Analytical Solution for Drainflows from Bilevel Multiple-Drain Subsurface Drainage Systems

Waterlogging and soil salinisation is widespread in the semiarid, irrigated areas of the world. Subsurface drainage is a useful tool in reducing these effects on crops; however, there has been negative downstream effects of drainage in the salt loads discharged to rivers, lakes, and wetlands. Thus, subsurface drainage in semiarid, irrigated areas needs to balance the demands of providing adequate waterlogging and salinity control while minimizing salt loads. Bilevel drainage, in which shallow drains are placed between deeper drains, is a potential method to meet this required balance. This paper describes the development of an analytical solution to this design approach. A previous potential theory was extended to incorporate multiple series of shallow drains placed between two deep drains. The analytical solution was then applied using the Mathematica software to provide useful information on flow rates and flow lines with varying configurations of deep and shallow drains. The theory was then used to compare spacing and drain flow characteristics between a drainage system with only deep drains and multilevel systems that combine shallow drains with deep drains. A large number of possible configurations of shallow drains between deeper drains exist. For ease of comparison, the concept of “drainage equivalence” was developed, representing the drainage discharge per unit spacing between drains. The analytical solution for bilevel drainage situations with single and multiple shallow drains between deeper drains showed that for equivalent rates of total drainage, spacing between deep drains could be increased significantly by the use of shallow drains. It also demonstrated that flow paths and drainage rates from shallow and deep drains and the total system drainage could be altered significantly by altering the number of shallow drains. This information should be useful when considering various drainage configurations to meet the dual objectives of root zone salinity control and minimization of drainage salt loads.