Generalized Analytical Solutions for Groundwater Head in Inclined Aquifers in the Presence of Subsurface Drains

Analytical solutions for groundwater head in the presence of subsurface drains are important in assessing the effectiveness of an existing drainage system under a probable extreme variation in the rate of recharge and designing a new drainage system. Generalized analytical solutions for groundwater head in inclined aquifers in the presence of parallel subsurface drains are obtained considering the transient rate of recharge as a power series (polynomial) function and depth-dependent rate of evapotranspiration. An appropriate function, new to analytical drainage studies, is used for correctly representing the depth-dependent rate of evapotranspiration. The solutions are obtained considering the practical situation of drains placed at shallow depth in a considerable depth of aquifer. Two conditions of large and small saturated thicknesses in comparison to the increase in groundwater head are considered. A mathematical criterion is proposed to distinguish between large and small saturated thicknesses. The analytical equations for discharge to drains for different cases considered are also obtained. The discharge equations used by prior investigators are found inappropriate.