Subsurface Drainage Solutions by Galerkin's Method

For the solution of drainage problems, a linearized form of Boussinesq's equation is often used. To improve the design, higher order approximations have been used. In this paper a variation of Galerkin's method is used to solve the nonlinear Boussinesq equation. By comparison it is found that the linearized method, when the drawdown to aquifer depth ratio, H/d, becomes large, provides too optimistic designs. The design criteria based on the linearized Boussinesq equation overestimates the rate of drainage for two reasons: (1) they do not account for important nonlinear effects; and (2) they do not account for the delaying effect of the unsaturated flow condition above the water table. The use of Galerkin's method makes it possible to account for the nonlinear effect which is quite significant. This is illustrated on a design example.