An analytical solution for bi-level drainage design in the presence of evapotranspiration

The linearized Boussinesq equation incorporating the effect of evapotranspiration with appropriate initial and boundary conditions was solved analytically to predict a fall in the water table in a bi-level drainage system. It was assumed that the evapotranspiration rate decreases linearly with a reduction in the elevation of the water table above the drains. A special case of this solution (i.e. with no evapotranspiration) was verified by comparison with an independent and accepted analytical method, and almost identical values of spatial and temporal distribution of water table heights were obtained. The effects of various parameters like evapotranspiration rate and depth-dependent reduction factor on spacing between bi-level and level drains were also studied. Results suggested that inclusion of evapotranspiration in the analytical solution for bi-level drainage design in arid and semi-arid regions is useful and makes a significant difference in spacing. We conclude that in a bi-level drainage system spacing between two drains can be increased by 9.61–13.75% for soils having a hydraulic conductivity of 3 m/day, if the contribution of evapotranspiration at a rate of 8 mm/day in lowering the water table is taken into account.