiency of the linearization method, the nonlinear Boussinesq equation is also solved using a fully explicit predictor-corrector numerical scheme. A numerical example is used for illustrating the effects of various parameters such as aquifer’s bed slope, spatial coordinate of the recharge basin, and recharge rate on the dynamic profiles of phreatic surface.
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References
Abramowitz, M., and Stegun, I. A. (1972). Handbook of mathematical functions, Dover, New York.
Akylas, E., and Koussis, A. D. (2007). “Response of sloping unconfined aquifer to stage changes in adjacent stream. I: Theoretical analysis and derivation of system response functions.” J. Hydrol., 338, 85–95.
Bansal, R. K. (2012). “Groundwater fluctuations in sloping aquifers induced by time-varying replenishment and seepage from a uniformly rising stream.” Transp. Porous Media, 94(3), 817–836.
Bansal, R. K., and Das, S. K. (2009). “Effects of bed slope on water head and flow rate at the interfaces between the stream and groundwater: Analytical study.” J. Hyrdrol. Eng., 14(8), 832–838.
Bansal, R. K., and Das, S. K. (2010a). “On the water table fluctuation in a sloping aquifer: Analytical expressions for water exchange between stream and groundwater with surface infiltration.” J. Porous Media, 13(4), 365–374.
Bansal, R. K, and Das, S. K. (2010b). “An analytical study of water table fluctuations in unconfined aquifers due to varying bed slopes and spatial location of the recharge basin.” J. Hydrol. Eng., 15(11), 909–917.
Bansal, R. K., and Das, S. K. (2011). “Response of an unconfined sloping aquifer to constant recharge and seepage from the stream of varying water level.” Water Resour. Manage., 25(3), 893–911.
Brown, J. W., and Churchill, R. V. (1996). Complex variables and applications, 6th Ed., McGraw-Hill, New York.
Chang, Y. C., and Yeh, H. D. (2007). “Analytical solution for groundwater flow in an anisotropic sloping aquifer with arbitrarily located multiwells.” J. Hydrol., 347, 143–152.
Chapman, T. G. (1980). “Modeling groundwater flow over sloping beds.” Water Resour. Res., 16(6), 1114–1118.
Chuang, M. H., and Yeh, H. D. (2007). “An analytical solution for the head distribution in a tidal leaky aquifer extending an infinite distance under the sea.” Adv. Water Resour., 30(3), 439–445.
Dahan, O., Tatarsky, B., Enzel, Y., Kulls, C., Seely, M., and Benito, G. (2008). “Dynamics of flood water infiltration and ground water recharge in hyperarid desert.” Groundwater, 46(3), 450–461.
Glover, R. E. (1961). Mathematical derivations pertaining to groundwater recharge, U.S. Department of Agriculture, Agricultural Research Service, Fort Collins, CO, 81.
Hantush, M. S. (1967). “Growth and decay of groundwater mounds in response to uniform percolation.” Water Resour. Res., 3(1), 227–234.
Hunt, B. W. (1971). “Vertical recharge of unconfined aquifer.” J. Hydraul. Dev., 97(7), 1017–1030.
Latinopoulos, P. (1984). “Periodic recharge to finite aquifer from rectangular areas.” Adv. Water Resour., 7(3), 137–140.
Li, H., and Jiao, J. J. (2001). “Analytical studies of groundwater-head fluctuation in a coastal confined aquifer overlain by a leaky layer with storage.” Adv. Water Resour., 24(5), 565–573.
Lockington, D. A. (1997). “Response of unconfined aquifer to sudden change in boundary head.” J. Irrig. Drain. Eng., 123(1), 24–27.
Manglik, A., Rai, S. N., and Singh, R. N. (1997). “Response of an unconfined aquifer induced by time varying recharge from a rectangular basin.” Water Resour. Manage., 11, 185–196.
Marino, M. (1973). “Water-table fluctuation in semipervious stream-unconfined aquifer systems.” J. Hydrol., 19(1), 43–52.
Moench, A. F., and Barlow, P. M. (2000). “Aquifer response to stream-stage and recharge variations. 1. Analytical step-response functions.” J. Hydrol., 230(3–4), 192–210.
Moutsopoulos, K. N. (2010). “The analytical solution of the Boussinesq equation for flow induced by a step change of the water table elevation revisited.” Transp. Porous Media, 85(3), 919–940.
