Design of Bi-Level Drainage Systems: An Analytical Solution Using Inversion Theorem

Abstract

The linearized Boussinesq equation was used to formulate a boundary value problem for a bi-level drainage system. The proposed solution had been validated by conducted desk exercises using existing solutions for conventional level and bi-level drainage systems. Field data reported in the literature were also used to validate the accuracy of the analytical solution. Simplified equations proposed in this paper were compared with the exact solutions to conclude that the underlying assumptions did not result in errors of undesirable magnitude. Thus, application of simplified equations for hi-level drainage design or for simulations of hydraulic heads is recommended. With the proposed solution, it should be possible to design a bi-level drainage system using a hand held calculator. Therefore, present investigation is a step ahead of the earlier paper by these authors.