Transient Drainage with Nonlinearity and Capillarity

A nonlinear partial differential equation is developed that includes the effects of capillary storage and flow above the water table. An approximate analytic solution is derived. The water table response at the midpoint between drains affected by capillary storage, flow above the water table, and the nonlinearity due to decreasing flow depth is predicted by one relatively simple expression. Indices to the degree of importance of each of these three effects are defined. Appropriate simplified forms of the solution can be selected based on the value of the indices. The method is applicable to a wide range of conditions including drains placed at any elevation relative to the impervious substratum and for shallow as well as deep water tables. The method removes three important restrictions necessarily imposed on the classical linear drainage equations but retains their familiar and desirable features. The equations are sufficiently simple to permit computations with a calculator and should be useful in routine design calculations.