Mathematical Modeling of Phreatic Line in Irrigation Canal Embankments
Mathematical Modeling of Phreatic Line in Irrigation Canal Embankments
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Date
2015-05-03
Authors
Rahman, Balla Ahmed Abdel
Journal Title
Journal ISSN
Volume Title
Publisher
UOFK
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.
Description
72page
Keywords
Mathematical,Modeling,Phreatic,Line,Irrigation,Canal,Embankments