Response of an Unconfined Sloping Aquifer to Constant Recharge and Seepage from the Stream of Varying Water Level

Abstract

This paper presents analytical solution of one-dimensional linearized Boussinesq equation characterizing unsteady groundwater flow in an unconfined aquifer, overlying an impervious downward sloping bed. At one end, the aquifer is in contact with a constant water level and at the other end; water level is rising exponentially from an adjoining stream. The aquifer also receives constant or cycle of time-varying vertical recharge. Analytical expressions for hydraulic head and flow rate in the aquifer are obtained by solving the seepage model using Laplace transform. The expressions derived here can explain sudden rise or very slow rise in the stream water related to sloping or horizontal beds and are represented under asymptotic case. Response of a short and long aquifer to the variation in bed slope, recharge rate and rise rate of the stream water is illustrated with the help of numerical examples. The sensitivity of the flow rate is also analyzed with respect to various parameters. NomenclatureK hydraulic conductivity [LT −1 ] h 0 piezometric head at the left boundary [L] initial water level in the stream [L] x horizontal x-axis [L] t time [T] t r time period in which recharge changes from N 1 to N 2 [T] S specific yield [-] h water table height above impermeable bed [L] H normalized water head height [-] . L length of the domain [L] D aquifer's depth [L] N(t) time-varying recharge rate [LT −1 ] N 1 , N 2 constant recharge rates [LT −1 ] p linearization constant [-] X distance ratio x/L [-] A, B constants [-] H* normalized steady-state value of water head q flow rate [steady-state flow rate at x = 0 [-] Q * (x = L) normalized steady-state flow rate at x = L [-] β Slope angle of the aquifer's bed [-] λ Rise constant [T −1 ] α (L tan β)/2pD. τ normalized time [-] τ r normalized time corresponding to t = t r [-]

A New Package in MODFLOW to Simulate Unconfined Groundwater Flow in Sloping Aquifers

“…Beven (1981), Brutsaert (1994), Verhoest and Troch (2000), Stagnitti et al (2004) and Verhoest et al (2002) derived solutions in the s-z coordinate system based on the Boussinesq assumption. Zissis et al (2001), Bansal and Das (2011), and Bansal (2012) presented solutions in the x-z coordinate system, also based on the Boussinesq assumption. Regardless of the skewed or orthogonal coordinate system used, a linearization method was inevitably adopted in above analytical solutions to deal with the nonlinear governing equations of flow.…”

“…Early works on the subject mainly focused on the steady seepage between ditches or rivers in a sloping unconfined aquifer with recharge (Schmid and Luthin 1964;Wooding and Chapman 1966;Childs 1971;Chapman 1980). Subsequently, many hydrogeologists devoted significant efforts to develop analytical solutions of transient flow in sloping aquifers (Chauhan et al 1968;Beven 1981;Brutsaert 1994;Verhoest and Troch 2000;Upadhyaya and Chauhan 2001;Zissis et al 2001;Verhoest et al 2002;Stagnitti et al 2004;Bansal and Das 2011;Asadi-Aghbolaghi et al 2012;Bansal 2012). Among these analytical solutions, Upadhyaya and Chauhan (2001) and Asadi-Aghbolaghi et al (2012) adopted the Dupuit-Forchheimer assumptions.…”

An analytical study of groundwater fluctuations in unconfined leaky aquifers induced by multiple localized recharge and withdrawal

“…Therefore, there is a need for developing efficient mathematical model that can describes both spatial and temporal distribution of the groundwater head and the capture zones associated with water sources or withdrawals. There are numerous mathematical models that have been presented in the literature to predict the groundwater response to the constant or periodically applied recharge in an unconfined aquifer (Hantush, 1967;Marino, 1974b;1975;Latinopoulos, 1984;Manglik et al 1997;Rai and Manglik 1999;Teloglou et al, 2008;Bansal and Das, 2011;Manglik et al, 2013). Rastogi and Pandey (1998) used a numerical model to simulate the groundwater head distribution in response to constant recharge from recharge basins of different shapes but equal areas.…”

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

“…In some studies, intermittently applied constant recharge has been used (e.g. Bansal and Das 2011). However, the rate of recharge largely depends on the infiltration rate which is influenced by several factors.…”