Rai, S. N., and Manglik, A. (1999). “Modelling of water table variation in response to time-varying recharge from multiple basins using the linearised Boussinesq equation.” J. Hydrol., 220(3–4), 141–148.
Rai, S. N., and 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. Manage., 26(1), 243–252.
Rai, S. N., Manglik, A., and Singh, V. S. (2006). “Water table fluctuation owing to time-varying recharge, pumping and leakage.” J. Hydrol., 324(1–4), 350–358.
Rai, S. N., and Singh, R. N. (1995). “Two-dimensional modelling of water table fluctuation in response to localized transient recharge.” J. Hydrol., 167(1–4), 167–174.
Rai, S. N., and Singh, R. N. (1996). “On the prediction of groundwater mound formation due to transient recharge from a rectangular area.” Water Resour. Manage., 10(3), 189–198.
Ram, S., and Chauhan, H. S. (1987). “Analytical and experimental solutions for drainage of sloping lands with time-varying recharge.” Water Resour. Res., 23(6), 1090–1096.
Ramana, D. V., Rai, S. N., and Singh, R. N. (1995). “Water table fluctuation due to transient recharge in a 2-d aquifer system with inclined base.” Water Resour. Manage., 9(2), 127–138.
Rao, N. H., and Sarma, P. B. S. (1980). “Growth of ground-water mound in response to recharge.” Groundwater, 18(6), 587–595.
Rao, N. H., and Sarma, P. B. S. (1981). “Recharge from rectangular areas to finite aquifers.” J. Hydrol., 53(3–4), 269–275.
Rao, N. H., and Sarma, P. B. S. (1984). “Recharge to aquifers with mixed boundaries.” J. Hydrol., 74(1–2), 43–51.
Serrano, S. E., and Workman, S. R. (1998). “Modeling transient stream/aquifer interaction with the nonlinear Boussinesq equation and its analytical solution.” J. Hydrol., 206(3–4), 245–255.
Sneddon, I. N. (1972). The use of integral transforms, McGraw-Hill, New York.
Sophocleous, M. (2002). “Interactions between groundwater and surface water: the state of the science.” Hydrogeol. J., 10(1), 52–67.
Teloglou, I. S., and Bansal, R. K. (2012). “Transient solution of stream-unconfined aquifer interaction due to time varying stream head and in the presence of leakage.” J. Hydrol., 428–429, 68–79.
Upadhyaya, A., and Chauhan, H. S. (2001). “Interaction of stream and sloping aquifer receiving constant recharge.” J. Irrig. Drain. Eng., 127(5), 295–301.
Vázquez-Suñé, E., Capino, B., Abarca, E., and Carrera, J. (2007). “Estimation of recharge from floods in disconnected stream-aquifer systems.” Groundwater., 45(5), 579–589.
Verhoest, N. E. C., Pauwels, V. R. N., Troch, P. A., and Troch, F. P. D. (2002). “Analytical solution for transient water table heights and outflow from ditch-drained terrains.” J. Irrig. Drain. Eng., 128(6), 358–364.
Verhoest, N. E. C., and Troch, P. A. (2000). “Some analytical solution of the linearized Boussinesq equation with recharge for sloping aquifer.” Water Resour. Res., 36(3), 793–800.
Woessner, W. W. (2000). “Stream and fluvial plane groundwater interactions: Rescaling hydrogeologic thought.” Groundwater, 38(3), 423–429.
Wörman, A., Packman, A. I., Johansson, H., and Johansson, K. (2002). “Effect of flow-induced exchange in hyporheic zones on longitudinal transport of solutes in streams and rivers.” Water Resour. Res., 38(1), 1001.
Zissis, T. S., Teloglou, I. S., and Terzidis, G. A. (2001). “Response of sloping aquifer to constant replenishment and to stream varying water level.” J. Hydrol., 243(3–4), 180–191.
Zomorodi, K. (1991). “Evaluation of the response of a water table to a variable recharge.” Hydrol. Sci. J., 36(1), 67–78.
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Information
Published In
Journal of Hydraulic Engineering
Volume 139 • Issue 11 • November 2013
Pages: 1165 - 1174
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Feb 25, 2013
Accepted: May 29, 2013
Published online: Jun 1, 2013
Published in print: Nov 1, 2013
Discussion open until: Nov 1, 2013
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