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

Abstract

Recharging and pumping are the integral part of any scheme of ground water resources development and both processes significantly affect the dynamic behavior of the aquifer system. Leakage from the aquifer's base, if present, is other process which affects the water table variation. Therefore, an accurate estimation of water table fluctuation induced by recharging, pumping and leakage is pre-requisite to ensure sustainability of groundwater resources. In the present work an analytical solution of a 2-D linearized Boussinesq equation is developed to predict water table fluctuations in the presence of time varying recharge, pumping and leakage from any number of recharge basins, wells and leakage sites of any dimension for any number of recharge and pumping cycles. The rate of time varying recharge (or pumping) is approximated by using a series of linear elements of different lengths and slopes which are dependent on the nature of variation in the recharge (or pumping) rate. Application of the solution in the prediction of water table fluctuation in the presence of time varying recharge, pumping and leakage is demonstrated with the help of a numerical example. These numerical results indicate significant effect of the time varying recharge/pumping rates and leakage on the water table variation. Such information is useful for the proper management of groundwater.

Numerical Modeling of Water Table Fluctuation in Unconfined Sloping Aquifer in Response to Multiple Localized Recharge

“…Parlange et al [6] developed a numerical model based on the onedimensional Boussinesq equation for a horizontal unconfined aquifer using finite element method Butler et al [7] shows the effect of leakage and partial penetration in his work using numerical simulation technique. Groundwater table variation in a semi-infinite unconfined aquifer described the fluctuations of the water table Rai and Manglik [8]. Singh [9] in his work gave an analytical approximation to calculate the groundwater mound due to artificial recharge for an unconfined aquifer and verified the existing solutions.…”

Mathematical Modeling of Groundwater Surface Water Interaction Represented using Boussinesq Equation – A Bibliometric Study

“…The flow mechanism in this process is often approximated in the form of nonlinear partial differential equation called as Boussinesq equation. Mathematical models based on the stream stage variations due to recharge/discharge are studied using Boussinesq equation by many researchers like Bansal and Das [22], Bansal et al, [23], Lande et al, [24], Bansal [25], Rai and Manglik [26], and Childs [27]. Many more researchers contributed from 1941 to till date and developed the models using mathematical tools.…”

Water table dynamics between two adjacent subsurface drainage laterals in a paddy field: A newly improved analytical solution

“…Basically, the flow in soil follows basic functions. The governing equation can be solved numerically or analytically (Rai & Manglik, 2012). A simpler approach that can finally present an equation is an analytical solution.…”