Steady flow to a horizontal drain in an unconfined aquifer with variable thickness Mazda Kompani-Zare a, * , Hongbin Zhan b,1 a Department of Desert Management, School of Agriculture, Shiraz University, Shiraz 71441-33111, Iran b Department of Geology and Geophysics, Texas A&M University, College Station, TX 77845-3115, USA Received 22 February 2005; received in revised form 9 November 2005; accepted 10 November 2005 Summary In this study, we have used an analytical element method together with genetic algorithm (GA) optimization to determine the steady-state flow rate to an infinite horizontal drain with a finite radius in an unconfined aquifer with a variable thickness. In this study, we first determine the water table position by using the GA optimization method, which is carried out by satisfying the zero pressure and the perpendicularity of iso-potential and iso-pressure gradients on the water table. Then, we illustrate that one has to use a weighting factor in implementing the above-mentioned two conditions simultaneously to optimize the objective function better. Here, we propose two methods to calculate the flow rate to the drain. The first method determines the flow rate based on the water table elevation using the Dupuit–Forch- heimer assumption. The second method determines the flow rate by differentiating the hydrau- lic head. The flow rates calculated by these two methods agree with each other, especially in the regions that are more than 1.8 dimensionless distance from the drain, where the dimension- less distance is defined as the ratio of distance over the drain elevation. The functionality of the flow rate with respect to the drain radius, the drain elevation, and the distance to the constant- head boundary is also studied. ª 2005 Elsevier B.V. All rights reserved. KEYWORDS Analytical element method; Water table; Horizontal drain; Variable thickness aquifer; Genetic algorithm Introduction Determination of the steady-state flow rates to horizontal drains is an important topic in agriculture and ground water studies. Such drains are used to collect the recharge water or contaminants from an aquifer, enhance sand accretion on beaches (Li et al., 1996), drain water from irrigation fields, lower groundwater levels in urban regions, and also exploit ground water. In general, flow to the drain approaches a stea- dy-state quite rapidly. Calculation of the steady-state flow rate to the drain is not simple because of non-negligible ver- tical flow component near the drain, existence of free water table surface, and variation of saturated aquifer thickness. 0022-1694/$ - see front matter ª 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2005.11.015 * Corresponding author. Tel.: +98 711 2286236. E-mail addresses: kompani@shirazu.ac.ir (M. Kompani-Zare), zhan@geo.tamu.edu (H. Zhan). 1 Tel.: +1 979 862 7961; fax: +1 979 845 6162. Journal of Hydrology (2006) 327, 174– 185 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/jhydrol