Drainage of Sloping Lands with Variable Recharge: Analytical Formulas and Model Development

Semianalytical transient equations for shallow subsurface transverse drainage systems installed in sloping lands are developed. They provide a general relationship between drain flow rates, water table elevations, and recharge rates. This relationship demonstrates that, depending on the recharge intensity, several drain flow rates can be observed at a given water table elevation. The recharge contribution is shown to depend on a water table shape factor and to decrease when the water table is low or the slope is steep. For very steep slopes, the recharge intensity no longer influences the drain flow rate. These equations can be used to confirm previous results obtained in steady-state conditions and to determine precisely under which conditions slope needs to be considered in drainage design. They have been incorporated into the field drainage model SIDRA, which simulates hourly values of water table elevations and drain flow rates. The model predictions are compared with the predictions of a steady-state equation and a numerical model, which solves the Boussinesq equation (SLOP model).