Bi-level Drainage System Design considering Upward Leakage from Semi-impermeable Barrier

Abstract

Bi-level drainage system, in which alternate shallow and deep subsurface drains are laid, seems to be an economical option as compared to the level drainage system due to substantial reduction in cost of excavation. Mathematical solutions are available to describe fall of water table between two bi-level drains located at some distance above the horizontal impermeable barrier. But, if the barrier is semi-impermeable, little information is available to account for the vertical upward leakage in the soil system and its effect on spacing, fall of water table and discharge of drains. In the present study, a boundary value problem consisting of one dimensional linearized Boussinesq equation incorporating vertical upward leakage from semi-impermeable barrier with appropriate initial and boundary conditions was formulated. Analytical solution of such linearized equation has been obtained after devising a simple transformation through which boundary value problem was transformed to a heat transfer problem for which a solution was available. Spatial and temporal variation of water table between two bi-level drains was obtained employing this solution. A special case of the proposed solution (without vertical leakage) was verified with the existing solution and identical values of water table heights were obtained. The effect of hydraulic resistance of semi-impermeable barrier on spacing, water table heights between two bi-level and level drains and discharge of drains was studied by considering a numerical example based on assumed and experimental data. It was observed that with increase in the value of hydraulic resistance the spacing and fall of water table between two drains increases. Discharge of the drains is also influenced due to vertical upward leakage. An increase in hydraulic resistance, discharge of the drain decreases. The solution can be employed to determine discharge, spacing and fall of water table between two level or bi-level subsurface drains considering the semi impermeable barrier.