Mathematical Modeling of Phreatic Line in Irrigation Canal Embankments

Abstract

This research addresses seepage flow through irrigation canal banks. The main objective of the research is to determine the seepage line (phreatic line) location within the canal banks expressed in terms of rationale scientific basis as an alternative to the thump rule approaches. The objective is extended to determine seepage quantities and resulting benefits, in different types of soils. Field data was obtained from the White Nile Irrigation Schemes. The data was obtained by direct measurements of the phreatic elevation of the seeping water through the canal banks. Also physical models representing canal banks were constructed and tested under different compaction efforts using the same soil at these irrigation schemes. It was found that proper determination of the location of the seepage line results in significant reduction in the volume of soil required for constructing the banks. This in turn reduces largely the amount of section over digging and hence improves the hydraulic efficiency of the section. The difficulty expected in the determination of the phreatic line in unconfined ground water flow using direct analytical method is also encountered in seepage flow through canal banks or embankments. The study adopted the approach of transforming the seepage complex physical plane into simple plane identifying clearly the seepage line. This was done by the use of complex variable functions and series of conformal mapping techniques. The mathematical model developed in the study involved non-linear relations and improper integrals. Numerical methods were used to arrive at the required solutions. Computer programs in FORTRAN language were developed to get model solutions. The output of the models was found in good agreement with the results obtained from field observations. The computer program was used further to develop tables and engineering charts that can be used easily for determination of the location of the seepage line and estimation of the seepage quantities for different soil permeability's of the canal banks and embankments. The application and use of the models developed in this study are demonstrated considering two different design cases of irrigation canals. The first case corresponds to the design of an elevated canal constructed on a fill as the case for main canals conveying water from the Nile to the upper terraces of the river. The second case corresponds to the situation where the canal section is partly cut and partly fills.